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Prepayment behavior of Canadian mortgage backed securities Fu, Seung Tak 1988

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PREPAYMENT BEHAVIOR OF CANADIAN MORTGAGE BACKED SECURITIES By FU, SEUNG TAK B . A . , E a s t e r n Washington U n i v e r s i t y , 1981 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE (BUSINESS ADMINISTRATION) i n 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 as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA October 1988 © F u , Seung Tak , 1988 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada DE-6 (2/88) ABSTRACT Mor tgage-Backed s e c u r i t i e s (MBS) r e p r e s e n t a f i n a n c i a l i n s t r u m e n t which " s e c u r i t i z e s " r e s i d e n t i a l f i r s t mor tgages . A l t h o u g h the t r a d i n g p r o c e s s e s o f MBS a r e s i m i l a r t o t h o s e o f b o n d s , t h e r e a r e s i g n i f i c a n t d i f f e r e n c e s between the v a l u a t i o n methods o f MBS and o t h e r s e c u r i t i e s . One o f the s o u r c e s o f t h e s e d i f f e r e n c e s i s the p o s s i b i l i t y o f prepayment o f t h e mor tgages . T h i s s tudy makes the d i s t i n c t i o n between f u l l prepayment and p a r t i a l prepayment . The r e s u l t s o f t h i s s t u d y s u g g e s t t h a t f u l l prepayment i s d i r e c t l y r e l a t e d t o h o u s i n g market a c t i v i t i e s and p a r t i a l prepayment i s a f f e c t e d m a i n l y by t h e prepayment p r o v i s i o n i n the mortgage c o n t r a c t s . i i TABLE OF CONTENT ABSTRACT i i L I S T OF TABLES V L I S T OF FIGURES v i I . INTRODUCTION 1 I I . HISTORY OF MORTGAGE BACKED SEC U R I T I E S 4 I I I . LITERATURE REVIEW 8 I V . MBS VALUATION MODEL 15 A. I n t e r e s t R a t e F o r e c a s t i n g 17 B. P r e p a y m e n t E s t i m a t i o n 17 C. P r e s e n t V a l u e C a l c u l a t i o n 18 D. S e n s i t i v i t y A n a l y s i s 19 V. PREPAYMENT ANALYSIS 21 A. F u l l P r e p a y m e n t s a n d R e f i n a n c i n g 23 B. F u l l P r e p a y m e n t s a n d R e l o c a t i o n s 2 4 C. F u l l P r e p a y m e n t s a n d D e f a u l t s 2 6 D. P a r t i a l P r e p a y m e n t s a s S a v i n g s 27 E. P a r t i a l P r e p a y m e n t s a n d T a x R u l e s 28 F. P a r t i a l P r e p a y m e n t s a n d In c o m e s 29 G. P a r t i a l P r e p a y m e n t s a n d House V a l u e s . . 29 H. P a r t i a l P r e p a y m e n t s a n d P r e p a y m e n t P r o v i s i o n . . . . 30 i i i VI. INPUT DATA 32 V I I . DEPENDENT AND INDEPENDENT VARIABLES 34 A. R e f i n a n c i n g B e n e f i t 35 B. Housing Turnover 36 C. P e n a l t i e s on Prepayments 36 D. Economic I n d i c a t o r s and F i n a n c i a l Rates 37 E. Geographic D i s t r i b u t i o n 38 F. Prepayment P r o v i s i o n 39 V I I I . DISCUSSION OF RESULTS 43 A. R e f i n a n c i n g B e n e f i t 43 B. Housing Turnover 44 C. P e n a l t i e s on Prepayment 45 D. Economic I n d i c a t o r s and F i n a n c i a l Rates 4 6 E. Geographic D i s t r i b u t i o n 47 F. Prepayment P r o v i s i o n 47 IX. CONCLUSION 49 BIBLIOGRAPHY 65 i v LIST OF TABLES 1 DIFINITION OF INDEPENDENT VARIABLES 51 2 STATISTICS OF DEPENDENT VARIABLE 53 3 REFINANCING BENEFIT 54 4 HOUSING TURNOVER 55 5 PENALTIES ON PREPAYMENT 56 6 ECONOMIC INDICATORS AND FINANCIAL RATES 57 7 GEOGRAPHIC DISTRIBUTION 58 8 GEOGRAPHIC DISTRIBUTION(ADJUSTED) 59 9 PREPAYMENT PROVISION 60 10 COMBINED RESULTS 61 11 FINAL ESTIMATION 62 12 FINAL ESTIMATION(STEPWISE REGRESSION) > 64 v LIST OF FIGURES 1 HOW MORTGAGE-BACKED SECURITY WORK 3 2 MORTGAGE-BACKED SECURITY PROCESS 7 3 MBS VALUATION MODEL 16 4 PREPAYMENT ANALYSIS 22 5 PREPAYMENT REASONS AND INDENPENT VARIABLES 41 6 INDENPENT VARIABLES AND INPUT DATA 42 v i PREPAYMENT BEHAVIOR OF CANADIAN MORTGAGE BACKED SECURITIES I. INTRODUCTION Mor tgage-Backed S e c u r i t i e s (MBS) r e p r e s e n t a f i n a n c i a l i n s t r u m e n t which " s e c u r i t i z e s " r e s i d e n t i a l f i r s t mor tgages . S e c u r i t i z a t i o n o f mortgages i s a p r o c e s s from which mortgages a r e repackaged and s o l d t o i n v e s t o r s i n the form o f s e c u r i t i e s . The t r a d i n g p r o c e s s e s o f MBS a r e s i m i l a r t o t h o s e o f b o n d s . However, t h e r e a r e s i g n i f i c a n t d i f f e r e n c e s between t h e v a l u a t i o n methods o f MBS and o t h e r s e c u r i t i e s . Most o f the e x i s t i n g MBS a r e i n the R e g i s t e r e d R e t i r e m e n t S a v i n g Program (RRSP) a c c o u n t s o f i n d i v i d u a l i n v e s t o r s . I n s t i t u t i o n a l i n v e s t o r s a r e , however, p a y i n g more a t t e n t i o n t o t h i s form o f h i g h i n t e r e s t (when compared w i t h government bonds o f s i m i l a r m a t u r i t i e s ) and p r o b l e m - f r e e ( c o l l e c t i o n and a d m i n i s t r a t i o n ) investment i n s t r u m e n t . 1 Investment d e a l e r s l i k e Wood Gundy, Dominion S e c u r i t i e s and M e r r i l l Lynch a r e e x p e c t i n g more i n s t i t u t i o n a l i n v e s t o r s t o t a k e a c t i v e r o l e s i n the new i s s u e and secondary market o f MBS. But i n s t i t u t i o n a l i n v e s t o r s s h o u l d d e v e l o p a c l e a r u n d e r s t a n d i n g o f the market v a l u e s and r e t u r n s o f MBS b e f o r e i n c l u d i n g MBS i n t h e i r ^yman Solomon, "Ottawa B a c k i n g the MBS m a r k e t " , F i n a n c i a l P o s t , J u l y 27, 1987. 1 INTRODUCTION 2 p o r t f o l i o s . I h o p e t h a t t h i s s t u d y w i l l i n c r e a s e t h e i r k n o w l e d g e a n d f a c i l i t a t e t h e i r i n v e s t m e n t d e c i s i o n s i n MBS. I n t h i s p a p e r , I w i l l f i r s t d e s c r i b e t h e h i s t o r y o f C a n a d i a n MBS. F o l l o w i n g t h i s I w i l l e x a m i n e s t u d i e s t h a t f o c u s o n t h e v a l u a t i o n o f MBS a n d m o r t g a g e p r e p a y m e n t p r e d i c t i o n . A s one w i l l f i n d o u t l a t e r , m o r t g a g e p r e p a y m e n t p r e d i c t i o n h a s a m a j o r r o l e i n MBS v a l u a t i o n . S u b s e q u e n t l y , I w i l l e x a m i n e t h e s t e p s o f a n v a l u a t i o n m o d e l a n d t h e i m p o r t a n c e o f p r e p a y m e n t p r e d i c t i o n i n t h e v a l u a t i o n o f MBS. The f o l l o w i n g c h a p t e r w i l l e x a m i n e t h e f a c t o r s t h a t a f f e c t p r e p a y m e n t b e h a v i o r s . T h e n I w i l l e s t i m a t e t h e e f f e c t s o f e a c h o f t h e s e f a c t o r s o n C a n a d i a n MBS p r e p a y m e n t b e h a v i o r s , u s i n g t h e i r f i r s t y e a r ' s p e r f o r m a n c e d a t a . The c o r e o f t h i s a n a l y s i s w i l l d e a l w i t h t h e q u e s t i o n -w h a t a r e t h e m a j o r f a c t o r s t h a t a f f e c t p r e p a y m e n t s i n C a n a d i a n MBS? By a n s w e r i n g t h i s q u e s t i o n , I i n t e n d t o p r o v i d e some s p e c i f i c MBS i n v e s t m e n t g u i d e l i n e s t o i n s t i t u t i o n a l i n v e s t o r s . INTRODUCTION 3 F i g u r e 1 HOW MORTGAGE-BACKED SECURITY WORK Homeowners M o n t h l y NHA m o r t g a g e p a y m e n t s M o r t g a g e i n s u r a n c e L e n d e r s / S e c u r i t i e s i s s u e r G u a r a n t e e f e e s S c h e d u l e d p a y m e n t s CMHC C e n t r a l p a y o r  a n d t r a n s f e r a g e n t G u a r a n t e e S c h e d u l e d p a y m e n t s I n v e s t o r s I I . HISTORY OF MORTGAGE BACKED SECURITIES HISTORY 4 The Canad ian MBS, sometimes c a l l e d Cann ie Mae, i s c r e a t e d by the Canada Mortgage and Hous ing C o r p o r a t i o n (CMHC) i n 1987 under the o b j e c t i v e o f d e v e l o p i n g a h i g h - q u a l i t y f i n a n c i a l i n s t r u m e n t which would encourage an a c t i v e and l i q u i d secondary market f o r r e s i d e n t i a l m o r t g a g e s . 2 O f f i c i a l s o f CMHC have hoped t h a t MBS would i n c r e a s e the a v a i l a b i l i t y o f mortgage c r e d i t by c h a n n e l l i n g funds from the f i n a n c i a l market d i r e c t l y i n t o t h e h o u s i n g market . They a l s o e x p e c t t h i s new f i n a n c i a l i n s t r u m e n t t o e n l a r g e t h e p o o l o f money a v a i l a b l e f o r r e s i d e n t i a l mortgages by i n c r e a s i n g the " t u r n o v e r " r a t e o f the money i n t h e h o u s i n g market . The t h i r d purpose f o r d e v e l o p i n g MBS i s t o b r i n g back l o n g e r term mortgages ( i . e . more than 5 y e a r s ) and more a f f o r d a b l e mortgages by b e t t e r match ing the a s s e t s and l i a b i l i t i e s o f mortgages l e n d i n g i n s t i t u t i o n s . 3 The a v a i l a b i l i t y o f r e s i d e n t i a l mortgage c r e d i t i s a f f e c t e d by many f a c t o r s i n c l u d i n g the o v e r a l l f i n a n c i a l market c o n d i t i o n . Any i n d i v i d u a l f a c t o r , such as the i n t r o d u c t i o n o f MBS, cannot have a dominant e f f e c t on i t . However, as a f i n a n c i a l i n s t r u m e n t , MBS does improve the l i q u i d i t y o f many mortgage l e n d i n g i n s t i t u t i o n s by a l l o w i n g them t o t r a n s f o r m the mortgages i n t h e i r p o r t f o l i o s from a h i g h l y i l l i q u i d a s s e t i n t o 2 , I NHA Mor tgage-Backed S e c u r i t i e s " , CMHC, NHA 5942 10 /86 . 3 T e l e p h o n e i n t e r v i e w w i t h Anthony Dye, Program A d m i n i s t r a t i o n C h i e f , MBS C e n t r e o f CMHC, November 9, 1987. HISTORY 5 an o f f - b a l a n c e s h e e t f i n a n c i n g account and , i n a way, reduce the p o s s i b i l i t y o f h a v i n g c a s h f lows problems caused by mismatch ing o f a s s e t s and l i a b i l i t i e s . * F u r t h e r more, t h e r e a r e s i g n s t h a t l o n g e r term mortgages a r e coming back t o Canada because o f MBS. A t l e a s t t h r e e mortgage l e n d i n g i n s t i t u t i o n s have o f f e r e d 10 y e a r term mortgages and one o f them i s o f f e r i n g 20 y e a r term r e s i d e n t i a l m o r t g a g e s . 5 However, l o n g e r term mortgages r e p r e s e n t o n l y a s m a l l f r a c t i o n o f the t o t a l v a l u e o f the e x i s t i n g MBS i n C a n a d a . 6 A l t h o u g h MBS have been i n Canada f o r l e s s than two y e a r s , they were i n t r o d u c e d i n the U . S . i n 1970 by the Government N a t i o n a l Mortgage A s s o c i a t i o n , which has i s s u e d about US$600 b i l l i o n worth o f them s i n c e t h e n . Up t o F e b r u a r y 1988, o v e r $600 m i l l i o n o f MBS have been s o l d and a n o t h e r $500 m i l l i o n o f new i s s u e s a r e expec ted t o come i n t o the Canad ian market i n 1988 . 7 I t appears t h a t the annua l new i s s u e o f MBS w i l l a c h i e v e the $2 b i l l i o n f i g u r e w i t h i n t h r e e y e a r s as CMHC o f f i c i a l s have p r e d i c t e d . MBS w i l l r e p r e s e n t a $20 t o $25 b i l l i o n inves tment v a l u e which w i l l account f o r 5% o f t h e f i x e d - t e r m , f i x e d - d e b t market o f Canada w i t h i n a decade i f the * M i c h a e l J . Lea and P e t e r M. Z o r n , " A d j u s t a b l e - R a t e M o r t g a g e s , Economic F l u c t u a t i o n , and Lender P o r t f o l i o " , AREUEA J o u r n a l , v o l . 14, n o . 3, 1986, 432-447. 5 K e v i n Cox and Mar ian S t i n s o n , " T r u s t O f f e r i n g 2 0 - y e a r M o r t g a g e " , The Globe and M a i l , March 5, 1988. 6 Guaran ty T r u s t ' s monthly NHA Mortgage Backed S e c u r i t i e s R e p o r t . 7Hyman Solomon. HISTORY 6 t r e n d c o n t i n u e s . 8 MBS i s a f i n a n c i a l i n s t r u m e n t w i t h v e r y h i g h p o t e n t i a l . To u n d e r s t a n d the t r a d i n g and v a l u a t i o n o f t h i s f i n a n c i a l i n s t r u m e n t , one s h o u l d s t a r t examin ing s t u d i e s t h a t f o c u s on MBS. B a r r y C r i t c h l e y , " F i n a n c i a l L e t t e r " , F i n a n c i a l P o s t . November 24, 1986. HISTORY 7 F i g u r e 2 MORTGAGE-BACKED SECURITY PROCESS Home b u y e r s F i n a n c i a l i n s t i t u t i o n s P o o l s o f NHA mortgages Guarantee o f t i m e l y payment Mor tgage -backed s e c u r i t i e s d e a l e r s Secondary home New c o n s t r u c t i o n market market I n v e s t o r s LITERATURE REVIEW 8 I I I . LITERATURE REVIEW S t u d i e s t h a t f o c u s on the v a l u a t i o n o f MBS u s u a l l y i n c l u d e prepayment e s t i m a t i o n . Prepayments can change a MBS's c a s h f l o w s p a t t e r n which i s one o f t h e d e t e r m i n i n g f a c t o r s o f t h a t MBS's v a l u e . Prepayments can be s e p a r a t e d i n t o f u l l prepayments and p a r t i a l prepayments . Most o f the s t u d i e s on MBS v a l u a t i o n and prepayments f o c u s on t h e p r e d i c t i o n o f f u l l p repayments . The t h r e e most commonly used t e c h n i q u e s a r e ( i ) the use o f o p t i o n - p r i c i n g m o d e l s , ( i i ) the use o f h o u s i n g t u r n o v e r r a t e s , and ( i i i ) t h e e s t i m a t i o n o f the expec ted " l i f e " o f an MBS. The t r a d i t i o n a l approach on f u l l prepayment p r e d i c t i o n i s t o use o p t i o n - p r i c i n g mode ls . H a l l ( 8 5 ) , i n h i s s t u d y , p o i n t e d out t h a t prepayments a r e a c t u a l l y c a l l o p t i o n s on the o u t s t a n d i n g p r i n c i p a l b a l a n c e s . He a l s o i l l u s t r a t e d t h a t t h e v a l u e s o f the o p t i o n s o f the mortgages t o homeowners a r e no t independent o f the v a l u e s o f the p r o p e r t i e s under t h o s e m o r t g a g e s . 9 F o s t e r and Van Order(84) i n t h e i r s t u d y o f mortgage d e f a u l t i n d i c a t e d t h a t mortgage d e f a u l t s a r e Amer ican p u t o p t i o n s which a l l o w homeowners t o s e l l t h e i r houses t o l e n d e r s i n exchange f o r mortgage e l i m i n a t i o n s . 1 0 However, so f a r , no o p t i o n - p r i c i n g model t h a t can a c c u r a t e l y p r e d i c t the 9 A r d e n R. H a l l , " V a l u i n g the Mortgage B o r r o w e r ' s Prepayment O p t i o n " , AREUEA J o u r n a l . V o l . 13, n o . 3 1985, p . 229-247. " C h e s t e r F o s t e r and Rober t van O r d e r , "An O p t i o n - B a s e d Model o f Mortgage D e f a u l t " , Hous ing F i n a n c e Review, v o l . 3, n o . 4 , 1984, p . 351-372. LITERATURE REVIEW 9 optimum t ime f o r a mortgagor t o r e f i n a n c e has been d e v e l o p e d . S i e g e l ( 8 4 ) e x p l a i n e d t h a t a l t h o u g h o p t i o n - p r i c i n g models can e s t i m a t e the p o t e n t i a l net g a i n s from r e f i n a n c i n g and t h e e f f e c t s o f i n t e r e s t r a t e changes on r e f i n a n c i n g b e n e f i t s , o p t i o n - p r i c i n g models do not work v e r y w e l l f o r mortgage prepayment p r e d i c t i o n because a l l f u t u r e c a s h f l o w s must be d i s c o u n t e d back by u s i n g an a r b i t r a t e d r a t e and a homeowner i s p u r c h a s i n g a new o p t i o n when he e x e r c i s e s the o r i g i n a l o p t i o n t o r e f i n a n c e . 1 1 A more r e c e n t t r e n d i n mortgage prepayment p r e d i c t i o n i s t h e use o f h o u s i n g t u r n o v e r r a t e s t o e s t i m a t e t h e p o s s i b i l i t y o f f u l l p repayments . Zemon(85) demonstra ted t h a t , u s i n g h o u s i n g s t a r t s s e r i e s as a proxy f o r h o u s i n g t u r n o v e r , f l u c t u a t i o n s i n h o u s i n g t u r n o v e r have s i g n i f i c a n t impacts on prepayments o f d i s c o u n t e d m o r t g a g e s . 1 2 Hu(87) found s i m i l a r r e s u l t on low coupon p a s s - t h r o u g h (coupon r a t e s 10% and below) when he u s e d the s a l e s o f e x i s t i n g homes w i t h r e s p e c t t o s t o c k o f s i n g l e f a m i l y h o u s i n g t o e s t i m a t e prepayment r a t e s . 1 3 Both Zemon(85) and Hu(87) have shown t h a t h o u s i n g a c t i v i t i e s have n J e r e m y J . S i e g e l , "The Mortgage R e f i n a n c i n g D e c i s i o n " , Hous ing F i n a n c e Review, v o l . 3, n o . 1, J a n u a r y 1984, p . 91 -97 . 1 2 Ray B. Zemon, " P o r t f o l i o S t r a t e g i e s U s i n g M o r t g a g e -Backed S e c u r i t i e s " from New developments i n M o r t g a g e - Backed S e c u r i t i e s . The I n s t i t u t e o f C h a r t e r e d F i n a n c i a l A n a l y s t s , Wash ington , D . C . , May 22 1984. " J o s e p h C . Hu, "Prepayment P r o j e c t i o n s " , Mortgage B a n k i n g . Oc tober 1987, p . 55-59 LITERATURE REVIEW 10 s i g n i f i c a n t e f f e c t s on prepayment b e h a v i o r s . However, they b o t h made the same i m p l i c i t assumpt ion t h a t a l l home mortgage c o n t r a c t s c o n t a i n a d u e - o n - s a l e c l a u s e . The d u e - o n - s a l e c l a u s e g i v e s a mortgage l e n d e r the r i g h t t o d e c l a r e the t o t a l o u t s t a n d i n g p r i n c i p a l b a l a n c e due immedia te ly i f t h e mortgaged p r o p e r t y i s t r a n s f e r r e d . Green and Shoven(86) i n d i c a t e d t h a t d u e - o n - s a l e c l a u s e s can reduce the number o f h o u s i n g t u r n o v e r s and mortgage prepayments , e s p e c i a l l y i n a h i g h i n t e r e s t r a t e e n v i r o n m e n t . 1 * F u r t h e r more, Dunn and Spat t (85 ) e x p l a i n e d t h a t , u n l e s s the d u e - o n - s a l e c l a u s e i s c o n t a i n e d i n e v e r y mortgage c o n t r a c t and the l e n d i n g i n s t i t u t i o n s w i l l e x e r c i s e t h e i r r i g h t under the c l a u s e each and e v e r y t ime a mortgaged p r o p e r t y i s t r a n s f e r r e d , h o u s i n g t u r n o v e r r a t e s might not be a v e r y a c c u r a t e i n d i c a t o r o f prepayment r a t e s . 1 5 T e c h n i q u e s used t o e s t i m a t e the e x p e c t e d " l i f e " o f an MBS p o o l u s u a l l y i m p l i c i t l y i n c l u d e the impacts o f p a r t i a l prepayments i n the c a l c u l a t i o n s . One o f the most p o p u l a r methods t o e s t i m a t e the expec ted " l i f e " o f an MBS i s t h e twe lve y e a r average mortgage l i f e . Based on h i s t o r i c a l d a t a t h e twe lve y e a r average mortgage l i f e method assumes t h a t a l l mortgages w i l l be f u l l y p a i d a f t e r twe lve y e a r s . But S h i l l i n g 1 A J e r r y Green and John B. Shoven, "The E f f e c t s o f I n t e r e s t Ra tes on Mortgage Prepayments" , J o u r n a l o f Money,  C r e d i t , and B a n k i n g , v o l . 18, n o . 1, F e b r u a r y 1986. " K e n n e t h B. Dunn and C h e s t e r S . S p a t t , " An A n a l y s i s o f Mortgage C o n t r a c t i n g : Prepayment P e n a l t i e s and the Due-o n - S a l e C l a u s e " , The J o u r n a l o f F i n a n c e , v o l . X L , n o . 1, March 1985. LITERATURE REVIEW 11 and S imians(87) demonstra ted t h a t t h i s method w i l l s y s t e m a t i c a l l y u n d e r s t a t e s the " t r u e " y i e l d when the y i e l d c u r v e i s downward s l o p p i n g and o v e r s t a t e the " t r u e " y i e l d when the y i e l d c u r v e i s upward s l o p i n g . 1 6 MacBain and G u a l t i e r i ( 8 7 ) s u p p o r t e d t h e argument by p o i n t i n g out t h a t homeowners' prepayment b e h a v i o r s a r e a f f e c t e d by c u r r e n t r e l a t i v e i n t e r e s t r a t e . 1 7 A n o t h e r p o p u l a r method i n e s t i m a t i n g the e x p e c t e d " l i f e " o f an MBS i s t h e Cons tan t Prepayment Rate (CPR), wh ich i s a l s o c a l l e d t h e c o n d i t i o n a l prepayment r a t e . CPR, which has been used by a number o f investment d e a l e r s , i s a r a t i o o f the p r e p a i d amounts t o the o u t s t a n d i n g p r i n c i p a l b a l a n c e s o f an MBS o v e r a p e r i o d o f t i m e . CPR works under the assumpt ion t h a t a MBS's e x p e c t e d f u t u r e prepayment o f any month would be a c o n s t a n t p e r c e n t a g e o f the p r i n c i p l e b a l a n c e o f the p r e v i o u s month. MacBain and G u a l t i e r i ( 8 7 ) , however, no ted t h a t prepayments do no t remain c o n s t a n t o v e r the l i f e o f a mor tgage . They found t h a t prepayment r a t e s show a d i s t i n c t upward t r e n d d u r i n g t h e f i r s t few y e a r s a f t e r o r i g i n a t i o n . 1 8 A l s o , P i n k u s and Chandoha(86) e x p l a i n e d t h a t a d u r a t i o n e s t i m a t i o n o f a MBS g e n e r a t e d from a s t a t i c f u t u r e prepayments a s s u m p t i o n , w i l l 1 6 James D. S h i l l i n g and C . F . S i r m a n s , " P r i c i n g F a s t - p a y M o r t g a g e s : Some s i m u l a t i o n R e s u l t s " , The J o u r n a l o f  F i n a n c i a l R e s e a r c h , v o l . X , n o . 1, S p r i n g 1987, p . 25 -32 . 1 7 M i c h a e l W. MacBain and C a r l o G u a l t i e r i , "Mortgage Backed S e c u r i t i e s - An Overview o f Prepayment" , R e s o u r c e . September 1987, p. 9 -14 . 1 8 I b i d . LITERATURE REVIEW 12 s e r i o u s l y m i s r e p r e s e n t t h e r e l a t i v e p r i c e v o l a t i l i t y o f t h e MBS under s t u d y . 1 9 I n s t e a d , P i n k u s and Chandoha(86) d e v e l o p e d a new approach t o e s t i m a t e the d u r a t i o n o f an MBS. T h e i r I m p l i e d D u r a t i o n t e c h n i q u e i s based on t h e i d e a t h a t the r a t i o o f t h e d u r a t i o n o f an MBS t o the d u r a t i o n o f ano ther s e c u r i t y ( i n t h e i r s t u d y t h e y had u s e d the 10 y e a r T reasury ) i s c l o s e l y r e l a t e d t o the r a t i o o f the p r i c e v o l a t i l i t y o f the MBS t o the p r i c e v o l a t i l i t y o f the s e c u r i t y . 2 0 T h i s t e c h n i q u e assumes t h a t the p r i c e s o f a c l a s s o f MBS c a r r y i n f o r m a t i o n about the l i k e l i h o o d o f prepayments and the r i s k o f l o s s s h o u l d the prepayments o c c u r . A n o t h e r advantage o f the I m p l i e d D u r a t i o n t e c h n i q u e o v e r t h e o t h e r two t e c h n i q u e s i s the i n c l u s i o n o f c o n v e x i t y o f MBS i n t h e e s t i m a t i o n . C o n v e x i t y d e s c r i b e s the r a t e s o f change o f d u r a t i o n i n r e s p o n s e t o changes i n i n t e r e s t r a t e s . " N e g a t i v e " c o n v e x i t y causes the d u r a t i o n o f a MBS t o l e n g t h e n when i n t e r e s t r a t e s r i s e but s h o r t e n when i n t e r e s t r a t e s f a l l . P i n k u s and Chandoha(86) showed t h a t by e s t i m a t i n g the I m p l i e d D u r a t i o n f o r a MBS, a r e l a t i v e p r i c e v o l a t i l i t y c u r v e can be 1 9 S c o t t M. P i n k u s and M a r i e A . Chandoha, " I m p l i e d D u r a t i o n " , Secondary Mortgage M a r k e t s , Summer 1986, p . 7 -13 . 2 0 D u r a t i o n o f MBS A C * P r i c e v o l a t i l i t y o f MBS A D u r a t i o n o f s e c u r i t y B P r i c e v o l a t i l i t y o f s e c u r i t y B C = c o n s t a n t LITERATURE REVIEW 13 d e v e l o p e d and used t o d e t e c t the p r i c e s e n s i t i v i t y o f t h e MBS when t h e r a t e c h a n g e . 2 1 The twe lve y e a r average mortgage l i f e , the c o n s t a n t prepayment r a t e and the I m p l i e d D u r a t i o n , a l t h o u g h i m p l i c i t l y i n c l u d e p a r t i a l prepayments i n the c a l c u l a t i o n , t h e y do no t f o c u s on the e f f e c t s o f p a r t i a l prepayments on t h e p r i c e s o f MBS. P a r t i a l prepayments , which a r e a f f e c t e d by t h e r i s k a v e r s i o n b e h a v i o r s o f homeowners and t h e i r c r a v i n g f o r lower i n t e r e s t c h a r g e s , have o n l y been i n c l u d e d i n a l i m i t e d number o f prepayment s t u d i e s . Lea and Z o r n ( 8 6 ) , i n t h e i r s t u d y o f Canad ian r o l l o v e r mor tgages , found t h a t p a r t i a l prepayments depend on t h e house p r i c e s and the a f t e r - t a x r a t e s o f r e t u r n on house i n v e s t m e n t s v e r s u s o t h e r a s s e t s . The p r i c e o f a house can a f f e c t the e q u i t y o f t h a t house which i s p a r t o f t h e d e s i r e d h o u s e h o l d s a v i n g s o f the owner. When house p r i c e s go u p , s a v i n g s i n the form o f e q u i t y w i l l i n c r e a s e and prepayments a r e e x p e c t e d t o s low down. A l s o , p a r t i a l prepayments a r e e x p e c t e d t o be r e l a t i v e l y more impor tan t i n t h e e s t i m a t i o n o f Canad ian MBS than i n Amer ican MBS because t h e r e i s a d i f f e r e n c e on t h e t a x d e d u c t i b i l i t y o f mortgage i n t e r e s t which has d i r e c t impact on the a f t e r - t a x r a t e o f r e t u r n on h o u s i n g . 2 2 Each o f the s t u d i e s d i s c u s s e d above p r o v i d e s some i n s i g h t s t o d i f f e r e n t a r e a s o f MBS v a l u a t i o n . However, the m a j o r i t y o f 2 1 I b i d . 2 2 L e a and Z o r n . LITERATURE REVIEW them f o l l o w a s i m i l a r v a l u a t i o n p a t t e r n r e g a r d l e s s o f t h e i r arguments and a s s u m p t i o n s . MBS VALUATION MODEL 15 IV. MBS VALUATION MODEL Most f i n a n c i a l a n a l y s t s agree t h a t the t o t a l r e t u r n a n a l y s i s s h o u l d be used i n MBS v a l u a t i o n . The t o t a l r e t u r n from a MBS i s g i v e n by the c a s h f lows r e c e i v e d and t h e change i n p r i c e s which o c c u r between the i n i t i a l p u r c h a s e and f i n a l s a l e o f t h e M B S . 2 3 The c a s h f lows f o r a MBS i s t h e sum o f i n t e r e s t payments , s c h e d u l e d p r i n c i p a l payments, p repayments , and prepayment p e n a l t i e s . A change i n the g e n e r a l l e v e l o f i n t e r e s t r a t e s , i n the y i e l d s p r e a d between MBS and o t h e r s e c u r i t i e s , and i n the prepayment e x p e c t a t i o n can have s i g n i f i c a n t impacts on the c a s h f lows and p r i c e s o f MBS. Any MBS v a l u a t i o n model must i n c l u d e t h e s e t h r e e f a c t o r s i n o r d e r t o have t r u e r e p r e s e n t a t i o n o f the MBS market . There s h o u l d be f o u r independent , but i n t e r r e l a t e d , s t e p s i n t h e v a l u a t i o n p r o c e s s o f MBS. These f o u r s t e p s a r e : ( 1 ) i n t e r e s t r a t e f o r e c a s t i n g , (2) prepayment e s t i m a t i o n , (3) p r e s e n t v a l u e c a l c u l a t i o n , and (4) p r i c e s e n s i t i v i t y a n a l y s i s . 23 T o t a l MBS R e t u r n F i n a l = ( S a l e i P r i c e I n i t i a l Cash Purchase ) + F lows P r i c e R e c e i v e d MBS VALUATION MODEL Figure 3 MBS VALUATION MODEL INTEREST RATE FORECASTING Short term rate forecast ing Long term rate forecast ing Short and long term rate v o l a t i l i t y PREPAYMENT ESTIMATION Estimated from h i s t o r i c a l data F u l l and p a r t i a l prepayments Calculate cash flows inc lud ing prepayment PRESENT VALUE CALCULATION Cash flows are discounted back to present Implied Duration SENSITIVITY ANALYSIS Duration est imation Convexity est imation MBS VALUATION MODEL 17 A . I n t e r e s t Rate F o r e c a s t i n g I n t e r e s t r a t e f o r e c a s t i n g i s the f i r s t s t e p i n MBS v a l u a t i o n . - I n t e r e s t r a t e changes can a f f e c t t h e v a l u e o f a MBS i n two a r e a s . F i r s t , i n t e r e s t r a t e changes can cause changes i n prepayment b e h a v i o r s which w i l l change the f u t u r e c a s h f lows o f t h e MBS. S e c o n d , i t w i l l change the p r i c e o f the MBS s i n c e market r a t e s a r e used t o d i s c o u n t f u t u r e c a s h f l o w s back t o p r e s e n t , and market r a t e s w i l l change as i n t e r e s t r a t e s change . In v a l u a t i n g Canad ian MBS, one s h o u l d f o c u s on s h o r t term i n t e r e s t r a t e f o r e c a s t i n g because most o f the Canad ian MBS have a term l e s s t h a n o r equa l t o 5 y e a r s . Long term i n t e r e s t r a t e f o r e c a s t i n g , i n t h i s c a s e , i s not n e c e s s a r y . Of c o u r s e , i f one i s d e a l i n g w i t h MBS t h a t have terms o f 10 y e a r o r 20 y e a r , he must ex tend h i s f o r e c a s t i n g h o r i z o n t o ensure t h a t a l l f u t u r e c a s h f l o w s can be e s t i m a t e d . In i n t e r e s t r a t e f o r e c a s t i n g , one must a l s o e s t i m a t e the i n t e r e s t r a t e v o l a t i l i t y because v o l a t i l i t y can i n c r e a s e o r d e c r e a s e the prepayment r a t e s and p r e s e n t v a l u e s o f the c a s h f l o w s , depending on whether the MBS's c o n t r a c t e d mortgage r a t e s a r e above o r below the c u r r e n t market r a t e s . B. Prepayment E s t i m a t i o n Prepayment e s t i m a t i o n i s the second s t e p i n the v a l u a t i o n p r o c e s s . Prepayments a r e what make MBS d i f f e r e n t from o t h e r t y p e s o f f i x e d - r a t e d s e c u r i t i e s , because no one knows i n advance the e x a c t amount o f prepayments and the c a s h f l o w s MBS VALUATION MODEL 18 p a t t e r n . C o n s e q u e n t l y , no one can c a l c u l a t e t h e p r i c e o f a MBS even i f t h e i n t e r e s t r a t e s a r e g i v e n . The b e s t anyone can do i n t h i s c a s e i s t o make an educated e s t i m a t i o n o f t h e amount o f prepayments under a s e t o f p r e d e t e r m i n e d c o n s t r a i n t s . T h i s educa ted e s t i m a t i o n s h o u l d be based on u n d e r s t a n d i n g s t h a t a r e d e r i v e d from c l o s e examina t ion o f h i s t o r i c a l prepayment d a t a . There a r e b a s i c a l l y t h r e e k i n d s o f prepayments - f u l l prepayments r e s u l t e d from moving o r r e f i n a n c i n g , f u l l prepayments caused by d e f a u l t s and f o r e c l o s u r e s , and p a r t i a l prepayments by homeowners. One must e s t i m a t e each k i n d o f prepayments i n d i v i d u a l l y and then sum up the i n d i v i d u a l r e s u l t s i n o r d e r t o ge t a f u l l p i c t u r e on prepayment b e h a v i o r s . However, one has t o u n d e r s t a n d t h a t b o t h t h e market s i t u a t i o n and t h e i n d i v i d u a l c h a r a c t e r i s t i c s o f each MBS w i l l a f f e c t the prepayment p a t t e r n o f t h a t MBS. A l s o , one must keep i n mind t h a t homeowners' b e h a v i o r s do change o v e r t ime and an e s t i m a t i o n , i n t h i s c a s e , i s more o f an a r t than an e x a c t s c i e n c e . C . P r e s e n t V a l u e C a l c u l a t i o n A f t e r the prepayment e s t i m a t i o n f u n c t i o n s . h a v e been d e v e l o p e d , t h e nex t s t e p i s t o combine the r e s u l t s o f i n t e r e s t r a t e f o r e c a s t i n g and prepayment e s t i m a t i o n s by one o r more v a l u a t i o n t e c h n i q u e s t o c a l c u l a t e the t h e o r e t i c a l p r i c e s o f MBS. The t h e o r e t i c a l p r i c e s can then be compared w i t h the market p r i c e s t o de termine which MBS a r e o v e r v a l u e d and which MBS VALUATION MODEL 19 MBS a r e u n d e r v a l u e d . There i s , however, the I m p l i e d D u r a t i o n t e c h n i q u e t h a t b y p a s s e s the prepayment e s t i m a t i o n and a r r i v e a t the t h e o r e t i c a l p r i c e s o f MBS by assuming t h a t t h e market i s e f f i c i e n t and a l l p a r t i c i p a n t s a r e l o g i c a l . 2 4 T h i s t e c h n i q u e , however , might not be s u i t a b l e i n the Canad ian MBS market u n t i l t h e market i s f u l l y d e v e l o p e d and a l l p a r t i c i p a n t s have g a i n e d b e t t e r e x p e r i e n c e and u n d e r s t a n d i n g on the o p e r a t i o n and b e h a v i o r s o f t h e m a r k e t . 2 5 O ther v a l u a t i o n t e c h n i q u e s , s u c h as d i s c o u n t e d c a s h f l o w s and o p t i o n - a d j u s t e d methods, might be more s u i t a b l e f o r t o d a y ' s Canadian MBS m a r k e t . 2 6 D. S e n s i t i v i t y A n a l y s i s S e n s i t i v i t y a n a l y s i s , the f i n a l s t e p i n t h e MBS v a l u a t i o n p r o c e s s , i s used t o de te rmine what w i l l happen t o the v a l u e o f a MBS when t h e r e a r e changes i n the i n t e r e s t r a t e s . S e n s i t i v i t y a n a l y s i s i s v e r y u s e f u l i n c o n s t r u c t i n g a p o r t f o l i o and i n s t i t u t i o n a l i n v e s t o r s s h o u l d i n c l u d e c a l c u l a t i o n s o f d u r a t i o n and c o n v e x i t y as i n t e g r a t e d p a r t s o f the MBS v a l u a t i o n p r o c e s s . To d e v e l o p a f u n c t i o n a l and e f f e c t i v e MBS v a l u a t i o n p r o c e s s , i t i s v i t a l t o i n c l u d e a l l o f the above f o u r s t e p s . 2 4 P i n k u s and Chandoha. 2 5 P i n k u s and Chandoha. 2 6 , , E x p l a i n s NHA Mor tgage-Backed S e c u r i t i e s " , M e r r i l l L y n c h , 1986. MBS VALUATION MODEL 20 The p u r p o s e o f t h i s s t u d y i s t o i n c r e a s e t h e u n d e r s t a n d i n g o n t h e l e a s t d e v e l o p e d s t e p , n a m e l y t h e p r e p a y m e n t e s t i m a t i o n . I n f o r m a t i o n f r o m t h e f i r s t t w e l v e m o n t h s o f e x i s t e n c e o f t h e C a n a d i a n MBS m a r k e t i s u s e d a s t h e b a s i c i n p u t . The r e s u l t s o f t h i s s t u d y w i l l b r i n g some i n s i g h t s t o t h e p r e p a y m e n t b e h a v i o r s o f t h e C a n a d i a n homeowners a n d s u g g e s t i o n s t o p r e s e n t a n d f u t u r e MBS i n v e s t o r s . B u t b e f o r e t h e p r e p a y m e n t e s t i m a t i o n i s d i s c u s s e d , one m u s t f i r s t u n d e r s t a n d w h a t f a c t o r s a f f e c t p r e p a y m e n t s . MBS VALUATION MODEL 21 V. PREPAYMENT ANALYSIS To study prepayment be h a v i o r s , one must examine the reasons o f p r e p a y i n g a mortgage from the stand p o i n t o f the homeowners. There are two k i n d s of prepayments - f u l l prepayments and p a r t i a l prepayments. F u l l prepayments are the r e s u l t s of l i q u i d a t i o n of the o r i g i n a l mortgages by the homeowners when they r e f i n a n c e , s e l l t h e i r houses or d e f a u l t . D e f a u l t s are i n c l u d e d i n the f u l l prepayments catego r y because every Canadian MBS p o o l r e c e i v e s the CMHC t i m e l y payment guarantee and i s i n s u r e d under the N a t i o n a l Housing A c t (NHA). 2 7 When a homeowner d e f a u l t s , CMHC, a c t i n g as a government agency, w i l l a u t o m a t i c a l l y s t e p i n t o ensure t h a t i n v e s t o r s w i l l r e c e i v e the promised r e t u r n o f the MBS i f the i s s u e r of t h a t MBS cannot f u l f i l l i t s o b l i g a t i o n s . P a r t i a l prepayments, on the o t h e r hand, are u s u a l l y motivated by n o n - f i n a n c i a l reasons l i k e the r i s k a v e r s i o n need o f the homeowners t o reduce t h e i r debt o b l i g a t i o n s . P a r t i a l prepayments r e p r e s e n t the p r e paying o f p a r t o f the o u t s t a n d i n g p r i n c i p a l b a lance of a mortgage b e f o r e the end of the term. 27CMHC. MBS VALUATION MODEL F i g u r e 4 PREPAYMENT ANALYSIS Prepayments F u l l prepayments P a r t i a l prepayments R e f i n a n c i n g R e l o c a t i o n D e f a u l t S a v i n g Tax r u l e s Income House v a l u e Prepayment p r o v i s i o n PREPAYMENT ANALYSIS 23 A . F u l l Prepayments and R e f i n a n c i n g F u l l prepayments r e s u l t i n g from r e f i n a n c i n g a r e u s u a l l y t r i g g e r e d by changes i n r e f i n a n c i n g b e n e f i t s from n e g a t i v e t o p o s i t i v e . R e f i n a n c i n g b e n e f i t i s the amount o f money a homeowner can save when he l i q u i d a t e s the o r i g i n a l mortgage and pays back the o u t s t a n d i n g p r i n c i p a l p l u s prepayment p e n a l t i e s by g e t t i n g a new mortgage a t the market i n t e r e s t r a t e . The market i n t e r e s t r a t e s have t o be lower than the o r i g i n a l c o n t r a c t e d i n t e r e s t r a t e s i n o r d e r f o r r e f i n a n c i n g b e n e f i t s t o be p o s i t i v e . F u r t h e r m o r e , the h i g h e r the r e f i n a n c i n g b e n e f i t s , t h e h i g h e r a r e the p o s s i b i l i t i e s o f f u l l prepayments by homeowners. As i n d i c a t e d i n p r e v i o u s s t u d i e s , t h i s t y p e o f f u l l prepayment b e h a v i o u r s can be t r e a t e d as Amer ican c a l l o p t i o n s on m o r t g a g e s . 2 8 L i k e o t h e r c a l l o p t i o n s , the p o s s i b i l i t y o f r e f i n a n c i n g f u l l prepayments depend on the d i f f e r e n c e s between t h e c o n t r a c t e d i n t e r e s t r a t e s and market i n t e r e s t r a t e s , and the r e m a i n i n g terms o f the mortgages ( i . e . the t ime p e r i o d s u n t i l t h e o p t i o n s e x p i r y ) . But u n l i k e o t h e r c a l l o p t i o n s , r e f i n a n c i n g p o s s i b i l i t y i s a l s o a f f e c t e d by the prepayment p e n a l t i e s o f the o r i g i n a l mor tgages , which w i l l change o v e r t i m e , and t h e amounts o f o u t s t a n d i n g p r i n c i p a l s , which d i c t a t e the amounts o f f u t u r e i n t e r e s t payments . I t i s r e a s o n a b l e t o assume t h a t the lower the market i n t e r e s t r a t e s r e l a t i v e t o the c o n t r a c t e d i n t e r e s t 2 8 H a l l . PREPAYMENT ANALYSIS 24 r a t e s , the h i g h e r the r e f i n a n c i n g b e n e f i t s w i l l b e . In a d d i t i o n , one s h o u l d u n d e r s t a n d t h a t the l o n g e r t h e r e m a i n i n g terms o f t h e o r i g i n a l mortgages and t h e l a r g e r the o u t s t a n d i n g p r i n c i p a l s , t h e h i g h e r the r e f i n a n c i n g b e n e f i t s w i l l be when t h e r e i s a l o w e r i n g o f i n t e r e s t r a t e s . However, r e f i n a n c i n g b e n e f i t s w i l l d e c r e a s e i f prepayment p e n a l t i e s i n c r e a s e . In a d d i t i o n t o c u r r e n t r e f i n a n c i n g b e n e f i t s , f u l l prepayments caused by r e f i n a n c i n g a r e a l s o a f f e c t e d by the v o l a t i l i t y o f the market i n t e r e s t r a t e s . The more v o l a t i l e the market i n t e r e s t r a t e s and the h i g h e r the e x p e c t e d f u t u r e r e f i n a n c i n g b e n e f i t s , the l e s s the c u r r e n t f u l l prepayments w i l l be because homeowners can see t h a t t h e r e i s a h i g h e r p o s s i b i l i t y t h a t f u t u r e i n t e r e s t r a t e s w i l l be lower than p r e s e n t r a t e s . B. F u l l Prepayments and R e l o c a t i o n s F u l l prepayments caused by r e l o c a t i o n s a r e u s u a l l y the r e s u l t s o f changes o f n a t i o n a l and l o c a l economic c o n d i t i o n s . A l l mortgages i n c l u d e d i n MBS p o o l s a r e NHA mortgages which a re g u a r a n t e e d by the p r i n c i p a l r e s i d e n t s o f the m o r t g a g o r s . When t h e s e mor tgagors move t o o t h e r l o c a t i o n s , they a r e u s u a l l y r e q u i r e d t o l i q u i d a t e the mortgages and pay the mortgagees the f u l l o u t s t a n d i n g p r i n c i p a l s p l u s p e n a l t i e s i f the l i q u i d a t i o n s do n o t happen a t t h e end o f t h e terms o f the mor tgages . The n a t i o n a l and l o c a l economies w i l l a f f e c t a homeowner's income and the house r e s a l e v a l u e . When a homeowner's income PREPAYMENT ANALYSIS 25 s u f f e r a s u b s t a n t i a l d e c r e a s e , h e m i g h t n o t b e a b l e t o f u l f i l l t h e m o n t h l y p a y m e n t s a n d m i g h t b e f o r c e d t o f i n d a c h e a p e r l i v i n g a r r a n g e m e n t . I n t h e e v e n t t h a t t h e homeowner l o s e s h i s j o b , h e m i g h t h a v e t o move t o a n o t h e r r e g i o n t h a t h a s a b e t t e r e m p l o y m e n t o p p o r t u n i t y . On t h e o t h e r h a n d , i f t h e homeowner r e c e i v e s a s u b s t a n t i a l i n c o m e i n c r e a s e , he m i g h t d e c i d e t o i m p r o v e h i s l i v i n g c o n d i t i o n b y m o v i n g t o a b e t t e r a n d b i g g e r h o u s e . The homeowner m i g h t a l s o move i f he f i n d s t h a t t h e l o c a l h o u s i n g m a r k e t h a s b e e n h e a t e d up a n d he c a n s e l l h i s h o u s e w i t h a s u b s t a n t i a l p r o f i t . I n a n y o f t h e a b o v e s i t u a t i o n s , t h e homeowner w i l l h a v e t o f u l l y p r e p a y t h e o u t s t a n d i n g p r i n c i p a l t o t h e m o r t g a g e e . I n a d d i t i o n t o s t u d y i n g how e c o n o m i c c o n d i t i o n s c a n a f f e c t f u l l p r e p a y m e n t b e h a v i o r s c a u s e d b y r e l o c a t i n g , o ne c a n s t u d y t h e r e l a t i o n s h i p b e t w e e n h o u s i n g t u r n o v e r r a t e s a n d f u l l p r e p a y m e n t r a t e s d i r e c t l y , a n d e s t a b l i s h a n e s t i m a t i o n o n how r e l o c a t i o n d e c i s i o n a f f e c t s t h e p o s s i b i l i t y o f f u l l p r e p a y m e n t s . S t u d i e s h a v e b e e n d o n e b y u s i n g h o u s i n g s t a r t a n d h o u s e s a l e s a s p r o x i e s o f h o u s i n g t u r n o v e r t o e s t i m a t e t h e p r e p a y m e n t r a t e o f MBS, a n d h a v e p r o v e d t h a t t h e r e i s a s t r o n g r e l a t i o n s h i p b e t w e e n h o u s i n g t u r n o v e r r a t e a n d p r e p a y m e n t r a t e . T h e s e s t u d i e s h a v e shown t h a t t h e h i g h e r t h e h o u s i n g t u r n o v e r r a t e , t h e h i g h e r t h e p r e p a y m e n t r a t e s w i l l b e . PREPAYMENT ANALYSIS 26 C . F u l l Prepayments and D e f a u l t s F u l l prepayments can a l s o be the r e s u l t s o f d e f a u l t s on t h e p a r t o f the homeowners. When a homeowner d e f a u l t s on h i s mor tgage , t h e i s s u e r o f the MBS which i n c l u d e t h a t mortgage i n i t s MBS mortgage p o o l w i l l have t o s t e p i n and p r o v i d e t h e i n v e s t o r s o f t h a t MBS w i t h t i m e l y payments o f t h e p romised amounts. I f t h e i s s u e r i s unab le t o do s o , CMHC w i l l t a k e o v e r under t h e t i m e l y payment g u a r a n t e e . 2 9 A l s o the o u t s t a n d i n g p r i n c i p a l b a l a n c e o f the mortgage i s i n s u r e d under t h e NHA, so i n v e s t o r s w i l l e v e n t u a l l y r e c e i v e the f u l l amount o f t h e i r s h a r e s o f the MBS p o o l . The t i m i n g o f the c a s h f l o w s , however, i s a f f e c t e d by t h e a c t i o n o f the d e f a u l t . D e f a u l t on a mortgage can be v iewed as an Amer ican put o p t i o n on t h e h o u s e . 3 0 The homeowner, i n a way, i s s e l l i n g the house t o t h e mortgagee a t an amount e q u a l l e d t o the o u t s t a n d i n g p r i n c i p a l i n exchange f o r mortgage e l i m i n a t i o n . D e f a u l t r a t e s can be a f f e c t e d by the economic c o n d i t i o n s , changes i n t h e house p r i c e s , and the l o a n - t o - v a l u e r a t i o s . When t h e r e i s a downturn i n l o c a l economy, homeowners f a c i n g a s u b s t a n t i a l income d e c r e a s e s o r even unemployment might d e c i d e t o move t o o t h e r r e g i o n s . When they move, they can e i t h e r s e l l t h e houses and pay back the mortgages o r they can go i n t o d e f a u l t s . The homeowners w i l l p r o b a b l y s e l l t h e i r houses i f they f i n d t h a t house p r i c e s a r e h i g h and they can make p r o f i t s 2 9 CMHC. 3 0 F o s t e r and van O r d e r . PREPAYMENT ANALYSIS 27 by s e l l i n g . I f however, the h o u s e s 7 p r i c e s a r e lower t h a n the o u t s t a n d i n g p r i n c i p a l b a l a n c e s o f t h e mor tgages , t h e n homeowners might choose t o d e f a u l t because they cannot r e c o v e r any p r o f i t o r t h e i r c o n t r i b u t i o n s t o the mor tgages . The l o a n - t o - v a l u e r a t i o s o f the mortgages w i l l a l s o a f f e c t t h e p o s s i b i l i t y o f homeowners r e c o v e r i n g t h e i r c o n t r i b u t i o n s . The h i g h e r t h e l o a n - t o - v a l u e r a t i o s , o r c o n v e r s e l y t h e lower t h e homeowners' e q u i t i e s , the h i g h e r t h e p o s s i b i l i t y t h a t the h o u s e s ' p r i c e s w i l l be lower than the o u t s t a n d i n g p r i n c i p a l b a l a n c e s and t h e h i g h e r t h e p o s s i b i l i t y t h a t t h e homeowner w i l l d e f a u l t . P a r t i a l prepayments a r e the p r e p a y i n g o f l e s s than the t o t a l o u t s t a n d i n g p r i n c i p a l b a l a n c e s o f mortgages by homeowners. P a r t i a l prepayments a r e a f f e c t e d by the s a v i n g b e h a v i o u r o f t h e homeowners, the income tax r a t e s , the economic c o n d i t i o n s and the prepayment p r o v i s i o n s o f t h e mor tgages . D. P a r t i a l Prepayments as S a v i n g s Mor tgages , t o many homeowners, a r e p a r t o f t h e i r s a v i n g s . By p a y i n g down the mor tgages , homeowners a r e a c t u a l i n c r e a s i n g t h e i r t o t a l s a v i n g s by a d d i n g t o t h e i r p o r t i o n o f the ownersh ips o f t h e i r p r i n c i p a l r e s i d e n t s which a r e u s u a l l y the l a r g e s t i n v e s t m e n t s they have e v e r made. S i m i l a r t o o t h e r forms o f s a v i n g s , the amount o f money homeowners a r e w i l l i n g t o c o n t r i b u t e t o p a y i n g down t h e i r mortgages depend on the PREPAYMENT ANALYSIS 28 s a v i n g / c o n s u m p t i o n r a t i o s t h a t have been e s t a b l i s h e d by t h e m s e l v e s a t t h a t t ime o f t h e i r l i v e s . 3 1 U n l i k e o t h e r forms o f s a v i n g s , however, mortgage-pay-downs c a r r y an a d d i t i o n a l p s y c h o l o g i c a l s a t i s f a c t i o n o f knowing t h a t o n e ' s most b a s i c p h y s i c a l need - a s h e l t e r - i s s e c u r e d . T h i s i s why, a l o t o f homeowners a r e w i l l i n g t o t r a n s f e r money out f rom t h e i r s a v i n g a c c o u n t s and pay down the mortgages on t h e i r houses even when t h a t mean l o s s e s i n i n t e r e s t e a r n i n g s . E . P a r t i a l Prepayments and Tax R u l e s A n o t h e r r e a s o n why homeowners a r e w i l l i n g t o t r a n s f e r money from i n t e r e s t b e a r i n g s a v i n g a c c o u n t s t o pay down t h e i r mortgages i s the f a c t t h a t i n t e r e s t payments on mortgages i n Canada a r e no t t a x d e d u c t i b l e . The i n t e r e s t p o r t i o n o f homeowners' monthly mortgage payments have t o come out from t h e i r a f t e r t a x incomes . U n l e s s a homeowner can f i n d an inves tment t h a t has a r e t u r n t w i c e as much as the mortgage i n t e r e s t r a t e , i t w i l l be more b e n e f i c i a l f o r t h a t homeowner t o pay down h i s mortgage, assuming t h a t the homeowner i s i n the 50% t a x b r a c k e t . 3 1 D e n n i s R. Capozza and George W. Gau, "Opt ima l Mortgage Inst rument D e s i g n s " , Nor th Amer ican Hous ing Markets  i n t o the T w e n t y - F i r s t C e n t u r y . B a l l i n g e r P u b l i s h i n g Company, Cambr idge, M a s s a c h u s e t t s , 1983. PREPAYMENT ANALYSIS 29 F . P a r t i a l Prepayments and Incomes A change i n a homeowner's income l e v e l can a l s o a f f e c t h i s w i l l i n g n e s s t o pay down h i s mortgage. When a homeowner r e c e i v e s an i n c r e a s e o f income w h i l e h i s s a v i n g / c o n s u m p t i o n r a t i o remain the same, he w i l l i n c r e a s e h i s s a v i n g by i n c r e a s i n g t h e mortgage pay down. But on the o t h e r hand , when t h e homeowner e x p e r i e n c e s a d e c r e a s e i n income c a u s e d by i n f l a t i o n and o t h e r economic c o n d i t i o n s o r when he e x p e c t s the economic c o n d i t i o n s t o become worse , he w i l l have a tendency t o change h i s s a v i n g / c o n s u m p t i o n r a t i o . The homeowner i n t h i s c a s e w i l l u s u a l l y reduce c u r r e n t consumpt ion bu t m a i n t a i n o r even i n c r e a s e h i s s a v i n g s i n t h e form o f mor tgage-pay -down. T h i s i s the r e s u l t o f an i n c r e a s e o f the p s y c h o l o g i c a l need o f a s h e l t e r by the homeowner when the economy t u r n b a d . The homeowner, by d o i n g s o , reduces h i s r i s k when the f u t u r e does no t appear t o o p r o m i s i n g . G . P a r t i a l Prepayments and House V a l u e s A change i n the house v a l u e due t o l o c a l h o u s i n g market c o n d i t i o n s can a l s o a l t e r a homeowner's c o n t r i b u t i o n t o mor tgage-pay-down. When the l o c a l h o u s i n g market e x p e r i e n c e s a boom, t h e v a l u e o f the homeowner's p r o p e r t y w i l l go u p , and because t h e o u t s t a n d i n g p r i n c i p a l b a l a n c e i s f i x e d , any i n c r e a s e i n t h e house v a l u e w i l l be p e r c e i v e d by t h e homeowner as an i n c r e a s e t o h i s e q u i t y . The homeowner w i l l i n t e r p r e t t h a t he has r e a c h e d h i s s a v i n g s g o a l , assuming t h a t h i s PREPAYMENT ANALYSIS 30 saving/consumption r a t i o remains the same.30 The r e s u l t i s a slow down i n p a r t i a l mortgage prepayments. H. P a r t i a l Prepayments and Prepayment Provision Another very important, but usually neglected factor that can have substantial impacts on the p a r t i a l prepayment behaviors of a homeowner i s the prepayment provision i n the mortgage contract. The prepayment provision put an upper l i m i t on how much p r i n c i p a l the MBS investors have to take back without receiving any additional benefit. The prepayment provision also dictates how much a homeowner can prepay h i s mortgage without penalty at any p a r t i c u l a r time. Penalties w i l l lower the return of the prepayment from the stand point of the homeowner. There are usually two sections i n a prepayment provision that can a f f e c t a homeowner's p a r t i a l prepayment behaviors. These are the sections that d i c t a t e how much a homeowners can increase the amount of h i s monthly payment and pay down the outstanding p r i n c i p a l balance annually. The mortgagee w i l l usually allow a homeowner to increase h i s monthly payment once a year. The increment w i l l usually be between ten and one hundred percent of the contracted monthly payment. In addition to that, the mortgagee w i l l usually allow a homeowner to reduce his outstanding p r i n c i p l e balance by a lump sum payment of ten Capozza and Gau. PREPAYMENT ANALYSIS 31 t o twenty p e r c e n t o f the o u t s t a n d i n g p r i n c i p l e b a l a n c e once a y e a r . There a r e t h r e e major r e a s o n s f o r f u l l prepayment and f i v e major r e a s o n s f o r p a r t i a l prepayment . A l l o f them, e x c e p t one , w i l l be t e s t e d i n t h i s s t u d y t o e v a l u a t e t h e i r l e v e l s o f s i g n i f i c a n t i n Canad ian MBS mortgage p o o l prepayment p a t t e r n s . The e f f e c t s o f t a x a t i o n on prepayments w i l l not be t e s t e d because t h e r e has not been any major change i n the t a x law. Input d a t a t h a t w i l l be used i n the t e s t s a r e c o l l e c t e d i n a way t h a t each r e a s o n can be t e s t e d i n d i v i d u a l l y . INPUT DATA 32 V I . INPUT DATA L i n e a r r e g r e s s i o n i s used i n t h i s s t u d y t o examine t h e prepayment b e h a v i o r s o f Canadian MBS. I have used SHAZAM, a computer r e g r e s s i o n program, t o probe the r e l a t i o n s h i p s between t h e prepayment r a t e s and o t h e r i n p u t s . 3 1 The i n p u t d a t a o f t h i s s t u d y came from f o u r d i f f e r e n t s o u r c e s . I n f o r m a t i o n o f the per formance o f each MBS p o o l under s t u d y came from the Guaranty T r u s t ' s monthly NHA Mortgage Backed S e c u r i t i e s R e p o r t s which i n c l u d e P o o l s T r a d i n g Data and P o o l s Payment A n a l y s i s . 3 2 Per formance d a t a o f each MBS p o o l i n c l u d e t h e amount o f o u t s t a n d i n g p r i n c i p a l b a l a n c e a t t h e b e g i n n i n g o f each p e r i o d , the we ighted average c o n t r a c t e d mortgage i n t e r e s t r a t e , the we ighted average a m o r t i z a t i o n p e r i o d r e m a i n i n g and numbers o f r e m a i n i n g payment u n t i l the end o f t e r m . The second s e t o f i n p u t d a t a came from t h e Bank o f Canada month ly r e p o r t s . T h i s s e t o f i n p u t s i n c l u d e two economic i n d i c a t o r s , v a r i o u s i n t e r e s t r a t e s , and one o f the two h o u s i n g t u r n o v e r i n d i c a t o r s . 3 3 The two economic i n d i c a t o r s a r e the consumer p r i c e i n d e x , and the unemployment r a t e . I n t e r e s t r a t e s e x t r a c t e d from the Bank o f Canada monthly r e p o r t s i n c l u d e 3 1SHAZAM - V e r s i o n 6.0 (September 1987) 3 2NHA Mortgage Backed S e c u r i t i e s R e p o r t s w i l l not be a v a i l a b l e u n t i l the 15th o f each month a t which t ime i n v e s t o r s w i l l a l s o r e c e i v e t h e i r monthly c a s h f l o w s . 3 3 Bank o f Canada Review, March 1988. INPUT DATA 33 the c u r r e n t mortgage ( 5 - y e a r term) i n t e r e s t r a t e , s a v i n g d e p o s i t i n t e r e s t r a t e , c u r r e n t T - B i l l r a t e s and c u r r e n t Government Bond (3-5 y e a r term) r a t e . The Bank o f Canada monthly r e p o r t s a l s o c o n t a i n the h o u s i n g s t a r t i n f o r m a t i o n which can be used as a h o u s i n g t u r n o v e r i n d i c a t o r . The nex t s e t o f i n p u t i n c l u d e the second h o u s i n g t u r n o v e r i n d i c a t o r which i s the house s a l e s r a t e . House s a l e s f i g u r e s a r e a v a i l a b l e from the n a t i o n a l and r e g i o n a l monthly MLS S t a t i s t i c a l Surveys which a r e p u b l i s h e d by t h e Canad ian R e a l E s t a t e A s s o c i a t i o n . 3 4 The l a s t s e t o f i n p u t i s the c h a r a c t e r i s t i c s o f each MBS p o o l s . These i n f o r m a t i o n can be e x t r a c t e d from t h e O f f e r i n g C i r c u l a r o f each MBS p o o l . 3 5 These i n f o r m a t i o n i n c l u d e the g e o g r a p h i c d i s t r i b u t i o n o f the mortgages w i t h i n each p o o l , the prepayment p r o v i s i o n , the d u e - o n - s a l e c l a u s e , and the MBS i s s u e r ' s l i n e o f b u s i n e s s and f i n a n c i a l s t a t u s . These f o u r groups o f i n p u t d a t a a r e used t o c r e a t e seven s e t s o f dependent and independent v a r i a b l e s f o r the r e g r e s s i o n s . 3 *The Canad ian R e a l E s t a t e A s s o c i a t i o n , Communicat ion Department , MLS S t a t i s t i c a l S u r v e y , J a n u a r y 1987 -December 1987. 3 5 E a c h MBS mortgage p o o l must have a o f f e r i n g c i r c u l a r a c c o r d i n g t o CMHC r e g u l a t i o n s , (see "NHA Mor tgage-Backed S e c u r i t i e s " , CMHC, NHA 5942 10 /86 . ) DEPENDENT AND INDEPENDENT VARIABLES 34 V I I . DEPENDENT AND INDEPENDENT VARIABLES The d e p e n d e n t v a r i a b l e o f t h i s s t u d y i s t h e p r e p a y m e n t r a t e w h i c h i s d e f i n e d a s t h e p e r c e n t a g e d e c r e a s e o f o u t s t a n d i n g p r i n c i p a l b a l a n c e o f e a c h MBS p o o l s w i t h i n e a c h p e r i o d s . P r e p a y m e n t r a t e i s c a l c u l a t e d f r o m d i v i d i n g t h e amount o f p r e p a y m e n t b y t h e o u t s t a n d i n g p r i n c i p a l b a l a n c e o f t h e p r e v i o u s m o n t h 3 6 . B o t h t h e amount o f p r e p a y m e n t s a n d t h e p r e v i o u s m o n t h ' s o u t s t a n d i n g p r i n c i p a l b a l a n c e s a r e r e a d i l y a v a i l a b l e f r o m t h e G u a r a n t y T r u s t ' s m o n t h l y NHA M o r t g a g e B a c k e d S e c u r i t y R e p o r t s . P r e p a y m e n t p e n a l t i e s o f e a c h p e r i o d , h o w e v e r , i s n o t i n c l u d e d i n t h e c a l c u l a t i o n o f p r e p a y m e n t r a t e . 3 7 T h e r e a r e s i x g r o u p s o f i n d e p e n d e n t v a r i a b l e s i n t h e p r i m a r y r e g r e s s i o n m o d e l . T h r e e o f t h e s i x g r o u p s o f i n d e p e n d e n t v a r i a b l e s a r e u s e d t o i n v e s t i g a t e f u l l p r e p a y m e n t b e h a v i o r s . T h e y a r e t h e a ) r e f i n a n c i n g b e n e f i t s , b ) h o u s i n g t u r n o v e r r a t e s , a n d c ) p e n a l t i e s o n f u l l p r e p a y m e n t s . The n e x t t w o g r o u p s o f i n d e p e n d e n t v a r i a b l e s a r e e x p e c t e d t o h a v e i n f l u e n c e s o n b o t h f u l l a n d p a r t i a l p r e p a y m e n t b e h a v i o r s . T h e y a r e t h e d ) n a t i o n a l e c o n o m i c i n d i c a t o r s a n d f i n a n c i a l r a t e s , a n d e ) g e o g r a p h i c d i s t r i b u t i o n o f m o r t g a g e s o f e a c h MBS p o o l . The 3 6 T o t a l p r e p a y m e n t P r e p a y m e n t r a t e = O u t s t a n d i n g B a l a n c e " P e n a l t i e s c a n , h o w e v e r , i n c r e a s e t h e r a t e o f r e t u r n a n d s h o u l d b e i n c l u d e d i n t h e v a l u a t i o n o f a MBS. DEPENDENT AND INDEPENDENT VARIABLES 35 l a s t group of independent v a r i a b l e s i n c l u d e s the f)prepayment p r o v i s i o n and the c h a r a c t e r i s t i c s o f each MBS p o o l s . T h i s group o f independent v a r i a b l e s i s expected t o i n f l u e n c e p a r t i a l prepayment b e h a v i o r s . A. R e f i n a n c i n g B e n e f i t The f i r s t group of independent v a r i a b l e o n l y has one v a r i a b l e - r e f i n a n c i n g b e n e f i t . R e f i n a n c i n g b e n e f i t i s d e f i n e d as the amount o f money, i n today's v a l u e , a homeowner can save by l i q u i d a t i n g the o r i g i n a l mortgage and a c q u i r i n g a new mortgage. I c a l c u l a t e r e f i n a n c i n g b e n e f i t by assuming t h a t a homeowner w i l l f i n a n c e the amount of prepayment p l u s prepayment p e n a l t i e s by g e t t i n g another mortgage w i t h the c u r r e n t market mortgage r a t e . I f u r t h e r assumed t h a t the homeowner w i l l m a i n t a i n t h e same amount of monthly payment and t h a t the term of the new mortgage i s equal t o the remaining term o f the o r i g i n a l mortgage. In t h i s case, the o n l y change i n p r e s e n t v a l u e w i l l come from the change i n o u t s t a n d i n g balance a t the end o f the term. The change i n o u t s t a n d i n g balance i s then d i s c o u n t e d back t o p r e s e n t . 3 8 R e f i n a n c i n g b e n e f i t i s expected t o have p o s i t i v e e f f e c t s on f u l l prepayments. The l a r g e r the 36 OSB a t end o f term R e f i n a n c i n g o f o r i g i n a l mortgage b e n e f i t = OSB a t end of term of new mortgage (1 + Discount r a t e ) * * ( T ) T = number of month remain u n t i l end of term DEPENDENT AND INDEPENDENT VARIABLES 36 amount o f the s a v i n g s i n p r e s e n t v a l u e , the h i g h e r the prepayment r a t e s h o u l d b e . B. Hous ing T u r n o v e r There a r e two methods t o e s t i m a t e the h o u s i n g t u r n o v e r r a t e . The f i r s t method i s t o use the monthly h o u s i n g s t a r t f i g u r e s as i n d i c a t o r s o f h o u s i n g t u r n o v e r r a t e s . The second method i s t o use monthly house s a l e s f i g u r e s as p r o x i e s o f h o u s i n g t u r n o v e r r a t e s . Both t h e h o u s i n g s t a r t and t h e house s a l e s f i g u r e s a r e d i v i d e d by the h o u s i n g s t o c k f i g u r e s i n o r d e r t o be m e a n i n g f u l i n the r e g r e s s i o n m o d e l . 3 9 Hous ing t u r n o v e r i s e x p e c t e d t o have a p o s i t i v e r e l a t i o n s h i p w i t h f u l l prepayment which i s caused by r e l o c a t i o n . One s h o u l d be a b l e t o o b s e r v e an i n c r e a s e i n prepayment r a t e s when t h e r e i s an i n c r e a s e i n h o u s i n g t h e t u r n o v e r r a t e s . C . P e n a l t i e s on Prepayments Prepayment p e n a l t y i s the a d d i t i o n a l sum o f money a homeowner must pay when he f u l l y p r e p a y s h i s o r i g i n a l mortgage. The prepayment p e n a l t y r a t e i s measured by d i v i d i n g t h e amount o f p e n a l t i e s o f a MBS a t a p a r t i c u l a r month by the amount o f 3 9 Month ly h o u s i n g s t a r t Hous ing s tar t (HSTART) = Hous ing s t o c k (Dec. 1986) Month ly house s a l e s House sa les (HSALES) = Hous ing s t o c k (Dec. 1986) DEPENDENT AND INDEPENDENT VARIABLES 37 p r e p a y m e n t o f t h a t MBS i n t h a t m o n t h . 4 0 T h e r e a r e u s u a l l y t w o p a t t e r n s o f p r e p a y m e n t p e n a l t y . A m o r t g a g e e c a n demand e i t h e r a p e n a l t y t h a t e q u a l s t o t h r e e month i n t e r e s t o n t h e o u t s t a n d i n g p r i n c i p a l b a l a n c e o r a p e n a l t y t h a t e q u a l s t o t h e d i f f e r e n c e i n p r e s e n t v a l u e s o f t h e m o r t g a g e i n t h e c o n t r a c t e d m o r t g a g e r a t e a n d i n m a r k e t m o r t g a g e r a t e . 4 1 P r e p a y m e n t p e n a l t y w i l l l o w e r t h e t o t a l s a v i n g s d u r i n g r e f i n a n c i n g a n d i n c r e a s e t h e r e l o c a t i o n c o s t when a homeowner moves. C o n s e q u e n t l y , p r e p a y m e n t p e n a l t y i s e x p e c t e d t o h a v e a n e g a t i v e e f f e c t o n p r e p a y m e n t r a t e . The r e s u l t o f t h e e s t i m a t i o n s h o u l d s u p p o r t t h e a r g u m e n t t h a t t h e l a r g e r t h e amount o f p e n a l t y , t h e l o w e r t h e p r e p a y m e n t r a t e w i l l b e . D. E c o n o m i c I n d i c a t o r s a n d F i n a n c i a l R a t e s I h a v e i n c l u d e d t w o e c o n o m i c i n d i c a t o r s - Consumer P r i c e I n d e x a n d Unemployment r a t e s i n t h e r e g r e s s i o n m o d e l . A s m e n t i o n e d e a r l i e r , i t i s d i f f i c u l t t o p r e d i c t how t h e s e e c o n o m i c i n d i c a t o r s w i l l a f f e c t t h e p r e p a y m e n t b e h a v i o r s o f C a n a d i a n homeowners. F i n a n c i a l r a t e s , h o w e v e r , a r e e x p e c t e d t o h a v e n e g a t i v e e f f e c t s o n p r e p a y m e n t r a t e s b e c a u s e a l l f i n a n c i a l 4 0 N o n s c h e d u l e d i n t e r e s t p a y m e n t P r e p a y m e n t p e n a l t y ( P E N A L ) = Amount o f p r e p a y m e n t 4 1 T h e a s s u m p t i o n , i n t h i s c a s e , i s t h a t homeowners w i l l n o t p a r t i a l l y p r e p a y t h e i r m o r t g a g e u n l e s s t h e r e i s n o t p e n a l t y . So a l l p r e p a y m e n t p e n a l t y m u s t be t h e s i d e p r o d u c t o f f u l l p r e p a y m e n t . DEPENDENT AND INDEPENDENT VARIABLES 38 r a t e s a r e i n t e r r e l a t e d and when any one o f the f i n a n c i a l r a t e s i n c r e a s e , market i n t e r e s t r a t e s w i l l a l s o i n c r e a s e . An i n c r e a s e i n i n t e r e s t r a t e s w i l l lower the r e f i n a n c i n g b e n e f i t a n d , h e n c e , s h o u l d l e a d t o the d e c l i n e i n t h e prepayment r a t e . * 2 E . G e o g r a p h i c D i s t r i b u t i o n The nex t two groups o f independent v a r i a b l e s a r e t h e g e o g r a p h i c d i s t r i b u t i o n s o f mortgages o f each MBS p o o l . Two d i f f e r e n t s e t s o f d a t a a r e t e s t e d u s i n g the same m o d e l . The d a t a i n t h e f i r s t s e t i n c l u d e the s i m p l y g e o g r a p h i c d i s t r i b u t i o n , by d o l l a r amount, o f each MBS p o o l , among Quebec, O n t a r i o , A l b e r t a , and B r i t i s h C o l u m b i a . These f o u r p r o v i n c e s a r e chosen f o r t h i s s tudy because o v e r 80% o f the mortgages i n a l l MBS a r e o r i g i n a t e d from t h e s e p r o v i n c e s . * 3 The d a t a o f t h e second s e t a r e the r e s u l t s o f the g e o g r a p h i c d i s t r i b u t i o n s m u l t i p l i e d by the monthly h o u s i n g t u r n o v e r r a t e s o f each o f the f o u r p r o v i n c e s . * * One s h o u l d expec t t h a t the e f f e c t s o f g e o g r a p h i c d i s t r i b u t i o n s on prepayment b e h a v i o r s a r e min ima l * 2 I n t e r e s t r a t e can a f f e c t r e f i n a n c i n g b e n e f i t b y : a) c h a n g i n g the market Mortgage r a t e , and b) c h a n g i n g the d i s c o u n t r a t e . * 3 The p e r c e n t a g e o f MBS mortgages o r i g i n a t e d from t h e s e f o u r p r o v i n c e s i s an e s t i m a t i o n based on the a v a i l a b l e MBS o f f e r i n g c i r c u l a r s . * * P r o v i n c i a l monthly house s a l e s d a t a a r e used as i n d i c a t o r s o f p r o v i n c i a l h o u s i n g t u r n o v e r i n t h i s s e t o f d a t a . DEPENDENT AND INDEPENDENT VARIABLES 39 because none o f the p r o v i n c e s have e x p e r i e n c e d any d r a m a t i c economic change w i t h i n the t ime p e r i o d o f t h i s s t u d y . F . Prepayment P r o v i s i o n The l a s t group o f independent v a r i a b l e s i s prepayment p r o v i s i o n . There a r e two major p a r t s i n each prepayment p r o v i s i o n s - the s e c t i o n s t h a t d i c t a t e how much a homeowner can i n c r e a s e h i s monthly payment and the maximum annua l pay down o f t h e o u t s t a n d i n g p r i n c i p l e b a l a n c e . 4 5 Prepayment p r o v i s i o n o f each MBS p o o l can a f f e c t p a r t i a l prepayment b e h a v i o r s . I t i s p r e d i c t e d t h a t t h e l a r g e r t h e amount a homeowner can pay down h i s mortgage w i t h o u t p e n a l t y , the h i g h e r the amount o f prepayment would b e . From t h e above e x p e c t a t i o n s , I have d e v e l o p e d s i x h y p o t h e s e s . F i r s t , r e f i n a n c i n g b e n e f i t s a r e p o s i t i v e l y and s i g n i f i c a n t l y r e l a t e d t o prepayment r a t e s . S e c o n d , h o u s i n g t u r n o v e r r a t e s a r e p o s i t i v e l y and s i g n i f i c a n t l y r e l a t e d t o prepayment r a t e s . T h i r d , prepayment p e n a l t i e s a r e n e g a t i v e l y and s i g n i f i c a n t l y r e l a t e d t o the amount o f p repayments . F o u r t h , a l l economic i n d i c a t o r s and f i n a n c i a l r a t e s a r e n e g a t i v e l y and not s i g n i f i c a n t l y r e l a t e d t o the prepayment r a t e s . Nex t , g e o g r a p h i c d i s t r i b u t i o n s have n o n s i g n i f i c a n t 4 5 The word ing o f prepayment p r o v i s i o n i s not t h e same i n a l l o f f e r i n g c i r c u l a r s . I n v e s t o r s s h o u l d s t u d y t h i s s e c t i o n c a r e f u l l y b e f o r e making any t r a d i n g d e c i s i o n . DEPENDENT AND INDEPENDENT VARIABLES 40 i n f l u e n c e on" prepayment r a t e s . F i n a l l y , prepayment p r o v i s i o n i s p o s i t i v e l y and s i g n i f i c a n t l y r e l a t e d t o prepayment r a t e s . In the next chapter I w i l l d i s c u s s the r e s u l t s from t e s t i n g these hypotheses. DEPENDENT AND INDEPENDENT VARIABLES 41 F i g u r e 5 PREPAYMENT REASONS  AND INDEPENDENT VARIABLES F u l l prepayments: - R e f i n a n c i n g - R e f i n a n c i n g b e n e f i t - F i n a n c i a l r a t e s - P e n a l t i e s on prepayment - Prepayment p r o v i s i o n - R e l o c a t i o n - Hous ing t u r n o v e r - Economic i n d i c a t o r s and f i n a n c i a l r a t e s - D e f a u l t - Economic i n d i c a t o r s and f i n a n c i a l r a t e s P a r t i a l prepayments: - S a v i n g - Economic i n d i c a t o r s and f i n a n c i a l r a t e s - Tax r u l e s - Income - House v a l u e - Prepayment p r o v i s i o n - Economic i n d i c a t o r s and f i n a n c i a l r a t e s - G e o g r a p h i c d i s t r i b u t i o n - Economic i n d i c a t o r s and f i n a n c i a l r a t e s - Hous ing t u r n o v e r - Prepayment p r o v i s i o n DEPENDENT AND INDEPENDENT VARIABLES 42 F i g u r e 6 INDEPENDENT VARIABLES  AND INPUT DATA R e f i n a n c i n g b e n e f i t Hous ing t u r n o v e r P e n a l t i e s on prepayment Economic i n d i c a t o r s and F i n a n c i a l r a t e s G e o g r a p h i c d i s t r i b u t i o n ( 4 ) 0SB(1) C o n t r a c t e d r a t e s ( 1 ) Market mortgage r a t e s ( 2 ) Amount o f prepayment(1) No. o f r e m a i n i n g payment(1) Hous i n g s t a r t s ( 2 ) House s a l e s ( 3 ) Amount o f p e n a l t i e s ( 1 ) Amount o f prepayment(1) Consumer p r i c e index(2 ) Unemployment(2) Market mortgage r a t e ( 2 ) S a v i n g d e p o s i t r a t e ( 2 ) T - b i l l r a t e ( 2 ) G o v t , bond r a t e ( 2 ) Quebec O n t a r i o A l b e r t a B r i t i s h Co lombia (1) (2) (3) (4) Prepayment p r o v i s i o n - Type o f l e n d e r ( 4 ) - D u e - o n - s a l e c l a u s e ( 4 ) - Prepayment p r o v i s i o n ( 4 ) Guaranty T r u s t ' s monthly NHA Mortgage Backed S e c u r i t i e s R e p o r t s . Bank o f Canada Month ly R e p o r t s . MLS S t a t i s t i c a l Surveys by Canadian R e a l E s t a t e A s s t . MBS O f f e r i n g C i r c u l a r DISCUSSION OF RESULTS 43 V I I I . DISCUSSION OF RESULTS The r e s u l t s o f t h e e s t i m a t i o n s a r e g i v e n i n t a b l e 2 t h r o u g h 12. F o r e a c h g r o u p o f i n d e p e n d e n t v a r i a b l e s , one e q u a t i o n i s e s t i m a t e d . S u b s e q u e n t l y , a l l i n d e p e n d e n t v a r i a b l e s a r e u s e d i n t h e f i n a l e s t i m a t i o n a n d a s t e p w i s e r e g r e s s i o n . The r e s u l t s f r o m t h e s e e s t i m a t i o n s r e f l e c t t h e i m p o r t a n c e o f two g r o u p s o f i n d e p e n d e n t v a r i a b l e s o v e r t h e o t h e r s a n d a number o f i n v e s t m e n t t a c t i c s c a n b e d e d u c e d f r o m t h e s e r e s u l t s . A. R e f i n a n c i n g B e n e f i t A s e x p e c t e d , homeowners a r e more l i k e l y t o p r e p a y when t h e y a r e a b l e t o s a v e money b y r e f i n a n c i n g . H o w e v e r , t h e e s t i m a t i o n d o e s n o t s u p p o r t t h e h y p o t h e s i s t h a t r e f i n a n c i n g b e n e f i t s a r e s i g n i f i c a n t l y r e l a t e d t o p r e p a y m e n t r a t e s . R e f i n a n c i n g b e n e f i t s do n o t a p p e a r t o b e a m a j o r f a c t o r i n C a n a d i a n homeowners' p r e p a y m e n t d e c i s i o n s a s d e m o n s t r a t e d b y t h e p o s i t i v e c o e f f i c i e n t o f r e f i n a n c i n g b e n e f i t (REFINAN) a n d t h e i n s i g n i f i c a n t t - r a t i o . 4 6 T h e s e f i n d i n g s a r e a l s o s u p p o r t e d b y t h e f i n a l e s t i m a t i o n a n d t h e s t e p w i s e r e g r e s s i o n w h e r e r e f i n a n c i n g b e n e f i t i s r e j e c t e d . 4 7 T h e s e r e s u l t s c o u l d b e c a u s e d b y t h e l a c k o f s i g n i f i c a n t c h a n g e s i n m o r t g a g e r a t e s . I f t h e r e i s a n y d r a m a t i c c h a n g e i n m o r t g a g e r a t e s , I w i l l S e e t a b l e 3. S e e t a b l e 11 a n d 1 2 . DISCUSSION OF RESULTS 44 expec t the t - r a t i o o f r e f i n a n c i n g b e n e f i t t o i n c r e a s e s i g n i f i c a n t l y . B. Hous ing T u r n o v e r S i m i l a r t o r e f i n a n c i n g b e n e f i t , h o u s i n g t u r n o v e r r a t e s a r e p o s i t i v e l y r e l a t e d t o prepayment r a t e s bu t the r e l a t i o n s h i p i s weak. The d a t a from h o u s i n g s t a r t s (HSTART) and house s a l e s (HSALES) have p o s i t i v e c o e f f i c i e n t s w i t h prepayment r a t e s and i n s i g n i f i c a n t t - r a t i o s . 4 8 Hous ing s a l e s , n e v e r t h e l e s s , shows a s l i g h t l y s t r o n g e r r e l a t i o n s h i p . T h i s s t r o n g e r r e l a t i o n s h i p between house s a l e s and prepayments i s more v i s i b l e when house s a l e s i s i n c l u d e d i n the s t e p w i s e r e g r e s s i o n w h i l e h o u s i n g s t a r t s i s n o t . 4 9 A l t h o u g h t h e s e r e s u l t s c o n t r a d i c t the Amer ican e x p e r i e n c e s , they do not imp ly t h a t h o u s i n g t u r n o v e r s h o u l d no t be c o n s i d e r e d . R a t h e r , i t s h o u l d be i n t e r p r e t e d as t h a t the r e l a t i o n s h i p between h o u s i n g s t a r t s and prepayments i s l e s s d e t e c t a b l e when MBS mortgages a r e r e l a t i v e l y new and few i n number r e l a t i v e t o the n a t i o n a l f i g u r e . I expec t t h i s r e l a t i o n s h i p t o s t r e n g t h e n when the Canad ian MBS market becomes more mature and a l a r g e number o f mortgage p o o l s move i n t o t h e i r t h i r d and f o u r t h y e a r o f e x i s t e n c e . 5 0 4 8 S e e t a b l e 4. 4 9 S e e t a b l e 12. 5 0 A c c o r d i n g t o Hu(87) , the p o s s i b i l i t y o f r e l o c a t i n g i n c r e a s e s much f a s t e r two y e a r a f t e r the l a s t r e l o c a t i n g . A l s o impor tan t i s the f a c t t h a t a l l t h e mortgages w i t h i n a MBS p o o l must be o r i g i n a t e d w i t h i n a s i x month p e r i o d . DISCUSSION OF RESULTS 45 C. P e n a l t i e s o n P r e p a y m e n t The p r e p a y m e n t p e n a l t y ( P E N A L ) , among a l l t h e i n d e p e n d e n t v a r i a b l e s , h a s t h e s t r o n g e s t r e l a t i o n s h i p w i t h t h e p r e p a y m e n t r a t e s . T h i s s t r o n g r e l a t i o n s h i p i s r e f l e c t e d i n t h e s t e p w i s e r e g r e s s i o n w h e r e p r e p a y m e n t p e n a l t y r a t e i s t h e f i r s t i n d e p e n d e n t v a r i a b l e c h o s e n . 5 1 The e s t i m a t e d c o e f f i c i e n t , h o w e v e r , i s p o s i t i v e w h i c h i s i n c o n t r a s t t o t h e h y p o t h e s i s . T h i s c o u l d b e t h e r e s u l t o f t h e s t r o n g r e l a t i o n s h i p b e t w e e n f u l l p r e p a y m e n t s a n d t h e r e l o c a t i n g d e c i s i o n s . When m a r k e t m o r t g a g e r a t e s a r e r e l a t i v e l y l o w , t h e h o u s i n g m a r k e t u s u a l l y b ecomes more a c t i v e a n d more homeowners a r e e x p e c t e d t o move. A t t h e same t i m e when t h e m a r k e t m o r t g a g e r a t e s a r e l o w e r t h a n t h e c o n t r a c t e d m o r t g a g e r a t e s , t h e p r e p a y m e n t p e n a l t i e s w i l l i n c r e a s e b e c a u s e t h e p e n a l t i e s a r e e q u a l t o t h e d i f f e r e n c e s i n p r e s e n t v a l u e s o f t h e m o r t g a g e s i n c o n t r a c t e d m o r t g a g e r a t e s a n d i n m a r k e t m o r t g a g e r a t e s . 5 2 T h i s i s a s u p p o r t t o t h e a r g u m e n t t h a t p r e p a y m e n t r a t e s w i l l i n c r e a s e when more p e o p l e move. The dummy i n d e p e n d e n t v a r i a b l e r e p r e s e n t i n g t h e d i f f e r e n t t y p e s o f i n s t i t u t i o n s ( I N S T I T ) a l s o shows a p o s i t i v e c o e f f i c i e n t a n d a s i g n i f i c a n t t - r a t i o . I t i n d i c a t e s t h a t 5 1 S e e t a b l e 12. 5 2 T h e p r e p a y m e n t p r o v i s i o n s o f some MBS p o o l s m i g h t b e d i f f e r e n t . DISCUSSION OF RESULTS 46 mortgage p o o l s i s s u e d by banks and l a r g e t r u s t companies have a h i g h e r prepayment p o s s i b i l i t y . 5 3 D. Economic I n d i c a t o r s and F i n a n c i a l Rates Out o f a l l t h e economic i n d i c a t o r s (CPI , UNEMPLO) and f i n a n c i a l r a t e s (SAVING, T B I L L , GBOND), o n l y t h e changes i n the consumer p r i c e index (CPI) have a s t r o n g and p o s i t i v e r e l a t i o n s h i p w i t h the prepayment r a t e s . 5 4 T h i s r e l a t i o n s h i p r e j e c t s t h e h y p o t h e s i s t h a t economic i n d i c a t o r s and f i n a n c i a l r a t e s a r e n e g a t i v e l y and not s i g n i f i c a n t l y r e l a t e d t o prepayments , and s u p p o r t s the argument t h a t homeowners a r e r i s k a v e r s e and w i l l lower t h e i r t o t a l r i s k as much as p o s s i b l e when they f e e l i n f l a t i o n i s coming . T h i s e s t i m a t i o n has a l s o shown one i n t e r e s t p o i n t . When T - b i l l r a t e s (TBILL) and government bond r a t e s (GBOND) a r e t aken away from the e s t i m a t i o n , I f i n d t h a t t h e s a v i n g d e p o s i t r a t e s become s i g n i f i c a n t and p o s t a n e g a t i v e r e l a t i o n s h i p w i t h the prepayment r a t e s . T h i s f i n d i n g demonst ra tes t h a t homeowners w i l l i n c r e a s e prepayments when i n t e r e s t r a t e s o f t h e i r s a v i n g a c c o u n t s d e c r e a s e . D e c r e a s i n g the mortgage o u t s t a n d i n g b a l a n c e , i n t h i s c a s e , become more a t t r a c t i v e w i t h compare t o o t h e r investment a l t e r n a t i v e s . However, none o f the economic i n d i c a t o r s and f i n a n c i a l r a t e s i s i n c l u d e d i n the s t e p w i s e r e g r e s s i o n . The i n d i c a t i o n i s t h a t the e f f e c t s o f 5 3 S e e t a b l e 5. 5 4 S e e t a b l e 6. DISCUSSION OF RESULTS 47 economic i n d i c a t o r s and f i n a n c i a l r a t e s on prepayments can be c a p t u r e d by o t h e r independent v a r i a b l e s such as house s a l e s and prepayment p e n a l t y r a t e . E. Geographic D i s t r i b u t i o n The e s t i m a t i o n s of the e f f e c t s o f geographic d i s t r i b u t i o n s on prepayment r a t e s have some c o n f u s i n g r e s u l t s . A l l e s timated c o e f f i c i e n t s , which are o r i g i n a t e d from the independent v a r i a b l e s o f pure geographic d i s t r i b u t i o n s and the geographic d i s t r i b u t i o n s a d j u s t e d by the r e g i o n a l housing t u r n o v e r r a t e s , a r e n e g a t i v e and a l l show s i g n i f i c a n t t - r a t i o s . 5 5 However, when the geographic d i s t r i b u t i o n v a r i a b l e s are t e s t e d i n the stepwise r e g r e s s i o n , the independent v a r i a b l e r e p r e s e n t i n g the c o n c e n t r a t i o n o f mortgages o r i g i n a t e d from Quebec i s i n c l u d e d . 5 6 T h i s r e s u l t i n d i c a t e s t h a t although geographic d i s t r i b u t i o n i s not a major determinant on prepayment p a t t e r n s , Quebec homeowners are l e s s l i k e l y t o prepay t h e i r mortgages than homeowners form o t h e r p a r t s o f Canada. F. Prepayment P r o v i s i o n Two o f the prepayment p r o v i s i o n v a r i a b l e s are proved t o have the second and t h i r d s t r o n g e s t r e l a t i o n s h i p s w i t h the prepayment r a t e s . The v a r i a b l e r e p r e s e n t i n g the maximum i n c r e a s e i n monthly mortgage payment has a h i g h t - r a t i o and a 5 5See t a b l e 7 and 8. 5 6See t a b l e 12. DISCUSSION OF RESULTS 48 p o s i t i v e c o e f f i c i e n t , so does the v a r i a b l e r e p r e s e n t i n g t h e maximum annua l d e c r e a s e i n o u t s t a n d i n g b a l a n c e . 5 7 These r e s u l t s i n d i c a t e t h a t a h i g h p e r c e n t a g e o f prepayment i s p a r t i a l prepayment . T h i s i s the most impor tan t d i s c o v e r y o f t h i s s t u d y . These r e s u l t s s u p p o r t the h y p o t h e s i s t h a t Canad ian homeowners a r e eager t o lower t h e i r mortgage i n t e r e s t expenses which have t o come out from t h e i r a f t e r t a x incomes . From t h e r e g r e s s i o n a n a l y s i s , one can see t h a t p e n a l t y on prepayment and prepayment p r o v i s i o n have t h e s t r o n g e s t i n f l u e n c e s on Canad ian MBS prepayment b e h a v i o r s . P e n a l t i e s on prepayments a r e the b y - p r o d u c t s o f f u l l p repayments . I t i l l u s t r a t e s the s t r o n g r e l a t i o n s h i p between f u l l prepayments and t h e n a t i o n a l h o u s i n g market a c t i v i t i e s . Prepayment p r o v i s i o n , on t h e o t h e r hand , d e s c r i b e s the w i l l i n g n e s s o f Canad ian homeowners t o p a r t i a l l y prepay t h e i r mor tgages . I n v e s t o r s , b o t h i n d i v i d u a l and i n s t i t u t i o n a l , s h o u l d have a c l e a r u n d e r s t a n d i n g o f t h e s e f i n d i n g s b e f o r e t h e y make t h e i r MBS inves tment d e c i s i o n s . " S e e t a b l e 9. CONCLUSION 49 IX. CONCLUSION To make p r o f i t a b l e MBS investment d e c i s i o n s , an i n v e s t o r must has an e f f e c t i v e MBS v a l u a t i o n model. Prepayment e s t i m a t i o n i s one o f the key elements i n a MBS v a l u a t i o n model. I have examined f a c t o r s t h a t can a f f e c t prepayment p a t t e r n s o f Canadian MBS i n t h i s study. The r e s u l t i n d i c a t e s t h a t one must d i s t i n g u i s h the d i f f e r e n c e s between f u l l prepayments and p a r t i a l prepayments i n order t o make a meaningful e s t i m a t i o n on prepayments. F u l l prepayments are d i r e c t l y r e l a t e d t o housing market a c t i v i t i e s . P a r t i a l prepayments, however, are a f f e c t e d m ainly by the prepayment p r o v i s i o n i n the mortgage c o n t r a c t s . Two s e t s o f investment t a c t i c s can be developed from these knowledge. One f o r market t i m i n g i n v e s t o r s and the o t h e r f o r pure p i c k - u p i n v e s t o r s . A market t i m i n g i n v e s t o r b e l i e v e s he can outperform the market by c o r r e c t l y p r e d i c t i n g the movements of the market. Before he makes a MBS t r a d i n g d e c i s i o n he should make p r e d i c t i o n s on the d i r e c t i o n and the magnitude of housing market a c t i v i t y based on h i s own a n a l y s i s . I f h i s p r e d i c t i o n s i s an i n c r e a s e i n housing market a c t i v i t y which can cause an i n c r e a s e i n f u l l prepayments, he should i n v e s t i n d i s c o u n t e d MBS because an i n c r e a s e i n prepayments w i l l reduce the d u r a t i o n and i n c r e a s e the r a t e o f r e t u r n o f a d i s c o u n t e d MBS. Based on the same argument, he should i n v e s t i n premium MBS i f he p r e d i c t s a decrease i n housing market a c t i v i t i e s . CONCLUSION 50 A pure p i c k - u p i n v e s t o r adds v a l u e t o h i s p o r t f o l i o by d e t e c t i n g m i s p r i c i n g o f a s e c u r i t y . M i s p r i c i n g appears when t h e market cannot f u l l y c a p i t a l i z e a l l the a v a i l a b l e i n f o r m a t i o n . There a r e two d i s c o u n t e d MBS, f o r example , w i t h t h e same m a t u r i t y and the same b i d and ask p r i c e s . One o f them i s i s s u e d by a bank o r a l a r g e t r u s t company, and has a h i g h e r prepayment p r o v i s i o n and a s m a l l e r p e r c e n t a g e o f i t s mortgages i n Q u e b e c . 5 8 T h i s d i s c o u n t e d MBS s h o u l d have a h i g h e r prepayment r a t e than the a l t e r n a t i v e . A h i g h e r prepayment r a t e , i n t h i s c a s e , r e p r e s e n t s a h i g h e r r a t e o f r e t u r n . An i n v e s t o r s h o u l d p r e f e r t h i s MBS o v e r the o t h e r one . The s i t u a t i o n f o r premium MBS i s the o p p o s i t e . In a d d i t i o n t o d e v e l o p i n g investment t a c t i c s , MBS i n v e s t o r s and f i n a n c i a l a n a l y s t s s h o u l d a l s o f o c u s t h e i r a t t e n t i o n on b u i l d i n g a MBS v a l u a t i o n model t h a t can t r u l y r e f l e c t the f i n a n c i a l p o t e n t i a l o f Canadian MBS. I e x p e c t f u t u r e s t u d i e s o f Canadian MBS t o c o n c e n t r a t e on the s e n s i t i v i t i e s o f MBS p r i c e s t o changes o f i n t e r e s t r a t e s and o t h e r economic f a c t o r s . I a l s o recommend t h a t , i n t h e f u t u r e , Canad ian homeowners' prepayment b e h a v i o r s s h o u l d be m o n i t o r e d and a n a l y z e d c o n t i n u o u s l y i n the f u t u r e . 'Higher prepayment p r o v i s i o n means homeowners can p a r t i a l l y prepay more o u t s t a n d i n g p r i n c i p a l b a l a n c e s w i t h o u t p e n a l t y . TABLES 51 TABLE 1 DEFINITION OF INDEPENDENT VARIABLES CONCEPTUAL VARIABLE EMPIRICAL PROXY CALCULATION R e f i n a n c i n g b e n e f i t REFINAN S a v i n g ( i n p r e s e n t v a l u e ) by r e f i n a n c e H o u s i n g t u r n o v e r HSTART HSALES Hous ing s t a r t House s a l e s (MLS) Economic i n d i c a t o r s and f i n a n c i a l r a t e s CPI UNEMPLO SAVING TBILL GBOND = Change i n Consumer p r i c e index = Unemployment r a t e = S a v i n g d e p o s i t r a t e = T r e a s u r y b i l l s r a t e = Government bonds (3-5 yr ) r a t e P e n a l t i e s on prepayment PENALTY RATEDIF INSTIT Amount o f p e n a l t y d i v i d e d by amount o f prepayment D i f f e r e n c e between c o n t r a c t e d and market mortgage r a t e s 1 i f i s s u e d by banks o r l a r g e t r u s t companies = 0 i f i s s u e d by s m a l l t r u s t companies TABLES 52 G e o g r a p h i c d i s t r i b u t i o n GDQUE = Parentage o f the mortgage p o o l l o c a t e d i n Quebec GDONT = Parentage o f t h e mortgage p o o l l o c a t e d i n O n t a r i o GDALB = Parentage o f t h e mortgage p o o l l o c a t e d i n A l b e r t a GDBC = Parentage o f t h e mortgage p o o l l o c a t e d i n B r i t i s h Columbia Prepayment p r o v i s i o n MONTHLY ANNUAL ADDIT = Maximum i n c r e a s e i n monthly payment w i t h o u t p e n a l t y = Maximum annua l d e c r e a s e i n o u t s t a n d i n g b a l a n c e w i t h o u t p e n a l t y = 0 I f no a d d i t i o n a l charge o t h e r than 3 month i n t e r e s t on prepayment = 1 A d d i t i o n a l c h a r g e s on prepayment TABLE 2 STATISTICS OF DEPENDENT VARIABLE DEPENDENT VARIABLE: OBSERVATIONS: MEAN: STANDARD DEVIATION: VARIANCE: MINIMUM: MAXIMUM: PREPAY 187 0.0028 0.0048 0.000023 0.0 0.0209 TABLES 54 TABLE 3 REFINANCING BENEFIT EQUATION: PREPAY = f(REFINAN) E s t i m a t e d V a r i a b l e C o e f f i c i e n t (T S t a t i s t i c ) REFINAN 0.01 (0.91) N = 187 R-SQUARE = 0.01 TABLES 55 TABLE 4 HOUSING TURNOVER EQUATION: PREPAY = f(HSTART, HSALES) Estimated V a r i a b l e C o e f f i c i e n t (T S t a t i s t i c ) HSTART 1.09 (1.20) HSALES 0.62 (1.43) N = 187 R-SQUARE = 0.02 TABLES 56 TABLE 5 PENALTIES ON PREPAYMENT EQUATION: PREPAY = f (PENALTY, RATEDIF, INSTIT) E s t i m a t e d V a r i a b l e C o e f f i c i e n t (T S t a t i s t i c ) PENALTY 29.92 ( 1 8 . 7 2 ) * * * RATEDIF -0 .002 ( -0.57) INSTIT 0.001 ( 3 . 5 7 ) * * N = 187 R-SQUARE = 0.71 * * S i g n i f i c a n t a t the .95 l e v e l o f c o n f i d e n c e * * * S i g n i f i c a n t a t the .99 l e v e l o f c o n f i d e n c e TABLES 57 TABLE 6 ECONOMIC INDICATORS AND FINANCIAL RATES EQUATION: PREPAY = f ( C P I , UNEMPLO, SAVING, T B I L L , GBOND) E s t i m a t e d V a r i a b l e C o e f f i c i e n t (T S t a t i s t i c ) CPI 0.66 ( 2 . 0 9 ) * * UNEMPLO - 0 . 0 5 (-0.20) SAVING - 0 . 1 3 (-0.31) -0.38# (-2.39)# * * TB ILL -0 .001 - 0 . 4 3 GBOND -0 .001 - 0 . 5 3 N = 187 R-SQUARE = 0.08 # When TBILL and GBOND a r e not i n c l u d e * * S i g n i f i c a n t a t t h e .95 l e v e l o f c o n f i d e n c e TABLES 58 TABLE 7 GEOGRAPHIC DISTRIBUTION EQUATION: PREPAY = f(GDQUE, GDONT, GDALB, GDBC) V a r i a b l e E s timated C o e f f i c i e n t (T S t a t i s t i c ) GDQUE -0.03 (-4.58)*** GDONT -0. 03 (-5.22)*** GDALB -0.03 (-5.45)*** GDBC -0.03 (-5.41)*** N = 187 R-SQUARE = 0.21 *** S i g n i f i c a n t a t the .99 l e v e l o f c o n f i d e n c e TABLES 59 TABLE 8 GEOGRAPHIC DISTRIBUTION EQUATION: PREPAY = f(GDAQUE, GDAONT, GDAALB, GDABC) V a r i a b l e E s timated C o e f f i c i e n t (T S t a t i s t i c ) GDAQUE GDAONT GDAALB GDABC 0.003 (0.74) -0.001 (-1.03) -0.001 (-1.81) -0.006 (-1.75) N = 187 R-SQUARE = 0.09 TABLES 60 TABLE 9 PREPAYMENT PROVISION EQUATION: PREPAY = f(MONTHLY, ANNUAL, ADDIT) E s t i m a t e d V a r i a b l e C o e f f i c i e n t (T S t a t i s t i c ) MONTHLY 0.006 ( 6 . 7 9 ) * * * ANNUAL 0.04 ( 1 . 9 5 ) * ADDIT -0 .0003 ( -0.38) N = 187 R-SQUARE = 0.2862 * S i g n i f i c a n t a t the .90 l e v e l o f c o n f i d e n c e * * * S i g n i f i c a n t a t the .99 l e v e l o f c o n f i d e n c e TABLES 61 TABLE 10 COMBINED RESULTS EQUATION: PREPAY = f (PENALTY, MONTHLY, ANNUAL) E s t i m a t e d V a r i a b l e C o e f f i c i e n t (T S t a t i s t i c ) PENALTY 0.23 ( 9 . 7 7 ) * * * MONTHLY 0.003 ( 5 . 3 2 ) * * * ANNUAL 0.04 ( 2 . 3 4 ) * * N = 187 R-SQUARE = 0.5306 * * S i g n i f i c a n t a t the .95 l e v e l o f c o n f i d e n c e * * * S i g n i f i c a n t a t the .99 l e v e l o f c o n f i d e n c e TABLES 62 TABLE 11 FINAL ESTIMATION EQUATION: PREPAY = f(REFINAN, HSTART, HSALES, CPI, UNEMPLO, SAVING, PENALTY, RATEDIF, INSTIT, GDQUE, GDONT, GDALB, GDBC, MONTHLY, ANNUAL, ADDIT) V a r i a b l e E s t i m a t e d C o e f f i c i e n t (T S t a t i s t i c ) REFINAN HSTART HSALES CPI UNEMPLO SAVING PENALTY RATEDIF INSTIT GDQUE GDONT 0.02 (1.83)** 1.74 (1.70)** -0.11 (-0.25) -0. 06 (-0.29) -0.15 (-1.23) -0.002 (-0.02) 31.45 21.45*** 0.003 (0.89) 0.0004 (0.62) 0.007 (1.31) 0.01 (2.09)** GDALB 0.01 (1.90)** TABLES 63 GDBC 0.01 (2.02)** MONTHLY 0.004 (5.95)*** ANNUAL 0.03 (3.13)*** ADDIT -0.003 (-4.53)*** N = 187 R-SQUARE = 0.82 * S i g n i f i c a n t a t the .90 l e v e l o f c o n f i d e n c e ** S i g n i f i c a n t a t the .95 l e v e l o f c o n f i d e n c e *** S i g n i f i c a n t a t the .99 l e v e l o f c o n f i d e n c e TABLES 64 TABLE 12 FINAL ESTIMATION (STEPWISE REGRESSION) EQUATION: PREPAY = f(PENALTY, ADDIT, MONTHLY, GDQUE, ANNUAL, HSALES, CPI, UNEMPLO) Estimated V a r i a b l e C o e f f i c i e n t (T S t a t i s t i c ) PENALTY 30.26 22.08*** ADDIT -0.002 (-3.82)*** MONTHLY 0.003 (6.05)*** GDQUE -0.004 (-5.21)*** ANNUAL 0.04 (3.18)*** HSALES -0.45 (-2.15)*** N = 187 R-SQUARE = 0.81 *** S i g n i f i c a n t a t the .99 l e v e l o f c o n f i d e n c e BIBLIOGRAPHY 65 BIBLIOGRAPHY C a p o z z a , Dennis R . , and George W. Gau, "Opt ima l Mortgage Inst rument D e s i g n s " , Nor th Amer ican Hous ing Markets i n t o the  T w e n t y - F i r s t C e n t u r y . B a l l i n g e r P u b l i s h i n g Company, Cambr idge , M a s s a c h u s e t t s , 1983. F o s t e r , C h e s t e r , and Rober t Van O r d e r , "An O p t i o n - B a s e d Model o f Mortgage D e f a u l t " , Hous ing F i n a n c e Review, v o l . 3 , n o . 4 , O c t o b e r 1984, p .351 -372 . Cox, K e v i n , and Mar ian S t i n s o n , " T r u s t O f f e r i n g 2 0 - y e a r M o r t g a g e " , The G lobe and M a i l . March 5, 1988. C r i t c h l e y , B a r r y , " F i n a n c i a l L e t t e r " , F i n a n c i a l P o s t . November 24, 1986. Dunn, Kenneth B . , and C h e s t e r S . S p a t t , "An A n a l y s i s o f Mortgage C o n t r a c t i n g : Prepayment P e n a l t i e s and the D u e - o n -s a l e C l a u s e " , The J o u r n a l o f F i n a n c e , v o l . X L , n o . 1, March 1985. G r e e n , J e r r y , and John B. Shoven, "The E f f e c t s o f I n t e r e s t R a t e s on Mortgage Prepayments" ' J o u r n a l o f Money. C r e d i t , and  B a n k i n g . v o l . 18, n o . 1, F e b r u a r y 1986. H a l l , A rden R . , " V a l u i n g the Mortgage B o r r o w e r ' s Prepayment O p t i o n " , AREUEA J o u r n a l , v o l . 1 3 , n o . 3 , 1985, p .229 -247 . Hu, J o s e p h C . , "Prepayment P r o j e c t i o n s " , Mortgage B a n k i n g . O c t o b e r 1987, p . 5 5 - 5 9 . K i r s c h n e r , L a r r y , "MBSs Made S i m p l e " , Mortgage B a n k i n g . May 1987, p . 6 7 - 7 4 . L e a , M i c h a e l J . , and P e t e r M. Z o r n , " A d j u s t a b l e - R a t e M o r t g a g e s , Economic F l u c t u a t i o n , and Lender P o r t f o l i o " , AREUEA J o u r n a l , v o l . 1 4 , n o . 3 , 1986,432-447. M a c B a i n , M i c h a e l W. , and C a r l o G u a l t i e r i , "Mortgage Backed S e c u r i t i e s - An Overview o f Prepayment" , R e s o u r c e . September 1987, p . 9 -14 . P i n k u s , S c o t t M . , and M a r i e A . Chandoha, " I m p l i e d D u r a t i o n " , Secondary Mortgage M a r k e t s , summer 1986, p . 7 - 1 3 . S h i l l i n g , James D . , and C . F . S i r m a n s , " P r i c i n g F a s t - P a y Mor tgages : Some S i m u l a t i o n R e s u l t s " , The J o u r n a l o f F i n a n c i a l  R e s e a r c h . v o l . X , n o . l , S p r i n g 1987, p . 2 5 - 3 2 . S i e g e l , Jeremy J . , "The Mortgage R e f i n a n c i n g D e c i s i o n " , Hous ing F i n a n c e Review, v o l . 3 , n o . l , J a n u a r y 1984, p . 9 1 - 9 7 . BIBLIOGRAPHY 66 Solomon, Hyman, "Ottawa Backing the MBS Market", F i n a n c i a l  Post. J u l y 27, 1987. Zemon, Ray B., " P o r t f o l i o S t r a t e g i e s U s i n g Mortgage-Backed S e c u r i t i e s " from New Developments i n Mortgage-Backed  S e c u r i t i e s , The I n s t i t u t e o f Chartered F i n a n c i a l A n a l y s t s , Washington, D.C, May 22 1984. 

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