Benefits and Risks of Alternative Investment Strategies*

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1 Benefts and Rsks of Alternatve Investment Strateges* Noël Amenc Professor of Fnance at Edhec Drector of Research and Development, Msys Asset Management Systems Lonel Martelln Assstant Professor of Fnance at the Marshall School of Busness, USC Los Angeles Matheu Vassé Research Engneer wth Edhec October 10 th 2002 (*) Ths artcle benefted from the proofreadng of Domnque Blanc, Jean - Franços Bouler, Domnque Forget, Bernard Bechetolle, Jean - Yves Gourn, Phlppe Malase, Ncolas Rousselet, Jean -René Graud, Jean - Yves Foucat, Axel Weytens, Gauter Henry and Sébasten Bonnet. We would lke to thank them for ther very valuable advce. All errors or omssons are, of course, the sole responsblty of the authors.

2 Benefts and Rsks of Alternatve Investment Strateges* Introducton T h e g r o w t h o f a l t e r n a t v e n v e s t m e n t h a s b e e n c o n s d e r a b l e n r e c e n t y e a r s. F o r b o t h n s t t u t o n a l a n d p r v a t e n v e s t o r s, t s e e m s t h a t a l t e r n a t v e n v e s t m e n t n o w c o n s t t u t e s a d s t n c t c l a s s w t h n t h e r o v e r a l l a s s e t a l l o c a t o n. A r e c e n t s u r v e y o f n s t t u t o n a l n v e s t o r s c a r r e d o u t b y G o l d m a n S a c h s a n d F r a n k R u s s e l l 1 r e v e a l e d t h a t t h e re s p o n d e n t s n v e s t e d m o r e t h a n 1. 7 % o f t h e r a s s e t s n h e d g e f u n d s n a n d p l a n t o n c r e a s e t h e n v e s t m e n t t o 3. 4 % f o r M o r e g e n e r a l l y, t h e y e a r r e p r e s e n t e d a r e c o r d y e a r f o r n v e s t m e n t s n h e d g e f u n d s, b r n g n g t o g e t h e r m o r e t h a n 3 0 b l l o n d o l l a r s. I n E u r o p e, t h e a l t e r n a t v e n v e s t m e n t n d u s t r y e x p e r e n c e d a g r o w t h r a t e o f 6 0 % n a n d 4 0 % n a n d t h e m a j o r a s s e t m a n a g e m e n t f r m s a n d n s t t u t o n a l n v e s t o r s a r e f o r e c a s t n g a l o n g-t e r m ( 5-y e a r ) g r o w t h r a t e o f m o r e t h a n 2 0 %. I n a r e l a t v e l y d f f c u l t c o n t e x t f o r t h e a s s e t m a n a g e m e n t n d u s t r y, t h e a l t e r n a t v e c l a s s ( c f. A p p e n d x 1 f o r a s h o r t d e s c r p t o n o f t h e m a n a l t e r n a t v e s t r a t e g e s ) r e p r e s e n t s a c o m m e r c a l e l d o r a d o. T h s a t t r a c t v e n e s s s r e n f o r c e d b y t h e d f f c u l t s t o c k m a r k e t s t u a t o n, w h c h n c r e a s e s n v e s t o r s ' n t e r e s t n n v e s t m e n t s e r v c e s t h a t b a s e t h e r s t r a t e g y o n t h e d e c o r r e l a t o n w t h t h e r s k s a n d r e t u r n s o f t h e f n a n c a l m a r k e t s a n d t h e r e f o r e t h e s e a r c h f o r a n a b s o l u t e r e t u r n. C o n s e q u e n t l y, h e d g e f u n d s, w h c h a r e o f t e n r e f e r r e d t o a s " p u r e a l p h a " f u n d s, w a r r a n t s g n f c a n t r e m u n e r a t o n, d e t e r m n e d n o t o n l y o n t h e b a s s o f m a n a g e d a s s e t s, b u t a l s o o n o u t p e r f o r m a n c e c o m p a r e d t o t h e r s k-f r e e r a t e. T h a t f o r m o f r e m u n e r a t o n a n d c o m m e r c a l a r g u m e n t s t h a t e q u a t e h e d g e f u n d s t o l o w-r s k n v e s t m e n t s, b e c a u s e t h e y h a v e b o t h l o w c o r r e l a t o n w t h t h e r s k s o f t h e f n a n c a l m a r k e t s a n d l o w v o l a t l t y, o b v o u s l y a t t r a c t s t h e a t t e n t o n o f n v e s t o r s a n d t h e r e g u l a t o r y a u t h o r t e s. A p a r t f r o m e v a l u a t n g t h e o p e r a t o n a l r s k s t h a t m a y b e n c u r r e d b y f u n d s t h a t a r e m a n a g e d n u n r e g u l a t e d z o n e s a n d t h a t n v e s t n n s t r u m e n t s t r a d e d o n m a r k e t s t h a t a r e t h e m s e l v e s u n r e g u l a t e d, t s a p p r o p r a t e t o e n q u r e n t o t h e n a t u r e o f t h e f n a n c a l r s k s o f a l t e r n a t v e n v e s t m e n t s. C a n w e b e s a t s f e d, a s w e h a v e o b s e r v e d f r o m t h e a r g u m e n t s o f E u r o p e a n a s s e t m a n a g e m e n t f r m s, w t h e v a l u a t n g t h e r s k-a d j u s t e d r e t u r n o f h e d g e f u n d s t h r o u g h t h e S h a r p e r a t o a l o n e? T h e a m o f o u r a r t c l e s t o l a y t h e f o u n d a t o n s f o r a r e a s o n e d d s c u s s o n o f t he s u b j e c t. W h a t a r e t h e r s k s n v o l v e d n a l t e r n a t v e n v e s t m e n t a n d h o w c a n a l t e r n a t v e n v e s t m e n t b e u s e d t o d v e r s f y n v e s t o r s ' p o r t f o l o s? I n a d d t o n, t o a n a l y s e t h e c h a l l e n g e s a n d o p p o r t u n t e s t h a t h e d g e f u n d s r e p r e s e n t n t e r m s o f r s k m a n a g e m e n t f o r n v e s t o r s, w e n t a l l y p r e s e n t t h e a r g u m e n t s n f a v o u r o f a l t e r n a t v e d v e r s f c a t o n. I n t h e s e c o n d p a r t o f t h e a r t c l e, w e w l l d s c u s s t h e n e e d f o r a n a p p r o p r a t e r s k m e a s u r e, a l o n g w t h t h e s p e c f c d f f c u l t e s r e l a t e d t o t h e m o n t o r n g o f r s k s. 1 Goldman Sachs and Frank Russell, Alternatve nvestng by tax exempt organzatons,

3 I. The advantages of alternatve dversfcaton I n v e s t o r s ' n t e r e s t n h e d g e f u n d s c a n b e e x p l a n e d n p a r t c u l a r t h r o u g h t h e f a c t t h a t a l t e r n a t v e f u n d s a c t u a l l y p r e s e n t r e a l d v e r s f c a t o n s t r e n g t h s t h r o u g h t h e r e x p o s u r e t o r s k s o t h e r t h a n m a r k e t r s k s. T h e s e s t r e n g t h s a r e a l l t h e m o r e a t t r a c t v e n a c o n t e x t o f r e l a t v e d e c l n e o f n v e s t m e n t o p p o r t u n t e s n t r a d t o n a l a s s e t c l a s s e s d u e t o t h e l o w d e g r e e o f d v e r s f c a t o n o f f e r e d b y a p u r e l y g e o g r a p h c a l o r s e c t o r a l a s s e t d s t r b u t o n. I t s a c t u a l l y w e l l k n o w n t h a t t h e l m t a t o n s o f n t e r n a t o n a l d v e r s f c a t o n t e n d t o t a k e e f f e c t a t t h e e x a c t m o m e n t t h a t t h e n v e s t o r h a s a n e e d f o r t, n a m e l y n p e r o d s w h e n t h e m a r k e t s d r o p s g n f c a n t l y ( s e e f o r e x a m p l e L o n g n a n d S o l n k ( ) ). I n s h o r t, t h e c o r r e l a t o n b e t w e e n t h e s t o c k m a r k e t s n d f f e r e n t c o u n t r e s c o n v e r g e s t o w a r d s 1 w h e n t h e r e s a s h a r p d r o p n t h e A m e r c a n m a r k e t s. C o n v e r s e l y, t s e e m s t h a t t h e d v e r s f c a t o n o f f e r e d b y h e d g e f u n d s, o r t o b e m o r e p r e c s e, c e r t a n h e d g e f u n d s, s r e l a t v e l y s t a b l e : t h e c o n d t o n a l c o r r e l a t o n s ( c a l c u l a t e d f r o m a s a m p l e t h a t o n l y c o n t a n s p e r o d s c o r r e s p o n d n g t o t h e m o s t s g n f c a n t d e c r e a s e s o r n c r e a s e s n a t r a d t o n a l r e f e r e n c e n d e x ) b e t w e e n t h e r e t u r n s o n a l t e r n a t v e f u n d s a n d t h o s e o f s t o c k a n d b o n d m a r k e t n d c e s a r e r e l a t v e l y s m l a r t o t h e u n c o n d t o n a l c o r r e l a t o n s ( o n t h s p o n t, s e e a l s o S c h n e e w e s a n d S p u r g n ( ) ). F o r e x a m p l e, t h e M a r k e t N e u t r a l a n d M a c r o s t r a t e g e s r e t a n a s t a b l e m a r k e t r s k e x p o s u r e w h a t e v e r t h e m a r k e t c o n d t o n s. Condtonal correlatons of hedge fund styles (HFR) wth the stock market (S&P 500) (02/ /2001) Correlaton coeffcents Market fallng sgnfcantly (1) Market stable (2) Market rsng sgnfcantly (3) (1) - (3) Convertble Arbtrage 0,49 0,30 0,07 0,42 Dstressed Securtes 0,64 0,32-0,18 0,82 Emergng Markets 0,75 0,32 0,32 0,43 Equty Hedge 0,60 0,46 0,15 0,45 Relatve Value 0,58 0,24-0,28 0,86 Type of correlaton Unfavourable* Equty Non-Hedge 0,74 0,59 0,36 0,38 Event Drven 0,79 0,54-0,12 0,91 Fxed Income Arbtrage 0,68 0,47-0,13 0,82 Market Neutral 0,03 0,05-0,06 0,09 Macro 0,29 0,18 0,21 0,08 Short Sellng -0,48-0,59-0,34-0,14 Market Tmng 0,15 0,53 0,29-0,14 * (1) - (3) > 0,10 ** - 0,10 < (1) - (3) < 0,10 *** (1) - (3) < - 0,10 Stable** Favourable*** M o r e o v e r, f o r c e r t a n s t r a t e g e s ( C o n v e r t b l e A r b t r a g e, E m e r g n g M a r k e t s, D s t r e s s e d S e c u r t e s, R e l a t v e V a l u e a n d E v e n t D r v e n ), w e o b s e r v e a n n c r e a s e n t h e c o r r e l a t o n c o e f f c e n t w h e n m a r k e t c o n d t o n s d e t e r o r a t e. T h s d e v e l o p m e n t s o b v o u s l y n o t f a v o u r a b l e f o r n v e s t o r s, s n c e t h e r d v e r s f c a t o n s t r a t e g y w l l l o s e t s e f f e c t v e n e s s a t p r e c s e l y t h e m o m e n t w h e n t h e y n e e d t t h e m o s t. O t h e r s t r a t e g e s, c o n v e r s e l y, w l l s e e t h e r c o r r e l a t o n c o e f f c e n t n c r e a s e a s t h e m a r k e t p e r f o r m a n c e m p r o v e s. T h e n v e s t o r w l l t h e r e f o r e b e e x p o s e d t o a r s e n t h e m a r k e t a n d h e d g e d a g a n s t a f a l l n t h e m a r k e t! T h e s e p a r t c u l a r l y f a v o u r a b l e s t r a t e g e s f o r t h e n v e s t o r a r e t h e f o l l o w n g : M a r k e t T m n g a n d S h o r t S e l l n g. 3

4 I t s n e v e r t h e l e s s a p p r o p r a t e, a t t h s s t a g e, t o r e c a l l t h e l m t a t o n s o f e v a l u a t n g c o n d t o n a l c o r r e l a t o n s. M o r e o f t e n t h a n n o t, t h e y a r e c a l c u l a t e d o n t h e b a s s o f h e d g e f u n d p e r f o r m a n c e c o m p a r e d t o t h a t o f a s a m p l e o f t h e m a r k e t n d c e s ' b e s t o r w o r s t m o n t h s o r d a y s f o r a g v e n p e r o d. T h e c o n d t o n a l c o r r e l a t o n s t h e r e b y o b t a n e d c o r r e s p o n d n o t t o e x t r e m e v a l u e s, b u t t o a m e a n t h a t s t s e l f s e n s t ve t o t h e s a m p l e c h o s e n. T h e n t e g r a t o n o f t h e r s k o f a n n c r e a s e n t h e c o r r e l a t o n c o e f f c e n t s n e x t r e m e m a r k e t c o n d t o n s h a s b e e n t h e s u b j e c t o f r e c e n t r e s e a r c h, n o t a b l y a f t e r t h e c r s s n t h e s u m m e r o f O n t h s t o p c, A n s o n ( ) n o t e s t h a t t h e r e t u r n s o n c o m p o s t e n d c e s o f h e d g e f u n d s t y l e s, w h e t h e r e q u a l l y w e g h t e d ( H F R ) o r p r o p o r t o n a l t o t h e a s s e t s m a n a g e d ( C F S B / T r e m o n t ), w e r e s g n f c a n t l y a f f e c t e d b y t h e d e b t m a r k e t c r s s ( A u g u s t ) a n d n o t b y t h e n e a r - b a n k r u p t c y o f L T C M ( S e p t e mb e r a n d O c t o b e r ). T h e r e f o r e, t h e s u d d e n a n d d r a m a t c n c r e a s e n t h e c o r r e l a t o n c o e f f c e n t s, a n d n o t t h e s y s t e m c c r s s n t h e a l t e r n a t v e u n v e r s e, w a s t h e m a n s o u r c e o f r s k d u r n g t h a t p e r o d. T h e q u e s t o n o f e v a l u a t n g c o n d t o n a l c o r r e l a t o n s s a c t u a l l y o n e o f t h e c o n s e q u e n c e s o f t h e n o n -l n e a r t y o f a l t e r n a t v e r e t u r n s. W e s h a l l c o m e b a c k t o t h e s e c o n s e q u e n c e s n t h e s e c o n d p a r t o f t h e a r t c l e. A d e t a l e d a n a l y s s o f t h e c o r r e l a t o n o f h e d g e f u n d r e t u r n s w t h t h o s e o f t r a d t o n a l m a r k e t s t e n d s t o p r o v e t h a t t s s m p l s t c t o c o n s d e r t h o s e f u n d s a s b e n g p a r t o f a h o m o g e n o u s a s s e t c l a s s. T h e r e a r e a c t u a l l y a l a r g e n u m b e r o f a l t e r n a t v e s t r a t e g e s, w t h e a c h h a v n g d f f e r e n t d v e r s f c a t o n c a p a b l t e s. C e r t a n s t r a t e g e s s u c h a s M a r k e t N e u t r a l, R e l a t v e V a l u e, o r C o n v e r t b l e A r b t r a g e g e n e r a l l y h a v e a l o w l e v e l o f c o r r e l a t o n w t h t h e p e r f o r m a n c e s o f t h e S & P 5 0 0, a n A m e r c a n s t o c k m a r k e t n d e x ( c o r r e l a t o n s t y p c a l l y l e s s t h a n 0. 5 a s a n a b s o l u t e v a l u e ), a n d w t h t h o s e o f t h e L e h m a n B r o t h e r s U S A g g r e g a t e I n d e x, t h e r e f e r e n c e b o n d n d e x. H o w e v e r, f o r o t h e r s t r a t e g e s s u c h a s E q u t y N o n H e d g e o r S h o r t S e l l n g, t h s s a b s o l u t e l y n o t t h e c a s e. Correlaton wth stock (S&P 500) and bond (LBGBI) ndces (02/ /2001) Correlaton Coeffcents S&P 500 Lehman US Convertble Arbtrage Dstressed Securtes Emergng Markets Equty Hedge Market Neutral Equty non-hedge Event Drven Fxed Income Arbtrage Macro Relatve Value Short Sellng Market Tmng

5 T h e v a r e t y o f d e c o r r e l a t o n s c o m p a r e d t o t h e r e t u r n s o n t r a d t o n a l a s s e t s a l l o w s u s t o e n v s a g e v e r y d v e r s e f o r m s o f a l t e r n a t v e d v e r s f c a t o n, a s s s h o w n n t h e g r a p h s b e l o w. Dversfcaton profles: ncluson of hedge fund styles (HFR) wth stock (S&P 500) and bond (LBGBI) portfolos (02/ /2001) Return Enhancers Rsk Reducers 25% 16% 14% 20% 12% Expected return 15% 10% Expected return 10% 8% 6% 5% 4% 2% 0% 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 0% 0% 2% 4% 6% 8% 10% 12% 14% 16% Std dev Std dev Dstressed Securtes Emergng Markets Equty Hedge Equty non Hedge Convertble Arbtrage Market Neutral Fxed Income Arbtrage Relatve Value Event Drven Macro S&P LB global bond Short Sellng S&P LB global bond Market Tmng F o l l o w n g o n f r o m t h s, c e r t a n h e d g e f u n d s h a v e a h g h l e v e l o f c o r r e l a t o n w t h t h e m a r k e t, a n d o f f e r r e t u r n s t h a t a r e p a r t c u l a r l y h g h. A d d n g t h s t y p e o f f u n d t o a p o r t f o l o m a d e u p o f s t o c k s a n d b o n d s w o u l d r e s u l t n a n n c r e a s e n t h e e x p e c t e d r e t u r n w h l e r e t a n n g a h g h d e g r e e o f v o l a t l t y. D s t r e s s e d S e c u r t e s, E m e r g n g M a r k e t s, E v e n t D r v e n, o r G l o b a l M a c r o p r e s e n t t h e s e c h a r a c t e r s t c s ; t h e s e s t r a t e g e s c a n t h e r e f o r e b e s e e n a s " R e t u r n E n h a n c e r s. " C o n v e r s e l y, n t e g r a t n g c e r t a n a l t e r n a t v e s t r a t e g e s w t h l o w e x p o s u r e t o m a r k e t r s k, o r n d e e d n e g a t v e e x p o s u r e, w l l r e s u l t n a l o w e r n g o f t h e p o r t f o l o ' s v o l a t l t y. T h e C o n v e r t b l e A r b t r a g e, F x e d I n c o m e A r b t r a g e, M a r k e t N e u t r a l o r S h o r t S e l l n g ( n e g a t v e c o r r e l a t o n ) s t r a t e g e s c o r r e s p o n d t o t h s p r o f l e. T h e s e s t r a t e g e s c a n t h e r e f o r e b e s e e n a s R s k R e d u c er s, o r e v e n a s P u r e D v e r s f e r s ( S h o r t S e l l n g ). I t s m p o r t a n t t o n o t e t h a t e v e n a t n y v a r a t o n n t h e v o l a t l t y, a n d e s p e c a l l y t h e r e t u r n, o f t h e a s s e t s u s e d t o c o n s t r u c t e f f c e n t f r o n t e r s c a n h a v e a m a j o r n f l u e n c e o n t h e s h a p e o f t h a t e f f c e n t f r o n t e r. F o r t h a t r e a s o n, t s n e c e s s a r y t o p a y p a r t c u l a r a t t e n t o n t o t h e c o n s e q u e n c e s o f t a k n g s u r v v o r s h p b a s n t o a c c o u n t w h e n e v a l u a t n g t h e p e r f o r m a n c e a n d v o l a t l t y o f a l t e r n a t v e s t r a t e g e s. W e s h a l l c o m e b a c k t o t h s p o n t n m o r e d e t a l l a t e r o n n t h s a r t c l e. T h e s e d f f e r e n c e s n c o r r e l a t o n w t h t h e s t o c k a n d b o n d m a r k e t s c a n b e e x p l a n e d t h r o u g h a d f f e r e n c e n e x p o s u r e t o a c e r t a n n u m b e r o f r s k f a c t o r s t h a t e x p l a n t h e r e t u r n s o f t h e a l t e r n a t v e a n d t r a d t o n a l a s s e t c l a s s e s. R e c e n t r e s e a r c h o n t h e a n a l y s s o f a l t e r n a t v e f u n d p e r f o r m a n c e ( F u n g a n d H s e h ( ), S c h n e e w e s a n d S p u r g n ( ), A m e n c, C u r t s a n d M a r t e l l n ( ) ) h a s h g h l g h t e d t h e f a c t t h a t a l t e r n a t v e f u n d s a r e n o t o n l y e x p o s e d t o m a r k e t r s k ( u n f o r e s e e a b l e v a r a t o n s n t h e p r c e s o f b a s c a s s e t s, s t o c k s, b o n d s, e t c. ), m e a s u r e d b y t h e t r a d t o n a l " b e t a, " b u t a l s o, a s a r e s u l t o f t h e v e r y n a t u r e o f t h e s t r a t e g e s m p l e m e n t e d, t o v o l a t l t y r s k s ( u n f o r e s e e a b l e v a r a t o n s n t h e v a r a b l t y o f t h e p r c e s ), d e f a u l t r s k s ( u n f o r e s e e a b l e v a r a t o n s n t h e p r o p e n s t y o f c e r t a n c o u n t e r p a r t e s t o n o l o n g e r b e a b l e t o r e s p e c t t h e r c o m m t m e n t s ) a n d l q u d t y r s k s ( u n f o r e s e e a b l e v a r a t o n s n t h e c a p a c t y t o m o v e q u a n t t e s o f a s s e t s n a " r e a s o n a b l e " t m e s c a l e a t m a r k e t p r c e s ). 5

6 I n t h e t a b l e b e l o w w e p r e s e n t t h e p e r f o r m a n c e c o r r e l a t o n s o f t h e d f f e r e n t s t r a t e g e s u n d e r c o n s d e r a t o n, w t h t h e p r n c p a l s o u r c e s o f r s k ( a p a r t f r o m m a r k e t r s k ) t h a t a f f e c t t h e r e t u r n s o f f n a n c a l n s t r u m e n t s. T h s s t u d y w a s c a r r e d o u t u s n g t h e p e r f o r m a n c e s o f t h e d f f e r e n t H F R n d c e s o v e r t h e p e r o d F e b r u a r y / O c t o b e r Table of correlatons between the dfferent Hedge Fund strateges (HFR) and rsk factors (02/ /2001) Correlaton coeffcents Volatlty Exchange rate Raw materals Lqudty Default 3 month US Treasury Bll Slope of the yeld curve Convertble Arbtrage Dstressed Securtes Emergng Markets Equty Hedge Market Neutral Equty non-hedge Event Drven Fxed Income Arbtrage Macro Relatve Value Short Sellng Market Tmng S&P Lehman US Aggregate The data used to characterse the dfferent sources of rsk s as follows: The volatlty rsk s measured by the relatve prce varatons of the VIX contract, the underlyng of whch s the mplct volatlty of the S&P 100 The currency rsk s measured by the evoluton of the exchange rate of the US dollar compared to a basket of foregn currences The raw materal rsk s measured by the relatve prce varatons of a barrel of crude ol The lqudty rsk s measured by the evoluton of the volume of securtes exchanged on the NYSE The default rsk s measured by the relatve varatons of the dfferental between the returns on bonds rated Baa and Aaa by Moody s The slope of the yeld curve s obtaned by calculatng the dfference between the rate of return of a bond wth a 30-year maturty and that of a 3- month Treasury bll. M o r e o v e r, p a r t o f t h e s t r a t e g e s ' r e t u r n c o m e s f r o m t h s e x p o s u r e t o d f f e r e n t r s k s. F o r n s t a n c e, t h a s o f t e n b e e n o b s e r v e d t h a t a c e r t a n n u m b e r o f h e d g e f u n d s p u r s u n g a f x e d - n c o m e a r b t r a g e t y p e s t r a t e g y a c t e d a s l q u d t y p r o v d e r s o n f x e d - n c o m e s e c u r t y m a r k e t s t h a t w e r e e x p o s e d t o d e f a u l t r s k, a r o l e t y p c a l l y t a k e n o n b y t h e t r a d n g d e s k s o f t h e m a j o r n v e s t m e n t b a n k s. I t s n f a c t n a t u r a l t o s e e k t o u s e t h e m u l t p l e f a c e t s o f r s k, a n d t h e r e f o r e o f r e t u r n. I t n c r e a s e s t h e d e g r e e o f l b e r t y n n v e s t m e n t d e c s o n s. A l t h o u g h t h e e x s t e n c e o f a l t e r n a t v e a l p h a s s s o m e t m e s q u e s t o n e d, a l t e r n a t v e b e t a s o f t e n c o r r e s p o n d t o r s k p r e m u m s t h a t a r e t r a d t o n a l l y a r b t r a t e d b y t h e p l a y e r s p r e s e n t n t h e m a r k e t a n d, a s a r e s u l t, c o r r e s p o n d t o m a r k e t p r c e s ( t h e v o l a t l t y, o r n o t a b l y t h e c r e d t, m a r k e t ). 2 It should be ponted out that monthly calculaton of the correlatons tends to smooth the results and therefore smoothes the mpact of changes n the factor values wthn the months. 6

7 II. The dffcultes n measurng alternatve nvestment rsks W a n t n g t o u s e h e d g e f u n d s a s a r s k d v e r s f c a t o n t o o l p r e s u p p o s e s t h a t w e h a v e m a s t e r y o v e r t h e s s u e s a t s t a k e n t h e c o n t r o l o f h e d g e f u n d r s k s. E v e n t h o u g h r e c e n t r e s e a r c h w o r k h a s g v e n u s a b e t t e r u n d e r s t a n d n g o f t h e s u b j e c t, t s c e r t a n l y t h e a r e a n w h c h t h e m o s t p r o g r e s s r e m a n s t o b e m a d e. A s s t r e s s e d b y, f o r e x a m p l e, L o ( ), A m e n c, C u r t s a n d M a r t e l l n ( ) a n d F u n g a n d H s e h ( ), t h e r e a r e n f a c t a t l e a s t t h r e e r e a s o n s f o r a l t e r n a t v e f u n d s p o s n g s p e c f c p r o b l e m s f o r m e a s u r n g a n d c o n t r o l l n g r s k s 3 : d f f c u l t e s n a c c o u n t n g f o r t h e d m e n s o n s o f c r e d t a n d l q u d t y r s k s d f f c u l t y n developng relevant benchmarks d f f c u l t e s n a c c o u n t n g f o r t h e d y n a m c a n d n o n -l n e a r a s p e c t s o f a l t e r n a t v e r s k. B e f o r e g o n g n t o t h e s e d f f c u l t e s n m o r e d e t a l, t s m p o r t a n t t o n o t e t h a t t s n o t b e c a u s e a f u n d s a h e d g e f u n d t h a t t h e r s k-f r e e a s s e t s n e c e s s a r l y a g o o d b e n c h m a r k. W h l e n e a r l y a l l h e d g e f u n d s h gh l g h t a s o -c a l l e d " a b s o l u t e r e t u r n " p o l c y, t h e r s k-f r e e r a t e s o n l y a g o o d b e n c h m a r k f t h e f o l l o w n g t w o c o n d t o n s a r e r e s p e c t e d : a s s u m p t o n 1 : t h e f u n d h a s a m a r k e t b e t a e q u a l t o z e r o a s s u m p t o n 2 : t h e C A P M s a n a p p r o p r a t e m o d e l f o r t h e a l t e r n a t v e u n v e r s e. W h l e t h e f r s t a s s u m p t o n s r e s p e c t e d f o r c e r t a n t y p e s o f a l t e r n a t v e f u n d s, s u c h a s e q u t y m a r k e t n e u t r a l o r f x e d - n c o m e a r b t r a g e, t s c e r t a n l y n o t v a l d f o r t h e o t h e r c a t e g o r e s ( c f. t a b l e p a g e 6 ). T h e s e c o n d a s s u m p t o n s e v e n m o r e d e b a t a b l e. I n o r d e r t o h a v e a b e t t e r c o m p r e h e n s o n o f t h e s s u e s a t s t a k e n t h e p e r f o r m a n c e o f a l t e r n a t v e f u n d s, t s m p o r t a n t t o u n d e r s t a n d f r s t o f a l l t h a t t h e e x c e s s r e t u r n o f a r s k y p o r t f o l o c o m p a r e d t o t h e r s k-f r e e r a t e, a s t s m e a s u r e d f o r a g v e n s a m p l e, c a n, n g e n e r a l, c o m e f r o m t h r e e d s t n c t s o u r c e s, a s d e s c r b e d n t h e f o l l o w n g e q u a t o n : E x c e s s r e t u r n o f t h e p o r t f o l o = n o r m a l r e t u r n + a b n o r m a l r e t u r n + s t a t s t c a l n o s e T h e f r s t t e r m, t h e " n o r m a l " r e t u r n, c o r r e s p o n d s t o t h e m a r k e t ' s f a r r e w a r d f o r t h e r s k s t o w h c h t h e p o r t f o l o s e x p o s e d. I t s t h e r e f o r e a p r e m u m ( o r p r e m u m s ) f o r t h e r s k ( s ), w h c h c a n b e e v a l u a t e d w t h t h e h e l p o f a s n g l e f a c t o r m o d e l l k e t h e C A P M o r w t h t h e h e l p o f a m o r e g e n e r a l, m u l t f a c t o r m o d e l, j u s t f e d o n t h e t h e o r e t c a l s d e t h r o u g h e q u l b r u m ( M e r t o n, ) o r a r b t r a g e ( R o s s, ) r e a s o n n g, a n d m p l e m e n t e d n t h e b u s n e s s w o r l d b y a c e r t a n n u m b e r o f f r m s s u c h a s, f o r e x a m p l e, B I R R, Q u a n t a l, A p t m u m a n d B A R R A. I n t h e a l t e r n a t v e u n v e r s e, a s w e m e n t o n e d e a r l e r, r e c e n t r e s e a r c h h a s h g h l g h t e d t h e n a d e q u a c y o f t h e C A P M a n d u n d e r l n e d t h e e x p o s u r e o f a l t e r n a t v e r e t u r n s t o f a c t o r s s u c h a s v o l a t l t y r s k, d e f a u l t r s k a n d l q u d t y r s k. I t s t h e r e f o r e w r o n g t o s t a t e t h a t a n o n -d r e c t o n a l a l t e r n a t v e s t r a t e g y,. e. a s t r a t e g y t h a t s n o t e x p o s e d t o m a r k e t r s k ( f o r e x a m p l e, f x e d - n c o m e a r b t r a g e, c o n v e r t b l e a r b t r a g e o r z e r o -b e t a s t r a t e g e s ), s h o u l d b e r e w a r d e d a t t h e r s k-f r e e r a t e. T h a t s a n o v e r l y r e s t r c t v e a p p l c a t o n o f a s n g l e f a c t o r m o d e l ( t h e C A P M ) w h c h d o e s n o t a l l o w f o r a g o o d d e s c r p t o n o f t h e b e h a v o u r o f a l t e r n a t v e f u n d s. F n a n c a l r s k s, p a r t c u l a r l y n t h e a l t e r n a t v e w o r l d, a r e a c t u a l l y m u l t f o r m, a n d c o n s e q u e n t l y r s k p r e m u m s a r e n u m e r o u s a n d, m o r e o f t e n t h a n n o t, u n s t a b l e. F o r e x a m p l e, a m e a n r e t u r n o f 1 0 % f o r a n o n -d r e c t o n a l f u n d l k e L T C M, w h e n t h a t o f t h e r s k-f r e e r a t e s 4 %, d o e s n o t n e c e s s a r l y r e f l e c t a n a b n o r m a l r e t u r n o f 6 %. W t h n t h e 6 %, t h e r e c o u l d b e v o l a t l t y, l q u d t y o r d e f a u l t r s k p remums (or any o t h e r r s k f a c t o r, t h e e x s t e n c e o f w h c h m a y h a v e e s c a p e d t h e w s d o m o f t h e m o d e l l e r s, t h a t s r e w a r d e d b y t h e m a r k e t a t e q u l b r u m ). I n t o t a l, t h e a b n o r m a l r e t u r n, t h e f u n d ' s a l p h a, c o u l d v e r y w e l l b e p o s t v e, n e g a t v e o r n l! 3 Other mportant problems to be taken nto account are the operatonal rsks and survvorshp bas (see, for example, Fung and Hseh (2001) on the latter pont). 7

8 T h e s e c o n d t e r m, t h e a b n o r m a l r e t u r n, r e p r e s e n t s t h e f r u t o f t h e p o r t f o l o m a n a g e r s ' e x p e r t s e. P o r t f o l o m a n a g e r s s o m e t m e s m a n a g e t o o b t a n a d d t o n a l p r o f t s t h a t a r e n o t s t r c t l y j u s t f e d n t e r m s o f e x p o s u r e t o r s k s t h a t a r e r e w a r d e d b y t h e m a r k e t. I n d e e d, o b t a n n g a b n o r m a l r e t u r n s s p r e c s e l y w h a t a c t v e m a n a g e r s n g e n e r a l, a n d h e d g e f u n d m a n a g e r s n p a r t c u l a r, d e v o t e t h e r e f f o r t s t o. II.1 Credt and lqudty rsks A m o n g t h e r s k f a c t o r s t h a t s h o u l d b e t a k e n n t o a c c o u n t t o e v a l u a t e b o t h t h e r e a l t y o f t h e r e t u r n a n d a l s o t h e a l t e r n a t v e n v e s t m e n t r s k, p a r t c u l a r a t t e n t o n s h o u l d b e p a d t o t h e l q u d t y a n d c r e d t r s k s, f o r t w o e s s e n t a l r e a s o n s : u n l k e o t h e r r s k s, w h e r e t h e r e s g e n e r a l c o n s e n s u s a s t o h o w t o m e a s u r e t h e m, a c c o u n t n g f o r c r e d t a n d l q u d t y r s k s s t l l c o n s t t u t e s b o t h a n o p e r a t o n a l a n d a t h e o r e t c a l c h a l l e n g e ; t h e n e a r -b a n k r u p t c y o f t h e L T C M f u n d s g n f c a n t l y h g h l g h t e d t h e n t e r d e p e n d e n c e b e t w e e n t h e t w o r s k s, w h c h m a k e s t d f f c u l t t o m o d e l t h e m s e p a r a t e l y, a s t h e m u l t f a c t o r a p p r o a c h s u g g e s t s. T h e m u l t f a c t o r a p p r o a c h s t h e d o m n a n t d o c t r n e n a n a l y s n g p o r t f o l o r s k a n d r e t u r n. I n t h e a r e a o f c r e d t r s k, t h e f n a n c a l l t e r a t u r e s p a r t c u l a r l y r c h n t e r m s o f b o t h m o d e l l n g a n d p r c n g 4. T h s a b u n d a n c e o f m o d e l s s a r e l a t v e r e f l e c t o n o f t h e l a c k o f m a t u r t y o f t h e p r a c t c e s ( c f. t h e m o s t r e c e n t r e s e a r c h c a r r e d o u t o n t h s s u b j e c t f o r d r a w n g u p t h e n e w B a s e l a c c o r d ) f a c e d w t h r s k s w t h r e t u r n s t h a t a r e n o t n o r m a l l y d s t r b u t e d 5 a n d w t h d v e r s f c a t o n t h a t s o n l y e f f e c t v e a f t e r t a k n g a v e r y l a r g e n u m b e r o f p o s t o n s n t o a c c o u n t. E v e n t h o u g h t h e c o n c e p t u a l f o u n d a t o n s o f t h e s e m o d e l s a r e v e r y s m l a r a n d c o n s t t u t e a n a p p l c a t o n / e x t e n s o n o f t h e w o r k o f M e r t o n ( ) 6, t h e m p l e m e n t a t o n c o n d t o n s a n d e m p r c a l t e s t s o f t h e m o d e l s, b e c a u s e t h e y a r e s t l l very approxmate 7, g v e r e s u l t s t h a t a r e n o t v e r y r o b u s t o n a c c o u n t o f t h e a s s u m p t o n s c h o s e n. I n t e g r a t n g t h e n t e r d e p e n d e n c e b e t w e e n c r e d t r s k a n d l q u d t y r s k s h o u l d n o t a b l y l e a d t o t h e m o d e l l n g o f t h e c o n s e q u e n c e s o f u s n g l e v e r a g e e f f e c t s n a r b t r a g e o p e r a t o n s. B u t t o d a y, w t h t h e e x c e p t o n o f h g h l y a c a d e m c r e s e a r c h, s u c h a s a p p l y n g m a t h e m a t c a l n e t w o r k t h e o r y t o t h e c o n s t r u c t o n o f s y s t e m c m e a s u r e s o f c r e d t a n d l q u d t y r s k 8, p r o f e s s o n a l s d o n o t h a v e r o b u s t a n d s m p l e m c r o e c o n o m c r e s u l t s a t t h e r d s p o s a l n t h s a r e a. F a c e d w t h t h e s e m o d e l l n g d f f c u l t e s, c e r t a n a u t h o r s h a v e p r o p o s e d m e a s u r n g t h e e x p o s u r e t o l q u d t y r s k b y u s n g t h e d e g r e e o f a u t o -c o r r e l a t o n o f f u n d r e t u r n s a s a m e a s u r e o f t h e f u n d ' s l q u d t y r s k. L o ( ), r e l e s o n t h e s t a t s t c s o f L j u n g a n d B o x ( ) t o d o t h s. A u t o-c o r r e l a t o n c o e f f c e n t a n a l y s s c o n c e n t r a t e s o n t h e p r o b l e m p o s e d b y t h e c o n s e q u e n c e s o f l q u d t y o r l l q u d t y o n a s s e t p r c e s a n d p o s t o n v a l u a t o n. I t s t h e r e f o r e o n l y a p a r t a l v e w o f t h e l q u d t y r s k s, b u t t d o e s n e v e r t h e l e s s c o r r e s p o n d t o a n a r e a t h a t s o f c o n s d e r a b l e c o n c e r n t o p r o f e s s o n a l s. A s n e s s, K r a l a n d L e w ( ) h g h l g h t e d t h e r s k s p o s e d b y t he v a l u a t o n o f l l q u d p o s t o n s. I n t h e s a m e w a y, a r e c e n t s t u d y c a r r e d o u t b y C a p t a l M a r k e t R s k A d v s o r s ( ) o b s e r v e d t h a t s u b s t a n t a l p r c e a n d v a l u a t o n d f f e r e n c e s ( % ) w e r e r e l a t e d t o t h e c h o c e o f v a l u a t o n m e t h o d s a n d / o r v a l u a t o n m o d e l s f o r t h e l e a s t l q u d a s s e t s ( h g h y e l d a n d d s t r e s s e d b o n d s, p r v a t e s e c u r t e s, O T C o p t o n s, s t r u c t u r e d n o t e s a n d m o r t g a g e d e r v a t v e s ). M a n a g n g t h e v a l u a t o n s o f l l q u d p o s t o n s a l l o w s h e d g e f u n d r e s u l t s t o b e s m o o t h e d a n d v e r y a t t r a c t v e r s k- ad j u s t e d r e t u r n n d c a t o r s t o b e c o n s t r u c t e d. T h e l a c k o f l q u d t y s, n a w a y, c o n c e v e d b y m a n a g e r s, n o l o n g e r a s a r s k b u t a s a s e l l n g p o n t f o r s e d u c n g n v e s t o r s ( B r o o k a n d K a t, ). T h e r e f o r e, c a l c u l a t e d a n d m a n p u l a t e d p r c e s m g h t b e t h e b e s t e x p l a n a t o n f o r t h e q u a r t e r l y p e r s s t e n c e o f f u n d s, h g h l g h t e d b y A g a r w a l a n d N a k ( ). 4 For a revew of the lterature, one could consult Kao (2000) and Saunde r ( ) 5 We wll examne ths pont n part II.4 6 For a comparatve revew of the models and ther applcaton, t would be useful to refer to Crouhy, Gala and Mark (2000), Gordy (2000) and Basle (1999) 7 A crtcal analyss of the emprcal tests of these models was carred out by Bohn (1999a, 1999b) 8 Notably Watts and Strogatz (1998) and Watts (1999) 8

9 II.2 Benchmarkng n alternatve nvestment S n c e w e h a v e c o n c l u d e d t h a t t h e r s k-f r e e r a t e s c e r t a n l y n o t a n a p p r o p r a t e b e n c h m a r k f o r a l l t y p e s o f h e d g e f u n d s, t r e m a n s t o b e s e e n w h a t c o n s t t u t e s a g o o d b e n c h m a r k. I t s e e m s t h a t t h e a l t e r n a t v e n v e s t m e n t n d u s t r y s c u r r e n t l y s w t c h n g f r o m " a b s o l u t e r e t u r n " l o g c t o " r e l a t v e r e t u r n " l o g c. T h e p r n c p l e t h e r e f o r e c o n s s t s o f c o m p a r n g t h e r e t u r n o f a g v e n f u n d t o t h a t o f a p o r t f o l o o f f u n d s f o l l o w n g t h e s a m e s t r a t e g y ( p e e r b e n c h m a r k n g ), o r t h a t o f a r e p r e s e n t a t v e n d e x ( n d e x b e n c h m a r k n g ). T h e d f f c u l t e s r e l a t e d t o t h e d e v e l o p m e n t o f q u a l t y n d c e s, w h c h a r e a l r e a d y e v d e n t n t h e t r a d t o n a l u n v e r s e, a r e e x a c e r b a t e d n t h e a l t e r n a t v e n v e s t m e n t w o r l d, n t h e a r e a s o f b o t h r e p r e s e n t a t v e n e s s a n d p u r t y (. e. h o m o g e n e t y o f t h e d a t a ). F r s t l y, t s h o u l d b e n o t e d t h a t t h e l o g c o f r e p r e s e n t a t v e n e s s t h r o u g h c a p t a l s a t o n c a n o n l y b e a p p l e d t o t h e a l t e r n a t v e u n v e r s e w t h g r e a t d f f c u l t y, s n c e n f o r m a t o n o n t h e a s s e t s m a n a g e d b y h e d g e f u n d s s g e n e r a l l y n o t a v a l a b l e n r e a l t m e. T h a t s w h y a l l h e d g e f u n d n d c e s, w t h t h e e x c e p t o n o f t h e C S F B / T r e m o n t n d c e s, o p e r a t e n e q u a l w e g h t n g mo d e t o d a y. S e c o n d l y, t h e f a c t t h a t t h e r e s n o o b l g a t o n t o p u b l s h p e r f o r m a n c e n t h e a l t e r n a t v e w o r l d r e n d e r s a c c e s s t o e x h a u s t v e d a t a b a s e s v e r y d f f c u l t. O n e o f t h e m o s t w d e l y u s e a l t e r n a t v e n d c e s, t h e E A C M n d e x, s c a l c u l a t e d f r o m t h e p e r f o r m a n c e s o f h e d g e f u n d s e x t r a c t e d f r o m a u n v e r s e t h a t c u r r e n t l y c o n t a n s o v e r 6, f u n d s! T h e c h a l l e n g e o f p u r t y s a l s o v e r y d f f c u l t t o h a n d l e n t h e a l t e r n a t v e u n v e r s e. I n a w o r l d w h e r e t h e c o m p e t t v e a d v a n t a g e o f m a n a g e r s s l a r g e l y b a s ed o n t h e s o p h s t c a t o n a n d c o n f d e n t a l t y o f t h e r " p r o p r e t a r y " m a n a g e m e n t t e c h n q u e s, t h e n d e x p r o v d e r s ( w t h t h e n o t a b l e e x c e p t o n o f Z u r c h ) a r e g e n e r a l l y c o n t e n t t o u s e t h e s e l f - p r o c l a m e d s t y l e s o f t h e m a n a g e r s. T h e r e s h o w e v e r g o o d r e a s o n t o b e l e v e t h a t s o m e m a n a g e r s, f a c e d w t h f e w e r a n d f e w e r o p p o r t u n t e s, o c c a s o n a l l y d e v a t e s g n f c a n t l y f r o m t h e r o s t e n s b l e m a n a g e m e n t s t y l e ( a p h e n o m e n o n c a l l e d " s t y l e d r f t " ). A s a r e s u l t o f t h e d f f c u l t y n a c c e s s n g d a t a, t h e s e t o f f u n d s t a k e n n t o a c c o u n t f o r a g v e n m a n a g e m e n t s t y l e v a r e s e n o r m o u s l y f r o m o n e p r o v d e r t o a n o t h e r. C o n s e q u e n t l y, t h e r e t u r n s o n c o m p e t n g n d c e s f o r t h e s a m e s e g m e n t o f t h e a l t e r n a t v e n v e s t m e n t m a r k e t c a n v a r y c o n s d e r a b l y. T h e f o l l o w n g t a b l e g v e s d e t a l s o n t h e m a x m a l r e t u r n d f f e r e n c e s f o r t h e p e r o d b e t w e e n t h e m o n t h l y r e t u r n s o f t h e v a r o u s c o m p e t n g n d c e s f o r a g v e n s t y l e. 9

10 Maxmal dfferences n the monthly returns of alternatve ndces ( ) M a n a g e m e n t S t y l e M a x m a l D f f e r e n c e n M o n t h l y R e t u r n s C o n v e r t b l e A r b t r a g e % ( O c t 9 8 ; C S F B ( ) / H e n n e s s e e ( ) ) E m e r g n g M a r k e t s % ( A u g 9 8 ; ( M A R H ) / A l t v e s t ( ) ) Equty Market Neutral % ( D e c 9 9 ; H e n n e s s e e ( 0. 2 ) / V a n H e d g e ( 5. 2 ) ) E v e n t D r v e n % ( A u g 9 8; CSFB ( % ) / A l t v e s t ( ) ) F x e d I n c o m e A r b t r a g e % ( O c t 9 8 ; H F N e t ( ) / V a n H e d g e ( 0. 2 ) ) G l o b a l M a c r o 17.80% (May 00: Van Hedge ( ) / H F N e t ( 1 2 ) ) L o n g / S h o r t % ( F e b 0 0 : E A C M ( ) / Z u r c h ( ) ) M e r g e r A r b t r a g e % ( S e p 9 8 : A l t v e s t ( ) / H F R ( ) ) R e l a t v e V a l u e % ( S e p 9 8 : E A C M ( ) / V a n H e d g e ( ) ) S h o r t S e l l n g % ( F e b 0 0 : V a n H e d g e ( ) / E A C M ( ) ) D s t r e s s e d S e c u r t e s % ( A u g 9 8 : H F N e t ( ) / V a n H e d g e ( ) ) Fu n d o f F u n d s % ( D e c 9 9 : M A R-Z u r c h ( ) / A l t v e s t ( ) ) G l o b a l % ( D e c 9 9 : C S F B ( ) / M a g n u m ( ) ) T h e s e d f f e r e n c e s n r e t u r n s c a n, a s w e s e e, b e g r e a t e r t h a n 2 0 %! A n d t s o b v o u s l y n o t t h e s a m e t h n g f o r a " l o n g / s h o r t " m a n a g e r t o b e c o m p a r e d n F e b r u a r y t o a b e n c h m a r k w t h a p e r f o r m a n c e o f % ( E A C M ) o r a b e n c h m a r k w t h a p e r f o r m a n c e o f % ( Z u r c h )! W e s h o u l d n o t e t h a t a l l t h e d a t a s e r e s u s e d n t h s a r t c l e t o c a l c u l a t e r e t u r n s a r e g v e n n U S d o l l a r s. T h e p r e s e n c e o f a h g h l e v e l o f h e t e r o g e n e t y n t h e d f f e r e n t a l t e r n a t v e n d c e s h a s m m e d a t e s t r a t e g c a l l o c a t o n c o n s e q u e n c e s f o r a n n v e s t o r w h o w s h e s t o u s e t h e a l t e r n a t v e c l a s s t o d v e r s f y a s t o c k a n d / o r b o n d p o r t f o l o. A s a n e x a m p l e, t h e f o l l o w n g g r a p h s h o w s t h e e f f c e n t f r o n t e r s o b t a n e d t h r o u g h a n o p t m a l c o m b n a t o n o f t h e t r a d t o n a l S & P ( s t o c k m a r k e t ) a n d L e h m a n B r o t h e r G l o b a l B o n d ( b o n d m a r k e t ) n d c e s w t h d f f e r e n t a l t e r n a t v e f x e d - n c o m e a r b t r a g e n d c e s o n t h e b a s s o f m o n t h l y d a t a f o r t h e p e r o d f r o m J a n u a r y t o O c t o b e r Effcent fronters usng stocks (S&P 500), bonds (LBGBI) and the Fxed Income Arbtrage Style (01/ /2001) 14.00% 12.00% 100% S&P % 8.00% 6.00% 4.00% 2.00% 0.00% 100% Lehman US aggregate 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% 18.00% CSFB HFR Van Hedge Hennessee HF net S&P + Lehman T h e d f f e r e n t p r o b l e m s p o s e d b y a l t e r n a t v e n d c e s, t o g e t h e r w t h p o s s b l e s o l u t o n s, a r e d s c u s s e d n d e t a l n S c h n e e w e s e t a l. ( ), A m e n c a n d M a r t e l l n ( ) a n d F u n g a n d H s e h ( ). 1 0

11 II.3 Impact of bas n the database T h e d e c s o n t o p o s t t h e p e r f o r m a n c e o f a l t e r n a t v e f u n d s n o n e o f t h e c o m p e t n g d a t a b a s e s ( T ASS, MAR, HFR) s p u r e l y v o l u n t a r y a n d o n l y a c e r t a n n u m b e r o f f u n d s d e c d e t o p a r t c p a t e. T h s l e a d s t o "self reportng bas " a n d s n c e t h e f u n d s t h a t h a v e r e f u s e d t o r e p o r t t o a n y o f t h e d a t a b a s e s a r e b y d e f n t o n u n o b s e r v a b l e, t s n o t p o s s b l e t o e va l u a t e t h e m p a c t o f t h s b a s. C e r t a n f u n d s c h o o s e n o t t o p u b l s h t h e r p e r f o r m a n c e b e c a u s e t h e p e r f o r m a n c e d o e s n o t a p p e a r s a t s f a c t o r y, o t h e r s b e c a u s e t h e y h a v e a l r e a d y r e a c h e d t h e r c r t c a l s z e. I t s t h e r e f o r e d f f c u l t t o k n o w w h e t h e r t h s b a s h a s a p o s t v e o r n e g a t v e m p a c t o n t h e p e r f o r m a n c e s a n n o u n c e d. S n c e h e d g e f u n d s t h a t h a v e p e r f o r m e d p o o r l y l e a v e t h e n d u s t r y, t h e f u n d s t h a t a r e s t l l p r e s e n t n a d a t a b a s e t e n d t o b e f u n d s t h a t h a v e p e r f o r m e d b e t t e r t h a n t h e a v e r a g e o f t h e w h o l e p o p u l a t o n. I n t h s c a s e w e s p e a k o f "survvorshp bas. " F u n g a n d H s e h ( ) v a l u e d t h e a v e r a g e m p a c t o f t h s b a s a t 3. 0 %, c o m p a r e d t o 2. 6 % f o r P a r k, B r o w n a n d G o e t z m a n n ( ). T h e v a r o u s d a t a b a s e s a r e a f f e c t e d n d f f e r e n t w a y s b y t h s b a s. F o r e x a m p l e, t h e T A S S d a t a b a s e h a s a h g h e r s u r v v o r s h p b a s t h a n t h e H F R d a t a b a s e b e c a u s e t h a s a d e f a u l t r a t e t h a t s h g h e r than HFR's. T h e f u n d s a l s o h a v e s e l e c t o n c r t e r a t h a t c a n b e v e r y d f f e r e n t f r o m o n e f u n d t o t h e n e x t, a n d t h e d a t a p r o v d e d w l l n o t b e r e p r e s e n t a t v e o f t h e s a m e m a n a g e m e n t u n v e r s e. T h s s r e f e r r e d t o a s "selecton bas. " F o r n s t a n c e, H F R e x c l u d e s m a n a g e d f u t u r e s f r o m t s d a t a b a s e s w h l e T A S S a n d M A R t a k e t h e m n t o a c c o u n t. M o s t f u n d s a r e p r e s e n t n o n e b u t n o t t h e o t h e r : o f t h e 1, H F R f u n d s a n d t h e 1, T A S S f u n d s, o n l y a r e c o m m o n t o b o t h d a t a b a s e s. 5 9 % o f t h e f u n d s t h a t a r e s t l l n a c t v t y a n d 6 8 % o f t h e f u n d s t h a t n o l o n g e r r e p o r t t o H F R a r e n o t p a r t o f t h e T A S S d a t a b a s e ( c f. L a n g ( ) ). F u n g a n d H s e h ( ) v a l u e d th e m p a c t o f t h s b a s a t 1. 4 %, c o m p a r e d t o 1. 9 % f o r P a r k, B r o w n a n d G o e t z m a n n ( ). O u t o f t h e f u n d s n c o m m o n b e t w e e n t h e H F R a n d T A S S d a t a b a s e s, o n l y ( o r % ) h a v e b e e n n c l u d e d n b o t h d a t a b a s e s a t t h e s a m e t m e. H o w e v e r, w h e n a f u n d s a d d e d t o a d a t a b a s e, a l l o r p a r t o f t s h s t o r c a l d a t a s r e c o r d e d e x-p o s t n t h e d a t a b a s e. S n c e t s n t h e f u n d s ' n t e r e s t t o d s p l a y t h e m o s t p o s t v e p e r f o r m a n c e p o s s b l e, t s p r o b a b l e t h a t t h e m e a n p e r f o r m a n c e d s p l a y e d b y t h e f u n d s d u r n g t h e r n c u b a t o n p e r o d w l l b e b e t t e r t h a n t h a t o f f u n d s t h a t h a v e b e l o n g e d t o t h e c o r r e s p o n d n g d a t a b a s e f o r a l o n g t m e. I n t h s c a s e w e t a l k a b o u t "nstant hstory bas. " F u n g a n d H s e h ( ) v a l u e d t h e m p a c t o f t h s b a s a t 1. 4 % p e r y e a r. I f t h e f u n d s ar e n o t r e c o r d e d a t t h e s a m e d a t e n t w o d f f e r e n t d a t a b a s e s, t s p r o b a b l e t h a t t h e t w o d a t a b a s e s w l l n o t b e e x p o s e d t o " n s t a n t h s t o r y b a s " n t h e s a m e w a y. T h s r s k s h e g h t e n e d b y t h e f a c t t h a t o n l y 4 7 % o f t h e p e r f o r m a n c e s r e c o r d e d a r e s t r c t l y de n t c a l. T o t e s t t h e m p a c t o f t h e b a s e s, a n d n p a r t c u l a r t h e s u r v v o r s h p b a s, n a n o p t m a l s e l e c t o n a p p r o a c h f o r p o r t f o l o s t h a t n c l u d e t h e a l t e r n a t v e c l a s s, w e h a v e g e n e r a t e d e f f c e n t f r o n t e r s t h a t n t e g r a t e a s u r v v o r s h p b a s e s t m a t e d a t 2. 6 %, w h c h s c o n s s t e n t w t h t h e r e s u l t s o f F u n g a n d H s e h ( ). M o r e o v e r, t h e g r a p h b e l o w w a s g e n e r a t e d u n d e r t h e a s s u m p t o n o f a n a n n u a l d e f a u l t r a t e f o r a l t e r n a t v e f u n d s o f 8. 3 % ( s e e A p p e n d x 2 f o r j u s t f c a t o n a n d m o r e d e t a l s o n t h s s u b j e c t ). T h e p o r t f o l o s u s e t h e S & P a s a p r o x y f o r t h e s t o c k c l a s s, t h e L e h m a n G l o b a l B o n d I n d e x a s a p r o x y f o r t h e b o n d c l a s s, a n d t h e G l o b a l T r e m o n t I n d e x a s a p r o x y f o r t h e a l t e r n a t v e c l a s s. 1 1

12 Survvorshp bas and effcent fronters usng stocks (S&P 500), bonds (LBGBI) and hedge funds (Global Tremont Index) (01/ /2002) 12.00% 10.00% 8.00% Annual Return 6.00% 4.00% 2.00% 0.00% 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% -2.00% Annual Volatlty S&P + Lehman Experment wthout bas Bas F&H (3%) Bas PB&G (2.6%) T h e s e r e s u l t s r e v e a l l e s s e r b e n e f t s f r o m a l t e r n a t v e f u n d d v e r s f c a t o n t h a n t h o s e o b t a n e d n t h e f r a m e w o r k o f a c l a s s c m e a n -v a r a n c e a n a l y s s w t h o u t n t e g r a t n g t h e s u r v v o r s h p b a s. T h e e f f c e n t f r o n t e r s t h a t n t e g r a t e t h e a l t e r n a t v e c l a s s c o n t n u e n o n e t h e l e s s t o d o m n a t e t h e e f f c e n t f r o n t e r o b t a n e d f r o m t h e t r a d t o n a l c l a s s e s ( s t o c k s a n d b o n d s ). F u r t h e r m o r e, t s e s p e c a l l y n t e r e s t n g t o no t e t h a t t h e a l t e r n a t v e c l a s s a l l o w s t h e e f f c e n t f r o n t e r t o b e m p r o v e d b y r e d u c n g t h e g l o b a l r s k o f t h e p o r t f o l o (. e. " R s k R e d u c e r " ). T h s s n s t a r k c o n t r a s t t o t h e a l a r m s t d s c o u r s e o f t h o s e w h o c o n t n u o u s l y w a r n n v e s t o r s o f t h e n u m e r o u s r sk s o f a l t e r n a t v e n v e s t m e n t. II.4 Dynamc and non-lnear dmensons of alternatve rsks M o s t h e d g e f u n d m a n a g e r s f o l l o w d y n a m c n v e s t m e n t s t r a t e g e s t h a t d s t n g u s h t h e m f r o m t h e b u y-a n d -h o l d t y p e s t r a t e g e s o f t e n p r a c t s e d n t r a d t o n a l n v e s t m e n t m a n a g e m e n t. M o r e o v e r, t h e u s e o f s t a t c p o s t o n s n d e r v a t v e a n d o p t o n a l n s t r u m e n t s r e n f o r c e s t h e n o n -l n e a r a n d d y n a m c c h a r a c t e r o f t h e a l t e r n a t v e s t r a t e g e s ( s e e F u n g a n d H s e h ( ) ). H o w e v e r, t s w e l l k n o w n t h a t r s k m e a s u r e s s u c h a s t h e b e t a o r t h e S h a r p e r a t o d o n o t a l l o w f o r a d e q u a t e e v a l u a t o n o f d y n a m c a n d n o n -l n e a r r s k s ( s e e f o r e x a m p l e D y b v g ( a, b ), L e l a n d ( ) o r L o ( ) ). N e v e r t h e l e s s, n s p t e o f t h s n a p p r o p r a t e n e s s, t h e S h a r p e r a t o s s t l l t h e m o s t w d e l y us e d m e a s u r n g n s t r u m e n t f o r e v a l u a t n g t h e r s k-a d j u s t e d r e t u r n o f a l t e r n a t v e n v e s t m e n t s. I n a r e c e n t s t u d y c a r r e d o u t b y E d h e c ( ), t s r e v e a l e d a s t h e m e a s u r e t h a t s t h e m o s t f r e q u e n t l y u s e d b y d s t r b u t o r s o f h e d g e f u n d s ( n o t a b l y f u n d s o f f u n d s ) t o p r o m o t e t h e s u p e r o r t y o f a l t e r n a t v e c l a s s r e t u r n s. 1 2

13 Indcators used n comparng the performance of European funds Indcator Total number of quotatons (1) Number of favoured quotatons (2) Sharpe Rato 100% 93% Sortno Rato 28% 3% M² and SRAP 19% NS Return/VaR 9% 2% Others (ncludng IR) 14% 2% S o u r c e : E d h e c ( ) ( 1 ) several answers possble ( 2 ) use of the ndcator as a favoured rsk-adjusted return measure n the sales lterature. T h s o m n p r e s e n c e o f t h e S h a r p e r a t o p o s e s a t h e o r e t c a l p r o b l e m, t o t h e e x t e n t t h a t t a s s u m e s t h a t n v e s t o r s a r e o n l y n t e r e s t e d n t h e f r s t a n d s e c o n d o r d e r m o m e n t s o f a l t e r n a t v e f u n d r e t u r n d s t r b u t o n s,. e. t h e r m e a n a n d v a r a n c e. T h s c a n o n l y b e j u s t f e d, h o w e v e r, a t t h e c o s t o f s m p l s t c a s s u m p t o n s r e l a t n g e t h e r t o t h e a g e n t s ' u t l t y f u n c t o n ( q u a d r a t c u t l t y, w h c h d o e s n o t, a s w e k n o w, e x h b t t h e d e s r a b l e p r o p e r t y o f d e c r e a s n g m a r g n a l u t l t y ), o r t o t h e r e t u r n p r o b a b l t y d s t r b u t o n ( G a u s s a n ( n o r m a l ) d s t r b u t o n ). H o w e v e r, t h e r e t u r n s o f a l t e r n a t v e f u n d s a r e c l e a r l y n o t G a u s s a n ( s e e f o r e x a m p l e B r o o k s a n d K a t ( ) ). I n t h e c a s e o f p o r t f o l o s t h a t n c l u d e d e r v a t v e n s t r u m e n t s, t h e a s s u m p t o n o f G a u s s a n r e t u r n s s n o t n f a c t t e n a b l e. E v e n f t h e r e t u r n o f t h e t r a d t o n a l a s s e t c l a s s w e r e G a u s s a n, t h e r e t u r n o f f u n d s u s n g d e r v a t v e n s t r u m e n t s o r d y n a m c s t r a t e g e s r e l a t n g t o t h o s e t r a d t o n a l c l a s s e s w o u l d n o t b e. I n p o n t o f f a c t, c e r t a n d e r v a t v e n s t r u m e n t s, s u c h a s o p t o n s, g e n e r a t e f n a l c a s h f l o w s t h a t a r e n o n -l n e a r f u n c t o n s o f t h e u n d e r l y n g a s s e t s, a n d t s w e l l k n o w n t h a t a n o n-l n e a r f u n c t o n o f a G a u s s a n v a r a b l e s n o t d s t r b u t e d n a G a u s s a n m a n n e r. A s a r e s u l t o f t a k n g t h e r n o n -l n e a r a n d n o n -G a u s s a n c h a r a c t e r n t o a c c o u n t, t h e n v e s t o r g e n e r a l l y d s p l a y s a n o n - t r v a l p r e f e r e n c e f o r t h e t h r d a n d f o u r t h o r d e r m o m e n t s o f r e t u r n d s t r b u t o n ( s k e w n e s s a n d k u r t o s s ), a s s e v d e n c e d, f u r t h e r m o r e, b y t h e d e v e l o p m e n t o f m e a s u r e s o f e x t r e m e r s k s u c h a s t h e V a R ( s e e b e l o w ). I t s p o s s b l e t o o b t a n t w o p r o b a b l t y d s t r b u t o n s w t h t h e s a m e m e a n a n d t h e s a m e v a r a n c e, b u t w t h e n t r e l y d f f e r e n t s k e w n e s s a n d k u r t o s s. F o r e x a m p l e, a n e q u a l l y w e g h t e d m x t u r e o f a G a u s s a n w t h a m e a n o f 0. 5 a n d a s t a n d a r d d e v a t o n o f 0. 5 a n d a G a u s s a n w t h a m e a n o f 0. 5 a n d a s t a n d a r d d e v a t o n e x h b t s t h e s a m e m e a n a n d v a r a n c e a s a s t a n d a r d s e d G a u s s a n ( 0 a n d 1, r e s p e c t v e l y ), b u t a s k e w n e s s o f a n d a k u r t o s s o f , c o m p a r e d t o 0 a n d 3, r e s p e c t v e l y, f o r t h e s t a n d a r d s e d G a u s s a n ( s e e g r a p h b e l o w ). On l y b y t a k n g n t o a c c o u n t t h e t h r d a n d f o u r t h o r d e r m o m e n t s c a n w e t r u l y d s t n g u s h t h e f u n d s w t h r e t u r n s t h a t f o l l o w t h o s e p r o b a b l t y d s t r b u t o n s Mxture of 2 Gaussans Standardsed Gaussan

14 T h e u s e o f t h e S h a r p e r a t o, b e s d e s t s s c e n t f c c h a r a c t e r, w h c h s o p e n t o c r t c s m, a l s o s e e m s t o u s t o b e r s k b e a r n g. I t m a y l e a d m a n a g e r s t o m p l e m e n t " s h o r t v o l a t l t y 9 " s t r a t e g e s b a s e d o n t h e s a l e o f " o u t o f t h e m o n e y " p u t a n d / o r c a l l o p t o n s. T h e s e s t r a t e g e s a l l o w t h e v o l a t l t y r s k, m e a s u r e d b y t h e s e c o n d o r d e r m o m e n t o f t h e r e t u r n d s t r b u t o n s, t o b e l m t e d, w h l e a t t h e s a m e t m e n c r e a s n g t s m e a n b y c a s h n g n p r e m u m s. B y s e l l n g o u t o f t h e m o n e y p u t o p t o n s ( s t r k e p r c e o n a v e r a g e 7 % b e l o w t h e m a r k e t p r c e ) o n t h e S & P 5 0 0, w t h a m a t u r t y o f 3 m o n t h s o r l e s s, L o ( ) m a n a g e s t o o b t a n a S h a r p e r a t o o f f o r t h e p e r o d f r o m J a n u a r y t o D e c e m b e r ( c o m p a r e d t o f o r t h e S & P 5 0 0! ). O f c o u r s e, t h e d o w n s d e o f t h s s t r a t e g y s t h e v e r y s g n f c a n t n c r e a s e n t h e r s k s o f e x t r e m e l o s s, wh c h o n l y a p p e a r n m o m e n t s g r e a t e r t h a n 2 ( s k e w n e s s a n d k u r t o s s ) a n d w h c h a r e t h e r e f o r e n o t t a k e n n t o a c c o u n t n t h e S h a r p e r a t o. I n L o ' s e x a m p l e, t h e m a x m a l l o s s r e c o r d e d b y t h e " C a p t a l D e c m a t o n P a r t n e r s " f u n d s %, c o m p a r e d t o 8. 9 % f o r t h e S & P M o r e g e n e r a l l y, q u t e a p a r t f r o m t h e s e m a n p u l a t o n s 1 0, t s p o s s b l e t o s h o w, t h r o u g h a s t a t s t c a l m o d e l n t e g r a t n g f a t t e r t a l s t h a n t h o s e o f t h e n o r m a l d s t r b u t o n, t h a t m n m s n g t h e s e c o n d o r d e r m o m e n t ( t h e v o l a t l t y ) s o f t e n a c c o m p a n e d b y a s g n f c a n t n c r e a s e n e x t r e m e r s k s a n d t h u s t h e V a l u e -a t -R s k ( S o r n e t t e, A n d e r s e n, S m o n e t t, ). T h e r e a r e t w o p o s s b l e t y p e s o f a p p r o a c h t h a t a l l o w t h e n o n -l n e a r t y o f h e d g e f u n d r e t u r n s t o b e t a k e n n t o a c c o u n t w t h n t h e f r a m e w o r k o f c l a s s c f n a n c a l t h e o r y. A n n t a l a p p r o a c h, w h c h r e q u r e s a m o r e s g n f c a n t m e t h o d o l o g c a l a d j u s t m e n t, n v o l v e s u s n g a n o n-l n e a r m o d e l t o e x p l a n t h e r e t u r n s o f a l t e r n a t v e f u n d s. F o r e x a m p l e, t o m o d e l t h e n o n -l n e a r t y o f r e t u r n s, t h e r e h a s b e e n a p r o p o s a l t o m p l e m e n t, n t h e d e c o m p o s t o n o f f u n d r e t u r n s, a l o n g s d e t h e n o r m a l a n d a b n o r m a l r e t u r n s, a " p h a s e - l o c k n g " t y p e a p p r o a c h, r e p r e s e n t n g b o t h m o d e l r s k n t h e c a s e o f e x t r e m e e v e n t s a n d e v o l u t o n n t h e c o r r e l a t o n s n t h e c a s e o f v e r y s g n f c a n t m o v e m e n t s n t h e m a r k e t s ( s e e L o, ). F r o m t h s p e r s p e c t v e, t h e p u b l c a t o n o f c o n d t o n a l b e t a s, b y c e r t a n h e d g e f u n d p r o m o t e r s, a l r e a d y r e p r e s e n t s s g n f c a n t p r o g r e s s n t a k n g t h e n o n-l n e a r c h a r a c t e r o f a l t e r n a t v e r e t u r n s n t o a c c o u n t. An o t h e r a p p r o a c h, w h c h s c l o s e r t o t h e a p p l c a t o n f r a m e w o r k o f c l a s s c f n a n c a l t h e o r y, n v o l v e s u s n g a l n e a r m o d e l t h a t e m p l o y s n o n -l n e a r r e g r e s s o r s ( o r e x p l a n a t o r y v a r a b l e s ). A m o n g t h e v a r a b l e s t h a t a l l o w t h e n o n - l n e a r t y o f h e d g e f u n d r e t u r n s t o b e r e p r e s e n t e d, t s e e m s n a t u r a l t o u s e p o r t f o l o s o f o p t o n s. 1 1 M t c h e l l a n d P u l v n o ( ) s h o w t h a t " m e r g e r a r b t r a g e " s t r a t e g e s e x h b t s m l a r r e t u r n s t o t h o s e o b t a n e d t h r o u g h t h e s a l e o f ( n a k e d ) p u t o p t o n s o n t h e s t o c k m a r k e t n d e x. A t t h e s a m e t m e, F u n g a n d H s e h ( ) n o t e t h a t " t r e n d f o l l o w n g " t y p e s t r a t e g e s e x h b t s m l a r r e t u r n s t o t h o s e o b t a n e d t h r o u g h a c o m b n a t o n o f l o o k b a c k t y p e o p t o n s. M o r e g e n e r a l l y, e v e n t h o u g h t h e r e s a p o t e n t a l l y n f n t e n u m b e r o f d f f e r e n t h e d g e f u n d s t r a t e g e s, A g a r w a l a n d N a k ( ) d e m o n s t r a t e t h a t a d y n a m c p o r t f o l o o f 3 o p t o n s o n t h e A m e r c a n R u s s e l l n d e x w t h d f f e r e n t s t r k e p r c e s e n a b l e s a s g n f c a n t f r a c t o n o f t h e r e t u r n s o f a f a r l y w d e s p r e a d c l a s s o f h e d g e f u n d s t o b e e x p l a n e d e x-p o s t. A n o t h e r p o s s b l e c h o c e o f n o n -l n e a r v a r a b l e s t h a t a l l o w s h e d g e f u n d r e t u r n s t o b e e x p l a n e d n v o l v e s u s n g h e d g e f u n d n d c e s. T h s a p p r o a c h h a s s g n f c a n t p r a c t c a l a d v a n t a g e s, e v e n f t s e e m s r e l a t v e l y u n a m b t o u s f r o m a c o n c e p t u a l p o n t o f v e w t o a t t e m p t t o e x p l a n t h e r e t u r n s o f h e d g e f u n d s t h r o u g h t h e r e t u r n s o f o t h e r h e d g e f u n d s. I n t h s w a y, s t y l e a n a l y s s, n s p r e d b y t h e w o r k o f S h a r p e ( ), a n d a d a p t e d f o r t h e a l t e r n a t v e u n v e r s e, a l l o w s t h e p e r f o r m a n c e o f a n a l t e r n a t v e f u n d t o b e a n a l y s e d, n t h e a b s e n c e o f n f o r m a t o n o n t h e s t r a t e g y f o l l o w e d b y t h e m a n a g e r ( s e e L h a b t a n t, , a n d A m e n c, C u r t s a n d M a r t e l l n, ). F n a l l y, t s h o u l d a l s o b e r e c a l l e d t h a t t h e V a l u e -a t -R s k, w h c h s t h e m o s t w d e l y u s e d c o m p o s t e n d c a t o r f o r e x t r e m e r s k n t h e t r a d t o n a l u n v e r s e, h a s a l s o b e e n s u b j e c t t o w d e s p r e a d c r t c s m a s t o t s a p p r o p r a t e n e s s f o r a n a l y s n g n o n -l n e a r a n d d y n a m c s t r a t e g e s. 9 c f. A n s o n ( ) a n d L o ( ). 1 0 Other more subtle manpulatons of the Sharpe rato can be envsaged. To ths end, one could consult Spurgn (1999). 1 1 We should note that the use of varables that allow mplct stock market volatlty to be approxmated, whch we mentoned earler, represents another way to take the optonal and non -lnear character of alternatve fund returns nto account. 1 4

15 A s g n f c a n t a m o u n t o f l t e r a t u r e 1 2 h a s c o m m e n t e d w d e l y o n t h e l m t a t o n s a n d n e c e s s a r y a d a p t a t o n s o f t h e V a R f o r a l t e r n a t v e n v e s t m e n t s : T h e V a R m e a s u r e s p o t e n t a l l o s s e s t h a t o c c u r n o r m a l l y o r r e g u l a r l y ; t h a s n o t h n g t o s a y a b o u t t h e c o n s e q u e n c e s o f e x c e p t o n a l e v e n t s ; T a k n g e x c e p t o n a l e v e n t s n t o a c c o u n t e x a c e r b a t e s t h e s t a t s t c a l e s t m a t o n p r o b l e m. I n t h e c a s e o f a V a R c a l c u l a t e d f r o m t h e d s t r b u t o n o f p a s t r e t u r n s, t s n e c e s s a r y t o h a v e a v e r y c o n s d e r a b l e a m o u n t o f d a t a t o o b t a n a s g n f c a n t s a m p l e o f " h s t o r c a l " V a R e v e n t s. T h s p r o b l e m, w h c h a l r e a d y e x s t s n t h e t r a d t o n a l u n v e r s e, s e x a c e r b a t e d n t h e a l t e r n a t v e u n v e r s e b y t h e f r e q u e n c y o f t h e d a t a, w h c h s o f t e n m o n t h l y ; T h e a l t e r n a t v e a p p r o a c h, c a l l e d " p a r a m e t r c, " n v o l v e s m a k n g a n e x p l c t a s s u m p t o n a b o u t t h e n o r m a l t y ( o r a b o u t a g v e n l a w ) o f r e t u r n s t o c a l c u l a t e t h e V a R a n d, a s s u c h, s n o t a p p r o p r a t e f o r t h e a l t e r n a t v e u n v e r s e. A s o l u t o n t o t h e c r t c s m a m e d a t t h e h s t o r c a l a n d p a r a m e t r c V a R s h a s b e e n p r o p o s e d, w t h t h e V a R b a s e d o n s m u l a t o n s t h a t u s e t h e M o n t e C a r l o m e t h o d. T h s V a R h a s t s e l f b e e n s u b j e c t t o c r t c s m, o n t h e o n e h a n d b e c a u s e o f t h e s z e o f t h e s m u l a t o n s a n d t h e r e f o r e t h e s z e o f t h e c a l c u l a t o n s r e q u r e d, a n d o n t h e o t h e r b e c a u s e, f r e q u e n t l y, t u s e s a n o r m a l d s t r b u t o n o f t h e r s k f a c t o r r e t u r n s ( s e m -p a r a m e t r c V a R ). T h e r e s u l t n g s m p l f c a t o n o f t h e M o n t e C a r l o s m u l a t o n s t h e n c o n t r a d c t s t h e o b j e c t v e o f o v e r c o m n g t h e u n r e a l s t c n t a l f r a m e w o r k o f t h e p a r a m e t r c V a R. F a c e d w t h t h e s e d f f c u l t e s, n v e s t o r s a n d m a n a g e r s h a v e m p l e m e n t e d n t e r e s t n g s o l u t o n s ( s t r e s s t e s t n g, s c e n a r o a n a l y s s a n d m o r e c o m p l e x m o d e l l n g o f t h e d s t r b u t o n t a l s w t h e x t r e m e v a l u e t h e o r y ). T h e s e " v a r a t o n s " o n t h e m a n a g e m e n t a n d m e a s u r e m e n t o f e x t r e m e r s k s s h o u l d, n o u r o p n o n, b e p o p u l a r s e d a n d g e n e r a l s e d a n d t h e r e b y p e r m t a r e l a t v e a p p r e c a t o n o f t h e p a r a m e t r c r s k a n d r e t u r n m e a s u r e s. T h e l a t t e r a r e t o t a l l y n a p p r o p r a t e f o r t h e a l t e r n a t v e u n v e r s e a n d t h s a p p r o a c h w o u l d a l l o w f o r b e t t e r m a n a g e m e n t o f t h e b e n e f t s o f a l t e r n a t v e d v e r s f c a t o n. W t h t h a t n m n d, w e p r e s e n t a p r a g m a t c a p p l c a t o n o f t h e V a R c a l c u l a t o n n a f a t t a l d s t r b u t o n e n v r o n m e n t, a l o n g w t h t s n t e g r a t o n n t o a n o p t m s a t o n p r o c e s s ( s e e F a v r e a n d G a l n a o ( ) ). T h s m e t h o d n t a l l y c o n s s t s o f c a l c u l a t n g a V a R u s n g a n o r m a l d s t r b u t o n f o r m u l a a n d t h e n a C o r n s h -F s h e r e x p a n s o n t o t a k e t h e s k e w n e s s a n d k u r t o s s n t o a c c o u n t. W t h n t h e G a u s s a n f r a m e w o r k, t h e V a R c a n b e c a l c u l a t e d e x p l c t l y b y u s n g t h e f o l l o w n g f o r m u l a : P ( dw VaR ) = 1 α VaR = nσwdt w h e r e n = n u m b e r o f s t a n d a r d d e v a t o n s a t ( 1 -α) σ = a n n u a l s t a n d a r d d e v a t o n W = c u r r e n t v a l u e o f t h e p o r t f o l o d t = f r a c t o n o f t h e y e a r T h e a n a l y t c a l s d e o f t h s n o r m a l V a R f o r m u l a 1 3 w a s t h e n a d j u s t e d u s n g t h e C o r n s h -F s h e r e x t e n s o n ( ) a s f o l l o w s : w h e r e Z c = t h e c r t c a l v a l u e o f t h e p r o b a b l t y ( 1 -α) S = t h e s k e w n e s s K = t h e e x c e s s k u r t o s s (. e. k u r t o s s m n u s 3 ) z = z c + ( z c 1 ) S + ( z c 3 z c ) K ( z c z c S ) W e c ould notably menton Chung (2000) 1 3 Mna and Ulmer, 1999, Delta-Gamma Four Ways and the RskMetrcs Group propose four VaR calculaton methods for assets that are non - normally dstrbuted: Johnson transformatons, Cornsh -Fsher expansons, Fourer methods and partal Monte-Carlo. They found that Cornsh - Fsher s fast and easy to follow but sometmes lacks accuracy for extreme dstrbutons. 1 5

16 T h e a d j u s t e d V a R s t h e r e f o r e e q u a l t o : VaR = W ( µ zσ ) I t s h o u l d b e n o t e d t h a t f t h e d s t r b u t o n s n o r m a l, S a n d K ( r e p r e s e n t s t h e e x c e s s k u r t o s s n t h e f o r m u l a ) a r e e q u a l t o z e r o a n d c o n s e q u e n t l y, z = Z c, a n d w e c o m e b a c k t o t h e G a u s s a n V a R. W e c a r r e d o u t a n e f f c e n t f r o n t e r c a l c u l a t o n n a m e a n -V a R s p a c e, w h e r e w e u s e t h e V a R a t a t h r e s h o l d o f 9 9 % n t e g r a t n g t h e C o r n s h -F s h e r c o r r e c t o n, a l l o w n g n v e s t o r s ' a v e r s o n t o t h e e x t r e m e r s k s r e l a t e d t o a l t e r n a t v e n v e s t m e n t t o b e t a k e n n t o a c c o u n t. T h e s e e f f c e n t f r o n t e r s w e r e c a l c u l a t e d f r o m H F R s t y l e p e r f o r m a n c e s o v e r t h e p e r o d F e b r u a r y M a r c h Modfed (Cornsh-Fsher) mean/var effcent fronters usng stocks (S&P 500), bonds (LBGBI) and hedge fund styles (HFR) (02/ /2002) 20.00% 18.00% 16.00% 14.00% Annual Return 12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% 0% 10% 20% 30% 40% 50% 60% 70% Modfed VAR S&P + Lehman Convertble Arbtrage Dstressed Securtes Emergng Markets Equty Hedge Market neutral Equty non hedge Event Drven Fx. Income Arbtrage Macro Relatve Value Market Tmng Short sellng I t s n t e r e s t n g t o a d d t h a t, a c c o r d n g t o o u r r e s e a r c h, t h e e f f c e n t f r o n t e r s o b t a n e d u s n g a G a u s s a n p a r a m e t r c V a R w t h o u t a C o r n s h -F s h e r c o r r e c t o n f o r a 9 9 % t h r e s h o l d a r e v e r y c l o s e t o t h o s e o b t a n e d w t h a V a R a d j u s t e d a c c o r d n g t o t h e C o r n s h-f s h e r e x t e n s o n, b u t a t a % t h r e s h o l d. W e c a n t h e r e f o r e c o n s d e r t h a t n v e s t o r s w h o o n l y t a k e f r s t a n d s e c o n d o r d e r m o m e n t s n t o a c c o u n t g r e a t l y u n d e r e s t m a t e ( a f a c t o r o f 2. 5 ) t h e e x t r e m e r s k t o w h c h t h e y a r e e x p o s e d. 1 4 We could also ntegrate the estmated survvorshp bas for each alternatve fund style (cf. part II.3). 1 6

17 A s a n e x a m p l e, w e s h a l l c o n s d e r t h e c a s e o f " d s t r e s s e d s e c u r t e s " s t r a t e g e s. Comparson of mean/var optmsatons n the case of "dstressed securtes" type strateges (HFR) for the perod (02/ /2002) 16.00% 14.00% 12.00% Annual Return 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% 0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 30.00% 35.00% 40.00% VAR Cornsh Fsher 99% Cornsh Fsher 97.5% Cornsh Fsher 95% VaR 99% W h a t s m o r e, t s a p p r o p r a t e t o n s s t o n t h e l m t a t o n s o f q u a n t t a t v e a p p r o a c h e s n t h e a r e a o f r s k m o n t o r n g a n d c o n t r o l. T h e r s k l n k e d t o a l t e r n a t v e f u n d s s h o u l d m p e r a t v e l y b e e v a l u a t e d w t h n a f r a m e w o r k o f t h o r o u g h a n a l y s s. III. Concluson: What atttude to adopt wth regard to alternatve nvestment rsks? C o n t r a r y t o w h a t c e r t a n h e d g e f u n d p r o m o t e r s w o u l d l e a d u s t o b e l e v e, a l t e r n a t v e n v e s t m e n t, e v e n w h e n t n v o l v e s n o n -d r e c t o n a l s t r a t e g e s w t h z e r o -b e t a, o r v e r y l o w v o l a t l t y, p r e s e n t s r s k s. T h a t s n f a c t t s p r n c p a l s t r e n g t h! G o o d q u a l t y p o r t f o l o d v e r s f c a t o n s b a s e d o n a s s e t s t h a t a r e e x p o s e d t o d f f e r e n t r s k s. T h e a l t e r n a t v e c l a s s, t h r o u g h t h e s t r a t e g e s a n d n s t r u m e n t s t c o n t a n s, p r o v d e s t h s d f f e r e n c e. O b v o u s l y, m o d e l l n g a n d m e a s u r n g t h e s e n e w r s k s, a n d t h e r e f o r e c o n t r o l l n g t h e m, p r e s e n t s s e v e r a l c h a l l e n g e s. I t w o u l d a l s o a p p e a r t o b e p r e j u d c a l f o r t h e d e v e l o p m e n t o f t h e h e d g e f u n d n d u s t r y a n d t h e r e c o g n t o n o f a l t e r n a t v e n v e s t m e n t a s a f u l l y-f l e d g e d a s s e t c l a s s t o n e g l e c t t h o s e c h a l l e n g e s. T h ro u g h t o o g r e a t a d e s r e t o p r o v e t h e s u p e r o r t y o f h e d g e f u n d a l p h a s a n d b y f o r g e t t n g c e r t a n s o u r c e s o f r s k o r t h e d f f c u l t y n m e a s u r n g t h o s e r s k s, t h e r e s a d a n g e r o f a s s e t m a n a g e m e n t p r o f e s s o n a l s o v e r s e l l n g a n a l t e r n a t v e c l a s s p e r f o r m a n c e t h a t s r e l a t e d t o t h e p r e v a l n g e c o n o m c s t u a t o n. T h a t w o u l d n o t s t a n d u p a g a n s t t h e o c c u r r e n c e o f e v e n t s t h a t w o u l d h g h l g h t t h e s p e c f c r s k s o f t h o s e n v e s t m e n t s. T h s w o u l d b e a l l t h e m o r e r e g r e t t a b l e s n c e, a s w e h a v e s h o w n, e v e n w h e n t a k n g e x t r e m e r s k s, d f f c u l t m a r k e t c o n d t o n s a n d d a t a b a s n t o a c c o u n t, a l t e r n a t v e n v e s t m e n t r e t a n s, f o r a l l t h a t, c o n s d e r a b l e a d v a n t a g e s n t h e a r e a o f e f f e c t v e p o r t f o l o d v e r s f c a t o n. 1 7

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19 L j u n g, G. M a n d B o x, G. E. P., , O n a m e a s u r e o f l a c k o f f t n t m e s e r e s m o d e l s, Bometrka, V o l. 6 5, n 2, L n t n e r J., , T h e e f f e c t o f s h o r t s e l l n g a n d m a r g n r e q u r e m e n t s n p e r f e c t c a p t a l m a r k e t s, Journal of Fnancal and Quanttatve Analyss, 6, 5, Lo, A., Nov-D e c , R s k m a n a g e m e n t f o r h e d g e f u n d s, n t r o d u c t o n a n d o v e r v e w, f o r t h c o m n g, Fnancal Analysts Journal, L o n g n F., S o l n k B., , I s t h e c o r r e l a t o n n n t e r n a t o n a l e q u t y r e t u r n s c o n s t a n t?, Journal of Internatonal Money and Fnance, 1 4. M a r k o w t z, H., , P o r t f o l o s e l e c t o n, Journal of Fnance, 7, M e r t o n, R. C., , O n t h e p r c n g o f c o r p o r a t e d e b t : t h e r s k s t r u c t u r e o f n t e r e s t r a t e s, J o u r n a l o f F n a n c e, 2 9, M e r t o n, R. C., , A n n t e r t e m p o r a l c a p t a l a s s e t p r c n g m o d e l, Econometrca, 4 1, M t c h e l l, M., a n d P u l v n o T., , C h a r a c t e r s t c s o f r s k n r s k a r b t r a g e, w o r k n g p a p e r, H a r v a r d B u s n e s s S c h o o l. P a r k J., S., B r o w n, a n d W. G o e t z m a n n, , P e r f o r m a n c e b e n c h m a r k s a n d s u r v v o r s h p b a s f o r h e d g e f u n d s a n d c o m m o d t y t r a d n g a d v s o r s, Hedge Fund News, A u g u s t P W G, H e d g e f u n d s, l e v e r a g e, a n d t h e l e s s o n s o f L o n g -T e r m C a p t a l M a n a g e m e n t, r e p o r t o f t h e P r e s d e n t s W o r k n g G r o u p o n F n a n c a l M a r k e t s R o s s, S., , T h e a r b t r a g e t h e o r y o f c a p t a l a s s e t p r c n g, Journal of Economc Theory, S a u n d e r, A., , C r e d t r s k m e a s u r e m e n t : n e w a p p r o a c h e s t o v a l u e a t r s k a n d o t h e r p a r a d g m s, Wley Fronter n Fnance, J o h n W l e y & S o n s. S c h n e e w e s, T., K a z e m H. a n d M a r t n G., , U n d e r s t a n d n g h e d g e f u n d p e r f o r m a n c e, r e s e a r c h p a p e r, L e h m a n B r o t h e r s. S c h n e e w e s, T., a n d S p u r g n R., , M u l t -f a c t o r m o d e l s n m a n a g e d f u t u r e s, h e d g e f u n d a n d m u t u a l f u n d e s t m a t o n, w o r k n g p a p e r, C I S D M, U n v e r s t y o f A r m h e s t. S h a r p e, W., , A s s e t a l l o c a t o n : m a n a g e m e n t s t y l e a n d p e r f o r m a n c e m e a s u r e m e n t, Journal of Portfolo Management, 1 8, S h a r p e, W., , C a p t a l a s s e t p r c e s : a t h e o r y o f m a r k e t e q u l b r u m u n d e r c o n d t o n s o f r s k, Journal of Fnance, 1 9, S o r n e t t e D., J., A n d e r s e n, V. a n d S m o n e t t P., P o r t f o l o T h e o r y f o r " F a t T a l s ' ', I n t e r n a t o n a l J o u r n a l o f T h e o r e t c a l a n d A p p l e d F n a n c e 3 ( 3 ), ( ) S p u r g n R., , H o w t o g a m e y o u r S h a r p e r a t o, C l a r k U n v e r s t y, workng paper. W a t t s, D., , S m a l l w o r l d s : t h e d y n a m c s o f n e t w o r k s b e t w e e n o r d e r a n d r a n d o m n e s s, P r n c e t o n U n v e r s t y P r e s s. W a t t s, D. a n d S t r o g a t z, S., J u n e , C o l l e c t v e d y n a m c s o f s m a l l -w o r l d n e t w o r k, N a t u r e, v o l , n 6,

20 Appendx 1: Defnton of hedge fund styles accordng to the HFR classfcaton Convertble arbtrage Dstressed securtes Emergng markets Equty hedge Market neutral Equty non-hedge Event drven Fxed ncome arbtrage Macro Relatve value Short sellng Market tmng Investment n convertble bonds. The strategy s to buy the convertble bond and sell short the common stock of the same company. Involves buyng back, at a low prce, the securtes of companes that are experencng fnancal dffcultes. The securtes targeted may cover a wde range, from senor secured debt (lowest rsk) to common stock (hghest rsk). Investment n equtes or bonds of emergng markets. Involves nvestng manly n equtes and dervatve products. The manager systematcally uses short sellng, but takes care to mantan a permanent overall net poston that s ether long or neutral. Explots neffcences n the market through balanced buyng of undervalued securtes and sellng of overvalued securtes enablng ether a beta or a dollar neutral approach to be obtaned. Manly nvolves holdng long postons n equtes, although managers may nvest n dervatve nstruments and engage n short sellng. Investment strategy that explots prce movements related to the antcpaton of events affectng the lfe of the company (merger, acquston, bankruptcy, etc.) The nvestment return s based on explotng prce anomales related to nterest rate nstruments. Investment strategy wth a strong leverage effect on market events or developments. The objectve of ths type of strategy s to take advantage of the relatve prce dfferentals between related nstruments. Mantans a net or smple short exposure relatve to the market. Conssts of nvestng systematcally n assets for whch an upward trend s antcpated. 2 0

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