UBC Theses and Dissertations

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UBC Theses and Dissertations

On the relationship between audit risk and security market measures of risk Stein, Michael T. 1988

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ON THE RELATIONSHIP BETWEEN AUDIT RISK AND SECURITY MARKET MEASURES OF RISK By MICHAEL THEODORE STEIN B.A., R u t g e r s C o l l e g e , 1975 B.B.A., U n i v e r s i t y of P e n n s y l v a n i a , 1980 M.A., U n i v e r s i t y o f P e n n s y l v a n i a , 1981 THESIS SUBMITTED IN PARTIAL FULFILLMENT THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES ( F a c u l t y o f Commerce) We a c c e p t t h i s t h e s i s as co n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA J u l y 1988 © M i c h a e l Theodore S t e i n , 1988 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6(3/81i Research S u p e r v i s o r : Dr. Dan A. Simunic ABSTRACT T h i s r e s e a r c h i n v e s t i g a t e s t h e r e l a t i o n s h i p between s e c u r i t y market measures o f r i s k and a u d i t r i s k . The a u d i t o r ' s d e c i s i o n making environment i s extended t o i n c l u d e t h e a c t i o n s o f t h e c l i e n t f i r m ' s s h a r e h o l d e r s . U s i n g t h e Nash e q u i l i b r i u m c o n c e p t i t i s shown t h a t , i n e q u i l i b r i u m , t h e e x p e c t e d c o s t s o f a u d i t i n g i n c r e a s e w i t h t h e p r o b a b i l i t y of a "bad" outcome i n t h e s e c u r i t i e s m a r k e t s . T h i s r e s u l t o b t a i n s i n b oth s t r i c t l i a b i l i t y and n e g l i g e n c e r e gimes. The r e s u l t i s d r i v e n , i n p a r t by t h e i n s u r a n c e r o l e o f a u d i t i n g . I n e m p i r i c a l t e s t s an a s s o c i a t i o n i s e s t a b l i s h e d between s e c u r i t y r i s k and a u d i t f e e s . These t e s t s s u ggest t h a t s e c u r i t y market measures o f r i s k may p r o v i d e i n f o r m a t i o n u s e f u l t o t h e a u d i t o r i n h i s d e c i s i o n making. TABLE OF CONTENTS ABSTRACT i i LIST OF TABLES v LIST OF FIGURES v i i ACKNOWLEDGEMENTS v i i i C h a p ter 1. INTRODUCTION AND LITERATURE REVIEW 1 I n t r o d u c t i o n . . 1 L i t e r a t u r e Review 2 D e f i n i t i o n of A u d i t R i s k 3 A u d i t o r D e c i s i o n Models . . 5 A u d i t o r ' s L e g a l L i a b i l i t y 7 R i s k Measures i n E m p i r i c a l A u d i t i n g R esearch . . 12 2. THE AUDITOR'S DECISION MODEL . 16 The A u d i t o r ' s D e c i s i o n Model 16 D e f i n i t i o n o f A u d i t R i s k 23 L e g a l L i a b i l i t y . . 26 F i r m R i s k and A u d i t R i s k 26 3. THE AUDITOR'S DECISION MODEL WITH AUTONOMOUS SHAREHOLDERS . 30 The A u d i t o r ' s D e c i s i o n Model . . . 31 E q u i l i b r i u m A n a l y s i s w i t h Autonomous S h a r e h o l d e r s 37 E q u i l i b r i a w i t h S t r i c t L i a b i l i t y 42 E q u i l i b r i a w i t h a N e g l i g e n c e Defence 49 4. EMPIRICAL IMPLICATIONS 55 E m p i r i c a l L i n k s 55 Hypotheses 65 Data 69 Models 7 3 D i a g n o s t i c T e s t s 75 T e s t o f N o r m a l i t y . 75 T e s t s f o r H e t e r o s c e d a s t i c i t y 76 S p e c i f i c a t i o n 77 T e s t s o f Hypotheses 79 5. SUMMARY AND CONCLUSIONS . . . 87 i i i APPENDIX 1. NUMERICAL EXAMPLES OF SHAREPRICE DETERMINATION . . . 141 2. MIXED EQUILIBRIUM IN THE NEGLIGENCE REGIME 143 3. CALCULATING CONDITIONAL EXPECTED LOSSES 145 BIBLIOGRAPHY 146 i v LIST OF TABLES T a b l e Page 1. N o t a t i o n 105 2. S h a r e h o l d e r s ' S t r a t e g i e s - S t r i c t L i a b i l i t y . . . 108 3. A u d i t o r S t r a t e g i e s 109 4. A u d i t o r C o s t s under S t r i c t L i a b i l i t y 110 5. Normal Form Game w i t h S t r i c t L i a b i l i t y I l l 6. A u d i t o r C o s t s w i t h a N e g l i g e n c e Defense 112 7. Normal Form Game w i t h N e g l i g e n c e Defense 113 8. Pure S t r a t e g y E q u i l i b r i a w i t h N e g l i g e n c e Defense . 114 9. C r o s s - t a b o f P e r c e n t Zero Change d u r i n g E s t i m a t i o n P e r i o d and Parameter E s t i m a t e s 115 10. D e s c r i p t i v e S t a t i s t i c s 116 11. E s t i m a t e d Market Parameters . . . . 118 12. C o r r e l a t i o n M a t r i x o f V a r i a b l e s 119 13. C o r r e l a t i o n M a t r i x of V a r i a b l e s 120 14. C r o s s - t a b o f t h e R e l a t i o n s h i p between b e t a and o ( e i ) 121 15. D i a g n o s t i c s - N o r m a l i t y 122 16. D i a g n o s t i c s - N o r m a l i t y 123 17. C h i - s q u a r e T e s t f o r H e t e r o s c e d a s t i c i t y 124 18. Ramsey RESET S p e c i f i c a t i o n T e s t s U s i n g Powers of yh a t F — T e s t 125 19. Z-score 126 20. P r o b a b i l i t y o f Loss 127 21. T e s t s on b e t a and o ( e i ) u s i n g Weekly Data and t h e Log Model 128 22. T e s t s on b e t a and o ( e i ) u s i n g Weekly Data and the Square Root Model 129 v 23. T e s t f o r Change o f b e t a S l o p e C o e f f i c i e n t 130 24. T e s t s on b e t a and o{ex) u s i n g Monthly Data and the Log Model 131 25. T e s t s on b e t a and o ( e A ) u s i n g Monthly Data and t h e Square Root Model . . . 132 26. T e s t f o r Change o f b e t a S l o p e C o e f f i c i e n t 133 27. D e s c r i p t i v e S t a t i s t i c s u s i n g Weekly Data f o r A l l , Low, and High Samples 134 28. D e s c r i p t i v e S t a t i s t i c s u s i n g Monthly Data f o r A l l , Low, and High Samples . . 135 29. C o n d i t i o n a l E x p ected N e g a t i v e R e t u r n 136 30. E x p e c t e d N e g a t i v e R e t u r n 137 31. S t a t i s t i c s o f R i s k Measures 138 32. Examples o f t h e R e l a t i o n s h i p among R i s k Measures . 139 33. Summary o f R e s u l t s on Proxy R i s k Measures . . . . 140 v i LIST OF FIGURES F i g u r e Page 1. A s i m p l i f i e d a u d i t o r ' s d e c i s i o n problem 91 2. The c o s t s o f t h e t y p e s o f a u d i t e r r o r s 92 3a. A u d i t o r - s h a r e h o l d e r game, h i g h a u d i t l e v e l 93 3b. A u d i t o r - s h a r e h o l d e r game, low a u d i t l e v e l 94 4. Expected a u d i t o r ' s c o s t s under a s t r i c t l i a b i l i t y regime 95 5. E xpected a u d i t o r ' s c o s t s under a n e g l i g e n c e d e f e nse regime 96 6. S h i f t i n t h e r e t u r n d i s t r i b u t i o n as b e t a i n c r e a s e s . . 97 7. The s i z e d i s t r i b u t i o n o f sample f i r m s ' a s s e t s . . . . 98 8. S i m u l a t i o n o f t h e change i n z - s c o r e as b e t a i n c r e a s e s . 99 9. S i m u l a t i o n o f t h e change i n t h e z - s c o r e as b e t a i n c r e a s e s 100 10. The market i n d e x from 1974 t o 1978 101 11. A n n u a l i z e d 52 week r e t u r n s t a t i s t i c s 102 12. S i m u l a t i o n o f t h e r e l a t i o n s h i p between t h e v a r i o u s p r o x y measures o f r i s k 103 13. The r e l a t i o n s h i p between t h e z - s c o r e and t h e CNR and UNR 104 v i i ACKNOWLEDGEMENT I would l i k e t o thank t h e many p e o p l e t o whom I am i n d e b t e d f o r a d v i c e , s u p p o r t , and encouragement d u r i n g t h e t o o many y e a r s i t t o o k t o complete t h i s r e s e a r c h . Foremost I would l i k e t o thank t h e members o f my committee, J i m Br a n d e r , J a c k Hughes, and e s p e c i a l l y Dan Simunic f o r g e n e r o u s l y s h a r i n g t h e i r i n s i g h t s and t i m e . A s p e c i a l note of acknowledgement i s made t o t h e memory o f P r o f e s s o r John B u t t e r w o r t h whom I knew to o b r i e f l y , but whose i n t e l l e c t u a l i n t e g r i t y and c u r i o s i t y s t i l l s e r v e s as an i n s p i r a t i o n . I g r a t e f u l l y acknowledge t h e f i n a n c i a l s u p p o r t o f t h e D e l l o i t t e H a s k i n s & S e l l s F o u n d a t i o n and UBC's A c c o u n t i n g Development Fund. Next, I warmly c r e d i t my f r i e n d s Lawrence, Mary Jane, Mary, Don, Dan, P a t r i c e , and Anna f o r t h e i r good humour and e m o t i o n a l s u p p o r t . F i n a l l y , I o f f e r a s p e c i a l t h a n k s t o my p a r e n t s f o r t h e i r u n f l a g g i n g encouragement and p a t i e n c e . v i i i Chapter 1 INTRODUCTION AND LITERATURE REVIEW I n t r o d u c t i o n The purpose o f t h i s r e s e a r c h i s t o i n v e s t i g a t e t h e r e l a t i o n s h i p between t h e r i s k f a c e d by a u d i t o r s i n p r o v i d i n g a u d i t s e r v i c e s t o c l i e n t f i r m s and t h e r i s k f a c e d by t h e s h a r e h o l d e r s o f t h o s e f i r m s . The e x i s t e n c e o f a r e l a t i o n s h i p i s o f i n t e r e s t s i n c e t h e t h e o r y o f f i n a n c e i n d i c a t e s how i n f o r m a t i o n from s e c u r i t y markets can be used t o p r o v i d e measures o f t h e r i s k f a c e d by s h a r e h o l d e r s . T h i s r e s e a r c h i s co n c e r n e d w i t h how a u d i t o r s might use t h i s i n f o r m a t i o n t o h e l p them a s s e s s a u d i t r i s k . The main i d e a i s t o i n v e s t i g a t e t h e h y p o t h e s i s t h a t : S e c u r i t y Market R e t u r n s (SMR) can p r o v i d e i n f o r m a t i o n u s e f u l t o t h e a u d i t o r i n a s s e s s i n g r i s k . For such a h y p o t h e s i s t o be t r u e a l o g i c a l c o n n e c t i o n between s h a r e h o l d e r r i s k and a u d i t o r r i s k must be e s t a b l i s h e d . The l i n k i n g o f t h e two t y p e s of r i s k i s p l a u s i b l e s i n c e , on t h e one hand, i t i s w e l l e s t a b l i s h e d t h a t t h e s y s t e m a t i c and r e s i d u a l components o f t h e v a r i a n c e o f a f i r m ' s s e c u r i t y r e t u r n s ( i n a CAPM mean-variance w o r l d ) a r e a f f e c t e d by t h e b u s i n e s s and f i n a n c i a l r i s k o f t h e f i r m and, on t h e o t h e r hand, i t a l s o seems p l a u s i b l e t o c o n j e c t u r e t h a t 1 a u d i t r i s k would be a f f e c t e d by t h e c l i e n t f i r m ' s b u s i n e s s and f i n a n c i a l r i s k 1 . Of p a r t i c u l a r i n t e r e s t i s how t h e f o r t u n e s o f s h a r e h o l d e r s and a u d i t o r s a r e l i k e l y t o be l i n k e d i n an economy where l e g a l l i a b i l i t y r u l e s a l l o w s h a r e h o l d e r s who i n c u r l o s s e s t o t a k e a c t i o n s which c o u l d r e s u l t i n p o s t a u d i t l o s s e s t o a u d i t o r s . The remainder o f t h e c u r r e n t c h a p t e r r e v i e w s th e r e l e v a n t l i t e r a t u r e . C h apter 2 d e s c r i b e s t h e a u d i t i n g e nvironment and s e t s up t h e a u d i t o r ' s d e c i s i o n model. Chapter 3 models t h e e f f e c t o f r i s k i n an environment where t h e a u d i t o r and s h a r e h o l d e r s oppose one a n o t h e r i n a non-c o o p e r a t i v e game. Chapter 4 d e r i v e s e m p i r i c a l h y p otheses about t h e use of market r i s k measures i n t h e c o m p e t i t i v e p r i c i n g o f a u d i t s e r v i c e s and p r o v i d e s t e s t s o f t h e h y p o t h e s e s . C h a p t e r 5 summarizes and c o n c l u d e s t h e r e s e a r c h . L i t e r a t u r e Review The l i t e r a t u r e r e v i e w c o v e r s s e v e r a l t o p i c s which a r e germane t o t h i s r e s e a r c h . They a r e : a d e f i n i t i o n o f a u d i t 1 One t y p e o f a u d i t i n g problem which s u g g e s t s a l i n k a g e between t h e b u s i n e s s r i s k o f t h e c l i e n t f i r m and a u d i t r i s k o c c u r s whenever the a u d i t o r must a s s i g n a v a l u e t o an a c c o u n t b a l a n c e which i s c o n t i n g e n t upon t h e r e a l i z a t i o n o f f u t u r e c a s l f l o w s . For example, c o n s i d e r t h e c a s e where b u s i n e s s r i s k i s t h e r e s u l t o f s t o c h a s t i c demand f o r t h e c l i e n t f i r m ' s p r o d u c t . I n such a case i t seems r e a s o n a b l e t o i n f e r a r e l a t i o n s h i p between, say, i n c r e a s e d v a r i a n c e i n t h e p r o c e s s g e n e r a t i n g demand and c e t e r i s paribus an i n c r e a s e d p r o b a b i l i t y t h a t t h e v a l u e a s s i g n e d t o i n v e n t o r i e s w i l l d i f f e r from t h e ex post r e a l i z e d v a l u e o f t h e i n v e n t o r i e s by an amount which exceeds a f i x e d l e v e l o f m a t e r i a l i t y . r i s k , t h e d e c i s i o n t h e o r y approach t o t h e a u d i t o r ' s d e c i s i o n p r o b l e m , a u d i t o r ' s l e g a l l i a b i l i t y , and t h e u t i l i z a t i o n o f r i s k measures i n e m p i r i c a l r e s e a r c h i n a u d i t i n g . D e f i n i t i o n o f A u d i t R i s k I t has l o n g been r e c o g n i z e d by t h e a u d i t i n g p r o f e s s i o n t h a t t h e a u d i t i n g a c t i v i t y t a k e s p l a c e i n an environment o f r i s k . R i s k i s t y p i c a l l y c a t e g o r i z e d as e i t h e r a u d i t r i s k o r b u s i n e s s r i s k . A u d i t r i s k has been d e f i n e d a s : ... t h e r i s k t h a t t h e a u d i t o r may unknowingly f a i l t o a p p r o p r i a t e l y m o d i f y h i s o p i n i o n on f i n a n c i a l s t a t e m e n t s t h a t a r e m a t e r i a l l y m i s s t a t e d . (SAS No. 47 AICPA 1983 p a r a . 2) I n o r d e r t o o p e r a t i o n a l i z e a u d i t r i s k i t has been decomposed i n t o v a r i o u s components. E l l i o t and Rogers (1972) s t a r t e d by r e l a t i n g t h e a u d i t o r ' s o b j e c t i v e s t o two h y p o t h e s e s . The f i r s t i s t h a t an ac c o u n t b a l a n c e shown on t h e a u d i t e e ' s f i n a n c i a l s t a t e m e n t i s c o r r e c t . The a l t e r n a t i v e h y p o t h e s i s i s t h a t t h e amount i s m a t e r i a l l y i n e r r o r . They go on t o d i s t i n g u i s h t h e two t y p e s o f e r r o r s which can o c c u r i n t h e c o n t e x t o f a s t a t i s t i c a l s a m p l i n g problem and a s s o c i a t e a r i s k measure w i t h each, a r i s k i s d e f i n e d t o be t h e p r o b a b i l i t y t h a t t h e a u d i t o r w i l l r e j e c t a c o r r e c t ( w i t h i n t h e bounds o f m a t e r i a l i t y ) a c c o u n t b a l a n c e , i . e . , commit a t y p e I e r r o r . P r i s k i s a n a l o g o u s l y d e f i n e d t o be t h e p r o b a b i l i t y t h a t t h e a u d i t o r w i l l a c c e p t an account b a l a n c e which i s m a t e r i a l l y i n e r r o r , i . e . , commit a t y p e I I e r r o r . They c o n c l u d e i t i s more c r i t i c a l f o r t h e a u d i t o r t o c o n t r o l 3 3 r i s k . They f u r t h e r s u ggest t h a t t h e c h o i c e o f t h e l e v e l o f t h e 0 r i s k be s e t i n response t o t h e l e v e l o f r e l i a n c e t h e a u d i t o r can a s s i g n t o o t h e r a u d i t i n g p r o c e d u r e s . The AICPA (1981) proposed t h e f o l l o w i n g r i s k model. UR = IC x AR x TD where: UR = u l t i m a t e r i s k , t h e r i s k o f an u n d e t e c t e d m a t e r i a l e r r o r , IC = i n t e r n a l c o n t r o l r i s k , r i s k o f t h e i n t e r n a l c o n t r o l system f a i l i n g t o d e t e c t a m a t e r i a l e r r o r , AR = a n a l y t i c a l r e v i e w r i s k , t h e r i s k t h a t a n a l y t i c a l r e v i e w w i l l not d e t e c t a m a t e r i a l e r r o r , TD = s u b s t a n t i v e t e s t o f d e t a i l s r i s k , t h e r i s k t h a t s u b s t a n t i v e t e s t s w i l l not d e t e c t a m a t e r i a l e r r o r . I t i s t h e u l t i m a t e o r j o i n t r i s k w hich t h e a u d i t o r a t t e m p t s t o c o n t r o l . The CICA (1980) p r o p o s e d a s i m i l a r r i s k model. U n f o r t u n a t e l y , l a c k i n g from b o t h o f t h e s e models i s an e x p l i c i t l i n k a g e t o t h e c o s t s o f a u d i t i n g e r r o r s . I n t h e p r o f e s s i o n a l l i t e r a t u r e a l i n k a g e between 0 r i s k and a u d i t e r r o r s i s noted by B r u m f i e l d , E l l i o t , and J a c o b s e n (1983). They p o i n t o ut t h a t a u d i t r i s k can t r a n s l a t e i n t o b u s i n e s s r i s k f o r t h e a u d i t o r . I n t h e i r usage b u s i n e s s r i s k i s t h e damage t o t h e a u d i t o r ' s p r a c t i c e which i s t h e r e s u l t o f l i t i g a t i o n , s a n c t i o n s , and l o s s o f r e p u t a t i o n due t o a u d i t f a i l u r e s . They a l s o note t h a t t h e c o n n e c t i o n between 4 a u d i t r i s k and b u s i n e s s r i s k i s t h r o u g h common f a c t o r s which i n f l u e n c e b o t h th e i n h e r e n t r i s k (such as t h e performance of t h e economy) of t h e a u d i t and b u s i n e s s r i s k . F u r t h e r d i s c u s s i o n s o f a u d i t r i s k can be found i n C u s h i n g and Loebbecke (1983) and Moore and T h o r n t o n (1987). The l a t t e r r e f e r e n c e i s o f p a r t i c u l a r i n t e r e s t s i n c e i t d e v e l o p s a model which r e l a t e s t h e a u d i t e e ' s b u s i n e s s and a u d i t r i s k t o t h e q u a n t i t y and q u a l i t y o f a u d i t i n g p u r c h a s e d . A u d i t o r D e c i s i o n Models S c o t t (1973) proposed t h e a p p l i c a t i o n o f B a y e s i a n s t a t i s t i c a l d e c i s i o n t h e o r y t o t h e a u d i t o r ' s p r o blem o f a s s e t v a l u a t i o n and a u d i t d e s i g n . I n h i s model t h e a u d i t o r must a s s e s s a l o s s f u n c t i o n , t y p i c a l l y d e r i v e d from t h e net b e n e f i t s o f t h e a u d i t t o u s e r s , i n o r d e r t o d e t e r m i n e how much a u d i t i n g t o p e r f o r m and what v a l u a t i o n t o r e p o r t . C o n c e p t u a l l y t h e advantage of t h i s approach i s t h a t i t i n c o r p o r a t e s a measure o f t h e b e n e f i t s from a u d i t i n g which can be compared w i t h t h e c o s t s , t h e r e b y a l l o w i n g f o r t h e endogenous c h o i c e o f o p t i m a l d e c i s i o n v a r i a b l e s . I n t h i s t y p e of model the a u d i t o r i s d e s c r i b e d as a r a t i o n a l economic agent. T h i s g r e a t l y adds t o t h e c r e d i b i l i t y o f n o r m a t i v e a n a l y s i s , w h i c h p r e s c r i b e s one t y p e of b e h a v i o r o r a n o t h e r t o t h e a u d i t o r 2 . One p r a c t i c a l 2 For example, i n terms o f economic m o d e l l i n g i t i s a p p e a l i n g t o have t h e c h o i c e o f t h e q u a n t i t y o f a u d i t i n g and t h e l e v e l s o f a and 0 r i s k d e t e r m i n e d endogenously i n response t o t h e c o s t s and b e n e f i t s f a c e d by t h e a u d i t o r . 5 d i f f i c u l t y i n t h i s approach i s t h a t f i n a n c i a l s t a t e m e n t s a r e used by many d i f f e r e n t p a r t i e s , making i t u n l i k e l y t h a t t h e r e e x i s t s a s i n g l e l o s s f u n c t i o n which can be used t o d e r i v e s o c i a l l y o p t i m a l r e s u l t s . S c o t t p o i n t s out t h a t a u d i t o r ' s l e g a l l i a b i l i t y i m p l i e s t h a t t h e l o s s f u n c t i o n i s asymmetric, because l e g a l l i a b i l i t y t y p i c a l l y a l l o w s r e c o v e r y o n l y f o r a c t u a l l o s s e s . I n a subsequent paper S c o t t (1975) i n v e s t i g a t e s how t h e a u d i t o r ' s l o s s f u n c t i o n i s d e r i v e d from t h e use s h a r e h o l d e r s make o f f i n a n c i a l s t a t e m e n t s i n making c o n s u m p t i o n - i n v e s t m e n t d e c i s i o n s . The i n n o v a t i o n i n t h i s l i n e o f r e s e a r c h i s t h a t i t f o r m a l l y l i n k s t h e p r o d u c t i o n o f a u d i t s w i t h t h e f a c t o r s t h a t d e t e r m i n e t h e demand f o r a u d i t i n g and t h e r e f o r e e n a b l e s t h e r e s e a r c h t o a d d r e s s i s s u e s o f s o c i a l w e l f a r e i n c o r p o r a t e d i n t h e i n s t i t u t i o n a l s t r u c t u r e o f a u d i t i n g . K i nney (1975) g i v e s an acc o u n t o f t h e use o f d e c i s i o n t h e o r y i n d e t e r m i n i n g o p t i m a l s a m p l i n g i n a u d i t i n g . He s e t s up a model i n which t h e a u d i t o r a s s i g n s c o s t s t o b o t h i n c r e m e n t a l a u d i t p r o d u c t i o n and t o each t y p e o f a u d i t e r r o r . I n t h e d e c i s i o n t h e o r y a pproach, t h e a u d i t o r g i v e s e x p l i c i t c o n s i d e r a t i o n t o h i s p r i o r b e l i e f s about t h e s t a t e t h a t d e s c r i b e s t h e f i n a n c i a l s t a t e m e n t s o f t h e c l i e n t ( i . e . , whether o r not th e y c o n t a i n m a t e r i a l e r r o r s ) . The a u d i t o r uses t h e s e b e l i e f s t o endogenously d e t e r m i n e a c o s t m i n i m i z i n g l e v e l o f a and P r i s k as w e l l as an o p t i m a l d e c i s i o n r u l e and a u d i t s i z e . T h i s i s i n c o n t r a s t t o t h e t r a d i t i o n a l approach 6 (such as E l l i o t and Rogers', where t h e p r o b a b i l i t i e s o f t h e two t y p e s of a u d i t i n g e r r o r s a r e s e t i n r e s ponse t o t h e a u d i t o r ' s assessment o f t h e e f f e c t i v e n e s s o f t h e i n t e r n a l c o n t r o l system. Kinney goes on t o show, t h r o u g h s i m u l a t i o n , how t h e c o s t parameters e f f e c t t h e o p t i m a l c h o i c e o f t h e a u d i t o r ' s d e c i s i o n v a r i a b l e s . F u r t h e r r e v i e w s of t h e l i t e r a t u r e r e l a t e d t o a u d i t o r d e c i s i o n making can be found i n e i t h e r F e l i x and Kinney (1982) o r S c o t t (1984). A u d i t o r ' s L e g a l L i a b i l i t y I n t h e d e c i s i o n t h e o r y approach an i m p o r t a n t f a c t o r i n t h e c h o i c e o f t h e o p t i m a l v a l u e s f o r a u d i t i n g d e c i s i o n v a r i a b l e s i s t h e assessment of t h e c o s t o f a t y p e I I e r r o r . One o f t h e p r i m a r y c o n t r i b u t o r s t o t h i s c o s t i s t h e a u d i t o r ' s p o t e n t i a l f o r l e g a l l i a b i l i t y when such an e r r o r o c c u r s . I t has been p o i n t e d out ( A n t l e 1982) t h a t a u d i t o r s may be f o r c e d t o bear r i s k s t h r o u g h l i a b i l i t y not o n l y t o a s s u r e t h e q u a l i t y o f t h e i n f o r m a t i o n t h e y p r o d u c e , but a l s o as a f a c e t o f an o p t i m a l r i s k - s h a r i n g c o n t r a c t . T h i s s e c t i o n p r o v i d e s some i n s t i t u t i o n a l d e t a i l s d e s c r i b i n g t h e a u d i t o r ' s exposure t o l e g a l l i a b i l i t y . Of p a r t i c u l a r i n t e r e s t i n t h i s t h e s i s i s t h e mechanism by w h i c h a u d i t o r s may s u f f e r ex post r e d i s t r i b u t i o n s o f 7 w e a l t h 3 based upon l e g a l c l a i m s o f i n a d e q u a t e a u d i t q u a l i t y . L e g a l l i a b i l i t y i s r e c o g n i z e d as a prominent cause of r i s k i n t h e c u r r e n t a u d i t i n g e nvironment. (See, f o r example, C o l l i n s (1985).) The main i s s u e s t o be r e v i e w e d a r e : under what c i r c u m s t a n c e s a r e a u d i t o r s l e g a l l y l i a b l e ? t o whom i s t h e a u d i t o r l i a b l e ? and f o r what measure of damages i s he p o t e n t i a l l y r e s p o n s i b l e ? C l a i m s a r e o f t e n ' b r o u g h t a g a i n s t a u d i t o r s i n t h e common law o f t o r t s f o r n e g l i g e n t m i s r e p r e s e n t a t i o n o r p u r s u a n t t o t h e c i v i l l i a b i l i t y p r o v i s i o n s o f t h e s e c u r i t i e s r e g u l a t i o n s , e s p e c i a l l y S e c t i o n 11 o f t h e S e c u r i t i e s A c t 4 and 3 An a u d i t o r ' s r e p u t a t i o n i s a n o t h e r a r e a where l o s s e s a r e p o t e n t i a l l y l a r g e . U n f o r t u n a t e l y , r e p u t a t i o n i s d i f f i c u l t t o q u a n t i f y and t h e r e a r e few r i g o r o u s models o f how r e p u t a t i o n s a r e d e v e l o p e d and m a i n t a i n e d . Dopuch and S i munic (1982) suggest t h a t t h e a u d i t o r ' s c r e d i b i l i t y i s a f f e c t e d by l a w s u i t s s i n c e t h e y a r e among t h e few o b s e r v a b l e c h a r a c t e r i s t i c s c o r r e l a t e d w i t h a u d i t q u a l i t y . I n S i munic and S t e i n (1987) i t was assumed t h a t t h e a u d i t o r can i n v e s t i n a r e p u t a t i o n , say, f o r q u a l i t y as a means o f d i f f e r e n t i a t i n g h i s p r o d u c t i n an e f f o r t t o o b t a i n economic r e n t s . W h i l e i t i s d i f f i c u l t t o measure t h e v a l u e of an a u d i t o r ' s r e p u t a t i o n , i f changes i n t h e r e p u t a t i o n a f f e c t t h e demand f o r t h e a u d i t o r ' s s e r v i c e s t h e n r e p u t a t i o n can be equated w i t h h i s f u t u r e stream o f c a s h f l o w s . Thus, changes i n r e p u t a t i o n a r e p o t e n t i a l l y an i m p o r t a n t s o u r c e o f a u d i t r i s k , though t h e y a r e not d e a l t w i t h e x p l i c i t l y i n t h i s paper. Palmrose (1988) p r o v i d e s e v i d e n c e t h a t non-Big E i g h t a c c o u n t i n g f i r m s had a h i g h e r i n c i d e n c e o f l i t i g a t i o n d u r i n g t h e p e r i o d 1960 - 1985 t h a n B i g E i g h t f i r m s . T h i s s u p p o r t s t h e c l a i m t h a t B i g E i g h t f i r m s may be q u a l i t y d i f f e r e n t i a t e d . I f , as seems l i k e l y , q u a l i t y and r e p u t a t i o n a r e a s s o c i a t e d w i t h one a n o t h e r by a c c o u n t i n g consumers, t h e n l a w s u i t s may be an i m p o r t a n t d e t e r m i n a n t o f t h e v a l u e o f an a u d i t o r ' s r e p u t a t i o n . 4 15 U.S.C. §§77k 8 R u l e 1 0 ( b ) 5 under t h e S e c u r i t i e s Exchange A c t s . I n t o r t s b r o u g h t f o r d e c e i t f i v e elements have emerged 7: 1. A f a l s e r e p r e s e n t a t i o n 2. Knowledge o r b e l i e f t h a t t h e r e p r e s e n t a t i o n i s f a l s e 3. I n t e n t i o n t o i n d u c e r e l i a n c e based upon t h e m i s r e p r e s e n t a t i o n 4. J u s t i f i a b l e r e l i a n c e upon t h e r e p r e s e n t a t i o n 5. Damages r e s u l t i n g from t h a t r e l i a n c e . I n t h e h i s t o r y o f a u d i t o r s ' l e g a l l i a b i l i t y t h e c r i t i c a l element has been t h e t h i r d p o i n t , w h i c h has been i n t e r p r e t e d as r e q u i r i n g e i t h e r a c t u a l o r c o n s t r u c t i v e f r a u d f o r t h e e x i s t e n c e o f l i a b i l i t y t o a t h i r d p a r t y not i n p r i v i t y t o t h e a u d i t o r 8 . R e c e n t l y t h i s r e q u i r e m e n t has been eroded as c o u r t s have expanded t h e c l a s s t o whom a u d i t o r s a r e l i a b l e f o r n e g l i g e n c e 9 . Some commentators ( f o r example, Minnow (1984)) have even s u g g e s t e d t h a t t h e r e i s a t r e n d towards s t r i c t 5 17 C.F.R 240.10b-5 (1980). 6 15 U.S.C. §§ 78 e t s e q . 7 W. P r o s s e r (1971). Taken from t h e Restatement o f T o r t s 525. s T h i s was e s t a b l i s h e d i n t h e famous case o f U l t r a m a r e s v. Touche 255 NY 170, 174 N.E. 441. 9 See O s t l i n g (1986). A l s o note t h e p o l i c y proposed i n t h e Restatement (Second) o f T o r t s would expand l i a b i l i t y f o r n e g l i g e n c e t o t h o s e p a r t i e s f o r whom t h e r e e x i s t s a "knowing r e l i a n c e . " T h i s i s a l a r g e r c l a s s o f u s e r s t h a n t h e one (expounded i n U l t r a m a r e s ) f o r which d e f a n d a n t s have " r e a s o n a b l e f o r e s e e a b i l i t y . " The former s t a n d a r d has been f o l l o w e d by some c o u r t s . See Ryan v. Kanne 170 NW 2d 395. and more r e c e n t l y , Rosenblum, I n c . v. A d l e r 93 NJ 324. 9 l i a b i l i t y (see Moore and Thornton (1987) f o r a f u r t h e r d i s c u s s i o n ) i n t h i s r e a l m analogous t o s i m i l a r t r e n d i n t h e law g o v e r n i n g p r o d u c t l i a b i l i t y c a s e s . Under t h e s e c u r i t i e s laws t h e s t a n d a r d i s one o f due d i l i g e n c e . T h i s s t a n d a r d i s s e v e r e under t h e S e c u r i t i e s A c t o f 1933 s i n c e t h e burden o f p r o o f i s upon t h e d e f e n d a n t t o show t h a t due d i l i g e n c e was t a k e n ( t h e p l a i n t i f f has t h e burden o f p r o o f under t h e S e c u r i t i e s Exchange A c t o f 1934). Damages under t h e s e c u r i t i e s a c t s a r e g e n e r a l l y c a l c u l a t e d as t h e d i f f e r e n c e between t h e s h a r e p r i c e a t t h e t i m e o f t h e m i s r e p r e s e n t a t i o n ( r e g i s t r a t i o n s t a tement f o r t h e S e c u r i t i e s A c t ) and t h e share p r i c e a t t h e t i m e t h e m i s r e p r e s e n t a t i o n was d i s c o v e r e d by t h e market ( K e l l o g (1984) d i s c u s s e s t h i s i s s u e ) . In b o t h s e c u r i t y and common law t h e a u d i t o r g e n e r a l l y has t h e r i g h t t o ask f o r c o n t r i b u t i o n from j o i n t t o r t f e a s o r s . T h i s would, i n p r i n c i p l e , reduce t h e amount o f damages t h e a u d i t o r must pay. However, a u d i t o r s u i t s f r e q u e n t l y f o l l o w i n th e wake o f c l i e n t f i r m i n s o l v e n c y (see S t . P i e r r e and Anderson (1984)) which makes t h i s r i g h t of l i t t l e p r a c t i c a l v a l u e 1 0 . A d d i t i o n a l l y , many c o u r t s a l l o w j o i n t and s e v e r a l x o T h i s may be t h e s o u r c e o f t h e p o p u l a r "deep p o c k e t s " t h e o r y under which a u d i t o r s a r e sued because t h e y a r e t h e o n l y p a r t y i n v o l v e d which e i t h e r has t h e w e a l t h t o pay t h e damages or has l i a b i l i t y i n s u r a n c e which can be drawn upon. See, however, t h e A u s t r a l i a n c a s e , Cambridge C r e d i t Corp. v. Hutcheson, i n which t h e damages awarded exceeded t h e w e a l t h o f the f i r m ' s p a r t n e r s ( a p p a r e n t l y t h e p o c k e t s were not deep enough). 10 l i a b i l i t y w h ich can r e s u l t i n t h e a u d i t o r h a v i n g t o pay f o r t h e e n t i r e amount o f t h e damages even though o t h e r p a r t i e s may have c o n t r i b u t e d t o t h e l o s s 1 1 . K e l l o g g (1984) l o o k e d a t t h e i s s u e o f whether s t o c k p r i c e s f a l l i n a n t i c i p a t i o n o f t h e d i s c o v e r y o f an a u d i t e r r o r o r subsequent t o d i s c o v e r y . A t i s s u e was whether l a w s u i t s (and t h e s e a r c h f o r a u d i t e r r o r s ) a r e t r i g g e r e d by s h a r e h o l d e r l o s s e s o r whether t h e d i s c o v e r y o f a u d i t e r r o r s r e s u l t s i n s h a r e h o l d e r l o s s e s . H i s s t u d y p r o v i d e s e v i d e n c e c o n s i s t e n t w i t h b o t h h y p o t h e s e s . S t . P i e r r e and Anderson (1984) l o o k e d t o c h a r a c t e r i z e f a c t o r s a s s o c i a t e d w i t h l a w s u i t s a g a i n s t a u d i t o r s . They found t h a t s i g n i f i c a n t a c c o u n t i n g l o s s e s , t h e o n s e t o f i n s o l v e n c y , and a drop i n share p r i c e were a l l f a c t o r s a s s o c i a t e d w i t h l a w s u i t s . A d d i t i o n a l l y , t h e y c l a s s i f i e d t h e a l l e g e d causes o f a c t i o n and found t h a t e r r o r s i n t h e i n t e r p r e t a t i o n o f GAAP and GAAS were f r e q u e n t l y c l a i m e d by p l a i n t i f f s . P almrose (1987) found e v i d e n c e t h a t t h e r e were more s u i t s a g a i n s t a u d i t o r s d u r i n g p e r i o d s o f economic downturns. She a l s o found t h a t b u s i n e s s f a i l u r e s and c l a i m s o f management f r a u d were o f t e n c o i n c i d e n t i n s u i t s a g a i n s t s a u d i t o r s . I n an a n a l y t i c a l paper DeJong (1985) demonstrated how 1 1 The case i s even worse under t h e c i v i l l i a b i l i t y p r o v i s i o n s o f t h e R a c k e t e e r I n f l u e n c e d and C o r r u p t O r g a n i z a t i o n s A c t , 18 U.S.C. §§ 1961 e t seq. The law a l l o w s f o r t r e b l e damages and has been a p p l i e d t o a u d i t o r s . See S c h a c t v. Brown, nos. 82-2089, 82-2090 ( 7 t h C i r . A p r i l 8, 1983). 11 t h e p r o c e d u r a l r u l e s o f law i n v o l v i n g a c c e s s t o c l a s s a c t i o n s u i t s and c o n t i n g e n t payment o f l e g a l f e e s would have t h e e f f e c t o f i n c r e a s i n g t h e number o f l a w s u i t s brought a g a i n s t a u d i t o r s . T h i s r e s u l t s , i n e q u i l i b r i u m , i n h i g h e r l e v e l s o f a u d i t i n g b e i n g p e r f o r m e d . Ebke (1984) and Causey (1979) p r o v i d e e x t e n s i v e commentary upon t h e development o f a u d i t o r l e g a l l i a b i l i t y . R i s k Measures i n E m p i r i c a l A u d i t i n g R e s e a r c h E m p i r i c a l a u d i t i n g r e s e a r c h f r e q u e n t l y must r e c o g n i z e and c o n t r o l t h e r i s k i n t h e a u d i t o r ' s e n v i r o n m e n t . Two l i n e s o f r e s e a r c h have g i v e n e x p l i c i t r e c o g n i t i o n t o a u d i t r i s k . One l i n e o f r e s e a r c h a t t e m p t s t o a s c e r t a i n t h e degree o f c o m p e t i t i v e n e s s i n a u d i t i n g markets by l o o k i n g f o r f e e d i f f e r e n t i a l s a f t e r c o n t r o l l i n g f o r f a c t o r s w h i c h c o n t r i b u t e t o t h e c o s t o f a u d i t p r o d u c t i o n . In t h e s e s t u d i e s i t i s n e c e s s a r y t o c o n t r o l f o r r i s k i n o r d e r t o s e p a r a t e f e e d i f f e r e n t i a l s a t t r i b u t a b l e t o r i s k b e a r i n g from t h o s e a t t r i b u t a b l e t o economic r e n t s . The second l i n e o f r e s e a r c h l o o k s f o r s y s t e m a t i c c l i e n t f i r m c h a r a c t e r i s t i c s l e a d i n g t o a u d i t q u a l i f i c a t i o n s . I n t h i s r e s e a r c h i t i s r e c o g n i z e d t h a t a u d i t o r s may q u a l i f y an o p i n i o n i n s i t u a t i o n s o f h i g h a u d i t r i s k i n o r d e r t o a v o i d p o t e n t i a l l e g a l l i a b i l i t y . Shank and Murdock (1978) i n v e s t i g a t e d t h e r e l a t i o n s h i p between f i n a n c i a l r i s k and u n c e r t a i n t y q u a l i f i c a t i o n s . They noted t h a t when f a c e d w i t h i s s u e s o f a s s e t r e a l i z a t i o n o r o f a 12 c l i e n t ' s a b i l i t y t o o b t a i n f u t u r e f i n a n c i n g t h e a u d i t o r must i n e s s ence make a f o r e c a s t o f f u t u r e f i n a n c i a l r e s u l t s . They c o n j e c t u r e d t h a t s y s t e m a t i c r i s k would be an a p p r o p r i a t e measure of t h e r i s k f a c e d by a u d i t o r s i n t h e s e s i t u a t i o n s 1 2 . D e f i n i n g a u d i t r i s k as t h e p r o b a b i l i t y t h e a u d i t o r w i l l q u a l i f y h i s a u d i t o p i n i o n t h e y found a r e l a t i o n s h i p between a f i r m ' s market b e t a and a u d i t r i s k f o r f i r m s w i t h b e t a s g r e a t e r t h a n .8. Dopuch, H o l t h a u s e n , and L e f t w i c h (1987) use b e t a and own v a r i a n c e t o c o n t r o l f o r r i s k i n t h e i r s t u d y o f a u d i t o r o p i n i o n q u a l i f i c a t i o n s . They argue t h a t i n c r e a s e s i n t h e s e r i s k measures i m p l y a g r e a t e r p r o b a b i l i t y o f a n e g a t i v e s t o c k market r e t u r n which can l e a d t o l i t i g a t i o n a g a i n s t t h e a u d i t o r . C o n s e q u e n t l y t h e y p r e d i c t t h e s e measures t o be u s e f u l i n d e t e r m i n i n g t h e p r o b a b i l i t y o f an a u d i t o r q u a l i f i c a t i o n . They f i n d t h a t t h e model i n c l u d i n g market measures o u t -p e r f o r m s t h e model u s i n g a c c o u n t i n g f i n a n c i a l v a r i a b l e s a l o n e . I n a n o t h e r o p i n i o n q u a l i f i c a t i o n s t u d y Dugan and S h r i v e r (1987) c o n c l u d e t h a t t h e e v i d e n c e i s mixed on t h e v a l u e o f b e t a as a p r o x y f o r u n c e r t a i n t y i n t h e a u d i t e n v i r o n m e n t . They e x t e n d t h e a n a l y s i s t o more fundamental n o t i o n s o f b u s i n e s s r i s k . They h y p o t h e s i z e t h a t t h e measures, 1 2 They assumed t h a t own v a r i a n c e would be d i v e r s i f i e d away i n an a n a l o g y t o t h e r e s u l t s i n t h e p o r t f o l i o t h e o r y o f f i n a n c e . A d i f f e r e n t i n t e r p r e t a t i o n o f t h e p o r t f o l i o e f f e c t i s g i v e n by Simunic and S t e i n (1988) who note t h a t , f o r i n s t a n c e , a u d i t o r i n d u s t r y s p e c i a l i z a t i o n may c r e a t e dependencies a c r o s s c l i e n t s i n t h e f u t u r e c a s h f l o w streams of t h e a u d i t o r . 13 t h e degree o f f i n a n c i a l l e v e r a g e and t h e degree o f o p e r a t i n g l e v e r a g e , may b e t t e r d e s c r i b e t h e f i r m - s p e c i f i c elements o f th e a u d i t environment t h a t l e a d s t o t h e a u d i t o r g i v i n g an u n c e r t a i n t y q u a l i f i c a t i o n . T h e i r e m p i r i c a l a n a l y s i s , however, f a i l s t o l e n d s u p p o r t f o r t h i s h y p o t h e s i s . S i m unic (1980) compares t h e a u d i t f e e s c h a r g e d by B i g E i g h t a u d i t i n g f i r m s and t h o s e c h a r g e d by non-Big E i g h t f i r m s i n a s t u d y of t h e c o m p e t i t i v e n e s s o f t h e U.S. a u d i t i n g market. To c o n t r o l f o r r i s k he n o t e s t h a t c e r t a i n t y p e s o f a s s e t s , i n v e n t o r i e s and r e c e i v a b l e s , a r e i n h e r e n t l y more r i s k y t h a n o t h e r s and i n c l u d e s t h e s e measures as e x p l a n a t o r y v a r i a b l e s . F u r t h e r he c o n j e c t u r e s t h a t t h e f i n a n c i a l c o n d i t i o n o f t h e c l i e n t w i l l a f f e c t t h e s h a r e o f any p o t e n t i a l l e g a l l o s s e s t h a t w i l l have t o be borne by t h e a u d i t o r . Thus v a r i a b l e s on p r o f i t i a b i l i t y and t h e e x i s t e n c e o f a " s u b j e c t t o " q u a l i f i c a t i o n were i n c l u d e d . H i s e m p i r i c a l r e s u l t s cannot r e j e c t t h e h y p o t h e s i s o f c o m p e t i t i o n i n t h e a u d i t i n g market. F r a n c i s (1984) r e p l i c a t e s much o f t h e Simunic s t u d y on A u s t r a l i a n d a t a . I n o r d e r t o c o n t r o l f o r r i s k s a s s o c i a t e d w i t h t h e a u d i t o r ' s l o s s exposure he i n c l u d e s t h e q u i c k r a t i o and t h e e q u i t y t o debt r a t i o , r e a s o n i n g t h a t t h e s e measures would e f f e c t t h e a u d i t o r ' s p e r c e p t i o n o f r i s k s i n c e t h e y a r e commonly used t o a s s e s s t h e f i n a n c i a l w e l l - b e i n g o f f i r m s . H i s e v i d e n c e does not s u p p o r t t h e use o f t h e s e r i s k measures. F i r t h (1985) l o o k e d a t t h e c o m p e t i t i v e n e s s i s s u e on New Z e a l a n d d a t a . He i n c l u d e d t h e market measure of r i s k i n 14 h i s r e g r e s s i o n s on f e e s . He found t h a t u n s y s t e m a t i c r i s k was a s t a t i s t i c a l l y s i g n i f i c a n t f a c t o r e x p l a i n i n g a u d i t f e e s . F i n a l l y Simon (1985), Palmrose (1986), and F r a n c i s and Simon (1987) p r o v i d e a d d i t i o n a l e v i d e n c e on a u d i t f e e d e t e r m i n a t i o n . Simon found a d d i t i o n a l e v i d e n c e f o r t h e e m p i r i c a l r e l a t i o n s h i p between f e e s and s i z e i n U.S. f e e d a t a w i t h o u t r i s k a d j u s t m e n t . Palmrose i n a n o t h e r s t u d y o f a u d i t f e e s found e v i d e n c e which s u p p o r t e d t h e h y p o t h e s i s o f p r o d u c t d i f f e r e n t i a t i o n between t h e B i g E i g h t and non-Big E i g h t segments o f t h e a u d i t i n g market. Her s t u d y d i d not i n c l u d e c o n t r o l s f o r p o s s i b l e r i s k d i f f e r e n c e s . F r a n c i s and Simon i n a st u d y o f B i g E i g h t f e e premia suggest t h e use o f own v a r i a n c e , debt t o e q u i t y r a t i o , and t h e e x i s t e n c e o f o p e r a t i n g l o s s e s t o c o n t r o l f o r r i s k . I n summary t h e l i t e r a t u r e s u g g e s t s s e v e r a l p o i n t s . I t i s r e c o g n i z e d t h a t r i s k i s an i m p o r t a n t c o n s i d e r a t i o n i n t h e a u d i t i n g e nvironment. U n f o r t u n a t e l y r e s e a r c h e r s and t h e p r o f e s s i o n a l i k e have found i t d i f f i c u l t t o q u a n t i f y and d e v e l o p good ex ante measures f o r r i s k . A number o f r e s e a r c h e r s have l o o k e d t o t h e t h e o r y o f f i n a n c e t o su g g e s t f a c t o r s which a f f e c t t h e market r i s k i n e s s o f c l i e n t f i r m s . I t has been c o n j e c t u r e d t h a t market r i s k and a u d i t r i s k a r e l i n k e d t h r o u g h e i t h e r t h e system o f a u d i t o r p r o d u c t l i a b i l i t y o r t h r o u g h t h e e f f e c t o f b u s i n e s s r i s k . C u r r e n t l y , t h e c o n n e c t i o n between c l i e n t f i r m market r i s k and a u d i t r i s k has not been r i g o r o u s l y e x p l o r e d i n t h e a u d i t i n g l i t e r a t u r e . C h a p t e r 2 THE AUDITOR'S DECISION MODEL T h i s c h a p t e r i n t r o d u c e s a s i m p l i f i e d v e r s i o n of t h e a u d i t o r ' s d e c i s i o n model and d e s c r i b e s t h e i m p o r t a n t i n s t i t u t i o n a l arrangements assumed i n t h i s p a p e r . A g e n e r a l d e s c r i p t i o n o f t h e a u d i t o r ' s d e c i s i o n problem, a d e f i n i t i o n o f a u d i t r i s k , t h e r e l a t i o n s h i p between c l i e n t f i r m r i s k and a u d i t r i s k , and t h e r o l e o f l e g a l l i a b i l i t y a r e g i v e n . The A u d i t o r ' s D e c i s i o n Model I n t h i s s e c t i o n a s i m p l i f i e d model o f t h e a u d i t i n g p r o c e s s i s p r e s e n t e d 1 3 . F i g u r e 1 d e p i c t s t h e a u d i t o r ' s d e c i s i o n problem. I assume t h e a u d i t o r e n t e r s i n t o a f i x e d f e e c o n t r a c t w i t h t h e c l i e n t f i r m ' s s h a r e h o l d e r s 1 4 and t h a t t h e 1 3 For a f u r t h e r development of t h i s p o i n t see S c o t t (1973) o r K inney (1975) . 1 4 The n a t u r e o f t h e c o n t r a c t i n g between t h e a u d i t o r and t h e f i r m i s s u b j e c t t o v a r i o u s i n t e r p r e t a t i o n s . W h i l e p u t a t i v e l y t h e a u d i t o r answers d i r e c t l y t o s h a r e h o l d e r s t h r o u g h t h e board of d i r e c t o r s t h e i n f l u e n c e o f management o r a subgroup of s h a r e h o l d e r s may be p e r v a s i v e , see Herman (1981). The management o f t h e f i r m may have c o n s i d e r a b l e i n f l u e n c e o v e r t h e h i r i n g , r e t e n t i o n , and f e e s o f t h e a u d i t o r which can s e r v e t o l e s s e n t h e a u d i t o r ' s independence. The p o s s i b i l i t y o f an auditor-management c o a l i t i o n adds g r e a t l y t o t h e c o m p l e x i t y of a n a l y z i n g a u d i t i n g c o n t r a c t s , A n t l e (1982). 16 a u d i t o r seeks t o maximize p r o f i t s 1 * 3 . F u r t h e r i t i s assumed t h a t t h e a u d i t o r o f f e r s h i s s e r v i c e i n a c o m p e t i t i v e market. T h i s i m p l i e s t h a t a u d i t f e e s do not i n c l u d e any economic r e n t s 1 6 . These assumptions a r e i n no way c o n t r a d i c t o r y . C o m p e t i t i o n r e q u i r e s t h e a u d i t o r t o o p e r a t e e f f i c i e n t l y i n o r d e r t o o b t a i n a normal r e t u r n . B e f o r e a n a l y z i n g t h e a u d i t o r ' s d e c i s i o n p roblem, d e p i c t e d i n F i g u r e 1, I w i l l i n t r o d u c e some n o t a t i o n . s € S = a r e t h e s t a t e s o f n a t u r e . To s i m p l i f y t h e a n a l y s i s t h e f i n a n c i a l s t a t e m e n t s a r e c o n s i d e r e d t o be e i t h e r F a i r o r Not F a i r . Not F a i r f i n a n c i a l s t a t e m e n t s a r e ones i n which t h e r e e x i s t r e l e v a n t 1 7 m a t e r i a l e r r o r s . a 6 A = t h e o p i n i o n o f t h e a u d i t o r about t h e 1 3 The assu m p t i o n o f p r o f i t m a x i m i z i n g b e h a v i o r by t h e a u d i t o r i s a r e a s o n a b l e f i r s t a p p r o x i m a t i o n f o r a u d i t f i r m s c o n s i s t i n g of many p a r t n e r s . E x p l i c i t r e c o g n i t i o n of a more comprehensive a u d i t o r o b j e c t i v e f u n c t i o n would r e q u i r e g r e a t e r knowledge t h a n i s c u r r e n t l y a v a i l a b l e about a u d i t o r ( a u d i t f i r m ) p r e f e r e n c e s . I f t h e a u d i t f i r m s o f i n t e r e s t were s i n g l e p r a c t i t i o n e r s a model i n c o r p o r a t i n g r i s k a v e r s i o n might be more a p p r o p r i a t e . However, t h e f i r m s i n t h e sample a r e s u f f i c i e n t l y l a r g e t o make i t u n l i k e l y t h e y were a u d i t e d by a s i n g l e i n d i v i d u a l . 1 S T h i s a s s u m p t i o n i s used i n t h e e m p i r i c a l t e s t s o f Chapter 4. I f f e e s c o n t a i n non-zero economic r e n t s t h e n t h e r e may be a c o n f o u n d i n g between f e e d i f f e r e n c e s due t o r i s k and t h o s e due t o market power. 1 7 The q u a l i f i e r , " r e l e v a n t " , i s used t o d i s c o u n t t h e case i n which t h e r e e x i s t s o f f - s e t t i n g m a t e r i a l e r r o r s i n , say, a c c o u n t b a l a n c e s t h e sum o f which does not e f f e c t t h e d e c i s i o n s o f f i n a n c i a l s t a t e m e n t u s e r s . 17 f a i r n e s s o f t h e f i n a n c i a l s t a t e m e n t s . The a u d i t o r can e i t h e r A c c e p t o r R e j e c t t h e f i n a n c i a l s t a t e m e n t s . An a c c e p t o p i n i o n i s i n t e r p r e t e d by f i n a n c i a l s t a tement u s e r s as a c e r t i f i c a t i o n t h a t t h e f i n a n c i a l s t a t e m e n t s do not c o n t a i n any r e l e v a n t m a t e r i a l e r r o r s . t h e a u d i t o r ' s c h o i c e o f a u d i t i n g i n t e n s i t y , e f f o r t , o r q u a l i t y , f o r a g i v e n c l i e n t . The a u d i t o r i s r e s t r i c t e d t o p e r f o r m i n g e i t h e r a h i g h q u a l i t y t e s t o r a low q u a l i t y t e s t . The low q u a l i t y t e s t may be a n u l l a u d i t , i . e . , no t e s t i n g i s done. t h e s e a r e t h e s i g n a l s w h i c h emerge from t h e a u d i t t e s t . A "good" s i g n a l r e s u l t s i n an upward r e v i s i o n o f t h e a u d i t o r ' s p r i o r p r o b a b i l i t y a s s i g n e d t o t h e event "The f i n a n c i a l s t a t e m e n t s a r e f a i r . " I t i s assumed t h e r e v i s i o n i s a c c o m p l i s h e d a c c o r d i n g t o Bayes' r u l e . i s t h e c o s t o f an a u d i t e r r o r . c ( I ) r e f e r s t o t h e c o s t s a s s o c i a t e d w i t h a t y p e I e r r o r , i . e . , a f a l s e r e j e c t i o n of a f a i r f i n a n c i a l s t a t e m e n t . c ( I I ) i s t h e c o s t o f f a l s e l y a c c e p t i n g an u n f a i r f i n a n c i a l s t a t e m e n t . The c o s t o f a t y p e I I e r r o r may 18 depend upon t h e a u d i t o r ' s t e s t , q, and s i g n a l , z, i f t h e c o u r t s use t h i s i n f o r m a t i o n t o d e t e r m i n e t h e p r e s e n c e of n e g l i g e n c e . h(q) = t h e i n c r e m e n t a l c o s t o f p e r f o r m i n g a u d i t t e s t s . T y p i c a l l y I w i l l a s s i g n a v a l u e o f z e r o as t h e c o s t o f t h e low a u d i t t e s t . S i n c e f e e s a r e assumed t o be f i x e d and c o n s t a n t t h e y p l a y no r e a l r o l e i n t h e a n a l y s i s . T h i s a l l o w s t h e a u d i t o r ' s p r o f i t m a x i m i z a t i o n problem t o be a n a l y z e d i n terms of an e q u i v a l e n t c o s t m i n i m i z a t i o n problem. On t h e f a r r i g h t s i d e of F i g u r e 1 t h e a u d i t o r ' s p a y o f f s ( i n c o s t s terms) a r e g i v e n f o r each t e r m i n a l node. The s t r u c t u r e encompasses s e v e r a l s i m p l i f i c a t i o n s . I t i s assumed t h a t branches o f t h e t r e e i n w hich t h e h i g h t e s t i s p e r f o r m e d i n c l u d e a f i x e d i n c r e m e n t a l c o s t , h. The a u d i t o r i s always a s s i g n e d t h e c o s t , c ( I ) , whenever a t y p e I e r r o r o c c u r s . I n c o n t r a s t , t h e c o s t , c ( I I ) , i s a s s i g n e d o n l y when b o t h a t y p e I I e r r o r o c c u r s and e i t h e r t h e a u d i t o r chose t h e low t e s t o r , i f t h e h i g h t e s t was c h o s e n , t h e a u d i t o r i g n o r e d t h e e v i d e n c e , i . e . , t h e outcome of t h e t e s t was t h e "bad" t e s t r e s u l t . Moving t o t h e l e f t , i t can be seen t h a t t h e a u d i t o r must d e c i d e upon an a u d i t o p i n i o n w i t h o u t knowing t h e t r u e c o n d i t i o n o f t h e f i n a n c i a l s t a t e m e n t s . However, t h e a u d i t o r does get t o update h i s b e l i e f s about t h e f a i r n e s s o f t h e 19 f i n a n c i a l s t a t e m e n t s by o b s e r v i n g t h e s i g n a l , z, from t h e t e s t , q, i f a t e s t was p e r f o r m e d . At t h e f a r l e f t t h e i n i t i a l node i n d i c a t e s t h e p o i n t a t which t h e a u d i t o r chooses whether o r not t o p e r f o r m an a u d i t t e s t . I t s h o u l d be noted t h a t i t i a t t h i s p o i n t t h e a u d i t o r i s assumed t o n e g o t i a t e t h e f i x e d f e e , and makes a s i m u l t a n e o u s c h o i c e 1 8 o f t h e l e v e l o f a u d i t t e s t i n g and a d e c i s i o n r u l e which maps a u d i t e v i d e n c e , z, ( i f any) i n t o h i s c h o i c e s e t A. H i s m i n i m i z a t i o n problem i s : 2.1) min Z z p ( z j q ) min { E g c ( a , s , z , q ) p ( s j z , q ) } + h(q) q€Q I aGA where, p ( s | z , q ) i s t h e p o s t e r i o r 1 9 p r o b a b i l i t y o f t h e a u d i t o r o v e r t h e s t a t e s , S. These p r o b a b i l i t i e s a r e c o n d i t i o n e d by t h e s i g n a l r e c e i v e d , z, and t h e a u d i t p l a n , q, and, p ( z j q ) i s t h e p r o b a b i l i t y o f r e c e i v i n g a s i g n a l , z, from t h e s e t Z g i v e n t h e a u d i t p l a n , q. I n a s s e s s i n g t h e p a r a m e t e r s , c(»), o f h i s c o s t m i n i m i z a t i o n problem, 2.1), t h e a u d i t o r must q u a n t i f y t h e a u d i t r i s k . The a u d i t o r ' s problem w i l l be examined i n more 1 S I t s h o u l d be emphasized t h a t t h e a u d i t o r ' s c h o i c e o f o p i n i o n i s c o n d i t i o n a l upon t h e i n f o r m a t i o n he r e c e i v e s from t h e a u d i t t e s t and t h e r e f o r e i s not independent o f t h e c h o i c e o f t h e a u d i t t e s t . 1 9 T h i s p r o b a b i l i t y i s a r r i v e d a t by means of Bayes' r u l e . T h i s i m p l i e s t h a t I a l s o assume t h e p r i o r p r o b a b i l i t i e s p ( s ) , and t h e l i k e l i k h o o d f u n c t i o n s , p ( z j s ) , e x i s t and a r e w e l l d e f i n e d . 20 d e t a i l i n Chapter 3; however, t h e i n t u i t i o n i s t h a t i n o r d e r f o r t h e a u d i t o r t o make h i s e x p e c t e d c o s t c a l c u l a t i o n he must be a b l e t o e s t i m a t e t h e outcomes, c(»), and a l s o be a b l e t o a s s e s s a p r o b a b i l i t y d i s t r i b u t i o n o v er t h o s e outcomes. I t i s a h y p o t h e s i s d e v e l o p e d i n t h i s t h e s i s t h a t i n f o r m a t i o n a c q u i r e d from s e c u r i t y market r e t u r n s (SMR) may be used by t h e a u d i t o r t o h e l p make t h e s e a s s e s s m e n t s . At t h i s p o i n t i t i s i m p o r t a n t t o r e c o g n i z e some o f t h e p o t e n t i a l l i m i t a t i o n s i n t h e m o d e l l i n g s t r a t e g y used i n t h i s r e s e a r c h . For i n s t a n c e , I t a k e t h e demand f o r a u d i t i n g as an exogenous f a c t . T h i s i s done i n o r d e r t o a v o i d t h e c o m p l i c a t i o n s which a r e i n d u c e d when a n o t h e r s t r a t e g i c p l a y e r , f o r example, t h e c l i e n t f i r m ' s management, i s added t o t h e a n a l y s i s . I n models u s i n g p r i n c i p a l - a g e n t f o r m u l a t i o n s t h e demand f o r a u d i t i n g may be d e r i v e d endogenously f o r e s s e n t i a l l y two r e a s o n s . A moral h a z a r d demand f o r a u d i t i n g can o c c u r i f t h e agent, t h e f i r m ' s management, i s e f f o r t a v e r s e and t h e agent's e f f o r t i s b o t h u n o b s e r v a b l e and a f f e c t s t h e p r o d u c t i v i t y o f t h e p r i n c i p a l ' s r e s o u r c e s . The demand f o r a u d i t i n g i s d e r i v e d from t h e a b i l i t y of p a r t i e s t o w r i t e an u t i l i t y i m p r o v i n g c o n t r a c t , c o n d i t i o n a l upon t h e a u d i t o r ' s r e p o r t . T h i s c o n t r a c t , which i s o n l y a v a i l a b l e when t h e r e i s an a u d i t o r , i n d u c e s t h e agent t o p r o v i d e a g r e a t e r amount o f e f f o r t and p r o v i d e s b oth t h e p r i n c i p a l and agent w i t h h i g h e r l e v e l s o f e x p e c t e d u t i l i t y . A r i s k - s h a r i n g demand f o r a u d i t i n g can o c c u r i n s i t u a t i o n s where t h e agent p o s s e s s e s asymmetric i n f o r m a t i o n w hich c o u l d be used f o r c o n t r a c t i n g but must be d i s c o u n t e d s i n c e t h e i n f o r m a t i o n can be s t r a t e g i c a l l y m a n i p u l a t e d by t h e a g e n t . I n t h e s e models t h e agent f r e q u e n t l y must bear more r i s k t h a n i n a f i r s t b e s t s o l u t i o n because c o n t r a c t s cannot be based upon t h e agent's i n f o r m a t i o n . The use o f an a u d i t o r t o v e r i f y t h e a g ent's r e p o r t s makes i t p o s s i b l e t o base c o n t r a c t s between t h e p r i n c i p a l and agent upon t h e s e r e p o r t s . I n t u r n t h e s e c o n t r a c t s may r e s u l t i n a more e f f i c i e n t r i s k - s h a r i n g arrangement. One problem i n i n t r o d u c i n g an a u d i t o r i n t o t h e p r i n c i p a l - a g e n t model i s t h a t t h e a u d i t o r ' s a c t i o n s may a l s o be s u b j e c t t o agency problems. With t h r e e p l a y e r s i n t h e game many subgaming i s s u e s a r i s e w hich need t o be a d d r e s s e d . For example, t h e p o s s i b i l i t y o f c o a l i t i o n f o r m a t i o n among t h e p l a y e r s may make i t i m p o s s i b l e f o r an e q u i l i b r i u m p o i n t t o o c c u r . Baiman e t a l (1987) have d e r i v e d some r e s u l t s i n a p r i n c i p a l - a g e n t model w i t h an a u d i t o r . However, t h e y use some v e r y r e s t r i c t i v e a s s u m p t i o n s i n o r d e r t o make t h e game t r a c t a b l e . The model d e v e l o p e d i n t h i s r e s e a r c h assumes t h e demand f o r a u d i t i n g e x i s t s and does not a d d r e s s t h e i s s u e o f why t h e a u d i t o r i s h i r e d i n t h e f i r s t p l a c e . The s p i r i t o f t h e r e s e a r c h does, however, r e l a t e t o t h e i s s u e o f t h e moral h a z a r d problem i n h i r i n g an a u d i t o r . I t i s c o n j e c t u r e d t h a t t h e i m p o s i t i o n o f l e g a l l i a b i l i t y i s an i m p o r t a n t i n s t i t u t i o n a l method f o r d i s c i p l i n i n g t h e a u d i t o r s h o u l d he d e c i d e t o s h i r k . The l e g a l l i a b i l i t y system i n e f f e c t i s a s u p r a - c o n t r a c t u a l arrangement i n an environment i n which i t may be d i f f i c u l t ( o r c o s t l y ) f o r t h e a u d i t o r and t h e u s e r s of f i n a n c i a l s t a t e m e n t s t o w r i t e e x p l i c i t c o n t r a c t s . A n other p o t e n t i a l l i m i t a t i o n i n t h e model i s t h e a s s u m p t i o n of r i s k - n e u t r a l i t y by t h e a u d i t o r . Above t h e r e q u i r e m e n t f o r a r i s k - a v e r s e a u d i t o r t o be compensated f o r b e a r i n g r i s k , i t i s unknown how r e l a x i n g t h i s a s s u m p t i o n would change t h e a n a l y s i s . I t i s p o s s i b l e t h a t d i f f e r e n t e q u i l i b r i u m b e h a v i o r c o u l d r e s u l t when r i s k - a v e r s i o n i s i n t r o d u c e d . I n p u r e l y d e s c r i p t i v e terms t h e s e r i o u s n e s s o f t h i s a s s u m p t i o n may not be g r e a t s i n c e a u d i t o r ' s who a r e v e r y r i s k - a v e r s e a r e u n l i k e l y t o be c o m p e t i t i v e i n t h e market f o r a u d i t s . D e f i n i t i o n o f A u d i t R i s k A b r i e f d i g r e s s i o n i s made t o c l a r i f y t h e usage of t h e term a u d i t r i s k a p p l i e d i n t h i s r e s e a r c h . As noted i n C hapter 1 i t i s common t o d e f i n e audit r i s k as the p r o b a b i l i t y that an auditor w i l l f a i l to give a q u a l i f i e d opinion to a set of f i n a n c i a l statements which are materially in error. T h i s d e f i n i t i o n i s a u s e f u l s t a r t i n g p o i n t i n an a t t e m p t t o i d e n t i f y t h e o p e r a t i o n a l causes of an a u d i t f a i l u r e . I f an a u d i t i s viewed as a s e t o f s e q u e n t i a l p r o c e d u r e s l e a d i n g t o an o p i n i o n , t h e n an a u d i t f a i l u r e i s t h e r e s u l t o f an e r r o r not b e i n g d e t e c t e d o r c o r r e c t e d by one o f t h o s e p r o c e d u r e s . I n t h i s v iew i t makes sense t o decompose a u d i t r i s k as i s done i n t h e v a r i o u s r i s k models (as d e s c r i b e d by C u s h i n g and Loebbecke (1983)) i n t o component r i s k s . The o v e r a l l c o n t r o l o f a u d i t r i s k can be d i s a g g r e g a t e d i n terms of t h e r e l i a b i l i t y o f t h e component p r o c e d u r e s and t h e i n i t i a l u n c e r t a i n t y o v er r e l e v a n t e v e n t s . I n c o n t r a s t , f o r t h e purposes of t h i s r e s e a r c h , i t i s u s e f u l t o broaden t h e d e f i n i t i o n o f a u d i t r i s k t o include both uncertainty about the p r o b a b i l i t y of an audit error and the d i s t r i b u t i o n of the costs of those errors20 2 1 . T h i s i s so s i n c e , i n t h e c o n t e x t o f d e c i s i o n t h e o r y , t h e a u d i t o r ' s ex ante c h o i c e o f an a u d i t t e s t , q, and a d e c i s i o n r u l e , a ( z | q ) , a r e endogenously d e t e r m i n e d and depend upon upon t h e c o s t s a s s o c i a t e d w i t h each d e c i s i o n v a r i a b l e . One way of s e e i n g t h e d i f f e r e n c e between t h e s e two approaches t o a u d i t r i s k i s by e x amining t h e p r o b a b i l i t y 2 0 For a r i s k n e u t r a l a u d i t o r , a d d i t i o n a l u n c e r t a i n t y i s not p r i c e d and he w i l l use e x p e c t e d v a l u e s i n o r d e r t o p i c k among a l t e r n a t i v e a c t i o n s . I n t h i s case t h e i n c r e m e n t a l c o s t s a s s o c i a t e d w i t h a d d i t i o n a l r i s k do not i n c l u d e a r i s k premium per s e , but r a t h e r t h e e x p e c t e d v a l u e o f any l o s s e s which can be a n t i c i p a t e d , as w e l l as t h e c o s t o f any a d d i t i o n a l a u d i t i n g e f f o r t u n d e r t a k e n i n r e s ponse t o t h e r i s k o f t h e e nvironment. 2 1 Another advantage o f i n t e g r a t i n g e x p e c t e d c o s t s i s t h a t i t n a t u r a l l y l e a d s t o c o n s i d e r a t i o n o f t h e impact of a u d i t i n g e r r o r s on t h i r d p a r t i e s . In C h apter 3 t h e b e h a v i o r of s h a r e h o l d e r s i s brought i n t o p l a y . The i m p o r t a n t a s p e c t t o keep i n mind i s t h a t a u d i t r i s k i s an i s s u e because of t h e e f f e c t s f a u l t y a u d i t s have upon f i n a n c i a l s t a tement u s e r s and t h a t t h e s e e f f e c t s a r e be t r a n s l a t e d i n t o c o s t s f a c e d by t h e a u d i t o r . 24 spaces which c o r r e s p o n d t o each approach. I n b o t h c a s e s i t may a p p r o p r i a t e t o c o n s i d e r t h e u n d e r l y i n g sample space as t h e net d o l l a r amount o f any a u d i t e r r o r s , i . e . , t h e d i f f e r e n c e between, say, t h e r e p o r t e d income and the t r u e income. In t h e t r a d i t i o n a l approach a p r o b a b i l i t y i s a s s i g n e d t o event t h a t t h e a u d i t e r r o r i s not a member o f t h e s e t tM~, M*], where t h e M's r e f e r t o t h e lower and upper m a t e r i a l i t y bounds. A u d i t r i s k i s t h i s p r o b a b i l i t y when an u n q u a l i f i e d o p i n i o n i s g i v e n . I n c o n t r a s t , under t h e a l t e r n a t i v e approach we can t h i n k o f f o r m i n g a random v a r i a b l e which i s a mapping from t h e space o f a u d i t e r r o r s i n t o t h e space o f a u d i t o r l o s s e s . T h i s random v a r i a b l e has a p r o b a b i l i t y d i s t r i b u t i o n which i s i n d u c e d by t h e p r o b a b i l i t y d i s t r i b u t i o n o f a u d i t e r r o r s . U s i n g t h i s d i s t r i b u t i o n t o a s s e s s a u d i t r i s k has g r e a t e r d e c i s i o n r e l e v a n c e s i n c e i t i n c o r p o r a t e s i n f o r m a t i o n about b o t h t h e l i k e l i h o o d o f a u d i t e r r o r s and s e v e r i t y o f t h e i r consequences. The o b v i o u s c o n c e p t u a l advantage o f t h i s broadened view o f a u d i t r i s k i s t h a t i t i s c o n s i s t e n t w i t h economic n o t i o n s o f how r a t i o n a l a gents w i l l behave. That i s , a u d i t o r s a r e m o d e l l e d as making e x p l i c i t t r a d e - o f f s between t h e p r o b a b i l i t y o f a u d i t e r r o r and t h e c o s t s o f t h o s e e r r o r s i n d e c i d i n g upon t h e o p t i m a l a l l o c a t i o n o f a u d i t r e s o u r c e s . T h i s s t i l l l e a v e s unanswered t h e q u e s t i o n : how does one o p e r a t i o n a l i z e a u d i t r i s k ? Note t h a t t h e r e l e v a n t u n c e r t a i n t y r e l a t e s t o b o t h t h e p r o b a b i l i t y and magnitude of p o s t a u d i t l o s s e s . I n s t i t u t i o n a l s t r u c t u r e can p r o v i d e some 25 g e n e r a l i n f o r m a t i o n u s e f u l t o a s s e s s i n g r i s k such a s : under what c i r c u m s t a n c e s a u d i t o r s may f a c e p o t e n t i a l r i s k s and a l s o , t o some e x t e n t , t h e s i z e o f t h o s e r i s k s 2 2 . L e g a l L i a b i l i t y From t h e w e a l t h o f i n s t i t u t i o n a l f a c t s a v a i l a b l e about a u d i t o r l i a b i l i t y (see c h a p t e r 1) t h i s paper w i l l a b s t r a c t t h e f o l l o w i n g e l ements: 1. A u d i t o r l i a b i l i t y has two p r e c o n d i t i o n s : t h a t some p a r t y has s u s t a i n e d a l o s s due t o t h e a u d i t o r ' s a c t i o n and t h a t t h e a u d i t o r has f a i l e d t o meet some l e g a l l y p r o s c r i b e d s t a n d a r d of c a r e . 2. The damages c l a i m e d by p l a i n t i f f s a r e f r e q u e n t l y r e l a t e d t o d e c l i n e s i n t h e market p r i c e o f t h e c l i e n t f i r m ' s s hare p r i c e and t h a t t h e subsequent a u d i t o r ' s l o s s e s a r e a f u n c t i o n o f t h e s h a r e h o l d e r l o s s e s . 3. A u d i t o r n e g l i g e n c e i s an i s s u e o f f a u l t y r e p r e s e n t a t i o n . T h e r e f o r e , whenever an a u d i t o r commits a t y p e I I e r r o r he i s p o t e n t i a l l y s u b j e c t t o p o s t a u d i t l o s s e s i f t h e r e q u i s i t e e v i d e n c e o f n e g l i g e n c e can be f o u n d . F i r m R i s k and A u d i t R i s k The u n c e r t a i n t y i n t h e f u t u r e cash f l o w s o f t h e c l i e n t f i r m i s a p r i m a r y s o u r c e o f a u d i t r i s k . C o n s i d e r t h e 2 2 For i n s t a n c e , t h e S e c u r i t i e s A c t s s e t out when and f o r what measure o f damages a u d i t o r s (and o t h e r s ) can be h e l d l i a b l e f o r a c t i o n s w h i c h come under t h e i r j u r i s d i c t i o n . 26 a u d i t o r ' s problem o f a s s i g n i n g a v a l u e t o a f i r m ' s a s s e t s . The t r u e v a l u e i s a f u n c t i o n o f t h e a s s e t s ' a b i l i t y t o g e n e r a t e c a s h f l o w s . B u s i n e s s r i s k r e p r e s e n t s t h e u n c e r t a i n t y 2 3 o f t h o s e c a s h f l o w s . For i n s t a n c e , a n o n - d i v e r s i f i e d f i r m i n an i n d u s t r y w i t h l a r g e demand u n c e r t a i n t y o p e r a t e s i n an environment o f h i g h b u s i n e s s r i s k . C o n s e q u e n t l y , t h e v a l u a t i o n of i t s a s s e t s may f l u c t u a t e g r e a t l y over t i m e . T h i s causes two problems f o r t h e a u d i t o r . F i r s t , t h e share p r i c e of t h e f i r m i s a l s o l i k e l y t o f l u c t u a t e t o t h e e x t e n t t h e demand u n c e r t a i n t y i s c o r r e l a t e d w i t h t h e m a r k e t 2 4 . I t i s c o n j e c t u r e d t h a t s h a r e p r i c e f l u c t u a t i o n can cause i n v e s t o r s t o s u f f e r l o s s e s f o r which t h e a u d i t o r may be h e l d l i a b l e . The second problem f o r t h e a u d i t o r i s t h a t i t i s i n h e r e n t l y d i f f i c u l t t o e s t i m a t e t h e v a l u e o f a s s e t s which g e n e r a t e h i g h l y v a r i a b l e c a s h f l o w s . T h i s i s so s i n c e t h e v a l u e s a s s i g n e d t o t h o s e a s s e t s depend upon a f o r e c a s t o f t h e f u t u r e c a s h f l o w s a s s o c i a t e d w i t h t h a t a s s e t . T h i s i s , a t b e s t , an i m p r e c i s e o p e r a t i o n which admits t o t h e p o s s i b i l i t y o f e r r o r . The f a i l u r e t o d e t e c t such an e r r o r c o u l d be i n t e r p r e t e d by a c o u r t as e v i d e n c e o f a u d i t o r n e g l i g e n c e . 2 3 Conine (1982) n o t e s t h a t b u s i n e s s r i s k i s d e t e r m i n e d by s e v e r a l f a c t o r s . Among them a r e t h e degree o f o p e r a t i n g l e v e r a g e , s t o c h a s t i c p r o d u c t demand and p r i c e s , and s t o c h a s t i c v a r i a b l e p r o d u c t i o n and m a r k e t i n g c o s t s . 2 4 R u b i n s t e i n (1973) o r i g i n a l l y d e v e l o p e d a model o f s y s t e m a t i c r i s k which i n c o r p o r a t e d s t o c h a s t i c p r o d u c t demand. 27 Another a s p e c t o f f i r m r i s k i s f i n a n c i a l r i s k 2 5 . F i n a n c i a l r i s k i s a f u n c t i o n o f t h e p r o p o r t i o n o f debt i n t h e f i r m ' s c a p t i a l s t r u c t u r e . F i n a n c i a l r i s k i n c r e a s e s t h e e x p e c t e d c o s t s t h e a u d i t o r might bear due t o a c l i e n t f i r m ' s b a n k r u p t c y 2 6 . F u r t h e r f i n a n c i a l r i s k can c o n t r i b u t e t o a u d i t r i s k by i n c r e a s i n g t h e p r o b a b i l i t y o f f i n a n c i a l d i s t r e s s , t h e r e b y l e a d i n g t o a s e a r c h f o r a u d i t e r r o r s 2 7 . From t h e above d i s c u s s i o n one may c o n c l u d e t h a t b u s i n e s s r i s k can l e a d t o a u d i t r i s k i n two ways. F i r s t , i n c r e a s e d b u s i n e s s r i s k i n c r e a s e s t h e p r o b a b i l i t y of s h a r e h o l d e r s s u f f e r i n g l o s s e s 2 8 , a p r e r e q u i s i t e f o r l a w s u i t s . Second, b u s i n e s s r i s k i n c r e a s e s t h e d i f f i c u l t y i n v a l u i n g f i r m a s s e t s and a s s e s s i n g t h e f i r m ' s f i n a n c i a l p o s i t i o n . T h i s makes i t more d i f f i c u l t f o r t h e a u d i t o r t o d e t e r m i n e t h e a p p r o p r i a t e amount o f a u d i t i n g e f f o r t and i t a l s o makes i t more l i k e l y t h a t i f a bad outcome s h o u l d o c c u r t h e a u d i t o r ' s judgment 2 3 Bowman (1979) l i n k s s y s t e m a t i c r i s k w i t h f i r m debt measures. A l s o see Hamada (1972). 2 6 Simunic (1980) d i s c u s s e s how t h e j o i n t and s e v e r a l p r o v i s i o n o f l i a b i l i t y laws w i l l cause t h e a u d i t o r o f a b a n k r u p t c l i e n t t o bear a g r e a t e r p e r c e n t a g e o f t h e l i a b i l i t y l o s s e s i n t h e case of a s u c c e s s f u l l a w s u i t . 2 7 Palmrose (1987) f i n d s e v i d e n c e l i n k i n g c l i e n t f i r m f i n a n c i a l d i s t r e s s and l i t i g a t i o n a g a i n s t a u d i t o r s . 2 3 T h i s i s , p e r h a p s , a t b e s t a crude a s s o c i a t i o n . N o n e t h e l e s s , i f a u d i t o r s a r e sometimes h e l d r e s p o n s i b l e f o r s h a r e h o l d e r l o s s e s which t h e y d i d not cause (due t o t h e i n a b i l i t y o f t h e c o u r t s e i t h e r t o c o r r e c t l y d e t e r m i n e t h e cause o r t o a s s o c i a t e t h e c o r r e c t amount o f damages w i t h t h e c a u s e ) , t h e n f a c t o r s which i n g e n e r a l i n c r e a s e t h e l i k e l i h o o d o f c l i e n t f i r m l o s s e s may r e s u l t i n p o s t a u d i t l i a b i l i t y . 28 w i l l be q u e s t i o n e d by t h e s h a r e h o l d e r s , and t h e c o u r t s w i l l f i n d t h e a u d i t o r ' s work t o be n e g l i g e n t . F i n a l l y , i t i s n o t e d t h a t f i n a n c i a l r i s k can a l s o a f f e c t a u d i t r i s k by i n c r e a s i n g t h e p r o b a b i l i t y o f f i n a n c i a l d i s t r e s s i n t h e c l i e n t f i r m . 29 Chapter 3 THE AUDITOR'S DECISION MODEL WITH AUTONOMOUS SHAREHOLDERS In t h i s c h a p t e r t h e e f f e c t s o f i n t r o d u c i n g autonomous s h a r e h o l d e r s i n t o t h e a u d i t o r ' s d e c i s i o n model a r e a n a l y z e d . The purpose i s t o l i n k s e c u r i t y market r e t u r n s (SMR) w i t h a u d i t r i s k t h r o u g h t h e impact o f SMR upon s h a r e h o l d e r b e h a v i o r . One i n t u i t i o n i s t h a t , ex post, s h a r e h o l d e r s may r e v i s e t h e i r b e l i e f s about t h e ex ante f a i r n e s s o f a f i r m ' s f i n a n c i a l s t a t e m e n t s i n l i g h t o f t h e o b s e r v e d r e t u r n . They t h e n use t h i s r e v i s e d b e l i e f a l o n g w i t h knowledge o f t h e i n s t i t u t i o n a l s e t t i n g ( i . e . , t h e e x i s t i n g l i a b i l i t y r u l e s and c o u r t ' s b e h a v i o r ) t o d e c i d e whether o r not t o sue t h e a u d i t o r . I n t u r n , once a u d i t o r s have a r u l e f o r p r e d i c t i n g s h a r e h o l d e r s ' b e h a v i o r t h e y can i n c o r p o r a t e t h i s knowledge i n t o t h e i r r i s k assessment o f t h e c l i e n t f i r m and make t h e a p p r o p r i a t e a d j u s t m e n t s i n t h e i r a u d i t p l a n and f e e 2 9 . One o f t h e g o a l s o f t h e f o l l o w i n g a n a l y s i s i s t o examine c o n d i t i o n s under w h i c h i n f o r m a t i o n about t h e r i s k o f a c l i e n t f i r m ' s common s t o c k can be used by t h e a u d i t o r t o a s s e s s t h e r i s k i n e s s o f t h e a u d i t i n g e n v i r o n m e n t . E q u i l i b r i a 2 9 I n t h e model t h e f e e i s assumed t o be c o n s t a n t and d e t e r m i n e d p r i o r t o t h e o n s e t o f any a u d i t i n g e f f o r t . However t h e f e e w i l l r e f l e c t any a n t i c i p a t e d r i s k . 30 a r e examined i n w h i c h , g i v e n t h e assumptions o f t h e model, a u d i t c o s t s i n c r e a s e w i t h t h e ex ante r i s k i n e s s o f t h e f i r m ' s s e c u r i t i e s . T h i s r e s u l t m o t i v a t e s t h e e m p i r i c a l t e s t s i n Chapter 4. The A u d i t o r ' s D e c i s i o n Model A common s i m p l i f i c a t i o n o f t h e a u d i t o r ' s d e c i s i o n p r oblem, as d e s c r i b e d i n Ch a p t e r 2, i s g i v e n i n F i g u r e 2. I t can be seen t h a t f o r a g i v e n a u d i t t e s t r e s u l t , z, and a u d i t i n g i n t e n s i t y , q, t h e a u d i t o r chooses an o p i n i o n , a, whic h m i n i m i z e s e x p e c t e d c o s t s . T h i s i s done by b a l a n c i n g t h e e x p e c t e d c o s t s o f c o m m i t t i n g a t y p e I e r r o r w i t h t h o s e o f c o m m i t t i n g a t y p e I I e r r o r . With r e f e r e n c e t o F i g u r e 1, t h i s c h o i c e i s d e p i c t e d i n t h e r i g h t - m o s t branches o f t h e d e c i s i o n t r e e . The e x p e c t e d v a l u e o f t h e l e a s t c o s t d e c i s i o n a t t h i s s t a g e i s t h e n used as d a t a f o r t h e a u d i t o r ' s c h o i c e o f t h e o p t i m a l l e v e l o f a u d i t i n g i n t e n s i t y . Note t h a t t h e c o s t s w i t h i n t h e boxes a r e n o r m a l i z e d such t h a t o n l y t h e i n c r e m e n t a l c o s t s t o t h e a u d i t o r o f i s s u i n g a f a l s e o p i n i o n 3 0 a r e g i v e n . I t i s i m p o r t a n t t o r e c o g n i z e t h a t i n most s t u d i e s o f th e a u d i t o r ' s d e c i s i o n problem t h e v a l u e a s s i g n e d t o each r e a l i z a t i o n o f t h e c o s t f u n c t i o n , c ( a , s , z , q ) , i s assumed t o be g i v e n e x o g e n o u s l y . (See, f o r example, Kinney (1975).) In 3 0 The c o s t s assume t h e a u d i t o r i s not a c t i n g f r a u d u l e n t l y . That i s , no at t e m p t i s made t o model t h e c o s t s and b e n e f i t s o f t h e a u d i t o r a c t i n g i n c o l l u s i o n w i t h o t h e r p a r t i e s i n v o l v e d w i t h t h e f i r m . c o n t r a s t , t h i s r e s e a r c h r e c o g n i z e s t h a t t h e c o s t s o f a t y p e I I e r r o r , c ( I I ) , a r e l i k e l y t o v a r y w i t h t h e s h a r e h o l d e r s ' r e t u r n . From F i g u r e 1 i t i s c l e a r t h a t t h e v a l u e a s s i g n e d t o c ( I I ) can a f f e c t t h e a u d i t o r ' s d e c i s i o n s and t h e r e f o r e t h e e x p e c t e d c o s t o f t h e a u d i t . The q u e s t i o n t o be a d d r e s s e d i s : how i s t h i s c o s t i n f l u e n c e d by t h e d i s t r i b u t i o n o f t h e c l i e n t f i r m ' s s t o c k r e t u r n s ? One approach t o a n s w e r i n g t h i s q u e s t i o n i s t o r e t u r n t o t h e i d e a o f r e p r e s e n t i n g t h e a u d i t o r ' s l o s s f u n c t i o n as a random v a r i a b l e i n which a u d i t i n g e r r o r s a r e mapped i n t o a u d i t o r ' s l o s s e s . I n t h i s c o n t e x t t h e i s s u e i s how t o a s s i g n a v a l u e t o a g i v e n a u d i t i n g e r r o r . Two s t y l i z e d f a c t s a r e used t o m o t i v a t e t h e use o f SMR i n making t h i s mapping. F i r s t , s h a r e h o l d e r s ' l o s s e s a r e used t o prompt t h e s e a r c h f o r a u d i t o r e r r o r s . T h i s makes sense under two q u i t e d i f f e r e n t s e t s o f c i r c u m s t a n c e s . On t h e one hand, i f n e g a t i v e s t o c k p r i c e r e t u r n s a r e more l i k e l y t o o c c u r when a u d i t i n g e r r o r s e x i s t t h e n i t makes sense t o s e a r c h f o r t h e s e e r r o r s f o l l o w i n g a n e g a t i v e r e t u r n . On t h e o t h e r hand, even i f a u d i t i n g e r r o r s were independent o f t h e r e a l i z e d r e t u r n t h e e x i s t i n g l e g a l l i a b i l i t y r u l e s i m p l y i t i s p o t e n t i a l l y b e n e f i c i a l f o r s h a r e h o l d e r s t o f i n d e r r o r s o n l y when th e y have d e m o n s t r a b l e l o s s e s . Second, t h e magnitude o f t h e u l t i m a t e s h a r e h o l d e r s ' l o s s e s w h i c h a r e a t t r i b u t a b l e ( o r pe r h a p s , more r e l e v a n t l y , a s s i g n e d by t h e c o u r t ) t o t h e a u d i t o r i s an i n c r e a s i n g f u n c t i o n o f t o t a l s h a r e h o l d e r s ' l o s s e s . The i n t u i t i o n b e h i n d t h i s " f a c t " i s t h a t even i f t h e c o u r t s c o u l d p e r f e c t l y d e t e r m i n e t h e e x i s t e n c e o f b o t h a u d i t e r r o r s and n e g l i g e n c e , i t would be d i f f i c u l t t o f a c t o r out t h e p o r t i o n o f t h e l o s s a t t r i b u t a b l e t o .the a u d i t o r . F u r t h e r , i f such f a c t o r i n g were p o s s i b l e , i t i s u n l i k e l y t h a t a u d i t e r r o r s map i n t o l o s s e s i n a way wh i c h i s independent o f o t h e r v a r i a b l e s . B e f o r e a n a l y z i n g t h e s e i s s u e s some a d d i t i o n a l n o t a t i o n i s r e q u i r e d ; i t i s g i v e n i n T a b l e 1. I n t h e model i t i s assumed t h e s t o c k p r i c e o f a g i v e n f i r m i s a f u n c t i o n , t ( 6 ± , s ^ ) , o f 6 i f a v a r i a b l e which r e p r e s e n t s a l l f a c t o r s t h a t a r e u n c o r r e l a t e d w i t h t h e f a i r n e s s o f t h e f i n a n c i a l s t a t e m e n t s , and s-j, t h e f a i r n e s s o f t h e f i n a n c i a l s t a t e m e n t s . The a u d i t o r ' s o p i n i o n , an, i s used by s h a r e h o l d e r s t o c o n d i t i o n t h e i r b e l i e f s about a g i v e n s-, . Thus, t h e ex ante s t o c k p r i c e i s g i v e n b y 3 1 : 3.1) t n = Z Z t ( 0 . , s . ) p(6.) p ( s . | a ) The ex post s t o c k p r i c e i s d e t e r m i n e d by t h e r e a l i z a t i o n of a p a i r ( 8 i , s - , ) . I n t h e a n a l y s i s t h a t f o l l o w s t h e r e a l i z e d s t o c k p r i c e i s r e s t r i c t e d t o f o u r v a l u e s w i t h t h e f o l l o w i n g 3 1 The ex ante s t o c k p r i c e i s assumed t o be t h e f i r s t p r i c e a t which i n f o r m a t i o n p r o v i d e d by t h e c u r r e n t a u d i t i s impounded. As a r e s u l t when l o s s e s a r e a s s e s s e d i t i s assumed t h e a u d i t o r i s not h e l d r e s p o n s i b l e f o r d e c l i n e s which p r e d a t e to* 33 s t r u c t u r e 3 2 : t l ( 0 l ' S l ) > t 2 ( 9 2 ' S l ) = t 3 ( e i ' s 2 ) >' t 4 ( 9 2 ' s 2 ) The s t r u c t u r e i s such t h a t s t o c k p r i c e r e v e a l s t h e t r u e c o n d i t i o n o f t h e f i n a n c i a l s t a t e m e n t s o n l y when b o t h f a c t o r s a r e e i t h e r "good" o r "bad". For t h e i n t e r m e d i a t e c a s e s th e p r i c e does not r e v e a l which f a c t o r i s good and which f a c t o r i s bad. I t i s assumed t h a t , i n t h e s e c a s e s , n e i t h e r t h e s h a r e h o l d e r s nor t h e c o u r t s can o b s e r v e th e t r u e s t a t e s 3 3 . C o s t s t o t h e a u d i t o r of t y p e I and t y p e I I e r r o r s a r e assumed t o be f u n c t i o n s : 3.2a) c(a2»s^,q,z) = c o n s t a n t , f o r a l l q and z. 3.2b) c(a^,S2> = f ( t g ( a ^ ) - t ^ ) , f o r each q, z and k= 3,4 The c o s t c ( a 2 , S i ) , a l s o denoted as c ( I ) , i s assumed t o be a f i x e d amount. The c o s t s i n c l u d e d i n t h i s q u a n t i t y i n c l u d e t h e expense o f a d d i t i o n a l a u d i t t e s t s (which may be r e q u i r e d by t h e c l i e n t ) , l o s s o f c l i e n t g o o d - w i l l , e t c 3 4 . The c o s t o f a t y p e I I e r r o r , c ( I I ) , can t a k e on many d i f f e r e n t v a l u e s , as 3 2 For a n u m e r i c a l example see appendix 1. 3 3 I n a n o i s y r a t i o n a l e x p e c t a t i o n s economy t h e p r i c e can r e f l e c t t h e t r u e s t a t e s w i t h o u t t h e i n d i v i d u a l i n v e s t o r s b e i n g a b l e t o p e r f e c t l y i n f e r t h e s t a t e s from t h e p r i c e . See Grossman and S t i g l i t z (1980). 3 4 Kinney (1975) o f f e r s a more complete d i s c u s s i o n o f t h e c o s t s t o t h e a u d i t o r o f a t y p e I e r r o r . Note t h a t i t i s assumed t h e a u d i t o r i s not h e l d l i a b l e t o s h a r e h o l d e r s f o r t y p e I e r r o r s , t h a t i s a u d i t o r s cannot be t o o " c o n s e r v a t i v e " from t h e s h a r e h o l d e r s p o i n t o f v i e w . 34 seen i n 3.2b), These c o s t s depend upon s e v e r a l f a c t o r s and w i l l be d i s c u s s e d l a t e r . A t t h i s p o i n t t h e c o n j e c t u r e i s made t h a t , i n e q u i l i b r i u m , t h e e x p e c t e d v a l u e o f c ( I I ) i s a non-d e c r e a s i n g f u n c t i o n o f t h e d e c l i n e ( i f any) o f t h e share p r i c e subsequent t o t h e a u d i t o r ' s o p i n i o n . B e f o r e t u r n i n g t o f u r t h e r a n a l y s i s o f c ( I I ) i t i s w o r t h w h i l e t o r e t u r n t o t h e " f a c t s " mentioned above, t a k i n g i n t o a c c o u n t t h e a d d i t i o n a l s t r u c t u r e imposed upon t h e model. The second f a c t i s t h e more e a s i l y a d d r e s s e d , t h a t i s , i t seems r e a s o n a b l e t o c o n c l u d e t h a t s e c u r i t y market r i s k i s p o s i t i v e l y a s s o c i a t e d w i t h t h e magnitude o f p o t e n t i a l a u d i t o r l o s s e s . The key i s t h e way i n whi c h a u d i t e r r o r s i n t e r a c t w i t h o t h e r f a c t o r s . C o n s i d e r t h e f o l l o w i n g extreme c a s e s : 1. The l o s s e s due t o a u d i t e r r o r s a r e independent o f o t h e r f a c t o r s , t h e c o u r t s can d e t e r m i n e t h e c a u s a l r e l a t i o n s h i p between t h e e r r o r and t h e l o s s , and t h e a u d i t o r i s h e l d r e s p o n s i b l e o n l y f o r l o s s e s a t t r i b u t a b l e t o a u d i t e r r o r . Here s e c u r i t y market r i s k would p l a y no r o l e s i n c e t h e c o u r t s c o r r e c t l y " f a c t o r o u t " l o s s e s a t t r i b u t a b l e t o o t h e r c a u s e s . 2. Same as 1, but t h e l o s s e s due t o a u d i t e r r o r s a r e not independent o f o t h e r f a c t o r s . C o n s i d e r t h e two f u n c t i o n s t ' and f ' g i v e n i n Appendix 1. I n t ' t h e s t o c k p r i c e i s an a d d i t i v e f u n c t i o n o f t h e f a i r n e s s o f t h e f i n a n c i a l s t a t e m e n t s and i n t ' ' t h e s t o c k p r i c e i s a m u l t i p l i c a t i v e f u n c t i o n o f f a i r n e s s . When t h e t ' model i s used t h e c o u r t s 35 can r e a d i l y d e t e r m i n e t h e l o s s a t t r i b u t a b l e t o a u d i t e r r o r c o n d i t i o n a l upon o b s e r v i n g a r e a l i z a t i o n o f (6j.,s-)), s i n c e t h e i n c r e m e n t a l l o s s caused by an a u d i t e r r o r i s 5 u n i t s r e g a r d l e s s of t h e r e a l i z a t i o n o f 6s.. I n c o n t r a s t , when the t ' 1 model d e t e r m i n e s s t o c k p r i c e s , t h e i n c r e m e n t a l l o s s caused by an a u d i t e r r o r depends upon t h e r e a l i z a t i o n o f 9 i . 3 S . T h e r e f o r e t h e magnitude o f t h e l o s s f o r which the a u d i t o r i s p o t e n t i a l l y a t r i s k can be seen t o be s e n s i t i v e t o f a c t o r s which a f f e c t t h e s t o c k p r i c e . The q u e s t i o n of an a s s o c i a t i o n between t h e d i s t r i b u t i o n o f s e c u r i t y market r e t u r n s and t h e e x i s t e n c e o f a u d i t e r r o r s i s more s u b t l e . There a r e two p o s s i b i l i t i e s w hich can be a d d r e s s e d . One i s whether t h e r e t u r n g e n e r a t i n g p r o c e s s changes when an a u d i t e r r o r o c c u r s . I f t h i s i s t h e c a s e t h e n a p r i c e s e r i e s w i t h a h i g h v a r i a n c e i n t h e h i s t o r i c a l p r i c e may s e r v e t o d i s g u i s e t h e change i n t h e p r o c e s s . T h i s i m p l i e s t h a t g r e a t e r u n c e r t a i n t y i n t h e SMR c o u l d r e s u l t i n fewer l a w s u i t s b e i n g brought a g a i n s t t h e a u d i t o r . An a l t e r n a t i v e i n t e r p r e t a t i o n i s t h a t t h e p r o b a b i l i t y of c o m m i t t i n g an a u d i t i n g e r r o r i s more l i k e l y i n an environment of g r e a t e r SMR r i s k . The argument r e s t s upon t h e e x i s t e n c e of common f a c t o r s w hich c o n t r i b u t e t o b o t h t h e 3 3 In t h i s case i t i s h a r d , i f not i m p o s s i b l e , t o f a c t o r out t h e i n c r e m e n t a l impact of t h e a u d i t e r r o r . I n such s i t u a t i o n s t h e r u l e f o r damages a p p l i e d by t h e c o u r t s becomes c r i t i c a l . 36 f i r m ' s measured s e c u r i t y market r i s k i n e s s and t o t h e r i s k o f c o m m i t t i n g a u d i t i n g e r r o r s . For example, i t may be argued t h a t i t i s more d i f f i c u l t t o c o r r e c t l y i n t e r p r e t and a p p l y GAAS and GAAP i n environments where t h e r e i s a good d e a l o f u n c e r t a i n t y about t h o s e elements which e f f e c t t h e c u r r e n t v a l u a t i o n and f u t u r e performance of t h e f i r m . I f t h e market measures o f r i s k r e f l e c t t h e u n c e r t a i n t y t h e n t h e y may be used as i n s t r u m e n t s f o r t h e u n d e r l y i n g u n c e r t a i n t y and t h e r e f o r e u s e f u l i n t h e assessment o f t h e a u d i t r i s k . I n summary t h e i n t u i t i o n i s t h a t i n c r e a s e d r i s k i n e s s 3 6 i n t h e f i r m ' s f u t u r e c a s h f l o w s i s impounded i n t h e measures o f s e c u r i t y market r i s k . I n t u r n , i n c r e a s e s i n t h e s e measures may be r e l a t e d t o an i n c r e a s e d p r o b a b i l i t y t h a t i t w i l l be r e v e a l e d , ex post, t h a t t h e a u d i t o r committed an a u d i t i n g e r r o r . E q u i l i b r i u m A n a l y s i s w i t h Autonomous S h a r e h o l d e r s I n t h i s s e c t i o n t h e c o s t s o f c ( I I ) a r e i n v e s t i g a t e d when t h e s h a r e h o l d e r s ' a c t i o n s a r e de t e r m i n e d endogenously. The framework f o r t h e a n a l y s i s i s i n terms o f a s i m p l i f i e d g a m e - t h e o r e t i c s t r u c t u r e where t h e s h a r e h o l d e r d e c i d e s whether o r not t o sue t h e a u d i t o r depending upon t h e l e g a l e n v i r o n m e n t , t h e a u d i t o r ' s o p i n i o n , and t h e r e a l i z e d s t o c k p r i c e . Two l e g a l l i a b i l i t y regimes a r e i n v e s t i g a t e d , one where t h e a u d i t o r i s s t r i c t l y l i a b l e f o r a u d i t i n g e r r o r s and a n o t h e r 3 S The n o t i o n o f i n c r e a s i n g r i s k i s d e t a i l e d by R o t h s c h i l d and S t i g l i t z (1970). 37 where t h e a u d i t o r has a n e g l i g e n c e d e f e n c e a v a i l a b l e t o him. F i g u r e s 3a and 3b d e p i c t t h e a u d i t o r - s h a r e h o l d e r game. These f i g u r e s add t h e s h a r e h o l d e r s ' d e c i s i o n t r e e t o t h a t o f t h e a u d i t o r . The a u d i t o r ' s d e c i s i o n t r e e ends w i t h " n a t u r e " moving t o d e c i d e t h e f a i r n e s s o f t h e f i n a n c i a l s t a t e m e n t s 3 7 . I t s h o u l d be p o i n t e d out t h a t t h e b e h a v i o r o f t h e c l i e n t f i r m ' s management i s t a k e n as exogenous. The a u d i t o r (and s h a r e h o l d e r s ) a s s e s s a p r i o r d i s t r i b u t i o n o v er management's p r o p e n s i t y t o r e p o r t t h e f i n a n c i a l s t a t e m e n t s t r u t h f u l l y , but t h e models used i n t h i s t h e s i s do not a l l o w f o r management t o behave s t r a t e g i c a l l y 3 8 . As s t a t e d p r e v i o u s l y t h e demand f o r a u d i t i n g i s t a k e n as exogenous. I n t h e model t h e a u d i t o r s e r v e s two p u r p o s e s . F i r s t , t h e s h a r e h o l d e r s c o u l d use t h e a u d i t o r ' s s i g n a l ( o p i n i o n ) t o update t h e i r p r i o r s about t h e f a i r n e s s o f t h e f i n a n c i a l s t a t e m e n t s 3 9 t h r o u g h t h e f u n c t i o n , p(s-j)a„), which 3 7 I t i s assumed t h a t t h e f i r m ' s management p r e p a r e s f i n a n c i a l s t a t e m e n t s p r i o r t o t h e a u d i t o r s t a r t i n g h i s a u d i t i n g p r o c e d u r e s . The a u d i t o r , however, does not l e a r n t h e t r u e c o n d i t i o n o f t h e f i n a n c i a l s t a t e m e n t s , but i s a l l o w e d t o p e r f o r m t e s t s i n o r d e r t o r e a c h a l e v e l o f a s s u r a n c e about t h e f i n a n c i a l s t a t e m e n t s ' f a i r n e s s . 3 8 Both A n t l e (1982) and Baiman e t a l (1987) d i s c u s s t h e c o m p l i c a t i o n s i n t h e a n a l y s i s which o c c u r when managers a r e t r e a t e d as p l a y e r s i n a t h r e e p e r s o n management-auditor-s h a r e h o l d e r game. 3 9 Once a p r i c e i s d e t e r m i n e d f o r each f i r m s ' s e c u r i t y • i n v e s t o r s t h e n can make o p t i m a l p o r t f o l i o d e c i s i o n s . T h i s s u g g e s t s a p r o d u c t i v e r o l e f o r t h e a u d i t o r . T h i s i s s u e i s not e x p l i c i t y m o d e l l e d i n t h i s r e s e a r c h . S c o t t (1975) f u r t h e r s t h e i d e a s by r e l a t i n g t h e i n v e s t o r s ' c o n s u m p t i o n - i n v e s t m e n t problem t o l o s s f u n c t i o n f a c e d by a u d i t o r s . T h i s t i e s t h e a u d i t o r ' s c h o i c e o f a c t i o n t o t h e w e l f a r e o f i n v e s t o r s . 38 appears i n e q u a t i o n 3.1). The r o l e o f t h e a u d i t o r i n t h i s c a s e would be t o p r o v i d e an independent assessment o f whether t h e f i r m ' s management communicated i n f o r m a t i o n t r u t h f u l l y . The o f t h e r o l e o f t h e a u d i t o r as an i n s u r e r i s not d e r i v e d from t h e model h e r e i n , however, under c e r t a i n c o n d i t i o n s t h e a u d i t o r may a c t as an i n s u r e r by b e a r i n g t h e r i s k of bad share p r i c e outcomes. T h i s i s l i k e l y t o happen when i t i s i m p o s s i b l e f o r t h e c o u r t s t o d i s t i n g u i s h between t h e l o s s e s caused by 9 i and t h o s e caused by s^. I n t h i s c a s e i t may be o p t i m a l f o r t h e a u d i t o r t o bear r i s k due t o h i s moral h a z a r d problem. Though, s t r i c t l y s p e a k i n g , i n t h i s model s i n c e t h e a u d i t o r i s r i s k -n e u t r a l b e a r i n g r i s k i n and o f i t s e l f imposes no p e n a l t y . s t a t e m e n t s i s not p e r f e c t l y r e v e a l e d even though i t i s a f a c t o r i n d e t e r m i n g t h e s h a r e p r i c e . The s h a r e h o l d e r s use t h e sh a r e p r i c e t o l e a r n what t h e y can about t h e f a i r n e s s o f t h e f i n a n c i a l s t a t e m e n t s and about t h e a u d i t o r ' s b e h a v i o r . The s h a r e h o l d e r s ' a c t i o n i s t o d e t e r m i n e whether o r not t o sue t h e a u d i t o r under t h e e x t a n t l i a b i l i t y regime. The s h a r e h o l d e r ' s d e c i s i o n problem i s g i v e n by: second purpose i s one o f i n s u r a n c e . Once a g a i n t h e o p t i m a l i t y I t i s assumed t h a t t h e t r u e c o n d i t i o n o f t h e f i n a n c i a l 3.3) max j € J { * L (VV # p ( s 2 l V ' P (V q + l a n ' V } q€Q - w ( j ) • j ( a , t , ) f o r a l l k. J p J n k 39 S t a r t i n g from t h e l e f t o f e x p r e s s i o n 3.3) a r e t h e v a r i o u s components t h a t e n t e r t h e s h a r e h o l d e r s ' d e c i s i o n problem. F i r s t , L(») r e p r e s e n t s t h e amount o f damages s u f f e r e d by t h e s h a r e h o l d e r s . T h i s i s a g r o s s amount and i n p r a c t i c e t h e a u d i t o r would not be h e l d a c c o u n t a b l e f o r t h e e n t i r e amount o f t h e l o s s . The c o u r t s w i l l a t t e m p t t o a d j u s t t h e g r o s s amount t o r e f l e c t t h e damages caused by t h e a u d i t f a i l u r e . p ( s 2 J t V c ; ) i s t h e p r o b a b i l i t y t h e c o u r t s and s h a r e h o l d e r s a s s i g n t o t h e ev e n t t h a t t h e f i n a n c i a l s t a t e m e n t s a r e f a l s e g i v e n t h e r e a l i z a t i o n o f a p a r t i c u l a r s h a r e p r i c e , p(q m<q' r | a„, t * ) i s t h e p r o b a b i l i t y t h a t s h a r e h o l d e r s and c o u r t s a s s i g n t o t h e event t h a t t h e a u d i t o r chose a l e v e l o f a u d i t i n g l e s s t h a n t h e due c a r e l e v e l . T h i s i s a c u m u l a t i v e measure where m r e p r e s e n t s t h e s e t o f a u d i t i n g i n t e n s i t i e s l e s s t h a n q"*. I t i s w o r t h n o t i n g t h a t i n a s t r i c t n e g l i g e n c e regime t h i s q u a n t i t y i s s e t e q u a l t o 1, i . e . , t h e r e i s no due d i l i g e n c e d e f e n s e . w<«) i s t h e c o s t 4 0 t o t h e s h a r e h o l d e r o f h i s a c t i o n , j , e i t h e r t o sue o r not sue t h e a u d i t o r . A n o t h e r i s s u e r e l a t e d t o t h e amount o f damages f o r whi c h t h e a u d i t o r i s t o be h e l d a c c o u n t a b l e i s t h e q u e s t i o n o f w h i c h p a r t i e s have a c t u a l l y s u f f e r e d a l o s s . For i n s t a n c e , what l o s s i n w e a l t h have s h a r e h o l d e r s who owned s h a r e s p r i o r t o t h e i n c i d e n c e o f an a u d i t e r r o r s u f f e r e d as a r e s u l t o f t h e 4 0 The c o s t o f s u i n g i s , f o r t h e sake o f s i m p l i c i t y , assumed t o be n o n - r e i m b u r s a b l e . P r o c e d u r a l a s p e c t s o f t h e law a r e a b s t r a c t e d from i n t h i s r e s e a r c h , though t h e y c l e a r l y i n f l u e n c e t h e c h o i c e o f s h a r e h o l d e r s ' a c t i o n s . 40 a u d i t o r ' s f a i l u r e t o uncover an e r r o r i n t h e f i n a n c i a l s t a t e m e n t s ? I n o r d e r t o a v o i d h a v i n g t o s p l i t t h e f i r m ' s s h a r e h o l d e r s i n t o d i f f e r e n t c l a s s e s (eg. o l d v s . new s h a r e h o l d e r s ) I w i l l somewhat o b s c u r e t h e i s s u e by c l a i m i n g t h a t t h e f a i l u r e t o uncover e r r o r s d e c r e a s e s t h e w e a l t h o f a l l s h a r e h o l d e r s . T h i s i s due t o t h e c o n j e c t u r e t h a t management would not p r o v i d e m a t e r i a l l y i n c o r r e c t f i n a n c i a l s t a t e m e n t s e x c e p t as p a r t o f an e f f o r t t o c o n c e a l e x p r o p r i a t i o n s o f w e a l t h from s h a r e h o l d e r s . As a consequence, t h e a u d i t o r ' s f a i l u r e t o uncover e r r o r s can reduce t h e s h a r e h o l d e r s ' a b i l i t y t o r e c o v e r l o s s e s o r p r e v e n t f u r t h e r e x p r o p r i a t i o n s . R e t u r n i n g t o t h e game d e p i c t e d i n F i g u r e s 3a and 3b, t h e t e r m i n a l nodes show t h e s h a r e h o l d e r s ' outcomes. L o s s e s s u b s c r i p t e d w i t h an "a" i n d i c a t e t h e a u d i t o r gave an u n q u a l i f i e d o p i n i o n . A n o t h e r s i m p l i f i i n g a s s u m p t i o n which i s made i s t h a t an u n q u a l i f i e d o p i n i o n i s t a k e n as a p r e - c o n d i t i o n f o r a u d i t o r l i a b i l i t y . The l o s s e s s u b s c r i p t e d w i t h an " r " i n d i c a t e t h a t t h e a u d i t o r q u a l i f i e d h i s o p i n i o n and hence immunizes h i m s e l f from t h e c o s t s , c ( I I ) . Moving t o t h e l e f t a r e t h e nodes d e p i c t i n g t h e s h a r e h o l d e r s ' i n f o r m a t i o n s e t s p r i o r t o c h o o s i n g j . The s i m i l a r l y shaded squares c o m p r i s e each i n f o r m a t i o n s e t . The s h a r e h o l d e r has s i x i n f o r m a t i o n s e t s a t t h i s p o i n t . The next two s e t s of nodes t o t h e l e f t i n d i c a t e n a t u r e ' s moves w i t h r e g a r d t o t h e f a i r n e s s o f t h e f i n a n c i a l s t a t e m e n t s and t h e r e a l i z a t i o n o f t h e v a r i a b l e 0*.. The remainder o f t h e nodes a r e t h e same as i n 41 F i g u r e 1. Comparing F i g u r e s 1 and 3 i t i s c l e a r t h a t t h e s h a r e h o l d e r s a r e i n t r o d u c e d i n such a way as t o e x t e n d t h e a u d i t o r ' s d e c i s i o n problem t o r e c o g n i z e t h e endogenous n a t u r e o f t h e c o s t s , c ( I I ) . These c o s t s can be r a t i o n a l l y a n t i c i p a t e d by t h e a u d i t o r o n l y i n a s e t t i n g where t h e r e e x i s t s an e q u i l i b r i u m i n a u d i t o r - s h a r e h o l d e r b e h a v i o r . I n o r d e r t o a n a l y z e t h e e q u i l i b r i u m s h a r e h o l d e r b e h a v i o r needed f o r t h e a u d i t o r t o c a l c u l a t e h i s e x p e c t e d c o s t s a s e t o f r u l e s must be s p e c i f i e d i n d i c a t i n g when and f o r what measure o f damages t h e a u d i t o r i s l i a b l e . The next two s e c t i o n s l o o k a t d i f f e r e n t s e t s o f l i a b i l i t y r u l e s and some o f t h e p o s s i b l e e q u i l i b r i a i n t h e s e regimes. E q u i l i b r i a w i t h S t r i c t L i a b i l i t y The Nash e q u i l i b r i u m c o n c e p t i s used i n t h e e n s u i n g a n a l y s i s . E q u i l i b r i a a r e found by, f i r s t , e l i m i n a t i n g dominated s t r a t e g i e s ( g i v e n c e r t a i n a s s u m p t i o n s about c o s t c o n d i t i o n s ) and t h e n i n s p e c t i n g t h e r e m a i n i n g s t r a t e g i e s t o see i f t h e y a r e Nash, i . e . , n e i t h e r o f t h e p l a y e r s would want t o d i v e r g e from t h e i r s t r a t e g y g i v e n t h e s t r a t e g y o f t h e o t h e r p l a y e r . I n t h e f i r s t regime t o be e x p l o r e d i t i s assumed t h e a u d i t o r i s l i a b l e f o r l o s s e s under t h e r u l e o f s t r i c t l i a b i l i t y . T h i s i s o f i n t e r e s t s i n c e , as p r e v i o u s l y d i s c u s s e d , t h e r e appears t o be an element of s t r i c t l i a b i l i t y i n t h e r e a s o n i n g o f some r e c e n t c a s e law"* 1. A l s o s t r i c t l i a b i l i t y p r o v i d e s a good benchmark f o r comparison w i t h t h e n e g l i g e n c e d e f e n s e regime i n t h e nex t s e c t i o n . S t r i c t l i a b i l i t y r e q u i r e s t h a t any t y p e I I e r r o r , r e g a r d l e s s o f t h e l e v e l o f c a r e , r e s u l t s i n t h e a u d i t o r b e i n g h e l d l i a b l e . I n terms o f t h e model a s t r i c t l i a b i l i t y regime i m p l i e s t h a t an a u d i t e r r o r e x i s t s whenever e i t h e r o f t h e f o l l o w i n g p a i r s o f e v e n t s a r e o b s e r v e d : { a i , t 3 { , and { a X f t 4 } . S i n c e i t i s assumed t h a t t 2 i s not d i s t i n g u i s h a b l e from t 3 i t i s l i k e l y t h a t t h e c o u r t s w i l l c o n c l u d e , w i t h some p r o b a b i l i t y , t h a t t h e r e i s e v i d e n c e f o r t h e e x i s t e n c e o f an a u d i t i n g e r r o r whenever e i t h e r t h e event {a±,t2} o r {aa.,t 3} o c c u r s . I f t h e c o u r t s cannot see beyond t h e e v i d e n c e g i v e n by t h e s t o c k p r i c e ( i . e . , i f t h e y cannot o b s e r v e e i t h e r s-j o r 6*.) th e p r o b a b i l i t y , p ( s 2 j a i , t 2 ) 4 2 , i s a s s i g n e d a number g r e a t e r t h a n z e r o but l e s s t h a n 1. The p r o b a b i l i t y , p ( s 2 | a ^ , t 4 ) , i s s e t e q u a l t o one and t h e p r o b a b i l i t y , p ( s 2 | a x , t x ) i s s e t e q u a l t o z e r o . The r u l e o f s t r i c t l i a b i l i t y i s e q u i v a l e n t t o s e t t i n g p(qm<q'-) a x , t , c ) e q u a l t o one, i . e . , t h e a u d i t o r i s assumed t o be n e g l i g e n t whenever an a u d i t e r r o r i s found by t h e c o u r t s . From F i g u r e s 3a and 3b i t can be seen t h a t t h e s h a r e h o l d e r s ' s i x i n f o r m a t i o n s e t s c o n s i s t o f t h e f o l l o w i n g 4 1 The New J e r s e y c o u r t i n Rosenblum v. A d l e r , c i t e d above, d i s c u s s e s t h e e f f i c i e n c y o f a u d i t o r s as i n s u r e r s o f r i s k s . T h i s i s a s t e p on t h e road t o s t r i c t l i a b i l i t y . 4 2 S i n c e t 2 and t 3 have t h e same v a l u e , t 2 i s i n c l u d e d i n t h e c o n d i t i o n i n g s t a t e m e n t s when e i t h e r o f t h e two v a l u e s i s used t o update a p r i o r p r o b a b i l i t y . 43 p a i r s o f o b s e r v a t i o n s : ! a i , t i l , l a l f t 2 o r t 3 } , { a a , t 4 } , {a 2,ta.}, { a 2 , t 2 o r t 3 } , and { a 2 , t 4 } . S i n c e t h e s h a r e h o l d e r s can choose e i t h e r t o sue, jx, o r not sue, j 2 , a t each i n f o r m a t i o n s e t t h i s r e s u l t s i n 2 s = 64 p o s s i b l e s h a r e h o l d e r s ' s t r a t e g i e s . To s i m p l i f y t h e a n a l y s i s t h o s e s t r a t e g i e s where t h e s h a r e h o l d e r chooses t o sue subsequent t o o b s e r v i n g a 2 a r e e l i m i n a t e d . T h i s i s because a q u a l i f i e d o p i n i o n i s assumed t o immunize t h e a u d i t o r from l i a b i l i t y . A s u i t w h i c h f o l l o w s a f t e r o b s e r v i n g a 2 f a i l s and c o s t s t h e s h a r e h o l d e r s w > 0, t h e r e f o r e t h e s e s t r a t e g i e s a r e dominated by ones i n which t h e s h a r e h o l d e r s do not sue subsequent t o a 2 . The r e m a i n i n g s h a r e h o l d e r s ' pure s t r a t e g i e s a r e g i v e n i n T a b l e 2. The t a b l e shows t h e mappings from t h e i n f o r m a t i o n s e t s i n t o t h e a c t i o n space. S h a r e h o l d e r s t r a t e g i e s 1-4 a r e e l i m i n a t e d s i n c e t h e y r e q u i r e t h e s h a r e h o l d e r t o sue whenever t j . o c c u r s and t h e s e s t r a t e g i e s a r e dominated s i n c e t h e s h a r e h o l d e r s w i l l always l o s e t h e s e s u i t s . A l s o s t r a t e g i e s 6 and 8 a r e e l i m i n a t e d s i n c e t h e y r e q u i r e t h e s h a r e h o l d e r s not t o sue when t 4 o c c u r s and t h i s i s a l s o assumed t o be n o n o p t i m a l u n l e s s t h e c o s t o f s u i n g , w, i s g r e a t e r t h a n t h e damages t o be r e c o v e r e d , i n t h i s c a s e w i t h c e r t a i n t y . The a u d i t o r has f o u r pure s t r a t e g i e s i f he chooses t h e h i g h a u d i t i n t e n s i t y , q^., and two i f he chooses t h e low a u d i t i n t e n s i t y , q 2 . They a r e g i v e n i n T a b l e 3. A u d i t o r s t r a t e g i e s 1 and 4 a r e assumed t o be dominated by 5 and 6, r e s p e c t i v e l y , 44 s i n c e t h e y r e q u i r e t h e a u d i t o r t o d i s r e g a r d t h e r e s u l t s o f a c o s t l y a u d i t i n g t e s t . S t r a t e g y 3 i s assumed t o be dominated s i n c e i t r e q u i r e s t h e a u d i t o r t o choose an a c t i o n t h a t i s i n c o n s i s t e n t w i t h t h e a u d i t t e s t . The e x p e c t e d damages which t h e s h a r e h o l d e r can c o l l e c t a r e g i v e n by: 3-4> V - L„k< VV' v • * ( s2l »»-tk » T h i s e x p r e s s i o n c o n s i s t s o f t h r e e e lements: a measure o f t h e s h a r e h o l d e r s ' damages, t h e p r o b a b i l i t y t h e c o u r t s f i n d an a u d i t i n g e r r o r , and t h e p r o b a b i l i t y t h e c o u r t s f i n d t h e a u d i t o r a c t e d n e g l i g e n t l y . The e x p e c t e d amount o f damages t h e a u d i t o r w i l l have t o pay a r e g i v e n by t h e e x p r e s s i o n * 3 : 3.5) c < a i , q x , 2 l f S 2> = [ J R iD n k * P < t k | S 2 , Z ± , q x ) ] • p ( s 2 | Z±, q 1 ) • p ( z 1 | q x ) where K' i s t h e s e t o f r e t u r n s f o r which t h e a u d i t o r can p o t e n t i a l l y be h e l d l i a b l e . The l a s t two p r o b a b i l i t i e s can be t a k e n t o g e t h e r as t h e p r o b a b i l i t y o f t h e o c c u r r e n c e o f a t y p e two e r r o r g i v e n t h e l e v e l o f a u d i t i n g i n t e n s i t y . T h i s i s a l s o denoted by p ( I I jqa.). There a r e s i x p o s s i b l e c o m b i n a t i o n s o f s h a r e h o l d e r s ' 4 3 T h i s a l l o w s t h e a u d i t o r t o c a l c u l a t e t h e c o s t s i n t h e upper r i g h t h a n d box o f F i g u r e 2, g i v e n a d e c i s i o n r u l e which a s s i g n s a*, t o t h e o b s e r v a t i o n o f z*.. 45 and a u d i t o r ' s pure s t r a t e g i e s i n t h i s game. T a b l e 4 g i v e s t h e e x p e c t e d c o s t s t o t h e a u d i t o r o f t h e p o s s i b l e e q u i l i b r i a . There a r e s e v e r a l t y p e s o f f a c t o r s which c o n t r i b u t e t o t h e c o s t s . For i n s t a n c e , from t h e f i r s t row o f T a b l e 4 i t can be seen t h a t t h e e x p e c t e d c o s t s t o t h e a u d i t o r a s s o c i a t e d w i t h t h e p l a y {AUD 2, SH 5} a r e : c(AUD 2| SH 5) = [ D n k • p ( t k | s 2 , z y q ± ) ] . p ( I I ( q ^ + C ( I ) • p ( I |q 1) + h ( q 1 ) T h i s e x p r e s s i o n has t h r e e components. The f i r s t i s t h e v a l u e o f t r a n s f e r payments t o t h e s h a r e h o l d e r s w e i g h t e d by t h e p r o b a b i l i t i e s t h a t t h e outcomes t k , k = 2, 3, 4 s h o u l d o c c u r and t h e l i k e l i h o o d o f a t y p e I I e r r o r g i v e n t h e h i g h a u d i t i n t e n s i t y . The second component i s t h e e x p e c t e d c o s t s o f a t y p e I e r r o r g i v e n t h e h i g h a u d i t i n t e n s i t y . The t h i r d element i s t h e i n c r e m e n t a l p r o d u c t i o n c o s t o f t h e h i g h a u d i t l e v e l . T a b l e 5 s e t s up t h e game i n normal form. The s h a r e h o l d e r s ' non-dominated pure s t r a t e g i e s a r e SH S and SH 7. The former c o n s i s t s o f t h e p l a y : do not sue i f tx i s o b s e r v e d , sue o t h e r w i s e . The l a t t e r s t r a t e g y i s : sue i f t 4 i s o b s e r v e d , do not sue o t h e r w i s e . The a u d i t o r ' s s t r a t e g i e s a r e A 2 (choose t h e h i g h a u d i t i n t e n s i t y , q x , and p i c k t h e u n q u a l i f i e d o p i n i o n , ax, i f t h e h i g h s i g n a l , zx, i s drawn and a 2 o t h e r w i s e ) , A 5 (low a u d i t i n t e n s i t y , u n q u a l i f i e d o p i n i o n ) , and A 6 (low a u d i t i n t e n s i t y , q u a l i f i e d a u d i t o p i n i o n ) . 46 I n t h e t a b l e t h e a u d i t o r ' s c o s t s a r e t h e e x p e c t e d c o s t s o f each s t r a t e g y d e s c r i b e d i n T a b l e 4. S i n c e t h e a u d i t o r , must choose h i s a c t i o n s b e f o r e t h e outcome, t t e , i s o b s e r v e d h i s d e c i s i o n i s based upon t h e s e e x p e c t e d c o s t s . I n c o n t r a s t t h e s h a r e h o l d e r s ' c h o i c e o f a c t i o n i s subsequent t o t h e r e a l i z a t i o n o f t k and, hence, can be a f u n c t i o n o f t h e r e a l i z e d s h are p r i c e . From T a b l e 5 i t can be seen t h a t t h e e q u i l i b r i a which a r e a t t a i n e d w i l l depend upon t h e v a r i o u s c o s t p a r a m e t e r s . For example, i f D 1 2 i s l e s s t h a n w, t h e n t h e o n l y e q u i l i b r i a which can o c c u r i n v o l v e t h e s h a r e h o l d e r u s i n g s t r a t e g y SH-7. On t h e o t h e r hand, i f D i 2 i s g r e a t e r t h a n w t h e n SH S may be o p t i m a l . I f SH 5 i s o p t i m a l f o r t h e s h a r e h o l d e r t h e n t h e r e a r e t h r e e p o s s i b l e e q u i l i b r i a . The c o s t c o n d i t i o n s o f t h e a u d i t o r w i l l d e t e r m i n e which one o b t a i n s . A t y p i c a l s i t u a t i o n i s d e p i c t e d i n F i g u r e 4. I n t h i s f i g u r e t h e t o t a l e x p e c t e d c o s t s t o t h e a u d i t o r o f each s t r a t e g y i s p l o t t e d a g a i n s t p ( 6 2 ) . The a u d i t o r ' s c o s t s f o r t h e c a s e s where t h e s h a r e h o l d e r p l a y s SH S a r e : c(AUD 2| SH 5) = [ I D n k • P < t k | s 2 , z , q 1 ) ] • n = 2 p ( I I |q 1) + C ( I ) • p ( I |q ) + h ( q ] 4 C ( A U D 5 | SH 5) = Z D n k P < t k ) c(AUD g| SH 5) = c ( I ) • p ( I jq 2> 47 As can be seen t h e c o s t s o f b o t h {A 2, SH S} and {A 5, SH S) depend upon t h e p r o b a b i l i t y d i s t r i b u t i o n o f t . The d i s t r i b u t i o n o f t i s d e t e r m i n e d by t h e j o i n t d i s t r i b u t i o n o f s and 9. I f we f i x p ( s 2 ) a t some l e v e l then i t can be seen t h a t f o r s m a l l p r o b a b i l i t i e s o f t h e "bad" s t a t e , 8 2, o c c u r r i n g t h e a u d i t o r chooses t h e low a u d i t l e v e l and i s s u e s an u n q u a l i f i e d r e p o r t , i . e . , JA S/ SH 5} i s t h e e q u i l i b r i u m . For h i g h p r o b a b i l i t i e s o f 8 2 t h e a u d i t o r q u a l i f i e s h i s r e p o r t and {A6t SH SJ i s t h e e q u i l i b r i u m . I t i s f o r t h e i n t e r m e d i a t e l e v e l s o f 9 2 t h a t i t t h e e q u i l i b r i u m , {A 2, SH 5}/ i n v o l v i n g t h e h i g h l e v e l o f a u d i t i n g o b t a i n s . C o n c l u s i o n s I n a s t r i c t l i a b i l i t y regime an i n c r e a s e d p r o b a b i l i t y o f t h e o c c u r r e n c e o f t h e "bad" s t a t e l e a d s t o h i g h e r ex ante e x p e c t e d c o s t s t o t h e a u d i t o r o f p r o d u c i n g an a u d i t . ( T h i s i s d e p i c t e d by t h e dark l i n e i n F i g u r e 5.) These h i g h e r c o s t s a r e th e r e s u l t o f t h e a u d i t o r b e i n g l i a b l e f o r s h a r e h o l d e r s ' l o s s e s which a r e p e r c e i v e d t o be caused by a u d i t o r ' s e r r o r s . The " r i s k " o f t h e bad s t a t e a f f e c t s t h e c o s t p a r a m e t e r i z a t i o n o f t h e a u d i t o r ' s s t r a t e g i e s s i n c e bad s t a t e s can e i t h e r : 1) be c o n f u s e d f o r bad a u d i t i n g , o r 2) e x a c e r b a t e t h e damage done by a f a u l t y a u d i t . I n e q u i l i b r i u m , g r e a t e r r i s k r e s u l t s i n t h e l e a s t c o s t s t r a t e g y b e i n g more e x p e n s i v e . One s u r p r i s i n g a s p e c t o f t h e r e s u l t i s t h a t t h e h i g h e r a u d i t i n g c o s t s a r e not n e c e s s a r i l y d r i v e n by t h e c o s t o f 48 p e r f o r m i n g h i g h e r i n t e n s i t y a u d i t s . I n s t e a d t h e c o s t s c o u l d r e s u l t from t h e a u d i t o r i s s u i n g a " p r o t e c t i v e " q u a l i f i c a t i o n and t h e r e b y a b s o r b i n g t h e c o s t s o f a r e l a t i v e l y l i k e l y t y p e I e r r o r . I n t h i s model t h e a u d i t o r sometimes a c t s as an i n s u r e r . T h i s o c c u r s when t h e e q u i l i b r i u m i n v o l v e s s t r a t e g i e s AUD 2 o r AUD S• I n t h e s e c a s e s t h e e x t e n t o f t h e i n a b i l i t y o f the c o u r t s t o d i s t i n g u i s h between share p r i c e d e c l i n e s caused by u n f a i r f i n a n c i a l s t a t e m e n t s and t h o s e caused by u n l u c k y and u n c o r r e l a t e d e v e n t s r e s u l t s i n t h e a u d i t o r b e i n g h e l d l i a b l e f o r l o s s e s when t h e s t a t e S i o b t a i n s " * 4 . T h i s f a c t can i n c r e a s e t h e e x p e c t e d l i a b i l i t y l o s s e s i f c o u r t s on average over e s t i m a t e t h e o c c u r r e n c e o f t h e event {8X# s 2 } . E q u i l i b r i a w i t h a N e g l i g e n c e Defence The s i t u a t i o n changes i f t h e a u d i t o r i s a l l o w e d a n e g l i g e n c e d e f e n s e . I n t h e model t h e a u d i t o r i s c o n s i d e r e d t o be n o n - n e g l i g e n t i f he pe r f o r m s t h e h i g h l e v e l o f a u d i t i n g , qa., and g i v e s an o p i n i o n c o n s i s t e n t w i t h t h e a u d i t t e s t . (That i s , t h e a u d i t o r c o u l d s t i l l be h e l d n e g l i g e n t i f he g i v e s t h e o p i n i o n a i f o l l o w i n g t h e r e c e i p t o f z 2 ) . I n o r d e r t o s i m p l i f y t h e a n a l y s i s i t i s assumed t h a t t h e c o u r t s can a c c u r a t e l y d e t e r m i n e ex post whether t h e a u d i t o r was n e g l i g e n t . The 4 4 In terms o f t h e model t h i s i n s u r a n c e a s p e c t i s d r i v e n by t h e i n a b l i l i t y o f t h e c o u r t s t o ob s e r v e s 2 d i r e c t l y . Hence t h e y sometimes i n f e r t h e e x i s t e n c e o f s 2 from a d e c l i n e i n s t o c k p r i c e when i n f a c t 6 2 was t h e r e a l cause o f t h e d e c l i n e . 49 s t r a t e g i e s a v a i l a b l e t o t h e p l a y e r s a r e t h e same as under t h e s t r i c t l i a b i l i t y regime (see T a b l e s 2 and 3 ) . Dominance arguments a l l o w t h e game t o be pa r e d down t o t h e same s e t of pure s t r a t e g i e s as i n t h e s t r i c t l i a b i l i t y c a s e . T a b l e 6 shows t h e a u d i t o r c o s t s f o r t h e v a r i o u s c o m b i n a t i o n s of pure s t r a t e g i e s , T a b l e 7 shows t h e normal form game, and T a b l e 8 shows t h e p o s s i b l e pure s t r a t e g y e q u i l i b r i a and c o r r e s p o n d i n g c o s t c o n d i t i o n s . From an e x a m i n a t i o n o f T a b l e 8 i t can be seen t h a t t h e r e i s no pure s t r a t e g y Nash e q u i l i b r i u m i n which t h e a u d i t o r chooses t h e h i g h a u d i t l e v e l , AUD 2. The f a c t t h a t t h e h i g h a u d i t l e v e l i s not an e q u i l i b r i u m even though i t may have t h e l o w e s t e x p e c t e d c o s t s i s s u r p r i s i n g . However, a mixed s t r a t e g y e q u i l i b r i u m i s p o s s i b l e . L e t t h e f o l l o w i n g c o s t c o n d i t i o n s h o l d (see T a b l e 6) : 3.6) c ( I | q 1 ) p d ^ ) + h(q±) < 4 min {I D p ( t ^ ) , c ( I j q 2 ) p(I|q 2>} and D 2 > w. An example o f a mixed s t r a t e g y e q u i l i b r i u m i s ( t h e d e t a i l s o f t h i s e q u i l i b r i u m a r e g i v e n i n i n Appendix 2 ) : 3.7) p(SH 5 ) = c ( I ) p(a | z 2 , q ^ + h:<q > - D 4 p ( t 4 > D 2 p ( t 2 > + D 3 p ( t 3 > p ( A 2 ) = ( D 2 - w ) / D 2 50 The e x p e c t e d c o s t t o t h e a u d i t o r o f t h i s mixed s t r a t e g y i s e q u a l t o : c ( I ) p(SjJZ2» * + n ^ i ' t h e c o s t o f AUD 2. I n t h i s e q u i l i b r i u m t h e a u d i t o r randomizes between t h e h i g h a u d i t and t h e low a u d i t u n q u a l i f i e d o p i n i o n a l t e r n a t i v e s . The e x p e c t e d c o s t i s e q u i v a l e n t t o t h a t o f t h e h i g h a u d i t a l t e r n a t i v e but i s a c h i e v e d t h r o u g h r a n d o m i z a t i o n . The s h a r e h o l d e r s always sue when t 4 o c c u r s , never sue when tx o c c u r s and randomize when t 2 o r t 3 o c c u r s . From t h e a n a l y s i s a p i c t u r e q u i t e s i m i l a r t o t h e s t r i c t n e g l i g e n c e case can be drawn. F i g u r e 5 shows t h a t f o r low l e v e l s o f p ( 8 2 ) , h o l d i n g p ( s 2 ) c o n s t a n t , t h e a u d i t o r w i l l choose t h e low l e v e l o f a u d i t i n g and g i v e an u n q u a l i f i e d o p i n i o n . T h i s can be seen from t h e c o s t s t o t h e a u d i t o r o f t h e pure s t r a t e g y p l a y s , {A 5, SH 5} and {A 5, S H 7 J • They have e x p e c t e d c o s t s : 4 c ( A U D 5 j SH 5) = I D n k P < t k ) k = 2 c(AUD 5| SH 7) = D n 4 p ( t 4 ) Both c o s t s i n c r e a s e w i t h t h e p r o b a b i l i t y o f 8 2. These c o s t s w i l l become l a r g e f o r h i g h l e v e l s o f 8 2. At some p o i n t t h e a u d i t o r w i l l , depending upon t h e r e l a t i v e c o s t s , e i t h e r g i v e a " p r o t e c t i v e " q u a l i f i c a t i o n o r choose t o p e r f o r m t h e h i g h e r i n t e n s i t y a u d i t . I n t h e l a t t e r case a mixed s t r a t e g y i s 51 r e q u i r e d . C o n c l u s i o n s When t h e a u d i t o r has a n e g l i g e n c e d e f e n s e t h e s h a r e h o l d e r s must a s s e s s p r o b a b i l i t i e s o f both an a u d i t i n g e r r o r and t h a t i t was committed n e g l i g e n t l y . T h i s changes t h e game between t h e a u d i t o r and t h e s h a r e h o l d e r s i n t h a t a h i g h i n t e n s i t y a u d i t i s not p a r t o f a pure s t r a t e g y e q u i l i b r i u m . As i n t h e s t r i c t l i a b i l i t y c a s e an i n c r e a s e d p r o b a b i l i t y o f a bad s t a t e r e a l i z a t i o n , 8 2, i n c r e a s e s t h e p r o b a b i l i t y o f a bad r e t u r n , t ^ , which i n t u r n i n c r e a s e s t h e e x p e c t e d c o s t s t o t h e a u d i t o r . Once a g a i n t h i s r e s u l t i s d r i v e n by i n c r e a s i n g l i a b i l i t y l o s s e s which a r e , i n p a r t , due t o t h e i n a b l i t y of c o u r t s t o always c o r r e c t l y d i s t i n g u i s h between l o s s e s (and t h e c o r r e s p o n d i n g amounts) caused a u d i t i n g e r r o r s and t h o s e caused by o t h e r f a c t o r s . The a n a l y s i s i n t h i s c h a p t e r p r o v i d e s a s i m p l i f i e d framework f o r showing t h e r e l a t i o n s h i p between s e c u r i t y market r i s k and a u d i t r i s k . The models assume t h a t n e i t h e r s h a r e h o l d e r s nor c o u r t s have s u f f i c i e n t i n f o r m a t i o n t o i n v e r t t h e f u n c t i o n used t o p r i c e s e c u r i t i e s . T h e r e f o r e a d e c l i n e i n a share p r i c e can be due t o e i t h e r a bad s t a t e r e a l i z a t i o n o r t o t h e f i n a n c i a l s t a t e m e n t s h a v i n g been i n e r r o r . S h a r e h o l d e r s may use a s t o c k p r i c e f a l l t o i n s t i g a t e t h e s e a r c h f o r a u d i t i n g e r r o r s and a r e o c c a s i o n a l l y rewarded f o r t h e i r e f f o r t s . 52 One a s p e c t of t h i s model i s t h a t a u d i t o r s sometimes appear t o a c t as i n s u r e r s o f s t o c k p r i c e outcomes. T h i s can o c c u r i f e i t h e r : 1) t h e c o u r t s a r e u n a b l e t o d e t e r m i n e t h e c a u s e s of s h a r e h o l d e r s ' l o s s e s o r 2) cannot a c c u r a t e l y d e t e r m i n e damages from c a u s e s . W h i l e t h i s r e s e a r c h does not a d d r e s s t h e s o c i a l o p t i m a l i t y o f a u d i t o r s ' l e g a l l i a b i l i t y as an i n s t i t u t i o n (nor t h e i r r o l e as i n s u r e r s ) , t h e i n s t i t u t i o n c o n t a i n s mechanisms which seem u s e f u l t o m i t i g a t i n g t h e problems of moral h a z a r d and t r u t h f u l r e p o r t i n g by t h e a u d i t o r . I t i s p o s s i b l e t h a t , g i v e n t h e c o s t s o f d e t e r m i n i n g t h e e x i s t e n c e , c a u s e ( s ) , and e f f e c t s o f a u d i t i n g e r r o r s , i t i s e f f i c i e n t t o sometimes p e n a l i z e t h e a u d i t o r i n c a s e s when he i s , i n f a c t , not a t f a u l t . The g o a l s e t out a t t h e b e g i n n i n g o f t h i s c h a p t e r was t o e s t a b l i s h a l i n k between r i s k i n s e c u r i t y markets and, u l t i m a t e l y , a u d i t c o s t s . The main economic i n s t i t u t i o n f o r t h i s l i n k i s t h e system o f l e g a l l i a b i l i t y . The games a r e used t o demonstrate a mechanism i n which th e c o s t s t o t h e a u d i t o r o f d i f f e r e n t e q u i l i b r i u m s t r a t e g i e s a r e p a r a m e t e r i z e d , i n p a r t , by t h e p r o b a b i l i t y o f t h e o c c u r r e n c e o f a bad s t a t e (and t h e r e b y a low s h a r e p r i c e ) . I n p a r t i c u l a r i t was seen t h a t t h e c o s t s o f a t y p e I I e r r o r a r e s e n s i t i v e t o bad outcomes. ( S i n c e bad outcomes a r e c o n j e c t u r e d t o t r i g g e r t h e s e a r c h f o r a u d i t i n g e r r o r s and may sometimes be used as e v i d e n c e f o r t h e e x i s t e n c e o f such e r r o r s . ) I n t u r n t h e c o s t p arameters i n f l u e n c e t h e a u d i t o r ' s c h o i c e o f a u d i t i n g i n t e n s i t y , d e c i s i o n r u l e , and o p i n i o n . Each of t h e s e a r e c r i t i c a l d e t e r m i n a n t s of t h e c o s t o f p r o d u c i n g an a u d i t . In Chapter 4 s e c u r i t y market measures o f r i s k a r e used t o p a r a m e t e r i z e t h e l i k e l i h o o d o f bad r e t u r n s . I n terms of t h e models i n Chapter 3 t h i s i n f o r m a t i o n i s v a l u a b l e t o t h e a u d i t o r s i n c e i t may a l l o w him t o a n t i c i p a t e t h e o c c u r r e n c e o f s i t u a t i o n s i n which s h a r e h o l d e r s w i l l sue and t h e r e b y expose t h e a u d i t o r t o p o s t a u d i t l o s s e s . 54 Chapter 4 EMPIRICAL IMPLICATIONS T h i s c h a p t e r d e v e l o p s t h e e m p i r i c a l i m p l i c a t i o n s o f t h e t h e o r y d e s c r i b e d i n t h e p r e c e d i n g c h a p t e r s . The f i r s t s e c t i o n s p e c i f i e s t h e h y p o t h e s e s t o be t e s t e d . The next s e c t i o n d i s c u s s e s t h e p a r t i c u l a r models chosen f o r t h e t e s t s and d e s c r i b e s t h e d a t a . The t h i r d s e c t i o n r e p o r t s t h e r e s u l t s o f v a r i o u s d i a g n o s t i c t e s t s made t o check t h e t h e m a i n t a i n e d a s s u m p t i o n s r e q u i r e d t o a p p l y O r d i n a r y L e a s t Squares (OLS). The f o u r t h s e c t i o n r e p o r t s t h e r e s u l t s o f t h e t e s t s o f hypotheses and o f s e n s i t i v i t y a n a l y s i s . The f i n a l s e c t i o n summarizes t h e e m p i r i c a l r e s u l t s . E m p i r i c a l L i n k s Above i t was shown t h a t t h e a u d i t o r o p e r a t e s i n a complex d e c i s i o n - m a k i n g e n v i r o n m e n t . The a u d i t o r must choose d e c i s i o n r u l e and a l e v e l o f a u d i t i n g e f f o r t i n o r d e r t o a c c o m p l i s h t h e a u d i t . T h i s c h o i c e depends upon t h e a u d i t o r ' s b e l i e f s about t h e p o s s i b l e outcomes and e s t i m a t e s o f t h e and c o s t p a r a m e t e r s . Of p a r t i c u l a r i n t e r e s t i s t h e e v a l u a t i o n o f t h e c o s t o f g i v i n g a f a l s e u n q u a l i f e d o p i n i o n , c ( a i , s a ) . E x p r e s s i o n s 3.4) and 3.5) d i s p l a y e d f a c t o r s which a f f e c t t h e s c o s t s . I n o r d e r t o s i m p l i f y t h e a n a l y s i s i t i s assumed t h a t l o s s e s a r e l i m i t e d t o t h e a c t u a l damages s u f f e r e d by s h a r e h o l d e r s . Thus t h e f u n c t i o n L(«) i s t a k e n as an a p p r o p r i a t e measure o f s h a r e h o l d e r s ' l o s s e s . I n Chapter 3 t h e argument was made t h a t s h a r e h o l d e r s l o o k a t t h e r e a l i z e d s t o c k p r i c e i n o r d e r t o d e c i d e whether o r not t o sue t h e a u d i t o r . I n t h e model s h a r e h o l d e r s can use t h e s t o c k p r i c e t o e i t h e r g a i n i n f o r m a t i o n about t h e e x i s t e n c e o f an e r r o r i n t h e f i n a n c i a l s t a t e m e n t s o r , a l t e r n a t i v e l y , t o d e t e r m i n e whether t h e l o s s e s from an a u d i t i n g e r r o r j u s t i f y t h e expense o f 1 i t i g a t i o n - * 5 . A r a t i o n a l a u d i t o r , a n t i c i p a t i n g t h e a c t i o n s o f s h a r e h o l d e r s , w i l l use an e x p r e s s i o n such as 3.5) i n o r d e r t o e v a l u a t e t h e c o s t of a t y p e I I e r r o r f o r each l e v e l o f a u d i t i n g e f f o r t . T h i s r e q u i r e s t h e a u d i t o r t o a s s e s s t h e p o s s i b l e v a l u e s o f t t e and t h e p r o b a b i l i t i e s o v er t h e s e v a l u e s . One way o f e s t i m a t i n g t h e p o s s i b l e d i s t r i b u t i o n o f s h a r e p r i c e s i s by l o o k i n g a t h i s t o r i c a l d a t a and u s i n g a model such as t h e e m p i r i c a l market model t o p r - e d i c t t h e f u t u r e d i s t r i b u t i o n o f t . The model i s g e n e r a l l y e a s i e r t o work w i t h i n r e t u r n form and s i n c e t h e r e i s a one-to-one mapping from p r i c e s i n t o r e t u r n s t h i s i s done f o r c o n v e n i e n c e . I w i l l assume s t o c k r e t u r n s a r e formed i n a ccordance w i t h an e m p i r i c a l market model: 4 3 There a r e v a r i o u s i n t e r p r e t a t i o n s o f t h e r e l a t i o n s h i p between s h a r e p r i c e s and a u d i t i n g e r r o r s which a r e c o n s i s t e n t w i t h t h e model. See pages 32-34 above f o r f u r t h e r d i s c u s s i o n . 56 4.1) r . = a + P . r + e . 1 1 m 1 4.1a) E ( r . ) = a + P. E ( r ) I l m where, E = t h e e x p e c t a t i o n o p e r a t o r , r i = t h e r e t u r n t o f i r m i ' s s h a r e s , e i = t h e r i s k f r e e r a t e , a = a c o n s t a n t , P i = t h e " b e t a " o f f i r m i , r r o = t h e r e t u r n t o t h e market i n d e x . The v a r i a n c e o f t h e r e t u r n t o f i r m i i s g i v e n by: 2 4.2) v a r ( r . ) = P v a r ( r ) + v a r ( e . ) l x m l In t h e p o r t f o l i o t h e o r y o f f i n a n c e t h e o w n - v a r i a n c e , i . e . , v a r ( e i ) , i s assumed t o be d i v e r s i f i a b l e and o n l y t h e "market r i s k " i s p r i c e d by s h a r e h o l d e r s . However, b o t h e l ements o f r i s k a r e i m p o r t a n t as p r e d i c t o r s o f s t o c k p r i c e r e t u r n s and p o s s i b l e s h a r e h o l d e r s ' l o s s e s . For i n s t a n c e , i f s h a r e h o l d e r s use t h e o c c u r r e n c e o f a n e g a t i v e r e t u r n t o i n s t i t u t e t h e s e a r c h f o r a u d i t o r e r r o r s 4 6 , t h e n i t may not m a t t e r whether t h e l o s s i s due t o s y s t e m a t i c o r u n s y s t e m a t i c f a c t o r s . I t s h o u l d be noted t h a t t h e own component o f t h e h i s t o r i c a l l y measured v a r i a n c e , l i k e t h e s y s t e m a t i c component, 4 6 The e v i d e n c e i n K e l l o g , p r e v i o u s l y c i t e d , i s c o n s i s t e n t w i t h t h i s c o n j e c t u r e . i s a f f e c t e d by t h o s e f a c t o r s which i n f l u e n c e b u s i n e s s and f i n a n c i a l r i s k v a r i a b l e s . As a r e s u l t , f i r m s w i t h h i g h b u s i n e s s and f i n a n c i a l r i s k w i l l u s u a l l y have l a r g e own v a r i a n c e s as w e l l . I t i s i n t e r e s t i n g t o ask whether one component o r t h e o t h e r o f t h e s e c u r i t y ' s v a r i a n c e i s more i m p o r t a n t from t h e a u d i t o r ' s p o i n t of v i e w . B o r r o w i n g t h e n o t a t i o n o f t h e s t a n d a r d r e g r e s s i o n model, d e f i n e r± t o be t h e a c t u a l r e t u r n t o f i r m i ; ? i t o be t h e p r e d i c t e d v a l u e of t h e r e t u r n , g i v e n b e t a and t h e r e a l i z e d r e t u r n on t h e market; and E T A t o be t h e ex ante e x p e c t e d r e t u r n g i v e n b e t a and t h e e x p e c t e d r e t u r n on th e market. The d e v i a t i o n f o r a g i v e n r e t u r n i s : r . - E r . = ( r . - r . ) + ( r . - E r . ; 1 1 1 1 1 1 where, r. = a. + f$. r i i 1 m where t h e l e f t hand s i d e o f t h e f i r s t e x p r e s s i o n r e p r e s e n t s t h e t o t a l d e v i a t i o n . The r i g h t hand s i d e i s decomposed i n t o two terms r e p r e s e n t i n g t h e d e v i a t i o n due t o f i r m s p e c i f i c f a c t o r s and t h e d e v i a t i o n due t o t h e market f a c t o r , r e s p e c t i v e l y . C l e a r l y a case c o u l d be made t h a t , i n terms of a u d i t o r l o s s e s , t h e p o r t i o n o f t h e d e v i a t i o n due t o f i r m s p e c i f i c f a c t o r s i s t h e more i m p o r t a n t . I t seems r e a s o n a b l e t o e x p e c t t h e f i r m s p e c i f i c d e v i a t i o n s t o be more c l o s e l y a s s o c i a t e d w i t h a u d i t o r e r r o r s t h a n d e v i a t i o n s due t o market 58 f a c t o r s 4 7 4 8 . A l i n e o f r e a s o n i n g would be t h a t a n e g a t i v e SMR i n a down market i s c o n s i s t e n t w i t h e x p e c t a t i o n s 4 9 and t h e r e f o r e p r o v i d e s no e v i d e n c e o f a u d i t o r n e g l i g e n c e 5 0 . I n c o n t r a s t , a l a r g e n e g a t i v e d e v i a t i o n from r± i n d i c a t e s a l a r g e w i t h i n p e r i o d f a l l i n t h e f i r m s p e c i f i c element of t h e r e t u r n . One p o s s i b l e e x p l a n a t i o n f o r such an event would be t h a t t h e market a c q u i r e d i n f o r m a t i o n which i m p l i e s an e r r o r i n a p r e v i o u s f i n a n c i a l s t a t e m e n t . U n f o r t u n a t e l y , n e i t h e r t h e i n v e s t o r nor t h e a u d i t o r can know t h e outcome o f t h e market a t t h e t i m e t h e a u d i t i s p l a n n e d . The r e l e v a n t i s s u e i s : which o f t h e a v a i l a b l e s e c u r i t y r i s k measures i s o f h e l p i n a s s e s s i n g a u d i t r i s k ex ante? S i n c e b o t h s y s t e m a t i c and n o n - s y s t e m a t i c f a c t o r s a r e a f f e c t e d by r e a l v a r i a b l e s , b o t h measures s h o u l d h e l p i n a s s e s s i n g t h e b u s i n e s s and f i n a n c i a l r i s k o f t h e f i r m . I n p a r t i c u l a r , t h e own v a r i a n c e measures t h e unexpected shocks 4 7 I f f i n a n c i a l s t a t e m e n t s a r e m i s s t a t e d t h e b e t a used t o e s t i m a t e t h e e x p e c t e d r e t u r n may a l s o be c a l l e d i n t o q u e s t i o n . However, i n v e s t o r s can be e x p e c t e d t o use many s o u r c e s o f i n f o r m a t i o n , not j u s t t i m e s e r i e s d a t a , t o a s s e s s t h e r i s k i n e s s o f a s e c u r i t y . 4 8 Some have c o n j e c t u r e d t h a t a u d i t o r l a w s u i t s a r e more common d u r i n g economic downturns. T h i s i s c o n j e c t u r e d s i n c e a u d i t o r s may be t h e o n l y p a r t y c o n n e c t e d w i t h t h e c l i e n t t h a t has s u f f i c i e n t f u n d s . (See Minnow p. 76.) 4 9 A d d i t i o n a l l y t h i s d e v i a t i o n r e p r e s e n t s t h e market r i s k w h ich i s p r i c e d i n t h e market and t h e i n v e s t o r e x p e c t s t o be a r . 5 0 A r e l a t e d i s s u e i s whether t h e c o u r t s can ( o r do?) e f f e c t i v e l y f a c t o r out t h e market i n f l u e n c e upon t h e s h a r e p r i c e i n l i g h t o f a d i s c o v e r e d a u d i t i n g e r r o r . I f t h e c o u r t s c o u l d do t h i s t h e n one would e x p e c t t o f i n d , a t most, a s m a l l r e l a t i o n s h i p between " b e t a " and a u d i t r i s k . 59 e x p e r i e n c e d by t h e f i r m w h i c h , t o t h e e x t e n t t h e s e shocks a r e not r e a d i l y u n d e r s t o o d by i n v e s t o r s , c o u l d provoke t h e s e a r c h f o r a u d i t i n g e r r o r s and s u b s e q u e n t l y l e a d t o a u d i t o r l o s s e s . L e t us assume t h e r e t u r n t o s e c u r i t y i i s n o r m a l l y d i s t r i b u t e d w i t h mean g i v e n by 4.1a) and v a r i a n c e g i v e n by 4.2). For any c r i t i c a l v a l u e , D s x, de t e r m i n e d by s h a r e h o l d e r s , a Z - s c o r e 5 2 can be computed. The v a l u e , D, r e p r e s e n t s t h e l a r g e s t (D w i l l u s u a l l y be n o n - p o s i t i v e ) r e t u r n f o r which s h a r e h o l d e r s w i l l s u e 5 3 t h e a u d i t o r . The Z-score can the n be used t o de t e r m i n e t h e p r o b a b i l i t y of a r e t u r n b e i n g l e s s t h a n t h e c r i t i c a l v a l u e . T h i s i s one way t o o p e r a t i o n a l i z e a pr o x y measure f o r a u d i t r i s k 3 " * . T h i s s u g g e s t s we can c o n c e r n o u r s e l v e s w i t h how changes i n t h e market model parameters a f f e c t t h e Z-score and s x Note t h a t t h e " D", an exogenously g i v e n s h a r e h o l d e r c u t o f f p o i n t , used i n t h i s c h a p t e r i s d i s t i n c t from "D^", a measure o f r e c o v e r a b l e s h a r e h o l d e r damages, used i n c h a p t e r 3. 5 2 The symbol " z " i n t h i s c h a p t e r i s d i s t i n c t from t h e z's used i n Ch a p t e r s 2 and 3 where t h e y denoted t h e r e s u l t o f an a u d i t t e s t . 5 3 N o r m a l l y D would be d e t e r m i n e d endogenously i n an e q u i l i b r i u m model o f s h a r e h o l d e r and a u d i t o r b e h a v i o u r . The a c t u a l D chosen w i l l be v e r y s e n s i t i v e t o t h e c o s t s o f l i t i g a t i o n . For now i t i s assumed D i s g i v e n e x o g e n o u s l y . 5 4 For example, l e t t h e r e be two f i r m s w i t h r e t u r n d i s t r i b u t i o n s Rj. and R 2. Assume t h e r e i s a common c r i t i c a l v a l u e , D, t h e n zx < z 2 i m p l i e s P r f r a . < D] < P r [ r 2 < D]. The l a r g e r t h e Z-score f o r a g i v e n D, t h e r i s k i e r t h e a u d i t . T h i s i s t r u e s i n c e i f one were t o t a k e t h e r A from t h e su p p o r t r 6 (-1,D) and t o form a new ( t r u n c a t e d ) d i s t r i b u t i o n , m, such t h a t n»i € [-1,D], t h e n t h e d i s t r i b u t i o n m 2 ( c o r r e s p o n d i n g t o r 2 ) i s r i s k i e r t h a n mi i n t h e sense of ( a t l e a s t ) second o r d e r s t o c h a s t i c dominance. 60 c o n s e q u e n t l y t h e p r o b a b i l i t y o f l i t i g a t i o n . 4.3) Z = [ D - E r . ] / s d ( r . ) = l 1 D - ( a + 8. E r ) l m [ P 2 v a r ( r ) + v a r ( e . ) ] 1 / 2 l m l E q u a t i o n 4.3) d e f i n e s t h e Z-score i n terms of t h e components of t h e market model. Note t h a t D i s used t o r e p r e s e n t t h e s h a r e h o l d e r s ' c r i t i c a l v a l u e i n r e t u r n s space. S i n c e t h e l e g a l system r e q u i r e s a c t u a l damages i n o r d e r t o s u s t a i n a s u i t t h e l a r g e s t v a l u e f o r D would be z e r o . T h i s i s c o n s i s t e n t w i t h d e f i n i n g t h e l o s s f u n c t i o n as t - t * . I n t h e s e q u e l D w i l l f r e q u e n t l y be assumed t o be e q u a l t o a z e r o r e t u r n . Next we t u r n t o how z[ 0 i f v a r f e * . ) , v a r ( r m ) ] changes w i t h changes i n t h e v a r i o u s market r i s k p a r a m e t e r s . The p a r a m e t e r s of i n t e r e s t a r e 3, var(e±), and, t o a l e s s e r e x t e n t , v a r ( r m ) . The d e r i v a t i v e o f z w . r . t . b e t a , Z i 5 5 , can be shown t o be p o s i t i v e i f : 4.4) E r + 3. m x v a r ( r ) m v a r ( r ^ ) [ D - (a + 3 . Er ) ] x m < 0 T h i s i n t u r n h o l d s when: 4.5) E r < ( E r . - D) 3• m x x v a r ( r ) m v a r ( r ^ ) w h ich can be w r i t t e n a s : s s Zx r e f e r s t o t h e p a r t i a l d e r i v a t i v e o f z w . r . t . i t s f i r s t argument, 3 i . z 2 and z 3 a r e t h e p a r t i a l s w . r . t . oie^.) and o ( r r o ) , r e s p e c t i v e l y . 61 E r v a r ( e . ) 4.6) m a - D x v a r ( r ) By i n s p e c t i o n c o n d i t i o n 4.6) seems l i k e l y t o h o l d t r u e i f 3 i i s l a r g e and the o p p o s i t e to be t r u e f o r 3 A s m a l l . However, the r e l a t i o n s h i p i s not t h i s s t r a i g h t f o r w a r d . There i s a mixed a s s o c i a t i o n between a f i r m ' s beta and the p r o b a b i l i t y of l o s s , which i s c o n j e c t u r e d to be a proxy f o r a u d i t r i s k . T h i s r e s u l t i s not i n i t i a l l y obvious. I n c r e a s i n g the beta has two e f f e c t s (see F i g u r e 6). As can be seen from the f i g u r e , i n c r e a s i n g the f i r m ' s beta w i l l cause the expected r e t u r n to the f i r m to s h i f t to the r i g h t 5 6 . Ceteris paribus t h i s w i l l decrease the p r o b a b i l i t y of a r e t u r n l e s s than D. The second e f f e c t i s i n the o p p o s i t e d i r e c t i o n . R e f e r r i n g to equation 4.2), and as can be seen i n the f i g u r e , i t i s c l e a r t h a t i n c r e a s i n g beta i n c r e a s e s the v a r i a n c e of r±. T h i s i n t u r n i n c r e a s e s the p r o b a b i l i t y of a r e t u r n l e s s than D. E x p r e s s i o n 4.6) i n d i c a t e s t h a t which of the two e f f e c t s dominates depends upon the v a l u e s of the other v a r i a b l e s . c o n s i d e r e d i s i n the same v e i n , though the r e s u l t s are s t r a i g h t f o r w a r d to i n t e r p r e t . 5 6 The diagram was generated u s i n g betas of .5 and 2, r e s p e c t i v e l y . These valu e s were chosen i n order to p r o v i d e a d i f f e r e n c e which c o u l d be e a s i l y d i s c e r n e d . A l l other parameter val u e s are i d e n t i c a l f o r the two d i s t r i b u t i o n s . Note t h a t i n t h i s p a r t i c u l a r case the higher beta f i r m has g r e a t e r weight i n the t a i l f o r a l l v a l u e s l e s s than -.07. The a n a l y s i s of the other two parameters to be 62 E r . - D 4-7) z2 = ;— -^7-73/2 y 0 2 v a r ( r . ) 1 4.8) z 3 Both v a r i a n c e e f f e c t s i n d i c a t e a p o s i t i v e r e l a t i o n s h i p between i n c r e a s e d v a r i a n c e and t h e p r o b a b i l i t y o f l o s s . The r e s u l t s a r e f a i r l y i n t u i t i v e . I n c r e a s i n g t h e s e v a r i a n c e components f a t t e n s t h e t a i l s o f t h e r e t u r n d i s t r i b u t i o n w i t h o u t i n c r e a s i n g t h e e x p e c t e d r e t u r n , and t h e r e f o r e p l a c e s more p r o b a b i l i t y w e i g h t i n t h e a r e a where l a w s u i t s can o c c u r . I t i s a l s o p o s s i b l e t o o b t a i n a few r e s u l t s i n terms of t h e e x p e c t e d v a l u e o f n e g a t i v e r e t u r n s . Two measures a r e used: t h e c o n d i t i o n a l e x p e c t e d v a l u e o f n e g a t i v e r e t u r n s (CNR) and t h e u n c o n d i t i o n a l e x p e c t e d v a l u e o f n e g a t i v e r e t u r n s (UNR). S i n c e t h e a u d i t o r may be f o r c e d t o s h a r e i n t h e l o s s e s of t h e s h a r e h o l d e r {but not i n t h e g a i n s ) when r e t u r n s a r e l e s s t h a n D, i t may be o f i n t e r e s t t o know t h e e x p e c t e d v a l u e of t h e s h a r e h o l d e r s ' r e t u r n 5 7 , g i v e n t h e y a r e l e s s t h a n D. T h i s i s t h e CNR. The UNR i s t h e CNR t i m e s t h e p r o b a b i l i t y o f t h e r e t u r n b e i n g l e s s t h a n D. To make t h e s e measures more c o n c r e t e , assume t h e 5 7 I f t h e CNR i s t h e e x p e c t e d v a l u e o f t h e r e t u r n g i v e n t h a t i t i s l e s s t h a n D, t h e n t h e e x p e c t e d amount o f t h e l o s s f o r w hich t h e a u d i t o r may be h e l d r e s p o n s i b l e c o u l d be some q u a n t i t y V - CNR, where V i s t h e v a l u e a t Which th e c o u r t s s t a r t t o accumulate l o s s e s . V, f o r i n s t a n c e , may c o r r e s p o n d t o t h e i n i t i a l p r i c e ( z e r o r e t u r n ) o f t h e s e c u r i t y . 63 ( E r . - D) 1 v a r ( e • ) 1 r e t u r n s a r e n o r m a l l y d i s t r i b u t e d w i t h mean, E [ r i ] , and v a r i a n c e , v a r ( r i ) . D e f i n e t h e n e g a t i v e r e t u r n 5 3 t o be e q u a l t o r± - D, where D i s t h e p o i n t a t which s h a r e h o l d e r s b e l i e v e i t i s b e n e f i c i a l t o s u e 5 9 . S i n c e o n l y r e a l i z e d s h a r e h o l d e r l o s s e s a r e a c t i o n a b l e t h e n e g a t i v e r e t u r n f u n c t i o n i s d e f i n e d a s : r ^ - D r i < D i f 0 o t h e r w i s e I t can t h e n be s h o w n 6 0 t h a t t h e CNR, g i v e n D, i s : E t r L I r . < D] = E r . + o ( r . ) • T g ( D ' * 1 , 1 1 1 U F(D) where g( ) i s a s t a n d a r d normal p r o b a b i l i t y d e n s i t y f u n c t i o n , F(») t h e c u m u l a t i v e d i s t r i b u t i o n f u n c t i o n o f r i ( and D' i s s t a n d a r d i z e d b y 6 1 : 5 8 The n e g a t i v e r e t u r n i s d e f i n e d " n e t " o f D. T h i s c o n v e n t i o n i s adopted s i n c e D can be thought o f as r e p r e s e n t i n g c o s t s t o t h e s h a r e h o l d e r o f s e a r c h i n g f o r e r r o r s and i n i t i a t i n g l i t i g a t i o n . I f t h e g a i n i n e x p e c t e d u t i l i t y o f c o l l e c t i n g p o t e n t i a l damages does not exceed t h e l o s s i n e x p e c t e d u t i l i t y o f t h e s e c o s t s , t h e n no s u i t i s b r o u g h t . The a u d i t o r i s immune t o s m a l l s h a r e h o l d e r l o s s e s s i n c e t h e c o s t s o f l i t i g a t i o n exceed t h e p o t e n t i a l b e n e f i t s . 5 9 The a u d i t o r ' s l o s s f u n c t i o n i s assumed t o be l i n e a r i n s h a r e h o l d e r s ' l o s s e s . G e n e r a l l y , t h e a u d i t o r ' s l o s s e s a r e some f u n c t i o n , f ( r i ) . I t seems l i k e l y t h a t f'<0 though t h e n a t u r e of f ' ' i s an e m p i r i c a l i s s u e . 6 0 The p r o o f i s f a i r l y s t r a i g h t f o r w a r d . See Appendix 3. 6 1 For example, i f r±. i s d i s t r i b u t e d n o r m a l l y w i t h a mean of .1, a s t a n d a r d d e v i a t i o n o f .2, and D s e t e q u a l t o z e r o t h e n t h e f o l l l o w i n g q u a n t i t i e s can be c a l c u l a t e d . 64 (D - E f r - ] ) D ' = — — 0 ( r . ) l The UNR i s d e f i n e d a s : 4.10) E ( r . ) = E ( r . | r . < D) • P r ( r . < D) 1 i l l l Hypotheses I n t h e above s e c t i o n v a r i o u s p r o x y measures f o r a u d i t r i s k were d e v e l o p e d . The s u p p o s i t i o n i s t h a t measures which q u a n t i f y t h e r i s k borne by s h a r e h o l d e r s 6 2 may be u s e f u l t o a u d i t o r s i n f o r e c a s t i n g t h e i r f u t u r e cash f l o w s s i n c e t h e l e g a l l i a b i l i t y system can compel a u d i t o r s t o s h a r e s t o c k market l o s s e s w i t h s e c u r i t y h o l d e r s . The e m p i r i c a l t e s t s l o o k f o r a r e l a t i o n s h i p between a u d i t f e e s and t h e v a r i o u s D' = (0-.1) / .2 = -.5 P r ( r i < 0 ) = P r ( z < -.5) =.3085 E(z | z < .-5) = -.352 / .3085 = -1.14 E ( r - i | r A < 0 > = (-1.14 x .2) + .1 = -.128 I f D i s s e t t o -.20 t h e n t h e v a l u e s a r e -1.5, .0668, -1.934, and -.130, r e s p e c t i v e l y . 6 2 I n Chapter 3 i t was noted t h a t l o s s e s can be s u f f e r e d by two c o n c e p t u a l l y d i s t i n c t groups of s h a r e h o l d e r s . C l e a r l y new s h a r e h o l d e r s who have p u r c h a s e d s h a r e s , r e l y i n g upon t h e a u d i t o r ' s a t t e s t a t i o n s u f f e r s a l o s s i f t h e f i n a n c i a l s t a t e m e n t s a r e f a l s e and t h e s t o c k p r i c e d e c l i n e s . I n Chapter 3 i t was argued t h a t c u r r e n t s h a r e h o l d e r s can s u f f e r a l o s s i f t h e a u d i t o r f a i l s t o d i s c o v e r management m a l f e a s a n c e and t h i s f a i l u r e a l l o w s f o r l o s s e s , which c o u l d have been p r e v e n t e d , t o ac c u m u l a t e . 65 c o n j e c t u r e d f o l l o w from measures o f s e c u r i t y market r i s k . The hypotheses the r e l a t i o n s d i s c u s s e d i n t h e p r e v i o u s s e c t i o n . HI: A u d i t f e e s i n c r e a s e as t h e p r o b a b i l i t y o f s h a r e h o l d e r s ' l o s s e s i n c r e a s e . T h i s h y p o t h e s i s can be based upon t h e c l a i m t h a t s h a r e h o l d e r s ' l o s s e s t r i g g e r t h e s e a r c h f o r a u d i t i n g e r r o r s . An i n c r e a s e d p r o b a b i l i t y o f s e a r c h t h e n i s assumed t o t r a n s l a t e i n t o g r e a t e r e x p e c t e d l o s s e s t o t h e a u d i t o r . Two i n t e r p r e t a t i o n s a r e p o s s i b l e . The f i r s t i s t h a t t h e e x i s t e n c e o f a u d i t i n g e r r o r s i s independent o f r e t u r n s and t h e c o u r t s r e q u i r e s h a r e h o l d e r s t o have l o s s e s i n o r d e r t o show damages. T h i s i n t e r p r e t a t i o n i s p l a u s i b l e i f t h e c o u r t s cannot s e p a r a t e t h e amount of damages caused by t h e a u d i t f a i l u r e from t h e amount a t t r i b u t a b l e t o o t h e r f a c t o r s . Under t h i s s c e n a r i o t h e c h a i n o f e v e n t s i s : 1) s h a r e h o l d e r s ' s u f f e r l o s s e s , 2) t h i s l e a d s t o a s e a r c h f o r a u d i t i n g e r r o r s and p o s s i b l e l i t i g a t i o n , and 3) i f a u d i t i n g e r r o r s a r e found t h e a u d i t o r s a r e c o m p e l l e d t o compensate t h e s h a r e h o l d e r s . The second i n t e r p r e t a t i o n i s t h a t t h e c o u r t s sometimes e r r i n a s s i g n i n g f a u l t t o t h e a u d i t o r i n t h e f a c e o f s h a r e h o l d e r s ' l o s s e s . I n Chapter 3 i t was seen t h a t due t o t h e i n a b i l i t y of c o u r t s t o a c c u r a t e l y d i s t i n g u i s h between l o s s e s c aused by a u d i t o r s and t h o s e caused by o t h e r f a c t o r s a u d i t o r s sometimes had t o bear t h e c o s t s o f bad outcomes r e g a r d l e s s o f 66 t h e t r u e c ause. T h i s r e q u i r e s a u d i t o r s t o a n t i c i p a t e t h i s p o s s i b i l i t y and a d j u s t t h e i r a u d i t i n g p l a n s and f e e s a p p r o p r i a t e l y . I t i s i n t e r e s t i n g t o note t h a t e i t h e r i n t e r p r e t a t i o n i s g e n e r a l l y c o n s i s t e n t w i t h b oth t h e e x i s t e n c e o f a r e l a t i o n s h i p between a u d i t f e e s and p ( 8 2 ) , as c o n j e c t u r e d i n Chapter 3, and an o b s e r v e d r e l a t i o n s h i p between a u d i t f e e s and measures o f s e c u r i t y market r i s k . I n t h e f i r s t i n t e r p r e t a t i o n c o u r t s a r e un a b l e t o d i s e n t a n g l e t h e amount o f t h e damages caused by t h e a u d i t o r ' s a c t i o n s i n t h e p r e s e n c e o f o t h e r f a c t o r s and i n t h e second t h e c o u r t s a r e u n a b l e t o d e t e r m i n e whether t h e a u d i t o r was t h e cause o f t h e damages. The l i n k i s t h a t t h e d i s t r i b u t i o n o f r e t u r n s i s p a r a m e t e r i z e d by p ( 8 2 ) i n such a way t h a t h i g h e r l e v e l s o f p<8 2) l e a d t o g r e a t e r v a r i a n c e i n t h e r e t u r n d i s t r i b u t i o n and t o l a r g e r e x p e c t e d l o s s e s by t h e a u d i t o r . To e x p l o r e t h e p l a u s i b i l i t y o f such a l i n k a g e c o n s i d e r two r e t u r n d i s t r i b u t i o n s c h a r a c t e r i z e d by p ' ' ( 8 2 ) > p ' ( 8 2 ) . The f i r s t i n t e r p r e t a t i o n i m p l i e s a g r e a t e r w e i g h t i s a s s i g n e d t o each element o f t h e s e t o f a u d i t o r ' s l o s s e s under p ' ' ( 8 2 ) t h a n f o r p ' ( 8 2 ) . T h i s i s r e l a t e d t o r e t u r n v a r i a b i l i t y by t h e o b s e r v a t i o n t h a t i n many c a s e s g r e a t e r v a r i a b i l i t y " f a t t e n s " t h e t a i l o f t h e r e t u r n d i s t r i b u t i o n from which a u d i t o r ' s l o s s e s a r e d e r i v e d . I n t h e second i n t e r p r e t a t i o n g r e a t e r w e i g ht i s g i v e n t o t h e s e t o f outcomes f o r which c o u r t s may c o n s t r u e a u d i t i n g e r r o r s under p ' ' ( 8 2 ) t h a n under p ' ( 8 2 ) . I n terms of r e t u r n s ' d i s t r i b u t i o n g r e a t e r v a r i a b i l i t y i n c r e a s e s t h e l i k e l i h o o d o f an outcome i n t h e s e t (say r e t u r n s l e s s t h a n D) i n which a u d i t o r ' s e r r o r s a r e c o n s t r u e d by t h e c o u r t s . There a r e two r e l a t e d sub-hypotheses: H l a : A u d i t f e e s i n c r e a s e w i t h t h e r e s i d u a l s t a n d a r d d e v i a t i o n , (Me*.), of s e c u r i t y r e t u r n s . T h i s h y p o t h e s i s i s d e r i v e d from e x p r e s s i o n 4.7). s i n g t h e r e s i d u a l v a r i a n c e , c e t e r i s paribus, has t h e o f i n c r e a s i n g t h e p r o b a b i l i t y o f l o s s . H l b : A u d i t f e e s may e i t h e r i n c r e a s e o r d e c r e a s e w i t h t h e market r i s k o f a f i r m ' s s e c u r i t y as measured by i t s b e t a . The s i g n and magnitude of t h e e f f e c t depend upon t h e f a c t o r s g i v e n i n e x p r e s s i o n 4.6). Hypotheses l a . and l b . a r e o f i n t e r e s t s i n c e p r e v i o u s r e s e a r c h e r s have used t h e s e measures i n an ad hoc way t o c o n t r o l f o r r i s k . These hypotheses may be d i f f i c u l t t o t e s t e m p i r i c a l l y s i n c e each r e l a t e s t o a component o f t o t a l r i s k w h i c h , i n c r o s s - s e c t i o n , i s not b e i n g h e l d c o n s t a n t 6 3 . T h i s i m p l i e s t h a t i f , as t h e t h e o r y s u g g e s t s , t h a t t o t a l v a r i a n c e i s t h e key c o n c e p t t h e i n d i v i d u a l components may not be good 6 3 I am i n d e b t e d t o J i m Brander f o r t h i s i n t u i t i o n . 68 I n c r e a e f f e c t p r o x i e s f o r t h e r e a l v a r i a b l e o f i n t e r e s t . H2: A u d i t f e e s i n c r e a s e w i t h measures o f e x p e c t e d s h a r e h o l d e r s ' l o s s e s . H2 i s based upon 4.10). I t i s c o n j e c t u r e d t h a t CNR and UNR may measure p o t e n t i a l s h a r e h o l d e r l o s s e s . As such t h e y may have g r e a t e r a s s o c i a t i o n w i t h a u d i t r i s k and hence a g r e a t e r a b i l i t y t o p r e d i c t a u d i t f e e s . Data I n o r d e r t o t e s t t h e above hypotheses e v i d e n c e was r e q u i r e d about f i r m s ' a u d i t f e e s and e s t i m a t e s o f t h e market r i s k p a r a m e t e r s . A u d i t f e e d a t a was o b t a i n e d from Dan S i m u n i c . T h i s d a t a i s d e s c r i b e d i n S i m u n i c (1980). Data on t h e share p r i c e r e t u r n s was o b t a i n e d from t h e CRSP d a i l y and monthly r e t u r n s t a p e s . A d d i t i o n a l s h a r e p r i c e d a t a was c o l l e c t e d from t h e S t a n d a r d and Poors D a i l y Over t h e Counter manual. R e g r e s s i o n a n a l y s e s were run u s i n g t h e SHAZAM (see K. White (1987)) e c o n o m e t r i c s program. The a u d i t f e e d a t a c o n s i s t e d o f 397 f i r m s w h i c h responded t o a s u r v e y done i n 1977. Most of t h e f i r m s had y e a r ends i n t h e p e r i o d from December 1975 t o June 1 9 7 7 6 4 . The 6 4 Of t h e 173 F i r m s i n t h e weekly sample t h e d i s t r i b u t i o n o f year-ends was: p r i o r t o J a n u a r y 1976 -- 14%, from J a n u a r y 1976 t h r o u g h June 1976 -- 14%, from J u l y 1976 t h r o u g h December d a t a c o n s i s t e d o f a u d i t f e e s f o r t h e most r e c e n t y e a r end as w e l l as i n f o r m a t i o n about a c c o u n t i n g v a r i a b l e s thought t o be i m p o r t a n t f a c t o r s i n e x p l a i n i n g a u d i t c o s t s 6 5 . From t h i s s e t of f i r m s a s e a r c h was made t o f i n d f i r m s whose common s t o c k s were r e g u l a r l y t r a d e d . A f i r m was c o n s i d e r e d f o r i n c l u s i o n i n t h i s s t u d y i f i t met one o f t h e f o l l o w i n g c r i t e r i a : 1. t h e r e e x i s t e d d a t a on t h e f i r m i n t h e CRSP monthly s t o c k p r i c e r e t u r n t a p e f o r t h e p e r i o d commencing 60 months p r i o r t o , and r u n n i n g t h r o u g h , t h e r e p o r t e d y e a r end f o r which a u d i t f e e d a t a was a v a i l a b l e , 2. t h e r e e x i s t e d d a t a on t h e f i r m i n t h e CRSP d a i l y s t o c k p r i c e r e t u r n tape f o r t h e p e r i o d commencing two y e a r s p r i o r t o , and r u n n i n g t h r o u g h , t h e r e p o r t e d y e a r end f o r which a u d i t f e e d a t a was a v a i l a b l e , 3. t h e r e e x i s t e d d a t a on t h e f i r m i n t h e S t a n d a r d and Poors D a i l y Over t h e Counter Manual f o r t h e p e r i o d commencing 1 y e a r p r i o r t o , and r u n n i n g t h r o u g h , t h e r e p o r t e d y e a r end f o r which a u d i t f e e d a t a was a v a i l a b l e . 1976 — 59%, and a f t e r December 1976 — 13%. 6 5 Simunic (1980) d e s c r i b e s f a c t o r s which he found c o n t r i b u t e d t o a u d i t c o s t s . They were s i z e , c o m p l e x i t y , and i n d u s t r y a f f i l i a t i o n . 70 One hundred and t w e n t y - f i v e f i r m s met t h e f i r s t c r i t e r i o n . T h i s sample i s r e f e r r e d t o as t h e monthly sample. One hundred and e i g h t y - t h r e e f i r m s met t h e second c r i t e r i o n , however, 10 f i r m s had t o be dropped from c o n s i d e r a t i o n a t t h i s s t a g e . These f i r m s were d i s c a r d e d because e i t h e r t h e i r r e t u r n s e r i e s i n c l u d e d many m i s s i n g o b s e r v a t i o n s o r I was u n a b l e t o p o s i t i v e l y match t h e f i r m s w i t h t h e a u d i t f e e d a t a . T h i s sample i s r e f e r r e d t o as t h e weekly sample. Many o f t h e s e f i r m s (116) were a l s o i n c l u d e d among t h e monthly sample. F i n a l l y , 79 f i r m s matched t h e t h i r d c r i t e r i o n . T h i s sample i s r e f e r r e d t o as t h e OTC (Over t h e Counter) sample. None o f t h e OTC f i r m s a r e i n c l u d e d i n e i t h e r o f t h e two p r e v i o u s samples. W i t h i n t h e samples an OLS r e g r e s s i o n was run f o r each f i r m on t h e f o l l o w i n g model: r . = a + P . • r + e. I l m I ) where, rm was o b t a i n e d u s i n g t h e a p p r o p r i a t e v a l u e w e i g h t e d market r e t u r n from t h e CRSP t a p e s . From t h i s r e g r e s s i o n e s t i m a t e s o f P i and o ( e i ) were o b t a i n e d . For t h e weekly sample, d a i l y r e t u r n d a t a was c o l l e c t e d and t h e n a g g r e g a t e d i n t o weekly d a t a . T h i s p r o c e d u r e was used i n o r d e r t o a v o i d t h e problems a s s o c i a t e d w i t h non-synchronous t r a d i n g d a t a (see S c h o l e s and W i l l i a m s ( 1 9 7 7 ) ) . A f t e r weekly r e t u r n s were c a l c u l a t e d t h e n parameter e s t i m a t i o n was a c c o m p l i s h e d as w i t h t h e monthly sample. For OTC f i r m s weekly p r i c e d a t a was hand c o l l e c t e d . R e t u r n s were c a l c u l a t e d u s i n g t h e m i d - p o i n t o f t h e end of week c l o s i n g b i d - a s k p r i c e s . R e t u r n s were a d j u s t e d f o r c a p i t a l changes and c a s h d i v i d e n d s . The i n d i v i d u a l f i r m r e t u r n s were r e g r e s s e d upon t h e CRSP D a i l y V a l u e Weighted Market r e t u r n s i n o r d e r t o o b t a i n t h e r e q u i r e d parameter e s t i m a t e s . However, t h i s sample s u f f e r e d from a d d i t i o n a l c o m p l i c a t i o n s s i n c e t h e r e were many weeks i n which t h e s e s e c u r i t i e s were t h i n l y t r a d e d (see T a b l e 9 ) . From t h e t a b l e i t can be seen, f o r example, t h a t f o r 60% o f t h i s sample t h e r e were no weekly changes i n p r i c e i n twenty p e r c e n t o r more of t h e weekly t r a d i n g p e r i o d s . I n a d d i t i o n , from t h e t a b l e i t can be seen t h a t t h e e x p l a n a t o r y power of t h e market model i s l i k e l y t o be a f f e c t e d by t h e l a c k o f p r i c e movement. I n f a c t , t h e average r 2 f o r t h e OTC sample i s but .06 (see T a b l e 1 1 ) . Many of t h e extreme v a l u e s 6 6 o f t h e b e t a e s t i m a t e o c c u r when t h e r e a r e a r e l a t i v e l y l a r g e number of z e r o change o b s e r v a t i o n s . C a s u a l o b s e r v a t i o n i n d i c a t e s t h a t t h e number of no-change o b s e r v a t i o n s may be a t t r i b u t e d t o t h e f a c t t h a t many of t h e f i r m s t r a d e d a t p r i c e s t h a t were s m a l l compared t o t h e 6 6 I t i s i n t e r e s t i n g t o note from t a b l e 11 t h a t t h e mean b e t a f o r t h i s sample i s .74, a r e l a t i v e l y low v a l u e , g i v e n p r i o r e x p e c t a t i o n s about t h e r i s k i n e s s of t h i s sample. T h i s v a l u e may be t h e r e s u l t o f s e v e r a l f a c t o r s . For i n s t a n c e , t h e b e t a s a r e not r e l i a b l y measured due t o t h e l a c k o f t r a d i n g . I would c o n j e c t u r e t h e l a c k o f p r i c e movement would t e n d t o weaken t h e c o v a r i a n c e w i t h t h e market and hence reduce th e e s t i m a t e o f b e t a ' s v a l u e . The r i s k o f t h e s e f i r m s appears i n t h e e s t i m a t e of o ( e i ) w h i c h , from t h e t a b l e , can be seen t o be q u i t e h i g h , remembering t h a t t h i s i s a weekly e s t i m a t e . 72 bid-ask spread. T h i s i m p l i e s t h a t even small p r i c e changes would r e f l e c t a r e l a t i v e l y l a r g e percentage i n c r e a s e or decrease i n the f i r m ' s v a l u e . Given t h a t f i r m p r i c e s were u s u a l l y quoted i n l / 8 t h of a p o i n t increments, small changes i n e q u i l i b r i u m p r i c e s might not be r e f l e c t e d i n changes i n the b i d - a s k spread. T h i s c o u l d make i t i m p o s s i b l e to d e t e c t changes i n the t r u e p r i c e of the s e c u r i t y . For these reasons the OTC sample was excluded from f u r t h e r a n a l y s i s s i n c e the e s t i m a t e s appear to be u n r e l i a b l e . D e s c r i p t i v e s t a t i s t i c s of the s a m p l e s 6 7 are d i s p l a y e d i n Tables 10 and 11. Not unexpectedly, the weekly sample i s comprised of f i r m s which are l a r g e r and more complex than the OTC f i r m s . The monthly sample f i r m s are, on average, the l a r g e s t f i r m s . F i g u r e 7 shows the d i s t r i b u t i o n of f i r m s ' a s s e t s i z e . Models Fo l l o w i n g Simunic (p. 178) two forms of the fee r e g r e s s i o n model were used. The f i r s t model r e g r e s s e s the l o g of the a u d i t fee on the l o g of a s s e t s and on other c o n t r o l v a r i a b l e s . The second model transforms the dependent v a r i a b l e by d i v i d i n g i t by the square ro o t of a s s e t s . These t r a n s f o r m a t i o n s are r e q u i r e d s i n c e f e e s and a s s e t s do not 6 7 The s t a t i s t i c s i n these t a b l e s r e f l e c t a l l a v a i l a b l e o b s e r v a t i o n s . S i m i l a r s t a t i s t i c s are given i n the sequel f o r the samples reduced by the e x t r a c t i o n of suspected o u t l i e r s . 73 appear t o be l i n e a r l y r e l a t e d 6 8 . As mentioned above t h e v a r i a b l e s p r o x y f o r fundamental f a c t o r s such as s c a l e , c o m p l e x i t y , and r i s k w hich can be e x p e c t e d t o c o n t r i b u t e t o t h e c o s t of p r o d u c i n g t h e a u d i t 6 9 . I n a d d i t i o n t o a s s e t s t h e o t h e r c o n t r o l v a r i a b l e s used a r e : t h e square r o o t o f s u b s i d i a r i e s , t h e number of i n d u s t r i e s t h e f i r m p a r t i c i p a t e s i n , a dummy v a r i a b l e i n d i c a t i n g whether t h e f i r m i s a u t i l i t y , t h e p e r c e n t a g e of a s s e t s which a r e e i t h e r i n v e n t o r i e s o r r e c e i v a b l e s and t h e p e r c e n t a g e of a s s e t s w h i c h a r e h e l d i n f o r e i g n s u b s i d i a r i e s . T e s t s a r e run by i n c l u d i n g t h e v a r i a b l e s P i , o(e±), and v a r i o u s o t h e r h y p o t h e s i z e d measures of a u d i t r i s k as e x p l a n a t o r y v a r i a b l e s i n t h e a u d i t f e e r e g r e s s i o n s . S p e c i f i c a l l y , t h e models used were: 6 8 The f u n c t i o n a l form used t o a n a l y z e t h e d a t a i n t h i s r e s e a r c h i s s i m i l a r t o t h e s p e c i f i c a t i o n s i n Simunic (1980), F r a n c i s (1984), Simon (1985), and Palmrose (1986). The r e l a t i o n s h i p between a u d i t f e e s and a u d i t s i z e i s q u i t e w e l l documented e m p i r i c a l l y , though t o t h e b e s t of my knowledge, t h e r e i s no t h e o r e t i c a l work s u g g e s t i n g a p a r t i c u l a r f u n c t i o n a l form. 6 9 As d i s c u s s e d i n S i m u n i c , t h e s e f a c t o r s may be r e l a t e d t o t h e r i s k o f t h e a u d i t as w e l l as t o t h e pure p r o d u c t i o n of t h e a u d i t . C o n c e p t u a l l y t h e a d d i t i o n a l r i s k v a r i a b l e s i n t r o d u c e d i n t h i s r e s e a r c h , s i n c e t h e y a r e based upon s e c u r i t y market measures of r i s k , can be i n t e r p r e t e d as m easuring t h e magnitude o f p o t e n t i a l l o s s e s , whereas t h e f o r m e r v a r i a b l e s measure a u d i t r i s k i n t h e sense o f t h e a u d i t o r c o m m i t t i n g a t y p e I I e r r o r . 74 Model 1 . 5 In f e e . = b n + b , l n a s s e t s . + b ~ s u b s i d i a r i e s * + b 0 d i v e r s i t y l O l 1 2 i 3 i + b. u t i l i t y . + b c c u r r e n t . + hc f o r e i g n . + . . .b r i s k 4 - ' I D I 6 3 I n measures. ...+ e. l l Model 2 .5 .5 f e e . / a s s e t s ! = b n + b.. s u b s i d i a r i e s ! + b n d i v e r s i t y , l l O l I 2 J i + b^ u t i l i t y ^ + b^ c u r r e n t ^ + b,- f o r e i g n ^ ...+ b r i s k measures. ...+ e. n i i D i a g n o s t i c T e s t s T a b l e s 12 and 13 show t h e c o r r e l a t i o n m a t r i c e f o r t h e weekly and monthly samples r e s p e c t i v e l y . M u l t i c o l l i n e a r i t y does not appear t o be a s e r i o u s problem i n t h e weekly d a t a . In th e monthly d a t a b e t a and o ( e i ) have a c o r r e l a t i o n o f .6. T h i s would i n d i c a t e a c o n s e r v a t i v e approach i n i n t e r p r e t i n g t h e c o e f f i c i e n t s when b o t h o f t h e s e v a r i a b l e s a r e p r e s e n t i n t h e r e g r e s s i o n . T a b l e 14 p r e s e n t s a c r o s s - t a b view o f t h e r e l a t i o n s h i p between t h e two v a r i a b l e s i n t h e monthly and weekly samples. T e s t o f N o r m a l i t y T a b l e s 15 and 16 i n d i c a t e t h a t t h e r e s i d u a l s o f t h e 75 o r i g i n a l samples v a r i e d from t h e normal d i s t r i b u t i o n i n t h e sense of h a v i n g non-zero t h i r d and f o u r t h moments. T h i s prompted a s e a r c h f o r p o s s i b l e o u t l i e r s . I n t h e monthly sample one f i r m had an u n u s u a l l y low f e e , $257,000 on a s s e t s o f over $4 b i l l i o n , and was removed from c o n s i d e r a t i o n . I t i s unknown whether t h e f e e i s c o r r e c t l y r e p o r t e d . A f t e r t h i s o b s e r v a t i o n was d e l e t e d t h e r e s i d u a l s o f t h e monthly d a t a a r e more n i c e l y b e h a v e d 7 0 . See T a b l e 16. For t h e weekly d a t a , f o u r o b s e r v a t i o n s were removed. One o b s e r v a t i o n was t h e one d e s c r i b e d i n t h e p r e v i o u s p a r a g r a p h and t h e o t h e r t h r e e were f i n a n c i a l i n s t i t u t i o n s . For t h e s e f i r m s , a s s e t s may not be a commensurable measure of s i z e i n c o m parison t o i n d u s t r i a l f i r m s . Once t h e s e f i r m s were removed t h e r e s i d u a l s appear t o be more "normal". However, t h e square r o o t model was somewhat skewed and " f a t - t a i l e d " , see T a b l e 15. A l l subsequent a n a l y s i s i s done u s i n g t h e samples w i t h t h e o u t l i e r s removed. T e s t s f o r H e t e r o s c e d a s t i c i t y Two t e s t s were used t o check f o r h e t e r o s c e d a s t i c i t y i n t h e r e s i d u a l s , see T a b l e 17. The Breusch-Pagan-Godfrey t e s t d e s c r i b e d i n Judge e t a l . (1980 p. 146) and t h e Harvey t e s t 7 0 The s e a r c h f o r o u t l i e r s was done u s i n g p l o t s of r e s i d u a l s a g a i n s t v a r i o u s v a r i a b l e s . An o b s e r v a t i o n was removed from th e sample o n l y i f , upon e x a m i n a t i o n of t h e f i r m ' s c h a r a c t e r i s t i c s i t seemed r e a s o n a b l e t o c o n c l u d e t h a t i t s r e p o r t e d f e e was e i t h e r i n e r r o r o r i n l a r g e measure d e t e r m i n e d by some f a c t o r ( s ) not i n c l u d e d i n t h e model. 76 (Judge e t a l . p. 149). The i n t u i t i o n b e h i n d t h e former t e s t i s t h a t i t checks t o see i f t h e r e s i d u a l s a r e a l i n e a r f u n c t i o n o f t h e independent v a r i a b l e s . I n b oth samples t h e r e s i d u a l s of t h e square r o o t model appear t o v i o l a t e t h e h o m o s c e d a s t i c i t y a s s u m p t i o n . Comparing the two models i t seems l i k e l y t h a t t h e cause of t h e h e t e r o s c e d a s t i c i t y i s due t o t h e n o n - l i n e a r r e l a t i o n s h i p between f e e s and a s s e t s . By t h i s c r i t e r i o n t h e l o g model i s t h e b e t t e r s p e c i f i c a t i o n . But l a c k i n g any c o n v i n c i n g t h e o r y about t h e f u n c t i o n a l form o f a u d i t i n g p r o d u c t i o n f u n c t i o n s b o t h models a r e used. To c o r r e c t t h e e s t i m a t e s a l l subsequent r e g r e s s i o n s o f t h e square r o o t model i n c o r p o r a t e d White's h e t e r o s c e d a s t i c i t y - c o n s i s t e n t method" 7 1. (See White (1980).) S p e c i f i c a t i o n S i n c e t h e t h e o r y d e v e l o p e d above does not s p e c i f y t h e f u n c t i o n a l r e l a t i o n s h i p between a u d i t f e e s and r i s k measures, t h e r e i s t h e p o s s i b i l i t y o f m i s - s p e c i f i c a t i o n . Ramsey's RESET t e s t p r o v i d e s one method t o t e s t f o r o m i t t e d v a r i a b l e s 7 2 . T h i s 7 1 White's method s u b s t i t u t e s a d i a g o n a l m a t r i x o f t h e s quared OLS e r r o r terms f o r G i n t o t h e OLS v a r i a n c e - c o v a r i a n c e m a t r i x o ^ X ' X ) " 1 (X'GX) ( X ' X ) " 1 . See Kennedy (1985 p.108). 7 2 I f t h e r e i s an o m i t t e d v a r i a b l e i n a r e g r e s s i o n model t h e i n f l u e n c e o f t h e o m i t t e d v a r i a b l e i s r e f l e c t e d i n the e r r o r term. The RESET t e s t uses powers of t h e e r r o r term t o p r o x y f o r o m i t t e d v a r i a b l e s . These t r a n s f o r m e d e r r o r terms a r e added t o t h e r e g r e s s i o n and an F - t e s t i s used t o t e s t f o r t h e 77 t e s t was run f o r each model and d a t a s e t . These t e s t s do not d e t e c t any s t r o n g p a t t e r n of m i s - s p e c i f i c a t i o n , see T a b l e 18. The t h e o r y i n d i c a t e s ( e x p r e s s i o n 4.6) t h a t i f b e t a i s a good p r o x y measure of r i s k t h r o u g h i t s c o n t r i b u t i o n t o t h e Z - s c o r e , t h e n t h e c o e f f i c i e n t on b e t a e f f e c t w i l l not be c o n s t a n t . Thus, r e g r e s s i o n s which i n c l u d e b e t a ( t o c o n t r o l f o r r i s k ) o v er a broad range o f o ( e i ) v a l u e s a r e l i k e l y t o be m i s -s p e c i f i e d . F i g u r e 8 p l o t s t h e r e s u l t s of a s i m u l a t i o n where, f o r a s e t o f f i x e d p a r a m e t e r s , t h e change i n t h e Z-score i s p l o t t e d a g a i n s t b e t a f o r v a r i o u s l e v e l s o f o f e ^ ) . The f i g u r e s u g g e s t s t h a t t h e c o n t r i b u t i o n o f b e t a t o r i s k i s t h e most v a r i a b l e when b o t h b e t a and o t e i ) a r e s m a l l . The e f f e c t s appear t o s t a b i l i z e when b e t a exceeds .5 and o ( e i ) exceeds .03, on an annual b a s i s . F i g u r e 9 shows t h e r e s u l t s o f t h e s i m u l a t i o n f o r v a l u e s more t y p i c a l o f t h e sample. Note t h a t .1 on an annual b a s i s i s a p p r o x i m a t e l y e q u a l t o .015 on a weekly b a s i s , t h e minimum i n t h e weekly sample. T a b l e 14 shows t h e r e l a t i o n s h i p between b e t a and o(ex) i n t h e weekly and monthly samples. The o(es.)'s i n T a b l e 14 a r e on a weekly and monthly b a s i s , r e s p e c t i v e l y . R e t u r n i n g t o F i g u r e s 8 and 9 i t i s c l e a r t h a t t h e u s u a l OLS a s s u m p t i o n o f a c o n s t a n t e f f e c t o f t h e independent v a r i a b l e s does not h o l d f o r c e r t a i n c o m b i n a t i o n s of b e t a and o w n - v a r i a n c e . I n c a s e s were th e e f f e c t v a r i e s o v e r t h e range o f t h e d a t a t h e e s t i m a t e s a r e measures of t h e average e f f e c t . s i g n i f i c a n c e o f t h e c o e f f i c i e n t s . 78 These f i g u r e s do suggest t h e importance o f p a r t i t i o n i n g t h e d a t a on t h e b a s i s o f own-variance as was done. They a l s o s u g gest t h a t a f u r t h e r p a r t i t i o n i n g on b e t a may a l s o be a p p r o p r i a t e . T h i s was not done s i n c e t h e r e were few o b s e r v a t i o n s w i t h b o t h v e r y s m a l l b e t a s and o w n - v a r i a n c e s . S i n c e t h e measures 8 and o(ei.) a r e t h e m s e l v e s e s t i m a t e s , t h e r e g r e s s i o n s may s u f f e r from an e r r o r s i n t h e v a r i a b l e s problem. The use o f OLS i n t h i s s i t u a t i o n can r e s u l t i n a s y m p t o t i c a l l y b i a s e d c o e f f i c i e n t s . A common method f o r d e a l i n g w i t h t h i s problem i s by t h e s u b s t i t u t i o n o f i n s t r u m e n t a l v a r i a b l e s f o r t h e v a r i a b l e s which a r e measured w i t h e r r o r . Note, however, t h a t i n t h i s s t u d y t h e measures a r e i n s t r u m e n t s f o r some more b a s i c r i s k measure. W h i l e t h e e x t e n t o f t h e b i a s i s unknown, i n c l u d i n g t h e s e i m p e r f e c t measures i s t a k e n t o be p r e f e r a b l e t o e x c l u d i n g r i s k measures from a u d i t f e e s t u d i e s . T e s t s T h i s s e c t i o n r e p o r t s t h e r e s u l t s of t h e hypotheses g i v e n above. HI h y p o t h e s i z e d t h a t a u d i t f e e s would be i n c r e a s i n g i n t h e p r o b a b i l i t y o f l o s s . Two measures o f p r o b a b i l i t y o f l o s s a r e used, t h e Z - s c o r e , and p l o s s . P l o s s i s t h e c u m u l a t i v e d e n s i t y o f t h e Z - s c o r e . I n o r d e r t o c a l c u l a t e t h e Z-score i t i s n e c e s s a r y t o a s s i g n v a l u e s t o D, E r m , r £ , and o ( r m ) . E s t i m a t e s o f t h e l a t t e r t h r e e v a l u e s were o b t a i n e d 79 L from CRSP market d a t a f o r t h e 4-year p e r i o d J a n u a r y 1974 t h r o u g h December 1977. F i g u r e 10 p l o t s t h e market i n d e x f o r t h i s p e r i o d . F i g u r e 11 shows an average annu a l r e t u r n and a n n u a l i z e d o ( e A ) f o r each 52 week p e r i o d . As can be seen from t h e f i g u r e t h e r e i s a g r e a t d e a l o f v a r i a n c e i n t h e a c t u a l market r e t u r n . T h i s makes i t d i f f i c u l t t o know how a u d i t o r s and s h a r e h o l d e r s used t h i s i n f o r m a t i o n t o p r e d i c t t h e e x p e c t e d f u t u r e r e t u r n . The average f o r t h e f o u r y e a r p e r i o d was about 15%. T h i s number was used t o c a l c u l a t e t h e z - s c o r e s 7 3 . A v a r i e t y of v a l u e s f o r D and o ( r m ) were t r i e d . I t s h o u l d be r e c o g n i z e d t h a t many o f t h e parameters used t o c a l c u l a t e t h e z - s c o r e s were p i c k e d on an ad hoc b a s i s . S e n s i t i v i t y a n a l y s i s i s used t o overcome some o f t h e s h o r t comings. The fundamental problem i s one o f r e c o n s t r u c t i n g t h e d e c i s i o n p r o c e s s used by s h a r e h o l d e r s and a u d i t o r s . For i n s t a n c e , i t i s unknown what model t h e s h a r e h o l d e r s used t o p r e d i c t t h e e x p e c t e d r e t u r n i n t h e market. W h i l e t h e CAPM assumes s t a b i l i t y w i t h r e s p e c t t o t h i s parameter c l e a r l y t h i s does not govern i n v e s t o r s e x p e c t a t i o n s . S i m i l a r l y w i t h o u t knowing t h e c o s t c o n d i t i o n s f a c e d by s h a r e h o l d e r s i t i s i m p o s s i b l e t o d e t e r m i n e t h e c o r r e c t D f o r each f i r m . The cr u d e n e s s o f t h e measures used s h o u l d work i n f a v o r o f t h e n u l l h y p o t h e s i s o f no a s s o c i a t i o n . To t h e e x t e n t t h a t t h e phenomena i s v i s i b l e t h r o u g h t h e l i m i t a t i o n s o f t h e a v a i l a b l e 7 3 S e n s i t i v i t y a n a l y s i s was done u s i n g 10% and 20%. The r e s u l t s d i d n ' t v a r y much w i t h t h e lower number, but were not as s t r o n g w i t h t h e h i g h e r number. 80 d a t a i n c r e a s e s t h e c o n f i d e n c e i n t h e r e s u l t . The r e s u l t s of r a n g i n g D and o ( r m ) a r e shown i n T a b l e s 19 and 20. T a b l e 19 d i s p l a y s t h e r e s u l t s on t h e z - s c o r e s . A s m a l l e r (more n e g a t i v e ) z - s c o r e i n d i c a t e s a s m a l l e r p r o b a b i l i t y o f l o s s , t h e r e f o r e an i n c r e a s e i n t h e z - s c o r e i s p r e d i c t e d t o be a s s o c i a t e d w i t h g r e a t e r r i s k . T h i s i m p l i e s a p o s i t i v e c o e f f i c i e n t i s p r e d i c t e d . From t h e t a b l e i t can be seen t h a t t h e c o e f f i c i e n t s a r e p o s i t i v e f o r a l m o s t a l l s p e c i f i c a t i o n s on both samples. The t - v a l u e s on t h e c o e f f i c i e n t s a r e s i g n i f i c a n t f o r most of t h e weekly sample c a s e s . The b e s t r e s u l t s a r e f o r a D o f -.75 and a h i g h e r v a l u e o f o ( r m ) . The r e s u l t s on t h e p r o b a b i l i t y o f l o s s a r e s i m i l a r , see T a b l e 20. The c o e f f i c i e n t i s e x p e c t e d t o have a p o s t i t i v e s i g n and t h i s i s borne out by t h e e v i d e n c e f o r most s p e c i f i c a t i o n s . Once a g a i n t h e r e s u l t s a r e s t r o n g e s t f o r t h e weekly sample. I n comparing t h e monthly and weekly samples i t i s i m p o r t a n t t o remember t h a t a u d i t o r s and i n v e s t o r s a r e t r y i n g t o e s t i m a t e f u t u r e r i s k , w h i l e t h e e s t i m a t e d parameters used a r e h i s t o r i c a l . The two samples p r o v i d e d i f f e r e n t t i m e frames f o r t h e s e e s t i m a t e s . I t i s l i k e l y t h a t i n v e s t o r s and a u d i t o r s use b o t h s e t s o f i n f o r m a t i o n , though how t h e y w e i g h t them i s unknown. The weekly sample h a v i n g a 2 y e a r e s t i m a t i o n p e r i o d i s more c u r r e n t t h a n t h e monthly sample. However, t h e b e t a e s t i m a t e s from t h e monthly sample p r o v i d e a b e t t e r f i t , see 81 T a b l e 11. A l s o s i n c e t h e f e e r e g r e s s i o n s use e s t i m a t e s o f b e t a and o ( e i ) e s t i m a t e d from o v e r - l a p p i n g t i m e p e r i o d s ( r e f e r t o T a b l e 8) t h e r e i s t h e p o s s i b l e problem of contemporaneous c r o s s - c o r r e l a t i o n . T h i s can l e a d t o s e r i o u s b i a s e s i n t h e s t a n d a r d e r r o r s . B e r n a r d (1987) i n d i c a t e s t h i s problem may be more s e r i o u s t h e l o n g e r t h e e s t i m a t i o n i n t e r v a l . T h i s c o u l d c o n t r i b u t e t o t h e monthly sample r e s u l t s . E v i d e n c e f o r H l a and H l b a r e found i n T a b l e s 21 t h r o u g h 26. G e n e r a l l y , t h e r e s u l t s s u p p o r t t h e h y p o t h e s i s , H l a , t h a t a u d i t f e e s a r e i n c r e a s i n g i n o ( e A ) . The s t r o n g e s t e v i d e n c e i s i n t h e weekly d a t a . The h y p o t h e s i s H l b was t e s t e d by p a r t i t i o n i n g t h e d a t a as s u g g e s t e d by e x p r e s s i o n 4.6). E r v a r ( e . ) < 3. a - D v a r ( r ) m I n terms o f f i r m s p e c i f i c p arameters t h i s may be r e w r i t t e n as: K • v a r ( e . ) < fJ . l l where, K i s a c o n s t a n t encompassing t h e non f i r m - s p e c i f i c e l e m e n t s . T h i s s u g g e s t s t h a t b e t a s c o n t r i b u t e t o r i s k when o ( e A ) i s s m a l l . T h i s was implemented by o r d e r i n g t h e samples on t h e b a s i s o f own v a r i a n c e . Low and High own v a r i a n c e subsamples were c r e a t e d by o m i t t i n g o b s e r v a t i o n s w i t h i n t e r m e d i a t e v a l u e s o f o ( e i > . The t a b l e s show t h e r e s u l t s o f t h e p a r t i t i o n i n g . As p r e d i c t e d t h e low samples t e n d t o have 82 l a r g e r p o s i t i v e c o e f f i c i e n t s t h a n h i g h samples. One subsample, weekly d a t a model 2, even had a n e g a t i v e c o e f f i c i e n t . G e n e r a l l y , t h e weekly sample s u p p o r t e d t h e h y p o t h e s i s more s t r o n g l y t h a n t h e monthly sample. Of p a r t i c u l a r i n t e r e s t a r e T a b l e s 23 and 26 where s t a t i s t i c s a r e g i v e n on a t e s t o f t h e d i f f e r e n c e between t h e b e t a c o e f f i c i e n t s i n t h e low and h i g h sub-samples. T h i s t e s t was a c c o m p l i s h e d by i n c l u d i n g a b e t a dummy v a r i a b l e t o i n d i c a t e o b s e r v a t i o n s from t h e low sample i n a s i n g l e r e g r e s s i o n t h a t c o n s i s t e d o f o b s e r v a t i o n s from b o t h t h e h i g h and low samples. A p o s i t i v e c o e f f i c i e n t on t h e b e t a dummy i n d i c a t e s a p o s i t i v e d i f f e r e n c e between t h e low sample b e t a c o e f f i c i e n t and t h a t o f t h e h i g h sample. The T t e s t of th e dummy v a r i a b l e i s e q u i v a l e n t t o a Chow t e s t . T a b l e s 27 and 28 r e p o r t summary s t a t i s t i c s f o r each o f th e sub-samples. T a b l e s 29 and 30 show t h e r e s u l t s o f u s i n g t h e CNR and UNR measures. In t h e s e c a s e s t h e e x p e c t e d c o e f f i c i e n t s a r e n e g a t i v e . F i g u r e 12 p l o t s t h e measures P l o s s , CNR and UNR a g a i n s t t h e z - s c o r e . These v a l u e s were d e t e r m i n e d u s i n g a s i m u l a t i o n model. The n e g a t i v e c o e f f i c i e n t i s , a t f i r s t l o o k , s u r p r i s i n g as i n t u i t i o n would l e a d one t o b e l i e v e t h a t f i r m s w i t h s m a l l e r (more n e g a t i v e ) z - s c o r e s a l s o would have s m a l l e r CNRs and UNRs. F i g u r e 13 shows two r e t u r n d i s t r i b u t i o n s . R' i s th e l e s s r i s k y d i s t r i b u t i o n h a v i n g both a s m a l l e r b e t a and o ( e A ) . For a f i x e d v a l u e , Z, t h e p r o b a b i l i t y r * < Z i s g r e a t e r 83 e x p e c t e d v a l u e o f r i r g i v e n t h a t r ± < Z, i s l a r g e r ( l e s s n e g a t i v e ) f o r R' t h a n R''. And s i n c e t h e p r o b a b i l i t y o f a r e t u r n b e i n g l e s s t h a n Z i s l e s s f o r R', t h e n UNR i s a l s o l a r g e r . Once a g a i n b oth samples a r e c o n s i s t e n t w i t h t h e h y p o t h e s i s , H2, i n terms o f t h e s i g n o f t h e e f f e c t . For a wide range of parameter v a l u e s t h e s e r e s u l t s show s i g n i f i c a n c e i n t h e weekly sample f o r b o t h t h e CNR and UNR measures. For t h e monthly sample t h e r e s u l t s a r e c o n s i s t e n t but not s i g n i f i c a n t a t c o n v e n t i o n a l l e v e l s . T a b l e 31 g i v e s t h e c o r r e l a t i o n s among t h e r i s k measures and T a b l e 32 g i v e s examples of how t h e r i s k measures map i n t o one a n o t h e r . T a b l e 33 summarizes t h e r e s u l t s o f t h e r e g r e s s i o n s on t h e p r o x y measures o f r i s k . C o n c l u s i o n s The d a t a s u g g e s t s t h a t t h e r e i s a r e l a t i o n s h i p between a u d i t f e e s and ex a n t e measures of s e c u r i t y market r i s k . The argument was made i n C hapter 3 t h a t a u d i t o r s would be s e n s i t i v e t o t h e l i k e l i h o o d o f "bad" c l i e n t f i r m s t o c k r e t u r n s . The hypotheses i n C h a p t e r 4 suggest t h a t c a r e must be t a k e n i n u s i n g t h e s e c u r i t y market measures s i n c e t h e i r e f f e c t i s not always s t r a i g h t f o r w a r d . I n p a r t i c u l a r , i t was shown t h a t t h e i n f l u e n c e o f b e t a upon a u d i t r i s k v a r i e s w i t h o t h e r f a c t o r s . W i t h r e g a r d t o t h e d a t a , i t i s a p p a r e n t t h a t s p e c i f i c a t i o n o f t h e p arameters and model a l s o a f f e c t t h e r e s u l t s , though t h e r e i s a f a i r amount of r o b u s t n e s s i n t h e 84 r e s u l t s . The weekly d a t a o u t p e r f o r m e d t h e monthly i n a l l c a s e s and t h e r e s u l t s f o r t h e monthly d a t a l a c k s t a t i s t i c a l s i g n i f i c a n c e . T h i s i s somewhat s u r p r i s i n g g i v e n t h a t t h e weekly e s t i m a t i o n p e r i o d i s a s u b s e t o f t h e monthly e s t i m a t i o n p e r i o d and t h a t t h e monthly e s t i m a t e s o f i n d i v i d u a l b e t a s have g r e a t e r e x p l a n a t o r y power as measured by an average r 2 . I n f a v o r o f t h e weekly d a t a a r e t h e f a c t s t h a t t h e i n f o r m a t i o n was more c u r r e n t , i n t h e sense t h a t t h e e s t i m a t e s were not i n f l u e n c e d by o b s e r v a t i o n s t h a t p r e c e ded t h e d e c i s i o n p o i n t by more t h a n two y e a r s , and t h a t t h e weekly d a t a had t w i c e as many degrees o f freedom. W i t h r e g a r d t o model s p e c i f i c a t i o n two a l t e r n a t i v e t r a n s f o r m a t i o n s were used t o c o n t r o l f o r t h e i n f l u e n c e o f c l i e n t f i r m s i z e . Both o f t h e t r a n s f o r m a t i o n s have been used and d i s c u s s e d i n t h e l i t e r a t u r e . I n t h e sample t h a t I used t h e square r o o t t r a n s f o r m a t i o n c o n s i s t e n t l y showed g r e a t e r s i g n i f i c a n c e on t h e c o e f f i c i e n t s o f i n t e r e s t t h a n d i d t h e l o g model. However t h e square r o o t model a l s o showed e v i d e n c e o f h e t e r o s c e d a s t i c i t y which was a d j u s t e d f o r u s i n g White's method. T e s t s o f t h e hypotheses showed s i g n i f i c a n c e a t c o n v e n t i o n a l l e v e l s u s i n g e i t h e r model i n c o n j u c t i o n w i t h t h e weekly sample. Some assumptions were needed about t h e v a l u e s o f parameters such as t h e e x p e c t e d r e t u r n on t h e market, t h e v a r i a n c e o f t h e market, and, most c r i t i c a l l y , about t h e s h a r e h o l d e r s ' d e c i s i o n r u l e , D, i n o r d e r t o p e r f o r m some o f 85 t h e t e s t s . S e n s i t i v i t y a n a l y s i s was done w i t h each of t h e s e p a r a m e t e r s . The r e s u l t s o f v a r y i n g the e x p e c t e d r e t u r n on t h e market were not r e p o r t e d as t h e y were a c c o m p l i s h e d a t a r e l a t i v e l y p r e l i m i n a r y p o i n t i n t h e r e s e a r c h , however t h e r e s u l t s , a t t h a t t i m e were r e l a t i v e l y i n s e n s i t i v e t o changes i n t h e v a l u e used. The measure used was crude and a b e t t e r model of how i n v e s t o r s a n t i c i p a t e t h e market o v e r t i m e would be u s e f u l . The D v a l u e o f -50% seemed t o p e r f o r m w e l l w i t h r e l a t i v e l y l i t t l e change i n s i g n i f i c a n c e between t h e t e s t s w i t h D's of t h i s v a l u e and t h o s e w i t h D's of -25% and -75%. Once a g a i n t h e t e s t s c o u l d be honed i f i n f o r m a t i o n were a v a i l a b l e on how t h i s v a l u e might v a r y c r o s s - s e c t i o n a l l y w i t h i n t h e samples. S e n s i t i v i t y on o ( r r o ) g e n e r a l l y i n d i c a t e s improvement as t h e parameter v a l u e i n c r e a s e s from .1 t o .2 and some a d d i t i o n a l m a r g i n a l improvement as t h e parameter v a l u e i n c r e a s e s t o .3. S e n s i t i v i t y was not performed a t h i g h e r l e v e l s s i n c e .3 seemed a r e a s o n a b l e upper bound f o r market v a r i a b i l i t y . The o v e r a l l i m p r e s s i o n o f t h e e m p i r i c a l t e s t s i s t h a t a u d i t f e e s do, t o some e x t e n t , r e f l e c t r i s k as measured i n c l i e n t f i r m ' s s e c u r i t i e s . The e x t e n t o f t h e r i s k a djustment i s r e l a t i v e l y s m a l l compared t o such p r o d u c t i o n f a c t o r s as t h e s i z e and c o m p l e x i t y o f t h e c l i e n t , but t h e d a t a i s c o n s i s t e n t w i t h t h e argument t h a t a u d i t f e e s i n c l u d e r i s k a d j u s t m e n t s w h i c h a r e a s s o c i a t e d w i t h s e c u r i t y market measures of r i s k . 86 Chapter 5 Summary and C o n c l u s i o n s T h i s t h e s i s s t a r t e d w i t h a d e c i s i o n t h e o r y model o f a u d i t i n g i n which t h e a u d i t o r chooses a c o s t m i n i m i z i n g a u d i t p l a n and a u d i t o p i n i o n t o a c c o m p l i s h an a u d i t . I n o r d e r t o make h i s c h o i c e s t h e a u d i t o r must a s s i g n v a l u e s t o t h e c o s t s o f making t y p e I and t y p e I I e r r o r s . I n p r e v i o u s r e s e a r c h t h e c o s t s a s s o c i a t e d w i t h t h e s e e r r o r s were m o d e l l e d as b e i n g d e t e r m i n e d exogenously and w i t h o u t r e g a r d t o whether t h e d e c i s i o n s made by t h e a u d i t o r r e s u l t i n a r a t i o n a l p l a y by t h e a f f e c t e d p a r t i e s . I n c o n t r a s t t h e a n a l y s i s i n Chapter 3 assumes t h a t t h e c o s t o f a t y p e I e r r o r , c ( I , ) i s f i x e d , but t h a t t h e c o s t o f a t y p e I I e r r o r , c ( I I ) , i s d e t e r m i n e d as t h e r e s u l t o f a game between a u d i t o r s and s h a r e h o l d e r s . The i m p o r t a n t l i n k i n t h e s t r a t e g i c p l a y o f t h e game i s t h e system o f p r o d u c t l i a b i l i t y i n w hich a u d i t o r s may havve t o make t r a n s f e r payments t o s h a r e h o l d e r s when a u d i t i n g e r r o r s a r e found by t h e c o u r t s . T h i s e s t a b l i s h e s a c o n f l i c t i n g s e t o f i n t e r e s t between t h e a u d i t o r s and s h a r e h o l d e r s which can be r e p r e s e n t e d by a non-c o o p e r a t i v e game. Employing t h e Nash e q u i l i b r i u m c o n c e p t , an a n a l y s i s o f 87 e q u i l i b r i u m s t r a t e g i e s shows how s t o c k p r i c e i n f o r m a t i o n i n f l u e n c e s s h a r e h o l d e r s ' b e h a v i o r . I n t u r n t h i s a f f e c t s t h e p l a y o f t h e game and t h e r e s u l t a n t e q u i l i b r i u m . The key p o i n t i s t h a t t h e r i s k o f "bad" outcomes maps i n t o t h e a u d i t o r ' s l o s s f u n c t i o n and r e s u l t s i n h i g h e r a u d i t i n g c o s t s . These c o s t s r e f l e c t v a r i o u s f a c t o r s such a s : t h e c o s t s o f g i v i n g a p r o t e c t i v e q u a l i f i c a t i o n , a d d i t i o n a l a u d i t i n g , i n s u r a n c e , o r t h e r e c o v e r y o f an e x p e c t e d l o s s . I n Chapter 4 e m p i r i c a l hypotheses a r e f o r m u l a t e d about t h e a s s o c i a t i o n o f s p e c i f i c market based measures o f s e c u r i t y r i s k and a u d i t r i s k . The main l i n k a g e between t h e t h e o r e t i c a l a n a l y s i s and t h e e m p i r i c a l work i s t h e c o n j e c t u r e t h a t v a r i a b i l i t y i n t h e d i s t r i b u t i o n o f s t o c k r e t u r n s i s a s s o c i a t e d w i t h t h e p r o b a b i l i t y w e i g h t s a s s i g n e d t o t h o s e outcomes f o r wh i c h a u d i t o r s a r e a t r i s k . F u r t h e r , i n s t i t u t i o n a l c o n s i d e r a t i o n s l i n k t h o s e f a c t o r s which a f f e c t r e t u r n v a r i a b i l i t y w i t h a u d i t o r h a v i n g t o sometimes bear t h e r i s k of bad outcomes i n s t o c k m a r k e t s . V a r i o u s o b s e r v a t i o n s s u p p o r t t h i s mechanism. For i n s t a n c e t h e i n a b i l i t y of c o u r t s t o d i s t i n g u i s h s h a r e h o l d e r s ' l o s s e s caused by a u d i t o r s from t h o s e caused by o t h e r f a c t o r s 7 4 . A s p e c i f i c h y p o t h e s i s o f i n t e r e s t i s t h e v a l u e o f a c l i e n t f i r m ' s market " b e t a " as a proxy f o r a u d i t r i s k . T h i s measure has p i q u e d some c u r i o s i t y i n t h e a c c o u n t i n g l i t e r a t u r e 7 4 A secondary argument i s t h a t f a c t o r s w h i c h d e t e r m i n e r i s k i n s e c u r i t i e s m a r k e t s , such as s t o c h a s t i c p r o d u c t demand, a l s o add t o t h e d i f f i c u l t y o f p r o d u c i n g an e r r o r - f r e e a u d i t . 88 because o f i t s prominence i n t h e t h e o r y o f f i n a n c e . I t i s found t h a t b e t a may be o f v a l u e i n measuring a u d i t r i s k i f i t i s r e c o g n i z e d t h a t i t s a f f e c t i s not c o n s t a n t . The main t e s t s i n Chapter 4 r e v o l v e around t h e a s s o c i a t i o n between a u d i t f e e s and t h e p r o b a b i l i t y o f a s e c u r i t y h a v i n g a " s u f f i c i e n t l y " ' 7 5 bad r e t u r n . E v i d e n c e i s found which s u p p o r t s t h e h y p o t h e s i s o f a u d i t f e e s i n c r e a s i n g i n t h i s measure which i n t u r n can be d e r i v e d u s i n g market measures o f r i s k . The r e s e a r c h , h e r e i n , r e l i e d upon many assumptions which p o t e n t i a l l y l i m i t i t s g e n e r a l i t y . I n t h e a u d i t o r -s h a r e h o l d e r s game t h e g r e a t e s t r e s t r i c t i o n s i n v o l v e t h e assumed r o l e o f management and t h e a b i l i t y o f t h e c o u r t s t o d i s e n t a n g l e t h e d e t e r m i n a n t s o f s t o c k p r i c e s . A more p r o f o u n d t r e a t m e n t o f t h e s u b j e c t would a l l o w t h e f i r m ' s management t o behave s t r a t e g i c a l l y . U n f o r t u n a t e l y t h i s e m b e l l i s h m e n t has an e x p o n e n t i a l impact upon t h e c o m p l e x i t y o f t h e game. The d i f f i c u l t i e s o f a n a l y z i n g such a regime a r e noted by A n t l e (1982). Changing t h e c o u r t ' s a c c e s s t o i n f o r m a t i o n would a l s o d r a s t i c a l l y change t h e a n a l y s i s . I n t h e extreme c a s e , p e r f e c t i n f o r m a t i o n by t h e c o u r t s would make market r i s k i r r e l e v a n t t o t h e a u d i t o r s i n c e t h e c o u r t s would 1) c o r r e c t l y i d e n t i f y a u d i t i n g e r r o r s , and 2) p r o p e r l y a s s i g n , g i v e n t h e l i a b i l i t y r u l e s , damages t o t h e a p p r o p r i a t e t o r t f e a s o r s . 7 5 S u f f i c i e n t l y means bad enough t o provoke t h e s h a r e h o l d e r s i n t o s e e k i n g compensation from t h e a u d i t o r t h r o u g h a l a w s u i t . 89 In t h e e m p i r i c a l a n a l y s i s many assumptions were made w i t h r e g a r d t o t h e v a r i o u s parameter v a l u e s needed t o a s s e s s t h e p r o b a b i l i t y o f a l o s s . These have been p r e v i o u s l y d i s c u s s e d . The assumptions about t h e s h a r e h o l d e r s ' d e c i s i o n r u l e , D, a r e , perhap s , t h e most h e r o i c . T h i s q u a n t i t y i s c l e a r l y endogenously d e r i v e d on a f i r m by f i r m b a s i s . T h i s r e s e a r c h would b e n e f i t from a b e t t e r model (and da t a ) o f t h e s h a r e h o l d e r s ' d e c i s i o n p r o c e s s . One c o n t r i b u t i o n o f t h i s t h e s i s i s t h a t i t r e f i n e s and extend s t h e u n d e r s t a n d i n g o f t h e a u d i t o r ' s d e c i s i o n problem t o i n c l u d e t h e assessment of r i s k when an a d d i t i o n a l economic agent i s a l l o w e d t o behave s t r a t e g i c a l l y . The e m p i r i c a l a n a l y s i s p r o v i d e s new i n f o r m a t i o n u s e f u l t o t h e u n d e r s t a n d i n g o f t h e impact o f r i s k i n t h e s u p p l y o f a u d i t i n g s e r v i c e s . 90 F i g u r e 1. A s i m p l i f i e d a u d i t o r ' s d e c i s i o n problem. 91 N a t u r e ( a c c e p t ) A u d i t o r ( r e j e c t ) s l s 2 ( f a i r ) (not f a i r ) 0 c [ a 1 , q , s 2 , z] ( a 2 , q , . s 1 , z ) 0 F.S. a r e F.S. a r e t r u e f a l se U n q u a l i f i e d O p i n i o n Q u a l i f i e d O p i n i o n F i g u r e 2. The c o s t s o f t h e t y p e s of a u d i t e r r o r s . 92 F i g u r e 3a. A u d i t o r - s h a r e h o l d e r game, h i g h a u d i t l e v e l 93 F i g u r e 3b. A u d i t o r - s h a r e h o l d e r game, low a u d i t l e v e l . 94 F i g u r e 4. Expected a u d i t o r ' s c o s t s under a s t r i c t l i a b i l i t y regime. 95 F i g u r e 5. E x p e c t e d a u d i t o r ' s c o s t s under a g l i g e n c e d e f e n s e regime. 96 I Expected Returns F i g u r e 6 . S h i f t i n t h e r e t u r n d i s t r i b u t i o n as b e t a i n c r e a s e s . 97 1 -r 0.9-0.8 -0.7-0.6->. u c g. 0-5-£ U . 0.4-0.3-0.2-0.1 -0 / aat f / # *-****•, 7 1 / ****** f J taa'r / , f / 'XSW X vy*v* / > &«S / y yAW / j # # A g VtVtV, / A AWA X vyyyy. V § l aa<z xaai aa<i< ia<a : < C C C v ****** xaa*. **,**,*' iaai iaa< **y**i' •A*AA* >\aa-%.aa< yyyyy. \aa-zaa ~aa< •aai yyyyy. '****,' \aa<. ****** \ai.a 10 50 100 250 500 1000 2000 4000 Assets (1,000,000's) Frequency Cumulative Freq. F i g u r e 7. The s i z e d i s t r i b u t i o n o f sample f i r m s ' a s s e t s , 98 0.5 1.5 2.5 3 Beta • se =.01 se =.03 F i g u r e 8. S i m u l a t i o n o f t h e change i n z - s c o r e as b e t a i n c r e a s e s . 99 F i g u r e 9. S i m u l a t i o n of t h e change i n t h e z - s c o r e as b e t a i n c r e a s e s . 100 Jan 1974 Jan 1975 Jan 1976 Jan 1977 Jan .1978 Note : December 31, 1973 Is set equal to 1.0 F i g u r e 10. The market inde x from 1974 t o 1978. 101 102 F i g u r e 12. S i m u l a t i o n o f t h e r e l a t i o n s h i p between t h e v a r i o u s p r o x y measures of r i s k . 103 Return F i g u r e 13. The r e l a t i o n s h i p between t h e z - s c o r e and t h e CNR and UNR. 104 TABLE 1 NOTATION a l ' a 2 = a U ( * l t c > r o p i n i o n : a c c e p t ( u n q u a l i f i e d o p i n i o n ) o r r e j e c t ( q u a l i f i e d o p i n i o n ) A^ = i s t h e a u d i t o r ' s i t h s t r a t e g y c(A^|SH_.) = t h e c o s t t o t h e a u d i t o r o f s t r a t e g y i when the s h a r e h o l d e r uses s t r a t e g y j . D , (a , t , ) = i s t h e amount o f damages awarded t o t h e nk n k s h a r e h o l d e r as a f u n c t i o n o f t h e a u d i t o p i n i o n and t h e r e a l i z e d s h a r e p r i c e . h ( q ) = t h e p r o d u c t i o n c o s t o f t h e a u d i t as a f u n c t i o n o f a u d i t i n t e n s i t y . j ( a - w t , ) = s h a r e h o l d e r a c t i o n : sue o r not sue t h e a u d i t o r p U k w = t h e c o s t t o t h e s h a r e h o l d e r of s u i n g t h e a u d i t o r . L k a ' ^ k r = s ^ a r e h o l d e r l o s s f u n c t i o n = t g - t ^ o r 0 i f t ^ > t g s u b s c r i p t "a" i n d i c a t e s t g based upon an u n q u a l i f i e d o p i n i o n , s u b s c r i p t " r " i n d i c a t e s t g based upon a q u a l i f i e d o p i n i o n . p ( I = t h e p r o b a b i l i t y o f making a t y p e I e r r o r g i v e n t h e l e v e l o f a u d i t i n t e n s i t y chosen. p ( I I |<3m) = t h e p r o b a b i l i t y o f making a t y p e I I e r r o r g i v e n t h e l e v e l o f a u d i t i n t e n s i t y chosen. 105 T a b l e l - - c o n t i n u e d p ( s 2 | ^ -^  ^  = t h e p r o b a b i l i t y o f t h e f i n a n c i a l s t a t e m e n t s b e i n g u n f a i r g i v e n t h e r e a l i z e d s hare p r i c e . T h i s p r o b a b i l i t y i s used by t h e c o u r t s and r e p r e s e n t s t h e i r a b i l i t y t o d i s t i n g u i s h l o s s e s due t o 6^ from t h o s e due t o s... Note t h a t t h e f o l l o w i n g s t r u c t u r e has been imposed: p ( s 2 | t ^ ) = 0 , 0 < p ( s 2 J t 2 ) = p ( s 2 | t . j ) < 1/ and p ( s 2 | t 4 > = 1. p(<3m< c 3 + l a 2 ' ^ k ^ = ^ n e P r°babil i t y t h e c o u r t s f i n d t h e a u d i t o r t o be n e g l i g e n t g i v e n t h e o p i n i o n , a2/ and t h e s t o c k p r i c e . Under a s t r i c t l i a b i l i t y regime t h i s q u a n t i t y i s s e t t o 1 f o r k = 2, 3, 4. W ith a n e g l i g e n c e r u l e i t i s a p o s i t i v e q u a n t i t y l e s s t h a n 1 f o r k= 2, 3, 4. q + i s t h e l e v e l o f due d i l i g e n c e . q^, q2 = a u d i t i n t e n s i t y : h i g h o r low. S l ' S 2 = t r u e c o n d i t i o n o f t h e f i n . s t a t e m e n t s : f a i r , not f a i r . SHj = t h e s h a r e h o l d e r s ' j t h s t r a t e g y . 6^, 02 = e v e n t s which a f f e c t s t o c k p r i c e and a r e ^ u n c o r r e l a t e d w i t h t h e f a i r n e s s o f t h e f i n a n c i a l s t a t e m e n t s . They a r e t h e "good" and "bad" outcomes. t g ( a n ) = ex ante s t o c k p r i c e c o n d i t i o n e d upon t h e a u d i t o p i n i o n , a n . 106 T a b l e l - - c o n t i n u e d = ex post s t o c k p r i c e s . They t a k e on v a l u e s : fcl = t(*Qi's±) ' fc2 = t O j f S ^ ) , t 3 = t(e i,S2>, and ^4 = t ^ 2 ' s 2 ^ * N o t e t n a t > t2 = fc3 > t 4 " 107 TABLE 2 SHAREHOLDERS' STRATEGIES STRICT LIABILITY S t r a t e g y { a 1 , t 1 } I n f o r m a t i o n S e t s i a 1 , t 2 3} i a 1 , t 4 ) SHj^ j l j l S H 2 j l j l h S H 3 j l j2 S H 4 j l j2 h ' SH C 5 j2 j l j i SH 6 j2 j l h SH 7 j2 j2 h SH 8 j2 j2 j2 Note: Each o f t h e above s t r a t e g i e s assumes t h e s h a r e h o l d e r does not sue when a " q u a l i f i e d " o p i n i o n i s g i v e n . = sue, j 2 = not sue a. = u n q u a l i f i e d o p i n i o n , a- = q u a l i f i e d o p i n i o n 108 TABLE 3 S t r a t e g y AUDITOR STRATEGIES High A u d i t I n t e n s i t y Low A u d i t I n t e n s i t y = h i g h a u d i t s i g n a l , z 2 = low a u d i t s i g n a l a- .= u n q u a l i f i e d o p i n i o n , a„ = q u a l i f i e d o p i n i o n 109 TABLE 4 AUDITOR COSTS UNDER STRICT LI A B I L I T Y P l a y E x p e c t e d Cost 4 ( A 2 } c ( A 2 | SH_ ) = 3 = [kl2 D n k ' P ( t k l S 2 ' Z l ' V 1 -p ( I I IV + c ( I ) • p ( I |q ) + h ( q 1 ) !A 2 , SH ? } c ( A 2 | SH 7 ) = = [ Dn4* p(t4l s 2 ' z l ' q l ) ] ' p ( I I | q x ) + C<I) • p ( I |q 1) + h(q 1> 4 , A 5 , SH 5 } c ( A 5 | SH 5). 1 D n k p ( t k ) k=2 n K K { v , SH ? } c ( A 5 | SH ? ) D A P ( t / I > n4 4 { A 6 ' S H 5 } c ( A 6 l SH 5) C ( I ) • p ( I |q 2) { A 6 , SH 7 1 C(A6I SH ? ) C ( I ) • p ( I |q ) 110 TABLE 5 NORMAL FORM GAME WITH STRICT L I A B I L I T Y S h a r e h o l d e r A u d i t o r S t r a t e g i e s s t r a t e g i e s and share A 2 A 5 \ p r i c e fcl c ( A 2 | SH5> 0 c ( A 5 | 0 SH_ ) 3 c ( A , 1 6 1 0 SH_ ) 3 S H 5 fc2,3 c ( A 2 | SH 5) D 2 - w c ( A 5 | V " SH C ) D W c ( A 6 | 0 SH C ) 3 *4 c ( A 2 | SH 5) D 4 ~ w c ( A 5 | D 4 " SH_ ) D W c ( A e l 0 SH_ ) 3 *1 c ( A 2 | SH7> 0 c ( A 5 | 0 SH ? ) c ( A 6 l ' 0 SH ? ) SH ? t 2 3 c ( A 2 | SH ?) 0 c ( A 5 | 0 SH ?) c ( A 6 | 0 SH ?) t4 c ( A 2 | SH ?) D 4 - w c ( A 5 | D 4 " SH ?) w c ( A e ! 0 SH ?) Note: The s h a r e h o l d e r s ' damage awards a r e g i v e n on t h e bottom row o f each box. I l l TABLE 6 AUDITOR COSTS WITH A NEGLIGENCE DEFENSE P l a y C ost t o t h e A u d i t o r , SH 5 } c ( A 2 1 SH 5) = c ( I ) • p ( I + h ( q 1 ) { A 2 , SH ? } c ( A 2 | SH ? ) = c ( I ) • p ( I | + h ( q x ) ( A 5 , SH 5 } c ( A 5 | SH 5) 4 = Z °nk P ( t k ) k=2 n k k I A 5 , SH ? } c ( A 5 | SH ? ) = Dn4 P < V { A 6 ' SH 5 •} c ( A e l SH 5) = c ( I ) • p ( I q 2> { A 6 , SH ? } c ( A e l SH ? ) = c ( I ) • p ( I q 2 ) 112 TABLE 7 NORMAL FORM GAME WITH NEGLIGENCE DEFENSE S h a r e h o l d e r s t r a t e g i e s and share p r i c e fcl S H 5 fc2,3 A u d i t o r S t r a t e g i e s A 2 A 5 A 6 c(A„| SH_) 0 c ( A 5 | SH5> 0 c ( A 6 | SH 5) 0 c ( A 2 | SH5> - w c ( A 5 | SH 5) D 2 - w c ( A 6 | SH5> 0 c ( A 2 | SH 5) - w c ( A 5 | SH 5) D 4 - w c ( A 6 | SH 5) 0 fcl SH ? t 2 f 3  fc4 c(A„| SH„) 2 1 7 0 c ( A 5 | SH ?) 0 c(A 1 SH„) 6 1 7 0 c ( A 2 | SH ?) 0 c ( A 5 | SH ?) 0 c ( A 6 | SH ?) 0 c ( A 2 | SH ?) - w c ( A 5 | SH ?) D 4 - w c ( A 6 | SH ?) 0 Note: The s h a r e h o l d e r s ' damage awards a r e g i v e n on t h e bottom row o f each box. 113 TABLE 8 PURE STRATEGY EQUILIBRIA WITH NEGLIGENCE DEFENSE A u d i t o r S h a r e h o l d e r S t r a t e g i e s S t r a t e g i e s Cost C o n d i t i o n s 2 5 Not an e q u i l i b r i u m 2 7 Not an e q u i l i b r i u m 5 5 c ( A 5 SH 5) < c ( A 2 | SH. ) 0 and c ( A e l SH 5) ; D 2 > w 5 7 c(A_ 1 s v < c ( A 2 | SH ? ) and c ( A c D | SH ?) ; D 2 < w 6 5 c ( A 6 1 S H 5 ) < c<A 2| SH C ) 0 and c ( A 5 | SH 5) 6 7 c ( A 6 1 S H7> and < c ( A 2 | c ( A 5 | SH 7 SH 7 ) ) 114 TABLE 9 CROSS-TAB OF PERCENT ZERO PRICE CHANGES DURING ESTIMATION PERIOD AND PARAMETER ESTIMATES FOR OVER THE COUNTER FIRMS. E s t i m a t e d V a l u e 0 - .2 Frequency o f .2 - .4 . Zero 4 - .6 Changes .6 - .8 ( A l l ) B e t a (2) - (1.25) - - 0.013 - 0.013 (1.25) - (.5) - 0.013 0.013 - 0.025 (.5) - .25 0.025 0.088 0.100 0.051 0.263 0.25 - 1 0.175 0.113 0.113 0.013 0.413 1 - 1.75 0.113 0.050 - 0.163 1.75 - 2.5 0.038 - 0.013 - 0.050 2.5 - 3.25 0.038 0.013 0.013 - 0.063 3.25 - 4 0.013 - - - . 0.013 T o t a l 0.400 0.275 0.263 0.063 1.000 R-squared 0 - .1 0.213 0.200 0.250 0.063 .725 .1 - .2 0.150 0.075 0.013 - .238 .2 - .3 0.038 - - - .038 T o t a l 0.400 0.275 0.263 0.063 1.00 115 TABLE 10 DESCRIPTIVE STATISTICS 1 Mean Maximum Minimum Standard Dev. A l l Firms (395) (See a l s o Table 7. Simunic[1980]) Assets(OOO's) 554,066 9,854,100 509 1,195,080 Fee 207,283 2,400,000 5,000 277,279 Fee//assets 13.06 48.32 0.92 8.58 / S u b s i d i a r i e s 3.17 17.32 0.00 2.67 D i v e r s i t y 0.90 5.00 0.00 1.23 U t i l i t y 0.06 1.00 0.00 0.23 %Current A s s e t s 0.46 1.61 0.01 0.23 % F o r e i g n 0.07 0.67 0.00 0.13 OTC Sample (73 Firms) Assets(OOO's) 85,894 572,370 2,553 111,259 Fee 111,630 700,000 7,000 117,800 Fee//assets 13.17 48.32 2.12 8.41 / S u b s i d i a r i e s 2.29 12.41 0.00 1.98 D i v e r s i t y 0.92 5.00 0.00 1.18 U t i l i t y 0.00 0.00 0.00 0.00 ^Current Assets 0.48 0.88 0.01 0.20 % F o r e i g n 0.06 0.56 0.00 0.11 116 TABLE 1 0 — c o n t i n u e d Mean Maximum Minimum S t a n d a r d Dev. Weekly Sample (173 F i r m s ) A s s e t s * 000's) 606,555 6,620,880 12,520 1,085,231 Fee 273,196 1,960,000 12,000 307,225 F e e / / a s s e t s 14.80 38.62 0.92 8.44 / S u b s i d i a r i e s 3.82 17.32 0.00 2.82 D i v e r s i t y 1.01 5.00 0.00 1.26 U t i l i t y 0.08 1.00 0.00 0.26 % C u r r e n t A s s e t s 0.45 0.83 0.01 0.20 % F o r e i g n 0.09 0.50 0.00 0.13 Monthly Sample (125 Firm s ) Assets(OOO's) 779,157 6,620,883 32,274 1,204,892 FEE 365,064 2,400,000 35,000 384,337 F e e / / a s s e t s 16.30 38.62 1.55 8.94 / S u b s i d i a r i e s 4.44 17.32 0.00 3.21 D i v e r s i t y 1.20 5.00 0.00 1.35 U t i l i t y 0.08 1.00 0.00 0.27 ^ C u r r e n t A s s e t s 0.44 0.83 0.03 0.19 % F o r e i g n 0.12 0.50 0.00 0.14 117 TABLE 11 ESTIMATED MARKET PARAMETERS 1 Mean Maximum Minimum S t a n d a r d Dev. OTC Sample B e t a 0.74 3.75 -1.40 0.89 R 2 0.06 0.27 0.00 0.06 o ( e i ) 0.07 0.22 0.02 0.04 Weekly Sample B e t a 1.04 2.53 0.05 0.48 R 2 0.19 0.58 0.00 0.13 o ( e J 0.05 0.19 0.02 0.02 Mon t h l y Sample Be t a 0.96 2.05 -.10 0.42 R 2 0.38 0.70 0.00 0.15 o ( e J 0.09 0.16 0.04 0.03 118 TABLE 12 CORRELATION MATRIX OF VARIABLES Weekly Data (173 O b s e r v a t i o n s ) Log A s s e t s 1.000 / " S u b s i d i a r i e s .433 1.000 D i v e r s i t y .124 .325 1.000 U t i l i t y - d u m m y .239 -.219 -.175 1.000 C u r r e n t -.384 .022 .129 -.491 1.000 F o r e i g n .248 .518 .050 -.204 .208 B e t a -.024 -.108 -.039 -.337 .109 o ( e J -.503 -.128 -.023 -.312 .362 A s s e t s /Subs D i v e r s i t y U t i l i t y C u r r e n t F o r e i g n 1.00 B e t a .134 1.00 o l e j -.077 .385 1.00 F o r e i g n B e t a o ( e J Note: C o r r e l a t i o n s g r e a t e r t h a n .19 a r e s i g n i f i c a n t a t t h e .05 l e v e l . 119 TABLE 13 CORRELATION MATRIX OF VARIABLES Monthly Data (125 O b s e r v a t i o n s ) Log A s s e t s 1.00 / S u b s i d i a r i e s .434 1.00 D i v e r s i t y .081 .325 1.00 U t i l i t y - d u m m y .297 -.245 -.197 1.00 C u r r e n t -.501 .041 .161 -.54 1.00 F o r e i g n .268 .604 .030 -.248 .242 B e t a -.536 -.297 -.009 -.297 .335 o ( e J -.392 -.04 -.029 -.422 .296 A s s e t s /Subs D i v e r s i t y U t i l i t y C u r r e n t F o r e i g n 1.00 Be t a -.228 1.00 o ( e A ) .038 .609 1.00 F o r e i g n B e t a o ( e i ) Note: C o r r e l a t i o n s g r e a t e r t h a n .19 a r e s i g n i f i c a n t a t t h e .05 l e v e l . 120 TABLE 14 CROSS-TAB OF THE RELATIONSHIP BETWEEN BETA AND o ( e i ) o ( e A ) B e t a <0.3 <0.5 <1 <1.5 (max ( a l l ) M o n t h ly < .03 0 0 0 0 0 0 < .05 0 3 3 0 0 6 < .10 1 10 48 18 3 80 < .15 1 0 5 17 14 38 < .20 0 0 0 0 0 0 ( a l l ) 2 13 56 35 17 124 Weekly Sample < .03 3 3 5 3 0 14 < .05 5 9 33 26 9 82 < .10 0 4 16 33 12 72 < .15 0 0 2 1 5 8 < .20 0 0 0 0 0 0 ( a l l ) 8 16 56 63 26 169 121 TABLE 15 DIAGNOSTICS - NORMALITY Log Model Square Root Model Weekly d a t a (173 obs. ) C o e f f i c i e n t o f Skewness -.982 a- .258 S t a n d a r d D e v i a t i o n .184 .184 C o e f f i c i e n t o f Excess K u r t o s i s 2.524 1 1.204 1 S t a n d a r d D e v i a t i o n .367 .367 Weekly Data (169 obs.) C o e f f i c i e n t o f Skewness -.289 .425 S t a n d a r d D e v i a t i o n .186 .186 1 C o e f f i c i e n t o f Excess K u r t o s i s .299 .798 S t a n d a r d D e v i a t i o n .371 .371 1 1 I n d i c a t e s s i g n i f i c a n c e a t t h e .05 l e v e l . Note: Three of t h e f o u r o b s e r v a t i o n s d e l e t e d were i n t h e f i n a n c i a l i n d u s t r y . The f o u r t h o b s e r v a t i o n was Sun O i l Co. 122 TABLE 16 DIAGNOSTICS - NORMALITY Log Model Square Root Model Monthly Data (125 obs.) C o e f f i c i e n t o f Skewness -.905 1 -.004 S t a n d a r d D e v i a t i o n .216 .216 C o e f f i c i e n t o f Excess K u r t o s i s 3.231 1 1.567* S t a n d a r d D e v i a t i o n .429 .429 M o n t h l y Date (124 obs.) C o e f f i c i e n t o f Skewness -.424 .243 S t a n d a r d D e v i a t i o n .217 .217 C o e f f i c i e n t o f E x c e s s K u r t o s i s 1.346 1 .712 S t a n d a r d D e v i a t i o n .431 .431 x I n d i c a t e s s i g n i f i c a n c e a t t h e .05 l e v e l . Note: One o b s e r v a t i o n was d e l e t e d . T h i s f i r m , Sun O i l Company, had an u n u s u a l l y low a u d i t f e e , c o n s i d e r i n g t h e a s s e t base o f t h e company. 123 TABLE 17 CHI-SQUARE TEST FOR HETEROSCEDASTICITY T e s t Df S i g n i f M o n t h ly Data - Log Model Breusch-Pagan-Godfrey 3.949 8 .86 Harvey 10.531 8 .23 Monthly Date - Square Root Model Breusch-Pagan-Godfrey 15.794 7 .03 Harvey 14.677 7 .04 Weekly Data - Log Model Breusch-Pagan-Godfrey 3.911 8 .86 Harvey 8.21 8 .41 Weekly Date - Square Root Model Breusch-Pagan-Godfrey 24.394 7 .01 Harvey 20.834 7 .01 124 TABLE 18 RAMSEY RESET SPECIFICATION TESTS USING POWERS OF YHAT F TEST T e s t D f l Df2 S i g n i f M onthly - Log Model R e s e t ( 2 ) 1.89 1 114 .17 R e s e t O ) 1.71 2 113 .19 R e s e t ( 4 ) 1.26 3 112 .29 Mon t h l y - Square Root Model .91 1 115 .34 .93 2 114 .40 .71 3 113 .54 Weekly - Log Model R e s e t ( 2 ) 2.35 1 159 .13 R e s e t ( 3 ) 3.15 2 158 .05 R e s e t ( 4 ) 2.09 3 157 .11 Weekly - Square Root Model .023 1 160 .87 1.02 2 159 .36 .68 3 158 .57 R e s e t ( 2 ) R e s e t ( 3 ) R e s e t ( 4 ) R e s e t ( 2 ) R e s e t ( 3 ) R e s e t ( 4 ) 125 TABLE 19 Z-SCORE Log Model Square Root Model D o ( r r o ) Coef. T Coef. T Weekly Sample 0 .000 0.100 0.206 0.690 4.501 1.163 0 .000 0.200 0.571 1.373 9.396 1.777 0 .000 0.300 1.089 2.017 16.433 2.468 0 .250 0.100 0.226 2.151 3.088 2.504 0 .250 0.200 0.337 2.721 4.589 3.206 0 .250 0.300 0.407 2.991 5.688 3.609 0 .500 0.100 0.148 2.397 1.977 2.775 0 .500 0.200 0.203 2.878 2.756 3.401 0 .500 0.300 0.234 3.069 3.259 3.689 0 .750 0.100 0.108 2.492 1.442 2.885 0 .750 0.200 0.145 2.933 1.958 3.470 0 .750 0.300 0.164 3.095 2.276 3.712 Mon t h l y Sample 0 .000 0 .100 -0 .056 -0 .163 0 .140 0 .029 0 .000 0 .200 0 .074 0 .160 2 .353 0 .366 0 .000 0 .300 0 .305 0 .506 5 .852 0 .729 -0 .250 0 .100 0 .061 0 .545 1 .095 0 .761 -0 .250 0 .200 0 .111 0 .828 1 .805 1 .077 -0 .250 0 .300 0 .163 1 .039 2 .495 1 .302 -0 .500 0 .100 0 .044 0 .669 0 .738 0 .893 -0 .500 0 .200 0 .071 0 .925 1 .122 1 .180 -0 .500 0 .300 0 .098 1 .103 1 .474 1 .362 -0 .750 0 .100 0 .033 0 .718 0 .548 0 .946 -0 .750 0 .200 0 .052 0 .963 0 .809 1 .220 -0 .750 0 .300 0 .070 1 .127 1 .043 1 .383 T v a l u e s of 1.96 a r e s i g n i f i c a n t a t t h e .05 l e v e l 126 TABLE 20 PROBABILITY OF LOSS Log Model Square Root Model D o ( r m ) Coef. T Coef. T Weekly Sample 0 .000 0 .100 0.553 0.663 13.087 1 .191 0 .000 0 .200 1.495 1.332 25.647 1 .778 0 .000 0 .300 2.841 1.988 43.728 2 .463 0 .250 0 .100 0.936 1.857 16.731 2 .584 0 .250 0 .200 1.292 2.437 21.005 3 .203 0 .250 0 .300 1.531 2.864 23.883 3 .679 0 .500 0 .100 1.216 1.997 23.250 2 .919 0 .500 0 .200 1.391 2.370 24.850 3 .317 0 .500 0 .300 1.505 2.779 25.357 3 .693 0 .750 0 .100 1.916 2.106 37.632 3 .230 0 .750 0 .200 1.904 2.267 36.151 3 .381 0 .750 0 .300 1.881 2.586 33.593 3 .565 Monthly Sample 0 .000 0 .100 -0 .245 -0 .250 -0 .115 -0 .008 0 .000 0 .200 0 .115 0 .090 5 .888 0 .329 0 .000 0 .300 0 .752 0 .463 15 .271 0 .701 -0 .250 0 .100 -0 .033 -0 .047 4 .241 .0 .443 -0 .250 0 .200 0 .287 0 .414 7 .721 0 .843 -0 .250 0 .300 0 .571 0 .835 10 .361 1 .193 -0 .500 0 .100 -0 .096 -0 .077 6 .461 0 .368 -0 .500 0 .200 0 .349 0 .343 10 .809 0 .796 -0 .500 0 .300 0 .629 0 .779 12 .509 1 .209 -0 .750 0 .100 0 .398 0 .126 22 .882 0 .502 -0 .750 0 .200 0 .912 0 .426 25 .426 0 .881 -0 .750 0 .300 1 .037 0 .763 21 .935 1 .268 T v a l u e s o f 1.96 a r e s i g n i f i c a n t a t t h e .05 l e v e l 127 TABLE 21 TESTS ON BETA AND o ( e J USING WEEKLY DATA AND THE LOG MODEL Sub-sample B e t a fl(ei) Coef. T - v a l u e S i g . Coef. T - v a l u e S i g . A l l obs. 160 df .130 1.78 .08 2.19 1.34 .18 Bet a o n l y .17 2.58 .01 o ( e A ) o n l y 3.41 2.29 .02 Low 25% o l e j 32 d f .25 1.33 .19 36.68 2.18 .05 Low 35% 47 d f .25 1.4 .16 33.02 2.41 .02 H i g h 25% 33 d f .043 .38 .7 4.07 1.47 .15 High 35% 50 d f .026 .27 •8 2.66 1.23 .20 128 TABLE 22 TESTS ON BETA AND o ( e A ) USING WEEKLY DATA AND THE SQUARE ROOT MODEL Sub-sample Be t a o ( e J Coef. J T - v a l u e S i g . Coef. T-value j S i g . A l l obs. 161 df 1.50 1.43 .14 49.67 2.40 .01 B e t a o n l y 2.38 2.57 .01 o(ei.) o n l y 61.12 3.41 .001 Low 25% 33 d f 3.31 2.49 .18 138.0 1.20 .22 Low 35% 48 df 4.13 2.25 .03 229.2 2.01 .05 High 25% 34 d f .46 .292 .78 99.9 2.92 .01 H i g h 35% 51 df -.13 -.08 .94 70.02 2.90 .01 129 TABLE 23 TEST FOR CHANGE OF BETA SLOPE COEFFICIENT 1. Sample Coef. on Be t a df T - v a l u e S i g n i f . I n d i c a t o r Log Model Low 25% and High 25% .31 72 2.2 .02 Low 35% and High 35% .19 104 1.68 .10 Square Root Model Low 25% and Hig h 25% 3.63 73 3.01 .01 Low 35% and High 35% 2.24 105 1.68 .10 1 T h i s i s a t e s t o f t h e d i f f e r e n c e between t h e b e t a c o e f f i c i e n t s e s t i m a t e d u s i n g a dummy v a r i a b l e t o i n d i c a t e t h e low and h i g h samples i n a s i n g l e p o o l e d r e g r e s s i o n . I t i s e q u i v a l e n t t o a Chow t e s t . 130 TABLE 24 TESTS ON BETA AND o ( e i ) USING MONTHLY DATA AND THE LOG MODEL Sub-sample Be t a o ( e A ) Coef. T - v a l u e S i g . Coef. | T-va l u e J S i g . a l l 115 d f Be t a o n l y o ( e i ) .184 1.61 .11 .14 1.49 .14 -1.10 -.67 .33 .24 Low 25% 22 d f Low 35% 33 d f .017 .03 .36 .86 15.61 1.32 3.66 .42 High 25% 23 Hi g h 35% 35 d f .029 .19 .052 .03 5.00 1.36 2.11 .56 131 TABLE 25 TESTS ON BETA AND o ( e J USING MONTHLY DATA AND THE SQUARE ROOT MODEL Sub-sample Be t a o ( e J Coef. T - v a l u e S i g . Coef. T - v a l u e S i g . a l l 1 116 d f 2.56 1.68 .09 -8.23 -.36 B e t a o n l y 2.23 1.82 .07 o ( e i ) o n l y 13.00 .69 Low 25% 23 df 4.13 1.14 .26 27.46 .33 Low 35% 34 d f 5.14 1.61 .12 -5.36 -.06 High 25% 24 df 3.09 1.54 .14 79.21 1.17 High 35% 36 d f 3.1 1.69 .1 46.47 .78 1 S i n c e t h e r e i s some e v i d e n c e o f h e t e r o s c e d a s t i c i t y i n t h e square r o o t model t h e c o e f f i c i e n t s a r e e s t i m a t e d u s i n g W hite's H e t e r o s c e d a s t i c i t y - c o n s i s t e n t c o v a r i a n c e m a t r i x . Which i s an a p p r o p r i a t e d i a g n o s t i c f o r unknown s o u r c e s o f h e t e r o s c e d a s t i c i t y . See Judge e t . a l . 132 TABLE 26 TEST FOR CHANGE OF BETA SLOPE COEFFICIENT 1. Sample Coef. on Be t a df T - v a l u e S i g n i f . I n d i c a t o r Log Model Low 25% and High 25% .39 52 1.46 .15 Low 35% and High 35% .31 75 1.47 .14 Square Root Model Low 25% and High 25% 3.77 53 1.08 .28 Low 35% and High 35% 4.61 76 1.59 .12 1 T h i s i s a t e s t o f t h e d i f f e r e n c e between t h e b e t a c o e f f i c i e n t s e s t i m a t e d u s i n g a dummy v a r i a b l e t o i n d i c a t e t h e low and h i g h samples w i t h i n a s i n g l e p o o l e d r e g r e s s i o n . I t i s e q u i v a l e n t t o a Chow t e s t . 133 TABLE 27 DESCRIPTIVE STATISTICS USING WEEKLY DATA FOR ALL, LOW, AND HIGH SAMPLES V a r i a b l e Mean Std. Dev. Minimum Maximum T o t a l Sample (169 obs. ) log a s s e t s 19.16 1.44 16.34 22.61 •f s u b s i d i a r i e s 3.82 2.74 0 17.32 Current Assets .45 .20 .03 .83 Beta 1.04 .49 .055 2.53 o ( e i ) .054 .024 .0155 .19 Lowest 25% (42 obs.) log a s s e t s 20.16 1.34 17.31 22.61 fsubsidiaries 4.09 3.04 0 11.79 Current A s s e t s .34 .20 .05 .76 Beta .79 .43 .20 1.97 o (e^.) .031 .005 .0155 .036 Highest 25% (57 obs. ) Log a s s e t s 18.23 1.13 16.39 21.28 TT s u b s i d i a r i e s 3.07 1.58 0 7.21 Current A s s e t s .54 .17 .06 .83 Beta 1.30 .54 .31 2.53 o ( e J .09 .022 .07 .19 134 TABLE 28 DESCRIPTIVE STATISTICS USING MONTHLY DATA FOR ALL, LOW, AND HIGH SAMPLES V a r i a b l e Mean S t d . Dev. Minimum Maximum T o t a l Sample (124) Log a s s e t s 19.63 1.27 17.29 22.61 •f s u b s i d i a r i e s 4.44 3.23 0 17.32 C u r r e n t A s s e t s .43 .19 .03 .50 B e t a .96 .42 -.12 2.05 o l e j .09 .028 .036 .16 Low 25% (31 obs. ) l o g a s s e t s 20.20 1.36 17.93 22.61 / s u b s i d i a r i e s 4.24 3.36 0 11.53 C u r r e n t A s s e t s .35 .22 .05 .76 B e t a .68 .18 .34 .98 o ( e J .06 .03 .04 .07 High 25% (43 obs. ) Log a s s e t s 18.99 1.18 17.34 22.09 Vsubsidiaries 4.45 3.37 0 17.32 C u r r e n t A s s e t s .50 .20 .04 .83 B e t a 1.34 .45 -.1 2.05 o l e j .13 .01 .11 .16 135 TABLE 29 CONDITIONAL EXPECTED NEGATIVE RETURN Log Model Square Root Model D o ( r m ) Coef. T Coef. T Weekly Sample 0 .000 0 .100 -0 .622 -2 .304 -11 .154 -3 .435 0 .000 0 .200 -0 .670 -2 .588 -11 .652 -3 .750 0 .000 0 .300 -0 .647 -2 .782 -11 .038 -3 .846 -0 .250 0 .100 -0 .658 -2 .320 -11 .870 -3 .486 -0 .250 0 .200 -0 .697 -2 .585 -12 .213 -3 .765 -0 .250 0 .300 -0 .667 -2 .770 -11 .442 -3 .838 -0 .500 0 .100 -0 .707 -2 .319 -12 .880 -3 .518 -0 .500 0 .200 -0 .739 -2 .566 -13 .082 -3 .765 -0 .500 0 .300 -0 .701 -2 .745 -12 .126 -3 .822 -0 .750 0 .100 -0 .765 -2 .315 -14 .056 -3 .537 -0 .750 0 .200 -0 .791 -2 .545 -14 .130 -3 .759 -0 .750 0 .300 -0 .744 -2 .717 -12 .975 -3 .802 M o n t h l y Sample 0 .000 0 .100 -0 .137 -0 .256 -5 .054 -0 .700 0 .000 0 .200 -0 .298 -0 .625 -6 .590 -1 .063 0 .000 0 .300 -0 .371 -0 .943 -6 .816 -1 .376 -0 .250 0 .100 -0 .157 -0 .269 -5 .680 -0 .721 -0 .250 0 .200 -0 .323 -0 .631 -7 .143 -1 .076 -0 .250 0 .300 -0 .391 -0 .945 -7 .214 -1 .384 -0 .500 0 .100 -0 .180 -0 .273 -6 .521 -0 .730 -0 .500 0 .200 -0 .358 -0 .632 -7 .983 -1 .083 -0 .500 0 .300 -0 .424 -0 .943 -7 .873 -1 .391 -0 .750 0 .100 -0 .209 -0 .278 -7 .522 -0 .737 -0 .750 0 .200 -0 .402 -0 .633 -9 .009 -1 .090 -0 .750 0 .300 -0 .465 -0 .941 -8 .696 -1 .397 T v a l u e s of 1.96 a r e s i g n i f i c a n t a t t h e .05 l e v e l 136 TABLE 30 EXPECTED NEGATIVE RETURN Log Model Square Root Model D o ( r m ) Coef. T Coef. T Weekly Sample 0 .000 0 .100 0 .000 0 .200 0 .000 0 .300 -0 .250 0 .100 -0 .250 0 .200 -0 .250 0 .300 -0 .500 0 .100 -0 .500 0 .200 -0 .500 0 .300 -0 .750 0 .100 -0 .750 0 .200 -0 .750 0 .300 -1 .223 -2 .066 -1 .387 -2 .407 -1 .408 -2 .689 -1 .182 -2 .102 -1 .320 -2 .433 -1 .335 -2 .715 -1 .244 -2 .103 -1 .305 -2 .348 -1 .290 -2 .632 -1 .494 -2 .098 -1 .454 -2 .218 -1 .370 -2 .447 -22 .795 -3 .157 -24 .713 -3 .573 -24 .381 -3 .827 -22 .169 -3 .227 -23 .617 -3 .614 -23 .094 -3 .848 -24 .136 -3 .312 -24 .311 -3 .578 -22 .977 -3 .775 -29 .670 -3 .305 -28 .292 -3 .462 -25 .461 -3 .600 Monthly Sample 0 .000 0 .100 0 .015 0 .012 -7 .500 -0 .429 0 .000 0 .200 -0 .479 -0 .423 -12 .908 -0 .856 0 .000 0 .300 -0 .765 -0 .827 -14 .823 -1 .259 -0 .250 0 .100 0 .029 0 .024 -7 .634 -0 .452 -0 .250 0 .200 -0 .447 -0 .421 -12 .307 -0 .873 -0 .250 0 .300 -0 .712 -0 .831 -13 .802 -1 .266 -0 .500 0 .100 0 .027 0 .016 -9 .870 -0 .415 -0 .500 0 .200 -0 .500 -0 .388 -14 .581 -0 .846 -0 .500 0 .300 -0 .731 -0 .794 -14 .830 -1 .263 -0 .750 0 .100 -0 .566 -0 .171 -25 .796 -0 .542 -0 .750 0 .200 -1 .001 -0 .465 -26 .831 -0 .923 -0 .750 0 .300 -0 .997 -0 .782 -21 .124 -1 .302 T v a l u e s o f 1.96 a r e s i g n i f i c a n t a t t h e .05 l e v e l 137 TABLE 31 STATISTICS OF RISK MEASURES 1 Means: Weekly Monthly Z-score P r o b a b i l i t y of Loss -2.02 .0448 C o n d i t i o n a l Ex. N e g a t i v e R e t u r n -.961 (CNR) U n c o n d i t i o n a l Ex. N e g a t i v e R e t u r n -.0487 (UNR) -2.31 .0256 -.9108 -.0256 C o r r e l a t i o n M a t r i c e s Weekly Sample. Z s c o r e P r . Loss CNR UNR 1.0 .784 .837 •.719 1.0 -.917 -.985 1.0 ,979 1.0 P r . L o s s CNR UNR Z s c o r e P r . L o ss CNR UNR M o n t h l y Sample. 1.0 .803 1.0 -.899 -.98 -.781 -.99 P.Loss 1.0 .97 CNR 1.0 UNR 1 T h e s e s t a t i s t i c s a r e based upon D b e i n g s e t t o -.75 and o ( r r o ) b e i n g s e t t o .3. 138 TABLE 32 EXAMPLES OF THE RELATIONSHIP AMONG RISK MEASURES 1 Sample V a l u e s o f R e l a t e d Measures BETA Z-score Pr.LOSS CNR UNR 0.9926 0.7174 -0.8726 0.2726 -0.9105 -0.1743 0.8553 0.7035 -0.8838 0.27 -0.8975 -0.1691 1.2358 0.6932 -0.9057 0.2647 -0.9007 -0.1644 1.0617 0.3931 -1.4644 0.1365 -0.6984 -0.05 0.7528 0.4051 -1.464 0.1366 -0.6919 -0.0495 0.7283 0.4021 -1.4754 0.1343 -0.6892 -0.0483 1.2129 0.1485 -2.3379 0.0259 -0.5961 -0.0058 1.3716 0.0717 -2.3843 0.0233 -0.5945 -0.0051 0.5153 0.2259 -2.4812 0.0184 -0.5806 -0.0038 R e l a t i v e V a l u e s of R e l a t e d R i s k Measures BETA o l e j Z-score Pr.LOSS CNR UNR High High Large Large S m a l l S m a l l H i g h Low •? ? Low High •? ? ? Low Low S m a l l S m a l l Large Large 1 T h e s e were c a l c u l a t e d w i t h t h e f o l l o w i n g parameter v a l u e s : D = -.50, E ( r m ) = .15, r£ = .08, and o ( r m ) = .20 139 TABLE 33 SUMMARY OF RESULTS ON PROXY RISK MEASURES Model Weekly- Monthly Log Model Sq. r t . Model Log Model Sq. r t Model z - s c o r e s s c c P r . L oss s s c c CNR s s c c UNR s s c c s... i n d i c a t e s s i g n i f i c a n t r e s u l t s c... i n d i c a t e s c o n s i s t e n t r e s u l t s w i t h H2. 140 Appendix 1 N u m e r i c a l Examples o f Share p r i c e D e t e r m i n a t i o n L e t ex ante share p r i c e s be d e t e r m i n e d by one o f t h e f o l l o w i n g f u n c t i o n s ( i t i s assumed t h a t everyone knows w h i c h ) : t ' ( 6 . , s .) = 5 ( 6 1 + s.) i I) 1 1 t " (0 . ,s .) = 12 - 3«(2 - 6.) (2 - s, ) where, 0 . l 1 i f good event 0 i f bad event and 1 i f f s a r e f a i r 0 i f f s a r e not f a i r Assume t h e f o l l o w i n g p r o b a b i l i t i e s a r e a s s e s s e d over t h e s t a t e s : p f e ^ = I - p<e 2> = .5 p ( s ^ ) = 1 - p ( s 2 > = .8 L e t s h a r e h o l d e r s a s s e s s t h e f o l l o w i n g j o i n t d i s t r i b u t i o n : Not F a i r .8 F a i r A c c e p t ( u n q u a l i f i e d ) Not A c c e p t ( q u a l i f i e d ) .72 .08 .08 .12 .2 .80 .20 141 The r e v i s e d p o s t e r i o r b e l i e f s o v er t h e f a i r n e s s o f t h e f i n a n c i a l s t a t e m e n t s a r e : p(F |A) = .9 p(F |NA) = .4 p(NF |A) = .1 p(NF |NA) = .6 and t h e ex ante and ex post s t o c k p r i c e s a r e : tg (A) = 7.0 tg (NA) =4.5 t j * (A) = 7.05 t'Q' (NA) = 4.8 and t j = 10, t'2 = 5, t ^ = 5, t ^ = 0 t j ' = 9, ty = 6, ty = 6, ty = 0 The s h a r e h o l d e r l o s s e s a r e g i v e n by: L i a -- 0 L i r ' = 0 = 0. = 0 L 2 a -= 2.0 L 2 r = = 0 L 2 a -= 2.05 = 0 L 3 a : = 2.0 L 3 r = = 0 L3a " = 2.05 3r = 0 L 4 a -= 7.0 L 4 r = = 4.5 L 4 a = = 7.05 4b 4.8 142 Appendix 2 Mixed E q u i l i b r i u m i n the Negligence Regime In t h i s appendix a mixed e q u i l i b r i u m i s c a l c u l a t e d f o r the case when the a u d i t o r has a negligence defense. I t i s assumed t h a t the c o s t c o n d i t i o n s are such t h a t the a u d i t o r would l i k e t o use the hig h a u d i t i n t e n s i t y , but as shown i n the t e x t , t h i s i s not a pure s t r a t e g y e q u i l i b r i u m . The a u d i t o r i s assumed to randomize between A 2 and A^. The shareholder randomizes between SH^ and SH^. Let p(A 2> = 1 - p(A^) and p(SHj.) = 1 - pCSH^) be the p r o b a b i l i t i e s t h a t the p l a y e r s p l a y a g i v e n pure s t r a t e g y . A l s o note t h a t the s h a r e h o l d e r s ' randomization i s e q u i v a l e n t t o always suing when t ^ oc c u r s , never suing when t ^ occurs and randomizing over t 2 and t ^ . The a u d i t o r has the f o l l o w i n g m i n i m i z a t i o n problem: min p(A 2> [ c ( I ) p ( s ^ | z 2 , q^) + h(q^) ] p( A 2 ) + (1 - p ( A 2 ) ) p(SH 5> (D 2 ( p ( t 2 ) + P ( t 3 ) ) + D 4 p ( t 4 ) The f i r s t order c o n d i t i o n y i e l d s the f o l l o w i n g r e s u l t : p(SH 5) = c ( I ) p ( s 1 ) z 2 , q 1 ) + h f q ^ - D 4 p ( t 4 > D 2 p ( t 2 ) + D 3 P<t 3) The s h a r e h o l d e r s have the f o l l o w i n g maximization problem c o n d i t i o n a l upon o b s e r v i n g t 2 or t 3 : max p( SH- ) p(SH 5) (D 2 - w) p(Aj.) - w p(A 2> The f i r s t order c o n d i t i o n y i e l d s : p ( A 2 ) = ( D 2 - w ) / D 2 S u b s t i t u t i n g these e q u i l i b r i u m v a l u e s i n t o the a u d i t o r ' s c o s t 143 f u n c t i o n y i e l d s t h e e x p e c t e d c o s t o f t h e mixed s t r a t e g y which i s e q u a l t o : c ( I ) p ( s ^ J z 2 / ) + h(q^) I t i s i n t e r e s t i n g t o note t h a t t h e a u d i t o r a c h i e v e s an e x p e c t e d c o s t which i s e q u a l t o t h e c o s t o f t h e h i g h a u d i t i n t e n s i t y , but t h a t i t i s done t h r o u g h a mixed s t r a t e g y . 144 Appendix 3 C a l c u l a t i n g C o n d i t i o n a l E x p ected L o s s e s Assuming t h e r e t u r n i s d i s t r i b u t e d n o r m a l l y , n ( E r ^ , o ( r ^ ) ) , t h e n t h e e x p e c t e d l o s s e q u a l s o ( r i ) ( 2TT ) .5 f D 1 J V G X P - 2 r i - E r i o ( r . ) l d r . A l . l L e t X i be d e f i n e d a s : x . l ( r . - E r . ) / o ( r . ) l i l t h e n A l . ) i s e q u i v a l e n t t o : k ( 2TT ) -.5 .D' 1 2 x. • exp -( z »x. ) dx. I . c 2 I I A2. ) where D' = (D - Er^) / o ( r ^ ) . and k, a n o r m a l i z i n g c o n s t a n t , i s e q u a l t o 1 / ( N(D) - N (-°») ). N o t i n g t h a t N(») i s t h e normal c u m u l a t i v e d e n s i t y f u n c t i o n . T h i s f u n c t i o n i s e a s i l y i n t e g r a t e d . The r e s u l t i s : -k m(x.) l D' = - m(D') / N(D) A 3 . ) where m i n d i c a t e s a s t a n d a r d normal d e n s i t y f u n c t i o n , and N(-°<>) i s s e t t o z e r o . 145 B i b l i o g r a p h y A r e n s , A l v i n , James Loebbecke, and W. M o r l e y Lemon. Auditing and Integrated Approach, Canadian t h i r d e d i t i o n . S c a r b o r o u g h , O n t a r i o : P r e n t i c e - H a l l , 1984. American I n s t i t u t e o f CPA's. Statements on Auditing Standards. AICPA, no. 39 (1981). , Statements on Auditing Standards. AICPA, no. 47 (1983). A n t l e , R i c k . " The A u d i t o r as an Economic Agent." Journal of Accounting Research 20, no. 2 P a r t I I , (Autumn 1982):503-527. A r n e t t , H a r o l d E., and P a u l Danos. CPA Firm V i a b i l i t y : A Study of Major Environmental Factors A f f e c t i n g Firms of Various Sizes and C h a r a c t e r i s t i c s . Ann A r b o r , M i c h i g a n : U n i v e r s i t y o f M i c h i g a n , 1979. Baiman, S t a n l e y , John H Evans I I I , and James N o e l . " O p t i m a l C o n t r a c t s w i t h a U t i l i t y M a x i m i n z i n g A u d i t o r . " Journal of Accounting Research 25, no. 2, (Autumn 1987): 217-244. Beaver, W i l l i a m , P a u l K e t t l e r , and Myron S c h o l e s . " The A s s o c i a t i o n between Market Determined and A c c o u n t i n g Determined R i s k Measures." The Accounting Review, (October 1970): 654-682. Bowman, R. "The T h e o r e t i c a l R e l a t i o n s h i p Between S y s t e m a t i c R i s k and F i n a n c i a l V a r i a b l e s , " Journal of Finance, (June 1979). B r u m f i e l d , C.A., R. E l l i o t , and P. J a c o b s o n . " B u s i n e s s R i s k and t h e A u d i t P r o c e s s . " Journal of Accountancy, ( A p r i l 1985): 60-68. Canadian I n s t i t u t e o f C h a r t e r e d A c c o u n t a n t s . The Extent of Audit Testing. T o r o n t o : CICA, 1980. Causey, D e n z i l J r . Duties and L i a b i l i t i e s of Public Accountants. Homewood. I I . : Dow J o n e s - I r w i n , 1979. C o l l i n s , S. H. " P r o f e s s i o n a l L i a b i l i t y : The S i t u a t i o n Worsens," The Journal of Accountancy (1985). C o n i n e , Thomas E., J r . "On t h e T h e o r e t i c a l R e l a t i o n s h i p between B u s i n e s s R i s k and S y s t e m a t i c R i s k . " Journal of Business Finance and Accounting 9, no. 2 (1982): 199-205. 146 C u s h i n g , B a r r y E., and James K. Loebbecke. " A n a l y t i c a l Approaches t o A u d i t R i s k : A Survey and A n a l y s i s . " Auditing a Journal of Practice & Theory 3, no. 1 ( F a l l 1983): 23-41. DeAngelo, L i n d a E. " A u d i t o r S i z e and A u d i t Q u a l i t y . " Journal of Accounting and Economics 3, (1981): 183-199. DeJong, Douglass V. " C l a s s - A c t i o n P r i v i l e g e s and C o n t i n g e n t L e g a l Fees: I n v e s t o r and Lawyer I n c e n t i v e s t o L i t i g a t e and t h e E f f e c t on A u d i t Q u a l i t y . " Journal of Accounting and Public P o l i c y 4, (1985): 175-200. Dopuch, N., and Dan S i m u n i c . " C o m p e t i t i o n i n A u d i t i n g : An Assessment." Fourth Symposium on Auditing Research. U n i v e r s i t y of I l l i n o i s , 1982, 401-450. Dopuch, N i c h o l a s , R o b e r t W. H o l t h a u s e n , and R i c h a r d W. L e f t w i c h . " P r e d i c t i n g A u d i t Q u a l i f i c a t i o n s w i t h F i n a n c i a l and Market V a r i a b l e s . " The Accounting Review 62, no. 3 ( J u l y 1987): 431-454. Dugan, M i c h a e l T., and K e i t h S h r i v e r . "An E x a m i n a t i o n o f t h e A s s o c i a t i o n Among t h e R e a l - A s s e t R i s k D e t e r m i n a n t s of S y s t e m a t i c R i s k and t h e I n c i d e n c e o f R e c e i p t o f U n c e r t a i n t y Q u a l i f i c a t i o n s . " U n p u b l i s h e d w o r k i n g paper, A r i z o n a S t a t e U n i v e r s i t y , 1987. Ebke, Werner. " I n S e a r c h o f A l t e r n a t i v e s : C omparative R e f l e c t i o n s on C o r p o r a t e Governance and The Independent A u d i t o r ' s R e s p o n s i b i l i t e s . " Northwestern University Law Review 79, no. 4 (November 1984): 663-720. E l l i o t t , R o b e r t K., and John Rogers. " R e l a t i n g S t a t i s t i c a l Sampling t o A u d i t O b j e c t i v e s . " Journal of Accountancy, ( J u l y 1972): 47-55. F e l i x , W. and W. R. Kinney J r . "Research i n t h e A u d i t o r ' s O p i n i o n F o r m u l a t i o n P r o c e s s : S t a t e o f t h e A r t . " The Accounting Review, ( A p r i l 1982): 245-271. F r a n c i s , J e r e R. "The E f f e c t o f A u d i t F i r m S i z e on A u d i t P r i c e s , a Study o f t h e A u s t r a l i a n Market." Journal of Accounting and Economics 6, (1984): 133-151. , and D a n i e l T. Simon. "A T e s t of A u d i t P r i c i n g i n t h e S m a l l - C l i e n t Segment of t h e U.S. A u d i t Market." The Accounting Review, ( J a n u a r y 1987): 145-157. F i r t h , M i c h a e l . "An A n a l y s i s o f A u d i t Fees and T h e i r D e t e r m i n a n t s i n New Z e a l a n d . " Auditing: A Journal of Practice & Theory 4, no. 2 ( S p r i n g 1985): 23 -37. 147 Grossman, S. J . , and Joseph S t i g l i t z . "The I m p o s s i b i l i t y o f I n f o r m a t i o n a l l y E f f i c i e n t M a r k e t s . " The American Economic Review, (June 1980): 393-408. Hamada, R. "The E f f e c t o f t h e Fi r m ' s C a p i t a l S t r u c t u r e on t h e S y s t e m a t i c R i s k o f Common S t o c k s . " Journal of Finance, (May 1972): 435-452. Herman, Edward S. Corporate Control, Corporate Power. Cambridge: Cambridge U n i v e r s i t y P r e s s , 1981. K e l l o g g , Robert L. " A c c o u n t i n g A c t i v i t i e s , S e c u r i t y P r i c e s , and C l a s s A c t i o n L a w s u i t s . " Journal of Accounting and Economics, (Dec. 1984): 185-204. Kennedy, P e t e r . A Guide to Econometrics, 2d ed. Cambridge: MIT P r e s s , 1985. Ki n n e y , W., J r . "A D e c i s i o n Theory Approach t o t h e Sampling Problem i n A u d i t i n g . " Journal of Accounting Research supplement, ( S p r i n g 1975): 117-132. Lev, Baruch. "On t h e A s s o c i a t i o n between O p e r a t i n g Leverage and R i s k . " Journal of Financial and Quantitative Analysis, (September 1974): 627-641. Ma n d e l k e r , G., and G. Rhee. "The Impact o f t h e Degrees o f O p e r a t i n g and F i n a n c i a l Leverage on S y s t e m a t i c R i s k o f Common S t o c k . " Journal of Financial and Quantitative Analysis, (March 1984): 45-57. Minnow, Newton. " A c c o u n t a n t s ' L i a b i l i t y and t h e L i t i g a t i o n E x p l o s i o n . " The Journal of Accountancy, 1984. Moore, G l o r i a , and D a n i e l B. T h o r n t o n . "A Model o f A u d i t Fee D e t e r m i n a n t s . " U n i v e r s i t y o f Tor o n t o F a c u l t y o f Management Working Paper, J u l y 1987. O s t l i n g , P a u l J . "Under t h e S p r e a d i n g C h e s t n u t Tree: A c c o u n t a n t s ' L e g a l L i a b i l i t y - - A H i s t o r i c a l P e r s p e c t i v e . " i n t h e Proceedings of the 1986 Touche Ross University of Kansas Symposium on Auditing Problems. U n i v e r s i t y of Kansas, 1986. Pal m r o s e , Zoe-Vonna. " A u d i t Fees and A u d i t o r S i z e F u r t h e r E v i d e n c e . " Journal of Accounting Research, ( S p r i n g 1986): 97-110. . " L i t i g a t i o n and Independent A u d i t o r s : The R o l e o f B u s i n e s s F a i l u r e s and Management Fr a u d . " Auditing: A Journal of Practice & Theory, ( S p r i n g 1987): 90-103. 148 . "An A n a l y s i s o f A u d i t o r L i t i g a t i o n and A u d i t S e r v i c e Q u a l i t y . " The Accounting Review 63, ( J a n u a r y 1988): 55-73. P r o s s e r , W i l l i a m . Law of Torts 4th ed. S t . P a u l : West P u b l i s h i n g Company, 1971. R o t h s c h i l d , M. and S t i g l i t z , J.E. " I n c r e a s i n g R i s k . I : A D e f i n i t i o n . " Journal of Economic Theory 2, (1970): 225-243. R u b i n s t e i n , M. "A Mean-Variance S y n t h e s i s o f C o r p o r a t e F i n a n c e Theory." Journal of Finance, (March 1973): 167-181. S t . P i e r r e , K., and J . Anderson. "An A n a l y s i s o f the F a c t o r s A s s o c i a t e d w i t h L a w s u i t s A g a i n s t P u b l i c A c c o u n t a n t s . " The Accounting Review 59, no. 2 ( A p r i l 1984): 242-263. S c h o l e s , M., and J . W i l l i a m s . " E s t i m a t i n g B e t a s From Non-synchronous Data." Journal of Financial Economics, (December 1977): 309-327. S c o t t , W. R. "A B a y e s i a n Approach t o A s s e t V a l u a t i o n and A u d i t S i z e . " Journal of Accounting Research 11, no. 2 (Autumn 1973): 304-330. . " A u d i t i o r s ' L o ss F u n c t i o n s I m p l i c i t i n Consumption Investment Models." Journal of Accounting Research supplement, (1975): 98-117. . "The S t a t e o f t h e A r t o f Academic R e s e a r c h i n A u d i t i n g . " Journal of Accounting L i t e r a t u r e 3, ( S p r i n g 1984): 153-200. Shank, J . and R. Murdock. " C o m p a r a b i l i t y i n t h e A p p l i c a t i o n of R e p o r t i n g S t a n d a r d s : Some F u r t h e r E v i d e n c e . " The Accounting Review, (October 1978): 824-835. Simon, D a n i e l T. "The A u d i t S e r v i c e s Market: A d d i t i o n a l E m p i r i c a l E v i d e n c e . " Auditing: A Journal of Practice & Theory 5, no. 1 ( F a l l 1985): 71-79. S i m u n i c , Dan A. "The P r i c i n g o f A u d i t S e r v i c e s : Theory and E v i d e n c e s . " Journal of Accounting Research 18, no. 1 ( S p r i n g 1980): 161-190. , and M i c h a e l S t e i n . Product D i f f e r e n t i a t i o n in Auditing: Auditor Choice in the Market for Unseasoned New Issues. Research Monograph No. 13. The Canadian C e r t i f i e d G e n e r a l A c c o u n t a n t s ' R e s e a r c h F o u n d a t i o n , 1987. , and . " A u d i t R i s k i n a C l i e n t P o r t f o l i o C o n t e x t . " U n p u b l i s h e d w o r k i n g paper, The U n i v e r s i t y o f B r i t i s h C o lumbia, June 1988. 149 W h i t e , H. "A H e t e r o s c e d a s t i c i t y - C o n s i s t e n t C o v a r i a n c e M a t r i x E s t i m a t o r and a D i r e c t T e s t f o r H e t e r o s c e d a s t i c i t y , " Econometrica 48, (1980): 817-838. Wh i t e , K.J. " SHAZAM: A G e n e r a l Computer Program f o r E c o n o m e t r i c Methods," American S t a t i s t i c i a n 41, no.1 ( F e b r u a r y 1987): 80. 150 

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