How Risk Averse are Fund Managers? Evidence from Irish Mutual Funds

How Risk A e se a e Fund Manage s? E idence om I ish Mu ual Funds Abs ac This pape in es iga es he deg ee o isk a e sion exhibi ed by I ish und manage s. Assuming a mean- a iance op imising manage , we employ he dynamic condi ional co ela ion speci ica ion (Engle, 2002) o he mul i a ia e GARCH model o es ima e he coe icien o ela i e isk a e sion. We ind ha und manage s whose emi is o “agg essi ely” manage hei po olios ha e coe icien s lying be ween 1.69 and 2.42, while he isk a e sion pa ame e o “balanced” managed unds ange om 3.24 o 3.69. Finally we discuss he implica ions o hese numbe s on he likelihood o hese manage s pa aking in isky in es men s. Keywo ds: Risk a e sion; Fund manage s; Dynamic condi ional co ela ions. JEL Classi ica ion: G11, G15, C32, G20. I. In oduc ion Risk a e sion is a cen al ene in inancial economics. Howe e , he deba e as o he magni ude o he coe icien o ela i e isk a e sion (CRRA) is one ha has long been o he o e on o he ield and he economics o unce ain y in gene al. In simula ing many o he popula models in inance, he coe icien o isk a e sion is a ee pa ame e ha equi es calib a ion. In hei amed pape on he ‘equi y p emium puzzle’, Meh a and P esco (1985) a gue ha alues g ea e han 10 a e implausibly la ge. Bo h Mankiw and Zeldes (1991) and Lucas (1994) s a e ha e en 10 is an ex eme case, wi h Lucas a guing ha any ‘solu ion’ o he equi y p emium puzzle ha elies on a CRRA g ea e han 2.5 is unlikely o be b oadly accep ed. Since he ea ly 1970s, esea ch on he CRRA has spawned a oluminous li e a u e. In his seminal wo k, A ow (1971) a gued ha due o he bounding condi ions o he u ili y unc ion, he coe icien should be close o uni y. E e since, he e ha e been nume ous s udies, spanning di e en ields o economics p o iding es ima es o his pa ame e and alues needed o ma ch he da a in simula ed models. F iend and Blume (1975) use in o ma ion on asse holdings, income and o he demog aphics o a la ge c oss-sec ion o households and conclude ha he CRRA is g ea e han uni y and “is mo e likely o be in excess o wo”. Gene ally, es ima es om inance applica ions end o be la ge. An excep ion is Hansen and Single on (1982) who epo es ima es be ween 0.35 and 1. Howe e , Meh a and P esco (1985) equi e he CRRA o be in excess o 10 (and may be as high as 50) o econcile he la ge p emium paid by equi y wi h heo e ical models. Szpi o (1986) using da a om insu ance ma ke s inds 1 suppo o cons an ela i e isk a e sion wi h a coe icien be ween 1.2 and 1.8. Howe e , Blake (1996) inds es ima es a y wi h weal h le el, wi h he poo es and iches g oups exhibi ing CRRA o 47.60 and 7.88 espec i ely. Cla e e al. (1998) in es iga e he app op ia eness o he CAPM o he UK ma ke and ail o ejec a CRRA o 2, an o en-hypo hesised alue in calib a ed models. Mo e ecen ly, Aï -Sahalia and Lo (2000) p o ide es ima es o CRRA using op ion-p icing models and ind es ima es anging om 1 o 60, wi h a weigh ed a e age o 12.7. In es ing he CAPM, Engel and Rod igues (1989), Gio annini and Jo ion (1990) and Thomas and Wickens (1993) gene a e es ima es o he CRRA. Howe e hese a e gene ally highly implausible, o en nega i e o a s a ic co a iance ma ix and no s a is ically signi ican ly di e en om ze o o ime- a ying speci ica ions o he condi ional co a iance ma ix. Ou pape sheds new ligh on he issue by ocusing exclusi ely on es ima ing he CRRA. We use a simple mean- a iance amewo k and show ha by ully co e ing he ange o asse s in a ypical po olio and employing ime- a ying co a iance ma ices as isk measu es, e en such a simple model can p o ide es ima es o CRRA ha a e consis en wi h heo e ical alues. P e iously, es ima ion o ime- a ying co a iance ma ices o a b oad ange o asse s p o ed di icul bu he e we adop he highly lexible dynamic condi ional co ela ion (DCC) speci ica ion o he mul i a ia e GARCH model due o Engle (2002). This allows us o cap u e changes in he in es men oppo uni y se and assess he eac ion o po olio manage s. Ou app oach is closes in spi i o Thomas and Wickens (1993), Engle and Rod igues (1989) and Gio annini and Jo ion (1989), bu di e s in a numbe o 2 impo an aspec s ha a e likely o in luence he pa ame e o in e es in ou analysis. Fi s ly, ou pape is he only one o ocus exclusi ely on es ima ing he coe icien o isk a e sion. The o he s concen a e on es s o he CAPM wi h he CRRA being a by-p oduc a he han he ocus o he es . Secondly, we use he ac ual weigh s employed by po olio manage s as opposed o he CAPM weigh s. The e o e we a e no imposing any es ic ions on he po olio alloca ions. Gi en ha obse ed asse weigh s di e subs an ially om hose implied by he CAPM, ou analysis ep esen s ac ual inancial ma ke beha iou and hence should p o ide a be e o es ima e o isk a e sion amongs und manage s. The CRRA om he o he s udies indica es he deg ee o isk a e sion equi ed o he CAPM o hold a he han ha displayed by ma ke pa icipan s. Thi dly, employing he highly lexible DCC e sion o he mul i a ia e GARCH model allows us o inc ease he asse co e age in he analysis. O he s udies cons ain hei asse co e age o include only he la ges ma ke s. While his is a legi ima e app oach, he po olio e ec s o he smalle and o en less co ela ed ma ke s a e ine i ably omi ed. In ou model, he a ac i eness o such ma ke s is cap u ed h ough he ( ime- a ying) co a iance e ms. The decision o he und manage as o whe he o no o in es in such asse s can be qui e e ealing as o hei a i udes o isk. We ocus on wo classes o unds; agg essi ely managed and balanced managed unds. Bo h unde ake signi ican in e na ional di e si ica ion and a e he e o e mos consis en wi h heo e ical models. I ish unds a e wo hy o a en ion o a numbe o easons. Fi s ly, he domes ic equi y ma ke is small, accoun ing o less han 1% o wo ld ma ke capi alisa ion, making 3 in e na ional in es men a necessa y ehicle o po olio choice. Secondly, I eland’s adi ion and cul u e mean ha agen s may be mo e amilia wi h o eign ma ke s and less p one o o e s a ing he isk o o eign asse s. Assuming ha und manage s a e mean- a iance op imise s, we es ima e hei implied CRRA. Ou esul s show ha agg essi ely managed unds exhibi lowe isk a e sion wi h CRRA es ima es anging om 1.69 o 2.42. Balanced managed unds ypically hold mo e iskless asse s and consequen ly, CRRA es ima es a y be ween 3.21 and 3.78. The emainde o he pape is s uc u ed as ollows; sec ion 2 ou lines he mean- a iance amewo k on which ou es ima ions a e based. Sec ion 3 discusses he econome ic model and he da a employed. Sec ion 4 p esen s ou esul s and discusses hei implica ions while Sec ion 5 con ains ou concluding ema ks. II. Mean- a iance amewo k We assume ha und manage s adop a simple mean- a iance amewo k1 (as in Engel and Rod igues, 1989; Gio annini and Jo ion, 1990; Thomas and Wickens, 1993) o alloca e unds among a ious asse classes. This is consis en wi h myopic in es men and a single pe iod model such as he CAPM. E en in a mul i-pe iod se ing, Shlei e and Vishney (1997) a gue ha und manage s can be mo i a ed o ake a myopic iew in hei in es ing s a egies i less sophis ica ed in es o s use sho - e m e u ns o e alua e hei pe o mance o compe ence. Hence we a gue ha ou assumed amewo k is jus i ied. We ha e a ep esen a i e manage who seeks o maximise end-o -pe iod eal weal h, gi en in o ma ion a ailable a he beginning o he pe iod. 4 0,0 )],(),([ 2111    UUWVWEMaxU (1) whe e E is he condi ional expec a ion o end-o -pe iod weal h, W +1, and V is he condi ional a iance. We can w i e ixW ExWWWE )1()( ' 1 ' 1  (2) and i s a iance as x VxWWV )()( 1 '2 1 . (3) x , +1 and i a e n- ec o s o po olio asse weigh s, asse e u ns and ones espec i ely. The isk ee a e is deno ed by . V ( +1) e e s o he condi ional a iance-co a iance ma ix o asse e u ns. The excess e u n on he po olio be ween and +1 is gi en by; ).( 1 ' 1, p x   (4) Subs i u ing Eqs. (2) and (3) in o (1) and maximising wi h espec o x gi es he i s o de condi ions: 0)()( 1 2 211   x VWU EWU dx dU (5) De ining he coe icien o ela i e isk a e sion, W U U 1 2 2  , and e- a anging he abo e exp ession, we ge he ollowing condi ion; x V E )()( 11     (6) Assuming ha agen s a e a ional, we ge he equa ion ha we wan o es ima e: .)( 111     x V   (7) This equa ion gi es us a ela ionship be ween asse e u ns, he isk associa ed wi h each asse , he co ela ion s uc u e be ween each pai o asse s, he 5 coe icien o ela i e isk a e sion and he po olio weigh a ibu ed o each asse . III. Econome ic Model and da a The model A key ea u e o Eq. (7) is ha we equi e an es ima e o he condi ional a iance o asse e u ns. The e is now ample e idence ha his ma ix is ime a ying (Bolle sle e al., 1988; Cla e e al., 1998 among o he s). The de elopmen o he amily o (G)ARCH models (Engle, 1982; Bolle sle , 1986) has made i possible o allow he co a iance ma ix o be con inuously changing. They also cap u e o he ea u es o asse e u ns such as hick ails and ola ili y clus e ing. As ou ocus is on po olio di e si ica ion, i ’s necessa y o adop a mul i a ia e GARCH speci ica ion. A well-documen ed p oblem o es ima ing hese models lies in he as numbe o po en ial pa ame e s o be es ima ed simul aneously.2 A ecen ad ance due o Engle (2002) combines he pa simony o ea lie speci ica ions wi h a model su icien ly lexible o inco po a e ime- a ying condi ional co ela ions. Fo an n- ec o o asse e u ns, he model equi es he es ima ion o n a iances bu i is assumed ha he ime a ia ion o he co a iance elemen s s ems om a common sou ce and can be cap u ed by jus wo pa ame e s. Thus he n(n-1)/2 co a iance e ms can be modelled o he p ice o wo addi ional pa ame e s. This is he echnique adop ed he e. We es ima e a mul i a ia e GARCH-in-mean model. I is speci ied as ollows: . ),0(~ )( 1111 11 111       DDH HN x V    (8) 6 D is a diagonal ma ix o condi ional s anda d de ia ions, which is gene a ed by ')(')(' 11,1, BDBAAVVD i i       . (9) Γ is a ime- a ying co ela ion ma ix wi h ypical elemen gi en by ).()()1( whe e, 1,1,1, _ , ,, , ,    ij j iij ij jj ii ij ij hh hh h   (10) whe e is he uncondi ional expec a ion o he co ela ion be ween i and j. _ ij  The da a Ou goal is o es ima e he CRRA om Eq. (8). We use da a on asse holdings o wo classes o I ish mu ual unds; agg essi ely managed and balanced managed unds. The asse holdings o bo h unds a e mon hly a e ages o all he in es men i ms ope a ing in his ma ke . A e age beha iou is aken o be mo e indica i e o ma ke beha iou . App oxima ely 20 and 50 unds ope a e in he agg essi ely and balanced managed ca ego ies espec i ely3. This da a is ob ained om Moneyma e and we also ely on hei und classi ica ions. Moneyma e ca ego ise agg essi ely managed unds as hose wi h a mix o equi ies, ixed in e es , p ope y, cash and a minimum 65% eal asse exposu e. Balanced managed unds also con ain a mix o he abo e asse ypes bu only equi e a 40% eal asse exposu e. All unds a e moni o ed on a mon hly basis. Ou sample ex ends om Janua y 1993 o Decembe 2002. Figu es 1 and 2 plo he asse holdings o agg essi ely and balanced managed unds espec i ely. As expec ed, balanced unds ha e ela i ely la ge holdings in he isk- ee asse . Consis en wi h he phenomenon o “home bias” in po olio composi ion, I ish 7 unds disp opo iona ely hold domes ic asse s. The deg ee o in e na ional di e si ica ion is less han sugges ed by inancial heo y. Howe e , he alloca ion o I ish equi y has allen o e ime, wi h an o se ing g ow h in o he Eu o zone equi ies. Asse holdings a e no gi en by indi idual asse s bu by geog aphical b eakdown. The e o e we assume ha he o eign asse holdings ha e a be a o uni y wi h espec o hei egional index. Re u ns on hese asse s a e compu ed using Da as eam cons uc ed indices o each egion. We wo k wi h a es o e u n in excess o he isk- ee a e o p e en ola ili y in his a iable om o e s a ing po olio isk. The isk ee a e is p oxied by he 1-mon h money ma ke a e. Nominal e u ns a e con e ed o eal e u ns using mon hly in la ion calcula ed om he CPI o all i ems. IV. Resul s Discussion o esul s The model ou lined abo e was es ima ed using he Quasi-maximum likelihood app oach o Bolle sle and Woold idge (1992). Table 1 summa ises ou esul s. We begin wi h an analysis o he agg essi ely managed unds. Using he asse weigh s as in Figu e 1, ou es ima e o he CRRA is 1.69. Fu he mo e, i is qui e p ecisely es ima ed wi h a s anda d e o o 0.005. The e o e manage s o agg essi ely managed unds exhibi a deg ee o isk a e sion ha is consis en wi h heo e ical models. A simila analysis o he balanced managed unds shows hese manage s a e mo e isk a e se. Howe e , he es ima e o 3.21, is s ill a he lowe end o heo e ically accep able pa ame e s. Table 2 epo s es ima es o he 8 Mankiw, N.G. and Zeldes, S.P. (1991) The consump ion o s ockholde s and non- s ockholde s, Jou nal o Financial Economics, 29, 97-112. Meh a, R. and P esco , E. (1985) The equi y p emium: a puzzle, Jou nal o Mone a y Economics, 15, 145-61. Shlei e , A. and Vishney, R. (1997) The Limi s o A bi age, Jou nal o Finance, 52(1), 35-55. Szpi o, G.S. (1986) Measu ing isk a e sion: an al e na i e app oach, Re iew o Economics and S a is ics, 68, 156-59. Thomas, S. and Wickens, M.R. (1993) An in e na ional CAPM o bonds and equi ies, Jou nal o In e na ional Money and Finance, 12, 390-412. 15 Table 1. Summa y o esul s Es ima ed CRRA Agg essi ely Managed Funds 1.69 (0.00) Agg essi ely Managed (inc. Eme ging ma ke s) 2.42 (0.00) Balanced Managed Funds 3.21 (0.00) Balanced Managed (inc. Eme ging ma ke s) 3.78 (0.00) *Numbe s in pa en heses a e p- alues. 16 Table 2: Es ima ed pa ame e s o he ime- a ying co a iance ma ix. Agg essi ely Agg essi ely* Balanced Balanced* V11 0.003 (0.00) 0.002 (0.00) 0.002 (0.00) 0.003 (0.00) V22 0.002 (0.00) 0.002 (0.00) 0.002 (0.00) 0.002 (0.00) V33 0.003 (0.00) 0.003 (0.00) 0.003 (0.00) 0.003 (0.00) V44 0.001 (0.00) 0.001 (0.00) 0.001 (0.00) 0.001 (0.00) V55 0.003 (0.00) 0.004 (0.00) 0.005 (0.00) 0.005 (0.00) V66 0.0005 (0.00) 0.0003 (0.00) 0.0002 (0.00) 0.0003 (0.00) V77 - 0.003 (0.00) - 0.003 (0.00) A11 0.067 (0.00) -0.069 (0.00) 0.026 (0.00) -0.049 (0.00) A22 -0.004 (0.53) 0.009 (0.00) 0.054 (0.00) 0.095 (0.00) A33 -0.024 (0.00) -0.023 (0.00) 0.059 (0.00) 0.037 (0.00) A44 0.376 (0.00) 0.303 (0.00) 0.303 (0.00) 0.258 (0.00) A55 0.260 (0.00) 0.016 (0.00) 0.128 (0.00) -0.003 (0.00) A66 -0.279 (0.00) 0.046 (0.00) 0.080 (0.00) 0.095 (0.00) A77 - 0.039 (0.00) - -0.014 (0.00) B11 0.079 (0.00) 0.248 (0.00) -0.039 (0.00) 0.114 (0.00) B22 0.039 (0.00) 0.091 (0.00) 0.271 (0.00) 0.077 (0.00) B33 -0.053 (0.00) 0.001 (0.02) -0.071 (0.00) -0.015 (0.00) B44 0.222 (0.00) 0.298 (0.00) 0.087 (0.00) 0.314 (0.00) B55 0.006 (0.24) 0.007 (0.00) 0.039 (0.00) -0.060 (0.00) B66 -0.055 (0.00) 0.017 (0.00) 0.087 (0.00) 0.062 (0.00) B77 - 0.005 (0.00) - -0.010 (0.00) α 0.022 (0.018) 0.067 (0.00) 0.039 (0.00) 0.071 (0.00) β 0.064 (0.00) 0.484 (0.00) 0.799 (0.00) 0.528 (0.00) Numbe s in pa en heses a e p- alues. S a ed columns e e o po olios including he eme ging ma ke index. 17 Figu e 1: Geog aphical b eakdown o Agg essi ely Managed Funds 0% 20% 40% 60% 80% 100% Ri sk less Asse Long Bond Fa Ea s Eq ui y US Equi y Eu o Equ i y UK Equi y I ish Equi y 18 Figu e 2: Geog aphical b eakdown o Balanced Managed Funds 0% 20% 40% 60% 80% 100% Jan-93 May-93 Sep-93 Jan-94 May-94 Sep-94 Jan-95 May-95 Sep-95 Jan-96 May-96 Sep-96 Jan-97 May-97 Sep-97 Jan-98 May-98 Sep-98 Jan-99 May-99 Sep-99 Jan-00 May-00 Sep-00 Jan-01 May-01 Sep-01 Jan-02 May-02 Sep-02 Riskless Asse Long Bond Fa Eas Equi y US Equi y Eu o Equi y UK Equi y I ish Equi y 19 Figu e 3: Odds equi ed by Agg essi e Funds Manage o pa icipa e in ac ua ially ai gamble 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 P opo ion o Weal h o Gamble Requi ed P obabili y o Winning 20 Figu e 4: Odds equi ed by Balanced Funds Manage o pa icipa e in ac ua ially ai gamble 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 P opo ion o Weal h o Gamble Requi ed P obabili y o Winning 21 Figu e 5: Odds equi ed by Agg essi e Funds (Inc. Eme ging Ma ke s) Manage o pa icipa e in ac ua ially ai gamble 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 P opo ion o Weal h o Gamble P obabili y o Winning 22 Figu e 6: Odds equi ed by Balanced Funds (Inc. Eme ging Ma ke s) Manage o pa icipa e in ac ua ially ai gamble 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 P opo ion o Weal h o Gamble P obabili y o Winning 23