UBC Theses and Dissertations

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UBC Theses and Dissertations

A decentralized model for loanable fund allocations in commercial banks Leung, Kwok Ki 1985

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A DECENTRAL IZED MODEL FOR LOANABLE FUND ALLOCATIONS IN COMMERCIAL BANKS By KWOK KI LEUNG B . B . A . , The U n i v e r s i t y o f NEW BRUNSWICK, 1983 A THESIS SUBMITTED IN P A R T I A L F U L F I L L M E N T OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF S C I E N C E (BUSINESS ADMINISTRATION) in THE FACULTY OF GRADUATE STUDIES THE FACULTY OF COMMERCE AND BUSINESS ADMINISTRATION We a c c e p t t h i s t h e s i s a s c o 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 B R I T I S H COLUMBIA J u n e 1985 Q KWOK KI L E U N G , 1 9 8 5 . I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e h e a d o f my d e p a r t m e n t o r by h i s o r h e r r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f O0hf\EfiCh. Aft ft tiOSMl&S ASMI/il, The U n i v e r s i t y o f B r i t i s h C o l u m b i a 1956 Main M a l l V a n c o u v e r , C a n a d a V6T 1Y3 D a t e " J img i i ABSTRACT T h i s t h e s i s p r o p o s e s a d e c e n t r a l i z e d p r o c e d u r e f o r o p t i m a l a l l o c a t i o n o f a s s e t s i n l o a n d i v i s i o n s w i t h i n c o m m e r c i a l b a n k s ; s i m u l a t i o n r u n s o f t h e p r o c e d u r e d e m o n s t r a t e t h e f e a s i b i l i t y o f s u c h an e s t a b l i s h m e n t i n c o m m e r c i a l b a n k s . The d e c e n t r a l i z e d p r o c e d u r e c a n n o t o n l y r e d u c e i n f o r m a t i o n i n p u t s o f t h e a s s e t a l l o c a t i o n s y s t e m , b u t a l s o p r o v i d e a s y s t e m a t i c p r o c e d u r e f o r e s t i m a t i o n s o f t h e c o s t o f f u n d s a nd t h e c o s t o f r i s k u s e d i n t h e p r o f i t a b i l i t y a n a l y s i s . The s i m u l a t i o n r e s u l t s a l s o s u g g e s t t h a t t h e a p p r o p r i a t e p r i c e p a i d f o r t h e f u t u r e c u s t o m e r r e l a t i o n s h i p s s h o u l d v a r y a c c o r d i n g t o t h e l e v e l o f l o a n a b l e f u n d s a v a i l a b l e t o t h e bank. M o r e o v e r , t h e s i m u l a t i o n s r e v e a l t h a t t h e i n t e r a c t i o n o f r i s k w i t h i n a bank i s v e r y c o m p l i c a t e d a n d p o i n t o u t t h e need f o r e s t a b l i s h i n g some s o r t o f p r o c e d u r e s t o t a k e i n t o a c c o u n t t h e s e i n t e r a c t i o n s . i i i TABLE OF CONTENTS T i t l e page i A b s t r a c t i i T a b l e o f c o n t e n t s i i i L i s t o f t a b l e s i v L i s t o f f i g u r e s v A c k n o w l e d g m e n t s v i 1 . I n t r o d u c t i o n 1 2. R e v i e w o f r e s e a r c h 6 3. P r o f i t a b i l i t y i n d e x 3.1 C a l c u l a t i o n a nd c o n t r i b u t i o n o f p r o f i t a b i l i t y i n d e x 13 3.2 I s s u e s o f p r o f i t a b i l i t y i n d e x 16 4. C o m p a r i s o n o f r o l e s o f d e p a r t m e n t s 4.1 O b j e c t i v e a n d c o n s t r a i n t s 21 4.2 The r o l e s o f v a r i o u s d e p a r t m e n t s 4.2.1 i n c e n t r a l i z e d e n v i r o n m e n t 23 4.2.2 i n d e c e n t r a l i z e d e n v i r o n m e n t 25 5. The m o d e l 5.1 D e v e l o p m e n t o f t h e m o d e l 28 5.2 S o l v i n g t h e model i n a c e n t r a l i z e d e n v i r o n m e n t 38 5.3 S o l v i n g t h e model i n a d e c e n t r a l i z e d e n v i r o n m e n t 40 6. S i m u l a t i o n s a n d t h e i n t e r p r e t a t i o n s 6.1 T e s t i n g t h e f e a s i b i l i t y o f t h e model 46 6.2 T e s t i n g t h e e f f e c t o f f u t u r e c u s t o m e r r e l a t i o n s h i p s on l o a n p r i c i n g 52 6.3 T e s t i n g t h e i m p a c t o f r i s k t i g h t e n i n g on l o a n a b l e f u n d a l l o c a t i o n s 56 7. C o n c l u s i o n 63 B i b l i o g r a p h y 65 A p p e n d i x 1 The s i m u l a t i o n p r o g r a m 67 A p p e n d i x 2 D a t a s e t s f o r t h e s i m u l a t i o n s 78 A p p e n d i x 3 S i m u l a t i o n r e s u l t s 90 A p p e n d i x 4 C a l c u l a t i o n o f t h e p o r t f o l i o r i s k ..... 99 i v L i s t o f t a b l e s p a g e T a b l e I V a l u e o f t h e c o s t o f f u n d s a nd t h e r i s k f a c t o r 49 T a b l e I I V a l u e o f t h e c o s t o f f u n d s a n d t h e r i s k f a c t o r 49 T a b l e I I I D i s t r i b u t i o n o f l o a n a b l e f u n d s ( f r a c t i o n ) 50 T a b l e I V D i s t r i b u t i o n o f l o a n a b l e f u n d s ( f r a c t i o n ) 50 T a b l e V D i s t r i b u t i o n o f l o a n a b l e f u n d s 51 T a b l e VI D i s t r i b u t i o n o f l o a n a b l e f u n d s 51 T a b l e V I I A v e r a g e i n t e r e s t r a t e s and a v e r a g e p r e s e n t v a l u e o f c u s t o m e r r e l a t i o n s h i p s 53 T a b l e V I I I The r e l a t i o n s h i p b e t ween c u s t o m e r r e l a t i o n s h i p and i n t e r e s t r a t e : l o a n t y p e 2 54 T a b l e I X The r e l a t i o n s h i p b e t ween c u s t o m e r r e l a t i o n s h i p a n d i n t e r e s t r a t e : l o a n t y p e 3 54 T a b l e X Movements o f l o a n a b l e f u n d s ( D a t a s e t 1; h i g h v a r i a n c e l o a n ) 59 T a b l e XI Movements o f l o a n a b l e f u n d s ( D a t a s e t 1; medium v a r i a n c e l o a n ) 59 T a b l e X I I Movements o f l o a n a b l e f u n d s ( D a t a s e t 2; h i g h v a r i a n c e l o a n ) 60 T a b l e X I I I Movements o f l o a n a b l e f u n d s ( D a t a s e t 2; medium v a r i a n c e l o a n ) 60 V L i s t o f f i g u r e s F i g u r e 1.1 A c e n t r a l i z e d e n v i r o n m e n t f o r l o a n a b l e f u n d a l l o t m e n t 4 F i g u r e 1.2 A d e c e n t r a l i z e d e n v i r o n m e n t f o r l o a n a b l e f u n d a l l o t m e n t 5 F i g u r e 3.1 D a t a f o r t h e c a l c u l a t i o n o f p r o f i t a b i l i t y i n d e x .... 14 F i g u r e 3.2 C a l c u l a t i o n o f t h e p r o f i t a b i l i t y i n d e x 15 v i A c k n o w l e d g m e n t s F o r t h e c o m p l e t i o n o f t h i s t h e s i s , I am d e e p l y i n d e b t e d t o D r . R o b e r t J o n e s , C h a i r m a n o f t h e T h e s i s S u p e r v i s o r y C o m m i t t e e , who p r o v i d e d c o n s t a n t g u i d a n c e a n d v a l u a b l e a d v i c e s t h r o u g h o u t my w o r k . I must a l s o e x p r e s s my a p p r e c i a t i o n t o D r . R o n a l d G i a m m a r i n o a n d D r . L a w r e n c e J o n e s f o r t h e i r a d v i c e s and a s s i s t a n c e w i t h t h i s t h e s i s . 1 1. INTRODUCTION T h i s t h e s i s p r o p o s e s a d e c e n t r a l i z e d p r o c e d u r e f o r o p t i m a l a l l o c a t i o n o f a s s e t s i n l o a n d i v i s i o n s w i t h i n a c o m m e r c i a l bank. T h i s d e c e n t r a l i z e d m o d e l i n t e g r a t e s t h e t e c h n i q u e of p r o f i t a b i l i t y a n a l y s i s d e v e l o p e d d u r i n g t h e 70s w i t h t h e o b j e c t i v e o f p r o f i t m a x i m i z a t i o n f o r c o m m e r c i a l bank o p e r a t i o n s . D u r i n g t h e p a s t 25 y e a r s c o m m e r c i a l b a n k i n g h a s u n d e r g o n e c o n s i d e r a b l e c h a n g e : l i f t i n g o f r e g u l a t i o n s on a s s e t s c o m p o s i t i o n , r e m o v a l of i n t e r e s t r a t e c e i l i n g s , emergence o f new r i v a l s , i n c r e a s e d v o l a t i l i t y o f i n t e r e s t r a t e movement. A t t h e same t i m e c o m m e r c i a l b a n k s have a d o p t e d a new p h i l o s o p h y t o w a r d t h e i r o p e r a t i o n s . P o r t e r [ 1 9 6 1 ] p o i n t e d o u t t h a t t h e o b j e c t i v e o f p r o f i t m a x i m i z a t i o n was n o t i n t r o d u c e d t o b a n k s u n t i l t h e e a r l y 6 0 s . T h e r e a f t e r , p r o f i t m a x i m i z a t i o n f o r c o m m e r c i a l bank o p e r a t i o n h a s become n o t o n l y t h e p r i m e o b j e c t i v e o f b a n k s i n t h e f r e e w o r l d b u t a l s o t h e f o c u s o f r e s e a r c h i n a c a d e m i c c i r c l e s . Numerous p r o f i t m a x i m i z a t i o n m o d e l s h a v e been d e v e l o p e d i n t h e p a s t 25 y e a r s ; a r e v i e w o f some of them c a n be f o u n d i n C h a p t e r Two. I n o r d e r t o a d a p t t o new e n v i r o n m e n t s and c o m p e t i t i o n , b a n k s h a v e d e v e l o p e d new o p e r a t i o n s a n d t e c h n i q u e s t o i m p r o v e t h e i r p e r f o r m a n c e ; among t h e s e i s t h e t e c h n i q u e of p r o f i t a b i l i t y a n a l y s i s w h i c h was d e v e l o p e d i n t h e e a r l y 7 0 s . T h i s t e c h n i q u e h a s p r i m a r i l y s e r v e d a s an i n f o r m a t i o n t o o l f o r i d e n t i f y i n g t h e s o u r c e o f p r o f i t s a n d t h e amount o f p r o f i t e a c h s o u r c e c o n t r i b u t e s . A t h o r o u g h s t u d y o f t h e c u r r e n t d e v e l o p m e n t and m a j o r i s s u e s of p r o f i t a b i l i t y a n a l y s i s c a n be f o u n d i n C h a p t e r 2 T h r e e . F u r t h e r m o r e , we w i l l s e e t h a t i n a d e c e n t r a l i z e d e n v i r o n m e n t ( s e e F i g u r e 1.2) p r o f i t a b i l i t y a n a l y s i s c a n be u t i l i z e d a s an a c t i v e component — a b a s i c t o o l f o r e v a l u a t i n g l o a n a p p l i c a t i o n s by l o a n d i v i s i o n s -- i n t h e o p e r a t i o n o f o p t i m a l a s s e t s a l l o c a t i o n i n c o m m e r c i a l b a n k s . A c e n t r a l i z e d e n v i r o n m e n t f o r a s s e t a l l o c a t i o n , s u c h a s t h a t i l l u s t r a t e d i n F i g u r e 1.1, i s r e q u i r e d t o i m p l e m e n t most o f t h e m o d e l s o f p r o f i t m a x i m i z a t i o n d e v e l o p e d i n t h e 60s and t h e 7 0 s . On t h e s u r f a c e , t h i s d o e s n o t seem t o be t o o g r e a t a r e q u i r e m e n t f o r a b a n k ; h o w e v e r , i n o r d e r t o e x e c u t e t h e s e o p t i m i z a t i o n m o d e l s , t h e r e a r e numerous p i e c e s o f i n f o r m a t i o n t h a t must be e f f e c t i v e l y a n d e f f i c i e n t l y t r a n s m i t t e d t o t h e c e n t r a l p l a n n i n g g r o u p . As s e e n i n F i g u r e 1.1, many p i e c e s o f i n f o r m a t i o n must f l o w f r o m t h e l o a n d i v i s i o n s , t h e a c c o u n t i n g g r o u p , a n d t h e a s s e t s / l i a b i l i t i e s c o m m i t t e e t o t h e l o a n p l a n n i n g g r o u p b e f o r e t h e c e n t r a l i z e d o p t i m i z a t i o n m o d e l s c a n be e x e c u t e d . O t h e r p r o b l e m s a s s o c i a t e d w i t h t h e s e m o d e l s a r e t h e i r l a c k o f f l e x i b i l i t y a n d t h e i r i n a b i l i t y t o a d j u s t t o new e n v i r o n m e n t s ; t h e e f f e c t i v e n e s s o f t h e s e m o d e l s d e p e n d s h e a v i l y on t h e a c c u r a c y o f f o r e c a s t i n g o v e r t h e p l a n n i n g h o r i z o n . F o r most m o d e l s , a d j u s t m e n t s c a n n o t be "made o r a r e t o p c o s t l y t o be made w i t h i n t h e p l a n n i n g h o r i z o n once t h e d e c i s i o n i s s e t . I n l i g h t o f t h e s e m a j o r i m p e d i m e n t s , t h i s t h e s i s p r o p o s e s a new t e c h n i q u e t o s o l v e t h e a s s e t s a l l o c a t i o n p r o b l e m f o r c o m m e r c i a l b a n k s . F i g u r e 1.2 i l l u s t r a t e s a d e c e n t r a l i z e d e n v i r o n m e n t f o r a s s e t a l l o c a t i o n among l o a n d i v i s i o n s w h i c h i s c o n s i s t e n t w i t h 3 t h e m o d el p r o p o s e d h e r e . The most o b v i o u s a d v a n t a g e s o f o u r m o d e l a r e t h e r e d u c t i o n i n t h e n e e d f o r i n f o r m a t i o n f l o w s and t h e s i m p l i f i c a t i o n o f t h e t a s k o f t h e l o a n p l a n n i n g g r o u p . I n t u r n , t h i s a l l o w s g r e a t e r f l e x i b i l i t y and l o w e r c o s t . The o b j e c t i v e a n d c o n s t r a i n t s o f t h e m o d e l a r e d i s c u s s e d i n C h a p t e r F o u r a l o n g w i t h c o m p a r i s o n s o f t h e r o l e s o f t h e v a r i o u s d e p a r t m e n t s i n t h e c e n t r a l i z e d and t h e d e c e n t r a l i z e d e n v i r o n m e n t s . The c o n s t r u c t i o n o f t h e t h e o r e t i c a l m o d e l i s d i s c u s s e d i n C h a p t e r F i v e , a n d a d e c o m p o s i t i o n a l p r o c e d u r e i s e m p l o y e d t o s o l v e t h e m o d e l . The p r o f i t a b i l i t y a n a l y s e s a r e i n d i s p e n s a b l e t o t h e d e c o m p o s i t i o n a l p r o c e d u r e : w h i l e t h e l o a n a b l e f u n d demands of d i f f e r e n t d i v i s i o n s a r e d e t e r m i n e d by t h e r e s u l t o f t h e a n a l y s e s , t h e i n p u t s of t h e a n a l y s e s -- c o s t of f u n d s and r i s k s — a r e a d j u s t e d t o r e f l e c t t h e t o t a l amount o f l o a n a b l e f u n d s and t h e l e v e l o f t h e maximum a c c e p t a b l e l o a n p o r t f o l i o r i s k . I n C h a p t e r S i x , s i m u l a t i o n t e c h n i q u e s a r e u s e d t o t e s t t h e f e a s i b i l i t y o f t h e p r o p o s e d d e c e n t r a l i z e d p r o c e d u r e a n d i t s i n t e r - r e l a t i o n s h i p w i t h l o a n p r i c i n g d e c i s i o n s . The f l e x i b i l i t y a n d a d a p t a b i l i t y o f t h i s new a p p r o a c h i s a l s o d e m o n s t r a t e d i n t h i s c h a p t e r . f i g u r e 1 . 1 4 g o v e r n m e n t r e g u l a t i o n s A S S E T S / L I A B I L I T I E S COMMITTEE l o a n d i s t r i b u t i o n d e c i s i o n s c o n s t r a i n t c o n d i t i o n s LOAN PLANNING GROUP An o p t i m i z a t i o n m odel u s e d t o d e t e r m i n e t h e l o a n m i x m a r g i a n l a n a l y s i s ACCOUNTING GROUP on d i v i s i o n s i ) l o a n demands i i ) l o a n p r i c i n g c o n d i t i o n s i i i ) r i s k e x p o s u r e l o a n d i v i s i o n p e r f o r m a n c e d a t a l o a n a b l e f u n d a l l o t m e n t d e c i s i o n i LOAN D I V I S I O N S P . I . i s u s e d t o a n a l y s e l o a n s ; P . I . m a i n l y s e r v e s a s a i n f o r m a t i o n t o o l . I l o a n p r i c i n g i I c r e d i t s c o r i n g e x t e r n a l f a c t o r s A CENTRALIZED ENVIRONMENT FOR LOANABLE FUNDS ALLOTMENT f i g u r e 1 . 2 5 g o v e r n m e n t r e g u l a t i o n s A S S E T S / L I A B I L I T I E S COMMITTEE i ) l o a n d i s t r i b u t i o n d e c i s i o n s THE MODEL d i v i s i o n a l " s t a t i s t i c s " ACCOUNTING GROUP i ) max. p o r t . r i s k . A i i ) l o a n f u n d s LOAN PLANNING GROUP A d j u s t : i ) c o s t o f f u n d s , X i i i ) r i s k f a c t o r , S\z i ) i i ) l o a n a b l e f u n d s r e q u e s t s s e n s i t i v i t i e s o f l o a n a b l e f u n d r e q u e s t s w . r . t . c h a n g e s i n A | a n d A2. i ) c o s t o f f u n d s i i ) r i s k f a c t o r LOAN D I V I S I O N S P . I . i s u s e d t o e v a l u a t e l o a n s ; P . I . i s a n a c t i v e c o m p o n e n t f o r a s s e t a l l o c a t i o n . 1 l o a n c r e d i t p r i c i n g s c o r i n g l o a n d i v i s i o n a l p e r f o r m a n c e d a t a e x t e r n a l f a c t o r s A C E N T R A L I Z E D ENVIRONMENT FOR LOANABLE FUNDS ALLOTMENT 6 2 REVIEW OF RESEARCH S i n c e e a r l y 60s many new d e v e l o p m e n t s h a v e o c c u r r e d i n t h e a r e a o f c o m m e r c i a l bank management. B a n k s h a v e become more a g g r e s s i v e i n many a s p e c t s . I n t h e a r e a o f a s s e t management, a m a j o r b r e a k t h r o u g h h a s t a k e n p l a c e . The f a l l i n g o f t h e a c c o m m o d a t i o n d o c t r i n e , w h i c h m a i n t a i n s t h a t bank l o a n a l l o c a t i o n s h o u l d be d e t e r m i n e d s o l e l y by demands o f t h e b o r r o w e r s , h a s l e d t o v i g o r o u s s t u d i e s o f bank l o a n p o r t f o l i o management. T h e s e s t u d i e s a l l u s e some' n o t i o n 5 o f p r o f i t m a x i m i z a t i o n a s t h e p r i m a r y o b j e c t i v e o f t h e b a n k . Many o f t h e f o l l o w i n g s t u d i e s h a v e a d a p t e d t h e m e r i t a n d i n s p i r a t i o n o f e a r l y w o r k s o f T o b i n , M a r k o w i t z , P o r t e r , a nd C h a m b e r s . The model d e v e l o p e d by Chambers a n d C h a r n e s [ 1 9 6 1 ] s e l e c t s a m i x o f bank a s s e t s — c a s h , g o v e r n m e n t s e c u r i t i e s , o t h e r s e c u r i t i e s a n d l o a n s -- w h i c h m a x i m i z e s t o t a l p r o f i t on t h e s e a s s e t s o v e r s e v e r a l t i m e p e r i o d s . The model a s s u m e s t h a t t h e b a n k e r knows t h e l e v e l o f demand f o r l o a n s a n d t i m e d e p o s i t s , r a t e s o f i n t e r e s t a n d t h e n e t w o r t h o f t h e bank o v e r t h e p l a n n i n g h o r i z o n . The m o d e l i n c o r p o r a t e s two r e s t r i c t i o n s : a r e s e r v e r e q u i r e m e n t w h i c h s t a t e s t h a t p a r t o f t h e b a n k ' s a s s e t s must be h e l d i n v a u l t c a s h o r s h o r t t e r m g o v e r n m e n t s e c u r i t i e s , a n d a l e v e r a g e r e q u i r e m e n t t h a t s e r v e s a s a p r o x y f o r l i q u i d i t y a n d c a p i t a l a d e q u a c y r e q u i r e m e n t s . B e s i d e s i n d i c a t i n g t h e o p t i m a l mix o f bank a s s e t s , t h e m o d e l g e n e r a t e s i n f o r m a t i o n w h i c h c a n be u s e d f o r s t u d y i n g t h e i m p l i c a t i o n o f F e d e r a l R e s e r v e p o l i c y a n d s o l v i n g some o f t h e o p e r a t i n g p r o b l e m s o f t h e b a n k . 7 P o r t e r [ 1 9 6 1 ] c l a s s i f i e s t h e t y p e s o f a s s e t s w h i c h b a n k s c a n h o l d i n t o t h r e e c a t e g o r i e s : c a s h a s s e t s , s e c u r i t i e s , and l o a n s . I n a d d i t i o n , he a s s u m e s t h a t e a c h o f t h e s e a s s e t s i s i n t e r n a l l y homogeneous. S i n c e c a s h a s s e t s a r e t h e o n l y non-e a r n i n g a s s e t s i n t h e p o r t f o l i o , t h e o b j e c t i v e o f P o r t e r ' s model i s t o m a x i m i z e t h e e x p e c t e d a d d i t i o n s t o n e t w o r t h w i t h r e s p e c t t o s e c u r i t i e s a s a f r a c t i o n o f i n i t i a l d e p o s i t s ( d e n o t e d by B) a n d l o a n s a s a f r a c t i o n o f i n i t i a l d e p o s i t s ( d e n o t e d by L ) . I t i s t h e b a n k e r ' s 1 r i s k t h a t r e s t r a i n s - t h e bank' f r o m a c q u r r i n g a-p o r t f o l i o c o n s i s t i n g e n t i r e l y o f t h e a s s e t s whose y i e l d i s g r e a t e s t . The bank must m a i n t a i n s u f f i c i e n t l i q u i d i t y i n t h e p o r t f o l i o i n o r d e r t o meet demand f o r w i t h d r a w a l s f r o m d e p o s i t o r s . The most i n t e r e s t i n g a s p e c t o f P o r t e r ' s model i s t h a t t h e c h o i c e o f t h e p o r t f o l i o i s assumed t o d e p e n d e n t i r e l y upon e x p e c t a t i o n s , s u c h a s f u t u r e l e v e l o f d e p o s i t l i a b i l i t i e s , f u t u r e m a r k e t v a l u e o f t h e n o n - m a t u r e d s e c u r i t i e s , a n t i c i p a t i o n o f t h e p r o p o r t i o n o f l o a n d e f a u l t s , a n d a n t i c i p a t i o n o f l o a n r e n e w a l s . F o l l o w i n g i n t h e t r a d i t i o n o f t h e p o r t f o l i o c h o i c e m o d el o f T o b i n and M a r k o w i t z , Kane a n d M a l k i e l [ 1 9 6 5 ] d e v e l o p a l o a n p o r t f o l i o m o d e l b a s e d on m a x i m i z i n g a u t i l i t y f u n c t i o n whose o n l y a r g u m e n t s a r e p r o f i t a b i l i t y i n d i c e s -- e x p e c t e d p r o f i t a n d r i s k — v a r i a n c e o f p r o f i t . U t i l i t y i s a s sumed t o be an i n c r e a s i n g f u n c t i o n o f e x p e c t e d p r o f i t a n d a d e c r e a s i n g f u n c t i o n o f r i s k . The b a n k e r a d j u s t s t h e c o n t e n t s o f t h e p o r t f o l i o b e t w e e n t h e two e x t r e m e s , 100% g o v e r n m e n t s e c u r i t i e s and 100% l o a n s , i n o r d e r t o m a x i m i z e t h e u t i l i t y f u n c t i o n . A maximum 8 a c c e p t a b l e r i s k l e v e l ( i . e . , maximum v a r i a n c e o f e x p e c t e d p r o f i t ) i s i m p o s e d . T h i s r e s t r i c t i o n , i n many c a s e s , a l t e r s t h e p o r t f o l i o c h o i c e f r o m t h e u s u a l i n d i f f e r e n c e - c u r v e a n a l y s i s . I n t h e s e c o n d s t a g e o f t h e i r a n a l y s i s , t h e a u t h o r s i n t r o d u c e two a d d i t i o n a l f a c t o r s : d e p o s i t v a r i a b i l i t y a n d c o n s i d e r a t i o n o f l o n g - r u n p r o f i t s . They s u p p o s e t h a t some l o a n s a r e d i s t i n g u i s h e d by t h e e x i s t e n c e o f a c o n t i n u i n g r e l a t i o n s h i p b e t w e e n t h e b o r r o w e r a n d t h e ba n k . T h e i r a n a l y s i s i n d i c a t e s t h a t t h e g r a n t i n g o f t h e s e s p e c i a l k i n d s o f l o a n s c a n a c t u a l l y r e d u c e t h e s h o r t - r u n v a r i a b i l i t y o f d e p o s i t a n d a t t h e same t i m e i m p r o v e l o n g - r u n e x p e c t e d p r o f i t s . The l i n e a r p r o g r a m m i n g m o d e l b u i l t by Cohen and Hammer [ 1 9 6 5 ] was s t r o n g l y i n s p i r e d by t h e work o f Chambers and C h a r n e s . Cohen's model s e l e c t s t h e a s s e t mix t h a t m a x i m i z e s t h e p r e s e n t v a l u e o f n e t income s t r e a m p l u s r e a l i z e d c a p i t a l g a i n ( a n d l o s s ) d u r i n g t h e p l a n n i n g h o r i z o n , p l u s t h e p r e s e n t v a l u e o f t h e s h a r e h o l d e r s ' e q u i t y a t t h e end o f t h e p l a n n i n g p e r i o d . A v a r i e t y o f c o n s t r a i n t s a r e i n c l u d e d i n t h e m o d e l : r i s k , f u n d s a v a i l a b i l i t y , p o l i c y c o n s i d e r a t i o n s , m a r k e t r e s t r i c t i o n s , i n t e r t e m p o r a l l i n k a g e s , e n d o g e n o u s c h a n g e s i n c a p i t a l , a n d l o a n -r e l a t e d f e e d b a c k m e c h a n i s m s . The i n c l u s i o n o f t h e s e c o n s t r a i n t s and t h e r e s u l t i n g d u a l p r i c e s p r o v i d e an i m p o r t a n t component i n t h e r e s p o n s i b i l i t y a c c o u n t i n g s y s t e m o f t h e ba n k . As w i t h many o t h e r l i n e a r p r o g r a m m i n g m o d e l s , t h e i n p u t s o f Cohen's model c o n s i s t o f t h e i n i t i a l b a l a n c e p o s i t i o n a n d a s e r i e s o f f u t u r e p r e d i c t i o n s : f o r e c a s t s o f f u t u r e i n t e r e s t r a t e s o v e r t h e p l a n n i n g h o r i z o n , f o r e c a s t s o f f u t u r e l o a n demands, f o r e c a s t s o f f u t u r e l e v e l o f d e p o s i t s , a n d f o r e c a s t s o f t h e e x o g e n o u s 9 v a r i a b l e s a f f e c t i n g f u n d s a v a i l a b i l i t y , c a p i t a l r e q u i r e m e n t s , e t c . A l t h o u g h t h e s o l u t i o n o f t h e p r o g r a m i n d i c a t e s a s e q u e n c e o f b a l a n c e s h e e t p o s i t i o n s o v e r t h e p l a n n i n g h o r i z o n , t h e a u t h o r s s u g g e s t t h a t t h e b a n k e r s h o u l d f o c u s on t h e f i r s t p e r i o d s o l u t i o n , w h i c h d e t e r m i n e s t h e b a n k ' s p r e s e n t a s s e t management p o s t u r e . E x t e n s i o n s o f t h i s i d e a c a n be f o u n d i n t h e t w o - p e r i o d a p p r o a c h o f m o d e l s d e v e l o p e d d u r i n g t h e 7 0 s . L i f s o n a n d B l a c k m a r r [ 1 9 7 3 ] u t i l i z e b o t h a s i m u l a t i o n m o d el and a l i n e a r p r o g r a m m i n g o p t i m i z a t i o n t e c h n i q u e f o r a s s e t a l l o c a t i o n . The s i m u l a t i o n m o d e l i s u s e d f o r s t a t i n g t h e g o a l ( p r o f i t ) -- and t h e l i m i t a t i o n s ( l i q u i d i t y , f l e x i b i l i t y , a n d g r o w t h ) o f a bank i n q u a n t i f i a b l e t e r m s . M a r g i n a l p r o f i t s o f e a c h t y p e o f a s s e t s a r e e s t i m a t e d . The a u t h o r s b e l i e v e t h a t t r a d e o f f s e x i s t b e t w e e n p r o f i t a n d l i q u i d i t y , a n d b e t w e e n c u r r e n t p r o f i t a n d g r o w t h . A l i n e a r p r o g r a m m i n g o p t i m i z a t i o n t e c h n i q u e i s t h e n i n t e g r a t e d i n t o t h e s i m u l a t i o n m o d e l s e r v i n g a s a v a l u a b l e t o o l f o r f u t u r e p r o f i t p l a n n i n g . L i f s o n a n d B l a c k m a r r show t h a t by u t i l i z i n g t h i s m e t hod t h e s i m u l a t e d bank c a n i m p r o v e i t s p r o f i t by 18.6 p e r c e n t o v e r t h e u n p l a n n e d p o r t f o l i o i n a s i m u l a t e d e n v i r o n m e n t . They a l s o p o i n t o u t t h a t d u a l p r i c e s o f t h e o p t i m i z a t i o n m o d e l c o n s t r a i n t s p r o v i d e a v a r i e t y o f p l a n n i n g d a t a w h i c h a r e e s s e n t i a l t o e f f e c t i v e p l a n n i n g a n d c o n t r o l o f bank o p e r a t i o n s . A g h i l i , Cramer and Thompson [ 1 9 7 5 ] i n d i c a t e t h e m e r i t a n d a p p e a l o f t w o - s t a g e p r o g r a m m i n g m o d e l s o v e r c o n v e n t i o n a l m u l t i p l e s t a g e l i n e a r p r o g r a m m i n g m o d e l s f o r t h e a p p l i c a t i o n s o f c o m m e r c i a l bank p o r t f o l i o management. They s u g g e s t t h a t t w o -10 s t a g e p r o g r a m m i n g u n d e r u n c e r t a i n t y c a n b r i d g e t h e gap b e t w e e n what i s p r a c t i c a l l y f e a s i b l e a n d what i s t h e o r e t i c a l l y d e s i r a b l e . In a d d i t i o n , t h e y p o i n t o u t t h a t t h e t w o - s t a g e p r o g r a m m i n g p r o b l e m i s more e a s i l y s o l v e d b e c a u s e o f t h e s m a l l e r l i n e a r p r o g r a m s i z e . The o b j e c t i v e f u n c t i o n o f t h e m o d e l i s e x p r e s s e d a s e x p e c t e d v a l u e m a x i m i z a t i o n o f s t o c k h o l d e r s ' e q u i t y u n d e r d i f f e r e n t e c o n o m i c e v e n t u a l i t i e s . T h e m o d e l i s b o u n d e d by 47 c o n s t r a i n t s p r i m a r i l y c l a s s i f i e d a s m a n a g e m e n t - p o l i c y , d e f i n i t i o n a l , a c c o u n t i n g , l e g a l , a n d f i n a n c i a l c o n s t r a i n t s . The s o l u t i o n o f t h e m o d e l p r o v i d e s an o p t i m a l f i r s t - s t a g e a s s e t a l l o c a t i o n p l u s a s e t o f r u l e s f o r r e s p o n d i n g t o t h e s t o c h a s t i c e v e n t s o f t h e s e c o n d s t a g e . H o w e v e r , i n p r a c t i c e , o n l y t h e f i r s t - s t a g e s o l u t i o n i s p u t i n t o e f f e c t , a n d t h e i n c l u s i o n o f s e c o n d - s t a g e r u l e s i s t o e n s u r e t h a t f u t u r e e v e n t s h a v e b e e n c o n s i d e r e d when t h e f i r s t - s t a g e d e c i s i o n s a r e m a d e . The m o d e l i s r e p o s i t i o n e d a t t h e b e g i n n i n g of e a c h d e c i s i o n p e r i o d a n d a new f i r s t - s t a g e s o l u t i o n i s i m p l e m e n t e d . T h i s g i v e s t h e b a n k e r a m e c h a n i s m w h i c h c a n c o r r e c t e r r o r s made i n t h e p r e v i o u s p e r i o d . A f t e r r e v i e w i n g a l l t h e a b o v e m o d e l s , we f i n d t h a t t h e y a l l f a l l i n t o t h e c a t e g o r y o f c e n t r a l i z e d m o d e l s . T h e y f i t i n t o t h e e n v i r o n m e n t d i s p l a y e d i n F i g u r e 1 . 1 . C o n c e p t u a l l y , t h e y d e t e r m i n e t h e o p t i m a l a s s e t mix f o r t h e b a n k ; h o w e v e r , t h e r e a r e p r o b l e m s a s s o c i a t e d w i t h t h e a p p l i c a t i o n s o f s u c h m o d e l s . F i r s t , b o t h t h e s e t up a n d e x e c u t i o n o f t h e m o d e l s r e q u i r e t h a t many p i e c e s o f i n f o r m a t i o n f l o w f r o m v a r i o u s d e p a r t m e n t s o f t h e b a n k t o t h e c e n t r a l l o a n p l a n n i n g g r o u p ; t h i s i n v o l v e s h i g h c o s t s a n d i s e r r o r p r o n e . T h e r e f o r e t h e s e m o d e l s may n o t be 11 a d m i n i s t r a t i v e l y f e a s i b l e . S e c o n d , we s e e t h a t i n o r d e r t o c a p t u r e t h e e s s e n c e o f t h e p r o b l e m f a c e d by t h e bank, t h e l i n e a r p r o g r a m m i n g m o d e l s a r e enor m o u s . T h e r e a r e more t h a n t h i r t y c o n s t r a i n t s i n t h e LP m o d e l s o f Co h e n , L i f s o n , a n d A g h i l i . E v en w i t h t h e a i d o f c o m p u t e r s a nd t h e a d v a n c e m e n t o f management s c i e n c e , s o l v i n g t h e s e mammoth LP m o d e l s i s s t i l l t e d i o u s and e x p e n s i v e . I t i s t h e p u r p o s e o f t h i s p a p e r t o s e a r c h f o r t h e mean and t h e method w h i c h c a n be u s e d t o s o l v e t h e a p p l i c a t i o n p r o b l e m o f o p t i m i z a t i o n m o d e l s . I n t h e n e x t c h a p t e r , we e x a m i n e an e x i s t i n g mean — p r o f i t a b i l i t y a n a l y s i s — w h i c h c a n be m o d i f i e d t o f i t i n t o t h e o v e r a l l o p t i m a l a s s e t a l l o c a t i o n o p e r a t i o n . I n C h a p t e r F o u r , we e x p l o r e a method -- a d e c e n t r a l i z e d p r o c e d u r e — w h i c h c a n be u s e d t o s o l v e t h e a s s e t a l l o c a t i o n p r o b l e m i n a more e f f i c i e n t a n d c o n s i s t e n t f a s h i o n . T h i s i s d i s p l a y e d by c o n t r a s t i n g t h e r o l e s o f v a r i o u s bank d e p a r t m e n t s i n t h e c e n t r a l i z e d a n d d e c e n t r a l i z e d e n v i r o n m e n t s . 1 2 3. P R O F I T A B I L I T Y ANALYSIS T h i s c h a p t e r r e v i e w s t h e c u r r e n t d e v e l o p m e n t and t h e c o n t r i b u t i o n o f t h e p r o f i t a b i l i t y a n a l y s i s . T h e n , we w i l l d i s c u s s t h e m a j o r i s s u e s o f t h e t e c h n i q u e and p o i n t o u t how t h e t e c h n i q u e s h o u l d be m o d i f i e d t o f i t i n t o t h e p r o p o s e d d e c e n t r a l i z e d a s s e t a l l o c a t i o n o p e r a t i o n . I n o r d e r t o i m p r o v e p r o f i t s , a b a n k e r must be a b l e t o i d e n t i f y t h e s o u r c e o f p r o f i t s a n d t h e amount o f p r o f i t e a c h s o u r c e c o n t r i b u t e s . As an a i d i n t h i s p r o c e s s t h e t e c h n i q u e o f p r o f i t a b i l i t y a n a l y s i s was d e v e l o p e d d u r i n g t h e 7 0 s . S e v e r a l s t u d i e s ( F a l k e n b e r g [ 1 9 7 3 ] , G r i m e s [ 1 9 7 0 ] , F l y n n [ 1 9 7 8 ] , and Hansen [ 1 9 7 3 ] i n t h e J o u r n a l o f Bank R e s e a r c h and t h e J o u r n a l o f  Commerc i a l Bank L e n d i n g ) have d i s c u s s e d t h e u t i l i z a t i o n o f t h e p r o f i t a b i l i t y i n d e x i n t h e e v a l u a t i o n o f c o m m e r c i a l bank l o a n s . Many b a n k s h a v e a d o p t e d t h i s t e c h n i q u e t o i d e n t i f y h i g h - p r o f i t and l o w - p r o f i t c u s t o m e r s . I n a d d i t i o n , w i t h t h e h e l p o f a g g r e g a t e p r o f i t a b i l i t y a n a l y s i s , t h e bank p l a n n i n g g r o u p c a n g a i n i n s i g h t s ( e . g . , p r o f i t g r o w t h p e r f o r m a n c e , o p e r a t i n g e f f i c i e n c y , l o a n l o s s e x p e r i e n c e , e t c . ) i n t o v a r i o u s p r o f i t c e n t e r s o f a b ank, p a r t i c u l a r l y l o a n d i v i s i o n s . P r o f i t a b i l i t y a n a l y s i s i s a f l e x i b l e t o o l f o r bank management. Under d i f f e r e n t g r o u p i n g s ( l o a n s i z e , l o c a t i o n , l o a n t y p e , o r e v e n by l o a n o f f i c e r ) a g g r e g a t e p r o f i t a b i l i t y a n a l y s i s c a n y i e l d v a l u a b l e p i e c e s o f i n f o r m a t i o n t o management, s u c h a s t h e r e t u r n s o f t h e f u n c t i o n a l g r o u p s , t h e i r c o s t 13 p a t t e r n s , t h e c o n t r i b u t i o n s o f d e p o s i t b a l a n c e s , e t c . T h e s e a r e i n f a c t t h e n e c e s s a r y i n g r e d i e n t s f o r e f f e c t i v e p l a n n i n g a n d c o n t r o l . We w i l l s e e i n C h a p t e r F i v e how i n d i v i d u a l p r o f i t a b i l i t y a n a l y s e s o f l o a n a p p l i c a t i o n s c a n be i n t e g r a t e d w i t h a d e c e n t r a l i z e d t e c h n i q u e . T h e s e p r o c e d u r e s a l l o w t h e bank t o d e t e r m i n e an o p t i m a l l o a n m i x w i t h minimum i n f o r m a t i o n f l o w s b e t w e e n t h e l o a n p l a n n i n g g r o u p a n d i n d i v i d u a l l o a n d i v i s i o n s . T h i s p r o v i d e s t h e bank management w i t h a l o a n a l l o c a t i o n p r o c e d u r e t h a t i s l e s s p r o n e t o e r r o r , a n d l e s s c o s t l y t o a d m i n i s t e r , t h a n more c e n t r a l i z e d a l t e r n a t i v e p r o c e d u r e s . 3.1 CALCULATION AND CONTRIBUTION OF P R O F I T A B I L I T Y INDEX 3.1.1 CALCULATION OF P R O F I T A B I L I T Y INDEX B e f o r e t h e t e c h n i q u e o f p r o f i t a b i l i t y a n a l y s i s i s d i s c u s s e d f u r t h e r , l e t us f i r s t i l l u s t r a t e how a p r o f i t a b i l i t y i n d e x i s c a l c u l a t e d . S u p p o s e a bank i s a n a l y z i n g a l o a n r e q u e s t f o r a $100,000 r e v o l v i n g c r e d i t i n t h e c o m m e r c i a l l o a n c a t e g o r y . A c ommitment f e e o f 1% p e r y e a r w i l l be i m p o s e d on t h e u n u s e d p o r t i o n o f t h e c ommitment. The b o r r o w e r a l s o a g r e e s t o m a i n t a i n c o m p e n s a t i n g b a l a n c e s of 10% o f t h e u s e d l i n e o f c r e d i t . The n o m i n a l l o a n r a t e i s 14% a n n u a l l y . I t i s e s t i m a t e d t h a t t h e u s a g e w i l l a v e r a g e 75% o f t h e commitment o r $75,000 d u r i n g t h e y e a r . The c o s t o f f u n d s a n d t h e c o s t o f r i s k f o r c o m m e r c i a l l o a n s a r e 7% a n d 2%, r e s p e c t i v e l y . F i x e d h a n d l i n g c o s t a n d v a r i a b l e o v e r h e a d c h a r g e s a r e $500 and 0.1%, r e s p e c t i v e l y . The c o m p u t e d p r o f i t a b i l i t y i n d e x b a s e d on t h i s d a t a i s p r e s e n t e d F i g u r e 3 . 1 a n d 3 . 2 . F IGURE 3 . 1 CALCULAT ION OF P R O F I T A B I L I T Y INDEX FOR A COMMERCIAL LOAN LOAN CATEGORY: T Y P E OF L O A N : COMMITMENT: T E R M : CONTRACT R A T E : COMMITMENT F E E : COMPENSATING BALANCES: EST IMATED U S A G E : RESERVE REQUIRMENT: COMMERCIAL REVOLVING CREDIT $ 1 0 0 , 0 0 0 1 YEAR 1'4%-1% ON UNUSED PORTION OF COMMITMNET 1 0% 75% 1 0% 1 5 F IGURE 3 . 2 INCOME I n t e r e s t Income $75000 x 14% $ 1 0 5 0 0 . 0 F e e Income $25000 x 1% $ 2 5 0 . 0 T o t a l Income $ 1 0 7 5 0 . 0 COST C o s t o f F u n d s Net O u t l a y x 7% $ 4 7 7 7 . 5 C o s t o f R i s k s $75000 x 2% $ 1 5 0 0 . 0 F i x e d H a n d l i n g C o s t $ 5 0 0 . 0 V a r i a b l e O v e r h e a d C o s t $75000 x 0 . 1 % $ 7 5 . 0 T o t a l C o s t $ 6 8 5 2 . 5 NET EXPECTED RETURN $ 3 8 9 7 . 5 OUTLAY A v e r a g e L o a n Amount $75000 l e s s r N e t Demand D e p o s i t B a l a n c e s $75000 x 0 . 1 x 0 . 9 $ 6750 Net O u t l a y $ 6 8 2 5 0 . 0 RETURN ON FUNDS ALLOCATED 3 8 9 7 . 5 / 6 8 2 5 0 . 0 5 . 7 1 % PROFIT GOAL R e q u i r e d R e t u r n on A s s e t s 5 . 5 0 % P R O F I T A B I L I T Y INDEX 5 . 7 1 % / 5 . 5 0 % 104 3 . 1 . 2 CONTRIBUTION OF THE P R O F I T A B I L I T Y ANALYSIS P r o f i t a b i l i t y i n d i c e s n o t o n l y i n d i c a t e how p r o f i t a b l e an l o a n a p p l i c a t i o n i s , b u t a l s o p r o v i d e g u i d e l i n e s f o r a c c e p t i n g a n d r e j e c t i n g l o a n s . In a d d i t i o n , t h e p r o f i t a b i l i t y a n a l y s i s c a n i d e n t i f y a n e e d e d c h a n g e i n t h e l o a n mix t o m a x i m i z e bank p r o f i t . O b v i o u s l y , a l o a n a p p l i c a t i o n w h i c h h a s an i n d e x o f 104 i s more p r o f i t a b l e t h a n an a p p l i c a t i o n w i t h an i n d e x o f 9 9 . 16 M o r e o v e r , an a p p l i c a t i o n w i t h an i n d e x l e s s t h a n 100 i s n o t a c h i e v i n g t h e p r o f i t a b i l i t y g o a l . I n s u c h an i n s t a n c e , t h e bank s h o u l d e i t h e r r a i s e t h e i n t e r e s t r a t e o r t u r n down t h e a p p l i c a t i o n . T h e r e a r e some s i t u a t i o n s where t h e bank c a n n o t i n c r e a s e t h e r a t e c h a r g e d : (1) c o m p e t i t i o n f r o m o t h e r f i n a n c i a l i n s t i t u t i o n s p r e v e n t s t h e b a n k s f r o m c h a r g i n g h i g h e r i n t e r e s t r a t e s ; ( 2) t h e g o v e r n m e n t i m p o s e s i n t e r e s t r a t e c e i l i n g s on l o a n s ; (3) t h e c u s t o m e r w i l l n o t pay more u n l e s s he i n t e n d s t o d e f a u l t on t h e loan'. When a bank i s f a c i n g t h e s e p r o b l e m s , t h e l o a n a b l e f u n d s must be r e a l l o c a t e d t o more p r o f i t a b l e a r e a s . I n a d d i t i o n s , c o n d i t i o n s c a n d e v e l o p i n w h i c h t h e bank w i l l w i s h t o a d j u s t i t s c u r r e n t l o a n m i x . F o r e x a m p l e , c h a n g e s i n m a c r o e c o n o m i c f a c t o r s s u c h a s t h e r a t e s o f g o v e r n m e n t t r e a s u r y b o n d s , t h e l e v e l o f c a p i t a l i n v e s t m e n t s , t h e demand f o r h o u s i n g , e t c , w i l l make some o f t h e l o a n s become more o r l e s s p r o f i t a b l e . I n a d d i t i o n t o t h e c u r r e n t c o n t r i b u t i o n s o f t h e p r o f i t a b i l i t y a n a l y s i s , we w i l l s e e i n t h e n e x t two c h a p t e r s how t h e t e c h n i q u e c a n be m o d i f i e d t o s e r v e a s a b a s i c t o o l f o r t h e bank management t o d i r e c t t h e r e s o u r c e s t o w a r d s t h e i r o p t i m a l d e s t i n i e s . 3.2 ISSUES OF P R O F I T A B I L I T Y ANALYSIS A l t h o u g h p r o f i t a b i l i t y a n a l y s i s h a s been a r o u n d f o r more t h a n t e n y e a r s , no u n i v e r s a l l y a c c e p t e d method h a s y e t emerged f o r d e t e r m i n i n g t h e c o s t o f f u n d s . I n f a c t , t h e d e t e r m i n a t i o n o f t h e c o s t o f f u n d s u s e d r e m a i n s t h e most c o n t r o v e r s i a l i s s u e i n p r o f i t a b i l i t y a n a l y s i s . The a p p r o p r i a t e e s t i m a t i o n o f t h e 17 c o s t o f r i s k s i s g e n e r a l l y i g n o r e d . B u t t h i s f a c t o r a c t u a l l y has s i g n i f i c a n t i m p a c t on t h e c a l c u l a t i o n o f t h e i n d e x . The c o s t o f r i s k s h o u l d somehow r e f l e c t t h e management p h i l o s o p h y o f t h e bank. 3.2.1 THE COST OF FUNDS C o n c e r n i n g t h e i s s u e o f t h e d e t e r m i n i n g t h e c o s t o f f u n d s u s e d , G r i m e s [ 1 9 7 0 ] , H a nsen [ 1 9 7 3 ] , a n d F l y n n [ 1 9 7 8 ] have p r o p o s e d two b a s i c a l l y d i f f e r e n t a p p r o a c h e s . F i r s t i s t h e p o o l of f u n d s c o n c e p t . T h i s w o u l d be t h e w e i g h t e d a v e r a g e c o s t o f a l l t h e l o a n a b l e f u n d s i n t h e ba n k , r e g a r d l e s s o f t h e u s e s t o w h i c h t h e y a r e p u t . S e c o n d i s t h e m a r g i n a l c o s t o f money c o n c e p t . H o w e v e r , t h e m e t h o d s o f e s t i m a t i n g m a r g i n a l c o s t d i f f e r f r o m one a u t h o r t o t h e n e x t . Some a u t h o r s , s u c h a s F l y n n [ 1 9 7 8 ] , s u g g e s t u s i n g t h e n e g o t i a b l e c e r t i f i c a t e o f d e p o s i t r a t e a s t h e m a r g i n a l c o s t ; o t h e r s , s u c h a s G r i m e s [ 1 9 7 0 ] a n d Hansen [ 1 9 7 3 ] , s u g g e s t u s i n g t h e number p r o v i d e d by a p r o f i t c e n t e r c o s t a c c o u n t i n g s y s t e m . Some l i t e r a t u r e ( A n d e r s o n [ 1 9 7 9 ] , L o n g b r a k e [ 1 9 7 3 ] , Watson [ 1 9 7 7 ] ) on t h e s u b j e c t o f c o s t o f f u n d s has e m p h a s i s e d t h e s u p p l y s i z e o f t h e f u n d s ( i . e . , t h e amount a bank h a s t o pay f o r g a i n i n g an a d d i t i o n a l d o l l a r o f l o a n a b l e f u n d s ) . I t h a s been c l e a r l y p o i n t e d o u t by F a l k e n b e r g [ 1 9 7 3 ] t h a t c o s t o f f u n d s f o r t h e p r o f i t a b i l i t y a n a l y s i s i s s o l e l y a number u s e d a s a t r a n s f e r p r i c e o f f u n d s b e t w e e n t h e f u n d - p r o v i d i n g f u n c t i o n s a n d t h e f u n d - u s i n g f u n c t i o n s . I t i s an i n t e r n a l r a t e t h a t f u n d - u s i n g f u n c t i o n s p a y a n d f u n d - p r o v i d i n g f u n c t i o n s 18 r e c e i v e f o r f u n d s t h a t f l o w w i t h i n t h e bank. I n a n o t h e r w o r d s , t h e m a g n i t u d e o f t h e c o s t o f f u n d s u s e d i n t h e c a l c u l a t i o n o f t h e p r o f i t a b i l i t y i n d e x s h o u l d be i n d e p e n d e n t o f t h e s o u r c e s o f t h e f u n d s a n d t h e i r u l t i m a t e s u s e s . E x t e r n a l l y , t h e c o s t o f f u n d s w i l l c l e a r l y be a f f e c t e d by t h e u s e s o f t h e f u n d s b e c a u s e t h e r e t u r n demanded by i n v e s t o r s and d e p o s i t o r s w i l l v a r y w i t h t h e l e v e l o f r i s k t o w h i c h t h e bank i s e x p o s e d ( i . e . , t h e t y p e o f i n v e s t m e n t s i n w h i c h t h e bank i s i n v o l v e d ) . T h i s c o s t o f c a p i t a l c o n c e p t i s w e l l d e v e l o p e d i n f i n a n c e . However, f o r t h e c a l c u l a t i o n o f p r o f i t a b i l i t y i n d e x , we h a v e b r o k e n down t h e c o s t o f c a p i t a l i n t o t h r e e c o m p o n e n t s : (1) t h e c o s t o f f u n d s , (2) t h e c o s t o f r i s k , a n d (3) a p r o f i t g o a l -- t h e r e q u i r e d r e t u r n on a s s e t s . T h i s i s done t o c a p t u r e t h o s e c o s t s i n c u r r e d i n n o n - l o a n a c t i v i t i e s , s u c h as a d m i n i s t r a t i o n c o s t s o f d e p o s i t a c c o u n t s , m a r k e t i n g c o s t s , e t c . I n t h i s p a p e r we a d o p t t h e m a r g i n a l c o s t c o n c e p t : u n l e s s t h e r i s k c h a r a c t e r i s t i c o f e a c h l o a n d i v i s i o n i s i d e n t i c a l t o t h e b a n k ' s o v e r a l l r i s k c h a r a c t e r i s t i c , t h e u s e of w e i g h t e d a v e r a g e c o s t o f c a p i t a l w i l l l e a d t o t h e a c c e p t a n c e o f some u n d e s i r a b l e l o a n s a n d r e j e c t i o n o f some p r o f i t a b l e l o a n s . H o w e v e r , t h e e s t i m a t i o n o f t h e m a g n i t u d e o f t h e t r a n s f e r c o s t i s b a s e d on an o p p o r t u n i t y c o s t n o t i o n b e t w e e n l o a n d i v i s i o n s . I f t h e t o t a l amount o f l o a n a b l e f u n d s i s p r e d e t e r m i n e d , t h e r e e x i s t s a n o p p o r t u n i t y c o s t f o r e a c h d o l l a r e m p l o y e d i n any p a r t i c u l a r l o a n d i v i s i o n . D e t a i l e d d i s c u s s i o n o f t h e e s t i m a t i o n o f t h i s o p p o r t u n i t y c o s t i s d e f e r r e d t o C h a p t e r F i v e where t h e c o s t o f f u n d s w i l l be r e p r e s e n t e d by Xi i n t h e p r o p o s e d m o d e l . 1 9 3.2.2 THE COST OF RISK The c o s t o f r i s k h a s been i g n o r e d by many a u t h o r s ( e . g . , D r a u g h o n [ 1 9 7 2 ] a n d B r i c k [ 1 9 8 4 ] ) w h i l e o t h e r s ( e . g . , F a l k e n b e r g [ 1 9 7 3 ] ) o n l y t a k e i t a s t h e p r o x y f o r t h e d e f a u l t r a t e o f t h e l o a n . They b e l i e v e t h a t t h e i n t e r e s t r a t e c h a r g e d on a l o a n s h o u l d a l r e a d y h a v e f u l l y c o m p e n s a t e d f o r t h e r i s k i n v o l v e d i n g r a n t i n g i t . T h i s s h o u l d be t r u e i f t h e p r i c i n g o f t h e l o a n c o m p l i e s p e r f e c t l y w i t h t h e c a p i t a l a s s e s t p r i c i n g m o d e l w i t h t h e l e v e l o f p o r t f o l i o r i s k o f a bank n o t r e s t r i c t e d i n any way. U n f o r t u n a t e l y , t h e o p e r a t i o n o f a bank i s r e s t r i c t e d i n many a s p e c t s a n d t h e management o f i t s l o a n p o r t f o l i o i s c e r t a i n l y no e x c e p t i o n . F i r s t , t h e bank p o r t f o l i o i s r e g u l a t e d by t h e g o v e r n m e n t f o r t h e s a k e o f s a f e t y , p r o t e c t i o n o f d e p o s i t o r s , a n d p r o m o t i o n o f c o m p e t i t i o n . One e x a m p l e i s t h e e x i s t e n c e o f t h e 10% m o r t g a g e l i m i t on c h a r t e r e d b a n k s . Under t h e c u r r e c t Bank A c t , c h a r t e r e d b a n k s a r e p r o h i b i t e d f r o m h o l d i n g more t h a n 10% o f t h e i r t o t a l C a n a d i a n d e p o s i t s a n d d e b e n t u r e s i n f o r m o f m o r t g a g e l o a n s , e x c l u d i n g t h e m o r t g a g e h o l d i n g s o f t h e i r s u b s i d i a r i e s . S e c o n d , s i n c e t h e m a j o r s o u r c e o f f u n d s i n a c o m m e r c i a l bank i s f r o m d e p o s i t o r s r a t h e r t h a n i n v e s t o r s , who s u p p o s e d l y h a v e b e t t e r a b i l i t y t o j u d g e t h e i r i n v e s t m e n t s , a g g r e s s i v e p o r t f o l i o c h o i c e s t o g e t h e r w i t h some a d v e r s e m a c r o e c o n o m i c c o n d i t i o n s may c r e a t e h a r m f u l e f f e c t s on t h e r e p u t a t i o n o f t h e bank w h i c h may e v e n t u a l l y l e a d t o a r u n . T h e r e c e r t a i n l y e x i s t some g r o u n d s f o r t h e e s t a b l i s h m e n t o f a r i s k c e i l i n g on t h e l o a n p o r t f o l i o ; j u s t i f i c a t i o n o f i t i s d e f e r r e d t o t h e n e x t c h a p t e r . M o r e o v e r , d i s c u s s i o n on l o a n 20 p o r t f o l i o r i s k management a n d i t s i n t e r a c t i o n w i t h r e g u l a t i o n s s e t o u t by t h e C a n a d i a n D e p o s i t I n s u r a n c e C o r p o r a t i o n w i l l be p o s t p o n e d u n t i l t h e n e x t c h a p t e r w h e r e t h e maximum l e v e l o f l o a n p o r t f o l i o r i s k i s t r e a t e d a s an e x o g e n o u s l y s p e c i f i e d c o n s t r a i n t . A t t h i s p o i n t , we c a n o n l y s a y t h a t t h e c o s t o f r i s k f o r any g i v e n l o a n must n o t o n l y i n c o r p o r a t e t h e p o s s i b i l i t y ' o f d e f a u l t on t h a t l o a n , b u t a l s o t h e amount o f r i s k t h a t t h a t l o a n c o n t r i b u t e s t o t h e o v e r a l l l o a n p o r t f o l i o ( i . e . , an a p p r o p r i a t e c o s t of r i s k f o r a g i v e n l o a n c a n n o t be d e t e r m i n e d i n i s o l a t i o n ) . A l o a n ' s c o n t r i b u t i o n t o t o t a l r i s k d e p e n d s on t h e c o r r e l a t i o n o f t h a t l o a n ' s r e t u r n w i t h o t h e r l o a n s ( i . e . , r i s k may be d i v e r s i f i a b l e w i t h i n b a n k s ) . L o a n s of s i m i l i a r t y p e ( e . g . , same c a t e g o r y ) w i l l l i k e l y be h i g h l y c o r r e l a t e d ; t h e r e f o r e , s m a l l e r g a i n s f r o m d i v e r s i f i c a t i o n w i t h i n c a t e g o r y . F o r e x a m p l e , m o r t g a g e l o a n s o f t h e same g e o g r a p h i c a l r e g i o n a r e h i g h l y c o r r e l a t e d . I n t h e f o l l o w i n g d e v e l o p m e n t o f t h e m o d e l , we assume p e r f e c t c o r r e l a t i o n o f d e f a u l t w i t h i n c a t e g o r y w h e r e a s no c o r r e l a t i o n e x i s t s a c r o s s c a t e g o r i e s . D i v e r s i f i c a t i o n o f t h e l o a n p o r t f o l i o a c r o s s c a t e g o r i e s c a n r e d u c e t o t a l r i s k ; t h u s , t h e g r e a t e r t h e f u n d s a l l o c a t e d t o a g i v e n l o a n c a t e g o r y , t h e h i g h e r s h o u l d be t h e c o s t o f r i s k c h a r g e d on l o a n s i n t h a t c a t e g o r y . T h i s i s due t o t h e a s s o c i a t e d r e d u c t i o n i n d i v e r s i f i c a t i o n o f t h e b a n k ' s p o r t f o l i o c o n s i d e r e d a s a w h o l e . 21 4. COMPARISONS OF THE DEPARTMENTAL ROLES IN THE TWO DIFFERENT ENVIRONMENTS I n t h i s c h a p t e r we f i r s t d e f i n e t h e o b j e c t i v e o f t h e a s s e t a l l o c a t i o n o p e r a t i o n and s e t o u t t h e c o n s t r a i n t s f a c e d by t h e bank management. Then we e x a m i n e t h e r o l e s u n d e r t a k e n by v a r i o u s d e p a r t m e n t s i n t h e c e n t r a l i z e d a n d t h e d e c e n t r a l i z e d e n v i r o n m e n t s i l l u s t r a t e d i n F i g u r e 1.1 and 1.2. 4.1 THE OBJECTIVE AND THE CONSTRAINTS The o b j e c t i v e o f t h e a s s e t a l l o c a t i o n o p e r a t i o n i s t o m a x i m i z e t h e e x p e c t e d r e t u r n o f t h e l o a n p o r t f o l i o s u b j e c t t o two c o n s t r a i n t s , a maximum a c c e p t a b l e l o a n p o r t f o l i o r i s k a n d a g i v e n amount o f f u n d s a v a i l a b l e f o r l e n d i n g . 4.1.1 MAXIMUM ACCEPTABLE LOAN PORTFOLIO RISK B a s e d on t h e g e n e r a l i z a t i o n o f t h e c a p i t a l a s s e t p r i c i n g m o d e l , t h e r e s h o u l d be no maximum a c c e p t a b l e p o r t f o l i o r i s k s e t a s a c o n s t r a i n t t o t h e p r o f i t m a x i m i z a t i o n p r o b l e m . The bank s h o u l d be w i l l i n g t o t a k e w h a t e v e r amount o f r i s k i s i n v o l v e d a s l o n g a s t h e r e t u r n p r o v i d e d by t h e c o r r e s p o n d i n g a s s e t p r o v i d e s s u f f i c i e n t c o m p e n s a t i o n . T h i s i m p l i e s t h a t t h e bank w o u l d a c q u i r e a p o r t f o l i o c o n s i s t i n g e n t i r e l y o f t h e a s s e t s f o r w h i c h t h e n e t r i s k - a d j u s t e d y i e l d i s g r e a t e s t ( i . e . , t h e bank w i l l t a k e e i t h e r a l l a s s e t s w h i c h h a v e a b n o r m a l r e t u r n s o r t h e m a r k e t p o r t f o l i o ) . The s t a t e d a r g u m e n t , h o w e v e r , w o u l d n o t be v a l i d i f we l o o k 22 a t t h e v e r y e s s e n c e o f b a n k i n g b u s i n e s s w h i c h i s t o p e r f o r m f i n a n c i a l i n t e r m e d i a t i o n , an i m p o r t a n t a s p e c t o f w h i c h i s t e r m i n t e r m e d i a t i o n . P o r t e r [ 1 9 6 1 ] h a s p o i n t e d o u t t h a t b a n k s must m a i n t a i n p o r t f o l i o s w h i c h o f f e r n o t o n l y t h e maximum money r e t u r n , b u t a l s o t h e l i q u i d i t y a nd c a p i t a l c e r t a i n t y . S i n c e demand d e p o s i t s o f c h a r t e r e d b a n k s a r e e s s e n t i a l l y w i t h d r a w a b l e on demand, i t w o u l d be a s e r i o u s p r o b l e m i f t h e b a n k s d e d i c a t e d l a r g e p o r t i o n s o f t h e i r a s s e t s i n f o r m o f h i g h y i e l d , i l l i q u i d l o a n s . S e c o n d , t h e e x i s t e n c e o f a g e n c y c o s t s , s u c h a s t h e r e p u t a t i o n o f t h e m a n a g e r s a n d t h e i r j o b s e c u r i t y , a nd b a n k r u p t c y c o s t s , s u c h a s l e g a l a nd a c c o u n t a n t f e e s , may impose a maximum amount o f r i s k t h a t t h e bank management i s w i l l i n g t o t a k e i n t h e l o a n p o r t f o l i o . T h i r d , t h e i n s u r a n c e premiums c h a r g e d by t h e C a n a d i a n D e p o s i t I n s u r a n c e C o r p o r a t i o n a r e u n i f o r m a c r o s s a l l f i n a n c i a l i n s t i t u t i o n s ; any i n s t i t u t i o n w h i c h t a k e s t o o a g g r e s s i v e a p o s i t i o n may f a c e t h e t h r e a t o f l o s s o f c o v e r a g e . S i n c e t h e s u c c e s s o f a bank i s d e p e n d e n t upon t h e c o n f i d e n c e p e o p l e p l a c e i n i t , i t i s i m p o r t a n t f o r t h e bank t o m a i n t a i n i t s p o r t f o l i o a t a l e v e l w h i c h s a t i s f i e s t h e r e g u l a t i o n s i m p o s e d by t h e I n s p e c t o r G e n e r a l a n d t h e CDIC. Any one o f t h e a r g u m e n t s w i l l j u s t i f y t h e i m p o s i t i o n o f a maximum a c c e p t a b l e l o a n p o r t f o l i o r i s k t o e n s u r e t h a t a bank i s h e a l t h y i n t e r m s o f c e r t a i n t y a nd c a p i t a l l i q u i d i t y . 23 4.1.2 MAXIMUM LEVEL OF LOANABLE FUNDS I t may be a r g u e d t h a t t h e r e s h o u l d ' h o t be- any c o n s t r a i n t On' t h e amount o f f u n d s a v a i l a b l e f o r l e n d i n g by a c o m m e r c i a l bank b e c a u s e t h e bank c a n a l w a y s r a i s e t h e n e e d e d f u n d s t h r o u g h v a r i o u s c h a n n e l s o f t h e f i n a n c i a l m a r k e t . B u t , l e t us assume t h a t t h e o p t i m a l amount o f l o a n a b l e f u n d s i s p r e d e t e r m i n e d by u p p e r l e v e l management ( i . e . , a s t r a t e g i c d e c i s i o n w h i c h a c c o u n t s f o r o t h e r n o n - l o a n a c t i v i t i e s i n t h e b a n k ) and i s g i v e n t o t h e l o a n p l a n n i n g g r o u p a s an e x o g e n o u s c o n s t r a i n t . 4.2.1 THE ROLES OF VARIOUS DEPARTMENTS I N THE CENTRALIZED ENVIRONMENT 4.2.1.1 The r o l e o f t h e a s s e t s / l i a b i l i t i e s c o m m i t t e e T h i s c o m m i t t e e o v e r s e e s t h e g e n e r a l a s s e t and l i a b i l i t y management o p e r a t i o n s o f t h e b a n k . The m a j o r f u n c t i o n o f t h e c o m m i t t e e i n t h e o p e r a t i o n o f l o a n a b l e f u n d a l l o c a t i o n s i s t o t r a n s f o r m t h e r u l e s s e t o u t by t h e g o v e r n m e n t , t h e m a n a g e r i a l d e c i s i o n s made by t h e t o p management, a n d t h e e x t e r n a l f a c t o r s t h a t impose r e q u i r e m e n t s on l o a n c o m p o s i t i o n i n t o a s e t o f c o n s t r a i n t s . The c o n t e n t s o f t h e s e t o f c o n s t r a i n t s d e p e n d on what d e g r e e o f c o n t r o l t h e c o m m i t t e e w a n t s t o e x e r t on t h e l o a n p l a n n i n g g r o u p . I n C h a p t e r Two, we f o u n d , p a r t i c u l a r l y f o r l i n e a r p r o g r a m m i n g m o d e l s , t h a t t h e s e t o f c o n s t r a i n t s i n a c e n t r a l i z e d p l a n i s f r e q u e n t l y l a r g e a n d r e s t r i c t i v e . T h i s i s n e c e s s a r y b e c a u s e t h e bank w a n t s t o c a p t u r e a l l i n f o r m a t i o n a b o u t i t s o p e r a t i o n i n t h e m o d e l a t t h e b e g i n n i n g o f t h e 24 p l a n n i n g h o r i z o n ; i t i s u n l i k e l y t h a t t h e bank w o u l d a d j u s t t h e l o a n mix w i t h i n t h e p l a n n i n g h o r i z o n . 4.2.1.2 The r o l e o f t h e a c c o u n t i n g g r o u p The a c c o u n t i n g d e p a r t m e n t f o r a l l l o a n d i v i s i o n s c o l l e c t s t h e p e r f o r m a n c e d a t a w h i c h w i l l be u s e d t o e s t i m a t e t h e c o s t a n d r e v e n u e f u n c t i o n s o f i n d i v i d u a l l o a n d i v i s i o n s . T h o s e f u n c t i o n s w i l l t h e n be s e n t t o t h e l o a n p l a n n i n g g r o u p a n d u s e d f o r t h e c o n s t r u c t i o n o f t h e o b j e c t i v e f u n c t i o n o f t h e m a x i m i z a t i o n m o d e l . 4.2.1.3 The r o l e o f a l o a n d i v i s i o n P a s s i v e l y , t h e l o a n d i v i s i o n o p t i m a l l y l e n d s o u t t h e amount o f l o a n a b l e f u n d s a s s i g n e d by t h e l o a n p l a n n i n g g r o u p . However, c e n t r a l i z e d m o d e l s do n o t p r o v i d e g u i d e l i n e s f o r t h e a c c e p t a n c e o r r e j e c t i o n o f l o a n s a t t h e d i v i s i o n a l l e v e l . P r o f i t a b i l i t y a n a l y s i s c a n be u t i l i z e d t o e v a l u a t e l o a n a p p l i c a t i o n s , b u t t h e c o s t o f r i s k a n d t h e c o s t o f f u n d s t o be u s e d a r e s t i l l a m b i g u o u s s i n c e t h e s e d e p e n d i n p a r t on t h e o p p o r t u n i t i e s o f o t h e r d i v i s i o n s . A c t i v e l y , t h e l o a n d i v i s i o n h a s t o p r o v i d e v a r i o u s p i e c e s o f i n f o r m a t i o n on i t s a c t i v i t i e s t o b o t h t h e a c c o u n t i n g d e p a r t m e n t and t h e l o a n p l a n n i n g g r o u p . I n f o r m a t i o n c o n c e r n i n g t h e l o a n p r i c i n g c o n d i t i o n s , l o a n demands, a n d r i s k e x p o s u r e h a s t o be p a s s e d t o t h e l o a n p l a n n i n g g r o u p i n o r d e r t o f a c i l i a t e t h e m o d i f i c a t i o n a n d e x e c u t i o n o f t h e o p t i m i z a t i o n m o d e l . A g g r e g r a t e f i g u r e s o f t h e e x p e n s e s a n d p r o f i t a b i l i t y a n a l y s e s 25 h a v e t o be s u b m i t t e d t o t h e a c c o u n t i n g g r o u p f o r f u n c t i o n a l a n a l y s e s . 4.2.1.4 The r o l e o f t h e l o a n p l a n n i n g g r o u p C e r t a i n l y t h e m a j o r t a s k o f t h e p l a n n i n g g r o u p i s t o d e t e r m i n e t h e a l l o c a t i o n o f l o a n a b l e f u n d s i n v a r i o u s l o a n d i v i s i o n s . The p l a n n i n g g r o u p w i t h a l l t h e n e c e s s a r y i n f o r m a t i o n a t hand w i l l c o n s t r u c t a n d e x e c u t e an o p t i m i z a t i o n m o d e l f r o m w h i c h a l l o c a t i o n o f o p t i m a l l o a n a b l e f u n d s w i l l t h e n be d e t e r m i n e d . The l o a n d i s t r i b u t i o n d e c i s i o n s w i l l b o t h be p a s s e d down t o l o a n d i v i s i o n s a n d p a s s e d b a c k t o t h e a s s e t s / l i a b i l i t i e s c o m m i t t e e . T h i s l a t t e r p r o c e d u r e i s n o t o n l y i m p o r t a n t f o r o t h e r p a r t s o f t h e a s s e t / l i a b i l i t y management o p e r a t i o n , b u t a l s o p r o v i d e s some b a s i s f o r s e t t i n g up c o n s t r a i n t s i n t h e n e x t p l a n n i n g p e r i o d . 4.2.2 THE ROLES OF VARIOUS DEPARTMENTS IN THE DECENTRALIZED ENVIRONMENT 4.2.2.1 The r o l e o f t h e a s s e t s / l i a b i l i t i e s c o m m i t t e e The g e n e r a l r o l e o f t h e a s s e t s / l i a b i l i t i e s c o m m i t t e e w i l l n o t c h a n g e i n t h e d e c e n t r a l i z e d e n v i r o n m e n t . I t s t i l l h a s t o t r a n s f o r m t h e e n v i r o n m e n t a l f a c t o r s a n d g o v e r n m e n t r e g u l a t i o n s i n t o some s o r t o f c o n s t r a i n t s t o be u s e d i n t h e d e c o m p o s i t i o n a l m o d e l . However, i n t h e c a s e o f a d e c e n t r a l i z e d c o m m i t t e e , i t s o n l y c o n c e r n s a r e t h e o v e r a l l l o a n p o r t f o l i o r i s k t h a t t h e bank i s w i l l i n g t o t a k e a n d t h e amount o f l o a n a b l e f u n d s t h a t i s a v a i l a b l e i n t h e c u r r e n t p e r i o d . 26 4.2.2.2 The r o l e o f t h e a c c o u n t i n g g r o u p I n t h e d e c e n t r a l i z e d e n v i r o n m e n t , t h e a c c o u n t i n g g r o u p i s no l o n g e r an a c t i v e p a r t i c i p a n t i n t h e a s s e t a l l o c a t i o n o p e r a t i o n . E x c e p t i n t h e i n i t i a l s t a g e o f t h e d e c o m p o s i t i o n a l p r o c e d u r e s when e d u c a t e d g u e s s e s o f t h e i n i t i a l c o s t o f f u n d s and t h e i n i t i a l r i s k f a c t o r a r e made, t h e l o a n p l a n n i n g g r o u p n e e d n o t know a n y t h i n g a b o u t t h e h i s t o r i c a l c o s t a n d / o r r e v e n u e f u n c t i o n s o f t h e l o a n d i v i s i o n s . H owever, l o a n d i v i s i o n p e r f o r m a n c e d a t a w i l l s t i l l be c o l l e c t e d a n d a n a l y s e d by t h e a c c o u n t i n g g r o u p . S t a t i s t i c s o f t h e l o a n d i v i s i o n s a r e r e p o r t e d t o t h e a s s e t s / l i a b i l i t i e s c o m m i t t e e a nd t o t o p management f o r f a c i l i t a t i n g o t h e r o p e r a t i o n s i n t h e bank. 4.2.2.3 The r o l e o f a l o a n d i v i s i o n The l o a n d i v i s i o n w i l l p e r f o r m p r o f i t a b i l i t y a n a l y s i s on e v e r y l o a n a p p l i c a t i o n b a s e d on t h e c o s t o f f u n d s a n d t h e r i s k f a c t o r g i v e n by t h e l o a n p l a n n i n g g r o u p . L o a n a p p l i c a t i o n s w h i c h c a r r y a p r o f i t a b i l i t y i n d e x o f l e s s t h a n 100 w i l l be r e j e c t e d , w h i l e l o a n a p p l i c a t i o n s w h i c h c a r r y a p r o f i t a b i l i t y i n d e x o f g r e a t e r t h a n o r e q u a l t o 100 w i l l be a c c e p t e d . The t o t a l amount o f t h e a c c e p t e d l o a n a p p l i c a t i o n s c o n s t i t u t e s t h e r e q u e s t e d l o a n a b l e f u n d s o f t h e d i v i s i o n . T h i s r e q u e s t f o r l o a n a b l e f u n d s w i l l t h e n be s u b m i t t e d t o t h e l o a n p l a n n i n g g r o u p . I n a d d i t i o n t o d e t e r m i n i n g an amount o f f u n d s r e q u e s t e d , t h e l o a n d i v i s i o n must a l s o d e t e r m i n e t h e s e n s i t i v i t y o f t h i s 27 r e q u e s t t o changes i n the c o s t of funds and changes i n the r i s k f a c t o r . Only these t h r e e numbers have t o be passed up t o t h e l o a n p l a n n i n g group from each l o a n d i v i s i o n . 4.2.2.4 The r o l e of the l o a n p l a n n i n g group In the d e c e n t r a l i z e d environment, the work l o a d of the l o a n p l a n n i n g group i s . d r a s t i c a l l y reduced. I t no l o n g e r has t o d e t e r m i n e a l l o t m e n t s of l o a n a b l e f unds. In f a c t , the l o a n a b l e funds a l l o t m e n t s a r e d e t e r m i n e d by the " i n t e r n a l market f o r c e s " e x i s t i n g among l o a n d i v i s i o n s . Whenever the d i s t r i b u t i o n of t h e l o a n a b l e funds i s n o n - o p t i m a l , t h e r e are d i s c r e p a n c i e s between the d e s i r e d and a c t u a l p o r t f o l i o r i s k and between the d e s i r e d amount of l o a n s and the a c t u a l amount of l o a n s . The major t a s k of the l o a n p l a n n i n g group i s a d j u s t i n g the magnitudes of t h e c o s t of funds and the r i s k f a c t o r i n o r d e r t o reduce the gaps between the d e s i r e d and a c t u a l v a l u e s . A djustments of the c o s t of funds and r i s k f a c t o r are made monthly. 28 5. THE MODEL In t h i s c h a p t e r an a s s e t a l l o c a t i o n o p t i m i z a t i o n m o d e l w i l l be d e v e l o p e d a n d t h e n two p o s s i b l e ways o f s o l v i n g t h e model w i l l be d i s c u s s e d : ( 1 ) s o l v i n g t h e model i n a c e n t r a l i z e d e n v i r o n m e n t w i t h t h e a p p l i c a t i o n o f L a g r a n g i a n m u l t i p l i e r t e c h n i q u e a n d (2) s o l v i n g t h e t h e model i n a d e c e n t r a l i z e d e n v i r o n m e n t w i t h t h e a p p l i c a t i o n s o f t h e d e c o m p o s i t i o n a l t e c h n i q u e p r o p o s e d - by Baumol [ 1964 3 and- the- t e c h n i q u e o f p r o f i t a b i l i t y a n a l y s i s d i s c u s s e d i n C h a p t e r T h r e e . 5.1 DEVELOPMENT OF THE MODEL As was s t a t e d i n t h e p r e v i o u s c h a p t e r , t h e m o d e l i s b a s e d on t h e o b j e c t i v e o f m a x i m i z i n g e x p e c t e d r e t u r n f o r a g i v e n t o t a l amount o f l o a n a b l e f u n d s a v a i l a b l e f o r l e n d i n g a n d a maximum a c c e p t a b l e l o a n p o r t f o l i o r i s k t o be t a k e n by a c o m m e r c i a l b a n k . 5.1.1 CONTRIBUTION OF THE MODEL The m o d e l p r o v i d e s means by w h i c h u p p e r l e v e l management o f a c o m m e r c i a l bank c a n s e a r c h f o r an o p t i m a l bank l o a n m i x . W h i l e i n c o m e f r o m l o a n s a c c o u n t s f o r a b o u t 7 0 % o f t h e o p e r a t i n g r e v e n u e s o f c o m m e r c i a l b a n k s , t h e l e n d i n g b u s i n e s s o f c o m m e r c i a l b a n k s i s b r o a d a n d d i v e r s e , r u n n i n g f r o m p e r s o n a l c o n s u m e r l o a n s t o f o r e i g n g o v e r n m e n t b o r r o w i n g s . A l l t h e s e h a v e d i f f e r e n t c h a r a c t e r i s t i c s : d e f a u l t r i s k i n e s s , y i e l d r a t e s , c o s t o f 29 c a r r y i n g s , e t c . T h e r e f o r e , i t i s p a r t i c u l a r l y i m p o r t a n t f o r t h e bank management t o s e a r c h f o r an o p t i m a l p l a n f o r t h e a l l o c a t i o n o f t h e f u n d s among d i f f e r e n t l o a n c a t e g o r i e s . I n C h a p t e r T h r e e , we p o i n t e d o u t t h e c o n t r o v e r s y s u r r o u n d i n g t h e c o n c e p t s o f c o s t o f f u n d s and c o s t o f r i s k w h i c h a r e u s e d i n t h e p r o f i t a b i l i t y i n d e x . We show them t o be e n d o g e n o u s l y d e t e r m i n e d i n s e c t i o n 5.3 where t h e m o d e l i s s o l v e d i n a d e c e n t r a l i z e d e n v i r o n m e n t by a d e c o m p o s i t i o n a l t e c h n i q u e , t h e v a l u e o f t h e c o s t o f f u n d s a n d t h e r i s k f a c t o r w h i c h i s u s e d f o r c a l c u l a t i n g t h e c o s t o f r i s k a r e a d j u s t e d c o n s e c u t i v e l y by t h e l o a n p l a n n i n g g r o u p u n t i l t h e o p t i m a l l o a n m i x i s a c h i e v e d . T h ey a r e t h e o n l y p i e c e s o f i n f o r m a t i o n t r a n s m i t t e d f r o m t h e c e n t r a l p l a n n i n g g r o u p t o i n d i v i d u a l l o a n d i v i s i o n s . 5.1.2 BACKGROUND OF THE MODEL L e t us assume t h a t t h e l o a n p o r t f o l i o o f a bank c o n s i s t s o f n t y p e s o f l o a n s , where e a c h t y p e o f l o a n c a r r i e s i t s own c h a r a c t e r i s t i c s o f r e t u r n p a t t e r n ( i . e . , e a c h t y p e o f l o a n may h a v e a d i f f e r e n t d e f a u l t r a t e a n d r e c o v e r y r a t e ) . C o l l e c t i v e l y , t h e r i s k i n e s s o f i n d i v i d u a l l o a n t y p e s c o n s t i t u t e s t h e l o a n p o r t f o l i o r i s k . N a t u r a l l y , d e p e n d e n c e may e x i s t among d i f f e r e n t l o a n t y p e s , b u t , f o r s i m p l i c i t y , we w i l l assume i n d e p e n d e n c e among d i f f e r e n t l o a n t y p e s t h r o u g h o u t t h e c o n s t r u c t i o n o f t h e m o d e l . 5.1.3 MAJOR ELEMENTS OF THE MODEL 30 The c o s t r e v e n u e f u n c t i o n s o f t h e l o a n d i v i s i o n s a r e u s e d t o f o r m t h e o b j e c t i v e f u n c t i o n o f t h e l o a n a b l e f u n d a l l o c a t i o n m o d e l i n a manner c o n s i s t e n t w i t h t h e m a x i m i z a t i o n o f e x p e c t e d r e t u r n . I n t h e f o l l o w i n g s e c t i o n s , we w i l l d i s c u s s t h e n e t r e v e n u e f u n c t i o n s a n d c o s t f u n c t i o n s f a c e d by t h e l o a n d i v i s i o n s r e s p e c t i v e l y . The e s t a b l i s h m e n t o f t h e c o n s t r a i n t s and t h e i r j u s t i f i c a t i o n s was made i n C h a p t e r F o u r . A d e t a i l e d d i s c u s s i o n of t h e e s t i m a t i o n o f t h e l o a n p o r t f o l i o r i s k c a n be f o u n d i n A p p e n d i x F o u r . 5.1.3.1 NET REVENUE Net y i e l d g e n e r a t e d by one t y p e o f l o a n i s d e t e r m i n e d by f o u r d i f f e r e n t c o m p o n e n t s : rt-3 = KHii^-fHL^- ml,*) -^ak.rc*) ($•') where r^Lca.) = a v e r a g e i n t e r e s t r e v e n u e f u n c t i o n o f l o a n t y p e i f^La.) = p e r d o l l a r p r e s e n t v a l u e o f c u s t o m e r r e l a t i o n s h i p s o f l o a n t y p e i = u n i t o v e r h e a d a n d c a r r y i n g c o s t f u n c t i o n o f l o a n t y p e i 31 h * " ( L £ = t h e e x p e c t e d d e f a u l t l o s s r a t e f u n c t i o n Z = t h e d e g r e e of c r e d i t s c r e e n i n g on t h e l o a n r e p r e s e n t e d by t h e c o s t of c r e d i t s c r e e n i n g [ 1 ] INTEREST REVENUE The bank c a n e x e r c i s e p r i c e d i s c r i m i n a t i o n a g a i n s t i n d i v i d u a l c u s t o m e r s so t h a t t h e r a t e c h a r g e d t o e a c h c u s t o m e r may be d i f f e r e n t b a s e d on h i s r e l a t i o n s h i p w i t h t h e b ank. B u t , on t h e a v e r a g e , we c a n assume t h a t t h e i n t e r e s t r e v e n u e o f a l o a n d i v i s i o n i n t h e bank c a n be r e p r e s e n t e d by a downward s l o p i n g demand c u r v e . I t i m p l i e s t h a t t h e bank i s c o m p e t i n g i n a m o n o p o l i s t i c e n v i r o n m e n t and i n a p a r t i c u l a r c a t e g o r y i f i t w i s h e s t o e x p a n d i t s b u s i n e s s , i t must r e d u c e t h e a v e r a g e p r i c e o f t h e l o a n s i n t h a t c a t e g o r y . T h i s phenomenon i s p a r t i c u l a r l y t r u e i n C a nada where t h e f i v e m a j o r b a n k s d o m i n a t e t h e e n t i r e b a n k i n g i n d u s t r y . F o r e x a m p l e , i f t h e demand f o r l o a n s o f t y p e i i s l i n e a r , t h e n where 0 r e p r e s e n t s t h e f i x e d r a t e c h a r g e d on l o a n t y p e i a n d (3 C i s t h e p e r d o l l a r i n c r e m e n t a l r a t e o f a d j u s t m e n t on t h e i n t e r e s t r a t e c h a r g e d on l o a n t y p e i . 32 [ 2 ] PRESENT VALUE OF CUSTOMER RELATIONSHIPS Cramer [ 1 9 8 2 ] o b s e r v e s t h a t i n many c a s e s i n i t i a t i o n o f l o a n s w i l l l e a d t o t h e v o l u n t a r y o p e n i n g o f demand d e p o s i t a c c o u n t s . I t h a s a l s o b een p o i n t e d o u t t h a t a t some p o i n t o f t i m e a f t e r t h e i n i t i a t i o n o f t h e l o a n s , t h e b a l a n c e s o f demand d e p o s i t o f t h e c u s t o m e r s may e x c e e d t h e amount o f l o a n s o u t s t a n d i n g . The bank may be w i l l i n g t o o f f e r a l o a n r a t e w h i c h r e f l e c t s t h e c u s t o m e r ' s l e v e l o f d e p o s i t s o v e r t i m e . A l t h o u g h t h e a d v a n c e m e n t of c a s h management i n l a r g e c o r p o r a t i o n s i n d i c a t e s t h a t t h e t r e a s u r e r s p r e f e r t o m a i n t a i n a z e r o b a l a n c e d e p o s i t a c c o u n t on a c o l l e c t e d f u n d b a s i s , i t i s s t i l l common p r a c t i c e f o r c o m m e r c i a l b a n k s t o a s k f o r a c o m p e n s a t i n g b a l a n c e i n t h e f o r m o f demand d e p o s i t s when l o a n s a r e g r a n t e d t o c o m m e r c i a l c u s t o m e r s . R a t h e r t h a n s p e c i f y a c o m p l e x d e p o s i t g e n e r a t i o n f u n c t i o n , we assume t h a t f o r e v e r y d o l l a r o f l o a n g r a n t e d t h e r e w i l l be some f u t u r e b e n e f i t s g e n e r a t e d o t h e r t h a n t h e i n t e r e s t r e v e n u e . L e t us d e n o t e t h e p e r d o l l a r p r e s e n t v a l u e o f c u s t o m e r r e l a t i o n s h i p s i n l o a n d i v i s i o n i by D c, where D l i s a c o n s t a n t a p p r o x i m a t e d by t h e p e r c e n t a g e o f c o m p e n s a t i n g b a l a n c e t i m e s t h e c o s t o f f u n d s i n t h e a s s e t p o o l . [ 3 ] OVERHEAD Lo a n o v e r h e a d s a n d c a r r y i n g c o s t s c o n s i t i t u t e t h e f i x e d a nd v a r i a b l e c o s t s i n c u r r e d i n t h e l o a n c a t e g o r i e s . T h e s e c o s t s i n c l u d e t h e m a r k e t i n g , p r o c e s s i n g a n d h a n d l i n g c o s t s o f l o a n s . 33 The i n i t i a l o v e r h e a d r a t e w i l l be v e r y h i g h , s i n c e t h e p e r u n i t f i x e d c o s t i s v e r y h i g h . However e c o n o m i e s of s c a l e a r e a c h i e v e d when t h e t o t a l amount i n v e s t e d i n a g i v e n l o a n t y p e i n c r e a s e s . We assume a c o s t m i n i m i z i n g l o a n q u a n t i t y ; h o w e v e r , b a s e d on t h e a s s u m p t i o n o f d e c r e a s i n g r e t u r n s o v e r some r a n g e a f t e r t h e o p t i m a l p o i n t h a s b e e n r e a c h e d , r e d u n d a n c y a n d i n e f f i c i e n c y may g e t i n t o t h e way a n d t h e o v e r a l l u n i t o v e r h e a d c o s t may i n c r e a s e a g a i n a s t h e l o a n s i z e i n c r e a s e s . F o r e x a m p l e , t h e bank may h a v e t o a c q u i r e e x t r a o f f i c e s p a c e , t r a i n new p e r s o n n e l , i n c r e a s e t h e m a r k e t i n g b u d g e t i n - o r d e r to* a t t r a c t -a n d a c c o m m o d a t e more l o a n s o f any c a t e g o r y . T h i s phenomenon c a n be r e p r e s e n t e d by a q u a d r a t i c f u n c t i o n : where P , L r e p r e s e n t s t h e v a r i a b l e o v e r h e a d c o s t s o f l o a n t y p e i ; r e p r e s e n t s t h e f i x e d o v e r h e a d c o s t s o f l o a n t y p e i ; ^ L r e p r e s e n t s t h e e l e m e n t s o f e c o n o m i e s o f s c a l e i n l o a n d i v i s i o n i . [4 ] EXPECTED DEFAULT LOSS The e x p e c t a t i o n o f t h e d e f a u l t l o s s w i l l d e p e n d on t h e c r e d i t s c r e e n i n g o f t h e l o a n a p p l i c a t i o n s a n d t h e g e n e r a l l e n d i n g p r a c t i c e o f t h e b a n k . F o r s i m p l i c i t y , t h e e x p e c t e d d e f a u l t l o s s i s a s s u m e d t o be homogeneous w i t h i n e a c h l o a n c a t e g o r y ( i . e . , t h e v a r i a n c e o f r e t u r n s o f l o a n s w i t h i n a l o a n c a t e g o r y i s a s s u m e d t o be t h e s a m e ) . T h i s a s s u m p t i o n w i l l be 34 r e l a x e d when t h e i n t e r - r e l a t i o n s h i p s b e t w e e n t h e a s s e t a l l o c a t i o n o p e r a t i o n and l o a n p r i c i n g a r e e x a m i n e d i n C h a p t e r S i x . I t i s p o s s i b l e , o f c o u r s e , t h a t w i t h i n e a c h l o a n c a t e g o r y c u s t o m e r s c a n be c l a s s i f i e d a s l o w r i s k c u s t o m e r s a n d h i g h r i s k c u s t o m e r s . L o a n s c a n f i r s t be g r a n t e d t o h i g h r i s k c u s t o m e r s who p r e s u m a b l y pay h i g h e r i n t e r e s t . Then when t h e l o a n a l l o t m e n t i n t h a t p a r t i c u l a r c a t e g o r y i n c r e a s e s , t h e bank w i l l move i n t o t h e c l a s s o f l o a n s w h i c h p r o v i d e s l o w e r r i s k a n d l e s s e x p e c t e d p r o f i t . C o n v e r s e l y , l o a n s c a n f i r s t be g r a n t e d t o t h o s e low r i s k c u s t o m e r s . So, t h e e x p e c t e d d e f a u l t l o s s w i l l d e p e n d on t h e l e n d i n g p r a c t i c e s o f t h e b a n k . where i s t h e e x p e c t e d d e f a u l t l o s s r a t e f o r l o a n t y p e i and ^ l ( $ ) i s a f u n c t i o n o f t h e o v e r h e a d c o s t w h i c h r e p r e s e n t s t h e c o s t o f c r e d i t s c r e e n i n g . The c o s t o f c r e d i t s c r e e n i n g i s . n o t e x p l i c t l y i n c l u d e d i n t h e n e t r e v e n u e c a l c u l a t i o n . I n f a c t , t h e p r o c e s s i n g c o s t c h a r g e d t o i n d i v i d u a l c u s t o m e r s h a s a l r e a d y a c c o u n t e d f o r t h e c o s t o f c r e d i t c o n t r o l . N a t u r a l l y , a more r e s t r i c t i v e c r e d i t c o n t r o l s y s t e m w i l l r e d u c e t h e e x p e c t e d d e f a u l t l o s s e s , b u t s u c h a s y s t e m w i l l c e r t a i n l y i n c u r h i g h e r c o s t s t h a n a more r e l a x e d o n e . From t h e r e s u l t s o f t h e d i s c u s s i o n o f t h e f o u r c o m p o n e n t s o f t h e n e t r e v e n u e , we c a n e x p r e s s e q u a t i o n (5 .1) a s 35 o r R where r\*"I_3= n e t r a t e °f r e t u r n on l o a n e d funds of l o a n t y p e i L>Q_ = the q u a n t i t y of l o a n a b l e fund a l l o c a t e d to l o a n c a t e g o r y i 5.1.3.2 COST OF FUNDS I f we l o o k a t t h e c o s t o f f u n d s f r o m t h e p e r s p e c t i v e o f f u l f i l m e n t o f t h e r e q u i r e m e n t s p o s e d by t h e i n v e s t o r s a n d d e p o s i t o r s , t h e c o s t o f f u n d s — e x t e r n a l c o s t o f f u n d s — i s a f u n c t i o n o f r i s k i n e s s ( i . e . , t h e r e q u i r e d r e t u r n s o f t h e d e p o s i t o r s a n d i n v e s t o r s a r e s u b j e c t t o t h e t y p e o f i n v e s t m e n t s i n w h i c h t h e bank i s i n v o l v e d ) . S i n c e t h e maximum l e v e l o f l o a n p o r t f o l i o r i s k i s f i x e d , t h e m a r g i n a l c o s t o f f u n d s f a c e d by l o a n d i v i s i o n s s h o u l d be e q u a l t o t h e e x p e c t e d r e t u r n on t h e c a p i t a l m a r k e t l i n e r e f l e c t i n g t h e maximum p o r t f o l i o r i s k t a k e n by t h e bank ( n o t e : when t h e o b j e c t i v e f u n c t i o n o f t h e m o d e l i s m a x i m i z e d , t h e l o a n p o r t f o l i o r i s k s h o u l d e q u a l t h e maximum a c c e p t a b l e l o a n p o r t f o l i o r i s k ) . B u t , s i n c e t h e s i z e o f 36 l o a n a b l e f u n d i s a s s u m e d t o be f i x e d , t h e c o s t o f f u n d s s h o u l d a c t u a l l y be a u n i q u e number w h i c h r e p r e s e n t s t h e t r a n s f e r p r i c e o f f u n d s among l o a n d i v i s i o n s . F u r t h e r m o r e , i f a d o l l a r i s e m p l o y e d i n l o a n t y p e i , i t w i l l n o t be a v a i l i a b l e f o r t h e o t h e r n-1 t y p e s o f l o a n s i n t h e l o a n p o r t f o l i o . T h e r e f o r e , t h e c o s t of f u n d s c a n be p e r c e i v e d a s t h e o p p o r t u n i t y c o s t o f f u n d s w i t h i n t h e l o a n p o r t f o l i o . 5.1.4 LAYOUT OF THE MODEL L e t us f i r s t d e f i n e t h e v a r i a b l e s : Tf = t h e t o t a l e x p e c t e d p r o f i t L = t h e t o t a l amount o f l o a n a b l e f u n d s a v a i l a b l e C = t h e m a r g i n a l c o s t o f f u n d s L ^ = t h e q u a n t i t y o f l o a n a b l e f u n d s a l l o t t e d t o l o a n c a t e g o r y i L p = t h e f r a c t i o n o f t h e l o a n p o r t f o l i o i n l o a n t y p e i = L £ / L <s»z = maximum a c c e p t a b l e l o a n p o r t f o l i o r i s k 37 SL.1 = t h e a c t u a l l o a n p o r t f o l i o r i s k c o v a r i a n c e b e t w e e n t h e p a y b a c k s of l o a n t y p e i a n d j cSr," = t h e v a r i a n c e o f t h e p a y b a c k o f l o a n t y p e i R.*£]= n e t r a t e o f r e t u r n on l o a n e d f u n d s of l o a n t y p e i Tl = number o f l o a n t y p e s The o p t i m a l l o a n a b l e fund a l l o c a t i o n model: Max TT = i Li • R L L- : - C L s. t . i L L = L 1 - JL L i £ O V L where 5 ^ = i (.LhU^y+4i^4^-N o t e : i f we assume i n d e p e n d e n c e among l o a n t y p e s , t h e n 38 5.2 SOLVING THE MODEL I N A CENTRALIZED ENVIRONMENT When t h e d e c i s i o n m e c h a n i s m o f t h e bank i s f u l l y c e n t r a l i z e d , t h e o p t i m a l a l l o t m e n t s o f l o a n a b l e f u n d s w i l l be t r a n s f e r r e d f r o m t h e c e n t r a l p l a n n i n g g r o u p t o i n d i v i d u a l l o a n d i v i s i o n s . I n s u c h i n s t a n c e s , t h e p l a n n i n g g r o u p knowns e x a c t l y what t h e o p e r a t i n g f u n c t i o n s a r e f o r a l l l o a n d i v i s i o n s . The a l l o t m e n t s o f f u n d s w i l l t h e n s i m p l y be g i v e n by s o l v i n g t h e model p r o p o s e d i n s e c t i o n 5.1.4. We s o l v e t h e p r o b l e m w i t h L a g r a n g i a n m u l t i p l i e r t e c h n i q u e : The L a r g r a n g i a n e x p r e s s i o n o f t h e p r o b l e m i s KiiM'-) = i Li - R 1 L ] - C L + \(L-i Li) and t h e p a r t i a l d e r i v a t i e s a r e J2Z - • L - 1 L i . C«) 9 X , 9 A . • A t o p t i m u m , t h e p a r t i a l d e r i v a t i v e s a r e e q u a t e d w i t h z e r o 39 l l * ' and t h e r e s u l t i n g e q u a t i o n s a r e s o l v e d s i m u l t a n e o u s l y f o r L ^ ^ h?. , a n a i t * ^ c ^ . x . * . n . A n a l y s i s o f t h e r e s u l t s o f f i r s t o r d e r c o n d i t i o n : L e t \- X/L We c a n r e w r i t e e q u a t i o n (5.4) a s Rl'r_i - A , -v'LK =-° (in) where fJJ , X ,and V^A*. c a n be i n t e r p r e t e d r e s p e c t i v e l y a s t h e m a r g i n a l ( n e t ) r e t u r n p e r c e i v e d by d i v i s i o n i f o p p o r t u n i t y c o s t o f f u n d s , a n d m a r g i n a l c o s t o f r i s k f o r l o a n d i v i s i o n i . As was m e n t i o n e d i n C h a p t e r T h r e e , t h e l a t t e r two numbers a r e v e r y i m p o r t a n t t o t h e c o m p l e t i o n o f t h e p r o f i t a b i l i t y a n a l y s i s . The c e n t r a l p l a n n i n g g r o u p o f t h e bank c a n p a s s A i , t h e m a r g i n a l c o s t o f f u n d s t o t h e l o a n d i v i s i o n s f o r t h e c a l c u l a t i o n o f t h e p r o f i t a b i l i t y i n d e x . I n a d d i t i o n , A*, a n d Lp c a n a l s o 40 be p a s s e d down t o t h e l o a n d i v i s i o n a l o f f i c e s where V*~ A i w i l l be u s e d a s t h e d e f a u l t r i s k p remium f o r a d d i t i o n a l l o a n ( i . e . , i t i s a r a t e , e . g . , 2% a p p l i e d t o s i z e o f i n c r e m e n t a l l o a n s ) . 5.3 SOLVING THE MODEL I N A DECENTRALIZED ENVIRONMENT The method o f s o l v i n g t h e model s u g g e s t e d i n s e c t i o n 5.2 demands l a r g e i n f o r m a t i o n f l o w s w i t h i n t h e bank s t r u c t u r e . The c e n t r a l p l a n n i n g g r o u p must know e x a c t l y what a l l t h e o p e r a t i n g f u n c t i o n s o f i n d i v i d u a l l o a n d i v i s i o n s l o o k l i k e . T h i s w o u l d be r a t h e r a d i f f i c u l t a n d c o s t l y t a s k p a r t i c u l a r l y i n an e n v i r o n m e n t where e a c h d i v i s i o n e x p e r i e n c e s d i f f e r e n t g r o w t h and c h a n g e . I t w o u l d be v e r y d i f f i c u l t f o r t h e bank t o c o n s t r u c t a c c u r a t e f u n c t i o n s i n e a c h d i v i s i o n w h i c h r e p r e s e n t t h e i r i n t e r e s t r e v e n u e s , d e p o s i t g e n e r a t i o n p a t t e r n s , e x p e c t e d l o a n l o s s e s , o v e r h e a d s , a n d c a r r y i n g c o s t s . M o r e o v e r , i t may i n v o l v e a huge amount o f i n f o r m a t i o n f l o w w i t h i n t h e bank s t r u c t u r e w h i l e t h e p o s s i b i l i t y o f t r a n s m i t t i n g t h e s e p i e c e s o f i n f o r m a t i o n e f f e c t i v e l y a n d e f f i c i e n t l y c o u l d be a d m i n i s t r a t i v e l y i n f e a s i b l e . However, t h e s e a r e t h e v i t a l s t e p s t h a t t h e bank must go t h r o u g h i f t h e bank w a n t s t o s o l v e t h e m o d e l s i m u l t a n e o u s l y a s i s i n s e c t i o n 5.2. As an a l t e r n a t i v e t o t h i s p r o c e d u r e , we c a n a p p l y a d e c o m p o s i t i o n a l t e c h n i q u e s u g g e s t e d by Baumol [ 1 9 6 4 ] w h i c h c o u l d be u s e d t o o b t a i n t h e same r e s u l t s a s w o u l d be o b t a i n e d i f t h e bank were s o l v i n g t h e s e t o f n o n - l i n e a r e q u a t i o n s g i v e n by t h e f i r s t o r d e r c o n d i t i o n s i m u l t a n e o u s l y . The d e c o m p o s i t i o n 41 p r o c e d u r e c o n s i t i t u t e s a d e c i s i o n m e c h a n i s m f o r t h e e n t i r e l o a n s e c t i o n of t h e bank where i n d i v i d u a l l o a n d i v i s i o n s f o r m u l a t e t h e i r own p l a n s and t h e c e n t r a l p l a n n i n g g r o u p p e r f o r m s a c o o r d i n a t i n g f u n c t i o n . I n e v i t a b l y , s u b o p t i m a l d e c i s i o n s w i l l be made i n d e p e n d e n t l y by l o a n d i v i s i o n s s t r i v i n g t o m a x i m i z e t h e i r d i v i s i o n a l p r o f i t s . H owever, t h e d e c o m p o s i t i o n a l p r o c e d u r e s o f f e r a method t o a l l o w t h e c e n t r a l p l a n n i n g g r o u p t o c o o r d i n a t e l o a n d i v i s i o n s y i e l d i n g a s o l u t i o n t h a t i s o p t i m a l f o r t h e e n t i r e l o a n s e c t i o n . R e c a l l f r o m t h e e q u a t i o n s y s t e m (5 . 7 ) t h a t /\, and r e s u l t f r o m t h e s o l u t i o n o f a s e t o f s i m u l t a n e o u s e q u a t i o n s . Assume t h a t t h e s e two number a r e c a l c u l a t e d a t t i m e t ; t h e n t h e m a r g i n a l c o s t o f f u n d s and t h e r i s k f a c t o r f o r c a l c u l a t i o n o f t h e c o s t o f r i s k c a n be w r i t t e n a s \ f and /\* r e s p e c t i v e l y . Now l e t us l o o k a t t h e d e c o m p o s i t i o n p r o c e d u r e w h i c h w o u l d e v e n t u a l l y p r o v i d e t h e bank an o p t i m a l l o a n p o r t f o l i o : 1. E a c h d i v i s i o n s u b m i t s t o t h e l o a n p l a n n i n g g r o u p t h e m a r g i n a l r e t u r n p e r c e i v e d by t h e d i v i s i o n t o g e t h e r w i t h t h e h i s t o r i c a l d a t a of l o a n r e t u r n . The l a t t e r w i l l be u s e d by t h e p l a n n i n g g r o u p f o r t h e c a l c u l a t i o n o f e x p e c t e d y i e l d a n d r i s k o f e a c h d i v i s i o n . 2. By s o l v i n g t h e e q u a t i o n s y s t e m . ( 5 . 7 ) , t h e p l a n n i n g g r o u p o b t a i n s t h e c o s t o f f u n d s u s e d , ^ and t h e r i s k f a c t o r f o r c o s t o f r i s k c a l c u l a t i o n , )\* . T h e s e two numbers a r e t h e n s e n t t o t h e l o a n d i v i s i o n s . A t t h i s p o i n t , e q u a t i o n s ( 5 . 5 ) and (5.6) a r e u n l i k e l y t o be s a t i s f i e d ; t h e r e f o r e , \ t a n d \ t a r e s u b o p t i m a l . 42 3 . B a s e d on and V , l o a n d i v i s i o n s w i l l d e t e r m i n e t h e i r i n d i v i d u a l o p t i m a l l o a n q u a n t i t i e s a t t i m e t , Lc^jfc- by u s i n g t h e p r o f i t a b i l i t y a n a l y s i s d i s c u s s e d i n C h a p t e r T h r e e . The c o s t o f f u n d s i s )\^ , w h i l e t h e c o s t o f r i s k i s \J L A*. L o a n a p p l i c a t i o n s w i l l be a c c e p t e d i f t h e i r p r o f i t a b i l i t y i n d i c e s a r e h i g h e r t h a n 1 0 0 ; t h e sum of t h e s e a c c e p t e d l o a n a p p l i c a t i o n s i n e a c h d i v i s i o n w i l l be t h e demand o f l o a n a b l e f u n d s o f t h a t d i v i s i o n a t t i m e t . I n a d d i t i o n , l o a n d i v i s i o n s h a ve t o d e t e r m i n e t h e i r p a r t i a l d e r i v a t i v e s o f l o a n a b l e f u n d s w i t h r e s p e c t t o A, , ^-— a n d t h e i r p a r t i a l d e r i v a t i v e s o f l o a n a b l e f u n d f r a c t i o n w i t h r e s p e c t t o /\* , s> ( m a t h e m a t i c a l l y s \ t ~ L V >• 1 1 seems t o be a d i f f i c u l t t a s k f o r l o a n d i v i s i o n m a n a g e r s ; h o w e v e r , t h e s e p a r t i a l d e r i v a t i v e s c a n be e s t i m a t e d by n u m e r i c a l p r o c e d u r e s . L o a n d i v i s i o n m a n a g e r s c a n e s t i m a t e t h e p a r t i a l d e r i v a t i v e s o f t h e l o a n q u a n t i t y w i t h r e s p e c t t o t h e c h a n g e o f t h e c o s t o f f u n d s by a d d i n g a n d s u b t r a c t i n g a s m a l l number t o and f r o m t h e c u r r e n t v a l u e o f ^hT a n d t h e n c a l c u l a t i n g t h e new demands o f l o a n a b l e f u n d s . The d i f f e r e n c e s b e t w e e n t h e s e new demands o f l o a n a b l e f u n d s and t h e o r i g i n a l demand o f l o a n a b l e f u n d s c a l c u l a t e d b a s e d on t h e "X? c a n s e r v e a s t h e n u m e r i c a l e s t i m a t i o n o f t h e p a r t i a l d e r i v a t i v e s o f demand f o r l o a n a b l e f u n d s w i t h r e s p e c t t o )\, . S i m i l a r p r o c e d u r e s c a n be a p p l i e d t o t h e e s t i m a t i o n o f t h e p a r t i a l d e r i v a t i v e s o f demand f o r l o a n a b l e f u n d s w i t h r e s p e c t t o • i *- ' 4. W i t h a l l t h e l o a n a b l e f u n d r e q u e s t s , L-Q/t S a n d p a r t i a l d e r i v a t i v e s o f l o a n a b l e f u n d s w i t h r e s p e c t t o \, a n d , 43 ^ — a n d ^ , t h e p l a n n i n g g r o u p w i l l c h o o s e A i and so a s t o s a t i s f y t h e c o n d i t i o n s e t o u t by e q u a t i o n s (5.5) and (5 .6) . E q u i v a l e n t l y , >\t + l and XC' c a n be c h o s e n by s o l v i n g t h e f o l l o w i n g s y s t e m : i LU + A\, i 4 aX- i 1% - L = ° ^ t - i *=» a X , = XT' - XT ( * * 0 A X , , x r - > c . When a n d a)\». t e n d t o be v e r y s m a l l , we c a n r e w r i t e e q u a t i o n s ( 5 . 8)'and (5.9) a s a X , ( 4 L ^ - r = ^ - ^ cs«) S o l v i n g e q u a t i o n s ( 5 . 1 2 ) a n d (5. 1 3 ) g i v e A A/ and ^ a n d , by s u b s t i t u t i n g them i n t o e q u a t i o n s ( 5 . 1 0 ) a nd 44 ( 5 . 1 1 ) , we g e t A i a n d / l i . T h e s e r e v i s e d numbers w i l l a g a i n be p a s s e d t o l o a n d i v i s i o n s . 5. P r o c e d u r e 3 a n d 4 a r e r e p e a t e d u n t i l we a r r i v e a t t h e o p t i m a l s o l u t i o n . 45 6 . SIMULATIONS AND THE INTERPRETATIONS A s i m u l a t i o n p r o g r a m w r i t t e n i n PL/1 i s u s e d to ' t e s t t h e f e a s i b i l i t y o f t h e p r o p o s e d bank a s s e t s a l l o c a t i o n m o d e l . In a d d i t i o n , t h e r e a r e two more i n t e r e s t i n g q u e s t i o n s t h a t t h e s i m u l a t i o n s i n t e n d t o a d d r e s s : (1) what s o r t o f a d j u s t m e n t s w o u l d be made among a n d w i t h i n t h e l o a n p o r t f o l i o i f t h e l e v e l o f a c c e p t a b l e r i s k i s c h a n g e d ? (2) a r e l o a n s w i t h h i g h e r d e p o s i t g e n e r a t i o n s / l o w e r i n t e r e s t r a t e s p r e f e r a b l e t o t h o s e l o a n s w i t h l o w e r d e p o s i t g e n e r a t i o n s / h i g h e r i n t e r e s t r a t e s , o r v i c e v e r s a ? In C h a p t e r F o u r , we d i s c u s s e d some o f t h e p o s s i b l e j u s t i f i c a t i o n s f o r t h e e s t a b l i s h m e n t o f t h e maximum a c c e p t a b l e l o a n p o r t f o l i o r i s k . We want t o s t u d y t h e t y p e o f a c t i o n s t h e bank c o u l d t a k e when t h e r e a r e c h a n g e s i n t h e f a c t o r s w h i c h d e t e r m i n e t h e l e v e l o f maximum p o r t f o l i o r i s k : t h e I n s p e c t o r G e n e r a l o r t h e CDIC may f i n d i t a c c e p t a b l e t o a l l o w t h e b a n k s t o t a k e u p h i g h e r l e v e l o f p o r t f o l i o r i s k ; t h e a g e n c y c o s t s a n d t h e b a n k r u p t c y c o s t may be r e d u c e d ; t h e bank management may f i n d t h a t i t i s p o s s i b l e t o a c c e p t h i g h e r r i s k w i t h o u t d a m a g i n g t h e l i q u i d i t y a n d c a p i t a l c e r t a i n t y o f t h e b a n k . In o u r m o d e l , t h e o p t i m a l amount o f l o a n a b l e f u n d s i s p r e d e t e r m i n e d . N a t u r a l l y , t h e most s i g n i f i c a n t f a c t o r w h i c h a f f e c t s t h e o p t i m a l amount o f l o a n a b l e f u n d w o u l d be t h e l e v e l o f d e p o s i t s i n t h e b a n k . When a l o a n i s m a d e , t h e bank may be w i l l i n g t o c h a r g e a l o w e r i n t e r e s t r a t e i f t h e l o a n i s e x p e c t e d t o g e n e r a t e d e p o s i t s i n t h e f u t u r e . T h i s i s done b e c a u s e t h e l o a n p r i c i n g d e c i s i o n h a s a c c o u n t e d f o r t h e f u t u r e b e n e f i t s o f 46 c u s t o m e r r e l a t i o n s h i p s . B u t , i s i t t r u e t h a t t h o s e l o a n s w i t h h i g h e r d e p o s i t g e n e r a t i o n / l o w e r i n t e r e s t r a t e s a r e a l w a y s p r e f e r a b l e t o t h o s e l o a n s w i t h l o w e r d e p o s i t g e n e r a t i o n s / h i g h e r i n t e r e s t r a t e s , o r v i c e v e r s a ? 6 . 1 TESTING THE F E A S I B I L I T Y OF THE MODEL C o n s i d e r a bank w i t h t h r e e l o a n d i v i s i o n s . T h e s e l o a n d i v i s i o n s a r e c h a r a c t e r i z e d by t h e a v e r a g e v a r i a n c e s o f t h e i r r e t u r n s on l o a n s . L o a n d i v i s i o n 1 c o n s i s t s - o f low v a r i a n c e l o a n s ( e . g . , t r e a s u r y b o n d s ) . L o a n d i v i s i o n 2 c o n s i s t s o f h i g h v a r i a n c e l o a n s ( e . g . , u n s e c u r e d p e r s o n a l l o a n s ) w h i l e l o a n d i v i s i o n 3 h a s medium v a r i a n c e l o a n s ( e . g . , s e c u r e d l o a n s ) . F o r s i m p l i c i t y , t h e f i x e d a nd v a r i a b l e o v e r h e a d c o s t s a r e assumed t o be i d e n t i c a l . A l l t h e l o a n s i n t h e t h r e e c a t e g o r i e s a r e c h a r g e d on a " r a t e o n l y " b a s i s ( i . e . , t h e r e i s no r e d u c t i o n on t h e o u t l a y o f f u n d s a n d no e x p e c t e d d e p o s i t g e n e r a t i o n i n t h e f u t u r e ) . The i n i t i a l p o s i t i o n o f t h e bank l o a n p o r t f o l i o i s 60 p e r c e n t i n t h e low v a r i a n c e l o a n c a t e g o r y , 25 p e r c e n t i n t h e medium v a r i a n c e l o a n c a t e g o r y , a n d 1 5 p e r c e n t i n t h e h i g h v a r i a n c e l o a n c a t e g o r y . The n a t u r e o f t h e l o a n o p p o r t u n i t i e s w i t h i n e a c h l o a n c a t e g o r y i s d i s p l a y e d i n A p p e n d i x Two. T h e r e a r e 360 l o a n a p p l i c a t i o n s i n e a c h l o a n c a t e g o r y . W h i l e t h e s e l o a n a p p l i c a t i o n s a r e d i s t i n g u i s h e d by t h e r a t e s c h a r g e d on them, t h e y a l l c a r r y t h e same amount o f f u n d s r e q u e s t e d . T h i s i s done t o s i m u l a t e t h e downward s l o p i n g n a t u r e of i n t e r e s t r e v e n u e o f e a c h l o a n d i v i s i o n . The m o d el i s t e s t e d u n d e r f o u r d i f f e r e n t l e v e l s o f l o a n a b l e f u n d s a n d e i g h t l e v e l s o f maximum 47 p o r t f o l i o r i s k — a t o t a l o f 32 r u n s . The s i m u l a t i o n s assume' t h a t the" bank a d j u s t s t h e c o s t o f f u n d v a l u e a n d t h e r i s k f a c t o r v a l u e m o n t h l y . The r e s u l t s o f t h e 32 s i m u l a t i o n r u n s l i s t e d i n A p p e n d i x T h r e e i n d i c a t e t h a t t h e bank c a n g e n e r a l l y a c h i e v e an o p t i m a l a l l o c a t i o n o f i t s l o a n a b l e f u n d s w i t h i n a s i x month p e r i o d a n d , i n f a c t , a f t e r m a k i n g t h r e e a d j u s t m e n t s f r o m i t s i n i t i a l p o s i t i o n , t h e bank i s v e r y c l o s e t o i t s optimum. The v a l u e s ' of- t h e c o s t o f f u n d s , a n d the' v a l u e s o f t h e r i s k f a c t o r , c o r r e s p o n d i n g t o t h e f o u r l e v e l s o f l o a n a b l e f u n d s a n d e i g h t l e v e l s o f maximum a c c e p t a b l e p o r t f o l i o r i s k , a r e shown i n T a b l e s I and I I Column one o f t h e t a b l e s r e p r e s e n t s d i f f e r e n t l e v e l s o f l o a n p o r t f o l i o r i s k t h a t t h e bank i s w i l l i n g t o t a k e . The c o l u m n s d e n o t e d by C.O.F. and R.F. r e p r e s e n t t h e c o r r e s p o n d i n g v a l u e s o f t h e c o s t o f f u n d s a n d r i s k f a c t o r a t d i f f e r e n t l e v e l s o f maximum a c c e p t a b l e l o a n p o r t f o l i o r i s k . Two s i m p l e p r o p o s i t i o n s a r e d i s p l a y e d by t h e movements of t h e c o s t o f f u n d s a n d t h e movements o f t h e r i s k f a c t o r : (1) t h e l o w e r t h e l e v e l o f l o a n a b l e f u n d s , t h e h i g h e r t h e c o s t o f f u n d s ; (2) t h e l o w e r t h e l e v e l o f t h e maximum a c c e p t a b l e p o r t f o l i o r i s k , t h e h i g h e r t h e r i s k f a c t o r . B e s i d e s t h e s e two s i m p l e p r o p o s i t i o n s , we s e e t h a t t h e t h e c o s t o f f u n d v a l u e i s i n c r e a s i n g when t h e l e v e l o f maximum a c c e p t a b l e p o r t f o l i o r i s k i s i n c r e a s i n g ; t h e r i s k f a c t o r v a l u e i s i n c r e a s i n g when t h e l e v e l o f l o a n a b l e f u n d s i s d e c r e a s i n g . T h e s e phenomena i l l u s t r a t e t h a t t h e p r o p o s e d d e c e n t r a l i z e d m o d e l i s a f e a s i b l e m e c h a n i s m f o r c r e d i t r a t i o n i n g a n d p o r t f o l i o r i s k c o n t r o l l i n g . 48 As w e l l , t h e movements o f t h e c o s t o f f u n d s c o i n c i d e w i t h t h e m a r g i n a l c o s t c o n c e p t o f t h e c o s t o f f u n d s d i s c u s s e d i n s e c t i o n 5.1.3.2. The o p t i m a l l o a n a b l e f u n d a l l o c a t i o n s i l l u s t r a t e d i n T a b l e s I I I a n d I V i n d i c a t e t h a t t h e d i s t r i b u t i o n o f l o a n a b l e f u n d s d e p e n d s s o l e l y on t h e l e v e l o f p o r t f o l i o r i s k w h i c h t h e bank i s w i l l i n g t o t a k e a n d i s i n d e p e n d e n t o f t h e amount o f l o a n a b l e f u n d s a v a i l a b l e t o t h e b a n k . S i n c e t h e r i s k i n e s s o f a l l l o a n s w i t h i n e a c h l o a n c a t e g o r y i s assumed t o be t h e same, t h e o n l y way t h e bank c a n r e d u c e l o a n p o r t f o l i o r i s k i s t o s h i f t l o a n a b l e f u n d s , o u t o f h i g h r i s k c a t e g o r i e s . T hese o p e r a t i o n s a r e e x p l i c i t l y shown i n t h e r e s u l t s . T A B L E I VALUES OF THE COST OF FUNDS AND THE R ISK FACTOR AMOUNT OF LOANABLE FUNDS A V A I L A B L E MAXIMUM PORTFOLIO R ISK 0 . 0 0 3 0 C . 6 , 5 0 0 , 0 0 0 R. C . 7 , 0 0 0 , 0 0 0 R. 3 . 7 0 6 5 E - 2 6 . 5000 3 . 2 9 3 5 E - 2 6 . 5000 0 . 0 0 3 5 4 . 0 9 4 5 E - 2 5 . 4961 3 . 7 7 1 2 E - 2 5 . 2941 0 . 0 0 4 0 4 . 6 2 9 5 E - 2 4 . 1989 4 . 3 6 3 2 E - 2 3 . 9063 0 . 0 0 4 5 5 . 0 9 1 5 E - 2 3 . 21 93 4 . 8 4 3 5 E - 2 2 . 9276 0 . 0 0 5 0 5 . 5 0 2 9 E - 2 2 . 4834 5 . 2 6 4 3 E - 2 2 . 1301 0 . 0 0 5 5 5 . 8 6 6 3 E - 2 1 . 7868 5 . 6 4 5 2 E - 2 1 . 44 56 0 . 0 0 6 0 6 . 1 8 7 8 E - 2 1 . 2482 6 . 0 0 1 3 E - 2 0 . 8700 0 . 0 0 6 5 6 . 4 8 7 1 E - 2 0 . 7730 6 . 3 0 3 0 E - 2 0 . 4096 C . O . F . = COST OF FUNDS; R . F . = R ISK FACTOR T A B L E II VALUE OF THE COST OF FUNDS AND THE R I S K FACTOR AMOUNT OF LOANABLE FUNDS A V A I L A B L E MAXIMUM PORTFOLIO RISK 0 . 0 0 3 0 C . 7 , 5 0 0 , 0 0 0 O . F . , X , R . F . , ^ 8 , 0 0 0 , 0 0 0 C . O . F . , \ t R 2 . 7 1 5 6 E - 2 6 . 5 0 0 0 1 . 1 9 8 7 E - 2 6 . 5 0 0 0 0 . 0 0 3 5 3 . 4 6 9 2 E - 2 4 . 9 9 4 2 3 . 1 2 1 0 E - 2 4 . 8 3 6 9 0 . 0 0 4 0 4 . 0 7 3 0 E - 2 3 . 6 7 6 0 3 . 7 8 0 3 E - 2 3 . 4 0 6 6 0 . 0 0 4 5 4 . 5 8 8 1 E - 2 2 . 6 1 5 9 4 . 3 1 4 5 E - 2 2 . 3 4 4 9 0 . 0 0 5 0 5 . 0 3 3 1 E - 2 1 . 8 1 2 2 4 . 7 9 6 7 E - 2 1 . 4 8 1 2 0 . 0 0 5 5 5 . 4 3 6 4 E - 2 1 . 1 169 5 . 2 2 2 2 E - 2 0 . 7 6 8 4 0 . 0 0 6 0 5 . 7 9 8 8 E - 2 0 . 5 3 9 1 5 . 5 9 0 4 E - 2 0 . 1 9 5 6 0 . 0 0 6 5 6 . 1 2 0 7 E - 2 0 . 0 5 7 4 5 . 9 5 7 8 E - 2 0 . 0 0 0 0 C . O . F . = COST OF FUNDS; R . F . = R ISK FACTOR T A B L E I I I D ISTR IBUT ION OF LOANABLE FUNDS (FRACTIONS) AMOUNT OF LOANABLE FUNDS AVAILABLE ' " MAXIMUM PORTFOLIO R ISK 0 . 0 0 3 0 LP1 6 , 5 0 0 , 0 0 0 LP2 LP3 LP1 7 , 0 0 0 , 0 0 0 LP2 L P 3 . 4 7 . 2 4 . 2 9 . 4 8 . 2 3 . 2 9 0 . 0 0 3 5 . 4 5 . 2 5 . 3 0 . 4 5 . 2 5 . 3 0 0 . 0 0 4 0 .41 . 2 7 . 3 2 . 4 1 . 2 8 .31 0 . 0 0 4 5 . 3 7 . 2 9 . 3 4 . 3 7 . 3 0 . 3 3 0 . 0 0 5 0 . 3 3 . 3 2 ' .35 . 3 4 . 3 2 . 3 4 0 . 0 0 5 5 . 3 0 . 3 4 . 3 & . 3 0 . 34 . 3 6 0 . 0 0 6 0 . 2 7 . 3 6 . 3 7 . 2 7 . 3 6 . 3 7 0 . 0 0 6 5 . 2 4 . 3 8 . 3 8 . 2 4 . 3 8 . 3 8 L P 1 = FRACTION OF LOANABLE FUNDS ALLOCATED TO D I V I S I O N 1 T A B L E IV D ISTR IBUT ION OF LOANABLE FUNDS (FRACTIONS) AMOUNT OF LOANABLE FUNDS A V A I L A B L E MAXIMUM PORTFOLIO R ISK 0 . 0 0 3 0 LP1 7 , 5 0 0 , 0 0 0 LP2 L P 3 LP1 B , 0 0 0 , 0 0 0 LP2 L P 3 . 4 8 . 2 3 . 2 9 . 4 5 . 2 5 . 3 0 0 . 0 0 3 5 . 4 5 . 2 5 . 3 0 . 4 5 . 2 5 . 3 0 0 . 0 0 4 0 . 4 1 . 2 8 .31 . 4 0 . 2 8 . 3 2 0 . 0 0 4 5 . 3 7 . 3 0 . 3 3 . 3 7 . 3 0 . 3 3 0 . 0 0 5 0 . 3 4 . 3 2 . 3 4 . 3 4 . 3 2 . 3 4 0 . 0 0 5 5 . 3 0 . 3 5 . 3 5 . 3 0 . 3 5 . 3 5 0 . 0 0 6 0 . 2 8 . 3 6 . 3 6 . 2 8 . 3 6 . 3 6 0 . 0 0 6 5 . 2 5 . 3 8 . 3 7 . 2 5 . 3 7 . 3 8 LP1 = FRACTION OF LOANABLE FUNDS ALLOCATED TO D I V I S I O N 1 T A B L E V D ISTRIBUT ION OF LOANABLE FUNDS ( 0 , 0 0 0 ) AMOUNT OF LOANABLE FUNDS' AVAILABLE-MAXIMUM PORTFOLIO R ISK 0 . 0 0 3 0 LQ1 5 , 5 0 0 , 0 0 0 LQ2 LQ3 7 , 0 0 0 , 0 0 0 LQ1 LQ2 LQ3 307 1 53 186 337 1 64 199 0 . 0 0 3 5 292 161 195 314 176 210 0 . 0 0 4 0 264 1 77 207 285 191 222 0 . 0 0 4 5 239 191 218 259 208 233 0 . 0 0 5 0 217 206 227 235 . 224 242 0 . 0 0 5 5 195 220- 235 21 2 238 250 0 . 0 0 6 0 1 76 232 242 191 251 258 0 . 0 0 6 5 1 57 245 248 170 265 263 LQ1 = QUANTITY OF LOANABLE FUNDS ALLOCATED TO D I V I S I O N 1 T A B L E VI D ISTR IBUT ION OF LOANABLE FUNDS ( 0 , 0 0 0 ) AMOUNT OF LOANABLE FUNDS A V A I L A B L E MAXIMUM PORTFOLIO RISK 0 . 0 0 3 0 7 , LQ1 5 0 0 , 0 0 0 LQ2 LQ3 LQ1 8 , 0 0 0 , 0 0 0 LQ2 LQ3 360 175 213 360 1 97 240 0 . 0 0 3 5 336 188 222 360 203 237 0 . 0 0 4 0 306 208 236 327 223 251 0 . 0 0 4 5 278 224 248 297 242 262 0 . 0 0 5 0 252 241 257 270 259 271 0 . 0 0 5 5 229 257 265 245 276 281 0 . 0 0 6 0 206 272 272 221 292 287 0 . 0 0 6 5 184 287 279 197 293 284 LQ1 = QUANTITY OF LOANABLE FUNDS ALLOCATED TO D I V I S I O N 1 52 6.2 TESTING THE EFFECT OF FUTURE CUSTOMER RELATIONSHIPS ON LOAN PRICING We now assume t h a t two o f t h e l o a n d i v i s i o n s have l o a n s w h i c h p r o v i d e f u t u r e demand d e p o s i t g e n e r a t i o n ; t h e r e f o r e , t h e a v e r a g e i n t e r e s t r a t e s a s k e d by t h e bank on t h e s e l o a n s w o u l d be r e d u c e d i n r e l a t i o n t o t h e e x p e c t e d p r e s e n t v a l u e o f f u t u r e c u s t o m e r r e l a t i o n s h i p . We h y p o t h e s i z e t h a t when t h e l e v e l o f l o a n a b l e f u n d s i s l o w , t h e h i g h d e p o s i t g e n e r a t i o n l o a n s w i l l become more a t t r a c t i v e e v e n t h o u g h t h e i r i n t e r e s t ' e a r n i n g s a r e l o w e r . T h i s h y p o t h e s i s i s made b a s e d on t h e a s s u m p t i o n t h a t t h e c u r r e n t l e v e l o f l o a n a b l e f u n d s i s d i r e c t l y r e l a t e d t o t h e f u t u r e l e v e l s o f l o a n a b l e f u n d s . When t h e l e v e l o f l o a n a b l e f u n d s i s l o w , t h e bank must t a k e a p p r o p r i a t e a c t i o n s , e . g . , g r a n t i n g more h i g h d e p o s i t g e n e r a t i o n l o a n s i n o r d e r t o i m p r o v e f u t u r e l e v e l s o f l o a n a b l e f u n d s . S i m u l a t i o n s were r u n u n d e r f o u r d i f f e r e n t l e v e l s o f l o a n a b l e f u n d s a nd t h e r e s u l t s a r e p r e s e n t e d i n t a b l e s V I I , V I I I , a n d I X . Columns one and two o f T a b l e V I I r e p r e s e n t , r e s p e c t i v e l y , t h e d i f f e r e n t a mounts o f l o a n a b l e f u n d s a v a i l a b l e t o t h e bank and t h e c o r r e s p o n d i n g v a l u e s o f t h e c o s t o f f u n d s . C o l u m n s t h r e e a n d f o u r i n d i c a t e t h e a v e r a g e i n t e r e s t r a t e s o f t h o s e l o a n s a c c e p t e d i n d i v i s i o n s two and t h r e e . Columns f i v e a n d s i x i n d i c a t e t h e a v e r a g e p r e s e n t v a l u e s o f f u t u r e c u s t o m e r r e l a t i o n s h i p s o f t h o s e l o a n s g r a n t e d i n d i v i s i o n s two and t h r e e . T h e r e a r e s i x d i f f e r e n t l e v e l s o f f u t u r e d e p o s i t g e n e r a t i o n r a t e s a s s o c i a t e d w i t h t h e l o a n s i n d i v i s i o n s two a n d t h r e e ; t h e y a r e p r e s e n t e d i n c o l u m n one o f T a b l e V I I I a n d I X . Columns two 53 a n d t h r e e o f t h e s e t a b l e s i n d i c a t e t h e l o w e s t i n t e r e s t r a t e s t h a t l o a n a p p l i c a t i o n s w i t h d i f f e r e n t d e p o s i t g e n e r a t i o n r a t e s must c a r r y b e f o r e t h e y w i l l be a c c e p t e d by t h e bank ( e . g . , a l o a n a p p l i c a t i o n i n d i v i s i o n two w i t h d e p o s i t g e n e r a t i o n r a t e o f 18 p e r c e n t w i l l be r e j e c t e d i f i t c a r r i e s an i n t e r e s t r a t e l o w e r t h a n 12.11 p e r c e n t when t h e amount o f l o a n a b l e f u n d s i s 6.5 m i l l i o n ) . C o lumns f o u r a n d f i v e o f T a b l e s 6.8 a n d 6.9 r e p r e s e n t t h e amount o f i n t e r e s t t h e bank i s w i l l i n g t o s a c r i f i c e f o r a h i g h e r l e v e l o f d e p o s i t g e n e r a t i o n ( e . g . , when t h e l e v e l o f l o a n a b l e f u n d s i s a t 6;. 5 m i l l i o n , a l o a n o f f i c e r i n ' d i v i s i o n two i s w i l l i n g t o a c c e p t a l o a n a p p l i c a t i o n w i t h 5 p e r c e n t more d e p o s i t g e n e r a t i o n t h a n an 8 p e r c e n t d e p o s i t g e n e r a t i o n l o a n a t t h e e x p e n s e o f 39 b a s i s p o i n t s ) . TABLE V I I AVERAGE INTEREST RATES AND AVERAGE PRESENT VALUES OF CUSTOMER RELATIONSHIPS AVERAGE AVERAGE PRESENT INTEREST RATE VALUE OF C.R.* LOANABLE COST OF LOAN LOAN LOAN LOAN FUNDS FUNDS TWO THREE TWO THREE 6500006 0.0569 0. 1553 0. 1884 0.2047 0. 1 120 7000000 0.0545 0. 1559 0.1809 0.2043 0.1117 7500000 0.0521 0. 1503 0.1770 0..2042 0.1117 8000000 0.0495 0.1481 0.1733 0.2036 0.1117 C.R. = c u s t o m e r r e l a t i o n s h i p ( a p p r o x i m a t e d by t h e d e p o s i t g e n e r a t i o n l e v e l ) 54 T A B L E V I I I THE RELAT IONSHIP BETWEEN CUSTOMER RELAT IONSHIP AND INTEREST R A T E : LOAN T Y P E 2 LOANABLE I FUNDS LOANABLE FUNDS DEPOSIT GENERATION 6500000 LOWEST RATE 8 0 0 0 0 0 0 LOWEST RATE 6 5 0 0 0 0 0 D I F F E R E N C E FROM . 1 3 0 9 8 0 0 0 0 0 0 D I F F E R E N C E FROM . 1 1 5 2 0 . 0 8 0 0 0 . 1 3 0 9 0 . 1152 0 . 0 0 0 0 0 . 0 0 0 0 0 . 1 300 0 . 1 2 7 0 0 . 1133 - 0 . 0 0 3 9 - 0 . 0 0 1 9 0 . 1 8 0 0 0 . 1 2 1 1 0 . 1 0 5 5 - 0 . 0 0 9 8 - 0 . 0 0 9 7 0 . 2 3 0 0 0 . 1 1 5 2 0 . 0 9 9 6 - 0 . 0 1 5 7 - 0 . 0 1 5 6 0 . 2 7 0 0 0 . 1 1 1 1 0 . 0 9 5 7 ' - 0 . 0 1 - 9 9 - 0 . 0 1 9 5 0 . 3 2 0 0 0 . 1 0 5 5 0 . 0 8 9 8 - 0 . 0 2 5 4 - 0 . 0 2 5 4 T A B L E IX THE RELAT IONSHIP BETWEEN CUSTOMER RELAT IONSHIP AND INTEREST R A T E : LOAN TYPE 3 \ LOANABLE FUNDS LOANABLE FUNDS DEPOSIT GENERATION 6500000 LOWEST RATE 8 0 0 0 0 0 0 LOWEST RATE 6 5 0 0 0 0 0 D I F F E R E N C E FROM . 1 5 8 2 8 0 0 0 0 0 0 D I F F E R E N C E FROM . 1 3 4 8 0 . 0 5 0 0 0 . 1 5 8 2 0 . 1 3 4 8 0 . 0 0 0 0 0 . 0 0 0 0 0 . 0 7 5 0 0 . 1 5 4 3 0 . 1 3 2 8 - 0 . 0 0 3 9 - 0 . 0 0 2 0 0 . 1 000 0 . 1 5 2 3 0 . 1 3 0 8 - 0 . 0 0 5 9 - 0 . 0 0 4 0 0 . 1250 0 . 1 4 8 4 0 . 1 2 8 0 . - 0 . 0 0 9 8 - 0 . 0 0 6 8 0 . 1500 0 . 1 4 6 4 0 . 1 2 5 0 - 0 . 0 1 1 8 - 0 . 0 0 9 8 0 . 1750 0 . 1 4 2 5 0 . 1 2 3 0 - 0 . 0 1 5 7 - 0 . 0 1 1 8 55 The r e s u l t s i l l u s t r a t e d i n T a b l e s V I I I a n d I X show t h a t a bank i s a l w a y s w i l l i n g t o s a c r i f i c e some o f t h e i n t e r e s t e a r n i n g s on l o a n s f o r f u t u r e d e p o s i t g e n e r a t i o n . However, t h e amount o f i n t e r e s t e a r n i n g s t h a t t h e bank i s w i l l i n g t o s a c r i f i c e s h o u l d be a d j u s t e d a c c o r d i n g t o t h e a v a i l a b i l i t y o f l o a n a b l e f u n d s . I t i s s i g n i f i c a n t t h a t l o a n a p p l i c a t i o n s w h i c h c a r r y h i g h e r d e p o s i t g e n e r a t i o n r a t e s become more a t t r a c t i v e when t h e a v a i l a b i l i t y o f l o a n a b l e f u n d s i s r e d u c e d ( i . e . , t h e amount o f i n t e r e s t t h a t t h e bank i s w i l l i n g t o s a c r i f i c e d e p e n d s on t h e l e v e l o f t h e l o a n a b l e - f u n d s ) . I t i s v e r y i m p o r t a n t f o r t h e bank t o c h o o s e an a p p r o p r i a t e p r i c e t o pay f o r t h e p r e s e n t v a l u e o f c u s t o m e r r e l a t i o n s h i p s . An a d j u s t m e n t m e c h a n i s m has been n a t u r a l l y b u i l t i n t o t h e p r o p o s e d m o d e l : t h e c o s t o f f u n d s u s e d i n t h e m o d e l i s d e t e r m i n e d by t h e a v a i l a b i l i t y o f l o a n a b l e f u n d s . When t h e a v a i l a b i l i t y o f l o a n a b l e f u n d s i s r e d u c e d , t h e c o s t o f f u n d s w i l l i n c r e a s e . S i n c e t h e v a l u e o f t h e f u t u r e c u s t o m e r r e l a t i o n s h i p s i s a f u n c t i o n o f t h e c o s t o f f u n d s , a h i g h e r v a l u e o f t h e c o s t o f f u n d s w o u l d make a l o a n w i t h h i g h d e p o s i t g e n e r a t i o n r a t e become more a t t r a c t i v e t h a n a l o a n w i t h low d e p o s i t g e n e r a t i o n r a t e . The c e n t r a l i z e d m o d e l s d i s c u s s e d i n C h a p t e r Two h a v e n o t a d d r e s s e d t h e i s s u e o f how much i n t e r e s t r e v e n u e s h o u l d be s a c r i f i c e d f o r t h o s e l o a n s w h i c h g e n e r a t e d e p o s i t s e v e n t h o u g h Kane a n d M a l k i e l [ 1 9 6 5 ] p o i n t o u t t h e i m p o r t a n c e o f them. W i t h an i n c o r r e c t f o r e c a s t i n g o f t h e f u t u r e f l e v e l o f l o a n a b l e f u n d s , a l i n e a r p r o g r a m m i n g m o d e l may b l i n d l y f o r c e t h e l o a n d i v i s i o n s t o t a k e i n l o a n s w i t h d e p o s i t g e n e r a t i o n a t u n d e s i r a b l e p r i c e s s i m p l y b e c a u s e t h e m o d e l 56 imposes some c o n s t r a i n t s on the average d e p o s i t g e n e r a t i o n l e v e l s of l o a n d i v i s i o n s . 6.3 TESTING THE IMPACT OF RISK TIGHTENING ON LOANABLE FUNDS ALLOCATIION As s t a t e d i n s e c t i o n 6 . 1 , i f the loans w i t h i n each ca tegory are homogeneous, then the o n l y mechanism which the bank can use to reduce o v e r a l l r i s k i s to s h i f t funds out of h i g h r i s k c a t e g o r i e s . However, i f there i s more than one r i s k c l a s s w i t h i n each loan c a t e g o r y , then two mechanisms are a v a i l a b l e for a d j u s t i n g o v e r a l l p o r t f o l i o r i s k : funds can be s h i f t e d e i t h e r among or w i t h i n loan c a t e g o r i e s . In o r d e r to accommodate heterogeneous r i s k c h a r a c t e r i s t i c s w i t h i n loan d i v i s i o n s , we modify the model proposed i n Chapter F i v e . Let us denote the average s t andard d e v i a t i o n of payback of loans i n ca tegory i by <?Si and the s t andard d e v i a t i o n of the payback of loan j i n l o a n c a t e g o r y i by ^ . F u r t h e r m o r e , we assume tha t the r i s k c h a r a c t e r i s t i c s of loan a p p l i c a t i o n s in a loan ca tegory can be ranked by a s c a l e system - - a r i s k adjustment f a c t o r denoted by ld{ . Then the s t a n d a r d d e v i a t i o n of the payback of loan a p p l i c a t i o n j i n c a t e g o r y i can be w r i t t e n as I f t h e r e are m l o a n a p p l i c a t i o n s w i t h i d e n t i c a l loan amounts reques ted i n c a t e g o r y i , then the loan p o r t f o l i o r i s k 57 a n d e q u a t i o n ( 5 . 9 ) s h o u l d be m o d i f i e d . ( N o t e : a d e t a i l e d d i s c u s s i o n on t h e c a l c u l a t i o n o f l o a n p o r t f o l i o r i s k c a n be f o u n d i n A p p e n d i x F o u r ) . The l o a n p o r t f o l i o r i s k a n d e q u a t i o n ( 5 . 9 ) a r e m o d i f i e d a s f o l l o w i n g s : L e t kL = t h e a v e r a g e r i s k a d j u s t m e n t f a c t o r c a t e g o r y i Two s e t s o f d a t a a r e u s e d t o t e s t a b a n k ' s r e a c t i o n t o a c h a n g e i n t h e maximum p o r t f o l i o r i s k . W i t h i n e a c h l o a n c a t e g o r y l o a n s a r e d i s t i n g u i s h e d by t h e i r i n t e r e s t r a t e s a n d r i s k c l a s s e s , . In t h e f i r s t s e t o f d a t a t h e i n t e r e s t r a t e s c h a r g e d do n o t v a r y w i t h t h e r i s k t h e i n d i v i d u a l l o a n c a r r i e s ( i . e . , b o r r o w e r s i n d i f f e r e n t r i s k c l a s s e s p a y t h e same r a t e ) . T h i s r e f l e c t s t h e s i t u a t i o n i n w h i c h t h e i n t e r e s t r a t e s c h a r g e d on l o a n s a r e n o t n e g o t i a t e d b e t w e e n t h e bank a n d t h e b o r r o w e r ( e . g . , c a r l o a n s , c r e d i t c a r d s , e t c . ) In t h e s e c o n d s e t o f d a t a t h e i n t e r e s t r a t e s c h a r g e d a r e d i r e c t l y r e l a t e d t o t h e r i s k i n e s s o f t h e l o a n ( e . g . , c o n s t r u c t i o n l o a n s ) . T e s t r e s u l t s o f t h e f i r s t a n d s e c o n d s e t s o f d a t a a r e g i v e n i n T a b l e s X , X I I , 58 X I I , a n d X I I I r e s p e c t i v e l y . Column one i n t h e t a b l e s s t a t e s t h e l e v e l o f p o r t f o l i o r i s k t h a t i s a c c e p t e d by t h e bank w h i l e c o l u m n two c a r r i e s t h e r i s k f a c t o r s a t v a r i o u s l e v e l s o f maximum p o r t f o l i o r i s k . Column t h r e e i n d i c a t e s t h e a v e r a g e i n t e r e s t r a t e o f t h o s e l o a n s a c c e p t e d by t h e b a n k ; c o l u m n f o u r i n d i c a t e s t h e a v e r a g e r i s k a d j u s t m e n t f a c t o r ( i . e . , t h e a v e r a g e r i s k c h a r a c t e r i s t i c s ) o f t h o s e l o a n s a c c e p t e d by t h e bank. The l a s t c o l u m n o f t h e t a b l e s i n d i c a t e s t h e amounts o f l o a n a b l e f u n d s a l l o c a t e d t o t h e l o a n c a t e g o r y u n d e r d i f f e r e n t l e v e l s o f maximum l o a n p o r t f o l i o r i s k . 59 T A B L E X MOVEMENTS OF LOANABLE FUNDS (DATA SET 1; HIGH VARIANCE LOAN) MAXIMUM PORTFOLIO RISK RISK FACTOR AVERAGE INTEREST RATE AVERAGE R . A . F . FRACTION IN THE PORTFOLIO 0 . 0 0 3 6 . 5 0 0 0 0 . 2 1 4 2 1 . 0 4 8 4 0 . 2 4 0 . 0 0 4 5 . 1 4 1 0 0 . 2 1 2 0 1 . 0 5 4 9 0 . 2 7 0 . 0 0 5 3 . 6 0 5 6 0 . 2 0 8 6 1 . 0 6 0 8 0 . 3 1 0 . 0 0 6 2 . 4 6 9 8 0 . 2 0 4 6 1 . 0 6 4 4 0 . 3 5 R . A . F . = R ISK ADJUSTMENT FACTOR 1 T A B L E XI MOVEMENTS OF LOANABLE FUNDS (DATA SET 1; MEDIUM VARIANCE LOAN) MAXIMUM PORTFOLIO RISK RISK FACTOR AVERAGE INTEREST RATE AVERAGE R . A . F . FRACTION IN THE PORTFOLIO 0 . 0 0 3 6 . 5 0 0 0 0 . 1884 0 . 9 4 3 0 0 . 2 9 0 . 0 0 4 5 . 1 4 1 0 0 . 1867 0 . 9 4 6 8 0 . 3 1 0 . 0 0 5 3 . 6 0 5 6 0 . 1845 0 . 9 5 3 1 0 . 3 4 0 . 0 0 6 2 . 4 6 9 8 0 . 1829 0 . 9 5 7 5 0 . 3 6 R . A . F . = R ISK ADJUSTMENT FACTOR 60 T A B L E X I I MOVEMENTS OF LOANABLE FUNDS (DATA SET 2 ; HIGH VARIANCE LOAN) MAXIMUM PORTFOLIO RISK RISK FACTOR AVERAGE INTEREST RATE AVERAGE R . A . F . FRACTION IN THE PORTFOLIO 0 . 0 0 4 5 . 9 4 8 0 0 . 2 1 8 9 1 . 1800 0 . 2 0 0 . 0 0 5 4 . 7 7 4 9 0 . 2 1 3 0 1 . 1 8 0 0 0 . 2 6 0 . 0 0 6 3 . 5 6 2 9 0 . 2 0 9 0 1 . 1780 0 . 3 0 0 . 0 0 7 2 . 6 7 3 1 0 . 2 0 6 0 1 . 1 7 5 0 0 . 3 6 R . A . F . = RISK ADJUSTMENT FACTOR T A B L E X I I I MOVEMENTS OF LOANABLE FUNDS (DATA SET 2 ; MEDIUM VARIANCE LOAN) MAXIMUM PORTFOLIO RISK RISK FACTOR AVERAGE INTEREST RATE AVERAGE R . A . F . FRACTION IN THE PORTFOLIO 0 . 0 0 4 5 . 9 4 8 0 0 . 1 8 8 1 1 . 0 6 8 2 0 . 3 0 0 . 0 0 5 4 . 7 7 4 9 0 . 1870 1 . 0 6 9 8 0 . 3 1 0 . 0 0 6 3 . 5 6 2 9 0 . 1 8 5 0 1 . 0 6 9 8 0 . 3 3 0 . 0 0 7 2 . 6 7 3 1 0 . 1 8 3 0 1 . 0 6 7 0 0 . 3 5 R . A . F . = RISK ADJUSTMENT FACTOR 61 The s i m u l a t i o n r e s u l t s f o r t h e f i r s t d a t a s e t i n d i c a t e t h a t t h e bank w i l l use b o t h m e c h a n i s m s t o r e d u c e i t s l e v e l o f p o r t f o l i o r i s k . L o a n a b l e f u n d s w i l l be s h i f t e d f r o m t h e h i g h t o t h e l o w r i s k l o a n c a t e g o r i e s , w h i l e w i t h i n l o a n d i v i s i o n s , p r i o r i t y i s g i v e n t o t h o s e l o a n a p p l i c a t i o n s w h i c h h a v e l o w e r r i s k c h a r a c t e r i s t i c s . T h i s phenomenon c o i n c i d e s w i t h t h e non-p r i c e r a t i o n i n g b e h a v i o u r s i n t h e l o a n m a r k e t . T h e r e a r e some i n s t a n c e s where t h e l o a n m a r k e t c a n n o t be c l e a r e d by t h e i n t e r e s t r a t e ; t h e r e f o r e , i n o r d e r t o c l e a r t h e m a r k e t , b a n k s g e n e r a l l y r e s o r t t o some n o n - p r i c e " mechanisms": down payment-r e q u i r e m e n t s , c r e d i t s c r e e n i n g , e t c . The s i m u l a t i o n s u s i n g t h e f i r s t d a t a s e t show t h e f u n c t i o n i n g o f s u c h a c r e d i t s c r e e n i n g m e c h a n i s m . T h i s i s b a s e d on t h e a s s u m p t i o n t h a t t h e r e a r e some r e j e c t e d l o a n s w h i c h w o u l d pay a h i g h e r i n t e r e s t r a t e t h a n some a c c e p t e d l o a n s . The s i m u l a t i o n s u s i n g t h e s e c o n d s e t of d a t a r e v e a l a v e r y i n t e r e s t i n g phenomenon. When t h e l e v e l o f maximum a c c e p t a b l e p o r t f o l i o r i s k i s d e c r e a s i n g , t h e two r i s k c o n t r o l m echanisms c a n work i n o p p o s i n g d i r e c t i o n s . A l t h o u g h l o a n a b l e f u n d s a r e m o v i n g o u t o f t h e h i g h a n d medium r i s k c a t e g o r i e s , t h e r e m a i n i n g f u n d s i n t h o s e c a t e g o r i e s a r e m o v i n g , t o w a r d s t h e h i g h e r r i s k l o a n a p p l i c a t i o n s . To u n d e r s t a n d t h i s phenomenon we have t o l o o k a t t h e c a l c u l a t i o n o f t h e c o s t o f r i s k i n t h e p r o f i t a b i l i t y a n a l y s i s . The c o s t o f r i s k o f a l o a n a p p l i c a t i o n i s t h e p r o d u c t o f t h e l o a n c a t e g o r y v a r i a n c e , f r a c t i o n o f l o a n a b l e f u n d s i n t h a t l o a n c a t e g o r y , a n d t h e r i s k a d j u s t m e n t f a c t o r o f t h a t a p p l i c a t i o n . S i n c e t h e i n t e r e s t r a t e c h a r g e d on a l o a n i n d a t a s e t two r e f l e c t s t h e r i s k a d j u s t m e n t f a c t o r o f t h e l o a n , a h i g h 62 r i s k a p p l i c a t i o n w i l l c e r t a i n l y p r o v i d e a h i g h i n t e r e s t r e t u r n . As l o a n a b l e f u n d s move o u t o f a g i v e n l o a n c a t e g o r y , t h e c o s t o f r i s k i n t h a t l o a n c a t e g o r y , i n f a c t , f a l l s . T h i s makes t h o s e l o a n a p p l i c a t i o n s w h i c h c a r r y h i g h r i s k a d j u s t m e n t f a c t o r s r e l a t i v e l y more a t t r a c t i v e . T h e o r e t i c a l l y , i f a l l t h e l o a n a b l e f u n d s a r e removed f r o m a g i v e n c a t e g o r y , t h e m a r g i n a l c o s t o f r i s k i n t h a t c a t e g o r y becomes z e r o . S i n c e t h e model a l w a y s s t r i v e s t o m a x i m i z e t h e b a n k ' s p r o f i t , t h e f i r s t l o a n t h a t w o u l d be made i n t h a t c a t e g o r y w o u l d be t h e one w h i c h c a r r i e s t h e h i g h e s t i n t e r e s t r a t e a n d h i g h e s t r i s k a d j u s t m e n t f a c t o r . 63 7 . CONCLUSION T h i s t h e s i s h a s s u c c e s s f u l l y d e m o n s t r a t e d t h e f e a s i b i l i t y o f e s t a b l i s h i n g a d e c e n t r a l i z e d p r o c e d u r e i n a c o m m e r c i a l bank f o r t h e o p e r a t i o n o f l o a n a b l e f u n d a l l o c a t i o n s . The m a j o r a d v a n t a g e o f a d e c e n t r a l i z e d p r o c e d u r e o v e r a c e n t r a l i z e d p r o c e d u r e i s t h e r e d u c t i o n o f i n f o r m a t i o n f l o w s w i t h i n t h e bank s t r u c t u r e . S i n c e t h e a l l o t m e n t s o f l o a n a b l e f u n d s a r e no l o n g e r d e t e r m i n e d by t h e l o a n p l a n n i n g g r o u p a n d i n f a c t t h e a l l o c a t i o n s o f l o a n a b l e f u n d s a r e d e t e r m i n e d by t h e " i n t e r n a l m a r k e t f o r c e s " e x i s t i n g among l o a n d i v i s i o n s , l e s s i n f o r m a t i o n f l o w s a r e r e q u i r e d i n a d e c e n t r a l i z e d e n v i r o m e n t . P r e s u m a b l y , t h e r e d u c t i o n of i n f o r m a t i o n f l o w s w i l l be a s s o c i a t e d w i t h r e d u c t i o n s i n e r r o r s a n d e x p e n s e s . B e s i d e s t h e r e d u c t i o n o f i n f o r m a t i o n f l o w s , a d e c e n t r a l i z e d p r o c e d u r e c a n r e d u c e t h e r e l i a n c e on f o r e c a s t i n g w h i c h i s v e r y i m p o r t a n t t o t h e e f f e c t i v e n e s s o f most c e n t r a l i z e d m o d e l s . To be e f f e c t i v e , a c e n t r a l i z e d m o d e l must be a b l e t o c a p t u r e a l l t h e r e l e v a n t i n f o r m a t i o n a t t h e b e g i n n i n g o f t h e p l a n n i n g h o r i z o n , w h e r e a s a d e c e n t r a l i z e d p r o c e d u r e , s u c h a s t h e one p r o p o s e d , c a n a l l o w t h e management t o c o r r e c t i t s e r r o r s a l o n g t h e way t o w a r d s t h e o p t imum. A n o t h e r m a j o r a c h i e v e m e n t o f t h i s t h e s i s i s t h e p r o v i s i o n of. a s y s t e m a t i c p r o c e d u r e f o r e s t i m a t i o n o f t h e c o s t o f f u n d s a n d t h e c o s t o f r i s k u s e d i n t h e p r o f i t a b i l i t y a n a l y s i s . W i t h o u t a p p r o p r i a t e e s t i m a t i o n s o f t h e s e two n u m b e r s , p r o f i t a b i l i t y a n a l y s i s c o u l d n o t p r o d u c e t h e d e s i r a b l e i n f o r m a t i o n t o t h e bank m a n a g e m e n t . In a d d i t i o n , a m e t h o d o f 64 i n t e g r a t i n g t h e p r o f i t a b i l i t y a n a l y s i s i n t o t h e a s s e t a l l o c a t i o n o p e r a t i o n i s d e m o n s t r a t e d i n t h i s p a p e r . As a b y - p r o d u c t o f t h e d e c e n t r a l i z e d p r o c e d u r e d e v e l o p e d i n t h i s p a p e r , a method o f d e t e r m i n i n g how much a bank s h o u l d pay f o r l o a n s g e n e r a t i n g f u t u r e b e n e f i t s f r o m t h e c o n t i n u i n g r e l a t i o n s h i p s b e t ween t h e b o r r o w e r s a n d t h e bank i s d e v e l o p e d . We c o n c l u d e t h a t t h e a p p r o p r i a t e p r i c e p a i d f o r t h e f u t u r e c u s t o m e r r e l a t i o n s h i p s s h o u l d v a r y a c c o r d i n g t o t h e l e v e l o f l o a n a b l e f u n d s a v a i l a b l e t o t h e bank. F i n a l l y , t h e s i m u l a t i o n s r e v e a l t h a t t h e i n t e r a c t i o n s o f r i s k w i t h i n a bank i s v e r y c o m p l i c a t e d . O v e r a l l p o r t f o l i o r i s k c a n be a d j u s t e d by s h i f t i n g f u n d s e i t h e r among o r w i t h i n l o a n c a t e g o r i e s . I n some i n s t a n c e s , t h e s e two mechanisms c a n work i n o p p o s i n g d i r e c t i o n s . T h i s s u g g e s t s t h a t b a n k s s h o u l d e s t a b l i s h some s o r t o f p r o c e d u r e s , s u c h a s t h e one p r o p o s e d , t o t a k e i n t o a c c o u n t t h e s e i n t e r a c t i o n s . 65 BIBLIOGRAPHY A g h i l i , P a r v i s , R o b e r t H . C r a m e r , a n d H . E . T h o m p s o n , " S m a l l Bank B a l a n c e S h e e t : A p p l y i n g T w o - S t a g e P r o g r a m m i n g M o d e l s , " J o u r n a l o f Bank R e s e a r c h , ( W i n t e r 1 9 7 5 ) : 2 4 6 - 2 5 6 . A n d e r s o n , P a u l S . , " C o s t a n d P r o f i t a b i l i t y o f Bank F u n c t i o n s , " New E n g l a n d E c o n o m i c R e v i e w , ( M a r c h 1 9 7 9 ) : 4 3 - 6 1 . B a u m o l , W i l l i a m J . a n d T i b o r F a b i a n , " D e c o m p o s i t i o n , P r i c i n g f o r D e c e n t r a l i z a t i o n a n d E x t e r n a l E c o n o m i e s , " Management S c i e n c e , V o l u m n 1 1 , 1 ( S e p t e m b e r 1 9 6 4 ) . B o o t h , G . G . , " p r o g r a m m i n g Bank P o r t f o l i o s u n d e r U n c e r t a i n t y , " J o u r n a l o f Bank R e s e a r c h , W i n t e r 1 9 7 2 . B r i c k , J o h n R . , " P r i c i n g C o m m e r c i a l L o a n , " C o m m e r c i a l B a n k i n g : T e x t a n d R e a d i n g s , 1 9 8 4 . B r o a d d u s , A l f r e d , " L i n e a r P r o g r a m m i n g : A New A p p r o a c h t o Bank P o r t f o l i o M a n a g e m e n t , " F e d e r a l R e s e r v e Bank o f R i c h m o n d , M o n t h l y R e v i e w , (November 1 9 7 2 ) : 3 - 1 1 . C h a m b e r , D a n d A . C h a r n e s , " I n t e r - T e m p o r a l A n a l y s i s a n d O p t i m i z a t i o n o f Bank P o r t f o l i o s , " Management S c i e n c e 7 ( J u l y 1 9 6 1 ) : 3 9 3 - 4 1 0 . C o h e n , K . J . , " L i n e a r P r o g r a m m i n g a n d O p t i m a l Bank A s s e t Management D e c i s i o n s , " J o u r n a l o f F i n a n c e , 22(May 1 9 6 7 ) : 1 4 7 - 1 6 5 . C o h e n , K . J . a n d S . T h o r e , " P r o g r a m m i n g Bank P o r t f o l i o s u n d e r U n c e r t a i n t y , " J o u r n a l o f Bank R e s e a r c h , S p r i n g 1 9 7 0 . C o h e n , K . J . , " D y n a m i c B a l a n c e S h e e t M a n a g e m e n t : A Management S c i e n c e A p p r o a c h , " J o u r n a l o f Bank R e s e a r c h , 2 ( W i n t e r 1 9 7 2 ) 9 - 1 9 . C r a m e r , R o b e r t H . a n d W i l l i a m E . S t e r k , " T h e P r e s e n t V a l u e A p p r o a c h t o C o m m e r c i a l L o a n P o l i c y , " J o u r n a l o f Bank R e s e a r c h , ( W i n t e r 1 9 8 2 ) : 2 0 7 - 2 1 7 . D r a u g h o n , C l y d e 0 . , " P r i c i n g Bank L o a n s , " J o u r n a l o f C o m m e r c i a l Bank L e n d i n g , A u g u s t 1 9 7 2 . F a l k e n b e r g , J o h n F . , " T h e S o u r c e o f Bank P r o f i t a b i l i t y , " J o u r n a l o f Bank R e s e a r c h , S e p t e m b e r 1 9 7 3 . F l y n n , Thomas M . , " L o a n P r o f i t a b i l i t y a m e t h o d t o t h e m a d n e s s , " J o u r n a l o f C o m m e r c i a l Bank L e n d i n g , M a r c h 1 9 7 8 . G r i m e s , R o b e r t H . , " P r o f i t a b i l i t y A n a l y s i s : some a d d i t i o n a l t h o u g h t s , " J o u r n a l o f C o m m e r c i a l Bank L e n d i n g , O c t o b e r 1 9 7 0 . H a n s e n , K e n n e t h D . , " I m p r o v i n g C o m m e r c i a l L o a n P r o f i t a b i l i t y , " J o u r n a l o f C o m m e r c i a l Bank L e n d i n g , May 1 9 7 3 . K a n e , E d w a r d J . , a n d B u r t o n G . M a l k i e l , " B a n k P o r t f o l i o 66 A l l o c a t i o n , D e p o s i t V a r i a b i l i t y , a n d t h e A v a i l i a b i l i t y D o c t r i n e , " Q u a r t e r l y J o u r n a l o f E c o n o m i c s , v o l . 1.79, ( F e b r u r a r y 1 9 6 5 ) : 1 1 3 - 1 3 4 . L i f s o n , K.A. and B r i a n R. B l a c k m a r r , " S i m u l a t i o n and O p t i m i z a t i o n M o d e l s f o r A s s e t D e p l o y m e n t a n d F u n d s S o u r c e s B a l a n c i n g P r o f i t , L i q u i d i t y , a n d G r o w t h , " J o u r n a l o f Bank R e s e a r c h , v o l . 3, 3(Autumn 1 9 7 3 ) : 139-255. L o n g b r a k e , W i l l i a m A., " S t a t i s t i c a l C o s t A n a l y s i s , " F i n a n c i a l Management, Volumn 2, 1 ( S p r i n g 1 9 7 3 ) : 4 8 - 5 5 . P o r t e r , R i c h a r d C, "A M o d e l o f Bank P o r t f o l i o S e l e c t i o n , " Y a l e E c o n o m i c E s s a y s , v o l . 1 2 ( F a l l 1 9 6 1 ) : 3 2 3 - 3 5 9 . W a t s o n , R o n a l d D., "The M a r g i n a l C o s t o f F u n d s C o n c e p t i n B a n k i n g , " J o u r n a l o f Bank R e s e a r c h , (Autumn 1 9 7 7 ) : 1 3 6 - 1 4 7 . 67 APPENDIX 1 The s i m u l a t i o n p r o g r a m y********************* * *•** **>******•* * * * * * * * * * *.* * * * * * * * * * * * * * * * * *y' /* */ / * > > > » ALLOT « « < * / /* */ / * A SIMULATION PROGRAM * / / * f o r c o m m e r c i a l bank l o a n a b l e f u n d a l l o t m e n t s * / / * * / ./* * / /* */ / * AUTHOR : KWOK KI LEUNG * / / * DATE : 15 MAY 1985 * / / * LOCATION : UNIVERSITY OF B R I T I S H COLUMBIA * / / * * / /* _ */ / * T h i s p r o g r a m i s w r i t t e n b a s e d on t h e a s s u m p t i o n t h a t t h e * / / * bank h a s t h r e e - l o a n d i v i s i o n s " ; The* t h r e e l o a n d i v i s i o n s * / / * c a r r y d i f f e r e n t r i s k c h a r a c t e r i s t i c s . The amount o f * / / * l o a n a b l e f u n d s a n d t h e maximum l e v e l o f l o a n p o r t f o l i o r i s k * / / * a r e p r e d e t e r m i n e d . L o a n a p p l i c a t i o n s i n t h o s e t h r e e l o a n * / / * c a t e g o r i e s a r e e v a l u a t e d by t h e t e c h n i q u e o f p r o f i t a b i l i t y * / / * a n a l y s i s . The p r o g r a m s t r i v e s t o m a x i m i z e t h e p r o f i t o f * / / * t h e c o m m e r c i a l bank by r e d i s t r i b u t i n g t h e l o a n a b l e f u n d s * / / * w i t h o u t e x c e e d i n g t h e maximum l e v e l o f l o a n p o r t f o l i o r i s k . * / / * * / /* */ / * INPUTS OF THE PROGRAM : * / / * (1) F I X E D OVERHEADS OF THE LOAN DIV IS IONS * / / * (2) V A R I A B L E OVERHEADS OF THE LOAN DIV IS IONS * / / * (3) S E R V I C E F E E S OF THE LOAN D IV IS IONS * / / * (4) VARIANCES OF LOAN RETURNS OF THE LOAN DIV IS IONS * / / * (5) CURRENT LOANABLE FUND DISTRIBUT IONS * / / * (6) I N I T I A L COST OF FUNDS * / / * (7) I N I T I A L RISK FACTOR * / / * (8) REQUIRED RATE OF RETURN ON A S S E T S * / / * (9) TOTAL LOANABLE FUNDS * / / * (10) MAXIMUM A C C E P T A B L E L E V E L OF LOAN PORTFOLIO RISK * / / * (11) INFORMATION OF LOAN APPL ICAT IONS IN A L L D IV IS IONS * / / * * / /* _ */ / * OUTPUT OF THE PROGRAM : * / / * (1) THE ALLOCATIONS OF THE LOANABLE FUNDS * / / * (2) THE AVERAGE I N T E R E S T RATES OF THE LOAN D IV IS IONS * / • / * (3) THE AVERAGE PER DOLLAR PRESENT VALUES OF CUSTOMER * / / * RELAT IONSHIPS * / / * (4) THE AVERAGE RISK CHARACTERIST ICS OF LOAN D IV IS IONS * / /* */ 68 y****************************** j /*MAIN PROGRAM: * / / * F i r s t , t h e p r o g r a m r e a d i n t h e d a t a of t h e l o a n * / / * d i v i s i o n s a n d t h e i n f o r m a t i o n a b o u t t h e l o a n a p p l i c a t i o n s i n * / / * e a c h l o a n d i v i s i o n . The i t e r a t i v e l o a n a b l e f u n d a l l o c a t i o n . * / / * p r o c e d u r e s w i l l t h e n be e x c e r c i s e d f o r a s i x month p e r i o d . * / / * W i t h i n e a c h p e r i o d i t e r a t i v e t e c h n i q u e i s e m p o l y e d t o * / / * s y n t h e s i s t h e s i m u l t a n e o u s s o l u t i o n s o f l o a n r e q u e s t s o f * / / * l o a n d i v i s i o n s . * / / * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * A L L O T : PROC O P T I O N S ( M A I N ) ; C A L L R E A D _ D I V I S I O N ; C A L L READ_CUSTOMER; C A L L P R I N T _ A S S I G ( I N _ F U N D _ C O S T , I N _ R I S K _ F A C T O R ) ; LQ1=0 ; LQ2=0 ; LQ3=0 ; L A G _ D I S T = 0 ; DO IR= 1 TO 6 ; PUT S K I P ED IT ( 'MONTH ' , I K ) ( A ( 6 ) , F ( 1 . 0 ) ) ; DO I J= 1 TO 4 ; PUT SKIP E D I T ( ' I T E R A T I O N ' , I J ) (A ( 1 0 ) , F ( 1 . 0 ) ) ; C A L L Q U A N T I T Y _ E L A S T I C I T Y ; C A L L NEW_VARIABLE( ' N O ' ) ; C A L L P R I N T _ A S S I G ( N E W _ C O S T , N E W _ R I S K ) ; END; L A G _ D I S T ( 1 ) = L P 1 ; L A G _ D I S T ( 2 ) = L P 2 ; L A G _ D I S T ( 3 ) = L P 3 ; C A L L N E W _ V A R I A B L E ( ' Y E S ' ) ; C A L L P R I N T _ A S S I G ( N E W _ C O S T , N E W _ R I S K ) ; END ; DCL N_LOAN_DIVISION FLOAT DEC ( 1 2 ) , ( F I X E D _ O H _ C O S T ( 3 ) , F I X E D _ S E R _ F E E ( 3 ) , V A R _ O H _ C O S T ( 3 ) , V A R _ S E R _ F E E ( 3 ) , L O A N _ V A R ( 3 ) , C U R R _ D I S T ( 3 ) , L A G _ D I S T ( 3 ) , P I V O T _ I N T ( 3 ) , IN_FUND_COST, I N _ R I S K _ F A C T O R , R E Q _ R E T , MAX_PORT_RISK , FUND C O S T , 69 R ISK FACTOR, P _ D G l 3 ) , P _ R F ( 3 ) , P _ I R ( 3 ) , L D 1 1 , L D 1 2 , L D 2 1 , L D 2 2 , L D 3 1 , L D 3 2 ) FLOAT DEC ( 1 2 ) ; DCL (TOTAL L O A N A B L E , A F , L Q 1 , L Q 2 , L Q 3 , E Q 1 , E Q 2 , E Q 3 ) FLOAT DEC ( 1 2 ) ; DCL 1 TYPE 1 A P P L I C A T I O N ( 3 6 0 ) , 2 APP AMOUNT1 FLOAT DEC ( 1 2 ) , 2 DEP GEN 1 FLOAT DEC ( 1 2 ) , 2 INT RATE 1 FLOAT DEC ( 1 2 ) , 2 RISK ADJ1 FLOAT DEC ( 1 2 ) ; DCL 1 TYPE2 A P P L I C A T I O N ( 3 6 0 ) , 2 APP AMOUNT2 FLOAT DEC (12) , 2 DEP GEN2 FLOAT DEC ( 1 2 ) , 2 INT RATE2 FLOAT DEC ( 1 2 ) , 2 RISK ADJ2 FLOAT DEC ( 1 2 ) ; DCL 1 TYPE3 A P P L I C A T I O N ( 3 6 0 ) , 2 APP AMOUNT3 FLOAT DEC ( 1 2 ) , 2 DEP GEN3 FLOAT DEC ( 1 2 ) , 2 INT RATE3 FLOAT DEC ( 1 2 ) , 2 RISK ADJ3 FLOAT DEC ( 1 2 ) ; DCL ( D I F F Q , D I F F V , X 1 , X 2 , X 3 , L P 1 , L P 2 , L P 3 , A , B , C , D , F , G , H , A D J M E N T 1 , A D J M E N T 2 , T O T A L LOAN) FLOAT DEC ( 1 2 ) ; DCL (NEW COST,NEW R I S K , P O R T R I S K , L A M D A 1 , L A M D A 2 , D E L T A ) FLOAT DEC ( 1 2 ) ; RETURN; / * R e a d i n d a t a o f l o a n d i v i s i o n s * / /* */ /************************************ / R E A D _ D I V I S I O N : PROCEDURE; N _ L O A N _ D I V I S I O N ) ( F ( 2 ) , X ( 7 8 ) ) ; N=N_LOAN_DIV IS ION; ( F I X E D _ O H _ C O S T ( l ) DO I = 1 TO N ) ) ( 3 ( F ( 3 ) , X ( 1 ) X ( 6 8 ) ( F I X E D _ S E R _ F E E ( I ) DO I = 1 TO N ) ) ( 3 ( F ( 3 ) , X ( 1 ) X ( 6 8 ) ( V A R _ O H _ C O S T ( l ) DO I = 1 TO N ) ) ( 3 ( F ( 5 , 3 ) , X ( 1 ) X ( 6 2 ) 1 TO N ) ) ( 3 ( F ( 5 , 3 ) , X ( 1 ) X ( 6 2 ) 1 TO N ) ) ( 3 ( F ( 5 , 3 ) , X ( 1 ) X ( 6 2 ) 1 TO N ) ) ( 3 ( F ( 5 , 3 ) , X ( 1 ) X ( 6 2 ) 1 TO N ) ) ( 3 ( F ( 5 , 3 ) , X ( 1 ) X ( 6 2 ) GET E D I T _LOAN GET E D I T GET E D I T GET E D I T GET E D I T GET E D I T GET E D I T GET E D I T ( V A R _ S E R _ F E E ( I ) DO I ( LOAN_VAR( I ) DO I ( C U R R _ D I S T ( I ) DO I (PIVOT I N T ( I ) DO I 70 GET E D I T ( I N _ F U N D _ C O S T , I N _ R I S K _ F A C T O R , R E Q _ R E T ) (3 ( F ( 6 , 4 ) , X ( 1 ) , X ( 5 9 ) ) ; GET L I S T (AF ,MAX_PORT R I S K ) ; GET L I S T ( E Q 1 , E Q 2 , E Q 3 7 ; TOTAL_LOANABLE=AF+ (EQ1 * 1 . 0 ) + (EQ2* 1 . 0 ) + (EQ3 * 1 . 0) ' ; END READ D I V I S I O N ; /************************************* / /* */ / * R e a d i n i n f o r m a t i o n a b o u t l o a n a p p l i c a t i o n s * / / * i n l o a n d i v i s i o n s * / /* */ /********************************** / READ_CUSTOMER: PROCEDURE; READ T Y P E 1 _ A P P L I C A T I O N ; READ T Y P E 2 _ A P P L I C A T I O N ; READ T Y P E 3 _ A P P L I C A T I O N ; END READ CUSTOMER; /************************************ / /* */ / * D e t e r m i n e t h e amount o f l o a n a b l e f u n d s demanded by l o a n * / / * d i v i s i o n s a n d t h e c h a n g e s o f r e q u e s t s w . r . t . t h e c h a n g e s i n * / / * t h e c o s t o f f u n d s a n d r i s k f a c t o r . T h i s p r o c e d u r e g i v e s * / / * c u r r e n t a v e r a g e i n t e r e s t r a t e s , t h e c u r r e n t a v e r a g e * / / * p r e s e n t v a l u e s o f c u s t o m e r r e l a t i o n s h i p s , a n d t h e c u r r e n t * / / * r i s k a d j u s t m e n t f a c t o r s o f t h e l o a n d i v i s i o n s * / /* /* T Y P E i A P P L I C A T I O N : i n f o r m a t i o n a b o u t l o a n a p p l i c a t i o n s i n -*/ */ /* d i v i s i o n i */ /* FUND COST : : c o s t o f f u n d s */ /* RISK FACTOR : : r i s k f a c t o r */ /* L Q i : : l o a n a b l e f u n d r e q u e s t s i n d i v i s i o n i */ /* L D i 1 : : t h e c h a n g e s o f f u n d r e q u e s t s i n d i v i s i o n i */ /* w . r . t . t h e c h a n g e s o f c o s t o f • f u n d s */ /* /* /* L D i 2 : P_DG : : t h e c h a n g e s o f f u n d r e q u e s t s i n d i v i s i o n i w . r . t . t h e c h a n g e s o f r i s k f a c t o r : t h e c u r r e n t a v e r a g e p e r d o l l a r p r e s e n t */ */ */ /* v a l u e s o f t h e l o a n d i v i s i o n s */ /* P_RF : : t h e c u r r e n t a v e r a g e r i s k a d j u s t m e n t f a c t o r s V /* o f t h e l o a n d i v i s i o n s V /* P_IR : : t h e c u r r e n t a v e r a g e i n t e r e s t r a t e s i n t h e */ /* l o a n d i v i s i o n s V /* V y*********************************** / Q U A N T I T Y _ E L A S T I C I T Y : PROCEDURE; 71 C A L L QE_DETERM (TYPE 1 _ A P P L I C A T I O N , F U N D _ C O S T , RISK F A C T O R , L Q 1 , L D 1 1 , L D 1 2 , P _ D G ( 1 ) , P _ R F ( 1 ) , P _ I R l l ) , 1 ) ; PUT SKIP L I S T ( L Q 1 , L D 1 1 , L D 1 2 ) ; C A L L QE_DETERM ( T Y P E 2 _ A P P L I C A T I O N , F U N D _ C O S T , RISK F A C T O R , L Q 2 , L D 2 1 , L D 2 2 , P _ D G ( 2 ) , P _ R F ( 2 ) , P _ I R l 2 ) , 2 ) ; PUT SKIP L I S T ( L Q 2 , L D 2 1 , L D 2 2 ) ; C A L L QE_DETERM ( T Y P E 3 _ A P P L I C A T I O N , F U N D _ C O S T , RISK F A C T O R , L Q 3 , L D 3 1 , L D 3 2 , P _ D G ( 3 ) , P _ R F ( 3 ) , P _ I R l 3 ) , 3 ) ; PUT SKIP L I S T ( L Q 3 , L D 3 1 , L D 3 2 ) ; END Q U A N T I T Y _ E L A S T I C I T Y ; y************************************************************** y / * * / / * T h i s p r o c e d u r e d e t e r m i n e s t h e l o a n a b l e f u n d demands a n d t h e * / / * c h a n g e s of demands by means o f t h e p r o f i t a b i l i t y a n a l y s i s . * / /* — V /* LOAN_DIV : an a r r a y w h i c h s t o r e s t h e i n f o r m a t i o n o f l o a n V /* a p p l i c a t i o n s i n a l o a n d i v i s i o n */ /* FC : c o s t o f f u n d s V /* RF : r i s k f a c t o r V /* Q i : l o a n a b l e f u n d r e q u e s t u n d e r c o n d i t i o n i V /* /* D i : a v e r a g e p e r d o l l a r p r e s e n t v a l u e o f c u s t o m e r r e l a t i o n s h i p s u n d e r c o n d i t i o n i */ */ /* R F i : a v e r a g e r i s k a d j u s t m e n t f a c t o r V /* u n d e r c o n d i t i o n i */ /* I R i : a v e r a g e i n t e r e s t r a t e u n d e r c o n d i t i o n i V /* T : l o a n d i v i s i o n V /* */ /***** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * y QE_DETERM: PROCEDURE ( L O A N _ D I V , F C , R F , L Q , L D 1 , L D 2 , S _ D G , S _ R F , S _ I R , T ) ; C A L L PI C A L C U L A T I O N (LOAN_DI V , FC , RF , Q1 , D1 , RF 1 ,1R1 , T , 1 ) ; F C C = F C + 0 . 0 1 ; C A L L PI _CALCULAT ION (LOAN_DI V", FCC , R F , Q 2 , D 2 , R F 2 , I R 2 , T , 0 ) ; RFF=RF+1; C A L L PI _ C A L C U L A T I O N (LOANJDI" V , F C , RFF , Q3 , D3 , RF3 , 1 R 3 , T , 0 ) ; F C C = F C - 0 . 0 1 ; C A L L PI C A L C U L A T I O N (L0AN_D1" V , F C C , RF , Q4 , D4 , R F 4 , 1 R 4 , T , 0 ) ; R F F = R F - 1 ; C A L L P I _ C A L C U L A T I O N ( L 0 A N _ D 1 " V , F C , R F F ,Q5 ,D5 , RF5 , IR5 , T , 0 ) ; S_DG=D1; S _ R F = R F 1 ; S _ I R = I R 1 ; LQ=Q1; 72 LD1=(ABS ( Q 2 - Q 1 ) + ABS ( Q 4 - Q l ) ) / 2 ; LD2=(ABS ( Q 3 - Q 1 ) + ABS ( Q 5 - Q 1 ) ) / 2 ; DCL 1 L O A N _ D I V ( 3 6 0 ) , 2 AMOUNT 2 RELATION 2 INT_CHAR 2 R_ADJ DCL ( F C , R F , F C C , R F F , L D 1 , L D 2 ) DCL ( L Q , Q 1 , Q 2 , Q 3 , Q 4 , Q 5 , S _ I R ) DCL ( T , D 1 , D 2 , D 3 , D 4 , D 5 , S _ D G , S _ R F ) DCL (RF1 , RF 2 , R F 3 , R F 4 , R F 5) DCL ( I R 1 , I R 2 , I R 3 , I R 4 , I R 5 ) FLOAT DEC (12) , FLOAT DEC ( 1 2 ) , FLOAT DEC" ( 12) , FLOAT DEC ( 1 2 ) ; FLOAT DEC ( 1 2 ) ; FLOAT DEC ( 1 2 ) ; FLOAT DEC ( 1 2 ) ; FLOAT DEC ( 1 2 ) ; FLOAT DEC ( 1 2 ) ; END QE DETERM; y*********************************** y /* * / / * T h i s p r o c e d u r e i s u s e d t o c a l c u l a t e t h e p r o f i t a b i l i t y * / / * i n d i c e s o f l o a n a p p l i c a t i o n s a n d t h e n s o r t s a n d p r i n t s a l l * / / * t h e l o a n a p p l i c a t i o n s a c c o r d i n g t o t h e i r p r o f i t a b i l i t y * / / * i n d i c e s i n a d e s c e n d i n g o r d e r . ( N o t e : t h o s e s o r t a n d p r i n t * / /*• s t a t e m e n t s c a n be p u t o u t o f e f f e c t by e n c l o s i n g them i n * / / * comment s y m b o l s . T h i s i s d o n e t o s a v e p r o c e s s i n g t i m e a n d * / / * t h e amount o f p a p e r p r i n t e d . ) * / /* */ / * LOAN_TO_CAL : an a r r a y w h i c h s t o r e s t h e i n f o r m a t i o n o f l o a n * / / * a p p l i c a t i o n s i n a l o a n d i v i s i o n * / / * COST : c o s t o f f u n d s * / / * R I S K F : r i s k f a c t o r * / / * QUAN : t o t a l amount o f l o a n a p p l i c a t i o n s b e i n g * / / * a c c e p t e d * / / * AVG_GEN : a v e r a g e p e r d o l l a r p r e s e n t v a l u e o f c u s t o m e r * / / * r e l a t i o n s h i p s * / / * AVG_R_ADJ : a v e r a g e r i s k a d j u s t m e n t f a c t o r * / / * AVG_IR : a v e r a g e i n t e r e s t r a t e * / / * TY : l o a n d i v i s i o n * / / * COUNT : t h e number o f l o a n a p p l i c a t i o n s b e i n g * / / * a c c e p t e d * / / * T _ R E L : t o t a l p e r d o l l a r p r e s e n t v a l u e o f c u s t o m e r * / / * r e l a t i o n s h i p s * / / * T _ R _ A D J : t o t a l r i s k a d j u s t m e n t f a c t o r * / / * T_ IR : t o t a l i n t e r e s t r a t e * / / * IR : i n t e r e s t r e v e n u e * / / * DG : p r e s e n t v a l u e o f c u s t o m e r r e l a t i o n s h i p s * / / * RC : c o s t o f r i s k * / / * T F C : t o t a l f i x e d c o s t * / / * TVC : t o t a l v a r i a b l e c o s t * / / * TC : c o s t o f f u n d s e m p l o y e d * / / * AR : a c t u a l r e t u r n * / /*PRO INDEX ( J ) : p r o f i t a b i l i t y i n d e x o f l o a n a p p l i c a t i o n j * / /* " */ /******* ********************^ /" P I _ C A L C U L A T I O N : PROCEDURE ( L O A N _ T O _ C A L , C O S T , R I S K F , Q U A N , A V G _ G E N , A V G _ R _ A D J , A V G _ I R , T Y , E ) ; 73 QUAN=0; COUNT=0; T _ R E L = 0 ; T _ R _ A D J = 0 ; T _ I R = 0 ; DO K=1 TO 3 6 0 ; I R = A M T ( K ) * ( P I V O T _ I N T ( T Y ) + I N T _ C H A R ( K ) ) ; D G = A M T ( K ) * R E L ( K ) * C O S T ; R C = 2 * L O A N _ V A R ( T Y ) * C U R R _ D I S T ( T Y ) * R I S K F * A M T ( K ) * R _ A D J ( K ) ; TFC=F IXED O H _ C O S T ( T Y ) - F I X E D _ S E R _ F E E ( T Y ) > T V C = A M T ( K I * ( V A R _ O H _ C ° S T ( T Y ) " V A R _ S E R _ F E E ( T Y ) ) ; TC=AMT(K)*COST; A R = ( I R + D G - R C - T F C - T V C - T C ) / ( A M T ( K ) * ( 1 - R E L ( K ) ) ) ; PRO_INDEX(K)=AR/REQ_RET ; IF PRO_INDEX(K) >= 1 THEN DO; Q U A N = Q U A N + A M T ( K ) * ( 1 - R E L ( K ) ) ; T_REL=T_REL + R E L ( K ) ; T_R_ADJ=T_R_ADJ + R _ A D J ( K ) ; T_I R=T_I R+INT_GHAR( K') ; COUNT=COUNT+1; END ; END; I F COUNT > 0 THEN DO; AVG_GEN=T_REL/COUNT; AVG_R_AD J=T R_ADJ/COUNT; AVG_IR=T_IR7COUNT; END; / * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * y / * T h i s s e c t i o n i s u s e d t o s o r t a n d p r i n t t h e l o a n * / / * a p p l i c a t i o n s a t month s i x . The t e c h n i q u e o f b u b b l e s o r t i n g * / / * h a s b e e n u t i l i z e d i n t h i s s e c t i o n . In t h e f u t u r e , i f t h e * / / * p r o g r a m i s m o d i f i e d t o a c c o m m o d a t e h i g h e r n u m b e r s o f l o a n * / / * a p p l i c a t i o n s , a b e t t e r m e t h o d o f s o r t i n g s h o u l d be e m p l o y e d * / / * i n o r d e r t o s a v e CPU t i m e . * / /******************************************** ******************/ I F IK=6 THEN DO; IF IJ=4 THEN DO; I F E=l THEN DO; S O R T _ F I N I S H = ' N O ' ; DO WHILE ( S O R T _ F I N I S H = ' N O ' ) ; S O R T _ F I N I S H = ' Y E S ' ; DO P=1 TO 3 5 9 ; IF PRO_INDEX(P) < PRO_INDEX(P+1) THEN DO; S O R T _ F I N I S H = ' N O ' ; T E M P = P R O _ I N D E X ( P ) ; T E M P _ F I L E = L O A N _ T O _ C A L ( P ) ; P R O _ I N D E X ( P ) = P R O _ I N D E X ( P + 1 ) ; L O A N _ T O _ C A L ( P ) = L O A N _ T O _ C A L ( P + 1 ) ; PRO_INDEX(P+1)=TEMP; L O A N _ T O _ C A L ( P + 1 ) = T E M P _ F I L E ; END; END; END; DO; PUT S K I P ( 3 ) L I S T ( L O A N _ T O _ C A L ( 1 ) , P R O _ I N D E X ( 1 ) ) ; DO P=2 TO 3 6 0 ; PUT SK IP L I S T ( L O A N _ T O _ C A L ( P ) , P R O _ I N D E X ( P ) ) ; END ; END; END; END; END; E = 0 ; DCL 1 L O A N _ T O _ C A L ( 3 6 0 ) , 2 AMT 2 REL 2 INT_CHAR 2 R_ADJ DCL PRO_INDEX(360) DCL TY DCL ( I R , D G , R C , T F C , T V C , T C , ACTUAL_RETURN, QUAN) DCL 1 T E M P _ F I L E , 2 T_AMT 2 T_REL 2 T_INT 2 T _ R _ C L A S S DCL ( T E M P , C O S T , R I S K F , E , C O U N T T _ R E L , A V G _ G E N , A V G _ R ADJ T _ R _ A D J , A V G _ I R , T _ I R T DCL SORT F I N I S H FLOAT DEC ( 1 2 ) , FLOAT DEC ( 1 2 ) , FLOAT DEC ( 1 2 ) , FLOAT DEC ( 1 2 ) ; FLOAT' DEC" ( 12) ; FLOAT DEC ( 1 2 ) ; FLOAT DEC ( 1 2 ) ; FLOAT DEC ( 1 2 ) , FLOAT DEC ( 1 2 ) , FLOAT DEC ( 1 2 ) , FLOAT DEC ( 1 2 ) ; FLOAT DEC ( 1 2 ) ; CHAR (3) ; END PI C A L C U L A T I O N ; 75 /************************************************************** / /* * / / * T h i s p r o c e d u r e w i l l a s s i g n new v a l u e s t o t h e c o s t o f f u n d s * / / * a n d t h e r i s k f a c t o r f o r t h e p r o f i t a b i l i t y a n a l y s i s w h e n e v e r * / / * t h e r e a r e d i s c r e p e n c y b e t w e e n - t h e a c t u a l l e v e l o f loan's 1 * / / * a n d t h e amount o f l o a n a b l e f u n d s o r t h e a c t u a l l e v e l o f * / / * r i s k a n d t h e maximum a c c e p t a b l e l o a n p o r t f o l i o r i s k . The * / / * m e t h o d u s e d i s a m o d i f i c a t i o n o f t h e N e w t o n ' s m e t h o d . * / / * P l e a s e r e f e r t o c h a p t e r 5 f o r d e t a i l e d e x p l a n a t i o n o f t h e * / / * v a r i a b l e s u s e d i n t h i s p r o c e d u r e . * / /* * / / * A (ADJMENT1) + B (ADJMENT2) = D I F F Q * / / * C (ADJMENT1) + D (ADJMENT2) = D I F F V * / /* . */ /* * / / * A , B, C , D : c o e f f i c i e n t s o f t h e s i m u l t a n e o u s e q u a t i o n s * / / * D I F F Q : d i f f e r e n c e b e t w e e n t h e a c t u a l q u a n t i t y * / / * of l o a n s a n d t h e l o a n a b l e f u n d s * / / * D I F F V : d i f f e r e n c e b e t w e e n t h e a c t u a l p o r t f o l i o r i s k * / / * a n d t h e maximum - a c c e p t a b l e l o a n p o r t f o l i o s r i s k * / / * ADJMENT1 : a d j u s t m e n t made t o c o s t o f f u n d s * / / * ADJMENT2 : a d j u s t m e n t made t o r i s k f a c t o r * / / * NEW_COST : new c o s t o f f u n d s f o r t h e n e x t m o n t h * / / * NEW_RISK : new r i s k f a c t o r f o r t h e n e x t m o n t h * / / * C U R R _ D I S T ( i ) : c u r r e n t amount o f l o a n a b l e f u n d s * / / * i n d i v i s i o n i * / / * L A G _ D I S T ( i ) : amount o f l o a n a b l e f u n d s i n d i v i s i o n i i n * / / * l a s t month * / /* * / y* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * NEW_VARIABLE : PROCEDURE(NEW); T 0 T A L _ L O A N = T O T A L _ L 0 A N A B L E ; L P 1 = L Q 1 / T O T A L _ L O A N ; L P 2 = L Q 2 / T O T A L _ L O A N ; L P 3 = L Q 3 / T O T A L _ L O A N ; ADJMENT1=0; ADJMENT2=0; F = L P 1 * * 2 * L O A N _ V A R ( 1 ) * P _ R F ( 1 ) * * 2 ; G = L P 2 * * 2 * L O A N _ V A R ( 2 ) * P _ R F ( 2 ) * * 2 ; H = L P 3 * * 2 * L O A N _ V A R ( 3 ) * P _ R F ( 3 ) * * 2 ; X 1 = L P 1 * P _ R F ( 1 ) ; X 2 = L P 2 * P _ R F ( 2 ) ; X 3 = L P 3 * P _ R F ( 3 ) ; PORT_RISK=F + G + H ; D I F F Q = ( L Q 1 + L Q 2 + L Q 3 ) - T O T A L _ L O A N A B L E ; DIFFV=PORT R I S K - M A X PORT R I S K ; 76 IF NEW='YES' THEN DO; A = 1 0 0 * ( L D 1 1 + L D 2 1 + L D 3 1 ) ; B= (LD12+LD22+LD32) ; C=(2 0 0/TOTAL_LOAN)* (LD11*F/X1+LD21*G/X2 +LD31*H/X3) D= (2/TOTAL_LOAN) * (LD12*F/X1+LD22*G/X2+LD32*H/X3) DELTA=(A * D) - (B * C) ; LAMDA1=(D * D IFFQ) - (B * D I F F V ) ; LAMDA2=(A * D I F F V ) - (C * D I F F Q ) ; ADJMENT1=LAMDA1/DELTA; ADJMENT2=LAMDA2/DELTA; END; NEW_COST=ADJMENT1+FUND_COST; NEW_RISK=ADJMENT2+RISK_FACTOR; I F NEW_RISK > 6 . 5 THEN DO; NEW_RISK = 6 . 5 ; ADJMENT1 = (D IFFQ - (B * ( 6 . 5 - R I S K _ F A C T O R ) ) ) / A ; NEW_COST = ADJMENT1 + FUND_COST; END; IF NEW_COST < 0 THEN NEW_COST = 0 ; I F NEW_RISK < 0 THEN NEW_RISK = 0 ; C A L L PRINT_ALLOTMENT; C U R R _ D I S T ( 1 ) = L P 1 * 0 . 7 + L A G _ D I S T ( 1 ) * 0 . 3 ; C U R R _ D I S T ( 2 ) = L P 2 * 0 . 7 + L A G _ D I S T ( 2 ) * 0 . 3 ; C U R R _ D I S T ( 3 ) = L P 3 * 0 . 7 + L A G _ D I S T ( 3 ) * 0 . 3 ; DCL NEW C H A R ( 3 ) ; END NEW V A R I A B L E ; y**************************************************************y y * * / / * T h i s p r o c e d u r e p r i n t s a n d a s s i g n s new v a l u e s o f t h e c o s t o f * / / * f u n d s a n d r i s k f a c t o r f o r t h e p r o f i t a b l i l i t y a n a l y s i s . * / / * * / y************************************************************** y P R I N T _ A S S I G : PROCEDURE ( P _ C O S T , P _ R I S K ) ; PUT S K I P ( 3 ) L I S T ( P _ C O S T ) ; PUT SK IP L I S T ( P _ R I S K ) ; FUND_COST=P_COST; R I S K _ F A C T O R = P _ R I S K ; DCL ( P _ C O S T , P _ R I S K ) FLOAT DEC ( 1 2 ) ; END PRINT A S S I G ; 77 y * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * /* * / / * T h i s p r o c e d u r e p r i n t s t h e r e s u l t s . * / / * * / y******************* * * * * * * * * * * * * * * * * *-*•* * * * * * * ^ ^ ^ ^ • i * * * **-*>* * * *•* * *'y/' PRINT ALLOTMENT: PROCEDURE; PUT SK IP EDIT PUT SK IP EDIT PUT SK IP EDIT PUT SK IP ED IT PUT S K I P EDIT PUT SK IP EDIT PUT S K I P ED IT PUT SKIP' EDIT PUT SK IP ED IT PUT SK IP ED IT PUT SK IP EDIT PUT SK IP ED IT PUT SK IP EDIT ' T O T A L L O A N : ' , T O T A L _ L O A N ) ( A ( 2 2 ) , F ( 1 2 . 2 ) ) ; 'ALLOTMENT OF LOAN 1 : ' , L Q 1 ) ( A ( 2 2 ) , F ( 1 2 . 2 ) ) 'ALLOTMENT OF LOAN 2 : ' , L Q 2 ) ( A ( 2 2 ) , F ( 1 2 . 2 ) ) 'ALLOTMENT OF LOAN 3 : ' , L Q 3 ) ( A ( 2 2 ) , F ( 1 2 . 2 ) ) ' LOAN PORTFOLIO R I S K : * , P O R T _ R I S K ) ( A ( 2 2 ) , E ( 1 2 , 4 , 5 ) ) ' F R A C T I O N OF LOAN 1 : ' , L P 1 ) ( A ( 2 2 ) , E ( 1 2 , 4 5 ) ) ' F R A C T I O N OF LOAN 2 : ' , L P 2 ) ( A ( 2 2 ) , E ( 1 2 , 4 5 ) ) ' F R A C T I O N OF LOAN' 3 : ' , L P 3 ) ( A ( 2 2 ) ,E ( '12 ' ,4 5 ) ) , D I F F Q ) ( A ( 2 2 ) , E ( 1 2 , 4 5 ) ) , D I F F V ) ( A ( 2 2 ) , E ( 1 2 , 4 5 ) ) , P _ D G ) ( A ( 2 2 ) , 3 E ( 1 2 , 4 , 5 ) ) ; , P _ R F ) ( A ( 2 2 ) , 3 E ( 1 2 , 4 , 5 ) ) ; , P _ I R ) ( A ( 2 2 ) , 3 E ( 1 2 , 4 , 5 ) ) ; ( ' L O A N D I F F E R E N C E : ( ' R I S K D I F F E R E N C E : ( ' A V G . NPV OF C . R . : ( ' A V G . R . A . F . : ( ' A V G . INTEREST : END PRINT ALLOTMENT; END A L L O T ; 78 APPENDIX 2 INPUT DATA SETS OF THE SIMULATIONS DATA SET FOR THE F E A S I B I L I T Y T E S T S LOAN D I V I S I O N 1 F I X E D OVERHEAD COST = 200 F I X E D SERVICE F E E = 200 V A R I A B L E OVERHEAD = 0 . 0 0 2 V A R I A B L E SERVICE F E E = 0 . 0 0 1 VARIANCE OF LOAN RETURN = 0 . 0 0 1 LOAN A P P L I C A T I O N S : LOAN # N LOAN AMOUNT INTEREST CHARGED PER DOLLAR P . V . OF CUSTOMER RELATIONSHIPS RISK ADJUSTMENT FACTOR 1 10000 0 . 0 9 1 8 + 1 ( 0 . 0 0 0 1 5 ) 0 . 0 1 . 0 2 10000 0 . 0 9 1 8 + 2 ( 0 . 0 0 0 1 5 ) 0 . 0 1 . 0 3 • 10000 0 . 0 9 1 8 + 3 ( 0 . 0 0 0 1 5 ) 0 . 0 • 1 . 0 • • 360 • 10000 • 0 . 0 9 1 8 + N ( 0 . 0 0 0 1 5 ) • o ! o 1 ! o 79 LOAN D I V I S I O N 2 F I X E D OVERHEAD COST = 200 F I X E D S E R V I C E F E E = 200 V A R I A B L E OVERHEAD = 0 . 0 0 2 VARIABLE S E R V I C E F E E = 0 . 0 0 1 VARIANCE OF LOAN RETURN = 0 . 0 2 8 LOAN A P P L I C A T I O N S : LOAN # N=1 20 LOAN AMOUNT INTEREST CHARGED PER DOLLAR P . V . OF CUSTOMER RELAT IONSHIPS RISK ADJUSTMENT FACTOR 1 1 0000 0 . 0 7 7 2 + 1 ( 0 . 0 0 1 4 ) 0 . 0 1 . 0 2 1 0000 0 . 0 7 7 2 + 2 ( 0 . 0 0 1 4 ) 0 . 0 1 . 0 3 1 0000 • 0 . 0 7 7 2 + 3 ( 0 . 0 0 1 4 ) • 0 . 0 1 . 0 • • 1 20 10000 • D . 0 7 7 2 + N ( 0 . 0 0 1 4 ) • o ! o 1 ! o 121 10000 0 . 0 8 6 2 + 1 ( 0 . 0 0 1 4 ) 0 . 0 1 . 0 122 10000 0 . 0 8 6 2 + 2 ( 0 . 0 0 1 4 ) 0 . 0 1 . 0 1 23 • 1 0000 • 0 . 0 8 6 2 + 3 ( 0 . 0 0 1 4 ) • 0 . 0 • 1 . 0 • 240 10000 0 . 0 8 6 2 + N ( 0 . 0 0 l 4 ) • o ! o 1 ! o 241 10000 0 . 0 9 0 7 + 1 ( 0 . 0 0 1 4 ) 0 . 0 1 . 0 242 1 0000 0 . 0 9 0 7 + 2 ( 0 . 0 0 1 4 ) 0 . 0 1 . 0 243 * 1 0000 * 0 . 0 9 0 7 + 3 ( 0 . 0 0 1 4 ) 0 . 0 • 1 . 0 • • 360 • 1 0000 • 0 . 0 9 0 7 + N ( 0 . 0 0 1 4 ) • o ! o • 1 ! o 80 LOAN D I V I S I O N 3 F I X E D OVERHEAD COST = 2 00 F I X E D S E R V I C E F E E = 200 V A R I A B L E OVERHEAD = 0 . 0 0 2 V A R I A B L E S E R V I C E F E E = 0 . 0 0 1 VARIANCE OF LOAN RETURN = 0 . 0 1 7 LOAN A P P L I C A T I O N S : LOAN # N=1 20 LOAN AMOUNT INTEREST CHARGED PER DOLLAR P . V . OF CUSTOMER RELAT IONSHIPS RISK ADJUSTMENT FACTOR 1 1 0000 0 . 0 7 4 9 + 1 ( 0 . 0 0 1 3 ) 0 . 0 1 . 0 2 1 0000 0 . 0 7 4 9 + 2 ( 0 . 0 0 1 3 ) 0 . 0 1 . 0 3 • 1 0000 • 0 . 0 7 4 9 + 3 ( 0 . 0 0 1 3 ) • 0 . 0 • 1 . 0 1 20 1 0000 0 . 0 7 4 9 + N ( 0 . 0 0 l 3 ) o ! o 1 ! o 121 10000 0 . 0 8 4 1 + 1 ( 0 . 0 0 1 3 ) 0 . 0 1 . 0 1 22 1 0000 0 . 0 8 4 1 + 2 ( 0 . 0 0 1 3 ) 0 . 0 1 . 0 1 23 10000 0 . 0 8 4 1 + 3 ( 0 . 0 0 1 3 ) • 0 . 0 1 . 0 • • 240 • 10000 • • 0 . 0 8 4 1 + N ( 0 . 0 0 1 3 ) • o ! o • 1 ! o 241 1 0000 0 . 0 8 8 6 + 1 ( 0 . 0 0 1 3 ) 0 . 0 1 . 0 242 1 0000 0 . 0 8 8 6 + 2 ( 0 . 0 0 1 3 ) 0 . 0 1 . 0 243 • 1 0000 • 0 . 0 8 8 6 + 3 ( 0 . 0 0 1 3 ) • 0 . 0 • 1 . 0 • 360 • 10000 • 0 . 0 8 8 6 + N ( 0 . 0 0 l 3 ) • o ! o • 1 ! o DATA SET FOR THE TEST INGS OF THE E F F E C T OF PRESENT VALUE OF FUTURE CUSTOMER RELAT IONSHIPS ON LOAN PRICING 8 1 LOAN D I V I S I O N 1 F I X E D OVERHEAD COST = 200 F I X E D SERV ICE F E E = 200 V A R I A B L E OVERHEAD = 0 . 0 0 2 V A R I A B L E SERVICE F E E = 0 . 0 0 1 VARIANCE OF LOAN RETURN = 0 . 0 0 1 LOAN A P P L I C A T I O N S : LOAN # N LOAN AMOUNT INTEREST CHARGED PER DOLLAR P . V . OF : CUSTOMER RELATIONSHIPS RISK •ADJUSTMENT FACTOR 1 10000 0 . 0 9 1 8 + 1 ( 0 . 0 0 0 1 5 ) 0 . 0 1 . 0 2 10000 0 . 0 9 1 8 + 2 ( 0 . 0 0 0 1 5 ) 0 . 0 1 . 0 3 1 0000 0 . 0 9 1 8 + 3 ( 0 . 0 0 0 1 5 ) • 0 . 0 • 1 . 0 • 360 10000 • 0 . 0 9 1 8 + N ( 0 . 0 0 0 1 5 ) o ! o • 1 ! o 82 LOAN D I V I S I O N 2 F I X E D OVERHEAD COST = 200 F I X E D SERVICE F E E = 200 V A R I A B L E OVERHEAD = 0 . 0 0 2 V A R I A B L E S E R V I C E F E E = 0 . 0 0 1 VARIANCE OF LOAN RETURN = 0 . 0 1 7 LOAN A P P L I C A T I O N S : LOAN # N=60 LOAN AMOUNT INTEREST CHARGED PER DOLLAR P . V . OF CUSTOMER RELAT IONSHIPS RISK ADJUSTMENT FACTOR 1 1 0 0 0 0 0 . 0 9 0 0 + 1 ( 0 . 0 0 2 ) 0 . 0 8 1 . 0 2 1 0 0 0 0 0 . 0 9 0 0 + 2 ( 0 . 0 0 2 ) 0 . 0 8 1 . 0 3 • 1 0 0 0 0 • 0 . 0 9 0 0 + 3 ( 0 . 0 0 2 ) • 0 . 0 8 • 1 . 0 • • 6 0 • 1 0 0 0 0 • 0 . 0 9 0 0 + N ( 0 . 0 0 2 ) • 0*.08 • 1 ! o 61 1 0 0 0 0 0 . 0 8 5 0 + 1 ( 0 . 0 0 2 ) 0 . 1 3 1 . 0 6 2 1 0 0 0 0 0 . 0 8 5 0 + 2 ( 0 . 0 0 2 ) 0 . 1 3 1 . 0 6 3 1 0 0 0 0 • 0 . 0 8 5 0 + 3 ( 0 . 0 0 2 ) • 0 . 1 3 • 1 . 0 • 1 2 0 • 1 0 0 0 0 • 0 . 0 8 5 0 + N ( 0 . 0 0 2 ) 0 . 1 3 • 1 ! o 121 1 0 0 0 0 0 . 0 8 2 0 + 1 ( 0 . 0 0 2 ) 0 . 1 8 1 . 0 1 2 2 1 0 0 0 0 * 0 . 0 8 2 0 + 2 ( 0 . 0 0 2 ) 0 . 1 8 1 . 0 1 2 3 1 0 0 0 0 • 0 . 0 8 2 0 + 3 ( 0 . 0 0 2 ) • 0 . 1 8 • 1 . 0 • 1 8 0 « 1 0 0 0 0 • 0 . 0 8 2 0 + N ( 0 . 0 0 2 ) • o ! 18 • 1 ! o 181 1 0 0 0 0 0 . 0 8 0 0 + 1 ( 0 . 0 0 2 ) 0 . 2 3 1 . 0 1 8 2 1 0 0 0 0 0 . 0 8 0 0 + 2 ( 0 . 0 0 2 ) 0 . 2 3 1 . 0 1 8 3 • 1 0 0 0 0 • 0 . 0 8 0 0 + 3 ( 0 . 0 0 2 ) • 0 . 2 3 • 1 . 0 • 2 4 0 • 1 0 0 0 0 0 . 0 8 0 0 + N ( 0 . 0 0 2 ) • 0 . 2 3 • 1 ! o 2 4 1 1 0 0 0 0 0 . 0 7 7 0 + 1 ( 0 . 0 0 2 ) 0 . 2 7 1 . 0 2 4 2 1 0 0 0 0 0 . 0 7 7 0 + 2 ( 0 . 0 0 2 ) 0 . 2 7 1 . 0 . 2 4 3 • 1 0 0 0 0 • 0 . 0 7 7 0 + 3 ( 0 . 0 0 2 ) 0 . 2 7 • 1 . 0 • • 3 0 0 • 1 0 0 0 0 • 0 . 0 7 7 0 + N ( 0 . 0 0 2 ) o ! 2 7 * . i ! o 3 0 1 1 0 0 0 0 0 . 0 7 2 0 + 1 ( 0 . 0 0 2 ) 0 . 3 2 1 . 0 3 0 2 1 0 0 0 0 0 . 0 7 2 0 + 2 ( 0 . 0 0 2 ) 0 . 3 2 1 . 0 3 0 3 • 1 0 0 0 0 • 0 . 0 7 2 0 + 3 ( 0 . 0 0 2 ) • 0 . 3 2 • 1 . 0 • • 3 6 0 • 1 0 0 0 0 • 0 . 0 7 2 0 + N ( 0 . 0 0 2 ) • o ! 3 2 • i . ! o 8 3 LOAN D I V I S I O N 3 F I X E D OVERHEAD COST = 200 F I X E D S E R V I C E F E E = 200 V A R I A B L E OVERHEAD = 0 . 0 0 2 V A R I A B L E S E R V I C E F E E = 0 . 0 0 1 VARIANCE OF LOAN RETURN = 0 . 0 2 8 LOAN A P P L I C A T I O N S : LOAN # N=60 LOAN AMOUNT INTEREST CHARGED PER DOLLAR P . V . OF CUSTOMER RELAT IONSHIPS RISK ADJUSTMENT FACTOR 1 1 0 0 0 0 0 . 1 2 0 0 + 1 ( 0 . 0 0 2 ) 0 . 0 5 0 1 . 0 2 1 0 0 0 0 0 . 1 2 0 0 + 2 ( 0 . 0 0 2 ) 0 . 0 5 0 1 . 0 3 • 1 0 0 0 0 • 0 . 1 2 0 0 + 3 ( 0 . 0 0 2 ) • 0 . 0 5 0 • 1 . 0 • • 60 • 1 0 0 0 0 • 0 . 1 2 0 0 + N ( 0 . 0 0 2 ) • 0 . 0 5 0 1 ! o 61 1 0 0 0 0 0 . 1 1 5 0 + 1 ( 0 . 0 0 2 ) 0 . 0 7 5 1 . 0 6 2 1 0 0 0 0 0 . 1 1 5 0 + 2 ( 0 . 0 0 2 ) 0 . 0 7 5 1 . 0 6 3 • 1 0 0 0 0 0 . 1 1 5 0 + 3 ( 0 . 0 0 2 ) • 0 . 0 7 5 • 1 . 0 1 2 0 • 1 0 0 0 0 • 0 . 1 1 5 0 + N ( 0 . 0 0 2 ) 0 . 0 7 5 • 1 ! o 121 1 0 0 0 0 0 . 1 1 0 0 + 1 ( 0 . 0 0 2 ) 0 . 1 0 0 1 . 0 1 2 2 1 0 0 0 0 0 . 1 1 0 0 + 2 ( 0 . 0 0 2 ) 0 . 1 0 0 1 . 0 1 2 3 1 0 0 0 0 • 0 . 1 1 0 0 + 3 ( 0 . 0 0 2 ) • 0 . 1 0 0 • 1 . 0 • 1 8 0 • 1 0 0 0 0 • 0 . 1 1 0 0 + N ( 0 . 0 0 2 ) • o ! 1 0 0 • 1 ! o 181 1 0 0 0 0 0 . 1 0 7 0 + 1 ( 0 . 0 0 2 ) 0 . 1 2 5 1 . 0 1 8 2 1 0 0 0 0 0 . 1 0 7 0 + 2 ( 0 . 0 0 2 ) 0 . 1 2 5 1 . 0 1 8 3 • 1 0 0 0 0 • 0 . 1 0 7 0 + 3 ( 0 . 0 0 2 ) * 0 . 1 2 5 • 1 . 0 • • 2 4 0 • 1 0 6 0 0 • 0 . 1 0 7 0 + N ( 0 . 0 0 2 ) • 0 . 1 2 5 • 1 ! o 2 4 1 1 0 0 0 0 0 . 1 0 5 0 + 1 ( 0 . 0 0 2 ) 0 . 1 5 0 1 .-o 2 4 2 1 0 0 0 0 0 . 1 0 5 0 + 2 ( 0 . 0 0 2 ) 0 . 1 5 0 1 . 0 2 4 3 • 1 0 0 0 0 0 . 1 0 5 0 + 3 ( 0 . 0 0 2 ) • 0 . 1 5 0 • 1 . 0 • • 3 0 0 • 1 0 0 0 0 • 0 . 1 0 5 0 + N ( 0 . 0 0 2 ) • 0 ! 1 5 0 • 1 ! o 3 0 1 1 0 0 0 0 0 . 1 0 0 0 + 1 ( 0 . 0 0 2 ) 0 . 1 7 5 1 . 0 3 0 2 1 0 0 0 0 0 . 1 0 0 0 + 2 ( 0 . 0 0 2 ) 0 . 1 7 5 1 . 0 3 0 3 • 1 0 0 0 0 • 0 . 1 0 0 0 + 3 ( 0 . 0 0 2 ) • 0 . 1 7 5 • 1 . 0 • • 3 6 0 • 1 0 0 0 0 • 0 . 1 0 0 0 + N ( 0 . 0 0 2 ) • o ! 1 7 5 • 1 ! o 84 DATA SETS FOR THE T E S T I N G S OF THE IMPACT OF RISK T IGHTENING ON LOANABLE FUNDS ALLOCAT ION DATA SET 1 LOAN D I V I S I O N 1 F I X E D OVERHEAD COST = 2 0 0 F I X E D SERVICE F E E = 2 0 0 V A R I A B L E OVERHEAD = 0 . 0 0 2 V A R I A B L E SERV ICE F E E = 0 . 0 0 1 VARIANCE OF LOAN RETURN = 0 . 0 0 1 LOAN A P P L I C A T I O N S : LOAN # N LOAN AMOUNT I N T E R E S T CHARGED PER DOLLAR P W . OF' CUSTOMER RELATIONSHIPS RISK ADJUSTMENT FACTOR 1 10000 0 . 0 9 1 8 + 1 ( 0 . 0 0 0 1 5 ) 0 .0 1 .0 2 10000 0 . 0 9 1 8 + 2 ( 0 . 0 0 0 1 5 ) 0 .0 1 .0 3 10000 • 0 . 0 9 1 8 + 3 ( 0 . 0 0 0 1 5 ) 0 .0 1 .0 360 * 10000 • 0 . 0 9 1 8 + N ( 0 . 0 0 0 1 5 ) • o!o » 1 !o 85 LOAN D IV IS ION 2 F I X E D OVERHEAD COST = 200 F I X E D S E R V I C E F E E = 200 V A R I A B L E OVERHEAD = 0 . 0 0 2 V A R I A B L E S E R V I C E F E E = 0 . 0 0 1 VARIANCE OF LOAN RETURN = 0 . 0 2 8 LOAN A P P L I C A T I O N S : LOAN # N=60 LOAN AMOUNT INTEREST CHARGED PER DOLLAR P . V . OF CUSTOMER RELAT IONSHIPS RISK ADJUSTMENT FACTOR 1 10000 0 . 1 0 5 0 + 1 ( 0 . 0 0 2 ) 0 . 0 0 . 8 2 10000 0 . 1 0 5 0 + 2 ( 0 . 0 0 2 ) 0 . 0 0 . 8 3 • 10000 • 0 . 1 0 5 0 + 3 ( 0 . 0 0 2 ) • 0 . 0 • 0 . 8 • • 60 • 10000 • 0 . 1 0 5 0 + N ( 0 . 0 0 2 ) • o ! o • o ! 8 61 10000 0 . 1 1 0 0 + 1 ( 0 . 0 0 2 ) 0 . 0 0 . 9 62 10000 0 . 1 1 0 0 + 2 ( 0 . 0 0 2 ) 0 . 0 0 . 9 63 • 10000 • 0 . 1 1 0 0 + 3 ( 0 . 0 0 2 ) 0 . 0 0 . 9 • • 1 20 • 1 0000 • 0 . 1 1 0 0 + N ( 0 . 0 0 2 ) • o ! o • o ! 9 121 10000 0 . 1 1 5 0 + 1 ( 0 . 0 0 2 ) 0 . 0 1 . 0 122 10000 0 . 1 1 5 0 + 2 ( 0 . 0 0 2 ) 0 . 0 1 . 0 123 • 1 0000 • 0 . 1 1 5 0 + 3 ( 0 . 0 0 2 ) • 0 . 0 • 1 . 0 • • 180 10000 • 0 . 1 1 5 0 + N ( 0 . 0 0 2 ) • o . ' o • 1 ! o 181 10000 0 . 1200+1 ( 0 . 0 0 2 ) 0 . 0 1 . 1 1 82 10000 0 . 1 2 0 0 + 2 ( 0 . 0 0 2 ) 0 . 0 i . r 183 • 10000 • 0 . 1 2 0 0 + 3 ( 0 . 0 0 2 ) • 0 . 0 • 1 . 1 • • 240 • 10000 • 0 . 1 2 0 0 + N ( 0 . 0 0 2 ) • o ! o • • 1 . 1 241 10000 0 . 1 3 5 0 + 1 ( 0 . 0 0 2 ) 0 . 0 1 . 2 242 1 0000 0 . 1 3 5 0 + 2 ( 0 . 0 0 2 ) 0 . 0 1 . 2 243 • 10000 • 0 . 1 3 5 0 + 3 ( 0 . 0 0 2 ) • 0 . 0 • 1 . 2 • • 300 • 10000 • 0 . 1 3 5 0 + N ( 0 . 0 0 2 ) • o ! o • 1 .2 301 10000 0 . 1 5 0 0 + 1 ( 0 . 0 0 2 ) 0 . 0 1 . 3 302 10000 0 . 1 5 0 0 + 2 ( 0 . 0 0 2 ) 0 . 0 1 . 3 . 303 • 10000 • 0 . 1 5 0 0 + 3 ( 0 . 0 0 2 ) • 0 . 0 • 1 . 3 « • 360 • 10000 • 0 . 1 5 0 0 + N ( 0 . 0 0 2 ) • o ! o • 1 ! 3 86 LOAN D I V I S I O N 3 F I X E D OVERHEAD COST = 200 F I X E D S E R V I C E F E E = 200 V A R I A B L E OVERHEAD = 0 . 0 0 2 V A R I A B L E S E R V I C E F E E = 0 . 0 0 1 VARIANCE OF LOAN RETURN = 0 . 0 1 7 LOAN A P P L I C A T I O N S : LOAN # N=60 LOAN AMOUNT INTEREST CHARGED PER DOLLAR P . V . OF CUSTOMER RELATIONSHIPS RISK ADJUSTMENT FACTOR 1 10000 0 . 0 9 0 0 + 1 ( 0 . 0 0 2 ) 0 . 0 0 . 7 2 10000 0 . 0 9 0 0 + 2 ( 0 . 0 0 2 ) 0 . 0 0 . 7 3 • 10000 • 0 . 0 9 0 0 + 3 ( 0 . 0 0 2 ) • 0 . 0 0 . 7 • 60 • 10000 0 . 0 9 0 0 + N ( 0 . 0 0 2 ) • o ! o • 0^7 61 10000 0 . 0 9 5 0 + 1 ( 0 . 0 0 2 ) 0 . 0 0 . 8 62 10000 0 . 0 9 5 0 + 2 ( 0 . 0 0 2 ) 0 . 0 0 . 8 63 10000 • 0 . 0 9 5 0 + 3 ( 0 . 0 0 2 ) • 0 . 0 0 . 8 120 • 1 0 6 0 0 • 0 . 0 9 5 0 + N ( 0 . 0 0 2 ) • o ! o • o ! 8 121 1 0000 0 . 1 0 0 0 + 1 ( 0 . 0 0 2 ) 0 . 0 0 . 9 1 22 1 0000 0 . 1 0 0 0 + 2 ( 0 . 0 0 2 ) 0 . 0 0 . 9 123 • 1 0000 0 . 1 0 0 0 + 3 ( 0 . 0 0 2 ) 0 . 0 • 0 . 9 180 • 1 0 6 0 0 • 0 . 1 0 0 0 + N ( 0 . 0 0 2 ) • o ! o • o ! 9 181 1 0000 0 . 1 0 5 0 + 1 ( 0 . 0 0 2 ) 0 . 0 1 .0 182 1 0000 0 . 1 0 5 0 + 2 ( 0 . 0 0 2 ) 0 . 0 1 .0 183 10000 • 0 . 1 0 5 0 + 3 ( 0 . 0 0 2 ) • 0 . 0 • 1 . 0 • • 240 1 0 6 0 0 • 0 . 1 0 5 0 + N ( 0 . 0 0 2 ) • 0 . 0 • 1 ! o 241 1 0000 0 . 1 1 0 0 + 1 ( 0 . 0 0 2 ) 0 . 0 1 . 1 242 10000 0 . 1 1 0 0 + 2 ( 0 . 0 0 2 ) 0 . 0 1 . 1 243 1 0000 • 0 . 1 1 0 0 + 3 ( 0 . 0 0 2 ) • 0 . 0 • 1 . 1 • • 300 • 1 0 6 0 0 • 0 . 1 1 0 0 + N ( 0 . 0 0 2 ) • o ! o • • 1 . 1 301 1 0000 0 . 1 1 5 0 + 1 ( 0 . 0 0 2 ) 0 . 0 1 . 2 302 1 0000 0 . 1 1 5 0 + 2 ( 0 . 0 0 2 ) 0 . 0 1 . 2 303 • 1 0000 • 0 . 1 1 5 0 + 3 ( 0 . 0 0 2 ) • 0 . 0 • 1 . 2 • • 360 • 1 0 6 0 0 • 0 . 1 1 5 0 + N ( 0 . 0 0 2 ) • o ! o • 1 '.2 87 DATA SETS FOR THE TEST INGS OF THE IMPACT OF RISK T IGHTENING ON LOANABLE FUNDS ALLOCATION DATA SET 2 LOAN D I V I S I O N 1 F I X E D OVERHEAD COST = 200 F I X E D S E R V I C E F E E = 200 V A R I A B L E OVERHEAD = 0.002 V A R I A B L E S E R V I C E F E E = 0.001 VARIANCE OF LOAN RETURN = 0.001 LOAN A P P L I C A T I O N S : LOAN # N LOAN AMOUNT' INTEREST CHARGED PER DOLLAR P . V . OF CUSTOMER RELAT IONSHIPS RISK ADJUSTMENT FACTOR 1 1 0000 0.0918+1(0.00015) 0.0 1 .0 2 1 0000 0.0918+2(0.00015) 0.0 1 .0 3 1 0000 0.0918+3(0.00015) • 0.0 • 1 .0 360 1 0000 • 0.0918+ N(0.00015) • o . ' o 1 !o 88 LOAN' D IV IS ION 2 F I X E D OVERHEAD COST = 200 F I X E D SERV ICE F E E = 200 V A R I A B L E OVERHEAD = 0 . 0 0 2 V A R I A B L E S E R V I C E F E E = 0 . 0 0 1 VARIANCE OF LOAN RETURN = 0 . 0 2 8 LOAN A P P L I C A T I O N S : LOAN # N=60 LOAN AMOUNT INTEREST CHARGED PER DOLLAR P . V . OF CUSTOMER RELAT IONSHIPS RISK ADJUSTMENT FACTOR 1 10000 0 . 1 0 5 0 + 1 ( 0 . 0 0 2 ) 0 . 0 0 . 8 + 1 ( . 0 0 3 3 ) 2 1 0000 0 . 1 0 5 0 + 2 ( 0 . 0 0 2 ) 0 . 0 0 . 8 + 2 ( . 0 0 3 3 ) 3 • 10000 • 0 . 1 0 5 0 + 3 ( 0 . 0 0 2 ) • 0 . 0 • 0 . 8 + 3 ( . 0 0 3 3 ) • 60 • 10000 0 . • 1 0 5 0 + N ( 0 . 0 0 2 ) o ! o 0.8+N( . 0 0 3 3 ) 61 10000 0 . 1 1 0 0 + 1 ( 0 . 0 0 2 ) 0 . 0 0 . 9 + 1 ( . 0 0 3 3 ) 62 10000 0 . 1 1 0 0 + 2 ( 0 . 0 0 2 ) 0 . 0 0 . 9 + 2 ( . 0 0 3 3 ) 63 • 10000 • 0 . 1 1 0 0 + 3 ( 0 . 0 0 2 ) 0 . 0 0 . 9 + 3 ( . 0 0 3 3 ) • 1 20 • 1 0000 0 . • 110 0 + N ( 0 . 0 0 2 ) o ! o 0.9+N( . 0 0 3 3 ) 121 10000 0 . 115 0 + 1 ( 0 . 0 0 2 ) 0 . 0 1 . 0+1( . 0 0 3 3 ) 1 22 1 0000 0 . 1 1 5 0 + 2 ( 0 . 0 0 2 ) 0 . 0 1 .0+2( . 0 0 3 3 ) 123 • 10000 0 . 1 1 5 0 + 3 ( 0 . 0 0 2 ) • 0 . 0 ft 1.0+3( . 0 0 3 3 ) • 180 • 10000 0 . • 1 1 5 0 + N ( 0 . 0 0 2 ) ft o ! o 1. 0+N*( . 0 0 3 3 ) 181 10000 0 . 1 2 0 0 + 1 ( 0 . 0 0 2 ) 0 . 0 1.1 + 1 ( . 0 0 3 3 ) 182 10000 0 . 1 2 0 0 + 2 ( 0 . 0 0 2 ) 0 . 0 1 . 1+2( . 0 0 3 3 ) 183 • 10000 • 0 . 1 2 0 0 + 3 ( 0 . 0 0 2 ) • 0 . 0 ft 1 . 1+3( . 0 0 3 3 ) • 240 • 10000 0 . • 1 2 0 0 + N ( 0 . 0 0 2 ) ft o ! o 1.1+N( . 0 0 3 3 ) 241 1 0000 0 . 1 3 5 0 + 1 ( 0 . 0 0 2 ) 0 . 0 1 .2+1( . 0 0 3 3 ) 242 10000 0 . 1 3 5 0 + 2 ( 0 . 0 0 2 ) 0 . 0 1 . 2 + 2( . 0 0 3 3 ) 243 • 1 0000 • 0 . 1 3 5 0 + 3 ( 0 . 0 0 2 ) • 0 . 0 • 1 . 2 + 3( . 0 0 3 3 ) • 300 10000 0 . • 1 3 5 0 + N ( 0 . 0 0 2 ) ft o ! o 1.2+N( . 0 0 3 3 ) 301 10000 0 . 1 5 0 0 + 1 ( 0 . 0 0 2 ) 0 . 0 1 .3+1( . 0 0 3 3 ) 302 1 0000 0 . 1 5 0 0 + 2 ( 0 . 0 0 2 ) 0 . 0 1 .3+2( . 0 0 3 3 ) 303 • 10000 • 0 . 1 5 0 0 + 3 ( 0 . 0 0 2 ) • 0 . 0 ft 1.3+3( . 0 0 3 3 ) • 360 • 10000 0 . • 1 5 0 0 + N ( 0 . 0 0 2 ) • o ! o 1.3+N( . 0 0 3 3 ) 8 9 LOAN D IV IS ION 3 F I X E D OVERHEAD COST = 200 F I X E D S E R V I C E F E E = 200 V A R I A B L E OVERHEAD = 0 . 0 0 2 V A R I A B L E S E R V I C E F E E = 0 . 0 0 1 VARIANCE OF LOAN RETURN = 0 . 0 1 7 LOAN A P P L I C A T I O N S : LOAN # N=60 LOAN AMOUNT INTEREST CHARGED PER DOLLAR P . V . OF CUSTOMER RELATIONSHIPS RISK ADJUSTMENT FACTOR 1 10000 0 . 0 9 0 0 + 1 ( 0 . 0 0 2 ) 0 . 0 0 . 7 + 1 ( . 0 0 3 3 ) 2 10000 0 . 0 9 0 0 + 2 ( 0 . 0 0 2 ) 0 . 0 0 . 7 + 2 ( . 0 0 3 3 ) 3 10000 0 . 0 9 0 0 + 3 ( 0 . 0 0 2 ) 0 . 0 • 0 . 7 + 3 ( . 0 0 3 3 ) • 60 • 1 0000 0 . • 0 9 0 0 + N ( 0 . 0 0 2 ) • o!o 0.7+N( . 0 0 3 3 ) 61 10000 0 . 0 9 5 0 + 1 ( 0 . 0 0 2 ) 0 . 0 0 . 8 + 1 ( . 0 0 3 3 ) 62 1 0000 0 . 0 9 5 0 + 2 ( 0 . 0 0 2 ) 0 . 0 0 . 8 + 2 ( . 0 0 3 3 ) 63 10000 • 0 . 0 9 5 0 + 3 ( 0 . 0 0 2 ) • • 0 . 0 • 0 . 8 + 3 ( . 0 0 3 3 ) 1 20 10000 0 . • 0 9 5 0 + N ( 0 . 0 0 2 ) o!o 0.8+N( . 0 0 3 3 ) 121 1 0000 0 . 1 0 0 0 + 1 ( 0 . 0 0 2 ) 0 . 0 0 . 9 + 1 ( . 0 0 3 3 ) 1 22 1 0000 0 . 1 0 0 0 + 2 ( 0 . 0 0 2 ) 0 . 0 0 . 9 + 2 ( . 0 0 3 3 ) 123 • 10000 • 0 . 1 0 0 0 + 3 ( 0 . 0 0 2 ) • 0 . 0 • 0 . 9 + 3 ( . 0 0 3 3 ) • 180 • 10000 0 . • 1 0 0 0 + N ( 0 . 0 0 2 ) • o!o 0.9+N( . 0 0 3 3 ) 181 10000 0 . 1 0 5 0 + 1 ( 0 . 0 0 2 ) 0 . 0 1 .0+1( . 0 0 3 3 ) 182 10000 0 . 1 0 5 0 + 2 ( 0 . 0 0 2 ) 0 . 0 1 .0+2( . 0 0 3 3 ) 183 • 10000 • 0 . 1 0 5 0 + 3 ( 0 . 0 0 2 ) • 0 . 0 • 1.0+3( . 0 0 3 3 ) • 240 • 10000 0 . • 1 0 5 0 + N ( 0 . 0 0 2 ) • o!o 1.0+N( . 0 0 3 3 ) 241 10000 0 . 1 1 0 0 + 1 ( 0 . 0 0 2 ) 0 . 0 1 . 1 + 1 ( . 0 0 3 3 ) 242 10000 0 . 1 1 0 0 + 2 ( 0 . 0 0 2 ) 0 . 0 V.1+2 ( . 0 0 3 3 ) 243 10000 • 0 . 1 1 0 0 + 3 ( 0 . 0 0 2 ) 0 . 0 • 1.1+3( . 0 0 3 3 ) • 300 • 10000 0 . • 1 1 0 0 + N ( 0 . 0 0 2 ) • o.'o 1.1+N( . 0 0 3 3 ) 301 10000 0 . 1 1 5 0 + 1 ( 0 . 0 0 2 ) 0 . 0 1 .2+1( . 0 0 3 3 ) 302 1 0000 0 . 1 1 5 0 + 2 ( 0 . 0 0 2 ) 0 . 0 1 .2+2( . 0 0 3 3 ) 303 • 10000 • 0 . 1 1 5 0 + 3 ( 0 . 0 0 2 ) • 0 . 0 • 1.2+3( . 0 0 3 3 ) • 360 • 10000 0 . • 1 1 5 0 + N ( 0 . 0 0 2 ) • o!o 1.2+N( . 0 0 3 3 ) APPENDIX 3 THE SIMULATION RESULTS OF THE F E A S I B I L I T Y T E S T S L E T L P 1 = FRACTION OF LOANABLE FUNDS IN LOAN D I V I S I O N 1 LP2 = FRACTION OF LOANABLE FUNDS IN LOAN D I V I S I O N 2 L P 3 = FRACTION OF LOANABLE FUNDS IN LOAN D I V I S I O N 3 D I F F Q = THE D I F F E R E N C E BETWEEN THE ACTUAL AMOUNT OF LOANS AND THE AMOUNT OF LOANABLE FUNDS A V A I L I A B L E D I F F V = THE D I F F E R E N C E BETWEEN THE ACTUAL LOAN PORTFOLIO RISK AND THE MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK C . O . F . = COST OF FUNDS R . F . = RISK FACTOR 91 LOANABLE FUNDS ' = 6 5 0 0 0 0 0 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 3 MONTH LP1 LP2 LP3 D I F F Q D I F F V C . O . R R . F . 1 0 . 3 4 0 . 3 3 0 . 3 6 160000 0 . 0 0 2 3 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 4 4 0 . 2 7 0 . 2 8 - 70000 0 . 0 0 0 6 0 . 0 4 1 7 6 . 1 9 2 6 3 0 . 4 5 0 . 2 5 0 . 2 8 - 1 1 0 0 0 0 0 . 0 0 0 3 0 . 0 3 9 6 6 . 5 0 0 0 4 0 . 4 6 0 . 2 4 0 . 2 9 - 80000 0 . 0 0 0 2 0 . 0 3 8 6 6 . 5 0 0 0 5 0 . 4 7 0 . 2 4 0 . 2 9 - 50000 0 . 0 0 0 2 0 . 0 3 7 9 6 . 5 0 0 0 6 0 . 4 7 0 . 2 3 0 . 2 8 - 40000 0 . 0 0 0 1 0 . 0 3 7 4 6 . 5 0 0 0 LOANABLE FUNDS = 6 5 0 0 0 0 0 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 3 5 MONTH LP1 LP2 LP3 D I F F Q D I F F V C . O . R R . F . 1 0 . 3 4 0 . 3 3 0 . 3 6 160000 0 . 0 0 1 9 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 4 1 0 . 2 6 0 . 2 9 - 3 0 0 0 0 0 - 0 . 0 0 0 1 0 . 0 4 5 0 5 . 4 6 3 8 3 0 . 4 5 0 . 2 5 0 . 3 0 - 60000 - 0 . 0 0 0 0 0 . 0 4 1 0 5 . 7 4 2 8 4 0 . 4 5 0 . 2 5 0 . 3 0 - 40000 0 . 0 0 0 0 0 . 0 4 0 7 5 . 6 7 5 2 5 0 . 4 5 0 . 2 5 0 . 3 0 - 30000 0 . 0 0 0 0 0 . 0 4 0 8 5 . 6 0 9 7 6 0 . 4 5 0 . 2 5 0 . 3 0 - 20000 0 . 0 0 0 0 0 . 0 4 0 7 5 . 5 5 8 7 LOANABLE FUNDS = 6 5 0 0 0 0 0 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 4 MONTH LP1 LP2 LP3 D I F F Q D I F F V C . O . R R . F . 1 0 . 3 4 0 . 3 3 0 . 3 6 160000 0 . 0 0 1 3 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 3 8 0 . 2 6 0 . 3 0 - 4 2 0 0 0 0 - 0 . 0 0 0 5 0 . 0 4 8 4 4 . 7 3 5 1 3 0 . 4 0 0 . 2 7 0 . 3 2 - 70000 - 0 . 0 0 0 1 0 . 0 4 6 4 4 . 4 3 0 0 4 0 . 4 1 0 . 2 7 0 . 3 2 - 40000 0 . 0 0 0 0 0 . 0 4 6 3 4 . 3 3 4 6 5 0 . 4 1 0 . 2 7 0 . 3 2 - 30000 0 . 0 0 0 0 0 . 0 4 6 3 4 . 2 7 3 2 6 0 . 4 1 0 . 2 7 0 . 3 2 - 20000 0 . 0 0 0 0 0 . 0 4 6 3 4 . 2 2 4 6 LOANABLE FUNDS = 6 5 0 0 0 0 0 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 4 5 MONTH L P 1 LP2 LP3 D I F F Q D I F F V C . O . R R . F . 1 0 . 3 4 0 . 3 3 0 . 3 6 160000 0 . 0 0 0 9 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 3 8 0 . 2 7 0 . 3 1 - 4 6 0 0 0 0 - 0 . 0 0 0 8 0 . 0 5 1 7 4 . 0 0 6 3 3 0 . 3 7 0 . 2 9 0 . 3 3 - 6 0 0 0 0 - 0 . 0 0 0 1 0 . 0 5 1 1 3 . 4 0 3 3 4 0 . 3 7 0 . 2 9 0 . 3 3 - 5 0 0 0 0 0 . 0 0 0 1 0 . 0 5 0 9 3 . 3 4 8 4 5 0 . 3 7 0 . 2 9 0 . 3 3 - 2 0 0 0 0 0 . 0 0 0 0 0 . 0 5 0 9 3 . 2 8 3 7 6 0 . 3 7 0 . 2 9 0 . 3 4 - 2 0 0 0 0 0 . 0 0 0 0 0 . 0 5 1 0 3 . 2 4 0 6 92 LOANABLE FUNDS = 6500000 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0.005 MONTH LP 1 LP2 LP3 D IFFQ D I F F V C . O . R R . F . 1 0 . 3 4 0 . 3 3 0 . 3 6 160000 0 . 0 0 0 4 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 3 3 0 . 2 8 0 . 3 2 - 4 8 0 0 0 0 - 0 . 0 0 1 0 0 . 0 5 5 1 3 . 2 7 7 5 3 0 . 3 3 0 . 3 2 0 . 3 5 - 50000 0 . 0 0 0 0 0 . 0 5 5 2 2 . 5 5 2 6 4 0 . 3 3 0 . 3 2 0 . 3 5 - 50000 0 . 0 0 0 0 0 . 0 5 4 9 2 . 5 2 8 7 5 0 . 3 3 0 . 3 2 0 . 3 5 0 0 . 0 0 0 0 0 . 0 5 5 0 2 . 4 4 4 9 6 0 . 3 3 0 . 3 2 0 . 3 5 0 0 . 0 0 0 0 0 . 0 5 5 0 2 . 4 4 1 6 LOANABLE FUNDS = 6500000 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 5 5 MONTH LP 1 LP2 LP3 D I F F Q D I F F V C . O . R R . F . 1 0 . 3 4 0 . 3 3 0 . 3 6 160000 - 0 . 0 0 0 1 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 3 0 0 . 3 0 0 . 3 4 - 4 3 0 0 0 0 - 0 . 0 0 0 1 0 . 0 5 8 5 2 . 5 4 8 8 3 0 . 3 0 0 . 3 4 0 . 3 6 - 50000 0 . 0 0 0 0 0 . 0 5 8 8 1 . 8 8 6 2 4 0 . 3 0 0 . 3 4 0 . 3 6 - 30000 0 . 0 0 0 0 0 . 0 5 8 5 1 . 8 5 8 6 5 0 . 3 0 0 . 3 4 0 . 3 6 - 20000 0 . 0 0 0 0 0 . 0 5 8 6 1 . 8 0 3 3 6 0 . 3 0 0 . 3 4 0 . 3 6 0 0 . 0 0 0 0 0 . 0 5 8 7 1 . 7 6 7 4 LOANABLE FUNDS = 6500000 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 6 MONTH LP 1 LP2 LP3 D IFFQ D I F F V C . O . R R . F . 1 0 . 3 4 0 . 3 3 0 . 3 6 160000 - 0 . 0 0 0 6 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 2 7 0 . 3 3 0 . 3 5 - 3 6 0 0 0 0 - 0 . 0 0 0 9 0 . 0 6 1 8 1 . 8 2 0 0 3 0 . 2 7 0 . 3 6 0 . 3 7 - 30000 0 .0000 0 . 0 6 2 1 1 . 2 8 7 9 4 0 . 2 7 0 . 3 5 0 . 3 7 - 40000 0 . 0 0 0 0 0 . 0 6 1 9 1 . 2 6 7 2 5 0 . 2 7 0 . 3 6 0 . 3 7 20000 0 . 0 0 0 0 0 . 0 6 1 8 1 . 2 2 8 4 6 0 . 2 7 0 . 3 6 0 . 3 7 0 0 . 0 0 0 0 0 . 0 6 1 9 1 .2511 LOANABLE FUNDS = 6500000 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 6 5 MONTH LP 1 LP2 LP3 D I F F Q D I F F V C . O . R R . F . 1 0 , 3 4 0 . 3 3 0 . 3 6 160000 - 0 . 0 0 1 1 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 2 4 0 . 3 6 0 . 3 7 - 2 4 0 0 0 0 - 0 . 0 0 0 5 0 . 0 6 5 2 1 . 0 9 1 2 3 0 . 2 4 0 . 3 7 0 . 3 8 - 40000 - 0 . 0 0 0 1 0 . 0 6 4 9 0 . 8 2 3 6 4 0 . 2 4 0 . 3 8 0 . 3 8 0 0 . 0 0 0 0 0 . 0 6 4 9 0 . 7 7 2 2 5 0 . 2 4 0 . 3 8 0 . 3 8 0 0 . 0 0 0 0 0 . 0 6 4 8 0 . 7 8 0 8 6 0 . 2 4 0 . 3 8 0 . 3 8 0 0 . 0 0 0 0 0 . 0 6 4 9 0 . 7 6 4 4 93 LOANABLE FUNDS = 7000000 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0.003 MONTH LP 1 LP2 LP3 D I F F Q D I F F V c . O . R R . F . 1 0 . 3 1 0 . 3 1 0 . 3 4 - 2 5 0 0 0 0 0 . 0 0 1 8 0 . 0550 3 . 0 0 0 0 2 0 . 4 4 0 . 2 5 0 . 2 7 - 2 0 0 0 0 0 0 . 0 0 0 3 0 . 0377 6 . 4 4 0 9 3 0 . 4 6 0 . 2 4 0 . 2 8 - 1 6 0 0 0 0 0 . 0 0 0 1 0 . 0355 6 . 5 0 0 0 4 0 . 4 7 0 . 2 3 0 . 2 8 - 70000 0 . 0 0 0 1 0 . 0339 6 . 5 0 0 0 5 0 . 4 8 0 . 2 3 0 . 2 8 - 20000 0 . 0 0 0 1 0 . 0332 6 . 5 0 0 0 6 0 . 4 8 0 . 2 3 0 . 2 8 0 0 . 0 0 0 1 0 . 0329 6 . 5 0 0 0 LOANABLE FUNDS = 7000000 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 3 5 MONTH LP 1 LP2 L P 3 D I F F Q D I F F V C . O . R R . F . 1 0 . 3 1 0 . 3 1 0 . 3 4 - 2 5 0 0 0 0 0 . 0 0 1 3 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 4 2 0 . 2 5 0 . 2 8 - 4 0 0 0 0 0 - 0 . 0 0 0 3 0 . 0 4 1 5 5 . 5 7 8 9 3 0 . 4 5 0 . 2 4 0 . 2 9 - 1 3 0 0 0 0 - 0 . 0 0 0 2 0 . 0 3 8 0 5 . 5 8 4 8 4 0 . 4 5 0 . 2 5 0 . 3 0 - 70000 0 . 0 0 0 1 0 . 0 3 7 8 5 . 3 8 7 7 5 0 . 4 5 0 . 2 5 0 . 3 0 0 0 . 0 0 0 1 0 . 0 3 7 7 5 . 2 8 8 6 6 0 . 4 5 0 . 2 5 0 . 3 0 0 0 . 0 0 0 1 0 . 0 3 7 7 5 . 2 9 1 4 LOANABLE FUNDS = 7000000 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 4 MONTH LP 1 LP2 LP3 D I F F Q D I F F V C . O . R R . F . 1 0 . 3 1 0 . 3 1 0 . 3 4 - 2 5 0 0 0 0 0 . 0 0 0 8 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 3 8 0 . 2 5 0 . 2 9 - 4 9 0 0 0 0 - 0 . 0 0 0 6 0 . 0 4 5 3 4 . 7 1 6 8 3 0 . 4 0 0 . 2 7 0 . 3 1 - 1 0 0 0 0 0 - 0 . 0 0 0 2 0 . 0 4 3 7 4 . 2 0 4 7 4 0 . 4 1 0 . 2 7 0 . 3 1 - 70000 - 0 . 0 0 0 1 0 . 0 4 3 5 4 . 0 7 9 5 5 0 . 4 1 0 . 2 7 0 . 3 2 - 10000 0 . 0 0 0 0 0 . 0 4 3 4 3 . 9 9 4 1 6 0 . 4 1 0 . 2 7 0 . 3 2 - 20000 0 . 0 0 0 0 0 . 0 4 3 6 3 . 9 4 4 5 LOANABLE FUNDS = 7 0 0 0 0 0 0 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 4 5 MONTH LP1 LP2 L P 3 D I F F Q D I F F V C . O . R R . F . 1 0 .31 0 .31 0 . 34 - 2 5 0 0 0 0 0.0003 0.0550 3.0000 2 0 . 3 6 0 . 2 6 0 . 3 0 - 5 1 0 0 0 0 -0.0008 0 . 0 4 9 1 3 . 8 5 4 7 3 0 .37 0 . 2 9 0 . 3 3 - 80000 - 0 . 0 0 0 1 0 . 0 4 8 7 3 . 0 9 8 6 4 0 . 3 7 0 . 2 9 0 . 3 3 - 50000 0.0000 0 . 0 4 8 4 3 . 0 4 3 4 5 0 . 3 7 0.30 0 . 3 3 - 20000 0.0000 0 . 0 4 8 3 2 . 9 7 9 2 6 0 . 37 0 .30 0 . 3 3 0 0.0000 0 . 0 4 8 4 2 . 9 3 7 7 94 LOANABLE FUNDS = 7000000 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO R ISK = 0 . 0 0 5 MONTH LP1 LP2 L P 3 D I F F Q D I F F V C . O . R R . F . 1 0 . 3 1 0 . 3 1 0 . 3 4 - 2 5 0 0 0 0 - 0 . 0 0 0 2 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 3 3 0 . 2 8 0 . 3 2 - 4 9 0 0 0 0 - 0 . 0 0 1 0 0 . 0 5 2 8 2 . 9 9 2 7 3 0 . 3 3 0 . 3 2 0 . 3 4 - 70000 - 0 . 0 0 0 1 0 . 0 5 3 0 2 . 2 2 9 7 4 0 . 3 3 0 . 3 2 0 . 3 4 - 50000 0 . 0 0 0 1 0 . 0 5 2 7 2 . 1 8 1 1 5 0 . 3 3 0 . 3 2 0 . 3 5 0 ' 0 . 0 0 0 0 0 . 0 5 2 7 2 . 1 1 4 6 6 0 . 3 3 0 . 3 2 0 . 3 5 0 0 . 0 0 0 0 0 . 0 5 2 7 2 . 1 1 4 6 LOANABLE FUNDS = 7000000 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 5 5 MONTH LP1 LP2 L P 3 D I F F Q D I F F V C . O . R R . F ; 1 0 . 3 1 0 . 3 1 0 . 3 4 - 2 5 0 0 0 0 - 0 . 0 0 0 7 0 . 0 5 5 0 - 3 . 0 0 0 0 2 0 . 3 0 0 . 3 1 0 . 3 3 - 4 1 0 0 0 0 - 0 . 0 0 0 8 0 . 0 5 6 6 2 . 1 3 0 6 3 0 . 3 0 0 . 3 4 0 . 3 5 - 50000 0 . 0 0 0 1 0 . 0 5 6 6 1 .5441 4 0 . 3 0 0 . 3 4 0 . 3 6 - 30000 0 . 0 0 0 0 0 . 0 5 6 5 1 . 4 9 3 3 5 0 . 3 0 0 . 3 4 0 . 3 6 - 10000 0 . 0 0 0 0 0 . 0 5 6 6 1 . 4 4 3 2 6 0 . 3 0 0 . 3 4 0 . 3 6 0 0 . 0 0 0 0 0 . 0 5 6 4 1 . 4 4 8 9 LOANABLE FUNDS = 7000000 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO R ISK = 0 . 0 0 6 MONTH L P 1 LP2 L P 3 D I F F Q D I F F V C . O . R R . F . 1 0 . 3 1 0 . 3 1 0 . 3 4 - 2 5 0 0 0 0 - 0 . 0 0 1 2 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 2 7 0 . 3 4 0 . 3 5 - 2 9 0 0 0 0 - 0 . 0 0 0 6 0 . 0 6 0 4 1 . 2 6 8 6 3 0 . 2 7 0 . 3 6 6 . 3 7 - 40000 0 . 0 0 0 0 0 . 0 6 0 0 0 . 9 3 8 3 4 0 . 2 7 0 . 3 6 0 . 3 7 - 10000 0 . 0 0 0 0 0 . 0 5 9 9 0 . 8 9 7 1 5 0 . 2 7 0 . 3 6 0 . 3 7 0 0 . 0 0 0 0 0 . 0 6 0 0 0 . 8 7 4 2 6 0 . 2 7 0 . 3 6 0 . 3 7 0 0 . 0 0 0 0 0 . 0 5 9 9 0 . 8 8 5 3 LOANABLE FUNDS = 7 0 0 0 0 0 0 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 6 5 MONTH LP1 LP2 L P 3 D I F F Q D I F F V C . O . R R . F . 1 0 . 3 1 0 . 3 1 0 . 3 4 - 2 5 0 0 0 0 - 0 . 0 0 1 7 1 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 2 3 0 . 3 8 0 . 3 7 - 1 3 0 0 0 0 - 0 . 0 0 0 1 0 . 0 6 4 2 0 . 4 0 6 5 3 0 . 2 4 0 . 3 8 0 . 3 8 1 0000 0 . 0 0 0 0 0 . 0 6 3 1 0 . 4 0 6 4 4 0 . 2 4 0 . 3 8 0 . 3 8 0 0 . 0 0 0 0 0 . 0 6 3 1 0 . 4 1 5 5 5 0 . 2 4 0 . 3 8 0 . 3 8 0 0 . 0 0 0 0 0 . 0 6 3 1 0 . 4 1 5 5 6 0 . 2 4 0 . 3 8 0 . 3 8 0 0 . 0 0 0 0 0 . 0 6 3 1 0 . 4 1 5 5 95 LOANABLE FUNDS = 7500000 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 3 MONTH LP1 LP2 LP3 D I F F Q D I F F V C . O . R R . F . 1 0 . 2 9 0 . 3 0 0 . 3 2 - 6 4 0 0 0 0 0 . 0 0 1 4 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 4 4 0 . 2 4 0 . 2 6 - 4 4 0 0 0 0 0 . 0 0 0 0 0 . 0 3 5 2 6 . 5 0 0 0 3 0 . 4 7 0 . 2 3 0 . 2 8 - 1 3 0 0 0 0 0 . 0 0 0 0 0 . 0 3 0 6 6 . 5 0 0 0 4 0 . 4 8 0 . 2 3 0 . 2 8 - 70000 0 . 0 0 0 0 0 . 0 2 9 0 6 . 5 0 0 0 5 0 . 4 8 0 . 2 3 0 . 2 8 - 50000 0 . 0 0 0 0 0 . 0 2 8 1 6 . 5 0 0 0 6 0 . 4 8 0 . 2 3 0 . 2 8 - 20000 0 . 0 0 0 1 0 . 0 2 7 4 6 . 5 0 0 0 LOANABLE FUNDS = 7 5 0 0 0 0 0 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 3 5 MONTH LP1 LP2 LP3 D I F F Q D I F F V C . O . R R . F . 1 0 . 2 9 0 . 3 0 0 . 3 2 - 6 4 0 0 0 0 0 . 0 0 0 9 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 4 2 0 . 2 4 0 . 2 7 - 5 0 0 0 0 0 - 0 . 0 0 0 5 0 . 0 3 8 1 5 . 7 7 9 2 3 0 . 4 5 0 . 2 4 0 . 2 9 - 1 3 0 0 0 0 - 0 . 0 0 0 2 0 . 0 3 4 4 5 . 4 9 5 0 4 0 . 4 5 0 . 2 5 0 . 2 9 - 80000 0 . 0 0 0 1 0 . 0 3 4 8 5 . 2 0 7 9 5 0 . 4 5 0 . 2 5 0 . 3 0 - 20000 0 . 0 0 0 0 0 . 0 3 4 5 5 . 1 1 6 9 6 0 . 4 5 0 . 2 5 0 . 3 0 - 20000 0 . 0 0 0 0 0 . 0 3 4 5 5 . 1 1 6 9 LOANABLE FUNDS = 7500000 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 4 MONTH LP1 LP2 LP3 D I F F Q D I F F V C . O . R R . F . 1 0 . 2 9 0 . 3 0 0 . 3 2 - 6 4 0 0 0 0 0 . 0 0 0 4 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 3 9 0 . 2 5 0 . 2 8 - 6 1 0 0 0 0 - 0 . 0 0 0 8 0 . 0 4 2 2 4 . 7 5 1 6 3 0 . 4 0 0 . 2 7 0 . 3 1 - 1 3 0 0 0 0 - 0 . 0 0 0 2 0 . 0 4 1 1 3 . 9 6 8 0 4 0 . 4 1 0 . 2 7 0 . 3 1 - 80000 0 . 0 0 0 1 0 . 0 4 0 6 3 . 8 5 6 8 5 0 . 4 1 0 . 2 7 0 . 3 1 - 20000 0 . 0 0 0 0 0 . 0 4 0 7 3 . 7 0 9 6 6 0 . 4 1 0 . 2 8 0 . 3 1 0 0 . 0 0 0 0 0 . 0 4 0 8 3 . 6 6 9 9 LOANABLE FUNDS = 7500000 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 4 5 MONTH LP1 LP2 LP3 D I F F Q D I F F V C . O . R R . F . 1 0 . 2 9 0 . 3 0 0 . 3 2 - 6 4 0 0 0 0 0 . 0 0 0 1 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 3 6 0 . 2 6 0 . 3 0 - 6 1 0 0 0 0 - 0 . 0 0 0 9 0 . 0 4 6 5 3 . 7 2 4 0 3 0 . 3 7 0 . 2 9 0 . 3 3 ' - 1 0 0 0 0 0 - 0 . 0 0 0 1 0 . 0 4 6 2 2 . 7 9 1 0 4 0 . 3 7 0 . 3 0 0 . 3 3 - 40000 0 . 0 0 0 0 0 . 0 4 5 7 2 . 7 2 6 0 5 0 . 3 7 0 . 3 0 0 . 3 3 - 20000 0 . 0 0 0 0 0 . 0 4 5 8 2 . 6 5 4 4 6 0 . 3 7 0 . 3 0 0 . 3 3 0 0 . 0 0 0 0 0 . 0 4 5 8 2 . 6 2 4 9 9 6 LOANABLE FUNDS = 7500000 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 5 MONTH LP1 LP2 L P 3 D I F F Q D I F F V C . O . R R . F . 1 0 . 2 9 0 . 3 0 0 . 3 2 - 6 4 0 0 0 0 - 0 . 0 0 0 6 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 3 3 0 . 2 9 0 . 3 2 - 5 2 0 0 0 0 - 0 . 0 0 0 9 0 . 0 5 0 6 2 . 6 9 6 5 3 0 . 3 3 0 . 3 2 0 . 3 4 - 6 0 0 0 0 0 . 0 0 0 0 0 . 0 5 0 6 1 . 9 1 0 9 4 0 . 3 4 0 . 3 2 0 . 3 4 - 40000 0 . 0 0 0 0 0 . 0 5 0 3 1 . 8 7 0 6 5 0 . 3 4 0 . 3 2 0 . 3 4 0 0 . 0 0 0 0 0 . 0 5 0 3 1 . 8 1 1 7 6 0 . 3 4 0 . 3 2 0 . 3 4 0 0 . 0 0 0 0 0 . 0 5 0 3 1 . 8 1 1 9 LOANABLE FUNDS = 7 5 0 0 0 0 0 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 5 5 MONTH LP1 LP2 L P 3 D I F F Q D I F F V C . O . R R . F . 1 0 . 2 9 0 . 3 0 0 . 3 2 - 6 4 0 0 0 0 - 0 . 0 0 1 V 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 3 0 0 . 3 2 0 . 3 3 - 3 9 0 0 0 0 - 0 . 0 0 0 7 0 . 0 5 4 8 1 . 6 6 8 9 3 0 . 3 0 0 . 3 4 0 . 3 5 - 50000 0 . 0 0 0 0 0 . 0 5 4 4 1 . 1 8 0 9 4 0 . 3 0 0 . 3 4 0 . 3 5 - 10000 0 . 0 0 0 0 0 . 0 5 4 3 1 . 1 2 5 4 5 0 . 3 0 0 . 3 4 0 . 3 6 0 0 . 0 0 0 0 0 . 0 5 4 3 1 .1201 6 0 . 3 1 0 . 3 4 0 . 3 5 0 0 . 0 0 0 0 0 . 0 5 4 2 1 . 1230 LOANABLE FUNDS = 7500000 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 6 MONTH LP1 LP2 L P 3 D I F F Q D I F F V C . O . R R . F . 1 0 . 2 9 0 . 3 0 0 . 3 2 - 6 4 0 0 0 0 - 0 . 0 0 1 6 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 2 6 0 . 3 5 0 . 3 6 - 1 9 0 0 0 0 - 0 . 0 0 0 3 0 . 0 5 9 0 0 . 6 4 1 3 3 0 . 2 7 0 . 3 6 0 . 3 6 0 0 . 0 0 0 0 0 . 0 5 7 9 0 . 5 4 6 7 4 0 . 2 7 0 . 3 6 0 . 3 6 - 10000 0 . 0 0 0 0 0 . 0 5 7 9 0 . 5 4 0 9 5 0 . 2 7 0 . 3 6 0 . 3 6 10000 0 . 0 0 0 0 0 . 0 5 7 9 0 . 5 4 3 3 6 0 . 2 7 0 . 3 6 0 . 3 6 0 0 . 0 0 0 0 0 . 0 5 7 9 0 . 5 4 4 9 LOANABLE FUNDS = 7 5 0 0 0 0 0 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 6 5 MONTH LP1 LP2 L P 3 D I F F Q D I F F V C . O . R R . F . 1 0 . 2 9 0 . 3 0 0 . 3 2 - 6 4 0 0 0 0 - 0 . 0 0 2 1 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 2 3 0 . 3 8 0 . 3 7 - 1 8 0 0 0 0 - 0 . 0 0 0 1 0 . 0 6 3 2 0 . 0 0 0 0 3 0 . 2 4 0 . 3 8 0 . 3 7 0 0 . 0 0 0 0 0 . 0 6 1 4 0 . 3 6 4 9 4 0 . 2 5 0 . 3 8 0 . 3 7 1 0 0 0 0 0 . 0 0 0 0 0 . 0 6 1 3 0 . 4 7 9 4 5 0 . 2 5 0 . 3 8 0 . 3 7 - 1 0 0 0 0 0 . 0 0 0 0 0 . 0 6 1 3 0 . 5 1 6 4 6 0 . 2 5 0 . 3 8 0 . 3 7 0 0 . 0 0 0 0 0 . 0 6 1 3 0 . 4 5 9 3 97 LOANABLE FUNDS = 8 0 0 0 0 0 0 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 3 MONTH LP1 LP2 L P 3 D I F F Q D I F F V C . O . R R . F . 1 0 . 2 8 0 . 2 8 0 . 3 1 - 1 0 9 0 0 0 0 0 . 0 0 0 9 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 4 4 0 . 2 2 0 . 2 6 - 5 4 0 0 0 0 0 . 0 0 0 2 0 . 0 3 1 6 6 . 5 0 0 0 3 0 . 4 5 0 . 2 3 0 . 2 8 - 3 6 0 0 0 0 0 . 0 0 0 0 0 . 0 2 5 1 6 . 5 0 0 0 4 0 . 4 5 0 . 2 4 0 . 2 9 - 2 1 0 0 0 0 0 . 0 0 0 2 0 . 0 1 9 4 6 . 5 0 0 0 5 0 . 4 5 0 . 2 4 0 . 3 0 - 1 0 0 0 0 0 0 . 0 0 0 2 0 . 0 1 4 8 6 . 5 0 0 0 6 0 . 4 5 0 . 2 5 0 . 3 0 - 3 0 0 0 0 0 . 0 0 0 1 0 . 0 1 2 6 6 . 5 0 0 0 LOANABLE FUNDS = 8 0 0 0 0 0 0 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 3 5 MONTH LP1 LP2 L P 3 D I F F Q D I F F V C . O . R R . F . 1 0 . 2 8 0 . 2 8 0 . 3 0 - 1 0 9 0 0 0 0 0 . 0 0 0 4 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 4 3 0 . 2 3 0 . 2 7 - 6 1 0 0 0 0 - 0 . 0 0 0 6 0 . 0 3 4 3 5 . 8 1 6 1 3 0 . 4 5 0 . 2 4 0 . 2 9 - 1 4 0 0 0 0 - 0 . 0 0 0 0 0 . 0 3 0 8 5 . 2 9 8 8 4 0 . 4 5 0 . 2 5 0 . 2 9 - 60000 0 . 0 0 0 0 0 . 0 3 1 0 5 . 0 0 8 6 5 0 . 4 5 0 . 2 5 0 . 3 0 - 20000 0 . 0 0 0 0 0 . 0 3 1 1 4 . 8 8 8 8 6 0 . 4 5 0 . 2 5 0 . 3 0 0 0 . 0 0 0 0 0 . 0 3 1 2 4 . 8 4 4 7 LOANABLE FUNDS = 8000000 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 4 MONTH LP1 LP2 LP3 D I F F Q D I F F V C . O . R R . F . 1 0 . 2 8 0 . 2 8 0 . 3 1 - 1 0 9 0 0 0 0 0 . 0 0 0 0 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 3 9 0 . 2 4 0 . 2 8 - 6 5 0 0 0 0 - 0 . 0 0 0 8 0 . 0 3 9 1 4 . 6 0 8 3 3 0 . 4 0 0 . 2 7 0 . 3 1 - 1 3 0 0 0 0 - 0 . 0 0 0 2 0 . 0 3 8 4 3 . 6 3 3 2 4 0 . 4 1 0 . 2 8 0 . 3 1 - 40000 0 . 0 0 0 0 0 . 0 3 7 7 3 . 5 3 0 4 5 0 . 4 1 0 . 2 8 0 . 3 1 - 40000 0 . 0 0 0 0 0 . 0 3 8 0 3 . 4 2 6 9 6 0 . 4 1 0 . 2 8 0 . 3 1 10000 0 . 0 0 0 0 0 . 0 3 7 8 3 . 3 9 0 0 LOANABLE FUNDS = 8000000 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 4 5 MONTH LP 1 LP2 L P 3 D I F F Q D I F F V C . O . R R . F . 1 0 . 2 8 0 . 2 8 0 . 3 1 - 1 0 9 0 0 0 0 - 0 . 0 0 0 6 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 3 6 0 . 2 7 0 . 3 0 - 5 9 0 0 0 0 - 0 . 0 0 0 9 0 . 0 4 3 9 3 . 4 0 0 6 3 0 . 3 7 0 . 3 0 0 . 3 2 - 1 0 0 0 0 0 - 0 . 0 0 0 1 0 . 0 4 3 8 2 . 4 6 9 5 4 0 . 3 7 0 . 3 0 0 . 3 3 - 4 0 0 0 0 0 . 0 0 0 0 0 . 0 4 3 2 2 . 4 2 9 2 5 0 . 3 7 0 . 3 0 0 . 3 3 - 3 0 0 0 0 0 . 0 0 0 0 0 . 0 4 3 2 2 . 3 6 9 8 6 0 . 3 7 0 . 3 0 0 . 3 3 10000 0 . 0 0 0 0 0 . 0 4 3 2 2 . 3 2 0 4 98 LOANABLE FUNDS = 8000000 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 5 MONTH LP1 LP2 LP3 D I F F Q D I F F V C . O . R R . F . 1 0 . 2 8 0 . 2 8 0 . 3 1 - 1 0 9 0 0 0 0 - 0 . 0 0 1 1 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 3 3 0 . 3 0 0 . 3 2 - 4 7 0 0 0 0 - 0 . 0 0 0 7 0 . 0 4 8 7 2 . 1 9 2 9 3 0 . 3 4 0 . 3 2 0 . 3 4 - 5 0 0 0 0 0 . 0 0 0 0 0 . 0 4 8 2 1 . 5 6 4 5 4 0 . 3 4 0 . 3 2 0 . 3 4 - 30000 0 . 0 0 0 0 0 . 0 4 7 9 1 . 5 3 2 6 5 0 . 3 4 0 . 3 2 0 . 3 4 0 0 . 0 0 0 0 0 . 0 4 8 0 1 . 4 8 2 6 6 0 . 3 4 0 . 3 2 0 . 3 4 0 0 . 0 0 0 0 0 . 0 4 8 0 1 . 4 8 1 9 LOANABLE FUNDS = 8 0 0 0 0 0 0 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 5 5 MONTH LP1 LP2 LP3 D I F F Q D I F F V C . O . R R . F . 1 0 . 2 8 0 . 2 8 0 . 3 1 - 1 0 9 0 0 0 0 - 0 . 0 0 1 6 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 2 9 0 . 3 3 0 . 3 4 - 2 6 0 0 0 0 - 0 . 0 0 0 3 0 . 0 5 3 5 0 . 9 8 5 1 3 0 . 3 0 0 . 3 4 0 . 3 5 - 30000 0 . 0 0 0 0 0 . 0 5 2 3 0 . 8 1 1 5 4 0 . 3 1 0 . 3 4 0 . 3 5 - 10000 0 . 0 0 0 0 0 . 0 5 2 1 0 . 8 0 3 1 5 0 . 3 1 0 . 3 4 0 . 3 5 - 20000 0 . 0 0 0 0 0 . 0 5 2 2 0 . 7 7 6 9 6 0 . 3 1 0 . 3 4 0 . 3 5 20000 0 . 0 0 0 0 0 . 0 5 2 1 0 . 7 5 9 7 LOANABLE FUNDS = 8000000 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 6 MONTH LP1 LP2 LP3 D I F F Q D I F F V C . O . R R . F . 1 0 . 2 8 0 . 2 8 0 . 3 1 - 1 0 9 0 0 0 0 - 0 . 0 0 2 1 0 . 0 5 5 0 3 . 0 0 0 0 2 0 . 2 6 0 . 3 7 0 . 3 6 - 1 2 0 0 0 0 - 0 . 0 0 0 0 0 . 0 5 8 3 0 . 0 0 0 0 3 0 . 2 8 0 . 3 6 0 . 3 6 - 10000 0 . 0 0 0 0 0 . 0 5 5 9 0 . 2 1 0 4 4 0 . 2 8 0 . 3 6 0 . 3 6 0 0 . 0 0 0 0 0 . 0 5 6 0 0 . 1 8 6 5 5 0 . 2 8 0 . 3 6 0 . 3 6 0 0 . 0 0 0 0 0 . 0 5 6 0 0 . 1 8 0 7 6 0 . 2 8 0 . 3 6 0 . 3 6 0 0 . 0 0 0 0 0 . 0 5 5 9 0 . 2 0 1 3 LOANABLE FUNDS = 8000000 MAXIMUM A C C E P T A B L E LOAN PORTFOLIO RISK = 0 . 0 0 6 5 MONTH LP1 LP2 LP3 DIFFQ D I F F V C.O.R R. F. 1 0 . 2 8 0 . 2 8 0 . 3 1 - 1 0 9 0 0 0 0 - 0 . 0 0 2 6 0 . 0 5 5 0 3 . 0 0 0 0 . 2 0 . 2 2 0 . 3 6 0 . 3 6 - 6 8 0 0 0 0 - 0 . 0 0 0 9 0 . 0 6 3 1 0 . 0 0 0 0 3 0 . 2 4 0 . 3 7 0 . 3 6 - 2 8 0 0 0 0 - 0 . 0 0 0 5 0 . 0 5 9 7 0 . 0 0 0 0 4 0 . 2 5 0 . 3 7 0 . 3 6 - 2 5 0 0 0 0 - 0 . 0 0 0 5 0 . 0 5 9 5 0 . 0 0 0 0 5 0 . 2 5 0 . 3 7 0 . 3 6 - 2 6 0 0 0 0 - 0 . 0 0 0 5 0 . 0 5 9 5 0 . 0 0 0 0 6 0 . 2 5 0 . 3 7 0 . 3 6 - 2 6 0 0 0 0 - 0 . 0 0 0 5 0 . 0 5 9 5 0 . 0 0 0 0 99 APPENDIX 4 CALCULATION OF LOAN PORTFOLIO RISK A l t h o u g h p a y b a c k s o f l o a n s a r e s e c u r e d i n most i n s t a n c e s , l o a n s may be d e f a u l t e d : o n l y p a r t i a l o r n u l l o f t h e l o a n w i l l be r e p a i d by t h e b o r r o w e r . The a c t u a l p a y b a c k o f a l o a n c a n be r e p r e s e n t e d by 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 f a l t e r n a t i v e p a y b a c k s . The r i s k o f a l o a n c a n be r e p r e s e n t e d by t h e v a r i a n c e o f a l l t h e p o s s i b l e o u t c o m e s o f p a y b a c k s . CALCULATION OF LOAN PAYBACK VARIANCE L e t X = t h e number o f a l t e r n a t i v e p a y b a c k s on a l o a n P*" = t h e p a y b a c k o f t h e i t h a l t e r n a t i v e P r c = t h e p r o b a b i l i t y a s s o c i a t e d w i t h t h e i t h a l t e r n a t i v e x E x p e c t e d p a y b a c k , E ( P ) = £ ( P M ( P r * - ) £ [ P l - E (P) ]*" V a r i a n c e o f p a y b a c k , V ( P ) = = X 1 0 0 I f we assume t h a t the payback of the l o a n i s e i t h e r z e r o or the f u l l amount, L, then X = 2 Pr' = p, p r o b a b i l i t y of d e f a u l t on l o a n of s i z e L Pr* = ( 1 - p ) , p r o b a b i l i t y of no d e f a u l t on loan* of" s i z e " L P' = 0 P 1 = L E(P) = ( 1 - p ) L V(P) = p [ ( 1 - p ) L ] 1 + ( l - p ) ( p L ) 2 -= p ( l - p ) L l T h e r e f o r e , ^1= p ( 1 - p ) = the d e f a u l t l o s s r a t e . where denotes the v a r i a n c e of payback of l o a n s i n l o a n d i v i s i o n i . 101 CALCULATION OF LOAN PORTFOLIO RISK case I : Assume homogeneous r i s k c h a r a c t e r i s t i c s among l o a n s w i t h i n a l o a n d i v i s i o n and t h e r e a re n l o a n d i v i s i o n s i n the bank. The t o t a l l o a n p o r t f o l i o r i s k can be r e p r e s e n t e d by the t o t a l v a r i a n c e of paybacks of a l l the l o a n d i v i s i o n s . L e t n = the number of l o a n d i v i s i o n s L p = the f r a c t i o n of l o a n a b l e funds i n d i v i s i o n i £^(,= the c o r e l a t i o n c o e f f i c i e n t of payback between d i v i s i o n i and d i v i s i o n k t h e n , th e t o t a l l o a n p o r t f o l i o r i s k - I «%* Lj l -+ a l l « S i . 6 , p u L> LkP I f we assume the paybacks of l o a n d i v i s i o n s a r e independent, P^ K =0 V i and k, then th e t o t a l l o a n p o r t f o l i o r i s k * > - -> 1 02 CASE I I Assume h e t e r o g e n e o u s r i s k c h a r a c t e r i s t i c s among l o a n s w i t h i n a l o a n d i v i s i o n . L e t • = t h e c o r e l a t i o n c o e f f i c i e n t o f p a y b a c k b e t w e e n "loan j and l o a n j ' i n l o a n d i v i s i o n i l^p = t h e f r a c t i o n o f l o a n a b l e f u n d s o c c u p i e d by l o a n j i n l o a n d i v i s i o n i (/)^ = t h e r i s k a d j u s t m e n t f a c t o r f o r l o a n j i n l o a n d i v i s i o n i = t h e a v e r a g e s t a n d a r d d e v i a t i o n o f p a y b a c k o f l o a n s i n l o a n d i v i s i o n i = t h e s t a n d a r d d e v i a t i o n o f p a y b a c k o f l o a n j i n l o a n d i v i s i o n i ( <S>^ /J£ ) m = t h e number o f l o a n s a p p l i c a t i o n s i n d i v i s i o n s t h e n , t h e t o t a l l o a n p o r t f o l i o r i s k - L U I P; L? L? &l si ) 1 03 Assume v a r i a n c e s o f p a y b a c k s among l o a n s w i t h i n a l o a n d i v i s i o n a r e p e r f e c t l y c o r r e l a t e d ( i . e ' . = 1 V j and j ' ) , t h e n t h e t o t a l l o a n p o r t f o l i o r i s k • K i l t f I? & ^ 2. — r — r K I f l o a n s i z e s a r e i d e n t i c a l , t h e n L lp = ^ , and t h e t o t a l l o a n p o r t f o l i o r i s k n , „ en L e t A c= a v e r a g e r i s k a d j u s t m e n t f a c t o r o f l o a n d i v i s i o n i t h e n , 1 04 t h e t o t a l l o a n p o r t f o l i o r i s k 

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