Grinblatt Titman 95 Performance Evaluation Chapter 19
-
Upload
pballispapanastasiou -
Category
Documents
-
view
26 -
download
0
description
Transcript of Grinblatt Titman 95 Performance Evaluation Chapter 19
-
5/20/2018 Grinblatt Titman 95 Performance Evaluation Chapter 19
R. Jarrow et al., Eds., Hand books in OR MS, Vol. 9
1995 Elsev ier Science B.V. All rights rese rved
Chapter 9
Pe r for manc e va luat ion
Mark rinblatt
And erson Graduate Schoo l of Management, University of California, Lo s Angeles, CA
90095-1481, U.S.A.
Sheridan Titman
W.E. Carroll Scho ol o f Managem ent, Bos ton College, Chestnut Hills', M A 02167, U.S./t.
1 I n tr o d u c t io n
T r i l l i o n s o f d o l l a r s a r e i n v e s t e d i n s t o c k s w o r l d w i d e b y i n s t i t u t i o n a l p o r t f o l i o
m a n a g e r s . F r o m a s o c i a l p e r s p e c t i v e it i s i m p o r t a n t t o k n o w w h e t h e r t h e s e i n -
v e s t o r s as a g r o u p a d d v a l u e t o t h e p o r t f o l io s t h e y m a n a g e o r w h e t h e r t h e y m e r e l y
g e n e r a t e w a s t e f u l t r a n s a c t i o n c o s t s t h r o u g h t h e i r ac t iv e m a n a g e m e n t . A t t h e m i c r o
l e ve l i t is i m p o r t a n t t o k n o w h o w t o s e l e c t a p o r t f o l i o m a n a g e r w i t h t h e a b i l it y t o
a d d v a l u e t o t h e p o r t f o l i o h e m a n a g e s . P e r f o r m a n c e e v a l u a t i o n i s a to p i c i n f i n an -
c i al e c o n o m i c s t h a t s e e k s t o a d d r e s s b o t h o f t h e s e i s su e s. I n p a r t i c u l a r , i t s t u d i e s
w h e t h e r s u p e r i o r r e t u r n s c a n b e g e n e r a t e d b y a c ti v e m a n a g e r s w h o a r e b e t t e r a b l e
t o c o l l ec t a n d i n t e r p r e t i n f o r m a t i o n t h a t h e l p s f o r e c a s t s e c u r i t i e s r e t u rn s . 1
T o e v a l u a t e w h e t h e r a m a n a g e r h a s g e n e r a t e d s u p e r i o r r e t u r n s w e n e e d t o a d j u s t
h is p o r t f o l i o r e t u r n f o r r is k . S i n c e t h e m e a n r e t u r n s o f s e c u ri t i e s a r e p o s i t iv e l y
r e l a t e d t o t h e i r r is k , p e r f o r m a n c e m e a s u r e s a r e b a s e d o n t e c h n i q u e s t h a t a d j u s t fo r
p r i c e d r is k . S o m e p e r f o r m a n c e m e a s u r e s u s e t h e d i v e r s i fi c a t i o n o f a p o r t f o l i o a s
a n a d d i t i o n a l c r i t e r i o n f or e v a l u a t i o n . T h i s r e q u i r e s a n a d j u s t m e n t f o r b o t h p r i c e d
r i sk a n d u n p r i c e d r is k , t y p i fi e d b y t h e p e r f o r m a n c e m e a s u r e k n o w n a s S h a r p e s
r a t i o [ S h a r p e , 1 96 6] . S h a r p e s r a t i o i s t h e e x c e s s r e t u r n o f t h e p o r t f o l i o ( a b o v e t h e
r i s k - f re e r e t u r n ) d i v i d e d b y t h e s t a n d a r d d e v i a t i o n o f t h e r e t u r n o f th e p o r t f o l i o .
A d j u s t i n g f o r p e r f o r m a n c e b a s e d o n t h e t o t a l r i sk o f a p o r t f o l i o r a t h e r t h a n t h e
p r i c e d r i s k o f a p o r t f o l i o i s n o l o n g e r p o p u l a r a n d w e t h i n k i n a p p r o p r i a t e . T h i s i s
I Many investors asse rt that they make money by arb itrag ing mispriced derivatives. F or example,
they may buy a European call option that is underpriced relative to the Black-Scholes model and
short the underlying stock in appropriate amounts so as to achieve a riskless return that exceeds
the current riskless rate available in the fixed income markets. This type of performance is based
on model failure, rath er than asymmetric information. Indee d, in the effectively com ple te mark ets
world of derivatives pricing, no asymmetric information about the mean returns of securities
is permitted. Since there is no available performance methodology that ad dresses the issue of
performance b ased on model failure, we do not discuss the issue here.
581
-
5/20/2018 Grinblatt Titman 95 Performance Evaluation Chapter 19
582 M. Grinblatt , S. Titrnan
b e c a u s e t h e m a n a g e r s w h o s e p e r f o r m a n c e is t y pi ca ll y e v a l u a t e d r a re l y m a n a g e t h e
e n t i r e s a v in g s o f a n i n v e s to r . I n v e s t o r s in m u t u a l f u n d s , f o r e x a m p l e , t y p ic a ll y h o l d
a n u m b e r o f fu n d s a n d m a y p e r s o n a ll y m a n a g e a l a rg e p o r t i o n o f th e i r w e a lt h .
T h e y m a y a l s o h o l d a s u b s t a n t i a l fr a c t i o n o f t h e i r w e a l t h i n t h e h o m e t h e y o w n
o r t h e h u m a n c a p i t a l th e y p o s s es s . E v e n i f w e a r g u e t h a t f o r s o m e i n d iv i d u a ls ,
m o s t o f t h e i r w e a l t h i s h e l d i n t h e i r p e n s i o n f u n d , m o s t p e n s i o n f u n d s f a r m o u t
t h e m a n a g e m e n t o f t h e i r a ss e ts t o a n u m b e r o f d if f e re n t f ir m s. It t h e r e f o r e s e e m s
m o r e i m p o r t a n t t o f o c us o n t h e m a r g i n a l c o n t r ib u t i o n s o f a m a n a g e d p o r t f o l i o t o
t h e r i s k a n d e x p e c t e d r e t u r n o f a n i n v e s to r . T h i s n e c e s s a r i ly in v o l v e s a d j u s ti n g f o r
r is k w i t h a m a r g i n a l r i s k m e a s u r e , l i k e b e t a .
T h e r e a r e t w o b a s i c c l as s es o f p e r f o r m a n c e m e a s u r e s a n a l y z e d i n t h is c h a p t e r .
A n i n tu i ti v e w a y to t h in k a b o u t b o t h c l a ss es o f p e r f o r m a n c e m e a s u r e s i s t h a t t h e y
c o m p a r e t h e r e t u r n s o f t h e a c ti v el y m a n a g e d p o r t f o l io t h a t i s b e i n g e v a l u a t e d
w i t h a p a s s i v e ( i . e . b u y a n d h o l d ) p o r t f o l i o w i t h t h e s a m e l e v e l o f r i s k . T h e f i r s t
c la s s r e q u i r e s t h e o b s e r v a t i o n o f th e r e t u r n s o f th e e v a l u a t e d p o r t f o l i o a s w e l l a s
t h e r e t u r n s o f a b e n c h m a r k t h a t c o n s is t s o f o n e o r m o r e p o r t f o l io s a l o n g w i th
a r is k - f r e e a ss e t . T h e s e c o n d c l a ss u t il iz e s i n f o r m a t i o n a b o u t t h e c o m p o s i t i o n o f
t h e e v a l u a t e d p o r t f o l io b u t d o e s n o t n e c e ss a r il y r e q u i r e a b e n c h m a r k p o r t fo l i o (s ) .
I n m o s t c a s e s t h e f i rs t c la s s o f m e a s u r e s a s s u m e s t h a t s t o c k r e t u r n s a r e n o r m a l l y
d i s t r ib u t e d . T h i s a s s u m p t i o n i s n o t n e e d e d f o r th e s e c o n d c l as s o f m e a s u r e s .
H o w e v e r , b o t h c la s se s o f m e a s u r e s r e q u i r e t h a t s t o c k r e t u rn s b e d r a w n f r o m a
s t a t i o n a r y d i s t ri b u t i o n .
T h e s t a t i o n a r i t y r e q u i r e m e n t i s c o n s i d e r e d b y s o m e t o b e a s e r i o u s w e a k n e s s
o f th e p e r f o r m a n c e e v a l u a t i o n l it e ra t u re . G i v e n t h e r e c e n t l i t e r a tu r e o n t h e
n o n s t a t i o n a r i t y o f e x p e c t e d s t o c k r e t u r n s , a s f o u n d , f o r e x a m p l e , i n F e r s o n [ 19 9 5,
c h a p t e r 5 i n t h is v o l u m e ] a n d H a w a w i n i K e i m [ 1 99 5 , c h a p t e r 17 i n t h is v o l u m e ] ,
t h is c o n c e r n s e e m s p a r ti c u l a r ly v a li d . H o w e v e r , t h is a s s u m p t i o n i s n e e d e d b e c a u s e
i t i s g e n e r a l l y i m p o s s i b l e f o r a n o b s e r v e r t o e m p i r i c a l l y d i s t i n g u i s h b e t w e e n
t h e p e r f o r m a n c e o f i n f o r m e d i n v e s to r s a n d t h e ' p e r f o r m a n c e ' o f u n i n f o r m e d
i n v e s to r s w h o o p t im a l l y r e s p o n d t o c h a n g e s i n t h e p a r a m e t e r s o f t h e r e t u r n
g e n e r a t i n g p r o c e s s . I n d e e d , a f a i r ' p h i l o s o p h i c a l ' d is t in c t i o n b e t w e e n a n e c o n o m y
w i t h i n f o r m e d i n v e s t o rs a n d a n e c o n o m y w i t h c h a n g in g p a r a m e t e r s i s o n e o f
m a g n i t u d e . I n t h e f o r m e r , o n l y a f e w i n v e s t o r s o b s e r v e t h e n o n s t a t i o n a r i t i e s ,
w h e r e a s i n t h e l a t t e r , v ir t ua l ly a ll in v e s t o rs o b s e r v e t h e n o n s t a t i o n a r i t i e s ( a n d o n l y
t h e e v a l u a t o r i s n a i v e ) . A m o r e s o p h i s t i c a t e d e v a l u a t i o n t e c h n i q u e t h a t m o d e l s t h e
n o n s t a t i o n a r it i e s k n o w n t o u n i n f o r m e d m a r k e t p a r t i c ip a n t s c a n in p r in c i p le a v o i d
t h is p r o b l e m , b u t m o d e l l i n g w h a t is k n o w n b y ' th e m a r k e t ' i s s p e c u l a t iv e a t b e st .
2 . M e a s u r e s b a s e d s o le ly o n r e t u r n s
2 .1 . Tr e y n o r s r at io , J e n s e n s a l p h a , a n d t h e Tr e y n o r - B l a c k a p p r a i s a l r a t io
A n u m b e r o f m e a s u r e s o f p e r f o r m a n c e a r e b a s e d o n t h e c a p i ta l a s s e t p r ic in g
m o d e l , a t h e o r y r e l a ti n g e x p e c t e d r e t u r n t o a m e a s u r e o f ri sk k n o w n a s ' b e t a '.
-
5/20/2018 Grinblatt Titman 95 Performance Evaluation Chapter 19
Ch. 19. Perform ance Evalua tion 583
~ p
r f + 1 3 p R ~ r f
J
Tre yn o r sRat io
Eva l u a te d 1
P o r t f ~ , i p h a / ~ e c u r i t ie s M a rk e tL i n e
P p
Fig. 1. Th e distinction betw een T reynor s ratio an d Jensen s alpha.
B e t a is t h e s l o p e c o e f f i c ie n t i n a r e g r e s s i o n o f t h e r e t u r n o f t h e p o r t f o l i o b e i n g
e v a l u a t e d a g a i n s t th e r e t u r n o f a p ro x y f o r th e m a r k e t p o r t f o l io . T h e r e l a t io n
b e t w e e n b e t w e e n b e t a a n d e x p e c t e d r e t u r n is g r a p h ic a ll y r e p r e s e n t e d b y t h e
s e c u r i t i e s m a r k e t l i n e , o b s e r v e d i n F i g u r e 1 ( a n d d i s c u s s e d i n F e r s o n [ 1 9 9 5 ,
c h a p t e r 5 i n t h i s v o l u m e ] ) . T h e t r u e m e a n r e t u r n s a n d b e t a s ( a s o p p o s e d t o t h e i r
e s t i m a t e d v a l u e s ) o f a l l s e c u r i t ie s a n d a ll p a s si v e p o r t f o l i o s o f s e c u r i t ie s l ie o n t h is
l in e if t h e C a p i t a l A s s e t P r i c in g M o d e l ( C A P M ) is t r u e .
2.1.1. Treynor s ratio
T r e y n o r s r a t io [ T r e y n o r , 19 6 5 ] w a s t h e f i rs t a c a d e m i c a t t e m p t t o a d j u s t r e t u r n s
w i t h b e t a s i n o r d e r t o m e a s u r e p e r f o r m a n c e . I t is c o m p u t e d a s
/ ~ p rf
L
t h e a v e r a g e r e t u r n o f t h e p o r t f o l i o in e x c e ss o f th e r i s k - f r e e r e t u r n d i v i d e d b y th e
p o r t f o l i o s b e t a . I t is th u s t h e s l o p e o f a l in e c o n n e c t i n g t h e r i s k - f r e e r e t u r n t o t h e
e v a l u a t e d p o r t f o l i o in m e a n - b e t a s p a c e, a s il lu s t ra t e d i n F i g u r e 1.
2.1.2. Jen sen s alpha
A v a r i a t i o n o f t h e ~ I? ey no r a p p r o a c h , k n o w n a s J e n s e n s a l p h a , is th e a r i t h m e t i c
d i f fe r e n c e o f th e p o r t f o l i o s r e t u r n f r o m t h e r e t u r n o f a p o r t f o l i o o n t h e s e c u ri ti e s
m a r k e t l i n e w i t h t h e s a m e b e t a , a s i l l u s t r a t e d i n F i g u r e 1 . S i n c e a l l s e c u r i t i e s
a r e e x p e c t e d t o l ie o n t h e s e c u r i ti e s m a r k e t l in e i f t h e C A P M h o l d s, t h e a l p h a s
o f p a s si v el y m a n a g e d p o r t f o l io s ( w i t h r e tu r n s m e a s u r e d b e f o r e t r a n s a c t i o n c o st s,
-
5/20/2018 Grinblatt Titman 95 Performance Evaluation Chapter 19
584 M. Grinblatt S. Titman
f e es , a n d e x p e n s e s ) , a r e e x p e c t e d t o b e z e r o . A n a c ti v el y m a n a g e d p o r t f o l i o w i t h
a s i g n i f i c a n t l y p o s i t i v e J e n s e n ' s a l p h a i s t h e r e f o r e i n t e r p r e t e d a s a p o r t f o l i o t h a t
i s m a n a g e d w i t h s u p e r i o r f o r e c a s t s . W e w i l l l a t e r e x a m i n e t h e c o n d i t i o n s u n d e r
w h i c h t h i s i n t e r p r e t a t i o n i s c o r r e c t .
J e n s e n ' s a l p h a i s a m o r e c o m m o n l y us e d m e a s u r e o f p e r f o r m a n c e t h a n T r e y n o r ' s
r a t io . O n e r e a s o n f o r i ts p o p u l a r i t y is t h a t i t i s e a s il y c o m p u t e d b y f i n d in g t h e
i n t e r c e p t i n t h e r e g r e s s i o n ,
R p re = l y p - J r - / ~ p k M - r f ) - ~ - 6 p
(1)
T h e i n t e r c e p t , O ~p, c o m p u t e d a s
l Y p =
Rp - rr
- f l p k M - r f ) ,
(2)
is t h e a v e r a g e e x c e s s r e t u r n o f t h e p o r t f o l i o le s s t h e p r o d u c t o f th e p o r t f o l i o ' s b e t a
a n d t h e a v e r a g e e x c e s s r e t u r n o f t h e m a r k e t p o r t f o l i o . I n tu i ti v e l y , J e n s e n ' s a l p h a
is th e d i f f e r e n c e b e t w e e n t h e r e t u r n o f t h e e v a l u a t e d p o r t f o l io a n d t h e r e t u r n o f
t h e p a s s iv e p o r t f o l i o c o n s is ti n g o f b e t a u n i ts o f th e b e n c h m a r k p o r t f o l i o a n d o n e
m i n u s b e t a u n i t s o f t h e r i s k - f r e e a s s et .
2.1.3. Ra nk ing o f forecasting abili ty and the Tre ynor -Blac k appraisal ratio
T r e y n o r ' s ra t i o w a s d e s i g n e d t o r a n k p o r t f o l i o s a n d d o e s n o t d e t e r m i n e w h e t h e r
a p a r t i c u l a r p o r t f o l i o w a s m a n a g e d b y s o m e o n e w i t h s u p e r i o r a b il it ie s . H o w e v e r ,
i f ' u n i n f o r m e d m a n a g e r s ' h a v e p o r t f o l i o s ( a b s e n t f e e s , e x p e n s e s , a n d t r a n s a c t i o n
c o s t s ) t h a t p l o t o n t h e s e c u r i t i e s m a r k e t l i n e , a n y m a n a g e r w i t h f o r e c a s t i n g
a b i li ty is e x p e c t e d t o h a v e a T r e y n o r r a t io ( a b s e n t t h e s e s a m e f r i c ti o n s ) t h a t i s
s i gn i f i c an t ly i n exces s o f t he s l ope o f t he s ec u r i t i e s m a r k e t l i ne , RM - - r f , w he r e /?M
is t h e a v e r a g e r e t u r n o f th e p r o x y f o r t h e m a r k e t p o r t fo l i o .
A m a n a g e r ' s a g g r e s s i v e n e s s i n u s i n g i n f o r m a t i o n w i l l a l t e r t h e e x p e c t e d r e t u r n
o f a p o r t f o l io . H e n c e a m a n a g e r w i th l ow r is k a v e r si o n a n d g o o d i n f o r m a t i o n m a y
o u t p e r f o r m a m a n a g e r w i th a h ig h d e g r e e o f r is k a v e rs i o n a n d g r e a t i n f o r m a t i o n .
M e a s u r e s l ik e T r e y n o r ' s , t h a t i n v o l v e a r a t i o o f r e t u r n t o r is k m i t i g a te t h i s p r o b l e m .
H o w e v e r , t h e r e is n o a p r io r i r e a s o n t o b e l ie v e th a t t h e b e t a a d j u s t m e n t s u g g e s te d
b y T r e y n o r is t h e c o r r e c t o n e f o r a c a r d i n a l r a n k i n g o f m a n a g e r i a l i n f o r m a t i o n
p r e c i s i o n . F o r e x a m p l e , a m a n a g e r w i t h t h e a b i l i t y t o f o r e c a s t t h e e p s i l o n i n a
m a r k e t m o d e l r e g r e ss io n
3 )
m i g h t h e d g e o u t t h e m a r k e t r i sk a s s o c i a t e d w i t h t h e a c q u i s i t i o n o f l a r g e p o s i t io n s
i n t h e s e c u r i t y . T h i s r e q u i r e s s h o r t i n g l i d o l la r s o f t h e m a r k e t p o r t f o l i o f o r e a c h 1
i n v e s t e d i n t h e i t h s e cu r i ty . I f t h e s e f o r e c a s t s a r e i m p e r f e c t , s o t h a t ~ i c o n d i t i o n e d
o n t h e m a n a g e r ' s i n f o r m a t i o n s t i l l h a s s o m e v a r i a b i l i t y , a l e s s r i s k a v e r s e m a n a g e r
wi l l gene r a l l y t ake a l a r ge r pos i t i on i n s ecu r i t y i . I n t h i s c a se , s i m p l e d i v i s i on by
t h e p o r t f o l i o b e t a w i l l n o t c a p t u r e t h e r e l a t i v e l y h i g h e r u n s y s t e m a t i c r i s k o f t h e
l es s ri s k a v e r s e m a n a g e r .
-
5/20/2018 Grinblatt Titman 95 Performance Evaluation Chapter 19
Ch. 19. Performance Evaluation 585
A m e a s u r e d e r i v ed f r o m J e n s e n ' s a l p h a ca n r a n k m a n a g e r s a c c o r d i n g t o
i n f o r m a t i o n p r e c i s io n . C o n n o r K o r a c z y k [ 19 8 6] d e s c r i b e a c a s e i n w h i c h th e
T r e y n o r B l a c k [ 19 7 3] a p p r a i s a l r a t io ,
O~p
Sp
w h i c h is J e n s e n ' s a l p h a d i v i d e d b y t h e s t a n d a r d d e v i a ti o n o f t h e e r r o r t e r m
i n t h e r e g r e s s i o n u s e d t o o b t a i n a l p h a , p r o p e r l y r a n k s m a n a g e r s a c c o r d i n g t o
t h e i r f o r e c a s t i n g a b i li ti es . H o w e v e r , t h i s r e s u l t re q u i r e s a n u m b e r o f a s s u m p t i o n s
b e f o r e i t is v a l id , in c l ud i n g : n o a b il it y to f o r e c a s t t h e m a r k e t , m u l t i v a r i a t e n o r m a l
r e t u r n s , e x p o n e n t i a l u t i li ty a s t h e c r i te r i o n f o r i n v e s t m e n t f o r a ll m a n a g e r s , a n d t h e
t r a d a b i l i t y o f a l l a s s e t s f o r a l l m a n a g e r s . T h e s e r e s t r i c t i o n s a p p e a r t o b e s t r i n g e n t
e n o u g h t o p r e c l u d e t h e u s e f u l n e s s o f t h is r a t io a s a t o o l f o r r a n k i n g
W h i l e t h e a b i l it y t o r a n k m a n a g e r s a c c o r d i n g t o t h e p r e c i s io n o f t h e i r f o r e c a s t -
i n g a b i l i t y i s a n i d e a l , w e m u s t g e n e r a l l y c o n t e n t o u r s e l v e s w i t h t h e s e p a r a t i o n
o f p o r t f o l i o m a n a g e r s i n t o t w o c l a ss e s: t h o s e w i t h s u p e r i o r f o r e c a s t i n g a b i li ty a n d
t h o s e w i t h o u t i t. O n e c a n n o t b e g r e a t l y d i s a p p o i n t e d t h a t r a n k i n g is p r o b a b l y i m -
p o s s i b l e b e c a u s e o f d if f e r e n c e s i n m a n a g e r i a l ( a n d u l t i m a t e l y c l i en t ) r i s k a v e r si o n .
H o w e v e r , t h e a b i li ty t o f o r e c a s t s e c u r i t ie s r e t u r n s is r a r e i f o n e l a r g e ly a c c e p t s t h e
c o m m o n a c a d e m i c v i ew o f t h e e f f ic ie n t m a r k e t s h y p o th e s is . A m e a s u r e o f p e r f o >
m a n c e t h a t m e r e l y id e n t if i es t h e f e w m a n a g e r s w i t h f o r e c a s t in g a b i li ty w o u l d t h e n
b e q u i t e u s e f u l .
2.2. Asset pricing, performance measurement, and Roll s critique
T h e m e a s u r e s o f p e r f o r m a n c e t h a t w e d is c us s ed i n t h e l as t se c t io n u s e d t h e
C a p i t a l A s s e t P r i c i n g M o d e l a s t h e t h e o r e t i c a l b a s i s f o r t h e i r c o n s t r u c t i o n . A s a
r e s u l t , t h e b e n c h m a r k s o r i g i n a l l y u s e d t o c o m p u t e t h e s e m e a s u r e s a r e p r o x i e s f o r
t h e v a l u e - w e i g h t e d m a r k e t p o r t f o l i o . H o w e v e r , o t h e r b e n c h m a r k s h a v e b e e n u s e d
t o e s t i m a t e J e n s e n ' s a l p h a , T r e y n o r ' s r a ti o , a n d t h e T r e y n o r - B l a c k r a ti o . O n e c a n
a ls o u s e a m u l t ip l e p o r t fo l i o b e n c h m a r k w i th J e n s e n ' s a lp h a . T h e s u m m e d p r o d u c t
o f t h e m u l t i p l e r e g r e s si o n b e t a s a n d t h e a v e r a g e e x ce ss r e tu r n s o f th e b e n c h m a r k
p o r t f o l i o s is t h e n s u b t r a c t e d f r o m t h e a v e r a g e ex c e ss r e t u r n o f t h e p o r t f o l i o
b e i n g e v a lu a t e d . T h e a l p h as o b t a i n e d f r o m a m u l ti p le p o r t f o l io b e n c h m a r k a r e
e q u i v a l e n t t o t h e a l p h a s t h a t w o u l d b e o b t a i n e d f r o m u s i n g th e e x - p o s t e f fi c ie n t
c o m b i n a t i o n o f th e p o r t f o l i o s in t h e b e n c h m a r k . 2
T h e c h o i c e o f a b e n c h m a r k p o r t f o l i o i s p r o b a b l y t h e m o s t c o n t r o v e r s i a l i s s u e
i n p e r f o r m a n c e e v a l u a ti o n . T h e d e b a t e a b o u t b e n c h m a r k s w a s in i ti a te d b y R o l l
[ 1 9 7 8 ] w h o n o t e d t h a t d i f f e r e n t b e n c h m a r k p o r t f o l i o s p r o v i d e d i f f e r e n t r i s k a d -
j u s t m e n t s a n d h e n c e d i f fe r e n t a s s e s sm e n t s o f a b n o r m a l p e r f o r m a n c e . H e s h o w e d
t h a t t w o b e n c h m a r k p o r t f o l i o s l y in g i n s id e t h e m e a n - v a r i a n c e e f f i c ie n t f r o n t i e r
2 Grinblan Titman [1987] sho w that the m ean-variance efficient combination of a set of
mu ltiple bench mark s will be itself mea n-variance efficient if and o nly if the Jen sen's alphas derived
from these m ultiple portfolio benchm arks are all zero.
-
5/20/2018 Grinblatt Titman 95 Performance Evaluation Chapter 19
586 M. Gr inb la tt S . T i tm an
c o u l d r e v e r s e t h e r a n k i n g s o f a g r o u p o f p a s s iv e p o r t f o l i o s . P o r t f o l i o s l y in g a b o v e
t h e s e c u r i t ie s m a r k e t l i n e w i t h o n e b e n c h m a r k l ie b e lo w t h e s e c u ri ti e s m a r k e t
l in e w i t h th e o t h e r b e n c h m a r k a n d v i ce v e r sa . O n t h e o t h e r h a n d , a b e n c h m a r k
p o r t f o l i o t h a t is m e a n - v a r i a n c e e f fi c ie n t c a n n o t d i s t in g u i sh b e t w e e n p a s si v e p o r t -
f o l i o s . Pa s s i ve po r t f o l i o s , l i ke a l l s ecu r i t i e s , l i e on t he s ecu r i t i e s m ar ke t l i ne i n
th i s case .
T h e r e a s o n f o r t h is is a m a t h e m a t i c a l r e l a t io n . T h e e q u a t i o n o f th e s e c u ri ti e s
m a r k e t l in e ,
w h e r e
r i = r f - - 1 - f l i / ~ E - - r f ) ,
for a l l i
c o y ff i , k E
var ( /~E)
is m e r e l y t h e ( n e c e s s a ry a n d s u ff ic ie n t) f ir st o r d e r c o n d i t i o n f o r th e m e a n -
v a r i a n c e e f f i ci e n c y o f th e b e n c h m a r k ( p o r t f o l io E ) u s e d t o c o m p u t e b e t a . B e c a u s e
o f th is m a t h e m a t i c a l p r o p e r t y o f m e a n - v a r i a n c e e f fi ci en c y , i t w o u l d s e e m t h a t
a p r o p e r b e n c h m a r k p o r t fo l i o n e e d s t o b e b o t h m e a n - v a r i a n c e e f fi ci en t a n d
m e a n - v a r i a n c e i n e ff ic i e n t a t t h e s a m e t i m e . I t n e e d s t o b e m e a n - v a r i a n c e e f fi c ie n t
s o t h a t t h e p o r t f o l io s o f u n i n f o r m e d m a n a g e r s a n d a ll p as si v e p o r t fo l i o s w i ll
h a v e J e n s e n ' s a l p h a s o f z e r o . I t n e e d s t o b e m e a n - v a r i a n c e i n e ff ic i e n t f o r th e
p o r t f o l i o s o f m a n a g e r s w i t h f o r e c a s t i n g a b i l i t y s o t h a t t h e s e p o r t f o l i o s c a n h a v e
n o n z e r o a l p h a s .
T h i s w o u l d s e e m t o b e a n i m p o s s ib l e t as k f o r a p o r t f o l i o , b u t f o r t h e f a c t
t h a t t h e i n f o r m a t i o n s e t s o f m a n a g e r s w i t h f o r e c a s ti n g a b i li ty d i ff e r f r o m t h o s e
w i t h o u t f o r e c a s t i n g a b i l i t y . T w o m a n a g e r s w i t h d i f f e r e n t i n f o r m a t i o n s e t s w o u l d
n e c e s s a r il y d r a w d i f f e re n t m e a n - s t a n d a r d d e v i a t i o n d ia g r a m s . I n p a r ti c u l a r, t h e
m a n a g e r w i t h f o r e c a s t in g a bi li ty w o u l d h a v e m e a n - v a r i a n c e f r o n t ie r s t h a t a r e
i m p r o v e d b y d y n a m i c p o r t f o l i o s t ra t e gi e s - - s t ra t e g ie s t h a t w e i g h t m o r e h e a v i ly
t h o s e s e c u r i t i e s t h a t a r e f o r e c a s t e d t o h a v e u n u s u a l l y h i g h r e t u r n s i n a p e r i o d .
M a n a g e r s l a ck i n g th i s a bi li ty c a n n o t a c h i e v e a b e t t e r m e a n - v a r i a n c e t r a d e o f f b y
d y n a m i c a l l y c h a n g i n g t h e i r p o r t f o l i o w e i g h t s . H e n c e , t h e i r e f f i c ie n t f r o n t i e r p l o t s
i n s i d e t h e e f f i c ie n t f r o n t i e r o f i n f o r m e d m a n a g e r s , a s i n F i g u r e 2 . T h i s i n s i g h t
i m p l ie s t h a t p o r t f o l i o p e r f o r m a n c e e v a l u a t i o n m a y e s c a p e R o l l' s c r it i q u e i f w e
u s e a b e n c h m a r k t h a t l i e s o n t h e l i n e c o n n e c t i n g p o i n t s A a n d B i n F i g u r e 2 .
T h i s b e n c h m a r k is m e a n - v a r i a n c e e f fi c ie n t w i t h r e s p e c t t o p a s s iv e p o r t f o li o s b u t
n o t w i th r e s p e c t t o t h e d y n a m i c p o r t f o l io s c h o s e n b y m a n a g e r s w i t h f o r e c a s t in g
abi l i ty .
T h e p e r f o r m a n c e o b t a i n e d w i t h a b e n c h m a r k h a v i n g t h i s p r o p e r t y i s a n a l y z e d
i n m o d e l s d e v e l o p e d b y M a y e r s R i c e [ 1 97 9 ], D y b v i g R o s s [ 1 9 85 a , b ] , a n d
G r i n b l a t t T i t m a n [1 9 8 9 b ]. I n t h e s e m o d e l s , i n v e s t o r s w i t h s u p e r i o r i n f o r m a o
t i o n a b o u t i n d i v i d u a l s e c u r i ti e s r e t u r n s ( i. e . s e l e c ti v i ty i n f o r m a t i o n ) b u t w i t h n o
i n t b r m a t i o n a b o u t t h e r e t u r n o n t h e b e n c h m a r k ( i . e . t i m i n g i n f o r m a t i o n ) a c h i e v e
p o s i ti v e a lp h a s i f t h e b e n c h m a r k is m e a n - v a r i a n c e e f fi c ie n t f r o m t h e p e r s p e c t i v e o f
-
5/20/2018 Grinblatt Titman 95 Performance Evaluation Chapter 19
Ch 19 Performance Evaluation 587
Efficient FrQ ntier of
M ea n Informed Managers
Return / j . ~ / EfficientF[ontierof
informedManagers
Risk free / / / \
Return A
Standard Deviation
of Return
Fig. 2. Differences betw een the eff icient frontiers of informed and u ninform ed po rtfolio managers.
a n i n v e s t o r w i t h o u t f o r e c a s t i n g a b i l i ty . F o r i n v e s t o r s w i th t i m i n g i n f o r m a t i o n , t h i s
r e s u l t d o e s n o t n e c e s s a r i ly h o ld . W e w i l l d e f e r d i s c u s s io n o f th i s t i m i n g p r o b l e m
u n t i l l a t e r .
A p r a c t i c a l c o m p l i c a t i o n s t il l r e m a i n s . F i g u r e 2 is b a s e d o n t h e e x - a n t e m e a n s
a n d s t a n d a r d d e v i a t i o n s o f p o r t f o l i o s r a t h e r t h a n t h e i r e s t i m a t e d m e a n s a n d
s t a n d a r d d e v i a t i o n s . I t su g g e s ts t h a t w e e m p l o y a b e n c h m a r k p o r t f o l i o o n t h e e x -
a n t e e f f ic i e n t f r o n t i e r , b u t f i n d i n g s u c h a p o r t f o l i o i s n o t a n e a s y t a s k . M o t i v a t e d
b y t h e C A P M , e a r ly e m p i r ic a l s tu d i es o f m u t u a l f u n d p e r f o r m a n c e m a d e u s e o f
v a l u e - w e i g h t e d p o r tf o l i o s a s b e n c h m a r k s . T h e s e s t u d i e s w e r e u n d e r t a k e n p r i o r
t o th e l a t e 1 9 70 s, w h e n a n u m b e r o f C A P M a n o m a l i e s w e r e d i s c o v e r e d . 3 G i v e n
t h e m o r e r e c e n t e m p i r i c a l e v i d e n c e , th e b e n c h m a r k s u s e d i n t h e s e s t u d i e s a p p e a r
t o b e i n a p p r o p r i a t e f o r s t u d y in g p o r tf o l i o p e r f o r m a n c e , s i n c e t h e y c a n b e g a m e d
b y m a n a g e r s a w a r e o f C A P M - r e l a t e d a n o m a l i e s , l ik e t h e w e l l - k n o w n f i rm s iz e o r
d i v i d e n d y i e l d e f fe c t s. I n t h e n e x t s e c t i o n , w e o u t l i n e t h e r e s u l t s f r o m e m p i r i c a l
s t u di e s o f f u n d p e r f o r m a n c e w i t h t e c h n i q u e s t h a t a r e b a s e d o n s e c u r i t i e s m a r k e t
l in e a n al y si s . W e c a n s e e h o w b e n c h m a r k s h a v e e v o l v e d a s w e a n a l y z e t h e s e s t u d ie s
i n c h r o n o l o g i c a l o r d e r .
3 W hile there was evidence in the early 1970s of a b eta-rela ted anomaly, this a nonlaly was
small for stocks with betas close to 1 (e.g. portfolios with betas from 0.85 to 1.1 de viate d by
at most 0.5 pe r year from the sec urit ies m arket l ine, which is well within levels of statistical
tolerance). Since most mutual funds, and certainly the average mutual fund, have betas closc
to 1 , ear ly empir ical s tudies of mutual fund p er formance fe l t that CA PM proxies w ere a pprop r ia te
benchmarks.
-
5/20/2018 Grinblatt Titman 95 Performance Evaluation Chapter 19
588 34. Gtinblatt S. Titman
2.3. Empirical studies that employ securi t ies market l ine analysis
2 .3.1 . S tudies that employ a s ingle port fo l io be nc hm ark
J e n s e n ' s d o c t o r a l d i s s e r t a t i o n , s u m m a r i z e d i n a r t i c l e s i n t h e Journa l o f F inance
[ 1 9 6 8 ] a n d t h e
Journa l o f Bus iness
[ 19 69 ], w a s o n e o f t h e e a r l i e s t a n d m o s t
i n fl u e n ti a l s tu d i e s o f m u t u a l f u n d p e r f o r m a n c e . T h e s t u d y u s e d J e n s e n ' s a l p h a t o
e v a l u a t e t h e y e a r l y r e t u r n s o f 1 15 m u t u a l f u n d s o v e r t h e 1 9 4 5 - 1 9 6 4 p e r i o d . T h e
s a m p l e i n c l u d e d a ll o f th e f u n d s t h a t w e r e f o l l o w e d b y W i e s e n b e r g e r ' s I n ves t m en t
C o m p a n i e s o v e r th e e n t i r e 1 9 5 5 - 1 9 6 4 p e r io d . T h e b e n c h m a r k u s e d t o e v a l u a te
t h e s e f u n d s w a s t h e S & P c o m p o s i t e i n d e x w h i c h i s a v a l u e - w e i g h t e d p o r t f o l i o
( c o n s i s t i n g o f 5 0 0 s to c k s a f t e r M a r c h 1 , 1 95 7 a n d 9 0 s t o c k s p r i o r t o t h i s d a t e ) .
J e n s e n c o n c l u d e d t h a t o v e r t h e 1 9 5 5 - 1 96 4 p e r i o d , m u t u a l f u n d s, o n a v e r a g e ,
a c h i e v e d a ri s k - a d ju s t e d p e r f o r m a n c e o f a b o u t - 0 . 9 % p e r y e a r. 4 W h e n t h e v a r i o u s
c o m m i s s io n s a n d e x p e n s e s o f t h e f u n d s w e r e a d d e d b a c k t o th e f u n d s ' r e t u rn s ,
t h e r i s k - a d j u s t e d p e r f o r m a n c e w a s v i rt u a ll y z e r o . T h u s , t h e a v e r a g e r e t u r n s o f t h e
f u n d s w e r e c o n s i s t e n t w i t h w h a t w o u l d b e e x p e c t e d i n a n e f f i c i e n t m a r k e t . S i m i l a r
r e s u l ts w e r e f o u n d b y M c D o n a l d [1 97 4] u s i n g t h e e q u a l l y - w e i g h t e d N Y S E i n d e x
a s hi s b e n c h m a r k .
F o r a s m a l l e r s a m p l e o f 5 6 f u n d s, J e n s e n a l s o e x a m i n e d w h e t h e r f u n d s t h a t d i d
r e l a ti v e l y w e l l ( p o o r l y ) f r o m 1 9 4 5 - 1 9 5 4 a l so d i d w e l l ( p o o r l y ) f r o m 1 9 5 5 - 1 9 6 4 .
T h e c o r r e l a t i o n b e t w e e n t h e f ir s t h a l f r e t u r n s a n d s e c o n d h a l f r e tu r n s w a s 0 .6 4
i n d ic a t in g t h a t t h e p e r f o r m a n c e o f s o m e m u t u a l f u n d s p e rs is ts o v e r t im e . T h i s
w o u l d b e e v i d e n c e a g a i n s t m a r k e t e f f i ci e nc y i f i t w e r e t h e p o s i t i v e p e r f o r m e r s
t h a t d i d w e l l p e r s i s t e n t l y . H o w e v e r , t h e e v i d e n c e s u g g e s t s t h a t i t i s p r i m a r i l y
t h e b a d p e r f o r m e r s t h a t e x h i b i t p e r s i s t e n t p e r f o r m a n c e . T h e s e p e r s i s t e n t l y b a d
p e r f o r m a n c e n u m b e r s c o u ld h a v e b e e n g e n e r a t e d b y fu n d s t ha t g e n e r a t e d v e r y
h i g h c o m m i s s i o n s a n d o t h e r e x p e n s e s . T h e s t u d y f a i l e d t o f i n d e v i d e n c e o f
p e r s i s t e n t l y p o s i t i v e p e r f o r m a n c e .
I n a c o m m e n t o n J e n s e n ' s s tu d y , M a i n s [1 97 7] a r g u e d t h a t t h e m u t u a l f u n d
r e t u r n s u s e d b y J e n s e n w e r e b i a s e d d o w n w a r d s. J e n s e n a s s u m e d t h a t t h e d i v i d en d s
o f th e f u n d w e r e p a i d o u t a t t h e e n d o f t h e y e a r w h i c h w a s in fa c t n o t t r u e . A s
a re s u l t, t h e i n t e r e s t i n c o m e o n t h e d i v i d e n d p a y m e n t s w a s i g n o r e d i n J e n s e n ' s
a n al ys is . T h e w a y in w h ic h J e n s e n a d d e d b a c k e x p e n s e s a n d c o m m i s si o n s p r o d u c e d
a s i m i la r b i as i n h is e s t i m a t e s o f g ro s s r e t u rn s . M a i n s a l s o q u e s t i o n e d J e n s e n ' s
e s t i m a t e s o f s y s t e m a t i c ri sk .
T o re a s s e s s t h e J e n s e n r e s ul ts , M a i n s a n a l y z e d t h e m o n t h l y r e t u r n s o f 70 of t h e
1 15 f u n d s e x a m i n e d b y J e n s e n o v e r th e s a m e 1 9 5 5 to 1 .9 64 t i m e p e r i o d . T h e u s e
o f m o n t h l y r e t u r n s , r a t h e r t h a n t h e y e a r ly r e t u r n s u s e d b y J e n s e n , e l i m i n a t e s t h e
b i a s a s s o c i a t e d w i t h t h e a s s u m p t i o n t h a t t h e d i v i d e n d s w e r e p a i d a t t h e e n d o f
t h e y e a r a n d p r o v i d e s s u p e r i o r e s t i m a t e s o f th e b e t a s a n d a l p h a s o f t h e f u n d s .
4 While some fu nds achieved positive abnorm al returns, it is difficult to ascertain the implications
of this for the efficient markets hypothesis because of the multiple comparison being ma de. That
is, even if no superior fund managem ent ability existed, we w ould expect som e funds to achiever
superior risk-adjusted returns b y chance.
-
5/20/2018 Grinblatt Titman 95 Performance Evaluation Chapter 19
Ch 19 Performan ce Evaluation 589
M a i n s c o n c l u d e d t h a t , o n a v e r a g e , t h e n e t ri s k -a d j u s te d r e t u r n s o f m u t u a l f u n d s
w e r e a b o u t z e r o . H o w e v e r , a f t e r a d d i n g b a c k e x p e n s e s , t h e i r g r o s s r i s k - a d j u s t e d
r e t u r n s w e r e a b o u t 1 p e r y e a r . A l t h o u g h t h e st u d y d i d n o t r e p o r t t h e s ta t is ti c al
s i g n if i c a n c e o f t h a t 1 a b n o r m a l r e t u r n , i t is u n l i k e ly t h a t a 1 r e t u r n si g n if i ca n t ly
d i f fe r s f r o m z e r o .
A m o r e r e c e n t a p p l i c a ti o n o f th e s e c u r it ie s m a r k e t l i n e m e t h o d o l o g y w as
u n d e r t a k e n b y I p p o l i t o [ 1 9 8 9 ] . U s i n g t h e S & P 5 0 0 b e n c h m a r k , I p p o l i t o f o u n d
s l ig h t ly p o s i t i v e a v e r a g e a lp h a s ( 0 . 8 3 p e r y e a r ) f o r h i s s a m p l e o f m u t u a l f u n d s
i n a l a t e r p e r i o d ( 1 9 6 5 - 1 9 8 4 ) . I p p o l i t o i n t e r p r e t s h i s f i n d i n g s a s i n d i c a t i n g t h a t
m u t u a l f u n d s a r e a b l e to u s e t h e i r s u p e r i o r in f o r m a t i o n t o g e n e r a t e a b n o r m a l
r e t u r n s . H o w e v e r , a s w e d i s cu s s i n t h e n e x t s u b s e c ti o n , s u c h c o n c l u s i o n s a r e h i g h l y
d e p e n d e n t o n t h e c h o i c e o f b e n c h m a r k p o r t fo l io s .
2 3 2 S t u d i e s w i t h m u l t i p l e p o r t f o l i o b e n c h m a r k s
M o r e r e c e n t s t u d i e s h a v e e x a m i n e d t h e s e n si ti vi ty o f p e r f o r m a n c e i n f e r e n c e s
t o t h e c h o i c e o f t h e b e n c h m a r k p o r t f o li o , e x a m i n in g m u l t ip l e a s w e l l as s i n gl e
p o r t f o l i o b e n c h m a r k s . T h e r e a r e a n u m b e r o f a d v a n ta g e s t o u s in g m u l t i p le
p o r t f o l i o b e n c h m a r k s . F i rs t, u n l e s s s to c k r e t u r n s a r e g e n e r a t e d b y o n l y o n e
c o m m o n f a c t o r , i t i s u n l i k e l y th a t a n a r b i t ra r i ly c h o s e n d i v e r s i f ie d p o r t f o l i o w i ll
b e m e a n - v a r i a n c e e f fi ci en t . H o w e v e r , as G r i n b l a t t & T i t m a n [ 19 8 7] e m p h a s i z e ,
i f s e c u r i ti e s r e t u r n s a r e g e n e r a t e d b y a t m o s t k fa c t o r s , t h e n i n t h e a b s e n c e
o f a r b i t ra g e , a n y k w e l l -d i v e r s if i e d p o r t f o l i o s w i ll s u m t o t h e m e a n - v a r i a n c e
e f f ic i e n t f r o n t i e r . F o r t h is r e a s o n w e g e n e r a l l y f e e l m o r e c o m f o r t a b l e w i t h m u l t i p l e
p o r t f o l i o b e n c h m a r k s t h a n w i t h s in g le p o r t f o l io b e n c h m a r k s . M o r e o v e r , t h e r e is a n
a l t e rn a t i v e a s se t p r ic i n g t h e o r y , th e A r b i t r a g e P r i ci n g T h e o r y ( A P T ) , s u m m a r i z e d
b y C o n n o r & K o r a j c z y k [1 9 95 , c h a p t e r 4 o f t h is v o lu m e ] , t h a t m a k e s u s e o f a
m u l t i p le p o r t f o l i o b e n c h m a r k a n d w h i c h p r o v id e s g u i d a n c e o n h o w t o s e l e c t a
m u l t i p le p o r t f o l i o b e n c h m a r k .
E m p i r i c a l in v e s ti g a ti o n s o f m u t u a l f u n d p e r f o r m a n c e w i t h m u l t i p l e p o r t f o l i o
b e n c h m a r k s c a n b e f o u n d i n p a p e r s b y L e h m a n n & M o d e s t [ 1 98 7 ], G r i n b l a t t &
T i t m a n [ 1 9 8 9 a , 1 9 9 4] , C o n n o r & K o r a j c z y k [1 99 1], a n d E l t o n , G r u b e r , D a s &
H l a v k a [1 99 3]. T h e s t u d y b y L e h m a n n a n d M o d e s t w a s t h e f ir st t o a d a p t t h e
A P T t o p e r f o r m a n c e e v a l u at io n . T h e b e n c h m a r k s c o n s i d e r e d b y L e h m a n n a n d
M o d e s t i n c lu d e d t h e C R S P v a l u e- w e i g h te d in d e x o f a ll N Y S E a n d A M E X l is te d
s to c k s ( V W ) , t h e C R S P e q u a l l y -w e i g h t e d i n d e x o f a ll N Y S E a n d A M E X l is te d
s t o ck s ( E W ) , a n d 5 , 10 , a n d 1 5 p o r t f o l i o b e n c h m a r k s f o r m e d u s i n g a v a r i e t y
o f f a c t o r a n a ly s i s m e t h o d s . O v e r t h e 1 96 8 to 1 9 8 2 t i m e p e r i o d t h e y f o u n d t h a t
b e n c h m a r k s f o r m e d w i t h t h e v a ri o u s f a c t o r a n al ys is m e t h o d s p r o d u c e d s i m i la r
p e r f o r m a n c e n u m b e r s. H o w e v e r , t h e p e r f o r m a n c e n u m b e r s w i t h t h e E W a n d V W
b e n c h m a r k s d i f f e r e d f r o m e a c h o t h e r a s w e l l a s f r o m t h e n u m b e r s g e n e r a t e d w i th
t h e f a c t o r a n al ys is b e n c h m a r k s . T h e f a c t o r a n al ys is b e n c h m a r k t h a t t h e y e x a m i n e d
i n t h e g r e a t e s t d e t a i l g e n e r a t e d v e r y n e g a t iv e p e r f o r m a n c e n u m b e r s o n a v e r a g e ,
a p p r o x im a t e l y - 4 p e r y e a r. T h e E W i n d e x g e n e r a t e d p e r f o r m a n c e n u m b e r s o f
s im i la r m a g n i t u d e w h i le t h e V W i n d e x g e n e r a t e d p e r f o r m a n c e n u m b e r s t h a t w e r e
c l o s e t o z e r o o n a v e r a g e .
-
5/20/2018 Grinblatt Titman 95 Performance Evaluation Chapter 19
590 M . G r i n b la t t S . T i t m a n
A l t h o u g h t h e f a c t o r an a ly s is b e n c h m a r k h a s s t ro n g t h e o r e t i c a l m o t i v a t io n , t h e
e x t r e m e n e g a t i v e a v e r a g e p e r f o r m a n c e n u m b e r s i t g e n e r a t e s i n d i ca t e t h a t th e
b e n c h m a r k m a y n o t b e a pp r o p r ia t e . G i v e n t h a t t h e 4 n e g a ti v e p e r f o r m a n c e
g r e a t ly e x c e e d s th e l e v e l o f e x p e n s e s a n d c o m m i s s i o n s, t h e p e r f o r m a n c e n u m b e r s
s u g g e s t t h a t t h e f u n d s m u s t , o n a v e r a g e , b e s y s t e m a t i c a l l y s e l e c ti n g b a d s t o ck s ,
w h i c h d o e s n o t s e e m p l a u s i b l e . L e h m a n n a n d M o d e s t p r o v i d e t w o p o s s i b l e
e x p l a n a t i o n s f o r t h i s p e r v e r s e f i n d i n g : o n e i s t h a t t h e m u t u a l f u n d s e x h i b i t t i m i n g
a b il it y , w h i c h b i a s e s t h e b e t a e s t i m a t e s u p w a r d s a n d t h e i n t e r c e p t s d o w n w a r d s
( s e e S e c t io n 2 . 4) ; th e s e c o n d is t h a t t h e b e n c h m a r k p o r t f o l io s c a n n o t b e c o m b i n e d
t o f o r m a p o i n t o n t h e m e a n - v a r i a n c e e f fi ci en t f r o n ti e r.
L e h m a n n a n d M o d e s t ' s e a r li e r w o r k 5 s u g ge s ts t h a t t h e s e c o n d e x p l a n a t i o n i s
v e r y p l a u s i b le . T h e f a c t o r a n a ly s is b e n c h m a r k , l ik e t h e E W b e n c h m a r k , e x h i b i ts
a s t r o n g s i z e - r e l a t e d b i a s . I n p a r t i c u l a r , t h e s t o c k s o f l a r g e f i rm s e x h i b i t n e g a t i v e
a l p h a s w h e n e v a l u a t e d b y th i s b e n c h m a r k . S i n c e m u t u a l f u n d s g e n e r a l l y s e l e c t
l a r g e r t h a n a v e r a g e s t o c k s , i t f o l l o w s t h a t t h e y a r e l i k e l y t o e x h i b i t n e g a t i v e
p e r f o r m a n c e w h e n m e a s u r e d a g a i ns t t hi s b e n c h m a r k . L e h m a n n & M o d e s t [1 98 7]
a l s o e x a m i n e d t h e p o s s ib i li ty t h a t t h e n e g a t i v e p e r f o r m a n c e e s t i m a t e s r e s u l t f r o m
t h e m u t u a l f u n d s t i m i n g th e m a r k e t . T h e y d i d t hi s b y e m p l o y i n g a T r e y n o r &
M a z u y [ 19 6 6] q u a d r a t i c r e g r e s s i o n , b u t f a i le d t o f i nd e v i d e n c e o f p e r v a s i v e ti m i n g
b e h a v i o r . 6
C o n n o r & K o r a j c z y k [1 9 91 ], u s in g a fi ve f a c t o r m o d e l , a n a l y z e d t h e s a m e s a m p l e
o f m u t u a l f u n d s o v e r t h e s a m e t i m e p e r i o d a s d i d L e h m a n n a n d M o d e s t . T o d e r iv e
t h e i r f i ve p o r t f o l i o b e n c h m a r k t h e y f ir s t c o n s t r u c t e d f iv e p o r t f o l io s u s i n g p r i n c i p a l
c o m p o n e n t s a n a ly s is . F o u r l i n e a r c o m b i n a t i o n s o f t h e s e f i ve p o r t f o l i o s t h a t b e s t
m i m i c a s et o f f o u r p r e sp e c i f ie d m a c r o e c o n o m i c f a ct o r s a re t h e n f o r m e d t o y i el d
f o u r n e w f a c t o r p o r t f o l i o s t h a t c o r r e s p o n d t o t h e f o u r m a c r o - f a c t o r s . A f i f t h
f a c t o r , th e r e s i d u a l o f th e r e g r e s s i o n o f t h e v a l u e - w e i g h t e d i n d e x o n t h e p r e v i o u s l y
d e s c r i b e d f o u r m a c r o - f a c t o r p o r t f o l io s , w a s a l s o u s e d . ( T h e p e r f o r m a n c e r e s u lt s
g e n e r a t e d w i th t h is r e s id u a l a r e t h e s a m e a s th o s e t h a t w o u l d h a v e b e e n g e n e r a t e d
b y i n c lu d i n g t h e v a l u e - w e i g h t e d i n d e x i t s el f a s t h e f i f th f a c t o r. ) B e c a u s e o f t h e
i n c l u si o n o f t h is f if th fa c t o r , C o n n o r a n d K o r a c z y k d i d n o t f in d th e s a m e e v i d e n c e
o f n e g a ti v e p e r f o r m a n c e f o u n d b y L e h m a n n a n d M o d e s t.
G r i n b l a t t & T i t m a n [ 1 9 8 9 a ] p r o v i d e d f u r t h e r e v i d e n c e t h a t t h e n e g a t i v e a b n o r -
m a l r e t u r n g e n e r a t e d w i t h L e h m a n n a n d M o d e s t ' s f a c t o r a n al ys is b e n c h m a r k is
t h e r e s u l t o f t h e i n e ff i ci e n cy o f th e b e n c h m a r k . I n a d d i t i o n t o e x a m i n i n g p e r f o r -
m a n c e w i t h t h e e q u a l l y - w e i g h t e d a n d v a l u e - w e i g h t e d i n d i c e s a n d t h e L e h m a n n
a n d M o d e s t 1 0 f a c t o r b e n c h m a r k , t h e y d e v e l o p e d a s e c o n d m u l t ip l e p o r t f o l io
b e n c h m a r k , r e f e r r e d t o a s 'P 8 ' , t h a t i s f o r m e d o n t h e b a s i s o f s e c u ri t ie s c h a r a c te r .-
5 Lehmann & Mo dest [1989], which developed the factor analysis technique used in L ehlnann &
M odest [1987], was published later than their mu tual fund study.
Even if timing ability w ere pervasive, it is unlikely that it wo uld result in neg ative intercepts.
Under reasonable parameter values, the intercept is likely to be positive for positive timers. It is
more plausible that the negative intercepts are cau sed by perverse timers. For example, mutual
funds m igh t choose to be v ery conservative w he n return variances and exp ected returns are
unusually high,
-
5/20/2018 Grinblatt Titman 95 Performance Evaluation Chapter 19
Ch 19 Performance Evaluation 591
is tic s. T h i s e i g h t p o r t f o l i o b e n c h m a r k c o n s i st e d o f fo u r s i z e - b a s e d p o r t f o l io s , t h r e e
d i v i d e n d - y i e l d - b a s e d p o r t f o l i o s , a n d t h e l o w e s t p a s t r e t u r n s p o r t f o l i o . T h e r a t i o -
n a l e f o r f o r m i n g b e n c h m a r k p o r t f o l i o s b a s e d o n s e c u r it ie s c h a r a c t e r i s ti c s is t h a t
t h e s e c h a r a c t e r is t i c s m a y b e b e t t e r p r o x i e s f o r t h e t r u e f a c t o r s t h a n f a c t o r s f o r m e d
w i t h s ta t is t ic a l f a c t o r a n al y si s. I n t h e i r s a m p l e p e r i o d , t h e P 8 b e n c h m a r k c o u l d n o t
b e g a m e d b y s i m p le s tr a te g ie s b a s e d o n w e l l -k n o w n C A P M a n d A P T a n o m a l i es ,
s u c h a s f i r m s i z e, d i v i d e n d y i e l d , b e t a , s k e w n e s s , i n t e r e s t r a t e s e n s i t i v i t y , o r p a s t
p e r f o r m a n c e ] I n a d d i t io n , t h e b e n c h m a r k d i d n o t g e n e r a t e s i g n if ic a n tl y d i f f er e n t
a l p h a s f o r p o r t f o l i o s g r o u p e d b y i n d u s tr y , s
I n a d d i t i o n t o e x a m i n i n g t h e a c t u a l r e t u rn s o f t h e m u t u a l f u n d s , G r i n b l a t t &
T i t m a n [ 1 98 9 a ] a n a l y z e d w h a t t h e y c a ll e d ' h y p o t h e t i c a l p o r t f o l i o s ' , f o r m e d f r o m
t h e q u a r t e r l y h o l d i n g s o f t h e m u t u a l f u n d s. I n c o n t r a s t t o t h e a c t u a l p o r t f o l i o s o f
t h e f u n d s , t h e h y p o t h e t i c a l p o r t f o l i o s c o n s i s t e d e n t i r e l y o f e q u i t y . S i n c e a m u t u a l
f u n d m a n a g e r ' s d e c i s i o n s t o a l l o c a t e a s s e t s b e t w e e n c a s h , b o n d s a n d s t o c k s d o
n o t a f f e c t t h e s e h y p o t h e t i c a l r e t u r n s , t h e i r b e t a s a r e l ik e l y t o v a r y m u c h l es s
t h a n t h e b e ta s o f t h e a c tu a l fu n d r e tu r n s. H e n c e , p e r f o r m a n c e m e a s u r e m e n t
b i a se s a r i s in g b e c a u s e o f t i m i n g t h e m a r k e t a r e s u b s ta n t ia l ly l o w e r w i t h t h e s e
h y p o t h e t i c a l r e t u r n s . I n a d d i t i o n , t h e h y p o t h e t i c a l p o r t f o l i o r e t u r n s i n c l u d e n o
e x p e ns e s o r t r a n s a c t io n c o st s a n d t hu s s h o u l d g e n e r a t e z e r o p e r f o r m a n c e u n d e r
t h e n u l l h y p o t h e s i s t h a t f u n d m a n a g e r s h a v e n o s p e ci a l i n f o r m a t i o n .
T h e G r i n b l a t t & T i t m a n [ 19 8 9a ] f in d in g s c o n f i rm e d t h e L e h m a n n a n d M o d e s t
c o n c l u s io n t h a t b e n c h m a r k c h o i ce d o e s m a t t e r. F o r t h e a c t u a l m u t u a l f u n d r e -
t u r ns , t h e E W i n d e x a n d t h e f a c t o r an a ly s is b e n c h m a r k g e n e r a t e d v e r y n e g at i v e
p e r f o r m a n c e n u m b e r s o n av e ra g e . I n c o n tr a st , t h e p e r f o r m a n c e n u m b e r s g e n e r -
a t e d by t h e V W i n de x a n d th e P 8 b e n c h m a r k y i e ld e d p e r f o r m a n c e n u m b e r s t h a t
w e r e c l o s e t o z e r o o n a v e r a g e . T h e v a r io u s b e n c h m a r k s a l so r a n k e d t h e m u t u a l
f u n d s d i ff e re n t ly , [ G r i n b l a t t & T i t m a n , 1 98 8] . T h e P 8 b e n c h m a r k r a n k e d f u n d s
v e r y d i f fe r e n tl y t h a n t h e E W i n d e x a n d t h e 1 0 f a c t o r b e n c h m a r k . H o w e v e r , t h e 1 0
f a c t o r b e n c h m a r k p r o v i d e d p e r f o r m a n c e s c o re s th a t w e r e s i m il ar t o th e E W i n de x
o n a f u n d b y f u n d b a s i s. T h e c r o s s - s e c t i o n a l c o r r e l a t i o n c o e f f i c i e n t [ f r o m G r i n b l a t t
& T i t m a n , 1 9 9 4 ] w a s 0 . 8 6. 9
A n e v a l u a t i o n o f t h e h y p o t h e t i c a l r e t u r n s o f t h e p o r t fo l i o s f o r m e d f r o m t h e
q u a r t e r l y h o l d i n g s r e v e a l e d s l ig h tl y p o s it iv e p e r f o r m a n c e w i t h t h e V W i n d ex
( 1 . 9 p e r y e a r ) a n d t h e P 8 b e n c h m a r k ( 1. 1 p e r y e a r ) b u t n e g a t i v e a v e r a g e
v See Hawaw ini & Keim [1995, chapter 17 of this volume) and De Bondt & Thaler [1995,
chapter 13 of this volume] for m ore detail.
s A recent paper by Sharpe [1992] forms benchm arks in a similar man ner. Sha rpe po stulates that
the 'style' of each m anaged portfolio can be ch aracterized as a linear function of 12 prespecified
passive portfolios th at represent the various dimension s of investment style. To find the com bination
of these 12 portfolios that has the same style as the managed portfolio that is being evaluated, he
regresses the m anaged portfolio 's return on the returns of the 12 style portfolios. T he estimated
betas from this regression are then used as portfolios weights to construct a passive portfolio with
the sam e style as the managed portfolio.
9 This distinction from the Lehmann and Modest results can be explained by differences in the
sample period.
-
5/20/2018 Grinblatt Titman 95 Performance Evaluation Chapter 19
592 M. Gr inb la tt S . T i tm an
p e r f o r m a n c e w i t h b o t h th e E W i n d ex ( - 3 . 0 p e r y e a r ) a n d th e f a c to r a na ly sis
b e n c h m a r k ( - 2 . 4 p e r y e a r ) . T h e p o si ti v e p e r f o r m a n c e w a s s ta ti st ic a ll y s ig n if i-
c a n t w i t h th e V W i n d e x b u t n o t w i th t h e P 8 b e n c h m a r k . T h e n e g a ti v e p e r f o r m a n c e
w a s s t a t is t ic a l ly s i g n i fi c a n t w i t h t h e f a c t o r a n a l y si s b e n c h m a r k b u t n o t w i t h t h e
E W i n de x . S i n c e w e c a n r u l e o u t t im i n g a n d e x p e n s e s a s a n e x p l a n a t i o n f o r t h e
n e g a t i v e p e r f o r m a n c e n u m b e r s g e n e r a t e d w i th t h e e q u a l ly - w e i g h t e d i n d e x a n d
t h e f a c t o r a n a l y s i s b e n c h m a r k , w e m u s t c o n c l u d e t h a t t h e s e b e n c h m a r k s a r e n o t
m e a n - v a r i a n c e e f fi c ie n t a n d a r e t h u s in a p p r o p r i a t e f o r t h e e v a l u a t i o n o f f u n d
p e r f o r m a n c e .
G r i n b l a t t & T i t m a n ' s [ 1 98 9 a ] an a l ys i s o f th e a g g r e s s iv e g r o w t h f u n d s i s e s p e -
c ia l ly u s e f u l f o r u n d e r s t a n d i n g t h e s u i t a b il it y o f t h e d i f f e r e n t b e n c h m a r k s . T h e
h y p o t h e t i c a l r e t u r n s o f th e s e f u n d s g e n e r a t e d s ig n i fi ca n t p o s i ti v e p e r f o r m a n c e
( 3 . 3 p e r y e a r ) w h e n m e a s u r e d re l a ti v e t o t h e P 8 b e n c h m a r k . H o w e v e r , t h e p e r -
f o r m a n c e is s u b st a nt iM l y n e g a t i v e ( - 3 . 7 ) w h e n m e a s u r e d r e la t iv e t o th e f a c t o r
a n a l y si s b e n c h m a r k . T o u n d e r s t a n d t h i s, c o n s i d e r t h e f a c t t h a t a g g r e s s iv e g r o w t h
f u n d s i n v e s t h e a v i l y in r e l a ti v e l y l a r g e f ir m s w i t h l o w d i v i d e n d y i e ld s . S i n c e t h e
r e t u r n s o f la r g e f i r m s w i t h l o w d i v i d e n d y i e ld s d o p o o r l y r e l a ti v e t o t h e f a c t o r
a n a l y s i s b e n c h m a r k ( a s s h o w n i n G r i n b l a t t & T i t m a n [ 1 9 8 8 ] ) , m u t u a l f u n d s t h a t
f o ll o w s u c h a s t ra t e g y w ill a ls o e x h i b it p o o r p e r f o r m a n c e w h e n m e a s u r e d w i th
r e s p e c t t o t hi s b e n c h m a r k e v e n i f s o m e o f t h e f u n d s r e a l ly d o h a v e s u p e r i o r
a b il it ie s . H o w e v e r , w h e n t h e s e b i a se s a r e e l i m i n a t e d w i th t h e P 8 b e n c h m a r k , t h e
h y p o t h e t i c a l r e t u r n s o f t h e a g g r e ss iv e g r o w t h f u n d s e x h ib i t p o s i ti v e p e r f o r m a n c e
o n a v e r a g e .
T h e p o s i ti v e p e r f o r m a n c e o f t h e h y p o t h e t i c a l r e t u r n s o f t h e a g g re s si v e g ro w t h
f u n d s d o e s n o t i m p l y t h a t i n v e s to r s c a n r e a li z e a b n o r m a l r e t u r n s b y h o l d i n g s h a re s
d i r e c tl y i n th e s e f u n d s . T h e a b n o r m a l p e r f o r m a n c e o f t h e a c t u a l f u n d r e t u r n s i s
c l o se t o z e r o o n a v e r a g e. T h e d i f f e r e n c e i n t h e p e r f o r m a n c e o f t h e h y p o t h e t i c a l
r e t u r n s a n d t h e a c t u a l r e t u rn s c a n b e a t t r i b u t e d t o t h e e x p e n s e s o f t h e f u n d s a n d
t h e c o s t s o f t r a d in g ( e. g. b r o k e r a g e c o m m i s io n s a n d t h e b i d - a s k s p r e a d ) . T h e
e s t i m a t e s o f t h e s e c o s t s t h a t a r e d e r i v e d f r o m t h i s d i f f e r e n c e is a b o u t 2 . 5 p e r
y e a r f o r t h e a v e r a g e m u t u a l f u n d in t h e s a m p l e ( a n d a b o u t 3 f o r t h e a v e r a g e
a g g r e s s i v e g r o w t h f u n d ) .
T h e w o r k o f E l t o n , G r u b e r , D a s & H l a v k a [ 1 99 3 ], p u n c t u a t e s t h is e v i d e n c e o n
t h e i m p o r t a n c e o f t h e b e n c h m a r k p o r t f o li o in d r a w i n g p e r f o r m a n c e e v a l u a ti o n
c o n c lu s io n s . T h e y p r o p o s e a 3 - i n d e x b e n c h m a r k t h a t i n c l u d es b o n d p o r t f o l io s a s
w e l l a s s to c k p o r t f o l i o s . S p e c i fi c al ly , t h e i r b e n c h m a r k is c o m p r i s e d o f t h e S & P 5 0 0
i n d e x , a s m a l l s to c k i n d e x , a n d a b o n d i n d e x . T h e y u s e d t h i s b e n c h m a r k t o r e e v a l -
u a t e I p p o l i t o 's c o n c l u s io n s a b o u t m u t u a l f u n d s g e n e r a t i n g a b n o r m a l r e tu r n s . T h e y
f o u n d t h a t w i t h t h e i r b e n c h m a r k , I p p o l i t o ' s s a m p l e o f m u t u a l f u n d s g e n e r a t e d
i n s i g n i f i c a n t n e g a t i v e a b n o r m a l p e r f o r m a n c e , a t t r i b u t i n g I p p o l i t o ' s ' p e r f o r m a n c e '
t o f u n d h o l d i n g s o f n o n - S & P 5 0 0 st o ck s a n d b o n d s .
T h e i m p o r t a n c e o f t h e c h o i c e o f a b e n c h m a r k p o r t f o l i o is n ic e ly i ll u s tr a t e d
b y th e c o n t r a d i c t o r y r e su l ts o n a v e r a g e f u n d p e r f o r m a n c e b e t w e e n s i n gl e p o r t f o -
l io a n d m u l t i p l e p o r t f o l i o b e n c h m a r k s a n d b e t w e e n d i f f e re n t m u l t ip l e p o r t f o l i o
b e n c h m a r k s . T h e l e ss o n o f R o l l [ 19 78 ] c o u l d n o t b e m o r e c le a r: W h e n e v a l u a ti n g
-
5/20/2018 Grinblatt Titman 95 Performance Evaluation Chapter 19
Ch. 19. Perform ance Evalua tion 593
t h e p e r f o r m a n c e o f a f u n d m a n a g e r , t h e b e n c h m a r k m u s t b e e x - a n t e e f f ic i e n t w i t h
r e s p e c t t o t h e m e a n - v a r i a n c e s e t g e n e r a t e d b y t h e p as s iv e i n v e s t m e n t s t r a te g i e s
t h a t t h e f u n d m a n a g e r c o n s i d e r s fe a s ib l e.
2.3 .3. I s there d i ff erent iaI pe r for m an ce?
T h e p o s i ti v e a b n o r m a l p e r f o r m a n c e o f t h e h y p o t h e ti c a l m u t u a l f u n d r e t u r n s
i n t h e G r i n b l a t t & T i t m a n [ 1 9 89 a ] s t u d y s u g g e s ts th a t a t l e a s t s o m e f u n d s h a v e
s u p e r i o r s e l e c t i o n a b i l i t y . G i v e n t h i s , i t i s n a t u r a l t o a s k w h e t h e r s o m e f u n d s
r e a l iz e b e t t e r p e r f o r m a n c e t h a n d o o t h e r f u n ds . W e w il l d is cu s s t w o w a y s to t e s t
t h i s p r o p o s i t i o n : T h e m o s t g e n e r a l t e s t i s t o s i m u l t a n e o u s l y e s t i m a t e t h e m a r k e t
m o d e l r e g r e ss i o n s f o r e a c h o f t h e m u t u a l f u n d s a n d t o j o i n tl y te s t t h e r e s t r i c t io n
t h a t t h e i r J e n s e n ' s a l p h a s a r e e q u a l t o e a c h o t h e r . T h i s t e s t d o e s n o t q u a n t i f y
d i f f e r e n t i a l p e r f o r m a n c e . I t m e r e l y r e j e c t s o r f a i l s t o r e j e c t t h e h y p o t h e s i s t h a t
a l l f u n d s h a v e t h e s a m e r i s k - a d j u s t e d r e t u r n s . A s e c o n d t e s t , w h i c h a n a l y z e s
w h e t h e r t h e p a s t p e r f o r m a n c e o f a m u t u a l f u n d i s a g o o d i n d i c a t o r o f its f u t u r e
p e r f o r m a n c e , h a s t h e a b il it y t o q u a n t i f y d i ff e r e n c es i n p e r f o r m a n c e .
W i t h i n t h e f ir s t c la s s o f te s t s, G r i n b l a t t & T i t m a n [ 1 98 9 a ] e s t i m a t e d a s e r ie s
o f j o i n t F - t e s t s t o d e t e r m i n e w h e t h e r m u t u a l fu n d s w i t h th e s a m e i n v e s t m e n t
o b j e c ti v e s al l g e n e r a t e t h e s a m e p e r f o r m a n c e , l T h e s e t e st s r e v e a l e d e v i d e n c e
o f d i f fe r e n t ia l p e r f o r m a n c e f o r t h e a c t u a l a s w e ll as t h e h y p o t h e t i c a l r e t u r n s o f
t h e a g g r e s s i v e g r o w t h a n d g r o w t h f u n d s . T h e r e w a s n o e v i d e n c e o f d i f f e r e n t i a l
p e r f o r m a n c e a m o n g t h e f u n d s w i th o t h e r i n v e s t m e n t o b j e ct iv e s .
T e s ts o f t h e p e r s i s t e n c e o f m u t u a l f u n d p e r f o r m a n c e m a y b e s o m e w h a t l e ss
g e n e r a l, b u t th e y m o r e d i r e ct ly a d d r e ss t h e q u e s t i o n t h a t is o f m o s t i n t e r e s t t o
m u t u a l f u n d i n v e st o rs . Is t h e p a s t p e r f o r m a n c e o f a f u n d a g o o d i n d i c a t o r o f i ts
f u t u re p e r f o r m a n c e ?
D i r e c t t e s ts o f t h is p r o p o s i t i o n a r e f o u n d i n G r i n b l a t t & T i t m a n [ 19 9 2] a n d
H e n d r i c k s , P a t e l & Z e c k h a u s e r [1 99 3]. G r i n b l a tt a n d T i t m a n e x a m i n e d t h e a c t u a l
r e t u r n s o f a s a m p l e o f 27 9 f u n d s o v e r t h e 1 97 5 t o 1 9 8 4 t i m e p e r i o d u s i n g t h e i r P 8
b e n c h m a r k . T h e y d iv i d e d t h e s a m p l e i n t o 1 9 7 5 - 1 9 7 9 a n d 1 9 8 0 - 1 9 8 4 s u b p e r i o d s
a n d e x a m i n e d w h e t h e r b e t t e r t h a n a v e r a g e p e r f o r m a n c e i n t h e e a r l i e r h a l f i s
i n d ic a t iv e o f b e t t e r t h a n a v e r a g e p e r f o r m a n c e i n th e l a t e r h a lf . T h e i r r e s u lt s
p r o v i d e w e a k s u p p o r t f o r t h e h y p o t h e s is t h at b e t t e r t h a n a v e r a g e p e r f o r m a n c e
p e r si st s o v e r ti m e . F o r e x a m p l e , th e s u b s a m p l e o f fu n d s t h a t a c h i e v e d p e r f o r m a n c e
i n t h e t o p d e c i l e i n t h e f i r s t s u b p e r i o d d i d n o t r e a l i z e a b n o r m a l p e r f o r m a n c e o n
a v e r a g e in t h e s e c o n d s u b p e r i o d ( a l th o u g h t h e p e r f o r m a n c e w o u l d b e p o s i t iv e if
e x p e n s e s w e r e a d d e d t o t h e r e t u r n s ) . I n c o n t r a s t , f u n d s t h a t p e r f o r m e d i n t h e
b o t t o m d e c i l e i n t h e f i r s t s u b p e r i o d r e a l i z e d a b n o r m a l p e r f o r m a n c e o f - 3 . 6
p e r y e a r . T h e d i f f e r e n c e b e t w e e n t h e p e r f o r m a n c e o f t h e s e g r o u p s o f f u n d s is
s t a t is t i c a ll y s i gn i f i c an t a t t he 5 l eve l.
T h e H e n d r i c k s , P a t e l , a n d Z e c k h a u s e r s t u d y , w h i c h l o o k s a t n o - l o a d g r o w t h -
o r i e n t e d m u t u a l f u n d s f r o m 1 9 7 4 - 1 9 8 8 , p r o v i d e s st r o n g e r e v i d e n c e t h a t f u n d s
m Because their sample included 157 mutual funds but only 120 monthly observations they did
not have enough degrees of freedom to jointly test the equality of all of the intercepts.
-
5/20/2018 Grinblatt Titman 95 Performance Evaluation Chapter 19
5 9 4
M . G rinblatt, S. Titrnan
t h a t d o w e l l i n t h e p a s t d o w e l l i n t h e f u t u r e . I n t h e i r s t u d y , f u n d s i n t h e t o p
o c t i l e o f p a s t p e r f o r m e r s o v e r t h e p a s t y e a r ( a s m e a s u r e d w i t h r a w r e t u r n s ) ,
o u t p e r f o r m e d t h e l o w e s t o c t il e p a s t p e r f o r m e r s i n t h e f o l lo w i n g y e a r, b y 1 0 - 1 6
p e r y e a r ( as m e a s u r e d b y r i s k - a d j u s t e d r e t u r n s , w i t h th e v a r i a t i o n d e p e n d i n g o n
t h e b e n c h m a r k ) . T h e i r a n a l y s is s u g g e s ts t h a t t h e b e s t w a y to p r o f i t f r o m t h is
p e r s i s t e n c e i s t o f o c u s o n t h e r a w r e t u r n s o f f u n d s i n th e p r i o r f o u r q u a r t e r s . 11
I n f o r m a t i o n a b o u t p e r f o r m a n c e b e y o n d t h e p r e v i o u s f o u r q u a r t e r s d o e s n o t s e e m
t o p r e d i c t f u t u r e p e r f o r m a n c e . I n c o n t r a s t t o G r i n b l a t t & T i t m a n [ 19 9 2] , t h e y f i nd
p r o f i t s f r o m b u y i n g t h e w i n n e r s a s w e l l a s f r o m s e l li n g th e l o s e rs . W h i l e t h e p r o f i ts
f r o m b u y i n g t h e p a s t p e r f o r m e r s i n t h e t o p o c t i l e a r e l a r g e f o r s o m e b e n c h m a r k s ,
t h e y g e n e r a l l y a r e n o t s t a t is t i c a ll y s i g n i f i c an t . 12
2. 4 . Timing, se lec t iv ity and b iases in Jensen s a lpha
W e n o w a n a l y z e h o w t i m i n g a n d s e l e c t iv i t y a b i li ty af f e c t p e r f o r m a n c e a n d
d i s cu s s m e t h o d s t o s e p a r a t e t h e s e t w o t y p e s o f p e r f o r m a n c e a b il it y . T h e d i s t i n c t i o n
b e t w e e n t i m i n g a n d s e le c t iv i ty is i m p o r t a n t i n th a t i t i s g e n e r a l l y m o r e d i ff i cu l t t o
e v a l u a t e p e r f o r m a n c e w h e n t h e r e is a n y t i m i n g a b i li ty c o n t r i b u t i n g t o it .
11 Th e pe r s i s t e nc e o f a bnorm a l p e r fo rm a nc e fo r on l y a bou t fou r qua r t e r s i s no t c ons i s te n t wi t h
the idea tha t so me fun d m anagers ha ve super ior abil ity. Ab i l i ty should la s t m ore than fo ur quar te rs .
In add i t ion , fou r qu ar te rs of h i s tor ica l re turns i s not a sufficiently long t ime se r ies tO draw pro per
s ta t i s ti ca l infe rences a bou t abi li ty , g iven the vola ti l ity of mu tua l fund re turns . H ence , the fun d
rankings o f Hendricks , Pa te l & Zec khau se r [1993] a re la rge ly due to noise in s tock re turns . Th e i r
e v i de nc e on pe r s i s t e nc e ma y be r e l a t e d t o r e c e n t e v i de nc e o f pe r s i st e nc e i n i nd i v idua l s toc k r e t u rns
[e .g . Jegadeesh & Ti tman, 1993] . Funds tha t happen to hold s tocks tha t do we l l , and cont inue to
hold tho se s tocks , wi l l cont inu e to do w e l l because of the pe rs i s tence in the indiv idua l s tock re turns .
W hi le Hend ricks , Pa te l & Zeck haus e r [1993] emp loy s imula t ions to conc lude tha t pe rs i s tence in
s tock re turns i s not dr iv ing the i r hot -hands e ffec t , the i r s imula t ions a re based on randomly he ld
equa l ly-w eighted por t fo l ios of 100 stocks . Re la t ive to ac tua l fund s t ra tegies over th i s t ime pe r iod ,
th i s approach may be b iased aga ins t f inding a s tock pe rs i s tence e ffec t .
12 A recen t pap er by Brown, G oe tzm ann, Ibbotson & Ross [1992] a rgues tha t re sul t s of
pe rs i s tenc e wi l l app ear spur ious ly in samples l imi ted to surviv ing mu tua l funds . T he i r a rg um ent
i s tha t funds tha t choose h igh r i sk s t ra tegies and survive in the f i rs t ha l f of the sample pe r iod
are l ike ly to hav e abov e average re turns . I f these funds cont inu e the i r h igh r i sk s t ra tegy and
con t inue to survive , they a re a l so l ike ly to achieve above norm al re turns in the se cond ha l f of
the sample . This b ias in favor of f inding pe rs i s tence i s offse t somewhat by the fac t tha t funds
which do poo r ly in the f i rst ha l f of the sample a re m ore l ike ly to exi t the samp le in the te s t
pe r i od (be c a use o f poo r pe r fo rma nc e i n t he t e s t pe r i od ) t ha n t hose funds t ha t d i d we l l i n t he
f i rs t ha l f . Survivorship b ias of th i s type i s the re fore more severe for the pas t lose rs than for the
pas t winners , b ias ing our te s t s aga ins t f inding pe rs i s tence . Apparent ly , these two e ffec t s a re e i the r
unim por tant in prac t ice , or a l te rna tive ly , they cance l each o the r out . Test s of the p e rs i s tence of
mutua l fund pe rformance on samples tha t a re not subjec t to a smwiva l requi rement [e .g . Grinbla t t
& Ti tm an, 1993, foo tno te 13] , prov ide evidence tha t is s imi la r to te st s on samples tha t requ i re
surviva l for the ent i re sample pe r iod . Malkie l ' s [1995] work , however , sugges ts tha t conc lus ions
a bou t t he u n i mp or t a nc e o f su rv ivo r sh ip ma y be s e ns i ti ve to t he t i me pe r i od s t ud ie d . In pa r t ic u l a r ,
he f inds tha t the re i s no eviden ce of pe rs i s tence am ong a sample of surviv ing an d no n-surviv ing
funds in the 1980s (but the re i s pe rs i s tence in the 1970s). Brown & Go e tzm ann [1995] , us ing da ta
on non-surviv ing funds , s imi la r ly f ind tha t survivorship b ias p lays som e ro le (a lbe i t a mo des t one)
in the h ot hand s pe rs i s tence f indings.
-
5/20/2018 Grinblatt Titman 95 Performance Evaluation Chapter 19
Ch. 19. P erformance Evaluation 595
W e c a n m o r e f o r m a l l y c la s s if y t h e s e t w o t y p e s o f a b i li t y w i t h a s i m p l e r e g r e s s i o n .
L e t
~ i = e x c e s s r e t u r n o f a s s e t j
x i = t h e i n v e s t o r s p o r t f o l i o w e i g h t o n a s s e t j , w h i c h i s r a n d o m , s i n c e t h e
i n v e s t o r m a y a l t e r h i s p o r t f o l i o i n r e s p o n s e t o ( re a l o r i m a g i n e d ) i n f o r m a -
t i o n .
/~p t h e s u m m e d p r o d u c t o f F j a n d x j
= e x c e s s r e t u r n o f t h e i n v e s t o r s p o r t f o l i o o f t h e N r i sk y a s s e t s
/~E = t h e e x c e s s r e t u r n o f th e p o r t f o l io o f ri sk y a s s et s t h a t is m e a n - v a r i a n c e
e f f i c ie n t f r o m t h e p e r s p e c t i v e o f a n u n i n f o r m e d o b s e r v e r .
A r e g r e s s i o n o f t h e e x c e s s r e t u r n o f s e c u r i ty i o n t h e e x c e s s r e t u r n o f a m e a n -
v a r i a n c e e f fi c ie n t b e n c h m a r k p o r t f o l i o i m p l i e s th a t t h e e x c e ss r e t u r n o f e a c h a s se t
is
w h e r e
c o y h E )
/3 -
v a r ( R E )
a n d , g i v e n t h e e f f i c ie n c y o f t h e b e n c h m a r k , t h e m e a n o f ~j i s z e r o . I t f o l l o w s t h a t
t h e e x c e s s r e t u r n o f t h e i n v e s t o r s p o r t f o l i o i s
R p = ~ p R E -~ - ~ :p 5 )
w h e r e
N N
t i p
= y ~ 2 j f l j
a n d g p = ~ 2 J ~ )
. j = l . i = l
l h k i n g t h e e x p e c t e d v a l u e o f b o t h s id e s o f e q u a t i o n ( 5) y i e ld s
E ( R p ) = E f i p ) E R E ) + c o v ( t i p , R E ) + g ~ : p ) ( 6 )
T h e f ir s t t e r m o n t h e r i g h t h a n d s i d e o f e q u a t i o n ( 6 ) is t h e e x p e c t e d e x c e s s r e t u r n
o f t h e p o r t f o l i o c o n d i t i o n a l o n k n o w i n g t h e p o r t f o l io s t a r g e t r is k le v el . T h e s e c o n d
t e r m , t h e c o v a r i a n c e b e t w e e n t h e p o r t f o l io b e t a a n d t h e r e tu r n o f t h e b e n c h m a r k ,
is t h e c o n t r i b u t i o n o f t i m i n g t o t h e e x c e s s r e t u r n . T h e t h i r d t e r m , w h i c h i s t h e
s u m o f t h e c o v a r i a n c e s b e t w e e n t h e p o r t f o l i o h o l d in g s a n d t h e r e s id u a l s , i s t h e
c o n t r i b u t i o n o f s e le c t iv i ty to t h e e x c e ss re t u r n . T o t a l a b n o r m a l p e r f o r m a n c e , t h e
s u m o f t h e l a t t e r t w o t e rm s , c a n b e s h o w n t o b e t h e s u m o f t h e c o v a r i a n c e s
b e t w e e n t h e p o r t f o l i o w e i g h t s a n d t h e r e t u r n s ,
N
cov 7)
j = l
-
5/20/2018 Grinblatt Titman 95 Performance Evaluation Chapter 19
596
M . G r in b l a t t, S . T i t m a n
G r i n b l a t t T i t m a n [ 19 8 9b ] h a v e sh o w n t h a t t h is c o v a r i a n c e s h o u l d b e p o s i t iv e f o r
i n v e s t o r s w i t h t h e a b i l i t y t o f o r e c a s t r e t u r n s . 13
I t is o f t e n d i f f ic u lt t o p r o p e r l y c a p t u r e p e r f o r m a n c e w i t h J e n s e n ' s a l p h a ,
T r e y n o r ' s r a t i o , o r t h e T r e y n o r - B l a c k a p p r a i s a l r a t i o if b e t a s c h a n g e . F o r e x -
a m p l e , i f t h e b e t a o f t h e p o r t f o l i o i n c r e a s e s as t h e f o r e c a s t e d b e n c h m a r k r e t u r n
i n c r e a se s , t h e s i ng l e p o r t fo l i o b e t a e s t i m a t e d w i t h J e n s e n ' s r e g r e s s i o n w i l l o v e r -
e s t i m a t e t h e a v e r a g e b e t a , E ( f ip ) . T h e r e s u l t i n g i n t e r c e p t i s t h e n u n d e r e s t i m a t e d
a n d u n d e r c e r t a i n c o n d i t i o n s c a n b e n e g a t i v e f o r in v e s t o r s w i t h t im i n g i n f o r m a -
t io n . 14 F i g u r e 3, d r a w n fr o m G r i n b l a t t T i t m a n [ 1 9 8 9b ] , p r o v i d e s a b i n o m i a l
i l lu s t r a t i o n o f th i s p h e n o m e n o n . P o p u l a r e x a m p l e s i n th e l i t e r a t u r e i l l u s t ra t e th a t
t h is p h e n o m e n o n c a n a ls o o c c u r fo r c e r t a i n p a r a m e t e r v a lu e s w h e n t h e p o r t f o l io
b e t a i s a l i n e a r f u n c t i o n o f a n o r m a l l y d i s t r i b u t e d t i m i n g s i g n al . 15
T h e l a r g e s a m p l e v a l u e ( o r p r o b a b i l i ty l im i t ) o f J e n s e n ' s a l p h a c a n b e d e -
c o m p o s e d t o b e t t e r a n a ly z e t h i s p h e n o m e n o n a n d t o p o i n t o u t th e r e l a t io n
o f t h is p e r f o r m a n c e m e a s u r e t o t i m i n g a n d s e le c ti v it y . G r i n b l a t t T i t m a n
[ 19 8 9b ] s h o w e d t h a t J e n s e n ' s a l p h a c a n b e d e c o m p o s e d i n t o t h e s u m o f t h r e e
t e r m s :
[ 1 ~ f i p t - b p ) l R E
o ~ = p l i m T t = l
+ p l i m
~ _ , f ip t [ ~ E t - R ,E )
( 8 )
t = l
+ p l i m ~ pt ,
w h e r e
b p = t h e p r o b a b i l i t y l i m i t o f t h e l e a s t s q u a r e s s l o p e c o e f f i c i e n t f r o m t h e t i m e -
s e r ie s r e g r e s s i o n o f ex c e ss r e t u r n s o f th e e v a l u a t e d p o r t f o l i o a g a i n s t th e
e x c e ss r e t u r n s o f t h e e f f ic i en t b e n c h m a r k p o r t f o l i o a n d
/~E = t h e p r o b a b i l i t y l i m i t o f t h e s a m p l e m e a n o f t h e e x c e s s r e t u r n s o f t h e
b e n c h m a r k p o r t f o l i o .
13 Vcrrecchia [1980 ] devised an example where betas w ere pro perly measured and wh ere
perfo rma nce was negative for an investor with t iming information. G rinbla tt Titm an [1989b]
showed that this was due to a wealth effect . Investors with posit ive information abou t the m arke t
reduced thei r betas because thei r informat ion m ade them weal th ier . The par t icular u t i l ity funct ion
used by Verrecchia, qua dratic uti l ity, is one w here in crease d we alth m ake th e investor's r isk aversion
arbitra ri ly large at larg e wealth levels. Hence, this was an r isky assets were Giffen goo ds-w ealth
effects dom ina ted su bsti tution effects.
14 See Jense n [1972], Dybvig Ross [ t985@ A dm ati Ross [1985], Ad ma ti , Bhattacharya,
Pfleide rer Ross [1986], and Gr inbla tt Titm an [1989b] for oth er conditions that lead to this
result.
15 See, for example, G ran t [1977], Dybvig Ross [1985@ and Grinb latt Titm an [1989b].
-
5/20/2018 Grinblatt Titman 95 Performance Evaluation Chapter 19
Ch. 19. PerJbrmance Evaluation
597
Excess Return
of Manage Portfolio
High Beta Portfolio Choice
A z
/7
Low Beta Portfolio Choice
Excess Return of
Hl~h Efficient Portfolio
Low
Return Retuln
/ rL r H
/
/
alpha
C
Fig. 3 . An example of a nega t ive Jensen measure for a marke t t imer . The two sol id l incs p lo t
the excess re turn of a managed por t fo l io of a r i sk-free inves tment and an inves tment in the r i sky
eff ic ient por t fo l io aga ins t the la t te r s excess re turn for two di f fe rent choices of be ta . A mark e t -
t iming s tra tegy, cons t ra ined to cho ose be twe en the two be tas , would p lo t a t point A (poin t B) i f
inform at ion in dica ted tha t th e excess re turn of the e ff ic ient por t fo l io was expec ted to be rn ( rL).
The s l ope o f t he do t t e d l i ne is t he e s t i ma t e d be t a i n t he J e nse n re g re s s i on , a nd t he i n t e rc e p t i s t he
Je nse n me a su re .
The three terms in equation (8) are respectively the component of performance
that results from large sample biases in estimated beta, the component that results
from timing, and the component that results from selectivity. If the first term is
zero, Jensen's alpha aggregrates the sum of the timing and selectivity components.
However, this is only the case in the absence of timing information [Grinblatt &
Titman, 198 , Lem ma 1].
2.5. Regress ion based t iming measures
T he re a r e s e ve ra l p roc e dure s t ha t ha ve be e n p ropos e d t o c o r r e c t f o r t he b i a s
in Jensen ' s a lpha induced b y the e f fec t of t iming abi li ty on the es t imate of be ta .
The f ir s t is a quadra t i c regress ion , prop osed by Treynor Mazu y [1966]. Thi s
regress ion,
/~p - - rf ~ O/p -Ic-f l 0 p (R E r f ) -}- f l i p ( R E r f ) 2 -I- ~ p , (9)
i s ident i ca l to the regress ion used to compute Jensen ' s a lpha , except tha t an
-
5/20/2018 Grinblatt Titman 95 Performance Evaluation Chapter 19
598 M. G r i n b l a t t , S . T i t m a n
a d d i t i o n a l t e r m , t h e s q u a r e d e x c e ss re t u r n o f t h e b e n c h m a r k p o r t f o l i o is i n c l u d e d .
A d m a t i , B h a t t a c h a r y a , P f l e i d e r e r R o s s [ 19 8 6] d e v e l o p e d c o n d i t io n s u n d e r w h i c h
t h e c o e f f i c i en t o n t h e q u a d r a t i c t e r m c a n b e u s e d t o d e t e c t t h e p r e c i si o n o f t h e
m a n a g e r ' s t i m i n g f o r ec a s ts . L i k e C o n n o r K o r a c z y k , A d m a t i, B h a t t a c h a r y a ,
P f l e i d e r e r R o s s a s s u m e e x p o n e n t i a l u t il it y a n d m u l t i v a r i a t e n o r m a l i t y . I t is e a s y
t o s h o w t h a t t h e s e a s s u m p t i o n s i m p l y th a t t h e p o r t f o l i o b e t a i s a li n e a r f u n c t i o n o f
t he t i m i ng s i gna l .
U n d e r t h e A d m a t i , B h a t t a c h a r y a , P f l e i d e r e r R o s s c o n d i ti o n s , o n e c a n r e l a t e
t h e p a r a m e t e r s o f t h e T r e y n o r - M a z u y r e g r e s s io n t o t h e t i m i n g a n d s e l e c ti v it y
c o m p o n e n t s d i s c u s s e d a b o v e . I n t h i s c a s e , f l l p v a r R E ) i s t h e t i m i n g c o m p o n e n t
o f p e r f o r m a n c e a n d O~p is t h e s e le c ti v it y c o m p o n e n t o f p e r f o r m a n c e . T o t a l p e r f o r -
m a n c e is th e s u m o f t h e t w o t e rm s . T h e r e i s n o m i s m e a s u r e m e n t o f b e t a i n t h is
c a se . H o w e v e r , t h e m o m e n t w e d e p a r t f r o m b e t a l i n e ar it y , w e c a n n o l o n g e r a s s e rt
t h is . T h i s m a k e s t h e a p p l i c a t i o n o f t h is r e g r e s s i o n s o m e w h a t n a r r o w .
T o s e e t h a t t i m i n g a n d s e le c ti v it y a r e r e p r e s e n t e d b y th e s e t e r m s u n d e r t h e
n a r r o w s e t o f a s s u m p t i o n s , im a g i n e t h a t t h e m a n a g e r o b s e r v e s t h e e x c es s r e t u r n o f
t h e b e n c h m a r k p l u s n o is e , FE 6 . H i s f o r e c a s t o f t h e b e n c h m a r k r e t u r n is a l in e a r
f u n c t i o n o f t h i s s ig n a l a n d h i s p o r t f o l i o b e t a i s a l i n e a r f u n c t i o n o f t h e o p t i m a l
f o r e c a s t . T h i s i m p l i e s t h a t
~p = o + ~ RE + ~)
a n d t h e e x c e ss r e t u r n o f th e p o r t f o l i o is
[ Y O ll - Y l / ~ E l l - g ) ] R E - 1 - 6 p .
F r o m t h i s e x p r e s s i o n , l e t u s r e g a r d
a s th e r e g r e s s i o n r e s id u a l in t h e T r e y n o r - M a z u y r e g r es s io n . G i v e n e x p o n e n t i a l
u t il it y a n d t h e i n d e p e n d e n c e o f th e s ig n al s, w e k n o w t h a t t h e p o r t f o l i o w e i g h t s
t h a t d e t e r m i n e ~ p a r e i n d e p e n d e n t o f / ? E b e c a u s e o f t h e ir i n d e p e n d e n c e f r o m b o t h
t h e f o r e c a s t o f th e b e n c h m a r k r e t u r n a n d o f t h e e x p e c t e d w e a l t h t h a t is t i e d t o t hi s
f o r e c a s t . I n a d d i t i o n , ~ , b e i n g n o i s e , i s i n d e p e n d e n t o f R E , m a k i n g t h e r e g r e s s i o n
res id ua l , Yl ~R E - ] - ~ p - - E
~ p ) ) ,
u n c o r r e l a t e d w i th b o t h o f th e i n d e p e n d e n t v a ri a b le s
i n t h e q u a d r a t i c r e g r e s s i o n [ e q u a t i o n ( 9 )] . y 0, w h i c h m u l t ip l i e s t h e f i r st v a r i a b l e i n
t h e T r e y n o r - M a z u y re g r e s si o n , m u s t t h e r e f o r e e q u a l t h e a s y m p t o t ic v a l u e o f i ll ,
w h i l e ) /1 , w h i c h m u l t ip l i e s t h e q u a d r a t i c t e r m , m u s t e q u a l t h e a s y m p t o t i c v a l u e o f
f1 2. E ( ~ p ) , w h i c h i s t h e l a r g e s a m p l e e x p e c t a t i o n o f w h a t i s l e ft , m u s t e q u a l t h e
a s y m