Treasury Yields and Corporate Bond Yield Spreads: An Empirical Analysis
Abstract
This paper empirically examines the relation between the Treasury term structure and spreads of investment grade corporate bond yields over Treasuries. I find that noncallable bond yield spreads fall when the level of the Treasury term structure rises. The extent of this decline depends on the initial credit quality of the bond; the decline is small for Aaa-rated bonds and large for Baa-rated bonds. The role of the business cycle in generating this pattern is explored, as is the link between yield spreads and default risk. I also argue that yield spreads based on commonly-used bond yield indexes are contaminated in two important ways. The first is that they are "refreshed" indexes, which hold credit ratings constant over time; the second is that they usually are constructed with both callable and noncallable bonds. The impact of both of these problems is examined.
T r e a s u r y y i e l d s a n d c o r p o r a t e b o n d y i e l d s p r e a d s : A n e m p i r i c a l a n a l y s i s G r e g o r y R . D u (cid:11) e e F e d e r a l R e s e r v e B o a r d M a il S t o p 9 1 W a s h in g t o n , D C 2 0 5 5 1 2 0 2 - 4 5 2 - 3 0 5 5 g d u (cid:11) e e @ fr b .g o v F ir s t v e r s io n J a n u a r y 1 9 9 5 C u r r e n t v e r s io n M a y 1 9 9 6 p r e v io u s ly c ir c u la t e d u n d e r t h e t it le T h e v a r ia t io n o f d e fa u lt r is k w it h T r e a s u r y y ie ld s A b s t r a c t T h is p a p e r e m p ir ic a lly e x a m in e s t h e r e la t io n b e t w e e n t h e T r e a s u r y t e r m s t r u c t u r e a n d s p r e a d s o f in v e s t m e n t g r a d e c o r p o r a t e b o n d y ie ld s o v e r T r e a s u r ie s . I (cid:12) n d t h a t n o n c a lla b le b o n d y ie ld s p r e a d s fa ll w h e n t h e le v e l o f t h e T r e a s u r y t e r m s t r u c t u r e r is e s . T h e e x t e n t o f t h is d e c lin e d e p e n d s o n t h e in it ia l c r e d it q u a lit y o f t h e b o n d ; t h e d e c lin e is s m a ll fo r A a a r a t e d b o n d s a n d la r g e fo r B a a - r a t e d b o n d s . T h e r o le o f t h e b u s in e s s c y c le in g e n e r a t in g t h is p a t t e r n is e x p lo r e d , a s is t h e lin k b e t w e e n y ie ld s p r e a d s a n d d e fa u lt r is k . I a ls o a r g u e t h a t y ie ld s p r e a d s b a s e d o n c o m m o n ly - u s e d b o n d y ie ld in d e x e s a r e c o n t a m in a t e d in t w o im p o r t a n t w a y s . T h e (cid:12) r s t is t h a t t h e y a r e \ r e fr e s h e d " in d e x e s , w h ic h h o ld c r e d it r a t in g s c o n s t a n t o v e r t im e ; t h e s e c o n d is t h a t t h e y u s u a lly a r e c o n s t r u c t e d w it h b o t h c a lla b le a n d n o n c a lla b le b o n d s . T h e im p a c t o f b o t h o f t h e s e p r o b le m s is e x a m in e d . J E L C la s s i(cid:12) c a t io n : G 1 3 I t h a n k F is c h e r B la c k , K e n S in g le t o n a n d s e m in a r p a r t ic ip a n t s a t t h e F e d e r a l R e s e r v e B o a r d ’s C o n fe r e n c e o n R is k M e a s u r e m e n t a n d S y s t e m ic R is k fo r h e lp fu l c o m m e n t s . N id a l A b u - S a b a p r o v id e d v a lu a b le r e s e a r c h a s s is t a n c e . A ll e r r o r s a r e m y o w n . T h e a n a ly s is a n d c o n c lu s io n s o f t h is p a p e r a r e t h o s e o f t h e a u t h o r a n d d o n o t in d ic a t e c o n c u r r e n c e b y o t h e r m e m b e r s o f t h e r e s e a r c h s t a (cid:11) , b y t h e B o a r d o f G o v e r n o r s , o r b y t h e F e d e r a l R e s e r v e B a n k s .
1 . I n t r o d u c t i o n T h is p a p e r e m p ir ic a lly e x a m in e s t h e r e la t io n b e t w e e n t h e T r e a s u r y t e r m s t r u c t u r e a n d s p r e a d s o f c o r p o r a t e b o n d y ie ld s o v e r T r e a s u r ie s . T h is r e la t io n is o f in t e r e s t in it s o w n r ig h t b e c a u s e it is e s s e n t ia l t o t h e c a lib r a t io n a n d t e s t in g o f m o d e ls t h a t p r ic e c r e d it s e n s it iv e in s t r u m e n t s . M o r e b r o a d ly , t h is in v e s t ig a t io n a llo w s u s t o a d d r e s s t h e n a t u r e o f t h e b ia s e s in c o m m o n ly - u s e d in d e x e s o f c o r p o r a t e b o n d y ie ld s ; b ia s e s in d u c e d b y t h e w a y t h e s e in d e x e s a r e c o n s t r u c t e d . I n d e x e s o f c o r p o r a t e b o n d y ie ld s a r e t y p ic a lly a v e r a g e s o f y ie ld s o n a s e t o f b o n d s t h a t a r e c h o s e n b a s e d o n t h e c h a r a c t e r is t ic s o f t h e b o n d a t t h e t im e t h e a v e r a g e is c o m p u t e d . F o r e x a m p le , t o d a y ’s M o o d y ’s I n d u s t r ia ls A a a - r a t e d B o n d Y ie ld is t o d a y ’s m e a n y ie ld o n a s e t o f A a a - r a t e d b o n d s is s u e d b y in d u s t r ia l (cid:12) r m s t h a t h a v e c u r r e n t p r ic e s n o t t o o fa r a w a y fr o m p a r a n d h a v e r e la t iv e ly lo n g r e m a in in g m a t u r it ie s . M u c h a c a d e m ic w o r k in t e r p r e t s c h a n g e s in y ie ld s p r e a d s c o n s t r u c t e d w it h s u c h in d e x e s a s in d ic a t iv e o f c h a n g e s in d e fa u lt r is k . T h is in t e r p r e t a t io n is s u b je c t t o a n u m b e r o f p o t e n t ia l p r o b le m s , t w o o f w h ic h a r e lik e ly m o r e im p o r t a n t t h a n o t h e r s . T h e (cid:12) r s t m a jo r p r o b le m , a s d is c u s s e d b y D u (cid:14) e a n d S in g le t o n ( 1 9 9 5 ) in t h e c o n t e x t o f in d e x e s o f n e w - is s u e s w a p s p r e a d s , is t h a t t h e s e a r e \ r e fr e s h e d " in d e x e s . T h e c h a n g e in t h e y ie ld fr o m o n e p e r io d t o t h e n e x t d o e s n o t m e a s u r e t h e c h a n g e in t h e m e a n y ie ld o n a (cid:12) x e d s e t o f b o n d s , b u t r a t h e r t h e c h a n g e in t h e m e a n y ie ld o n t w o s e q u e n t ia l s e t s o f b o n d s t h a t s h a r e t h e s a m e fe a t u r e s ; in p a r t ic u la r , t h a t s h a r e t h e s a m e c r e d it r a t in g . H e n c e u s in g t h e s e in d e x e s t o in v e s t ig a t e in t e r t e m p o r a l c h a n g e s in b o n d s ’ d e fa u lt r is k is p r o b le m a t ic b e c a u s e t h e in d e x e s h o ld c o n s t a n t a m e a s u r e o f c r e d it q u a lit y . T h e s e c o n d m a jo r p r o b le m is t h a t c o r p o r a t e b o n d y ie ld in d e x e s a r e o ft e n c o n s t r u c t e d u s in g b o t h c a lla b le a n d n o n c a lla b le b o n d s . G iv e n t h e o b je c t iv e s o f t h o s e c o n s t r u c t in g t h e in d e x e s , s u c h a s M o o d y ’s , t h is is s e n s ib le . U n t il r e la t iv e ly r e c e n t ly , fe w c o r p o r a t io n s is s u e d n o n c a lla b le b o n d s , h e n c e a n in d e x d e s ig n e d t o m e a s u r e t h e y ie ld o n a t y p ic a l c o r p o r a t e b o n d w o u ld h a v e t o b e c o n s t r u c t e d p r im a r ily w it h c a lla b le b o n d s . H o w e v e r , y ie ld s o n c a lla b le b o n d s w ill b e a (cid:11) e c t e d b y t h e v a lu e o f t h e o p t io n t o c a ll. V a r ia t io n s o v e r t im e in y ie ld s p r e a d s o n c a lla b le b o n d s w ill r e (cid:13) e c t , in p a r t , v a r ia t io n s in t h e o p t io n v a lu e . O t h e r , le s s im p o r t a n t p r o b le m s t h a t a (cid:11) e c t m o s t in d e x e s o f c o r p o r a t e b o n d y ie ld s in c lu d e c o u p o n - in d u c e d c h a n g e s in d u r a t io n a n d s t a t e t a x e s . G iv e n a ll o f t h e s e b ia s e s , h o w a p p r o p r ia t e is t h e a s s u m p t io n t h a t c h a n g e s in y ie ld s p r e a d s fo r s u c h in d e x e s a r e d r iv e n b y c h a n g e s in d e fa u lt r is k ? I u s e m o n t h - e n d d a t a o n in d iv id u a l in v e s t m e n t - g r a d e b o n d s in c lu d e d in L e h m a n B r o t h e r s B o n d I n d e x e s fr o m J a n u a r y 1 9 8 5 t h r o u g h M a r c h 1 9 9 5 t o e x a m in e h o w y ie ld s p r e a d s v a r y w it h c h a n g e s in t h e le v e l a n d s lo p e o f t h e T r e a s u r y t e r m s t r u c t u r e . T o illu s t r a t e t h e r e s u lt s d is c u s s e d in t h is p a p e r , c o n s id e r t h e a v e r a g e m o n t h - t y ie ld s p r e a d ( o v e r t h e a p p r o p r ia t e 1
T r e a s u r y in s t r u m e n t ) fo r a g r o u p o f n o n c a lla b le c o u p o n b o n d s w it h id e n t ic a l c r e d it r a t in g s a n d s im ila r m a t u r it ie s . I f t h e T r e a s u r y y ie ld c u r v e s h ift s d o w n b y 1 0 b a s is p o in t s b e t w e e n m o n t h s t a n d t + 1 , t h e a v e r a g e y ie ld s p r e a d o n t h is g r o u p o f b o n d s r is e s b y b e t w e e n 0 .6 a n d 3 .6 b a s is p o in t s . I n o t h e r w o r d s , t h e p r ic e in c r e a s e in a c o r p o r a t e b o n d t h a t a c c o m p a n ie s a g iv e n d e c r e a s e in T r e a s u r y y ie ld s is b e t w e e n 6 a n d 3 6 p e r c e n t le s s t h a n it w o u ld b e if b o n d y ie ld s a n d T r e a s u r y y ie ld s m o v e d o n e - fo r - o n e . T h e r e s p o n s iv e n e s s o f t h e s p r e a d is w e a k fo r h ig h - r a t e d b o n d s ( e .g ., it is s t a t is t ic a lly in s ig n i(cid:12) c a n t fo r A a a - r a t e d b o n d s ) a n d s t r o n g fo r lo w - r a t e d b o n d s . A lt h o u g h t h e s e r e s u lt s a r e fo r c o u p o n b o n d s , a n y c o u p o n - in d u c e d b ia s in t h e s e r e s u lt s is q u it e s m a ll. I a ls o c o n c lu d e t h a t , a ft e r a d ju s t in g fo r c o u p o n - in d u c e d b ia s e s , c h a n g e s in t h e s lo p e o f t h e t e r m s t r u c t u r e o f T r e a s u r y y ie ld s a r e v e r y w e a k ly n e g a t iv e ly r e la t e d t o c h a n g e s in y ie ld s p r e a d s . S u r p r is in g ly , a lt h o u g h b o t h y ie ld s o n T r e a s u r y b o n d s a n d c o r p o r a t e b o n d y ie ld s p r e a d s a r e lin k e d t o t h e b u s in e s s c y c le ( w e ll- k n o w n fa c t s t h a t I c o n (cid:12) r m h e r e ) , I (cid:12) n d it d i(cid:14) c u lt t o e x p la in t h e r e la t io n b e t w e e n y ie ld s p r e a d s a n d T r e a s u r y y ie ld s in t e r m s o f v a r ia t io n s in d e fa u lt r is k d r iv e n b y t h e b u s in e s s c y c le . I (cid:12) n d t h a t , c o m p a r e d w it h t h e r e s u lt s d is c u s s e d a b o v e , c h a n g e s in y ie ld s p r e a d s c o n s t r u c t e d w it h r e fr e s h e d in d e x e s o f n o n c a lla b le b o n d s h a v e m u c h w e a k e r lin k s t o c h a n g e s in T r e a s u r y y ie ld s . T h is e v id e n c e in d ic a t e s t h a t r e fr e s h e d in d e x e s u n d e r r e a c t t o v a r ia t io n s in c r e d it q u a lit y b e c a u s e c h a n g e s in c r e d it r a t in g s c a p t u r e p a r t o f t h e v a r ia b ilit y o f y ie ld s p r e a d s o v e r t im e . B y c o n t r a s t , c h a n g e s in y ie ld s p r e a d s c o n s t r u c t e d w it h in d e x e s o f c a lla b le b o n d s h a v e m u c h s t r o n g e r lin k s t o c h a n g e s in T r e a s u r y y ie ld s b e c a u s e t h e v a lu e o f t h e c a ll o p t io n n e g a t iv e ly v a r ie s w it h T r e a s u r y y ie ld s . F o r h ig h - p r ic e d c a lla b le b o n d s , m o s t o f t h e v a r ia t io n in y ie ld s p r e a d s is c a u s e d b y v a r ia t io n s in t h e v a lu e o f t h e c a ll o p t io n . T h e n e x t s e c t io n d is c u s s e s w h y t h e r e la t io n b e t w e e n y ie ld s p r e a d s a n d T r e a s u r y y ie ld s is im p o r t a n t a n d r e v ie w s s o m e p r e v io u s r e s e a r c h . T h e t h ir d s e c t io n d e s c r ib e s t h e d a t a b a s e I u s e . T h e fo u r t h s e c t io n a n a ly z e s t h e r e la t io n b e t w e e n y ie ld s p r e a d s o n n o n c a lla b le b o n d s a n d T r e a s u r y y ie ld s . I t a ls o d is c u s s e s p o s s ib le b ia s e s in d u c e d b y c o u p o n s a n d s t a t e t a x e s . T h e (cid:12) ft h s e c t io n a t t e m p t s t o in t e r p r e t t h is r e la t io n in t e r m s o f d e fa u lt r is k a n d t h e b u s in e s s c y c le . T h e s ix t h s e c t io n e x p lo r e s t h e b e h a v io r o f y ie ld s p r e a d s c o n s t r u c t e d w it h b o t h r e fr e s h e d in d e x e s o f n o n c a lla b le b o n d y ie ld s a n d in d e x e s o f c a lla b le b o n d y ie ld s . C o n c lu d in g c o m m e n t s a r e c o n t a in e d in t h e (cid:12) n a l s e c t io n . 2 . Y i e l d s p r e a d s a n d t h e T r e a s u r y t e r m s t r u c t u r e : A n o v e r v i e w P r ic e s o f c r e d it - s e n s it iv e in s t r u m e n t s d e p e n d o n t h e c o v a r ia n c e s b e t w e e n d is c o u n t e d fu t u r e o b lig a t e d c a s h (cid:13) o w s a n d t h e p r o b a b ilit ie s o f d e fa u lt a t fu t u r e d a t e s . H e n c e in o r d e r t o p a r a m e t e r iz e p r ic in g m o d e ls fo r c r e d it - s e n s it iv e in s t r u m e n t s , (cid:12) n a n c ia l e c o n o m is t s m u s t 2
u n d e r s t a n d t h e jo in t b e h a v io r o f d e fa u lt - fr e e d is c o u n t r a t e s a n d t h e m a r k e t ’s p e r c e p t io n o f d e fa u lt r is k . R o u g h ly s p e a k in g , is t h e r is k o f d e fa u lt la r g e r o r s m a lle r w h e n t h e p r e s e n t v a lu e o f t h e o b lig a t e d c a s h (cid:13) o w s is h ig h ? A n u m b e r o f m o d e ls p r ic e in t e r e s t r a t e s e n s it iv e , d e fa u lt - r is k y in s t r u m e n t s , s u c h a s c o r p o r a t e b o n d s a n d in t e r e s t r a t e s w a p s , a llo w in g fo r d e p e n d e n c e b e t w e e n t h e p r o c e s s g e n e r a t in g d e fa u lt a n d t h e p r o c e s s g e n e r a t in g in t e r e s t r a t e s . O n e c la s s o f m o d e ls fo llo w s t h e p a t h la id b y M e r t o n ( 1 9 7 4 ) a n d m o d e ls d e fa u lt a s a fu n c t io n o f t h e v a lu e o f t h e (cid:12) r m ; c h a n g e s in t h e v a lu e o f t h e (cid:12) r m c a n b e c o r r e la t e d w it h in t e r e s t r a t e s . T h is c la s s in c lu d e s t h e m o d e ls o f C o o p e r a n d M e llo ( 1 9 9 1 ) , A b k e n ( 1 9 9 3 ) , S h im k o , T e jim a , a n d v a n D e v e n t e r ( 1 9 9 3 ) , a n d L o n g s t a (cid:11) a n d S c h w a r t z ( 1 9 9 5 ) . T h e y (cid:12) n d t h a t t h e p r ic e s o f t h e s e in s t r u m e n t s c a n b e v e r y s e n s it iv e t o t h e c o r r e la t io n b e t w e e n t h e (cid:12) r m ’s v a lu e a n d in t e r e s t r a t e s . A n o t h e r , m o r e r e c e n t c la s s o f m o d e ls s im p ly s p e c i(cid:12) e s a d e fa u lt p r o c e s s w it h o u t t y in g d e fa u lt t o t h e v a lu e o f t h e (cid:12) r m . T h e p r o b a b ilit y o f d e fa u lt c a n b e c o r r e la t e d w it h in t e r e s t r a t e s , a s in L a n d o ( 1 9 9 4 ) a n d D u (cid:14) e a n d H u a n g ( 1 9 9 5 ) . H o w e v e r , o n e r e a s o n t h is c la s s o f m o d e ls w a s d e v e lo p e d is t h a t t h e m o d e ls a r e v e r y t r a c t a b le if d e fa u lt p r o b a b ilit ie s a r e in d e p e n d e n t o f in t e r e s t r a t e s . H e n c e e m p ir ic a l im p le m e n t a t io n h a s c o n c e n t r a t e d o n t h e c a s e o f in d e p e n d e n c e , a s in J a r r o w , L a n d o , a n d T u r n b u ll ( 1 9 9 4 ) a n d M a d a n a n d U n a l ( 1 9 9 4 ) . I f t h e e v id e n c e h e r e in d ic a t e s t h a t in d e p e n d e n c e is a p o o r a s s u m p t io n , t h e n a m a jo r a d v a n t a g e o f t h is c la s s o f m o d e ls d is a p p e a r s . M o d e ls o f n o n c a lla b le z e r o - c o u p o n c o r p o r a t e b o n d p r ic e s , s u c h a s L a n d o ( 1 9 9 4 ) a n d L o n g s t a (cid:11) a n d S c h w a r t z ( 1 9 9 5 ) , im p ly t h a t v a r ia t io n s o v e r t im e in d e fa u lt r is k a r e a c c o m p a n ie d b y v a r ia t io n s in y ie ld s p r e a d s , h e n c e p a t t e r n s in t h e b e h a v io r o f s p r e a d s c a n b e u s e d t o m a k e in fe r e n c e s a b o u t t h e r e la t io n b e t w e e n d e fa u lt r is k a n d in t e r e s t r a t e s . L o n g s t a (cid:11) a n d S c h w a r t z ( 1 9 9 5 ) (cid:12) n d t h a t s p r e a d s b e t w e e n M o o d y ’s B o n d Y ie ld I n d e x e s a n d T r e a s u r y b o n d y ie ld s a r e s t r o n g ly n e g a t iv e ly r e la t e d t o T r e a s u r y y ie ld s . H o w e v e r , o v e r t h e ir s a m p le p e r io d , M o o d y ’s I n d e x e s w e r e la r g e ly c o m p o s e d o f y ie ld s o n c a lla b le b o n d s . I a r g u e la t e r t h a t t h is s t r o n g n e g a t iv e r e la t io n is d r iv e n b y v a r ia t io n s in t h e v a lu e o f t h e c a ll o p t io n . K w a n ( 1 9 9 6 ) (cid:12) n d s s im ila r r e s u lt s ( a lt h o u g h h is o b je c t iv e is d i(cid:11) e r e n t ) u s in g in d iv id u a l b o n d y ie ld s , b u t h e a ls o in c lu d e s b o t h c a lla b le a n d n o n c a lla b le b o n d s in h is a n a ly s is . T h is c a ll- o p t io n b ia s is a v o id e d b y I w a n o w s k i a n d C h a n d r a ( 1 9 9 5 ) , w h o e x a m in e t h e r e la t io n b e t w e e n T r e a s u r y y ie ld s a n d y ie ld s p r e a d s o f n o n c a lla b le b o n d s d u r in g t h e la t e 1 9 8 0 s a n d e a r ly 1 9 9 0 s . T h e y (cid:12) n d a s m a ll n e g a t iv e r e la t io n b e t w e e n t h e le v e l o f t h e T r e a s u r y y ie ld a n d y ie ld s p r e a d s , a n d n o s ig n i(cid:12) c a n t r e la t io n b e t w e e n t h e T r e a s u r y s lo p e a n d s p r e a d s . H o w e v e r , t h e y u s e r e fr e s h e d y ie ld in d e x e s in t h e ir a n a ly s is . I a r g u e la t e r t h a t t h is c h o ic e u n d e r e s t im a t e s t h e r e s p o n s iv e n e s s o f y ie ld s p r e a d s t o T r e a s u r y y ie ld s b e c a u s e it c a n n o t c a p t u r e c h a n g e s in y ie ld s p r e a d s o n b o n d s t h a t w e r e u p g r a d e d o r d o w n g r a d e d in t h e m o n t h . ( T h e M o o d y ’s in d e x e s u s e d b y L o n g s t a (cid:11) a n d S c h w a r t z a r e a ls o r e fr e s h e d in d e x e s , b u t t h e 3
e (cid:11) e c t o f t h e c a ll o p t io n d o m in a t e s t h e e (cid:11) e c t o f t h e r e fr e s h e d in d e x e s .) A r e la t e d lit e r a t u r e e x a m in e s t h e r e t u r n p e r fo r m a n c e o f lo w - g r a d e c o r p o r a t e b o n d s r e la t iv e t o o t h e r a s s e t s . T h e a d v a n t a g e o f lo o k in g a t b o n d r e t u r n s in s t e a d o f y ie ld in d e x e s is t h a t b o n d r e t u r n s a r e n o t s u b je c t t o t h e p r o b le m o f r e fr e s h e d in d e x e s . C o r n e ll a n d G r e e n ( 1 9 9 1 ) (cid:12) n d t h a t r e t u r n s t o lo w - g r a d e b o n d s a r e m u c h le s s r e s p o n s iv e t o c h a n g e s in T r e a s u r y y ie ld s t h a n a r e r e t u r n s t o h ig h - g r a d e b o n d s . T h e y a t t r ib u t e t h is r e s u lt t o t h e lo w e r d u r a t io n o f lo w - g r a d e b o n d s , o w in g t o le s s r e s t r ic t iv e c a ll fe a t u r e s a n d h ig h e r c o u p o n s . A lt h o u g h c a lla b ilit y lik e ly a c c o u n t s fo r p a r t o f t h is r e s u lt , I (cid:12) n d t h a t lo w - q u a lit y n o n c a lla b le b o n d y ie ld s p r e a d s a r e v e r y s e n s it iv e t o T r e a s u r y y ie ld s , a n d t h a t t h is r e s u lt is n o t d r iv e n b y h ig h c o u p o n p a y m e n t s . H e n c e p a r t o f t h e w e a k r e s p o n s iv e n e s s o f lo w - g r a d e b o n d r e t u r n s t o c h a n g e s in T r e a s u r y y ie ld s lik e ly is d r iv e n b y a n e g a t iv e c o r r e la t io n b e t w e e n in t e r e s t r a t e r is k a n d d e fa u lt r is k . 3 . D a t a b a s e d e s c r i p t i o n T h e F ix e d I n c o m e D a t a b a s e fr o m t h e U n iv e r s it y o f W is c o n s in - M ilw a u k e e c o n s is t s o f m o n t h - e n d d a t a o n t h e b o n d s t h a t m a k e u p t h e L e h m a n B r o t h e r s B o n d I n d e x e s . T h e v e r s io n u s e d h e r e c o v e r s J a n u a r y 1 9 7 3 t h r o u g h M a r c h 1 9 9 5 . I n a d d it io n t o r e p o r t in g m o n t h e n d p r ic e s a n d y ie ld s , t h e d a t a b a s e r e p o r t s m a t u r it y , v a r io u s c a ll, p u t , a n d s in k in g fu n d in fo r m a t io n , a n d a b u s in e s s s e c t o r fo r e a c h b o n d : e .g ., in d u s t r ia l, u t ilit ie s , a n d (cid:12) n a n c ia l. I t a ls o r e p o r t s m o n t h ly M o o d y ’s a n d S & P r a t in g s fo r e a c h b o n d . U n t il 1 9 9 2 t h e L e h m a n B r o t h e r s I n d e x e s c o v e r e d o n ly in v e s t m e n t - g r a d e (cid:12) r m s , h e n c e t h e a n a ly s is in t h is p a p e r is r e s t r ic t e d t o b o n d s r a t e d B a a o r h ig h e r b y M o o d y ’s ( o r B B B b y S & P ) . T h e s e c o n d a r y m a r k e t fo r c o r p o r a t e b o n d s is v e r y illiq u id c o m p a r e d t o t h e s e c o n d a r y m a r k e t fo r c o r p o r a t e e q u it y ( s t o c k s ) , w h ic h p o s e s p r o b le m s fo r r e s e a c h e r s w h o w is h t o u s e c o r p o r a t e b o n d p r ic e s . N u n n , H ill, a n d S c h n e e w e is ( 1 9 8 6 ) a n d W a r g a ( 1 9 9 1 ) d is c u s s t h e s e p r o b le m s in d e t a il. A u s e fu l fe a t u r e o f t h is d a t a s e t is t h a t it d is t in g u is h e s b e t w e e n \ q u o t e " p r ic e s a n d \ m a t r ix " p r ic e s . Q u o t e p r ic e s a r e b id p r ic e s e s t a b lis h e d b y L e h m a n t r a d e r s . I f a t r a d e r is u n w illin g t o s u p p ly a b id p r ic e b e c a u s e t h e b o n d h a s n o t t r a d e d r e c e n t ly , a m a t r ix p r ic e is c o m p u t e d . B e c a u s e q u o t e p r ic e s a r e m o r e lik e ly t o r e (cid:13) e c t a ll a v a ila b le in fo r m a t io n t h a n a r e m a t r ix p r ic e s , I u s e o n ly q u o t e p r ic e s in t h is p a p e r . F o r m o r e in fo r m a t io n o n t h is d a t a b a s e , s e e W a r g a ( 1 9 9 1 ) . M u c h o f t h e e m p ir ic a l w o r k in t h is p a p e r u s e s y ie ld s o n n o n c a lla b le b o n d s . U n fo r t u n a t e ly fo r t h is a r e a o f r e s e a r c h , c o r p o r a t io n s is s u e d fe w n o n c a lla b le b o n d s p r io r t o t h e m id - 1 9 8 0 s . F o r e x a m p le , t h e d a t a s e t h a s J a n u a r y 1 9 8 4 p r ic e s a n d y ie ld s fo r 5 ,4 9 7 s t r a ig h t b o n d s is s u e d b y in d u s t r ia l, (cid:12) n a n c ia l, o r u t ilit y (cid:12) r m s . O n ly 2 7 1 o f t h e s e b o n d s w e r e n o n c a lla b le fo r life . B y J a n u a r y 1 9 8 5 , t h e n u m b e r o f n o n c a lla b le b o n d s w it h p r ic e a n d y ie ld in fo r m a t io n h a d r is e n t o 3 8 2 ( o f 5 ,7 5 5 ) . B e g in n in g w it h 1 9 8 5 , t h e n u m b e r o f n o n c a lla b le 4
b o n d s r o s e d r a m a t ic a lly , s o t h a t t h e d a t a s e t c o n t a in s M a r c h 1 9 9 5 p r ic e a n d y ie ld in fo r m a t io n o n 2 ,8 1 4 n o n c a lla b le b o n d s ( o f 5 ,2 9 1 ) . B e c a u s e o f t h e p a u c it y o f n o n c a lla b le b o n d s in e a r lie r y e a r s , I r e s t r ic t m y a t t e n t io n t o t h e p e r io d J a n u a r y 1 9 8 5 t h r o u g h M a r c h 1 9 9 5 . 4 . A n a n a l y s i s o f n o n c a l l a b l e c o r p o r a t e b o n d y i e l d s p r e a d s I n t h is s e c t io n I e x a m in e t h e r e la t io n b e t w e e n T r e a s u r y y ie ld s a n d y ie ld s p r e a d s o n c o r p o r a t e b o n d s t h a t h a v e n o o p t io n - lik e fe a t u r e s . T h e r e fo r e I c o n s id e r o n ly t h o s e c o r p o r a t e b o n d s t h a t a r e n o n c a lla b le , n o n p u t a b le , a n d h a v e n o s in k in g fu n d o p t io n . 4 .1 . D a t a c o n s t r u c t io n I c o n s t r u c t m o n t h ly c o r p o r a t e y ie ld s , y ie ld s p r e a d s ( o v e r T r e a s u r ie s ) a n d c h a n g e s in s p r e a d s fo r fo u r b u s in e s s s e c t o r s ( in d u s t r ia l, u t ilit ie s , (cid:12) n a n c ia l, a n d t h e s e t h r e e c o m b in e d ) , fo u r r a t in g c a t e g o r ie s ( A a a , A a , A , a n d B a a ) , a n d t h r e e b a n d s o f r e m a in in g m a t u r it ie s ( 2 (cid:2) (cid:2) t o 7 y e a r s , 7 t o 1 5 y e a r s , a n d 1 5 t o 3 0 y e a r s ) . H e n c e 4 8 ( 4 4 3 ) d i(cid:11) e r e n t t im e s e r ie s o f s p r e a d s a n d c h a n g e s in s p r e a d s a r e c o n s t r u c t e d . T h e ir c o n s t r u c t io n is d e s c r ib e d in d e t a il in t h e A p p e n d ix a n d s u m m a r iz e d h e r e . M y m e a s u r e o f t h e m o n t h t y ie ld s p r e a d fo r s e c t o r s , r a t in g i , a n d r e m a in in g m a t u r it y m is d e n o t e d S . I t is t h e m e a n y ie ld s p r e a d a t t h e e n d o f m o n t h t fo r a ll b o n d s w it h s ;i;m ;t q u o t e p r ic e s in t h e s e c t o r / r a t in g / m a t u r it y g r o u p . I d e (cid:12) n e t h e m o n t h ly c h a n g e in t h e s p r e a d (cid:1) S a s t h e m e a n c h a n g e in t h e s p r e a d fr o m t t o t + 1 o n t h a t e x a c t g r o u p o f b o n d s . s ;i;m ;t+ 1 N o t e t h a t b o n d s t h a t w e r e d o w n g r a d e d b e t w e e n t a n d t + 1 o r t h a t h a v e fa lle n o u t o f t h e m a t u r it y r a n g e b e t w e e n t a n d t + 1 w ill n o t b e in c lu d e d in t h e s e t o f b o n d s u s e d t o c o n s t r u c t t h e m o n t h t + 1 s p r e a d S , b u t t h e y w ill b e in c lu d e d in m y m e a s u r e o f t h e c h a n g e s ;i;m ;t+ 1 in t h e s p r e a d fr o m m o n t h t t o m o n t h t + 1 . M o s t o f t h e r e s u lt s d is c u s s e d b e lo w u s e y ie ld s a n d s p r e a d s b a s e d o n a ll c o m b in e d b u s in e s s s e c t o r s , h e n c e I u s u a lly d r o p t h e b u s in e s s s e c t o r s u b s c r ip t s . S u m m a r y s t a t is t ic s fo r t h e s e t im e s e r ie s o f s p r e a d s a n d c h a n g e s in s p r e a d s a r e d is p la y e d in T a b le 1 . N o t e t h a t t h e r e a r e m a n y m o n t h s fo r w h ic h s p r e a d s fo r a g iv e n s e c t o r ’s A a a - r a t e d b o n d s a r e m is s in g , o w in g t o a la c k o f n o n c a lla b le A a a b o n d s . T h o s e o b s e r v a t io n s t h a t a r e n o t m is s in g a r e b a s e d o n v e r y fe w b o n d s . F o r e x a m p le , a n a v e r a g e o f t w o b o n d s a r e u s e d t o c o n s t r u c t e a c h n o n m is s in g o b s e r v a t io n fo r lo n g - t e r m in d u s t r ia l A a a b o n d s . A ls o n o t e t h a t c h a n g e s in m e a n y ie ld s p r e a d s fo r t h e c o m b in e d b u s in e s s s e c t o r s a r e t y p ic a lly p o s it iv e ly a u t o c o r r e la t e d a t o n e la g . T h is p o s it iv e a u t o c o r r e la t io n lik e ly is t h e r e s u lt o f s t a le y ie ld s p r e a d s fo r in d iv id u a l b o n d s . 5
4 .2 . T e s t M e t h o d o lo g y I n o r d e r t o in v e s t ig a t e r e la t io n s b e t w e e n c h a n g e s in y ie ld s p r e a d s a n d c h a n g e s in t h e T r e a s u r y t e r m s t r u c t u r e , I n e e d v a r ia b le s t h a t s u m m a r iz e t h e in fo r m a t io n in t h e T r e a s u r y t e r m s t r u c t u r e . L it t e r m a n a n d S c h e in k m a n ( 1 9 9 1 ) a n d C h e n a n d S c o t t ( 1 9 9 3 ) d o c u m e n t t h a t t h e v a s t m a jo r it y o f v a r ia t io n in t h e T r e a s u r y t e r m s t r u c t u r e c a n b e e x p r e s s e d in t e r m s o f c h a n g e s in t h e le v e l a n d t h e s lo p e . I t h e r e fo r e u s e t h e m o n t h ly c h a n g e in t h e t h r e e - m o n t h T r e a s u r y b ill y ie ld , d e n o t e d (cid:1) Y , a n d t h e m o n t h ly c h a n g e in t h e s p r e a d b e t w e e n t h e 3 m ;t 3 0 - y e a r c o n s t a n t m a t u r it y T r e a s u r y y ie ld a n d t h e t h r e e - m o n t h T r e a s u r y b ill y ie ld , d e n o t e d S L (cid:1) S L fo r o p e . T h e s e m o n t h ly c h a n g e s a r e m o n t h - e n d t o m o n t h - e n d c h a n g e s s o t h a t t h e y t a r e p r o p e r ly a lig n e d w it h t h e c o r p o r a t e b o n d d a t a . T o d e t e r m in e h o w c o r p o r a t e b o n d s p r e a d s v a r y w it h t h e T r e a s u r y t e r m s t r u c t u r e , I r e g r e s s c h a n g e s in s p r e a d s o n t h e fu t u r e , c u r r e n t a n d la g g e d c h a n g e s in m y T r e a s u r y t e r m s t r u c t u r e v a r ia b le s . T h e n o n - c o n t e m p o r a n e o u s c h a n g e s a r e in c lu d e d t o c o r r e c t fo r n o n t r a d in g , a n a p p r o a c h b a s e d o n S c h o le s a n d W illia m s ( 1 9 7 7 ) t h a t is u s e d b y K w a n ( 1 9 9 6 ) , C o r n e ll a n d G r e e n ( 1 9 9 1 ) , a n d o t h e r s . I t h e r e fo r e e s t im a t e r e g r e s s io n s o f t h e fo r m 1 1 (cid:0) (cid:0) (cid:1) S = b + b (cid:1) Y + b (cid:1) S L + e : ( 1 ) s ;i;m ;t+ 1 0 3 m ;j 3 m ;t+ 1 j s l;j t+ 1 j i;m ;t+ 1 (cid:0) (cid:0) j = 1 j = 1 X X T h is d e c o m p o s it io n o f t h e T r e a s u r y t e r m s t r u c t u r e o n t h e r ig h t - h a n d - s id e o f ( 1 ) is a r b it r a r y in t h e s e n s e t h a t I c o u ld h a v e m e a s u r e d c h a n g e s in t h e le v e l o f t h e t e r m s t r u c t u r e w it h c h a n g e s in t h e 3 0 - y e a r y ie ld in s t e a d o f c h a n g e s in t h e t h r e e - m o n t h b ill y ie ld . T h e fo r m o f ( 1 ) im p lie s t h a t t h e p r o p e r in t e r p r e t a t io n o f t h e s lo p e c o e (cid:14) c ie n t s is t h e e (cid:11) e c t o f a c h a n g e in t h e lo n g y ie ld h o ld in g t h e s h o r t y ie ld c o n s t a n t . 4 .3 . R e g r e s s io n r e s u lt s T a b le 2 r e p o r t s O L S e s t im a t e s o f e q u a t io n ( 1 ) fo r v a r io u s m a t u r it ie s a n d c r e d it r a t in g s . T o s a v e s p a c e , t h e o n ly r e s u lt s d is p la y e d a r e t h o s e fo r a ll t h r e e b u s in e s s s e c t o r s c o m b in e d . R e g r e s s io n s a r e r u n s e p a r a t e ly fo r e a c h m a t u r it y / c r e d it r a t in g g r o u p . I a d ju s t t h e v a r ia n c e c o v a r ia n c e m a t r ix o f t h e e s t im a t e d c o e (cid:14) c ie n t s fo r g e n e r a liz e d h e t e r o s k e d a s t ic it y a n d t w o 2 la g s o f m o v in g a v e r a g e r e s id u a ls . T h e s ig n i(cid:12) c a n c e o f a s y m p t o t ic (cid:31) t e s t s t h a t t h e s u m s o f t h e c o e (cid:14) c ie n t s o n t h e le a d in g , c o n t e m p o r a n e o u s , a n d la g g e d v a r ia b le s e q u a l z e r o a r e s h o w n in b r a c k e t s . T h e r e s u lt s in d ic a t e t h a t a n in c r e a s e in t h e le v e l o f t h e t e r m s t r u c t u r e c o r r e s p o n d s t o a d e c lin e in y ie ld s p r e a d s . T h is r e la t io n h o ld s fo r e v e r y c o m b in a t io n o f m a t u r it y a n d c r e d it 6
r a t in g . T h e p o in t e s t im a t e s im p ly t h a t fo r a 1 0 0 b a s is p o in t d e c r e a s e in t h e t h r e e m o n t h T r e a s u r y y ie ld , y ie ld s p r e a d s r is e b y b e t w e e n 6 b a s is p o in t s ( m e d iu m - t e r m A a a - r a t e d b o n d s ) a n d 3 6 b a s is p o in t s ( lo n g - t e r m B a a - r a t e d b o n d s ) . T h is r e la t io n is w e a k fo r A a a - r a t e d b o n d s ( it is s t a t is t ic a lly in s ig n i(cid:12) c a n t fo r lo n g - m a t u r it y a n d m e d iu m - m a t u r it y A a a - r a t e d b o n d s ) a n d s t r e n g t h e n s a s c r e d it q u a lit y fa lls . H e n c e t h e c o v a r ia n c e s b e t w e e n c h a n g e s in t h e le v e l o f t h e T r e a s u r y c u r v e a n d c h a n g e s in b o n d s p r e a d s a r e im p o r t a n t in p r ic in g n o n - A a a c o r p o r a t e b o n d s . F o r s u c h b o n d s , t h e a v e r a g e p r ic e in c r e a s e in a c o r p o r a t e b o n d t h a t a c c o m p a n ie s a g iv e n d e c r e a s e in t h e le v e l o f T r e a s u r y y ie ld s is n e a r ly 2 0 p e r c e n t le s s t h a n it w o u ld b e if b o n d y ie ld s a n d T r e a s u r y y ie ld s m o v e d o n e - f o r - o n e . T a b le 2 a ls o r e p o r t s t h a t t h e r e la t io n b e t w e e n t h e s lo p e o f t h e t e r m s t r u c t u r e a n d y ie ld s p r e a d s is w e a k . A n in c r e a s e in t h e s lo p e t y p ic a lly c o r r e s p o n d s t o a d e c r e a s e in y ie ld s p r e a d s , b u t t h is r e la t io n is e c o n o m ic a lly a n d s t a t is t ic a lly s ig n i(cid:12) c a n t o n ly fo r lo n g - m a t u r it y b o n d s . L a t e r I a r g u e t h a t t h is s t r o n g n e g a t iv e r e la t io n fo r lo n g - m a t u r it y b o n d s is la r g e ly t h e r e s u lt o f a c o u p o n - in d u c e d b ia s . T h e r e is n o t h e o r e t ic a l r e a s o n t o b e lie v e t h a t c o r p o r a t e b o n d s s p r e a d s fr o m v a r io u s b u s in e s s s e c t o r s s h o u ld r e a c t t h e s a m e w a y t o c h a n g in g T r e a s u r y y ie ld s . I n fa c t , g iv e n t h a t d i(cid:11) e r e n t s e c t o r s a r e a (cid:11) e c t e d b y m a c r o e c o n o m ic (cid:13) u c t u a t io n s in d i(cid:11) e r e n t w a y s , it w o u ld b e s u r p r is in g t o (cid:12) n d t h a t b o n d s p r e a d b e h a v io r w a s id e n t ic a l a c r o s s s e c t o r s . T o t e s t w h e t h e r b o n d s s p r e a d s fr o m m y t h r e e b u s in e s s s e c t o r s ( in d u s t r ia l, u t ilit ie s , (cid:12) n a n c ia l) b e h a v e d s im ila r ly , I jo in t ly e s t im a t e e q u a t io n ( 1 ) fo r e a c h s e c t o r w it h S e e m in g ly U n r e la t e d R e g r e s s io n s ( S U R ) . I e s t im a t e 1 2 d i(cid:11) e r e n t S U R s , o n e fo r e a c h c o m b in a t io n o f c r e d it r a t in g a n d m a t u r it y 2 b a n d . T h e (cid:31) ( 4 ) t e s t o f e q u a lit y o f b a n d b a c r o s s t h e t h r e e s e c t o r s is r e p o r t e d 3 m ;j s l;j j j in t h e (cid:12) n a l c o lu m n o f T a b le 2 . P P 2 T h e (cid:31) t e s t r e je c t s , a t t h e 5 % le v e l, t h e h y p o t h e s is o f c o n s t a n t c o e (cid:14) c ie n t s a c r o s s t h e b u s in e s s s e c t o r s o n ly fo r s h o r t - m a t u r it y A a a - r a t e d b o n d s , a n d t h is r e je c t io n is lik e ly s p u r io u s . A s c a n b e s e e n in T a b le 1 , t h e r e a r e o n ly 2 5 m o n t h ly o b s e r v a t io n s a v a ila b le t o jo in t ly e s t im a t e t h e r e g r e s s io n s fo r t h e s e y ie ld s p r e a d s . H e n c e fr o m t h e p e r s p e c t iv e o f s t a t is t ic a l s ig n i(cid:12) c a n c e , t h e r e is n o c o m p e llin g e v id e n c e t h a t y ie ld s p r e a d s fo r d i(cid:11) e r e n t b u s in e s s s e c t o r s r e a c t d i(cid:11) e r e n t ly t o T r e a s u r y y ie ld s . P e r h a p s m o r e r e le v a n t is t h e e c o n o m ic s ig n i(cid:12) c a n c e o f t h e r e s u lt s . I n r e s u lt s t h a t a r e a v a ila b le o n r e q u e s t , I (cid:12) n d t h a t t h e e s t im a t e d c o e (cid:14) c ie n t s fo r in d u s t r ia ls a n d u t ilit ie s a r e v e r y s im ila r , w h ile e s t im a t e d le v e l a n d s lo p e c o e (cid:14) c ie n t s fo r (cid:12) n a n c ia ls a r e s o m e w h a t la r g e r t h a n t h o s e fo r t h e o t h e r s e c t o r s . T h e a v e r a g e b fo r (cid:12) n a n c ia ls is r o u g h ly 0 .0 6 g r e a t e r t h a n t h e a v e r a g e b fo r o t h e r (cid:12) r m s , 3 m ;j 3 m ;j j j w h ile t h e a v e r a g e b fo r (cid:12) n a n c ia ls is r o u g h ly 0 .0 9 g r e a t e r t h a n t h e c o r r e s p o n d in g s l;j j P P a v e r a g e fo r o t h e r (cid:12) r m s . H e n c e t h e r e is s o m e w e a k e v id e n c e t h a t y ie ld s p r e a d s fo r (cid:12) n a n c ia l P (cid:12) r m s b e h a v e s o m e w h a t d i(cid:11) e r e n t ly t h a n y ie ld s p r e a d s fo r o t h e r (cid:12) r m s . I n t h e r e m a in d e r o f t h is p a p e r , I ig n o r e t h is p o s s ib le d i(cid:11) e r e n c e a n d u s e o n ly y ie ld s p r e a d s c o n s t r u c t e d w it h a ll 7
b u s in e s s s e c t o r s c o m b in e d . 4 .4 . A n a n a ly s is o f t a x - in d u c e d b ia s e s R e t u r n s t o h o ld in g c o r p o r a t e b o n d s a r e t a x e d a t t h e F e d e r a l, s t a t e , a n d lo c a l le v e ls , w h ile r e t u r n s t o h o ld in g T r e a s u r y in s t r u m e n t s a r e t a x e d a t o n ly t h e F e d e r a l le v e l. A s lo n g a s t h e m a r g in a l in v e s t o r fa c e s a p o s it iv e s t a t e a n d lo c a l m a r g in a l t a x r a t e , t h is t a x w e d g e w ill a (cid:11) e c t t h e y ie ld s p r e a d b e t w e e n c o r p o r a t e b o n d s a n d T r e a s u r y b o n d s . T h e w e d g e a ls o a (cid:11) e c t s t h e c o v a r ia n c e b e t w e e n t h e y ie ld s p r e a d a n d T r e a s u r y y ie ld s . A c a r e fu l a d ju s t m e n t o f y ie ld s fo r t a x e (cid:11) e c t s is b e y o n d t h e s c o p e o f t h is p a p e r . B e c a u s e t a x e s a r e p a id o n r e t u r n s , n o t y ie ld s , a c o m p le t e a n a ly s is r e q u ir e s e m b e d d in g t a x e s in a n e q u iv a le n t m a r t in g a le m o d e l o f s t o c h a s t ic in t e r e s t r a t e s a n d d e fa u lt r is k , s u c h a s t h o s e m e n t io n e d in S e c t io n 2 . I n t h is p a p e r I t a k e a s im p le r a p p r o a c h . I a s s u m e t h a t t h e t a x a b le r e t u r n o n b o t h T r e a s u r y a n d c o r p o r a t e b o n d s o f a g iv e n m a t u r it y m e q u a ls t h e T r e a s u r y y ie ld fo r t h a t m a t u r it y , d e n o t e d Y . E s s e n t ia lly , t h is m ;t e q u a t e s t h e T r e a s u r y y ie ld w it h t h e r e a liz e d r e t u r n , w h ic h is o b v io u s ly in a c c u r a t e . N o t e t h a t I d o n o t a s s u m e t h a t t h e t a x a b le r e t u r n o n c o r p o r a t e b o n d s e q u a ls t h e c o r p o r a t e y ie ld | s u c h a n a s s u m p t io n ig n o r e s t h e fa c t t h a t t h e c o r p o r a t e y ie ld im p o u n d s t h e p o s s ib ilit y o f d e fa u lt . I n a d d it io n , I a d o p t a s im p le v ie w o f t h e t a x s y s t e m . I ig n o r e a n y d i(cid:11) e r e n c e s a m o n g t a x r a t e s o n lo n g - t e r m c a p it a l g a in s , s h o r t - t e r m c a p it a l g a in s , a n d o r d in a r y in c o m e . I a ls o ig n o r e t a x t im in g is s u e s . I s im p ly a s s u m e t h e r e is o n e F e d e r a l m a r g in a l t a x r a t e a n d o n e s t a t e m a r g in a l t a x r a t e d e n o t e d (cid:28) . B o t h t a x r a t e s a r e a s s u m e d t o b e n o n s t o c h a s t ic . C o r p o r a t e s b o n d s a r e t a x e d a t b o t h t h e F e d e r a l a n d s t a t e le v e l, w h ile T r e a s u r y b o n d s a r e t a x e d o n ly a t t h e F e d e r a l le v e l. G iv e n t h e s e a s s u m p t io n s , t h e ‘a ft e r - t a x ’ y ie ld s p r e a d ( d e n o t e d A T S ) b e t w e e n c o r p o r a t e b o n d s a n d T r e a s u r ie s is ( s u p r e s s in g n o t a t io n a l d e p e n d e n c e o n t h e b u s in e s s s e c t o r ) : (cid:0) A T S = S (cid:28) Y ( 2 ) i;m ;t i;m ;t s m ;t C a lc u la t io n s o f a ft e r - t a x s p r e a d s a r e v e r y s e n s it iv e t o a s s u m p t io n s a b o u t m a r g in a l s t a t e a n d lo c a l t a x r a t e s . F o r e x a m p le , t h e m e a n T r e a s u r y y ie ld c o r r e s p o n d in g t o t h e m a t u r it y o f t h e s h o r t - t e r m A a a - r a t e d b o n d s in m y d a t a s e t is 7 .3 4 % a n d t h e m e a n s p r e a d fo r s h o r t - t e r m A a a - r a t e d b o n d s is 6 7 b a s is p o in t s . I f t h e m a r g in a l in v e s t o r h a s a 5 % s t a t e a n d lo c a l t a x r a t e , t h e m e a n a ft e r - t a x s p r e a d o n t h e s e b o n d s is 3 0 b a s is p o in t s . W it h a 7 % t a x r a t e , t h e m e a n a ft e r - t a x s p r e a d is o n ly 1 6 b a s is p o in t s . S im ila r ly , t h e r e s p o n s iv e n e s s o f a ft e r - t a x s p r e a d s t o c h a n g e s in T r e a s u r y y ie ld s a ls o d e p e n d s o n t a x r a t e a s s u m p t io n s . T o s im p lify t h e a n a ly s is o f t h e b ia s in ( 1 ) , a s s u m e t h a t t h e c h a n g e in t h e m - m a t u r it y T r e a s u r y y ie ld Y c a n b e w r it t e n a s a lin e a r c o m b in a t io n o f m ;t 8
t h e c h a n g e in t h r e e - m o n t h T r e a s u r y y ie ld a n d t h e c h a n g e in t h e s lo p e b e t w e e n t h e t h ir t y - y e a r y ie ld a n d t h e t h r e e - m o n t h y ie ld : (cid:1) Y = (cid:11) (cid:1) Y + (cid:11) (cid:1) S L ( 3 ) m ;t+ 1 m ;1 3 m ;t+ 1 m ;2 t+ 1 O b v io u s ly (cid:11) = 1 a n d (cid:11) = 0 fo r t h e t h r e e - m o n t h y ie ld , w h ile (cid:11) = 1 a n d m ;1 m ;2 m ;1 (cid:11) = 1 fo r t h e t h ir t y - y e a r y ie ld . F o r m a t u r it ie s o f t h r e e y e a r s o r m o r e , (cid:11) r a n g e s fr o m m ;2 m ;1 1 1 .1 t o 1 .3 a n d (cid:11) r a n g e s fr o m 0 .8 t o 1 .0 . m ;2 A ls o a s s u m e t h a t t h e r e la t io n b e t w e e n a ft e r - t a x y ie ld s p r e a d s a n d c h a n g e s in p r e - t a x T r e a s u r y y ie ld s is lin e a r : (cid:1) A T S = (cid:12) + (cid:12) (cid:1) Y + (cid:12) S L ( 4 ) i;m ;t+ 1 0 1 3 m ;t+ 1 2 t+ 1 S u b s t it u t in g ( 2 ) a n d ( 3 ) in t o ( 4 ) : (cid:1) S = (cid:12) + ( (cid:12) + (cid:28) (cid:11) ) (cid:1) Y + ( (cid:12) + (cid:28) (cid:11) ) S L ( 5 ) i;m ;t+ 1 0 1 s m ;1 3 m ;t+ 1 2 s m ;2 t+ 1 E q u a t io n ( 5 ) in d ic a t e s t h a t t h e s u m s b a n d b fr o m e q u a t io n ( 1 ) a r e 3 m ;j s l;j j j u p w a r d - b ia s e d e s t im a t e s o f t h e e (cid:11) e c t o f c h a n g e s in T r e a s u r y y ie ld s o n a ft e r - t a x b o n d s p r e a d s . P P B e c a u s e (cid:11) a n d (cid:11) a r e in t h e n e ig h b o r h o o d o f o n e fo r t h e m a t u r it ie s e x a m in e d in t h is m ;1 m ;2 p a p e r , t h e b ia s in b o t h s u m s is r o u g h ly e q u a l t o (cid:28) . T h is b ia s c a n b e la r g e r e la t iv e t o s b , e s p e c ia lly fo r A a a - r a t e d b o n d s . B e c a u s e o f t h e p o t e n t ia l im p o r t a n c e o f s t a t e 3 m ;j j t a x e s in t h e c a lc u la t io n o f c r e d it s p r e a d s , w e n e e d t o h a v e a g o o d id e a o f t h e m a r g in a l s t a t e P a n d lo c a l t a x r a t e fo r t h e m a r g in a l h o ld e r o f c o r p o r a t e b o n d s b e fo r e w e c a n e v a lu a t e t h e r e la t io n b e t w e e n a ft e r - t a x s p r e a d s a n d T r e a s u r y y ie ld s . U n fo r t u n a t e ly fo r o u r p u r p o s e s , it is d i(cid:14) c u lt t o id e n t ify t h e a p p r o p r ia t e m a r g in a l s t a t e t a x r a t e . T a x r a t e s v a r y w id e ly a c r o s s s t a t e s . I n 1 9 9 2 , t h e h ig h e s t m a r g in a l s t a t e a n d lo c a l t a x r a t e s o n d iv id e n d s , in t e r e s t in c o m e a n d c a p it a l g a in s w e r e a s lo w a s z e r o in a fe w s t a t e s a n d a s h ig h a s t w e lv e p e r c e n t in o t h e r s ( C o m m e r c e C le a r in g H o u s e 1 9 9 2 ) . S e v e r n a n d S t e w a r t ( 1 9 9 2 ) m a k e s o m e h e r o ic a s s u m p t io n s t o a r g u e t h a t t h e m a r g in a l s t a t e t a x r a t e is n o g r e a t e r t h a n (cid:12) v e p e r c e n t , a n d lik e ly in r e g io n o f t w o t o t h r e e p e r c e n t . T h is is a n a r e a w h e r e fu r t h e r r e s e a r c h is n e e d e d , b u t c a r e fu l in v e s t ig a t io n o f m a r g in a l s t a t e t a x r a t e s is b e y o n d t h e s c o p e o f t h is p a p e r . 1 T h e s e (cid:12) g u r e s a r e b a s e d o n t r e a t in g ( 3 ) a s a r e g r e s s io n e q u a t io n a n d e s t im a t in g it o v e r m y s a m p le p e r io d u s in g c o n s t a n t - m a t u r it y T r e a s u r y y ie ld s . 9
4 .5 . A n a n a ly s is o f c o u p o n - in d u c e d b ia s e s T h e b u ild in g b lo c k s in m o d e ls o f d e fa u lt - r is k y in s t r u m e n t s a r e n o t s p r e a d s o n c o u p o n b o n d s , b u t s p r e a d s o n z e r o - c o u p o n b o n d s ( o r , e q u iv a le n t ly , fo r w a r d r a t e s p r e a d s ) . H o w e v e r , t h e y ie ld s p r e a d o n a n m - m a t u r it y c o u p o n b o n d o v e r a n m - m a t u r it y T r e a s u r y c o u p o n b o n d w ill d i(cid:11) e r fr o m t h e y ie ld s p r e a d o n a n m - m a t u r it y z e r o - c o u p o n b o n d o v e r a n m - m a t u r it y T r e a s u r y s t r ip if e it h e r t h e d e fa u lt - fr e e t e r m s t r u c t u r e o r t h e t e r m s t r u c t u r e o f z e r o - c o u p o n b o n d c r e d it s p r e a d s is n o t (cid:13) a t ( L it t e r m a n a n d I b e n 1 9 9 1 ) . A s I w a n o w s k i a n d C h a n d r a ( 1 9 9 5 ) n o t e , c o u p o n b o n d y ie ld s p r e a d s w ill a ls o v a r y w it h T r e a s u r y y ie ld s e v e n if z e r o - c o u p o n b o n d y ie ld s p r e a d s a r e u n r e la t e d t o T r e a s u r y y ie ld s . F o r e x a m p le , a n in c r e a s e in t h e le v e l o f t h e T r e a s u r y t e r m s t r u c t u r e w ill s h o r t e n t h e d u r a t io n o f c o u p o n b o n d s . B e c a u s e c r e d it s p r e a d s a r e h ig h e r fo r lo n g e r - m a t u r it y in s t r u m e n t s , t h is d e c r e a s e in d u r a t io n w ill c o r r e s p o n d t o a d e c lin e in o b s e r v e d c o r p o r a t e c o u p o n b o n d y ie ld s p r e a d s . H e r e I in v e s t ig a t e t h e e m p ir ic a l im p o r t a n c e o f t h is c o u p o n - in d u c e d r e la t io n b e t w e e n 2 T r e a s u r y y ie ld s a n d c o r p o r a t e b o n d y ie ld s p r e a d s . T o p r e v ie w t h e r e s u lt s , I (cid:12) n d t h a t c h a n g e s in t h e le v e l o f T r e a s u r y y ie ld s h a v e a n e g lig ib le e (cid:11) e c t o n y ie ld s p r e a d s , b u t c h a n g e s in t h e s lo p e o f t h e T r e a s u r y t e r m s t r u c t u r e c a n h a v e a la r g e e (cid:11) e c t o n y ie ld s p r e a d s o f lo n g - m a t u r it y in s t r u m e n t s . T h is \ s lo p e b ia s " a p p e a r s t o e x p la in m u c h o f t h e fa c t t h a t , a s d o c u m e n t e d in T a b le 2 , y ie ld s p r e a d s o n lo n g - m a t u r it y in s t r u m e n t s a r e m o r e s e n s it iv e t o c h a n g e s in t h e s lo p e o f t h e y ie ld c u r v e ( h o ld in g t h e s h o r t e n d (cid:12) x e d ) t h a n a r e y ie ld s p r e a d s o n s h o r t e r - m a t u r it y in s t r u m e n t s . I e x p lo r e t h is is s u e b y a s s u m in g t h a t a t a g iv e n in s t a n t , b o t h t h e im p lic it T r e a s u r y z e r o - c o u p o n t e r m s t r u c t u r e a n d t h e z e r o - c o u p o n y ie ld s p r e a d c u r v e fo r a p a r t ic u la r (cid:12) r m o r r a t in g c la s s a r e lin e a r in m a t u r it y . I t h e n e x a m in e t h e c o m p a r a t iv e s t a t ic s o f c h a n g in g t h e le v e l a n d s lo p e o f t h e T r e a s u r y z e r o - c o u p o n t e r m s t r u c t u r e . H e n c e in s t e a d o f c o n s id e r in g c h a n g e s in t h e s lo p e a n d in t e r c e p t o f t h e T r e a s u r y t e r m s t r u c t u r e o v e r t h e p e r io d o f a m o n t h , w h ic h w o u ld r e q u ir e a s t o c h a s t ic m o d e l o f t h e t e r m s t r u c t u r e , I s im p ly c o n s id e r in s t a n t a - 2 I n a n e a r lie r v e r s io n o f t h e p a p e r I r e p o r t r e s u lt s fo r z e r o - c o u p o n b o n d y ie ld s p r e a d s o v e r T r e a s u r y s t r ip s . H o w e v e r , r e la t iv e ly f e w z e r o - c o u p o n b o n d s h a v e b e e n is s u e d b y c o r p o r a t io n s ( fo r e x a m p le , n o r e g r e s s io n s c o u ld b e e s t im a t e d fo r B a a - r a t e d b o n d s ) a n d t h e y ie ld s o n t h e s e b o n d s a p p e a r t o b e c o n t a m in a t e d b y s u b s t a n t ia l t r a n s it o r y n o is e . T h e r e s u lt s , w h ic h a r e a v a ila b le o n r e q u e s t , a r e m ix e d . T h e c h a n g e in t h e le v e l o f t h e t e r m s t r u c t u r e is n e g a t iv e ly r e la t e d t o s p r e a d s ( e x c e p t fo r lo n g - m a t u r it y A a a b o n d s ) , b u t t h is r e la t io n is s t a t is t ic a lly in s ig n i(cid:12) c a n t fo r a ll b u t s h o r t - m a t u r it y A a - r a t e d a n d A - r a t e d b o n d s . T h e c h a n g e in t h e s lo p e o f t h e t e r m s t r u c t u r e is n o t s t a t is t ic a lly s ig n i(cid:12) c a n t in a n y r e g r e s s io n . T h e o v e r a ll la c k o f s ig n i(cid:12) c a n c e m a y b e a c o n s e q u e n c e o f a la c k o f p o w e r o w in g t o a la c k o f d a t a . N o r e g r e s s io n is e s t im a t e d o v e r a ll o b s e r v a t io n s , a n d fo r t w o r e g r e s s io n s , o v e r h a lf o f t h e o b s e r v a t io n s a r e m is s in g . 1 0
n b c r t m a a w w s a s t e o u s c h a n g e s . D e n o t e t h e c o n t in u o u s ly - c o m p o u n d e d y ie ld o n a d e fa u lt - fr e e z e r o - c o u p o n o n d w it h r e m a in in g m a t u r it y (cid:28) , m e a s u r e d in y e a r s , a s r ( (cid:28) ) . D e n o t e t h e c o n t in u o u s ly o m p o u n d e d y ie ld o n a z e r o - c o u p o n b o n d is s u e d b y a p a r t ic u la r (cid:12) r m w it h r e m a in in g m a t u - (cid:0) it y (cid:28) a s f ( (cid:28) ) , h e n c e t h e y ie ld s p r e a d , d e n o t e d s , is g iv e n b y s ( (cid:28) ) = f ( (cid:28) ) r ( (cid:28) ) . T h e t w o (cid:28) e r m s t r u c t u r e s a r e d e s c r ib e d b y ( 6 ) . r ( (cid:28) ) = a + b (cid:28) ; s ( (cid:28) ) = a + b (cid:28) ( 6 ) r r s s C o n s id e r a T r e a s u r y b o n d w it h c o u p o n c ( c = 2 is p a id e v e r y s ix m o n t h s ) a n d m a t u r it y r r . T h is b o n d h a s a c o n t in u o u s ly - c o m p o u n d e d y ie ld Y , w h e r e t h e \ r " s u b s c r ip t d e n o t e s r ;c ;m r d e fa u lt - fr e e b o n d . S o m e a lg e b r a r e v e a ls t h a t t h e e (cid:11) e c t s o n Y o f c h a n g e s in t h e le v e l r ;c ;m r 3 n d s lo p e o f t h e z e r o - c o u p o n t e r m s t r u c t u r e a r e g iv e n b y : 2 m (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) r ( m ( i 1 ) = 2 ) ( m ( i 1 ) = 2 ) r ( m ) m (cid:0) (cid:0) c = 2 e ( m ( i 1 ) = 2 ) + e m r @ Y r ;c ;m r i= 1 = ( 7 ) X 2 m @ a r (cid:0) (cid:0) (cid:0) (cid:0) Y ( m ( i 1 ) = 2 ) Y m r ;c ;m r ;c ;m r r (cid:0) (cid:0) c = 2 e ( m ( i 1 ) = 2 ) + e m r i= 1 X 2 m (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) r ( m ( i 1 ) = 2 ) ( m ( i 1 ) = 2 ) 2 r ( m ) m 2 (cid:0) (cid:0) c = 2 e ( m ( i 1 ) = 2 ) + e m r @ Y r ;c ;m r i= 1 = ( 8 ) X 2 m @ b r (cid:0) (cid:0) (cid:0) (cid:0) Y ( m ( i 1 ) = 2 ) Y m r ;c ;m r ;c ;m r r (cid:0) (cid:0) c = 2 e ( m ( i 1 ) = 2 ) + e m r i= 1 X S im ila r ly , c o n s id e r a c o r p o r a t e b o n d w it h c o u p o n c , m a t u r it y m , a n d y ie ld Y , f f ;c ;m f h e r e t h e \ f " s u b s c r ip t d e n o t e s a b o n d is s u e d b y a (cid:12) r m . T h e p a r t ia l d e r iv a t iv e s o f Y f ;c ;m f it h r e s p e c t t o t h e le v e l a n d s lo p e o f t h e z e r o - c o u p o n t e r m s t r u c t u r e ( i.e ., h o ld in g t h e t e r m t r u c t u r e o f z e r o - c o u p o n c r e d it s p r e a d s c o n s t a n t ) a r e g iv e n b y s im p le m o d i(cid:12) c a t io n s o f ( 7 ) 4 n d ( 8 ) . T o s a v e s p a c e I d o n o t in c lu d e t h e r e le v a n t e x p r e s s io n s h e r e . W e a r e in t e r e s t e d in t h e e (cid:11) e c t s o f c h a n g e s in t h e le v e l a n d s lo p e o f t h e T r e a s u r y t e r m (cid:0) t r u c t u r e o n t h e c o u p o n b o n d s p r e a d Y Y . T o fa c ilit a t e c o m p a r is o n s b e t w e e n f ;c ;m r ;c ;m r f h e s e e (cid:11) e c t s a n d t h e r e g r e s s io n e q u a t io n ( 1 ) , I d e (cid:12) n e t h e \ le v e l b ia s " a n d \ s lo p e b ia s " a s : 3 T h e s e e x p r e s s io n s a s s u m e t h a t t h e (cid:12) r s t c o u p o n p a y m e n t is m a d e in e x a c t ly s ix m o n t h s . 4 I n ( 7 ) a n d ( 8 ) , r e p la c e Y , c , a n d r ( ) w it h Y , c , a n d r ( ) + s ( ) r e s p e c t iv e ly . r ;c ;m r f ;c ;m f r f 1 1
(cid:0) (cid:0) (cid:0) 1 @ Y Y @ Y Y f ;c ;m r ;c ;m f ;c ;m r ;c ;m r r f f @ Y r ;0 ;0 :2 5 (cid:17) (cid:18) (cid:19) (cid:18) (cid:19) = le v e l b ia s ( 9 ) @ a @ a @ a r r r ( ) (cid:0) 1 (cid:0) (cid:0) @ Y Y @ Y Y f ;c ;m r ;c ;m r ;0 :0 8 ;3 0 r ;0 ;0 :2 5 r f (cid:17) (cid:18) (cid:19) (cid:18) (cid:19) s lo p e b ia s ( 1 0 ) 8 9 @ b @ b r r > > > > < = > > > > : ; T h e le v e l b ia s is e q u iv a le n t t o t h e c o u p o n - in d u c e d b ia s in b in e q u a t io n ( 1 ) , 3 m ;j j w h ile t h e s lo p e b ia s is r o u g h ly e q u iv a le n t t o t h e b ia s in b . ( T h e e q u iv a le n c e is o n ly s l;j j P a p p r o x im a t e b e c a u s e t h e 3 0 - y e a r b o n d y ie ld s in ( 9 ) a n d ( 1 0 ) a r e b a s e d o n 8 % c o u p o n s . T h e P c o n s t a n t - m a t u r it y T r e a s u r y y ie ld u s e d in ( 1 ) is b a s e d o n a c o u p o n b o n d s e llin g a t p a r .) T h e s e b ia s e s w ill d e p e n d o n t h e le v e ls a n d s lo p e s o f T r e a s u r y a n d c o r p o r a t e t e r m s t r u c t u r e s . F o r t h is e x e r c is e , I a s s u m e t h a t r ( (cid:28) ) = 0 :0 7 + 0 :0 0 1 (cid:28) . T h is u p w a r d - s lo p in g z e r o - c o u p o n y ie ld c u r v e r e s u lt s in y ie ld s o n 8 % c o u p o n b o n d s t h a t r o u g h ly m a t c h t h e m e a n le v e l a n d s lo p e o f t h e T r e a s u r y c o u p o n b o n d t e r m s t r u c t u r e fo r m a t u r it ie s o f t h r e e , t e n a n d t h ir t y y e a r s o v e r m y s a m p le p e r io d . I a s s u m e t h a t s ( (cid:28) ) = 0 :0 1 2 + 0 :0 0 0 5 (cid:28) , w h ic h r e s u lt s in y ie ld s p r e a d s o n 9 .5 % c o u p o n b o n d s ( o v e r 8 % T r e a s u r y b o n d s ) t h a t r o u g h ly m a t c h t h e 5 m e a n y ie ld s p r e a d s fo r B a a b o n d s in P a n e l D o f T a b le 1 . F o r t h is c h o ic e o f p a r a m e t e r s , t h e le v e l b ia s is s m a ll. F o r T r e a s u r y b o n d c o u p o n s o f 8 % (cid:0) a n d c o r p o r a t e b o n d c o u p o n s o f 9 .5 % , t h e b ia s is a p p r o x im a t e ly 0 :0 2 6 fo r 2 5 - y e a r b o n d s . (cid:0) F o r b o n d s w it h m a t u r it ie s le s s t h a n 1 0 y e a r s , t h e b ia s is b e t w e e n 0 a n d 0 :0 0 4 . I n t u it iv e ly , t h e le v e l b ia s is s m a ll b e c a u s e b o n d d u r a t io n s a r e n o t v e r y s e n s it iv e t o c h a n g e s in t h e d e fa u lt fr e e z e r o - c o u p o n t e r m s t r u c t u r e a n d b e c a u s e t h e t e r m s t r u c t u r e o f c r e d it s p r e a d s is fa ir ly (cid:13) a t . B y c o n t r a s t , t h e s lo p e b ia s is la r g e , a t le a s t fo r lo n g - m a t u r it y b o n d s . F o r 2 5 - y e a r b o n d s , (cid:0) it is 0 :1 3 8 . F o r s h o r t e r - m a t u r it y b o n d s , t h e s lo p e b ia s d is a p p e a r s . F o r e x a m p le , it is o n ly (cid:0) 0 :0 1 9 fo r t e n - y e a r b o n d s . N a t u r a lly , fo r s m a lle r z e r o - c o u p o n y ie ld s p r e a d s , t h e b ia s is s m a lle r . F o r e x a m p le , if t h e z e r o - c o u p o n y ie ld s p r e a d is d e s c r ib e d b y s ( (cid:28) ) = 0 :0 0 6 + 0 :0 0 0 2 (cid:28) , w h ic h r o u g h ly m a t c h e s t h e y ie ld s p r e a d s fo r A a a - r a t e d b o n d s in P a n e l D o f T a b le 1 , t h e (cid:0) b ia s fo r 2 5 - y e a r c o r p o r a t e b o n d s w it h c o u p o n s o f 8 .8 % is 0 :0 6 4 . 5 I w a n o w s k i a n d C h a n d r a ( 1 9 9 5 ) e s t im a t e s u c h lin e a r s p r e a d r e la t io n s fo r v a r io u s b u s in e s s s e c t o r s o v e r r o u g h ly t h e s a m e t im e p e r io d . T h e m e a n , a c r o s s b u s in e s s s e c t o r s , o f t h e ir fu lls a m p le r e la t io n s fo r B B B - r a t e d (cid:12) r m s is s ( (cid:28) ) = 0 :0 1 2 8 + 0 :0 0 0 3 (cid:28) . 1 2
T h e in t u it io n is s t r a ig h t fo r w a r d . F u t u r e p r o m is e d c a s h (cid:13) o w s fr o m c o r p o r a t e b o n d s a r e d is c o u n t e d m o r e h ig h ly t h a n a r e c a s h (cid:13) o w s fr o m T r e a s u r y b o n d s . I n a d d it io n , c o r p o r a t e b o n d s t y p ic a lly h a v e h ig h e r c o u p o n s t h a n T r e a s u r y b o n d s . T h e s e d i(cid:11) e r e n c e s im p ly t h a t c o r p o r a t e b o n d s h a v e s h o r t e r d u r a t io n s t h a n e q u a l- m a t u r it y T r e a s u r y b o n d s , a n d h e n c e a r e r e la t iv e ly m o r e s e n s it iv e t o c h a n g e s in s h o r t - m a t u r it y d is c o u n t r a t e s a n d le s s s e n s it iv e t o c h a n g e s in lo n g - m a t u r it y d is c o u n t r a t e s . T h e n a c h a n g e in t h e s lo p e o f t h e y ie ld c u r v e , h o ld in g ( s a y ) t h e s h o r t r a t e (cid:12) x e d , w ill h a v e a la r g e r e (cid:11) e c t o n a T r e a s u r y b o n d y ie ld t h a n o n a e q u iv a le n t - m a t u r it y c o r p o r a t e b o n d , a n d t h e r e fo r e w ill a (cid:11) e c t t h e s p r e a d b e t w e e n t h e s e b o n d s . O n b a la n c e , fo u r c o n c lu s io n s c a n b e d r a w n fr o m t h e r e s u lt s in T a b le 2 , c o m b in e d w it h t h e b ia s e s in d u c e d b y t a x e s a n d c o u p o n s . F ir s t , c o r p o r a t e b o n d y ie ld s p r e a d s m o v e in v e r s e ly w it h s h o r t T r e a s u r y y ie ld s . S e c o n d , t h e in v e r s e r e la t io n is s lig h t ly s t r o n g e r w h e n s p r e a d s a r e c o m p u t e d o n a n a ft e r - t a x b a s is . T h ir d , t h e in v e r s e r e la t io n is s t r o n g e r fo r lo w e r - q u a lit y b o n d s t h a n fo r h ig h e r - q u a lit y b o n d s . F o r e x a m p le , it is in s ig n i(cid:12) c a n t fo r A a a - r a t e d b o n d s , w h e r e a s fo r B a a - r a t e d b o n d s , t h e p o in t e s t im a t e s im p ly t h a t a 1 0 0 b a s is p o in t d e c r e a s e in t h e le v e l o f t h e T r e a s u r y c u r v e c o r r e s p o n d s t o a 2 5 b a s is p o in t in c r e a s e in t h e le v e l o f y ie ld s p r e a d s . F o u r t h , h o ld in g t h e s h o r t e n d o f t h e T r e a s u r y y ie ld c u r v e (cid:12) x e d , c h a n g e s in t h e s lo p e o f t h e c u r v e a r e in v e r s e ly r e la t e d t o y ie ld s p r e a d s , b u t , a ft e r a d ju s t in g fo r a c o u p o n - in d u c e d b ia s in lo n g m a t u r it ie s , t h is in v e r s e r e la t io n is w e a k . 5 . I n t e r p r e t i n g t h e l i n k b e t w e e n y i e l d s p r e a d s a n d i n t e r e s t r a t e s W h y a r e d e fa u lt - fr e e in t e r e s t r a t e s a n d y ie ld s p r e a d s r e la t e d ? A n o b v io u s p o s s ib ilit y is t h a t t h e y a r e b o t h t ie d t o t h e b u s in e s s c y c le . M u c h r e s e a r c h , s u c h a s S t o c k a n d W a t s o n ( 1 9 8 9 ) , C h e n ( 1 9 9 1 ) , E s t r e lla a n d H a r d o u v e lis ( 1 9 9 1 ) , a n d E s t r e lla a n d M is h k in ( 1 9 9 6 ) h a s lin k e d t h e s h a p e o f t h e T r e a s u r y t e r m s t r u c t u r e t o fu t u r e v a r ia t io n s in t h e b u s in e s s c y c le , m e a s u r e d e it h e r b y N B E R d a t in g o r t h e g r o w t h r a t e o f G r o s s D o m e s t ic P r o d u c t ( G D P ) . E a r lie r r e s e a r c h a ls o lin k s m e a s u r e s o f c o r p o r a t e d e fa u lt r is k t o t h e b u s in e s s c y c le . F o n s , C a r t y , a n d K a u fm a n ( 1 9 9 4 ) (cid:12) n d t h a t fu t u r e d e fa u lt r a t e s o n b o n d s r a t e d b y M o o d y ’s a r e p o s it iv e ly c o r r e la t e d w it h fo r e c a s t s o f fu t u r e G D P g r o w t h . C h e n ( 1 9 9 1 ) (cid:12) n d s t h a t a g g r e g a t e c o r p o r a t e b o n d y ie ld s p r e a d s a r e lin k e d t o s t o c k r e t u r n s , w h ic h in t u r n a r e lin k e d t o fu t u r e 6 G D P g r o w t h . F u r t h e r e v id e n c e , s p e c i(cid:12) c t o t h e 1 9 8 5 { 1 9 9 5 t im e p e r io d e x a m in e d in t h is p a p e r , is p r o v id e d in T a b le 3 . I r e g r e s s q u a r t e r ly lo g c h a n g e s in r e a l c h a in - w e ig h t e d G D P o n c u r r e n t 6 A p r o b le m w it h C h e n ’s a n a ly s is is t h a t t h e a g g r e g a t e m e a s u r e s o f y ie ld s p r e a d s d o n o t e x c lu d e c a lla b le b o n d s . A s s h o w n in S e c t io n 6 , t h e v a lu e o f t h e c a ll o p t io n w ill v a r y w it h t h e T r e a s u r y t e r m s t r u c t u r e . H e n c e e v e n if d e fa u lt r is k is u n r e la t e d t o t h e b u s in e s s c y c le , a g g r e g a t e y ie ld s p r e a d s w ill v a r y w it h t h e b u s in e s s c y c le b e c a u s e T r e a s u r y y ie ld s v a r y w it h t h e b u s in e s s c y c le . 1 3
a n d la g g e d q u a r t e r ly c h a n g e s in y ie ld s p r e a d s , w h ic h I c o n s t r u c t b y s u m m in g t h e t h r e e m o n t h ly c h a n g e s in y ie ld s p r e a d s in t h e q u a r t e r . F o r e a c h c r e d it r a t in g i a n d m a t u r it y b a n d m , t h e q u a r t e r ly c h a n g e in y ie ld s p r e a d d u r in g t h e t h r e e m o n t h s o f q u a r t e r t is d e n o t e d q (cid:1) S . T a b le 3 r e p o r t s t h e r e s u lt s o f O L S e s t im a t io n o f ( 1 1 ) : i;m ;t 2 q (cid:0) (cid:1) 1 0 0 lo g ( G D P ) = b + (cid:1) S + e ( 1 1 ) t+ 1 0 i;m ;t+ 1 i;m ;t+ 1 i i= 0 X O n b a la n c e , t h e r e s u lt s in d ic a t e t h a t y ie ld s p r e a d s o f a ll m a t u r it ie s a n d c r e d it r a t in g s fa ll a s e c o n o m ic g r o w t h in c r e a s e s . I n a ll r e g r e s s io n s , t h e s u m o f t h e c o e (cid:14) c ie n t s o n t h e c u r r e n t a n d la g g e d c h a n g e s in y ie ld s p r e a d s is n e g a t iv e . F o r s ix o f t h e t w e lv e r e g r e s s io n s , t h is s u m is 7 s ig n i(cid:12) c a n t ly d i(cid:11) e r e n t fr o m z e r o a t t h e 5 % le v e l. T h e m e a n s u m o f t h e s e c o e (cid:14) c ie n t s a c r o s s (cid:0) t h e 1 2 r e g r e s s io n s is 2 :1 3 , im p ly in g t h a t a n in c r e a s e in y ie ld s p r e a d s o f 5 0 b a s is p o in t s c o r r e s p o n d s t o a d e c lin e in t h e g r o w t h r a t e o f G D P o f 1 .0 7 p e r c e n t a g e p o in t s . T h e r e is n o p a t t e r n a p p a r e n t a c r o s s m a t u r it ie s o r c r e d it r a t in g s . F o r e x a m p le , t h e lin k b e t w e e n G D P a n d y ie ld s p r e a d s o n B a a - r a t e d b o n d s is n o t a p p r e c ia b ly d i(cid:11) e r e n t fr o m t h e lin k b e t w e e n G D P a n d y ie ld s p r e a d s o n A a a - r a t e d b o n d s . H o w e v e r , t h e e v id e n c e in T a b le 2 lin k in g y ie ld s p r e a d s a n d T r e a s u r y y ie ld s is n o t c o m p le t e ly c o n s is t e n t w it h a b u s in e s s c y c le s t o r y . T o e x a m in e t h e s e in c o n s is t e n c ie s , w e n e e d t o t a k e a c lo s e r lo o k a t t h e r e la t io n b e t w e e n t h e t e r m s t r u c t u r e a n d t h e b u s in e s s c y c le . T h e s t y liz e d fa c t s a r e t h a t lo w y ie ld s a n d a s t e e p ly s lo p e d t e r m s t r u c t u r e b o t h c o r r e s p o n d t o a fu t u r e e c o n o m ic e x p a n s io n . T h is p a p e r u s e s (cid:12) r s t d i(cid:11) e r e n c e s o f y ie ld s a n d s lo p e s , s o w e n e e d t o u n d e r s t a n d t h e r e la t io n b e t w e e n t h e s e (cid:12) r s t d i(cid:11) e r e n c e s a n d e c o n o m ic g r o w t h . I n s o m e s e n s e , t h is r e la t io n is t h e o p p o s it e o f t h e s t y liz e d r e la t io n , a lt h o u g h o f c o u r s e t h e r e la t io n in v o lv in g (cid:12) r s t d i(cid:11) e r e n c e s is in e x t r ic a b ly lin k e d w it h t h e r e la t io n in v o lv in g le v e ls . I s u m m a r iz e t h e e m p ir ic a l e v id e n c e h e r e ; m o r e d e t a ils a r e a v a ila b le o n r e q u e s t . O v e r 1 9 8 5 t o 1 9 9 5 , q u a r t e r ly c h a n g e s in t h e le v e l o f t h e t h r e e - m o n t h T r e a s u r y b ill y ie ld w e r e s t r o n g ly p o s it iv e ly a s s o c ia t e d w it h c o n t e m p o r a n e o u s c h a n g e s in t h e q u a r t e r ly g r o w t h r a t e o f r e a l, c h a in - w e ig h t e d G D P a n d w e a k ly p o s it iv e ly a s s o c ia t e d w it h fu t u r e c h a n g e s in t h e g r o w t h r a t e o f r e a l G D P . Q u a r t e r ly c h a n g e s in t h e s lo p e o f t h e T r e a s u r y t e r m s t r u c t u r e w e r e s t r o n g ly n e g a t iv e ly a s s o c ia t e d w it h c o n t e m p o r a n e o u s c h a n g e s in t h e c o n t e m p o r a n e o u s r e a l G D P g r o w t h r a t e , a n d w e a k ly n e g a t iv e ly a s s o c ia t e d w it h fu t u r e c h a n g e s in t h is g r o w t h r a t e . 7 T h e v a r ia n c e - c o v a r ia n c e m a t r ix o f t h e e s t im a t e d c o e (cid:14) c ie n t s is a d ju s t e d fo r g e n e r a liz e d h e t e r o s k e d a s t ic it y a n d o n e la g o f m o v in g a v e r a g e r e s id u a ls . B e c a u s e t e s t s t a t is t ic s a r e v a lid o n ly a s y m p t o t ic a lly a n d t h e s e r e g r e s s io n s h a v e v e r y fe w o b s e r v a t io n s , t h e s e s t a t is t ic s s h o u ld b e in t e r p r e t e d c a u t io u s ly . 1 4
T h e s e r e s u lt s a r e c o n s is t e n t w it h t h e s t y liz e d fa c t s t h a t lo w y ie ld s a n d a s t e e p s lo p e fo r e c a s t fu t u r e h ig h e c o n o m ic g r o w t h . T h is a d d it io n a l e v id e n c e t e lls u s t h a t w h e n t h e g r o w t h a r r iv e s , y ie ld s r is e a n d t h e s lo p e fa lls . A n o t h e r w a y t o t h in k a b o u t t h e s e r e la t io n s is t h a t lo w y ie ld s ( o r a s t e e p s lo p e ) fo r e c a s t b o t h fu t u r e e c o n o m ic g r o w t h a n d fu t u r e in c r e a s e s in y ie ld s ( o r fu t u r e d e c r e a s e s in t h e s lo p e ) . T h e r e s u lt s in T a b le 2 t e ll u s t h a t y ie ld s p r e a d s fa ll w h e n T r e a s u r y b ill y ie ld s r is e . T h is c a n e a s ily b e e x p la in e d w it h a b u s in e s s c y c le s t o r y . W h e n T r e a s u r y y ie ld s r is e , t h e e c o n o m y is e x p a n d in g , s o (cid:12) r m s a r e b e t t e r o (cid:11) , a n d d e fa u lt p r o b a b ilit ie s fa ll. H o w e v e r , T a b le 2 a ls o t e lls u s y ie ld s p r e a d s a ls o fa ll, a lb e it w e a k ly , w h e n t h e s lo p e o f t h e T r e a s u r y y ie ld c u r v e s t e e p e n s . B u t w h e n t h e s lo p e o f t h e y ie ld c u r v e s t e e p e n s , t h e e c o n o m y is c o n t r a c t in g , s o d e fa u lt p r o b a b ilit ie s s h o u ld b e r is in g . H e n c e t h e s lo p e c o e (cid:14) c ie n t s in T a b le 2 a r e in c o n s is t e n t w it h a b u s in e s s c y c le s t o r y . I n fa c t , t h e o b s e r v e d v a r ia t io n o f y ie ld s p r e a d s w it h T r e a s u r y y ie ld s m a y h a v e lit t le t o d o w it h d e fa u lt r is k . I f t h is v a r ia t io n w e r e d r iv e n b y v a r ia t io n s in d e fa u lt r is k , a t le a s t p a r t o f t h e e x p la n a t o r y p o w e r o f t h e t e r m s t r u c t u r e s h o u ld c a p t u r e d b y s t o c k r e t u r n s . I n o t h e r w o r d s , a d d in g a g g r e g a t e s t o c k r e t u r n s t o t h e r ig h t h a n d s id e o f ( 1 ) s h o u ld r e d u c e t h e e x p la n a t o r y p o w e r o f t h e t e r m s t r u c t u r e . C h a n g e s in t h e le v e l a n d s lo p e o f t h e T r e a s u r y t e r m s t r u c t u r e a r e n o is y s ig n a ls o f c h a n g e s in a g g r e g a t e o u t p u t , w h ic h in t u r n is a n o is y s ig n a l o f c h a n g e s in (cid:12) r m s ’ v a lu e s ( w h ic h a (cid:11) e c t t h e lik e lih o o d t h a t (cid:12) r m s w ill d e fa u lt ) . A g g r e g a t e s t o c k r e t u r n s a r e d ir e c t m e a s u r e s o f c h a n g e s in (cid:12) r m s ’ a g g r e g a t e e q u it y v a lu e s , t h e r e fo r e t h e m a r g in a l e x p la n a t o r y p o w e r o f t h e t e r m s t r u c t u r e s h o u ld b e r e d u c e d o r e v e n e lim in a t e d w h e n t h e s t o c k r e t u r n s a r e in c lu d e d in t h e r e g r e s s io n . T a b le 4 d o c u m e n t s t h a t t h is c o n c lu s io n is n o t s u p p o r t e d b y t h e d a t a . I t r e p o r t s e s t i- (cid:0) m a t e s o f ( 1 2 ) , in w h ic h t h e lo g m o n t h ly r e t u r n t o t h e S & P 5 0 0 fr o m t h e e n d o f m o n t h t 1 t o t is d e n o t e d R E T : t 1 (cid:0) (cid:0) (cid:0) (cid:1) S = b + b (cid:1) Y + b (cid:1) S L + b R E T + e ( 1 2 ) i;m ;t+ 1 0 3 m ;j 3 m ;t+ 1 j s l;j t+ 1 j r e t;j t+ 1 j i;m ;t+ 1 (cid:0) j = 1 (cid:20) (cid:21) X T h e r e s u lt s in T a b le 4 s h o w t h a t s t o c k r e t u r n s m o v e in v e r s e ly w it h y ie ld s p r e a d s , ju s t a s e x p e c t e d . A ls o a s e x p e c t e d , t h is r e la t io n is s t r o n g e r fo r lo w e r - r a t e d b o n d s . H o ld in g t h e t e r m s t r u c t u r e c o n s t a n t , t h e p o in t e s t im a t e s im p ly t h a t a t e n p e r c e n t in c r e a s e in t h e S & P 5 0 0 c o r r e s p o n d s t o a 2 0 b a s is p o in t d e c r e a s e in B a a - r a t e d y ie ld s p r e a d s ( r e g a r d le s s o f m a t u r it y ) . T h e s a m e in c r e a s e in s t o c k p r ic e s c o r r e s p o n d s t o a 1 0 b a s is p o in t d e c r e a s e in A - r a t e d y ie ld s p r e a d s a n d s m a lle r d e c r e a s e s in h ig h e r - r a t e d y ie ld s p r e a d s . H o w e v e r , a c o m p a r is o n o f t h e r e s u lt s in T a b le 4 w it h t h o s e in T a b le 2 r e v e a ls t h a t t h e in c lu s io n o f s t o c k r e t u r n s h a d n o im p o r t a n t e (cid:11) e c t o n t h e e x p la n a t o r y p o w e r o f t h e le v e l o f 1 5
t h e t e r m s t r u c t u r e . T h e p o in t e s t im a t e s o f b a r e lit t le c h a n g e d b y t h e a d d it io n o f 3 m ;j j s t o c k r e t u r n s a s a n e x p la n a t o r y v a r ia b le . I f a n y t h in g , t h e e s t im a t e s a r e fu r t h e r fr o m z e r o P w it h e q u a t io n ( 1 2 ) t h a n w it h e q u a t io n ( 1 ) . T h e in c lu s io n o f s t o c k r e t u r n s h a s a s o m e w h a t g r e a t e r e (cid:11) e c t o n t h e e x p la n a t o r y p o w e r o f t h e s lo p e o f t h e t e r m s t r u c t u r e , b u t t h is e (cid:11) e c t is a ls o in t h e u n e x p e c t e d d ir e c t io n . T h e s lo p e c o e (cid:14) c ie n t s u m s in ( 1 2 ) a r e m o r e n e g a t iv e in e v e r y c a s e t h a n c o r r e s p o n d in g s u m s in ( 1 ) . A s w it h ( 1 ) , t h e s t a t is t ic a l s ig n i(cid:12) c a n c e o f t h e s e s u m s in ( 1 2 ) is , o n b a la n c e , w e a k . T h e r e s u lt s in T a b le 4 a r e t r o u b lin g . I f t h e s e v a r ia t io n s in y ie ld s p r e a d s a r e n o t d r iv e n b y v a r ia t io n s in d e fa u lt r is k , t h e n w e c a n n o t u s e t h e b e h a v io r o f c o r p o r a t e b o n d y ie ld s t o p a r a m e t e r iz e m o d e ls o f c r e d it r is k fo r t h e p u r p o s e s o f p r ic in g o t h e r t y p e s o f d e fa u lt - r is k y in s t r u m e n t s . T a b le 4 is , h o w e v e r , n o t t h e (cid:12) n a l w o r d o n t h e s u b je c t . E q u a t io n ( 1 2 ) is a lm o s t c e r t a in ly m is s p e c i(cid:12) e d b e c a u s e it a s s u m e s a lin e a r r e la t io n b e t w e e n s t o c k r e t u r n s a n d y ie ld s p r e a d s . A n y c o r r e la t io n b e t w e e n m is s p e c i(cid:12) c a t io n e r r o r a n d c h a n g e s in T r e a s u r y y ie ld s w ill s h o w u p in t h e e s t im a t e d c o e (cid:14) c ie n t s o f ( 1 2 ) . N o n e t h e le s s , w e s h o u ld a t le a s t c o n s id e r t h e p o s s ib ilit y t h a t t h e v a r ia t io n b e t w e e n y ie ld s p r e a d s a n d T r e a s u r y y ie ld s is u n r e la t e d t o d e fa u lt r is k . A n a lt e r n a t iv e p o s s ib ilit y , s u g g e s t e d b y b o n d t r a d e r s , is a s u p p ly a n d d e m a n d s t o r y . W h e n b o n d y ie ld s ( b o t h T r e a s u r y a n d c o r p o r a t e ) fa ll, (cid:12) r m s r e s p o n d b y is s u in g m o r e b o n d s , b u t t h e T r e a s u r y d o e s n o t d o lik e w is e . T h e r e la t iv e in c r e a s e in t h e s u p p ly o f c o r p o r a t e b o n d s lo w e r s t h e p r ic e o f c o r p o r a t e d e b t r e la t iv e t o T r e a s u r y d e b t , a n d h e n c e w id e n s t h e y ie ld s p r e a d . A lt h o u g h I c o n je c t u r e t h a t t h e e la s t ic it y o f d e m a n d fo r c o r p o r a t e b o n d s im p lie d b y t h e r e s u lt s in t h is p a p e r is im p la u s ib ly c lo s e t o z e r o , t h e h y p o t h e s is is n o t t e s t e d h e r e . A n o t h e r p o s s ib lit y is s u g g e s t e d b y t h e w o r k o f G r in b la t t ( 1 9 9 5 ) . H e a r g u e s t h a t y ie ld s p r e a d s o n s h o r t - t e r m c o r p o r a t e in s t r u m e n t s a r e m o r e lik e ly d r iv e n b y t h e liq u id it y o f T r e a s u r y in s t r u m e n t s t h a n t h e r is k o f d e fa u lt . I t is n o t im p la u s ib le t o b e lie v e t h a t t h e v a lu e o f liq u id it y v a r ie s w it h t h e T r e a s u r y t e r m s t r u c t u r e . T h is h y p o t h e s is c a n p r e s u m a b ly b e t e s t e d w it h s p r e a d s o n e s s e n t ia lly d e fa u lt - fr e e in s t r u m e n t s s u c h a s g o v e r n m e n t a g e n c y b o n d s , b u t I d o n o t p u r s u e t h is r e s e a r c h h e r e . 6 . A n a n a l y s i s o f a l t e r n a t i v e l y - c o n s t r u c t e d y i e l d s p r e a d s 6 .1 . R e fr e s h e d y ie ld s p r e a d s A ll c o r p o r a t e b o n d y ie ld in d e x e s o f w h ic h I a m a w a r e a r e r e fr e s h e d in d e x e s , w h ic h h o ld c r e d it r a t in g s (cid:12) x e d o v e r t im e . T h is in c lu d e s t h e in d e x e s p r o d u c e d b y M o o d y ’s , S a lo m o n B r o t h e r s ’, a n d M e r r ill L y n c h . T h e e m p ir ic a l r e s e a r c h t h a t u s e s a g g r e g a t e m e a s u r e s o f c o r p o r a t e b o n d y ie ld s p r im a r ily r e lie s o n s u c h in d e x e s . F o r c e r t a in p u r p o s e s , s u c h a s t r a c k in g y ie ld s o n n e w ly - is s u e d b o n d s , t h e u s e o f s u c h in d e x e s is a p p r o p r ia t e . H o w e v e r , t h e r e is a 1 6
c le a r p o t e n t ia l p r o b le m u s in g t h e s e in d e x e s t o in v e s t ig a t e in t e r t e m p o r a l c h a n g e s in b o n d s ’ c r e d it q u a lit y , b e c a u s e t h e in d e x e s h o ld c o n s t a n t a m e a s u r e o f c r e d it q u a lit y . U n fo r t u n a t e ly , t h is p r o b le m is t y p ic a lly n o t e v e n m e n t io n e d , m u c h le s s a d d r e s s e d in t h is r e s e a r c h . ( D u (cid:14) e a n d S in g le t o n ( 1 9 9 5 ) is a n e x c e p t io n .) S p r e a d s o f s u c h y ie ld in d e x e s o v e r T r e a s u r y y ie ld s a r e lik e ly t o u n d e r r e a c t t o a s y s t e m a t ic s h o c k t o (cid:12) r m s ’ c r e d it q u a lit ie s b e c a u s e p a r t o f t h e s h o c k w ill b e r e (cid:13) e c t e d in c h a n g e s in c r e d it r a t in g s . A t t h e e x t r e m e , if g r a d a t io n s in c r e d it r a t in g s w e r e s u (cid:14) c ie n t ly (cid:12) n e , if r a t in g a g e n c ie s r e s p o n d e d in s t a n t a n e o u s ly t o n e w in fo r m a t io n , a n d if r a t in g a g e n c ie s s e t r a t in g s in t h e s a m e w a y t h a t t h e m a r k e t s e t y ie ld s p r e a d s , t h e n y ie ld s p r e a d s o f r e fr e s h e d in d e x e s w o u ld b e c o n s t a n t o v e r t im e . O f c o u r s e , t h e s e e x t r e m e c o n d it io n s a r e n o t s a t is (cid:12) e d , t h e r e fo r e t h e e m p ir ic a l r e le v a n c e o f t h is p o t e n t ia l p r o b le m is u n c le a r . I in v e s t ig a t e t h is is s u e b y e s t im a t in g e q u a t io n ( 1 ) w it h s p r e a d s , o v e r T r e a s u r ie s , o f r e fr e s h e d y ie ld in d e x e s . T h e r e le v a n t q u e s t io n is t o w h a t e x t e n t t h e r e s u lt s d i(cid:11) e r fr o m t h e r e s u lt s in T a b le 2 . F o r e a c h c r e d it r a t in g i , r e m a in in g m a t u r it y b a n d m , a n d m o n t h - e n d t , I c o n s t r u c t e d 8 m e a n y ie ld s p r e a d s o n n o n c a lla b le c o r p o r a t e b o n d s . F o r e a c h c r e d it r a t in g a n d m a t u r it y b a n d , I e s t im a t e d e q u a t io n ( 1 ) u s in g (cid:12) r s t d i(cid:11) e r e n c e s in t h e t im e s e r ie s o f y ie ld s p r e a d s a s t h e d e p e n d e n t v a r ia b le . T h e r e s u lt s a r e d is p la y e d in T a b le 5 . T h e n e g a t iv e r e la t io n b e t w e e n c h a n g e s in y ie ld s p r e a d s a n d c h a n g e s in t h e le v e l o f T r e a s u r y y ie ld s is w e a k e r in T a b le 5 t h a n in T a b le 2 . T h e m e a n o f t h e t w e lv e p o in t e s t im a t e s (cid:0) (cid:0) o f b is 0 :1 1 6 in T a b le 5 , c o m p a r e d t o 0 :1 5 2 in T a b le 2 . A s in T a b le 2 , t h e s t r e n g t h 3 m ;j j o f t h is n e g a t iv e r e la t io n r is e s a s c r e d it q u a lit y fa lls . B u t in T a b le 2 , t h is n e g a t iv e r e la t io n P is s t a t is t ic a lly s ig n i(cid:12) c a n t a t t h e 5 % le v e l fo r o n e r e g r e s s io n u s in g A a a - r a t e d b o n d s a n d fo r a ll r e g r e s s io n s u s in g b o n d s r a t e d A a o r b e lo w . B y c o n s t r a s t , in T a b le 5 , t h is r e la t io n is s ig n i(cid:12) c a n t o n ly fo r t h e r e g r e s s io n s u s in g B a a - r a t e d b o n d s a n d o n e r e g r e s s io n u s in g A - r a t e d b o n d s . T h e r e a r e t w o c o n c lu s io n s t o d r a w fr o m t h is e v id e n c e . F ir s t , c h a n g e s in y ie ld s p r e a d s p r o d u c e d w it h r e fr e s h e d in d e x e s u n d e r r e a c t t o c h a n g e s in c r e d it q u a lit y . H e n c e t h e u s e o f s u c h s p r e a d s c a n le a d t o in c o r r e c t in fe r e n c e s . F o r e x a m p le , if w e h a d o n ly t h e r e s u lt s in T a b le 5 t o g u id e o u r a n a ly s is , w e w o u ld c o n c lu d e t h a t fo r b o n d s r a t e d A o r a b o v e , it w o u ld b e r e a s o n a b le t o t r e a t y ie ld s p r e a d s a n d T r e a s u r y y ie ld s a s u n c o r r e la t e d . B u t a s T a b le 2 d o c u m e n t s , t h is c o n c lu s io n is fa ls e . S e c o n d , t h e s e r e s u lt s s u p p o r t t h e v ie w t h a t t h e v a r ia t io n o f y ie ld s p r e a d s w it h T r e a s u r y y ie ld s is r e la t e d t o v a r ia t io n in d e fa u lt r is k . I f t h is v a r ia t io n o f y ie ld s p r e a d s w e r e u n r e la t e d t o d e fa u lt r is k , t h e n w o u ld n o t b e a lt e r e d b y a p r o c e d u r e t h a t h e ld c r e d it q u a lit y c o n s t a n t o v e r t im e . 8 D e t a ils a r e in t h e a p p e n d ix . 1 7
6 .2 . C a lla b le b o n d s p r e a d s M o s t c o m m o n ly a v a ila b le y ie ld in d e x e s u s e b o t h c a lla b le a n d n o n c a lla b le b o n d s . C o n s id e r , fo r e x a m p le , t h e c o m p o s it io n o f M o o d y ’s I n d u s t r ia l I n d e x e s a s o f M a y 1 9 8 9 . I n t h is m o n t h t h e r e w e r e n in e b o n d s in c lu d e d in t h e A a a I n d e x . A ll w e r e c a lla b le , a lt h o u g h t w o o f t h e n in e h a d n o t y e t r e a c h e d t h e ir d a t e o f (cid:12) r s t c a ll. E le v e n o f t h e t w e lv e b o n d s in M a y 1 9 8 9 ’s A a I n d e x w e r e c a lla b le ; t e n o f t h e e le v e n w e r e c u r r e n t ly c a lla b le . E s s e n t ia lly , t h e c o m p o s it io n o f M o o d y ’s I n d e x e s r e (cid:13) e c t e d t h e c o m p o s it io n o f t h e u n iv e r s e o f c o r p o r a t e b o n d s . A s m e n t io n e d e a r lie r , (cid:12) r m s h a v e h is t o r ic a lly is s u e d m a n y m o r e c a lla b le b o n d s t h a n n o n c a lla b le b o n d s . L o n g s t a (cid:11) a n d S c h w a r t z ( 1 9 9 5 ) r e g r e s s e d c h a n g e s in b o n d y ie ld s p r e a d s c o n s t r u c t e d w it h M o o d y ’s I n d e x e s o n c h a n g e s in T r e a s u r y y ie ld s . T h e y fo u n d m u c h m o r e n e g a t iv e r e g r e s s io n c o e (cid:14) c ie n t s t h a n t h o s e r e p o r t e d in T a b le 2 . P a r t o f t h e d i(cid:11) e r e n c e b e t w e e n t h e ir r e s u lt s a n d t h o s e h e r e a r e a c o n s e q u e n c e o f t h e d i(cid:11) e r e n c e s in t h e s a m p le p e r io d a n d t h e fo r m o f t h e r e g r e s s io n . N o n e t h e le s s , a q u a lit a t iv e d i(cid:11) e r e n c e b e t w e e n M o o d y ’s I n d e x e s a n d m y s e r ie s r e m a in s a ft e r a d ju s t in g fo r t h e s e e (cid:11) e c t s . F o r e x a m p le , w h e n e q u a t io n ( 1 ) is e s t im a t e d fo r M o o d y ’s A a a I n d u s t r ia ls I n d e x o v e r m y s a m p le p e r io d , t h e e s t im a t e s o f b a n d 3 m ;j j (cid:0) (cid:0) b a r e 0 :2 2 4 a n d 0 :2 8 3 r e s p e c t iv e ly , w h ic h a r e r o u g h ly 2 .5 t im e s t h e c o r r e s p o n d in g s l;j j P 9 e s t im a t e s fo r A a a - r a t e d b o n d s in T a b le 2 . P T h e c a lla b ilit y o f t h e b o n d s is a n o b v io u s p o s s ib le e x p la n a t io n fo r t h e la r g e s e n s it iv it ie s o f t h e M o o d y ’s s p r e a d s . W h e n y ie ld s o n ( n o n c a lla b le ) T r e a s u r ie s fa ll, y ie ld s o n s e a s o n e d c a lla b le b o n d s d o n o t fa ll a s m u c h b e c a u s e t h e v a lu e o f t h e e m b e d d e d c a ll o p t io n r is e s . T h e r e fo r e t h e s p r e a d b e t w e e n c a lla b le b o n d y ie ld s a n d n o n c a lla b le T r e a s u r y y ie ld s w ill m o v e in v e r s e ly w it h n o n c a lla b le T r e a s u r y y ie ld s . T o t e s t w h e t h e r t h e c a lla b ilit y o f t h e b o n d s in t h e M o o d y ’s I n d e x e s a c c o u n t s fo r t h e s e d i(cid:11) e r e n c e s , I in v e s t ig a t e t h e fo llo w in g t w o q u e s t io n s . F ir s t , a r e c a lla b le c o r p o r a t e b o n d s p r e a d s m o r e s e n s it iv e t o m o v e m e n t s in T r e a s u r y y ie ld s t h a n a r e n o n c a lla b le c o r p o r a t e b o n d s p r e a d s ? S e c o n d , d o e s t h e s e n s it iv it y o f c a lla b le b o n d s p r e a d s d e p e n d o n h o w c lo s e t h e b o n d p r ic e is t o t h e c a ll p r ic e ? F o r t h is in v e s t ig a t io n , I r e s t r ic t m y a t t e n t io n t o lo n g - t e r m A a b o n d s . I c o n s t r u c t c a lla b le lo n g - t e r m A a b o n d s p r e a d s in t h e s a m e w a y t h a t I e a r lie r c r e a t e d s p r e a d s o n n o n c a lla b le b o n d s . F o r e a c h m o n t h t , I fo r m s ix g r o u p s o f c a lla b le lo n g - t e r m A a b o n d s , d is t in g u is h e d b y t h e ir m o n t h t p r ic e s a n d t h e ir c u r r e n t c a ll s t a t u s . O n e a p p r o a c h w o u ld b e t o d iv id e b o n d s in t o t h o s e t h a t a r e c u r r e n t ly c a lla b le a n d t h o s e t h a t a r e c u r r e n t ly c a ll p r o t e c t e d . I n s t e a d , in o r d e r t o a llo w c o m p a r is o n o f m y r e s u lt s w it h t h o s e o f F o n s 9 F o r t h is r e g r e s s io n , I c r e a t e d a y ie ld s p r e a d b y s u b t r a c t in g t h e 3 0 - y e a r c o n s t a n t m a t u r it y T r e a s u r y y ie ld fr o m t h e M o o d y ’s A a a I n d u s t r ia ls y ie ld . T h e r e s u lt s a r e n o t s e n s it iv e t o t h e p r e c is e c a lc u la t io n o f t h e s p r e a d . 1 8
( 1 9 9 4 ) , I d is t in g u is h b e t w e e n b o n d s t h a t a r e c u r r e n t ly c a lla b le a n d b o n d s t h a t w ill r e m a in c a ll p r o t e c t e d fo r a t le a s t a n o t h e r y e a r . I d r o p b o n d s t h a t a r e c u r r e n t ly c a ll p r o t e c t e d b u t w ill b e c a lla b le w it h in a y e a r . I fu r t h e r d iv id e e a c h o f t h e s e t w o g r o u p s u s in g t h r e e p r ic e 1 0 c a t e g o r ie s : B e lo w 9 0 , b e t w e e n 9 0 a n d 1 0 0 , a n d g r e a t e r t h a n 1 0 0 ( p a r e q u a ls 1 0 0 ) . I e s t im a t e e q u a t io n ( 1 ) fo r e a c h t im e s e r ie s o f s p r e a d c h a n g e s . T h e r e s u lt s a r e d is p la y e d in T a b le 6 . T w o im p o r t a n t c o n c lu s io n s c a n b e d r a w n fr o m a c o m p a r is o n o f t h e r e s u lt s in t h is t a b le w it h t h o s e in T a b le 2 . F ir s t , t h e s e n s it iv it y o f a c a lla b le b o n d ’s s p r e a d t o c h a n g e s in T r e a s u r y y ie ld s is p o s it iv e ly r e la t e d t o t h e b o n d ’s p r ic e , a s o p t io n p r ic in g t h e o r y im p lie s . Y ie ld s p r e a d s o n c a lla b le b o n d s w it h lo w p r ic e s ( le s s t h a n 9 0 ) b e h a v e s im ila r ly t o s p r e a d s o n n o n c a lla b le b o n d s . F o r b o t h n o n c a lla b le b o n d s a n d c u r r e n t ly c a lla b le , lo w - p r ic e d b o n d s , t h e (cid:0) p o in t e s t im a t e o f b is 0 :1 7 , t h e p o in t e s t im a t e o f b is in s ig n i(cid:12) c a n t ly d i(cid:11) e r e n t 3 m ;j s l;j j j 2 fr o m z e r o , a n d t h e a d ju s t e d R is b e t w e e n 0 .2 2 a n d 0 .2 5 . P P B y c o n t r a s t , y ie ld s p r e a d s o n h ig h - p r ic e d c a lla b le b o n d s e x h ib it v e r y s t r o n g in v e r s e r e la t io n s h ip s w it h c h a n g e s in T r e a s u r y y ie ld s . F o r h ig h - p r ic e d ( p r ic e s a b o v e p a r ) c u r r e n t ly - (cid:0) c a lla b le b o n d s , t h e p o in t e s t im a t e o f b is 0 :5 6 . T h e p o in t e s t im a t e o f b 3 m ;j s l;j j j is a lm o s t id e n t ic a l, im p ly in g t h a t t h e r e la t io n b e t w e e n y ie ld s p r e a d s o n t h e s e lo n g - t e r m P P c a lla b le b o n d s a n d T r e a s u r y t e r m s t r u c t u r e c a n b e c o lla p s e d in t o a r e la t io n b e t w e e n t h e y ie ld s p r e a d s a n d t h e lo n g - t e r m T r e a s u r y y ie ld . T h is is n o t s u r p r is in g ; t h e c a ll o p t io n v a lu e o f a c o r p o r a t e b o n d s h o u ld d e p e n d o n t h e T r e a s u r y y ie ld o f a n e q u iv a le n t - m a t u r it y T r e a s u r y 2 b o n d . T h e a d ju s t e d R o f t h is r e g r e s s io n is 0 :8 0 . Y ie ld s p r e a d s o n m e d iu m - p r ic e d b o n d s fa ll b e t w e e n h ig h - p r ic e d b o n d s a n d lo w - p r ic e d b o n d s in t h e ir r e s p o n s iv e n e s s t o T r e a s u r y y ie ld s . S e c o n d , y ie ld s p r e a d s c o n s t r u c t e d w it h c a lla b le , b u t c u r r e n t ly c a ll p r o t e c t e d , b o n d s b e h a v e s im ila r ly t o y ie ld s p r e a d s c o n s t r u c t e d w it h c u r r e n t ly c a lla b le b o n d s . F o r e a c h p r ic e b a n d , t h e e s t im a t e d s u m s b a n d b fo r c u r r e n t ly c a lla b le b o n d s a r e s lig h t ly m o r e 3 m ;j s l;j j j n e g a t iv e t h a n t h e c o r r e s p o n d in g s u m s fo r c u r r e n t ly c a ll- p r o t e c t e d b o n d s . T h is c o n c lu s io n P P s u g g e s t s t h a t , fo r c e r t a in p u r p o s e s , it is in a p p r o p r ia t e t o u s e y ie ld s o n t e m p o r a r ily c a llp r o t e c t e d b o n d s a s p r o x ie s fo r y ie ld s o n n o n c a lla b le b o n d s . F u r t h e r e v id e n c e t h a t c a lla b le b o n d y ie ld s p r e a d s a r e fu n d a m e n t a lly d i(cid:11) e r e n t fr o m n o n c a lla b le b o n d y ie ld s p r e a d s is illu s t r a t e d in F ig . 1 . I n t h is (cid:12) g u r e I fo c u s o n lo n g m a t u r it y A - r a t e d b o n d s , w h ic h is t h e o n ly c a t e g o r y o f lo n g - m a t u r it y b o n d s fo r w h ic h I h a v e n o m is s in g o b s e r v a t io n s fo r n o n c a lla b le b o n d y ie ld s p r e a d s . P a n e l A o f t h e (cid:12) g u r e d is p la y s t h e 3 0 - y e a r c o n s t a n t m a t u r it y T r e a s u r y y ie ld . P a n e l B d is p la y s b o t h t h e y ie ld s p r e a d I c o n s t r u c t e d fo r n o n c a lla b le lo n g - m a t u r it y A - r a t e d b o n d s a n d t h e s p r e a d b e t w e e n M o o d y ’s 1 0 I t w o u ld b e m o r e a p p r o p r ia t e t o s o r t b o n d s b y t h e d i(cid:11) e r e n c e s b e t w e e n t h e ir c u r r e n t b o n d p r ic e s a n d t h e ir c a ll p r ic e s . H o w e v e r , t h e d a t a s e t d o e s n o t r e p o r t a c a ll p r ic e fo r c a lla b le b o n d s t h a t a r e in t h e ir c a ll- p r o t e c t io n p e r io d . T h e r e fo r e I h a v e n o c a ll p r ic e s fo r c a lla b le b o n d s t h a t r e a c h t h e ir (cid:12) r s t c a ll d a t e a ft e r M a r c h 1 9 9 5 . 1 9
I n d u s t r ia l A - r a t e d B o n d Y ie ld A v e r a g e s a n d t h e 3 0 - y e a r c o n s t a n t m a t u r it y T r e a s u r y y ie ld . T h e r e a r e t h r e e in t e r e s t in g fe a t u r e s d is p la y e d in P a n e l B . F ir s t , t h e s h a r p d e c lin e in T r e a s u r y y ie ld s d u r in g 1 9 8 5 a n d 1 9 8 6 w a s m a t c h e d b y a d r a m a t ic ju m p in t h e M o o d y ’s y ie ld s p r e a d , w h ile t h e in c r e a s e in t h e s p r e a d fo r n o n c a lla b le b o n d s w a s m u c h s m a lle r . S e c o n d , d u r in g 1 9 9 1 , t h e s p r e a d o n t h e n o n c a lla b le b o n d s ju m p e d , t h e n q u ic k ly fe ll; t h e M o o d y ’s s p r e a d r o s e o n ly s lig h t ly . T h is r e (cid:13) e c t s t h e in c lu s io n o f b o n d s is s u e d b y (cid:12) n a n c ia l (cid:12) r m s in m y s e r ie s o f n o n c a lla b le y ie ld s p r e a d s . T h ir d , b y t h e e n d o f t h e s a m p le , t h e M o o d y ’s s p r e a d a n d t h e n o n c a lla b le b o n d s p r e a d t r a c k e d c lo s e ly , e v e n w h ile T r e a s u r y y ie ld s f e ll, t h e n r o s e s h a r p ly . T h is r e c e n t p a t t e r n is lik e ly t h e r e s u lt o f a s e c u la r c h a n g e in t h e c o m p o s it io n o f M o o d y ’s B o n d I n d e x e s . O v e r t im e , (cid:12) r m s s h ift e d t h e ir d e b t is s u a n c e a w a y fr o m c a lla b le in s t r u m e n t s , a n d t h e M o o d y ’s I n d e x e s s h ift e d a s w e ll. B y O c t o b e r 1 9 9 4 , 1 2 o f t h e 1 6 b o n d s in c lu d e d in M o o d y ’s A - r a t e d I n d u s t r ia l B o n d I n d e x w e r e n o n c a lla b le . M o r e o v e r , t h r e e o f t h e fo u r c a lla b le b o n d s in c lu d e d in t h e I n d e x h a d p r ic e s b e lo w 9 0 in O c t o b e r 1 9 9 4 ( t h e o t h e r b a r e ly e x c e e d e d 9 0 ) . H e n c e t h e s e c a lla b le b o n d s a c t m o r e lik e n o n c a lla b le b o n d s in t h e ir r e s p o n s iv e n e s s t o T r e a s u r y y ie ld s . S p r e a d s o n c u r r e n t ly c a lla b le A - r a t e d b o n d s a r e d is p la y e d in P a n e l C , w h ile P a n e l D d is p la y s s p r e a d s o n c a lla b le A - r a t e d b o n d s t h a t a r e c a ll- p r o t e c t e d fo r a t le a s t a y e a r . I n b o t h p a n e ls it is c le a r t h a t t h e c a ll o p t io n a (cid:11) e c t s y ie ld s p r e a d s b e c a u s e s p r e a d s o n h ig h - p r ic e d b o n d s ( i.e ., t h o s e c lo s e r t o t h e ir c a ll p r ic e ) a r e h ig h e r t h a n s p r e a d s o n lo w - p r ic e d b o n d s . T h is s u g g e s t s t h a t a t t e m p t s t o m e a s u r e d e fa u lt r is k u s in g y ie ld s p r e a d s o n c a lla b le b o n d s , e v e n if t h e y a r e n o t c u r r e n t ly c a lla b le , is p r o b le m a t ic . M o r e o v e r , t h e d is p la y e d d i(cid:11) e r e n c e b e t w e e n h ig h - p r ic e d b o n d s p r e a d s a n d lo w - p r ic e d s p r e a d s lik e ly u n d e r s t a t e s t h e t r u e d i(cid:11) e r e n c e o w in g t o im p r e c is io n in c r e d it r a t in g s . S o r t in g b o n d s b y p r ic e t e n d s t o a ls o s o r t b o n d s b y c r e d it q u a lit y , le a d in g t o a n in v e r s e r e la t io n b e t w e e n b o n d p r ic e s a n d y ie ld s p r e a d s . T o illu s t r a t e t h is b ia s , c o n s id e r t w o b o n d s w it h id e n t ic a l fe a t u r e s , is s u e d b y t w o d i(cid:11) e r e n t (cid:12) r m s . T h e b o n d s h a v e t h e s a m e c r e d it r a t in g , b u t t h e m a r k e t m a y v ie w t h e t w o (cid:12) r m s a s h a v in g s o m e w h a t d i(cid:11) e r e n t c r e d it q u a lit ie s . T h e b o n d is s u e d b y t h e (cid:12) r m w it h h ig h e r p e r c e iv e d c r e d it q u a lit y w ill h a v e a h ig h e r p r ic e , a n d a lo w e r y ie ld s p r e a d , t h a n t h e o t h e r b o n d . A c u r io u s fe a t u r e o f F ig . 1 t h a t is n o t e x p lo r e d in t h is p a p e r is w h y s p r e a d s o n h ig h p r ic e d c a ll- p r o t e c t e d b o n d s d id n o t ju m p in 1 9 9 3 a s T r e a s u r y y ie ld s fe ll. S p r e a d s o n h ig h p r ic e d , c u r r e n t ly c a lla b le b o n d s ju m p e d w h e n T r e a s u r y y ie ld s fe ll d u r in g 1 9 8 6 { 1 9 8 7 a n d d u r in g 1 9 9 3 , w h ile s p r e a d s o n h ig h - p r ic e d , c a ll- p r o t e c t e d b o n d s ju m p e d o n ly d u r in g t h e e a r lie r p e r io d . E x p lo r in g t h is is s u e is le ft fo r fu t u r e w o r k . 2 0
7 . C o n c l u d i n g R e m a r k s Y ie ld s p r e a d s o n in v e s t m e n t g r a d e n o n c a lla b le b o n d s fa ll w h e n t h e le v e l o f t h e T r e a s u r y t e r m s t r u c t u r e r is e s . T h e e x t e n t o f t h is d e c lin e d e p e n d s o n t h e in it ia l c r e d it q u a lit y o f t h e b o n d ; fo r e x a m p le , t h e d e c lin e is s m a ll fo r A a a - r a t e d b o n d s a n d la r g e fo r B a a - r a t e d b o n d s . A p p ly in g t h e s a m e e m p ir ic a l a n a ly s is t o c h a n g e s in y ie ld s p r e a d s b a s e d o n r e fr e s h e d in d e x e s o f n o n c a lla b le b o n d y ie ld s p r o d u c e s m u c h w e a k e r r e s u lt s . T h e u s e o f s u c h in d e x e s h o ld s o n e m e a s u r e o f c r e d it q u a lit y ( c r e d it r a t in g s ) c o n s t a n t o v e r t im e , t h u s a t t e n u a t in g t h e r e s p o n s iv e n e s s o f y ie ld s p r e a d s t o o t h e r v a r ia b le s c o r r e la t e d w it h c r e d it q u a lit y . I n o t h e r w o r d s , t h e u s e o f r e fr e s h e d y ie ld in d e x e s t o m e a s u r e c h a n g e s in c r e d it q u a lit y o v e r t im e w ill s y s t e m a t ic a lly u n d e r e s t im a t e s u c h c h a n g e s a n d , a t le a s t fo r t h e q u e s t io n s e x a m in e d in t h is p a p e r , r e s u lt in in c o r r e c t in fe r e n c e s . B y c o n t r a s t , t h e r e is a v e r y s t r o n g n e g a t iv e r e la t io n b e t w e e n T r e a s u r y y ie ld s a n d y ie ld s p r e a d s b a s e d o n M o o d y ’s y ie ld in d e x e s . M o o d y ’s in d e x e s , lik e m a n y o t h e r in d e x e s , h a v e h is t o r ic a lly b e e n c o n s t r u c t e d p r im a r ily w it h c a lla b le b o n d s . S u c h y ie ld in d e x e s a r e s e n s it iv e t o v a r ia t io n s in t h e v a lu e s o f t h e b o n d s ’ c a ll o p t io n s , w h ic h in t u r n a r e s e n s it iv e t o t h e le v e l o f in t e r e s t r a t e s . T h is s e n s it iv it y is t h e s o u r c e o f t h e s t r o n g n e g a t iv e r e la t io n : W h e n T r e a s u r y y ie ld s r is e , t h e v a lu e o f t h e o p t io n t o c a ll a b o n d fa lls , lo w e r in g t h e y ie ld o n t h e c a lla b le c o r p o r a t e b o n d , a n d t h e r e fo r e lo w e r in g t h e y ie ld s p r e a d . H e n c e v a r ia t io n s in y ie ld s p r e a d s b a s e d o n s u c h in d e x e s s h o u ld n o t b e v ie w e d a s d r iv e n p r im a r ily b y v a r ia t io n s in c r e d it q u a lit y . B o t h T r e a s u r y y ie ld s a n d c o r p o r a t e b o n d s p r e a d s a r e lin k e d t o fu t u r e v a r ia t io n s in a g g r e g a t e o u t p u t . H o w e v e r , it is n o t o b v io u s t h a t t h is jo in t lin k is r e s p o n s ib le fo r t h e r e la t io n b e t w e e n T r e a s u r y y ie ld s a n d y ie ld s p r e a d s o b s e r v e d in t h is p a p e r . I n fa c t , p r e lim in a r y e v id e n c e c a s t s s o m e d o u b t o n t h e n o t io n t h a t t h is r e la t io n is d r iv e n b y v a r ia t io n s in c r e d it q u a lit y . T h is is s u e , a s w e ll a s m a n y o t h e r s id e n t i(cid:12) e d h e r e , a w a it fu t u r e r e s e a r c h . A p p e n d i x M e a n y ie ld s , y ie ld s p r e a d s , a n d m o n t h ly d i(cid:11) e r e n c e d y ie ld s p r e a d s a r e c o n s t r u c t e d fo r a n u m b e r o f s e t s o f c o r p o r a t e b o n d s . T h e r e a r e fo u r b u s in e s s s e c t o r s e x a m in e d : ( 1 ) in d u s t r ia l (cid:12) r m s ; ( 2 ) u t ilit ie s ; ( 3 ) (cid:12) n a n c ia l (cid:12) r m s ; ( 4 ) a ll o f t h e a b o v e . T h e r e a r e a ls o fo u r r a t in g c a t e g o r ie s e x a m in e d : A a a , A a , A , a n d B a a . T h r e e r a n g e s o f r e m a in in g m a t u r it y a r e c o n s id e r e d : ( 1 ) S h o r t ( t w o t o s e v e n y e a r s ) ; ( 2 ) m e d iu m ( s e v e n t o (cid:12) ft e e n y e a r s ) ; ( 3 ) lo n g ( (cid:12) ft e e n t o t h ir t y y e a r s ) . T h e t im e s e r ie s o f c o r p o r a t e b o n d y ie ld s , s p r e a d s , a n d c h a n g e s in s p r e a d s a r e c o n s t r u c t e d a s fo llo w s . F ix a b u s in e s s s e c t o r , a r a t in g c a t e g o r y , a n d a m a t u r it y r a n g e . F o r e a c h m o n t h t in 2 1
[J a n u a r y 1 9 8 5 , F e b r u a r y 1 9 9 5 ], I c o n s id e r a ll s t r a ig h t b o n d s ( e .g ., n o t c o n v e r t ib le o r C M O lik e ) in t h e g iv e n b u s in e s s s e c t o r t h a t h a v e , in m o n t h t , t h e a p p r o p r ia t e r a t in g a n d t im e - t o m a t u r it y . I a ls o r e q u ir e t h a t c o u p o n p a y m e n t s ( if a n y ) b e m a d e s e m ia n n u a lly , in s t e a d o f, s a y , m o n t h ly . ( T h is la t t e r r e s t r ic t io n e x c lu d e s v e r y fe w b o n d s .) I u s e t h e M o o d y ’s r a t in g if it is a v a ila b le , o t h e r w is e I u s e S & P ’s r a t in g . I t h e n e x c lu d e a ll b o n d s t h a t a r e c a lla b le o r p u t a b le a t s o m e p o in t in t h e b o n d ’s life , o r t h a t h a v e a s in k in g fu n d o p t io n . I fu r t h e r e x c lu d e a ll b o n d s t h a t d o n o t h a v e \ q u o t e " p r ic e s ( in s t e a d o f \ m a t r ix " p r ic e s ) in b o t h m o n t h s t a n d t + 1 . I a ls o e x c lu d e b o n d s t h a t a r e , in e it h e r m o n t h t o r t + 1 , n o t in a L e h m a n B r o t h e r s in d e x o r a r e a b o u t t o le a v e a L e h m a n B r o t h e r s in d e x . S u c h b o n d s t e n d t o h a v e m o r e d a t a e r r o r s t h a n o t h e r b o n d s in t h e D a t a b a s e . T o e lim in a t e s o m e o b v io u s e r r o r s in t h e d a t a , I a ls o e x c lu d e b o n d s t h a t h a v e a r e p o r t e d c o u p o n g r e a t e r t h a n 2 5 % , a p r ic e le s s t h a n 1 / 1 0 0 o f p a r o r a p r ic e g r e a t e r t h a n t w ic e p a r . T h e r e s u lt is a s e t o f N b o n d s w it h c o r r e s p o n d in g m o n t h - e n d t y ie ld s . ( N o t e t h a t t t h e r e w ill b e a d i(cid:11) e r e n t s e t o f N b o n d s fo r e a c h c o m b in a t io n o f b u s in e s s s e c t o r , r a t in g t c a t e g o r y , a n d m a t u r it y r a n g e .) T h e s e y ie ld s a r e q u o t e d o n a b o n d - e q u iv a le n t b a s is , n o t a s c o n t in u a lly c o m p o u n d e d y ie ld s . T h e m e a n o f t h e s e y ie ld s is m y m e a s u r e o f t h e m o n t h t y ie ld fo r t h is s e c t o r / r a t in g / m a t u r it y . I c o n s t r u c t y ie ld s p r e a d s fo r e a c h b o n d b y s u b t r a c t in g a n a p p r o p r ia t e T r e a s u r y y ie ld . T h e T r e a s u r y D e p a r t m e n t c o n s t r u c t s c o n s t a n t m a t u r it y y ie ld s b y in t e r p o la t in g b o n d - e q u iv a le n t y ie ld s o n a c t iv e ly - t r a d e d T r e a s u r y n o t e s a n d b o n d s . I u s e t h e ir r e p o r t e d m o n t h - e n d y ie ld s o n 2 , 3 , 5 , 7 , 1 0 , a n d 3 0 y e a r c o u p o n b o n d s . F o r e a c h c o r p o r a t e b o n d i , I c o n s t r u c t t h e a p p r o p r ia t e T r e a s u r y y ie ld b y in t e r p o la t in g b e t w e e n t h e c lo s e s t c o n s t a n t m a t u r it y y ie ld s o n e it h e r s id e o f b o n d i ’s r e m a in in g t im e - t o - m a t u r it y . T h e m o n t h t s p r e a d fo r t h is b u s in e s s s e c t o r , r a t in g , a n d m a t u r it y is t h e m e a n ( o v e r t h e N b o n d s ) t o f t h e in d iv id u a l b o n d s p r e a d s . I f N = 0 , t h e o b s e r v a t io n is s e t t o a m is s in g v a lu e . t T h e s e N b o n d s a ls o h a v e m o n t h - e n d t + 1 y ie ld s . I c o n s t r u c t m o n t h - e n d t + 1 s p r e a d s t fo r t h e s e b o n d s in t h e m a n n e r d e s c r ib e d a b o v e . I t h e n c a lc u la t e , fo r e a c h b o n d i , t h e c h a n g e in t h e s p r e a d fr o m t t o t + 1 . F in a lly , I c a lc u la t e t h e m e a n ( o v e r t h e N b o n d s ) c h a n g e in t t h e s p r e a d fr o m t t o t + 1 . T h is m e a n is m y o b s e r v a t io n o f (cid:1) S fo r t h e g iv e n b u s in e s s s ;i;m ;t+ 1 s e c t o r s , r a t in g i , a n d m a t u r it y r a n g e m . A g a in , if N = 0 , t h is o b s e r v a t io n is s e t t o a t m is s in g v a lu e . W h e n c o n s t r u c t in g \ r e fr e s h e d " in d e x e s o f b o n d s p r e a d s , I a lt e r t h e a b o v e p r o c e d u r e in t w o w a y s . F ir s t , w h e n c o n s t r u c t in g t h e s e t o f N b o n d s fo r m o n t h t , I ig n o r e a n y m o n t h t t + 1 in fo r m a t io n . F o r e x a m p le , a b o n d c a n b e in c lu d e d in t h e s e t o f b o n d s fo r m o n t h t e v e n if it h a s n o q u o t e p r ic e fo r m o n t h t + 1 . S e c o n d , t h e m o n t h ly c h a n g e in t h e s p r e a d is d e (cid:12) n e d a s t h e d i(cid:11) e r e n c e b e t w e e n t h e m e a n s p r e a d o n t h e N b o n d s in m o n t h t + 1 a n d t h e t+ 1 m e a n s p r e a d o n t h e N b o n d s in m o n t h t . H e n c e t h e m e a s u r e o f t h e c h a n g e in t h e s p r e a d t is s im p ly t h e (cid:12) r s t d i(cid:11) e r e n c e o f t h e t im e s e r ie s o f s p r e a d s . 2 2
A C C C C C D D E E F b h h o o o u u s s o R e f e r e n c e s k e n , P e t e r , 1 9 9 3 , \ V a lu a t io n o f d e fa u lt - r is k y in t e r e s t - r a t e s w a p s ," A d v a n c e s in F u t u r e s a n d O p t io n s R e s e a r c h 6 , 9 3 - 1 1 6 . e n , N a i- fu , 1 9 9 1 , \ F in a n c ia l in v e s t m e n t o p p o r t u n it ie s a n d t h e m a c r o e c o n o m y ," J o u r n a l o f F in a n c e 4 6 , 5 2 9 - 5 5 4 . e n , R e n - r a w , a n d L o u is S c o t t , 1 9 9 3 , \ M a x im u m lik e lih o o d e s t im a t io n fo r a m u lt ifa c t o r e q u ilib r iu m m o d e l o f t h e t e r m s t r u c t u r e o f in t e r e s t r a t e s ," J o u r n a l o f F ix e d I n c o m e 3 , 1 4 - 3 1 . m m e r c e C le a r in g H o u s e , 1 9 9 2 , S t a t e T a x H a n d b o o k , C o m m e r c e C le a r in g H o u s e , I n c . ( C h ic a g o , I L ) . r n e ll, B r a d fo r d , a n d K e v in G r e e n , 1 9 9 1 , \ T h e in v e s t m e n t p e r fo r m a n c e o f lo w - g r a d e b o n d fu n d s ," J o u r n a l o f F in a n c e 4 6 , 2 9 - 4 8 . o p e r , I a n , a n d A n t o n io M e llo , 1 9 9 1 , \ T h e d e fa u lt r is k o f s w a p s ," J o u r n a l o f F in a n c e 4 6 , 5 9 7 - 6 2 0 . (cid:14) e , D a r r e ll, a n d M in g H u a n g , 1 9 9 5 , \ S w a p r a t e s a n d c r e d it q u a lit y ," W o r k in g p a p e r , S t a n fo r d G r a d u a t e S c h o o l o f B u s in e s s ( S t a n fo r d , C A ) . (cid:14) e , D a r r e ll, a n d K e n n e t h J . S in g le t o n , 1 9 9 5 , \ A n e c o n o m e t r ic m o d e l o f t h e t e r m s t r u c t u r e o f in t e r e s t r a t e s w a p y ie ld s ," W o r k in g p a p e r , S t a n fo r d G r a d u a t e S c h o o l o f B u s in e s s ( S t a n fo r d , C A ) . t r e lla , A r t u r o , a n d G ik a s A . H a r d o u v e lis , 1 9 9 1 , \ T h e t e r m s t r u c t u r e a s a p r e d ic t o r o f r e a l e c o n o m ic a c t iv it y ," J o u r n a l o f F in a n c e 4 6 , 5 5 5 - 5 7 6 . t r e lla , A r t u r o , a n d F r e d e r ic S . M is h k in , 1 9 9 6 , \ P r e d ic t in g U .S . r e c e s s io n s : F in a n c ia l v a r ia b le s a s le a d in g in d ic a t o r s ," W o r k in g p a p e r , F e d e r a l R e s e r v e B a n k o f N e w Y o r k ( N e w Y o r k , N Y ) . n s , J e r o m e S ., 1 9 9 4 , \ U s in g d e fa u lt r a t e s t o m o d e l t h e t e r m s t r u c t u r e o f c r e d it r is k ," F in a n c ia l A n a ly s t s J o u r n a l, S e p t e m b e r / O c t o b e r , 2 5 - 3 2 . 2 3
F G I J K L L L L M M N S o n s , J e r o m e S ., L e a C a r t y , a n d J e r e m y K a u fm a n , 1 9 9 4 , \ C o r p o r a t e b o n d d e fa u lt s a n d d e fa u lt r a t e s 1 9 7 0 { 1 9 9 3 ," M o o d y ’s S p e c ia l R e p o r t , J a n u a r y . r in b la t t , M a r k , 1 9 9 5 , \ A n a n a ly t ic a l s o lu t io n fo r in t e r e s t r a t e s w a p s p r e a d s ," W o r k in g p a p e r , U C L A ( L o s A n g e le s , C A ) . w a n o w s k i, R a y m o n d , a n d R a x e s h C h a n d r a , 1 9 9 5 , \ H o w d o c o r p o r a t e s p r e a d c u r v e s m o v e o v e r t im e ? " W o r k in g p a p e r , S a lo m o n B r o t h e r s ( N e w Y o r k , N Y ) . a r r o w , R o b e r t , D a v id L a n d o , a n d S t u a r t T u r n b u ll, 1 9 9 4 , \ A M a r k o v m o d e l fo r t h e t e r m s t r u c t u r e o f c r e d it r is k s p r e a d s ," W o r k in g p a p e r , C o r n e ll U n iv e r s it y ( I t h a c a , N Y ) . w a n , S im o n H ., \ F ir m - s p e c i(cid:12) c in fo r m a t io n a n d t h e c o r r e la t io n b e t w e e n in d iv id u a l s t o c k s a n d b o n d s ," J o u r n a l o f F in a n c ia l E c o n o m ic s 4 0 , 6 3 - 8 0 . a n d o , D a v id , 1 9 9 4 , \ T h r e e e s s a y s o n c o n t in g e n t c la im s p r ic in g ," P h .D . d is s e r t a t io n , C o r n e ll ( I t h a c a , N Y ) . it t e r m a n , R o b e r t , a n d T h o m a s I b e n , 1 9 9 1 , \ C o r p o r a t e b o n d v a lu a t io n a n d t h e t e r m s t r u c t u r e o f c r e d it s p r e a d s ," J o u r n a l o f P o r t fo lio M a n a g e m e n t , S p r in g , 5 2 - 6 4 . it t e r m a n , R o b e r t , a n d J o s (cid:19)e S c h e in k m a n , 1 9 9 1 , \ C o m m o n fa c t o r s a (cid:11) e c t in g b o n d r e t u r n s ," J o u r n a l o f F ix e d I n c o m e 1 , 5 4 - 6 1 . o n g s t a (cid:11) , F r a n c is , a n d E d u a r d o S c h w a r t z , 1 9 9 5 , \ A s im p le a p p r o a c h t o v a lu in g r is k y (cid:12) x e d a n d (cid:13) o a t in g r a t e d e b t ," J o u r n a l o f F in a n c e 5 0 , 7 8 9 - 8 2 0 . e r t o n , R o b e r t C ., 1 9 7 4 , \ O n t h e p r ic in g o f c o r p o r a t e d e b t : T h e r is k s t r u c t u r e o f in t e r e s t r a t e s ," T h e J o u r n a l o f F in a n c e 2 9 , 4 4 9 - 4 7 0 . a d a n , D ilip B . a n d H a lu k U n a l, 1 9 9 4 , \ P r ic in g t h e r is k s o f d e fa u lt ," W o r k in g p a p e r , W h a r t o n ( P h ila d e lp h ia , P A ) . u n n , K e n n e t h P ., J r ., J o a n n e H ill, a n d T h o m a s S c h n e e w e is , 1 9 8 6 , \ C o r p o r a t e b o n d p r ic e d a t a s o u r c e s a n d r e t u r n / r is k m e a s u r e m e n t ," J o u r n a l o f F in a n c ia l a n d Q u a n t it a t iv e A n a ly s is 2 1 , 1 9 7 - 2 0 8 . e v e r n , A la n K ., a n d W illia m J . S t e w a r t , 1 9 9 2 , \ T h e c o r p o r a t e - T r e a s u r y y ie ld s p r e a d a n d s t a t e t a x e s ," J o u r n a l o f E c o n o m ic s a n d B u s in e s s 4 4 , 1 6 1 - 1 6 6 . 2 4
S S S W h c t im h o o c a r k o , D a v id C ., N a o h ik o T e jim a , a n d D o n a ld R . r is k y d e b t w h e n in t e r e s t r a t e s a r e s t o c h a s t ic ," le s , M y r o n , a n d J o s e p h W illia m s , 1 9 7 7 , \ E s t im J o u r n a l o f F in a n c ia l E c o n o m ic s 5 , 3 0 9 - 3 2 7 . k , J a m e s H ., a n d M a r k W . W a t s o n , 1 9 8 9 , \ N e w n o m ic in d ic a t o r s ," in O liv ie r J . B la n c h a r d a n d c o n o m ic s A n n u a l 1 9 8 9 ( M I T P r e s s , C a m b r id g e g a , A r t h u r D ., 1 9 9 1 , \ C o r p o r a t e b o n d p r ic e d is m a r k e t s ," J o u r n a l o f F ix e d I n c o m e 1 , 7 - 1 6 . 2 5 v a n D e v e J o u r n a l o a t in g b e t in d e x e s S t a n le y F ) 4 , 3 5 1 - 3 c r e p a n c ie n t e r , 1 9 f F ix e d a s fr o m o f c o in c is c h e r , 9 3 . s in t h e 9 3 , \ T h e p r ic in g o f I n c o m e 3 , 5 8 - 6 5 . n o n s y n c h r o n o u s d a t a id e n t a n d le a d in g e c o e d s .: N B E R M a c r o e d e a le r a n d e x c h a n g e ," -
T a b l e 1 . S u m m a r y s t a t i s t i c s f o r c o r p o r a t e b o o p t i o n - l i k e f e a t u r e s , J a n u a r y 1 9 8 5 t o F e b r u a r y F o r a g iv e n g r o u p o f b o n d s ( d e (cid:12) n e d b y s e c t o r , m o n t h t m e a n y ie ld s p r e a d in m o n t h ( o v e r t h e a p p r o p r ia t e b o n d s w it h n o s in k in g fu n d o p t io n t h a t h a v e y ie ld s b a is t h e m e a n c h a n g e in t h e s p r e a d s o n t h e s e b o n d s fr o m t S S t t+ 1 , a n d (cid:1) a r e s e t t o m is s in g v a lu e s . P a n e l A . I n d N u m . o f M e a n N u m . M o n t h ly o f B o n d s p e r a M a t u r it y R a t in g O b s e r . M o n t h ly O b s . L o n g A a a 6 2 2 .3 A a 1 0 1 7 .5 A 1 2 2 3 3 .7 B a a 1 0 5 2 1 .5 M e d iu m A a a 4 0 3 .9 A a 1 1 6 1 1 .8 A 1 2 2 5 0 .6 B a a 1 2 2 2 9 .6 S h o r t A a a 1 0 7 6 .0 A a 1 2 2 1 5 .1 A 1 2 2 5 8 .4 B a a 1 2 2 3 3 .7 P a n e l B . U N u m . o f M e a n N u m . M o n t h ly o f B o n d s p e r a M a t u r it y R a t in g O b s e r . M o n t h ly O b s . L o n g A a a 3 8 2 .7 A a 9 1 1 .0 A 9 8 4 .1 B a a 6 6 4 .8 M e d iu m A a a 3 8 5 .6 A a 9 8 1 1 .5 A 1 2 0 1 7 .9 B a a 1 1 9 2 0 .1 S h o r t A a a 2 5 2 .0 A a 9 0 1 0 .4 A 1 2 2 1 5 .8 B a a 1 2 2 2 1 .6 n d s i n L e h m a n B r o t h e r s d a t a s e t 1 9 9 5 . t t S t m a t u r it y , a n d m o n t h r a t in g ) , is T r e a s u r y in s t r u m e n t ) o n a ll n o n c a lla b t s e d o n q u o t e p r ic e s in b o t h m o n t h s a n t t m o n t h t o + 1 . I f t h e r e a r e n o s u c h b u s t r ia l s e c t o r M e a n S t d . D e v . S S t t+ 1 Y e a r s t o M a t . o f (cid:1) 2 8 .4 0 .5 9 0 .0 4 2 2 0 .8 0 .8 7 0 .0 9 5 2 2 .1 1 .1 7 0 .1 4 1 2 1 .0 1 .9 8 0 .1 9 2 1 0 .4 0 .4 7 0 .0 4 8 9 .5 0 .6 9 0 .0 9 7 9 .6 0 .9 6 0 .1 0 8 8 .9 1 .4 8 0 .1 6 1 3 .4 0 .4 6 0 .0 9 5 4 .0 0 .5 6 0 .0 8 3 4 .5 0 .8 7 0 .1 0 8 4 .7 1 .4 9 0 .2 2 2 t ilit y s e c t o r M e a n S t d . D e v . S S t t+ 1 Y e a r s t o M a t . o f (cid:1) 2 6 .1 0 .5 9 0 .0 4 7 2 7 .4 0 .8 0 0 .0 8 5 2 0 .9 1 .0 1 0 .1 1 0 2 3 .9 1 .7 3 0 .1 4 2 9 .8 0 .3 9 0 .0 3 3 9 .2 0 .5 8 0 .0 8 6 9 .1 0 .7 9 0 .0 9 6 9 .7 1 .3 2 0 .1 7 0 6 .1 0 .3 4 0 .0 2 6 4 .5 0 .5 4 0 .0 7 6 4 .4 0 .7 8 0 .0 9 1 4 .3 1 .1 5 0 .1 4 5 t h d le d o A A a t h a v e n o e (cid:12) n e d a s t h e , n o n p u t a b le t S t+ 1 + 1 . (cid:1) n d s in m o n t h R : ( 1 ) c o e f S t+ 1 fo r (cid:1) : 0 1 1 2 (cid:0) : 0 0 0 2 : 0 1 9 5 : 0 0 0 7 : 0 1 2 8 (cid:0) : 0 0 1 6 (cid:0) : 0 1 1 7 : 0 1 1 0 (cid:0) : 0 2 6 5 (cid:0) : 0 0 6 8 : 0 0 8 5 : 0 0 6 4 R : ( 1 ) c o e f S t+ 1 fo r (cid:1) : 0 1 2 4 (cid:0) : 0 0 0 8 : 0 1 3 4 : 0 2 0 5 (cid:0) : 0 1 9 4 (cid:0) : 0 3 2 9 : 0 0 0 6 (cid:0) : 0 0 1 7 (cid:0) : 0 2 2 1 (cid:0) : 0 2 4 6 (cid:0) : 0 0 0 7 : 0 0 1 1
7 M L M S M L M S a a a t u r it y o n g e d iu m h o r t a t u r it y o n g e d iu m h o r t ‘L o n g ’ n d 1 5 y a a m e a a t r s R A A A B A A A B A A A B R A A A B A A A B A A A B u t a t in g a a a a a a a a a a a a a a a a t in g a a a a a a a a a a a a a a a r it y b o m a t o u n r N M N M d s it y u m o n O b u m o n O b a r , a . o f t h ly s e r . 7 7 9 6 1 1 8 7 5 1 1 5 1 2 2 1 2 2 1 2 0 1 2 2 1 2 2 1 2 2 1 2 2 . o f t h ly s e r . 1 0 5 1 0 3 1 2 2 1 0 9 1 1 5 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 e b e t w n d ‘s h T a b l e 1 . ( c o P a n e l C . F in a M e a n N u m . o f B o n d s p e r M o n t h ly O b s . Y 1 0 .4 2 .0 7 .7 2 .7 7 .2 8 .0 3 9 .5 1 7 .0 1 1 .1 3 6 .4 9 6 .5 2 9 .7 P a n e l D . C o m b M e a n N u m . o f B o n d s p e r M o n t h ly O b s . Y 1 0 .0 1 0 .1 4 4 .4 2 5 .5 1 0 .4 2 8 .4 1 0 7 .6 6 5 .9 1 6 .7 5 9 .1 1 7 0 .7 8 4 .9 e e n 1 5 a n d 3 0 y e a r s o r t ’ m a t u r it y b o n d s n t i n u e d n c e s e c t o M e a n e a r s t o M 1 9 .1 1 9 .1 2 0 .0 1 9 .8 1 1 .0 9 .0 9 .2 8 .8 3 .6 3 .9 4 .0 4 .3 in e d s e c t M e a n e a r s t o M 2 3 .9 2 1 .3 2 1 .7 2 1 .2 1 0 .1 9 .2 9 .4 9 .1 3 .8 4 .0 4 .2 4 .4 t o m a t u a r e b e t w ) r a t . o r s a t . r it y , e e n 2 ‘m a 0 1 1 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 e n S t .8 9 .0 6 .3 0 .4 9 .8 1 .7 9 .1 4 .5 6 .8 3 .7 5 .9 9 .5 0 S t .7 9 .9 1 .1 8 .8 4 .7 7 .7 1 .0 1 .4 7 .6 7 .6 9 .9 3 .4 2 d iu d 7 m y ’ e S t d . o f (cid:1) 0 .1 0 .0 0 .1 0 .1 0 .1 0 .0 0 .1 0 .2 0 .0 0 .0 0 .1 0 .2 S t d . o f (cid:1) 0 .0 0 .0 0 .1 0 .1 0 .1 0 .0 0 .1 0 .1 0 .0 0 .0 0 .1 0 .1 m a t u a r s t o D S 0 8 3 8 0 9 5 2 9 8 2 4 D S 8 8 2 7 0 8 0 5 8 8 0 8 r e v t+ 7 9 1 4 6 4 2 3 2 8 0 3 e v t+ 8 7 5 7 2 4 6 3 3 3 7 4 it y m a . 1 . 1 b t u o r A A n d it y R fo R fo s a . ( 1 ) r (cid:1) (cid:0) (cid:0) (cid:0) (cid:0) ( 1 ) r (cid:1) (cid:0) (cid:0) r e c o e S t+ : 0 0 7 : 0 0 2 : 0 0 3 : 0 1 5 : 0 0 5 : 0 1 0 : 0 1 6 : 0 1 6 : 0 0 7 : 0 2 4 : 0 2 2 : 0 3 4 c o e S t+ : 0 1 1 : 0 0 0 : 0 1 5 : 0 0 3 : 0 0 4 : 0 0 8 : 0 1 4 : 0 1 7 : 0 1 2 : 0 1 9 : 0 1 8 : 0 2 3 b e t w : f 1 7 8 3 7 2 4 4 7 9 1 6 8 : f 1 5 5 0 3 6 8 9 0 7 1 3 6 e e n
(0:44) (5:22) (2:16) (0:87) (3:12) (0:70) [:006] [:341] [.061] Medium Baa 122 0:018 0:251 0:090 0:035 0:147 0:040 0:179 0:071 0:183 9.02 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (1:39) (6:00) (3:74) (0:29) (3:73) (3:01) [:005] [:667] [.415] Medium A 122 0:037 0:178 0:092 0:009 0:118 0:087 0:124 0:022 0:242 3.94 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (0:00) (5:25) (1:66) (0:52) (2:84) (0:72) [:016] [:214] [.108] Medium Aa 122 0:000 0:157 0:043 0:015 0:102 0:019 0:114 0:068 0:230 7.59 (cid:0) (cid:0) (cid:0) (cid:0) (0:17) (0:24) (1:19) (1:02) (0:02) (1:34) [:237] [:649] [.924] Medium Aaa 115 0:005 0:009 0:056 0:031 0:001 0:059 0:061 0:028 0:010 0.91 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (0:68) (6:72) (1:88) (0:81) (5:35) (0:04) [:000] [:004] [.526] Long Baa 109 0:050 0:416 0:104 0:042 0:317 0:002 0:362 0:278 0:397 3.20 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (1:03) (5:20) (1:38) (1:15) (0:44) (1:40) [:006] [:017] [.206] Long A 122 0:051 0:235 0:053 0:004 0:217 0:005 0:232 0:226 0:336 5.91 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (0:56) (5:35) (0:53) (0:11) (2:03) (0:15) [:012] [:064] [.373] Long Aa 103 0:020 0:168 0:021 0:003 0:119 0:005 0:167 0:121 0:221 4.25 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (1:09) (1:11) (2:34) (1:37) (1:56) (3:16) [:167] [:070] [.317] Long Aaa 105 0:034 0:035 0:078 0:048 0:048 0:113 0:080 0:114 0:135 4.73 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) P P Maturity a Rating Obs. b3m;(cid:0)1 b3m;0 b3m;1 bsl;(cid:0)1 bsl;0 bsl;1 b3m;j bsl;j Adj: R 2 across sectors b equality of coefs (cid:31) (4) test of 2 brackets. adjusted for generalized heteroskedasticity and two lags of moving average residuals. T-statistics are in parentheses. P-values of (cid:31) tests are in 2 Estimation is with OLS. The data range is January 1985 through March 1995. The variance-covariance matrix of the estimated coe(cid:14)cients is j=(cid:0)1 j=(cid:0)1 (cid:1)Si;m;t+1 =b0+ X b3m;j(cid:1)Y3m;t+1(cid:0)j + X bsl;j(cid:1)SLt+1(cid:0)j +ei;m;t+1 1 1 bill yield is denoted (cid:1)SLt+1. Treasury bill yield is denoted (cid:1)Y3m;t+1 and the change in the spread between the 30-year constant maturity Treasury yield and the three-month each group, mean changes in month-end yield spreads over Treasury yields from t to t+1 are denoted (cid:1)Si;m;t+1. The change in the three-month Noncallable bonds issued by industrial, utility, and (cid:12)nancial (cid:12)rms are grouped by their month-t credit rating i and remaining maturity m. For Table 2. Regressions of changes in corporate bond yield spreads on changes in Treasury yields.
(SUR) estimation. The(cid:31) (4)testsofequalityofthesumsofcoe(cid:14)cientsacrossindustrial,utility, and(cid:12)nancialbondsarebasedonSeeminglyUnrelatedRegression b 2 maturity bonds are between 2 and 7 years to maturity. ‘Long’ maturity bonds are between 15 and 30 years to maturity, ‘medium’ maturity bonds are between 7 and 15 years to maturity, and ‘short’ a (0:91) (6:84) (2:12) (1:11) (2:44) (1:80) [:000] [:714] [.363] Short Baa 122 0:034 0:280 0:088 0:051 0:091 0:112 0:226 0:030 0:141 4.33 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (0:03) (6:20) (3:28) (0:54) (2:36) (2:24) [:018] [:944] [.129] Short A 122 0:001 0:190 0:089 0:016 0:060 0:074 0:101 0:003 0:206 7.13 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (1:05) (5:43) (2:40) (0:40) (1:47) (1:96) [:007] [:816] [.171] Short Aa 122 0:025 0:140 0:068 0:010 0:033 0:052 0:098 0:009 0:212 6.41 (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) (0:21) (2:15) (0:43) (1:57) (1:01) (0:14) [:043] [:975] [.000] Short Aaa 122 0:004 0:104 0:015 0:031 0:035 0:006 0:085 0:001 0:088 30.94 (cid:0) (cid:0) (cid:0) Maturity Rating Obs. b3m;(cid:0)1 b3m;0 b3m;1 bsl;(cid:0)1 bsl;0 bsl;1 Pb3m;i Pbsl;i Adj: R acrosssectors a 2 b equality of coefs (cid:31) (4) test of 2 Table 2. (continued)
T y N m a y T r 1 m c 7 a b l e 3 . R e g r e s s i o n s o f c h a n g e s i n G D P o n c u r r e n t a n d l a g g e d c h a n g e s i n c o r p o r a t e b o n d i e l d s p r e a d s t o n c a lla b le b o n d s a r e s o r t e d b y t h e ir m o n t h - c r e d it r a t in g a n d r e m a in in g m a t u r it y . F o r e a c h g r o u p , m e a n o n t h ly c h a n g e s in m o n t h - e n d y ie ld s p r e a d s o v e r T r e a s u r y y ie ld s a r e c o n s t r u c t e d , t h e n q u a r t e r ly c h a n g e s r e c o n s t r u c t e d b y s u m m in g t h e t h r e e m o n t h ly c h a n g e s in t h e q u a r t e r . S p r e a d s a r e e x p r e s s e d in p e r c e n t p e r e a r . (cid:2) t t h e p e r c e n t c h a n g e ( 1 0 0 lo g c h a n g e ) in r e a l U .S . G r o s s D o m e s t ic P r o d u c t fr o m q u a r t e r t o q u a r t e r + 1 is e g r e s s e d o n la g s 0 , 1 , a n d 2 o f c h a n g e s in y ie ld s p r e a d s . E a c h r e g r e s s io n is e s t im a t e d o v e r 1 9 8 5 :Q 4 t h r o u g h 9 9 5 :Q 1 , a lt h o u g h s o m e o b s e r v a t io n s a r e m is s in g . E a c h v a r ia n c e - c o v a r ia n c e m a t r ix is a d ju s t e d fo r o n e la g o f 2 T P (cid:31) o v in g a v e r a g e r e s id u a ls . - s t a t is t ic s a r e in p a r e n t h e s e s . - v a lu e s o f ( 1 ) t e s t s t h a t t h e s u m o f t h e t h r e e o e (cid:14) c ie n t s e q u a ls z e r o a r e in b r a c k e t s . : C r e d it C h a n g e in s p r e a d : C o e f a 2 : R M a t u r it y R a t in g O b s . C u r r e n t F ir s t la g S e c o n d la g S u m A d j (cid:0) (cid:0) (cid:0) (cid:0) : : : : : L o n g A a a 2 9 0 6 9 9 0 0 8 5 0 6 8 8 1 3 0 2 0 0 5 0 : : : : ( 1 8 6 ) ( 0 2 9 ) ( 1 4 7 ) [ 0 8 6 ] (cid:0) (cid:0) (cid:0) (cid:0) : : : : : L o n g A a 3 0 2 1 1 5 1 7 7 6 1 0 7 0 4 9 6 1 0 2 1 4 : : : : ( 2 4 8 ) ( 1 7 5 ) ( 1 3 8 ) [ 0 0 5 ] (cid:0) (cid:0) (cid:0) : : : : : L o n g A 3 8 0 0 6 1 0 5 6 9 0 1 7 9 0 6 8 7 0 0 0 0 : : : : ( 0 1 3 ) ( 2 0 0 ) ( 0 9 9 ) [ 2 8 2 ] (cid:0) (cid:0) (cid:0) (cid:0) : : : : : L o n g B a a 3 4 0 4 8 8 0 6 5 8 0 3 7 3 1 5 1 8 0 0 8 9 : : : : ( 1 2 0 ) ( 1 7 1 ) ( 1 3 8 ) [ 0 4 2 ] (cid:0) (cid:0) (cid:0) (cid:0) : : : : : M e d iu m A a a 3 0 0 6 5 9 0 4 4 8 1 6 5 3 2 7 6 0 0 1 1 5 : : : : ( 1 2 2 ) ( 1 3 0 ) ( 3 1 0 ) [ 0 0 0 ] (cid:0) (cid:0) (cid:0) (cid:0) : : : : : M e d iu m A a 3 8 0 1 3 1 0 5 7 3 0 2 7 8 0 7 2 0 0 0 5 2 : : : : ( 0 1 6 ) ( 1 0 0 ) ( 0 6 3 ) [ 4 3 4 ] (cid:0) (cid:0) (cid:0) (cid:0) (cid:0) : : : : : M e d iu m A 3 8 0 2 9 4 0 4 5 6 0 1 9 8 0 9 4 8 0 0 2 6 : : : : ( 0 5 6 ) ( 1 0 4 ) ( 0 7 7 ) [ 1 1 0 ] (cid:0) (cid:0) (cid:0) (cid:0) : : : : : M e d iu m B a a 3 8 0 2 7 0 0 5 9 1 0 4 3 4 1 2 9 5 0 0 8 4 : : : : ( 0 5 9 ) ( 1 4 9 ) ( 1 5 3 ) [ 1 3 2 ] (cid:0) (cid:0) (cid:0) (cid:0) : : : : : S h o r t A a a 3 8 1 1 2 1 1 5 9 1 1 1 5 5 3 8 6 7 0 1 2 0 : : : : ( 1 1 5 ) ( 1 6 0 ) ( 2 0 3 ) [ 0 4 4 ] (cid:0) (cid:0) (cid:0) (cid:0) : : : : : S h o r t A a 3 8 0 7 9 7 1 6 0 3 0 5 5 0 2 9 4 9 0 0 8 3 : : : : ( 0 7 8 ) ( 1 7 7 ) ( 0 9 0 ) [ 1 6 0 ] (cid:0) (cid:0) (cid:0) (cid:0) : : : : : S h o r t A 3 8 0 7 6 6 1 3 0 6 0 7 6 0 2 8 3 2 0 1 9 9 : : : : ( 1 2 3 ) ( 2 8 0 ) ( 1 8 9 ) [ 0 2 0 ] (cid:0) (cid:0) (cid:0) (cid:0) : : : : : S h o r t B a a 3 8 0 5 3 8 0 6 7 5 0 4 7 7 1 6 8 9 0 2 8 2 : : : : ( 1 8 1 ) ( 2 5 7 ) ( 1 7 1 ) [ 0 0 5 ] a ‘L o n g ’ m a t u r it y b o n d s a r e b e t w e e n 1 5 a n d 3 0 y e a r s t o m a t u r it y , ‘m e d iu m ’ m a t u r it y b o n d s a r e b e t w e e n a n d 1 5 y e a r s t o m a t u r it y , a n d ‘s h o r t ’ m a t u r it y b o n d s a r e b e t w e e n 2 a n d 7 y e a r s t o m a t u r it y .
T a b l e 4 . R e g r e s s i o n a n d s t o c k r e t u r n s N o n c a lla b le b o n d s a r e c h a n g e s in m o n t h - e n d t h r e e - m o n t h T r e a s u r y m a t u r it y T r e a s u r y y ie R E T in d e x , d e n o t e d . t 1 9 8 5 t h r o u g h M a r c h 1 T h e t a b le r e p o r t s t h e P v a r ia b le s . - v a lu e s o f o f t h e e s t im a t e d c o e (cid:14) r e s id u a ls . a M a t u r it y L o n g L o n g L o n g L o n g M e d iu m M e d iu m M e d iu m M e d iu m S h o r t S h o r t S h o r t S h o r t a ‘L o n g ’ m a t u r it y b 7 a n d 1 5 y e a r s t o m a t s o f c h a n g e s i n c o r p o r a t e b o n d y i e l d s p r e a d s o n c h a n g e s i n T r e a s u r y y i e l d s t s o r t e d b y t h e ir m o n t h - c r e d it r a t in g a n d r e m a in in g m a t u r it y . F o r e a c h g r o u p , m e a n t t y ie ld s p r e a d s o v e r T r e a s u r y y ie ld s fr o m t o + 1 a r e r e g r e s s e d o n t h e c h a n g e in t h e 3 Y b ill y ie ld , d e n o t e d (cid:1) , t h e c h a n g e in t h e s p r e a d b e t w e e n t h e 3 0 - y e a r c o n s t a n t m ;t S L ld a n d t h e t h r e e - m o n t h b ill y ie ld , d e n o t e d (cid:1) , a n d t h e lo g r e t u r n t o t h e S & P 5 0 0 t A le a d a n d la g o f a ll e x p la n a t o r y v a r ia b le s a r e in c lu d e d . T h e d a t a r a n g e is J a n u a r y 9 9 5 . s u m s o f t h e c o e (cid:14) c ie n t s o n t h e le a d in g , c o n t e m p o r a n e o u s , a n d la g g e d e x p la n a t o r y 2 (cid:31) ( 1 ) t e s t s t h a t t h e s u m e q u a ls z e r o a r e in b r a c k e t s . T h e v a r ia n c e - c o v a r ia n c e m a t r ix c ie n t s is a d ju s t e d fo r g e n e r a liz e d h e t e r o s k e d a s t ic it y a n d t w o la g s o f m o v in g a v e r a g e S u m o f c o e fs o n : 2 3 Y S L R E T : R R a t in g O b s . (cid:1) (cid:1) A d j m ;t t t (cid:0) (cid:0) (cid:0) : : : : A a a 1 0 5 0 0 8 4 0 1 2 9 0 1 4 0 0 1 1 7 : : : [ 1 5 3 ] [ 0 5 3 ] [ 6 6 3 ] (cid:0) (cid:0) (cid:0) : : : : A a 1 0 3 0 1 7 6 0 1 3 9 0 1 4 7 0 2 0 0 : : : [ 0 0 8 ] [ 0 5 3 ] [ 7 3 0 ] (cid:0) (cid:0) (cid:0) : : : : A 1 2 2 0 2 6 5 0 3 0 7 0 9 5 8 0 3 7 0 : : : [ 0 0 2 ] [ 0 0 2 ] [ 0 2 0 ] (cid:0) (cid:0) (cid:0) : : : : B a a 1 0 9 0 4 2 8 0 4 5 2 2 1 9 6 0 5 0 1 : : : [ 0 0 0 ] [ 0 0 0 ] [ 0 0 0 ] (cid:0) (cid:0) (cid:0) (cid:0) : : : : A a a 1 1 5 0 0 6 9 0 0 6 5 0 6 8 3 0 0 1 1 : : : [ 1 9 7 ] [ 3 4 6 ] [ 1 9 0 ] (cid:0) (cid:0) (cid:0) : : : : A a 1 2 2 0 1 3 1 0 1 2 1 0 6 3 2 0 3 0 0 : : : [ 0 0 6 ] [ 0 4 2 ] [ 0 1 2 ] (cid:0) (cid:0) (cid:0) : : : : A 1 2 2 0 1 4 7 0 0 8 5 0 9 1 0 0 2 6 4 : : : [ 0 0 1 ] [ 1 5 4 ] [ 0 1 6 ] (cid:0) (cid:0) (cid:0) : : : : B a a 1 2 2 0 2 0 8 0 1 9 8 2 1 0 6 0 3 3 3 : : : [ 0 0 4 ] [ 0 2 6 ] [ 0 0 5 ] (cid:0) (cid:0) (cid:0) : : : : A a a 1 2 2 0 0 9 8 0 0 4 3 0 6 3 1 0 1 1 8 : : : [ 0 1 9 ] [ 3 1 3 ] [ 0 0 6 ] (cid:0) (cid:0) (cid:0) : : : : A a 1 2 2 0 1 1 9 0 0 7 1 1 3 1 1 0 3 8 7 : : : [ 0 0 8 ] [ 1 2 7 ] [ 0 0 0 ] (cid:0) (cid:0) (cid:0) : : : : A 1 2 2 0 1 1 5 0 0 6 8 1 1 9 5 0 2 8 6 : : : [ 0 0 8 ] [ 2 2 3 ] [ 0 0 7 ] (cid:0) (cid:0) (cid:0) : : : : B a a 1 2 2 0 2 4 2 0 1 2 7 1 9 8 0 0 2 1 0 : : : [ 0 0 0 ] [ 2 3 1 ] [ 0 5 4 ] o n d s a r e b e t w e e n 1 5 a n d 3 0 y e a r s t o m a t u r it y , ‘m e d iu m ’ m a t u r it y b o n d s a r e b e t w e e n u r it y , a n d ‘s h o r t ’ m a t u r it y b o n d s a r e b e t w e e n 2 a n d 7 y e a r s t o m a t u r it y .
T a b l e 5 . R e g r e s s i o n s o f T r e a s u r y y i e l d s N o n c a lla b le b o n d s a r e s o r t e o f y ie ld s p r e a d s . F ir s t d i(cid:11) e 3 Y y ie ld s ( (cid:1) ) a n d t h e d i(cid:11) m ;t S L t h r e e - m o n t h b ill y ie ld ( (cid:1) is J a n u a r y 1 9 8 5 t h r o u g h M a T h e t a b le r e p o r t s t h e s u m s 2 P (cid:31) v a r ia b le s . - v a lu e s o f ( 1 ) o f t h e e s t im a t e d c o e (cid:14) c ie n t s r e s id u a ls . a M a t u r it y L o n g L o n g L o n g L o n g M e d iu m M e d iu m M e d iu m M e d iu m S h o r t S h o r t S h o r t S h o r t a ‘L o n g ’ m a t u r it y b o n d s a 7 a n d 1 5 y e a r s t o m a t u r it y , c h a n g e s i n \ r e f r e s h e d " c o r p o r a t e b o n d y i e l d s p r e a d s o n c h a t d b y t h e ir m o n t h - c r e d it r a t in g a n d r e m a in in g m a t u r it y t o c r e a t e t im r e n c e s in t h e s e s p r e a d s a r e r e g r e s s e d o n d i(cid:11) e r e n c e d t h r e e - m o n t h T r e a e r e n c e d s p r e a d b e t w e e n t h e 3 0 - y e a r c o n s t a n t m a t u r it y T r e a s u r y y ie ld ) . A le a d a n d la g o f b o t h e x p la n a t o r y v a r ia b le s a r e in c lu d e d . T h e d a t r c h 1 9 9 5 . o f t h e c o e (cid:14) c ie n t s o n t h e le a d in g , c o n t e m p o r a n e o u s , a n d la g g e d e x p t e s t s t h a t t h e s u m e q u a ls z e r o a r e in b r a c k e t s . T h e v a r ia n c e - c o v a r ia n c is a d ju s t e d fo r g e n e r a liz e d h e t e r o s k e d a s t ic it y a n d t w o la g s o f m o v in g S u m o f c o e fs o n : 2 3 Y S L : R R a t in g O b s . (cid:1) (cid:1) A d j m ;t t (cid:0) (cid:0) : : : A a a 1 0 5 0 0 8 3 0 1 1 3 0 1 2 7 : : [ 1 4 9 ] [ 0 6 6 ] (cid:0) (cid:0) : : : A a 1 0 2 0 0 7 1 0 0 6 3 0 2 0 8 : : [ 0 7 7 ] [ 0 9 3 ] (cid:0) (cid:0) : : : A 1 2 2 0 1 6 6 0 1 4 9 0 3 2 6 : : [ 0 0 0 ] [ 0 0 4 ] (cid:0) (cid:0) : : : B a a 1 0 9 0 3 5 5 0 2 9 7 0 2 9 6 : : [ 0 0 0 ] [ 0 0 5 ] (cid:0) (cid:0) (cid:0) : : : A a a 1 1 3 0 0 4 9 0 0 3 2 0 0 1 7 : : [ 3 0 3 ] [ 5 7 6 ] (cid:0) : : : A a 1 2 2 0 0 3 0 0 0 1 0 0 1 4 0 : : [ 4 7 3 ] [ 8 1 8 ] (cid:0) (cid:0) : : : A 1 2 2 0 0 7 3 0 0 1 0 0 2 2 1 : : [ 0 8 2 ] [ 8 5 0 ] (cid:0) (cid:0) : : : B a a 1 2 2 0 1 8 3 0 1 5 9 0 1 0 1 : : [ 0 3 9 ] [ 1 5 9 ] (cid:0) (cid:0) : : : A a a 1 2 2 0 0 4 5 0 0 0 8 0 0 5 4 : : [ 2 4 4 ] [ 8 0 9 ] (cid:0) : : : A a 1 2 2 0 0 7 0 0 0 1 3 0 1 4 8 : : [ 0 6 9 ] [ 7 5 2 ] (cid:0) (cid:0) : : : A 1 2 2 0 0 8 9 0 0 0 2 0 1 9 6 : : [ 0 4 0 ] [ 9 6 2 ] (cid:0) (cid:0) : : : B a a 1 2 2 0 1 7 8 0 0 5 1 0 0 9 9 : : [ 0 0 6 ] [ 5 8 9 ] r e b e t w e e n 1 5 a n d 3 0 y e a r s t o m a t u r it y , ‘m e d iu m ’ m a t u r it y b o n d s a r e a n d ‘s h o r t ’ m a t u r it y b o n d s a r e b e t w e e n 2 a n d 7 y e a r s t o m a t u r it y . n g e s i n e s e r ie s s u r y b ill a n d t h e t a r a n g e la n a t o r y e m a t r ix a v e r a g e b e t w e e n
T a b l e 6 . R e g r e s s i o n s o f c h a n g e s i n l o n g - t e r m A a - r a t e d c a l l a b l e c o r p o r a t e b o n d y i e l d s p r e a d s o n c h a n g e s i n T r e a s u r y y i e l d s . t L o n g - t e r m , A a - r a t e d c a lla b le b o n d s a r e s o r t e d b y t h e ir m o n t h - c a ll s t a t u s ( c u r r e n t ly c a lla b le o r c a ll p r o t e c t e d t t t fo r a t le a s t a n o t h e r y e a r ) a n d m o n t h - p r ic e . M e a n m o n t h ly c h a n g e s in t h e ir y ie ld s p r e a d s fr o m t o + 1 Y 3 + 1 ( o v e r T r e a s u r ie s ) a r e r e g r e s s e d o n t h e c h a n g e in t h e t h r e e - m o n t h T r e a s u r y b ill y ie ld , d e n o t e d (cid:1) , m ;t a n d t h e c h a n g e in t h e s p r e a d b e t w e e n t h e 3 0 - y e a r c o n s t a n t m a t u r it y T r e a s u r y y ie ld a n d t h e t h r e e - m o n t h S L + 1 b ill y ie ld , d e n o t e d (cid:1) . A le a d a n d la g o f b o t h e x p la n a t o r y v a r ia b le s a r e in c lu d e d . T h e d a t a r a n g e is t J a n u a r y 1 9 8 5 t h r o u g h M a r c h 1 9 9 5 . T h e t a b le r e p o r t s t h e s u m s o f t h e c o e (cid:14) c ie n t s o n t h e le a d in g , c o n t e m p o r a n e o u s , a n d la g g e d e x p la n a t o r y 2 P (cid:31) v a r ia b le s . - v a lu e s o f ( 1 ) t e s t s t h a t t h e s u m e q u a ls z e r o a r e in b r a c k e t s . T h e v a r ia n c e - c o v a r ia n c e m a t r ix o f t h e e s t im a t e d c o e (cid:14) c ie n t s is a d ju s t e d fo r g e n e r a liz e d h e t e r o s k e d a s t ic it y a n d t w o la g s o f m o v in g a v e r a g e r e s id u a ls . B o n d p r ic e S u m o f c o e fs o n : 2 Y S L : R 3 B o n d t y p e ( 1 0 0 = p a r ) O b s . (cid:1) (cid:1) A d j m ;t t (cid:0) (cid:0) < p : : : C u r r e n t ly c a lla b le 1 0 0 1 0 9 0 5 6 2 0 5 2 7 0 7 9 7 t : : [ 0 0 0 ] [ 0 0 0 ] (cid:0) (cid:0) < p < : : : 9 0 1 0 0 1 1 9 0 2 6 3 0 2 3 6 0 3 2 5 t : : [ 0 0 1 ] [ 0 0 1 ] (cid:0) (cid:0) p < : : : 9 0 1 1 4 0 1 6 6 0 0 4 8 0 2 4 8 t : : [ 0 0 2 ] [ 3 1 1 ] (cid:0) (cid:0) < p : : : N o t y e t c a lla b le 1 0 0 1 2 2 0 4 7 1 0 4 2 1 0 7 8 8 t : : [ 0 0 0 ] [ 0 0 0 ] (cid:0) (cid:0) < p < : : : 9 0 1 0 0 1 1 8 0 1 9 2 0 2 2 4 0 4 6 0 t : : [ 0 0 4 ] [ 0 0 2 ] (cid:0) (cid:0) p < : : : 9 0 6 9 0 0 7 2 0 0 4 2 0 2 1 0 t : : [ 0 8 3 ] [ 2 5 6 ]
)tnecrep( dleiY A. 30-year constant maturity(cid:9) Treasury bond yield 12 11 10 9 8 7 6 1/86 1/90 1/94 ).p.b( daerps dleiY B. Noncallable bonds and(cid:9) Moody’s Industrial Bond Yield Index Noncallable bonds 300 Moody’s Index 250 200 150 100 50 1/86 1/90 1/94 ).p.b( daerps dleiY C. Currently callable bonds 400 350 bond price > 100 100 > bond price > 90 300 250 200 150 100 50 1/86 1/90 1/94 ).p.b( daerps dleiY D. Callable bonds, but(cid:9) call-protected for at least another year 400 350 bond price > 100 100 > bond price > 90 300 250 200 150 100 50 1/86 1/90 1/94 F ig . 1 . T r e a s u r y y ie ld s a n d m I n d u s t r ia l, (cid:12) n a n c ia l, a n d u t ilit y A - r a t e d fe a t u r e s , a n d , if c a lla b le , b y t h e ir p r ic e . T fr o m e a c h b o n d ’s y ie ld t o fo r m y ie ld s p r e g r o u p s ; p a n e l B a ls o d is p la y s t h e s p r e a d c o n s t a n t m a t u r it y T r e a s u r y y ie ld . e a n y ie ld s p r e a d s o n v a r io u b o n d s w it h b e t w e e n 1 5 a n d h e a p p r o p r ia t e in t e r p o la t e d a d s . P a n e ls B , C , a n d D d is b e t w e e n M o o d y ’s A - r a t e d s g r o u p s o 3 0 y e a r s c o n s t a n t p la y m e a n I n d u s t r ia l f A - r a t e d c o r p o r a t e b o n d s t o m a t u r it y a r e g r o u p e d b y t h m a t u r it y T r e a s u r y y ie ld is s u b y ie ld s p r e a d s , in b a s is p o in t s , B o n d Y ie ld A v e r a g e a n d t h e e ir t r a c fo r 3 0 - y c a ll t e d t h e e a r
Cite this document
Gregory R. Duffee (1997). Treasury Yields and Corporate Bond Yield Spreads: An Empirical Analysis (FEDS 1996-20). Board of Governors of the Federal Reserve System, Finance and Economics Discussion Series. https://whenthefedspeaks.com/doc/feds_1996-20
@techreport{wtfs_feds_1996_20,
author = {Gregory R. Duffee},
title = {Treasury Yields and Corporate Bond Yield Spreads: An Empirical Analysis},
type = {Finance and Economics Discussion Series},
number = {1996-20},
institution = {Board of Governors of the Federal Reserve System},
year = {1997},
url = {https://whenthefedspeaks.com/doc/feds_1996-20},
abstract = {This paper empirically examines the relation between the Treasury term structure and spreads of investment grade corporate bond yields over Treasuries. I find that noncallable bond yield spreads fall when the level of the Treasury term structure rises. The extent of this decline depends on the initial credit quality of the bond; the decline is small for Aaa-rated bonds and large for Baa-rated bonds. The role of the business cycle in generating this pattern is explored, as is the link between yield spreads and default risk. I also argue that yield spreads based on commonly-used bond yield indexes are contaminated in two important ways. The first is that they are "refreshed" indexes, which hold credit ratings constant over time; the second is that they usually are constructed with both callable and noncallable bonds. The impact of both of these problems is examined.},
}