EDHEC-Risk Istitute 393-4 roeade des Aglais 622 Nice Cedex 3 Tel.: +33 ()4 93 18 32 53 E-ail: research@edhec-risk.co Web: www.edhec-risk.co Market Risks i Asset Maageet Coaies May 211 Berd Scherer Profesor of Fiace at EDHEC Busiess School
Abstract This aer shows that reveues fro a sale of ublicly traded US asset aageet coaies carry substatial arket risks. Not oly does this challege the acadeic risk aageet literature about the redoiace of oerative risks i asset aageet. It also is at odds with curret ractice i asset aageet firs. Asset aagers do ot hedge arket risks eve though these risks are systeatically built ito the reveue geeratio rocess. This is surrisig as shareholders would ot otially choose asset aageet coaies as their source of arket beta. They rather refer to articiate i the alha geeratio ad fud gatherig exertise of ivestet aagers as fiacial iterediaries. At the very iiu asset aagers eed to oitor their fees at risk to uderstad what iact roduct desig, bechark choice ad fee cotract desig have o reveue volatility. This calls for a uch wider iterretatio of the risk aageet fuctio that too arrowly focuses o cliet risks. Keywords: Asset aageet, arket risk, rado coefficiet odel, hierarchical rior, GIBBS salig, cororate fiace JEL classificatio : G11, C33, G3 Berd Scherer, Ph.D. (berd.scherer@edhec.edu) is rofessor of fiace at EDHEC Busiess School, Lodo. The article beefitted fro y discussios with Michael Kliek (Kliek Advisors) who also rovided the dataset. My views have bee shaed by discussios with Do Chew (Morga Staley), Ke Wisto (Morga Staley), Be Golub (Blackrock), Greg va Iwege (Ivory), Da Di Bartoloeo (Northfield), Ed Fishwick (Blackrock), Phillie Jorio (UCSD), Lioel Martellii (EDHEC) ad Noel Aec (EDHEC). EDHEC is oe of the to five busiess schools i Frace. Its reutatio is built o the high quality of its faculty ad the rivileged relatioshi with rofessioals that the school has cultivated sice its establishet i 196. EDHEC Busiess School has decided to draw o its extesive kowledge of the rofessioal eviroet ad has therefore focused its research o thees that satisfy the eeds of rofessioals. 2 EDHEC ursues a active research olicy i the field of fiace. EDHEC-Risk Istitute carries out uerous research rograes i the areas of asset allocatio ad risk aageet i both the traditioal ad alterative ivestet uiverses. Coyright 211 EDHEC
Itroductio The textbook view o risks i asset aageet coaies is suarized by HULL (27,. 372): For a asset aager the greatest risk is oeratioal risk. 1 This view is seriously challeged by the evets i 28. Asset aageet coaies cae uder severe rofitability ressure fro arket ot oeratioal risks. Resosible for this is the direct arket exosure built ito asset aageet fee odels. Asset aageet fees are usually aid as a ercetage of assets uder aageet. A 5 basis oits asset based fee o 1 billio US equity assets traslates ito a directioal arket exosure of 5 illio USD. What has bee see as a auity strea ( auity busiess view ) that was thought to exose asset aageet firs to little or o earigs risk, aterialized as directioal stock arket exosure cobied with high oeratioal leverage (high ratio of fixed to variable costs). While oeratioal leverage leads to what has bee raised as a scalable busiess (low costs of takig o additioal busiess) i good ties it creates the otetial for large losses whe reveues fade. As cliet becharks wet dow, so did asset based fees (ercetage fee alied o average assets uder aageet withi a year) ad hece reveues. I accordace with STULZ (23) it ca be argued that asset aageet coaies should hedge their fees at risk. The gist of this arguet is that while the beta cooet i asset based fees are zero et reset value (NPV) rojects, they still create reveue risks that i a world with caital arket frictios ad taxes are costly. Reovig those risks fro the P&L accout of a asset aageet coay would free u risk caital for ew vetures, icrease the observability of effort by seior aageet ad reduce frictioal bakrutcy costs. 2 Our objective is to test for the direct relatioshi betwee asset aageet reveues ad arket returs. The estiated sesitivity is a easure of arket risks iheret i the reveues of a asset aageet fir. If differet fro zero it eeds to be icororated ito the risk aageet rocess of a asset aageet fir. 3 So far the acadeic literature exclusively focuses o aagig cliet risks ot busiess risks. I the view of this aer, this eeds addressig as the volatility of asset arkets has a first order effect o asset aageet reveues P&L, while it gets virtually o etioig i the risk aageet literature. 4 The oly aer close to ours is SCHERER (21). He first argued that arket risks have a doiat effect o reveue volatility for large asset aageet coaies with a well diversified cliet base. 5 For a sale of ie asset aageet firs ad for a liited uber of data oits (eight aual data observatios fro 2 to 27 er fir), he uses various ael regressio techiques to show that the reveue beta of asset aageet reveues is ideed oe as iitially cojectured. We exted the above aalysis i various ways. First, we look at a ael that is both loger ad broader. Our data cosist of 24 quarterly observatios of 17 ure asset aagers. Our dataset is higher i frequecy ad cotais ore asset aageet firs. I the laguage of Pael data aalysis, this is a broader ad loger ael. Secod, cotrary to SCHERER (21), we iclude the crisis years 28 ad 29. This should hel us to ivestigate ay otetial asyetry i the sesitivity of asset aageet reveues to severe dow arkets. Third, we ow distiguish betwee u ad dow arket betas. Fourth, we eloy a Bayesia rado coefficiet odel that allows us to ore flexibly deal with the data without akig strog structural assutios. The data ad our rior views will lead us to the correct odel, which will be reassurigly sile oce we coclude our research. Moreover our research cofirs the results of SCHERER for a differet data set, tie eriod ad ecooetric ethodology. 1 - See SCHERER (29) for a review of this toic. 2 - See BASU (21) for a review o firs' diversificatio ad refocusig i the last three decades. 3 - Couicatios with risk aagers fro leadig Wall Street firs as well as ersoal exeriece cofir the author s view that these risks reai uaaged. We fid evidece for this i our data set. Sectio 4 gives a accout of the ost oular arguet agaist hedgig fees at risk ad why they fail i the face of oder fiace. 4 - Market risk i asset aageet reveues ca be hedged usig Asia forwards (stacked stadard forwards with differet aturities), that better rereset the averagig rocess i asset based fees. 5 - Sall asset aageet coaies with few cliets ad oe star fud aager (that could leave to a coetitor), will be exosed to a lot ore idiosycratic risk. However, these risks are hardly oerative i ature ad as such the coo view that the biggest risk i asset aageet is oerative risk ight be islaced. 3
Sectio 2 outlies odel ad data used i this aer i cobiatio with soe iitial data aalysis. Sectio 3 resets our eirical results for the Bayesia rado coefficiets odel, while sectio 4 ad 5 iterret these results fro a cororate fiace ersective. 2 Model ad Data 2.1 Maager Data Our focus o listed asset aageet coaies arises fro the fact that reveue data are sily ot available for rivate artershis or bak owed asset aageet uits. Table 1 rovides a suary of the statistical roerties for our data set. The ublicly listed asset aageet coaies i our sale cover active as well as assive ivestets, asset aageet ifrastructure ad rivate equity alteratives. First, observe that ucoditioal average reveue growth varies cosiderably across asset aageet firs. Ivesco (IVZ) shows the largest average reveue growth for our sale, drive by exteral asset uder aageet growth. Noe of the ucoditioal eas is statistically sigificat at the 99% cofidece level, eve though aecdotic evidece tells us that asset aageet firs beefitted fro strog et iflows over the sale eriod. Give the liited uber of data oits for each idividual ea cobied with the high volatility of reveue growth this is hardly surrisig. It also is ria facie evidece for the otetial advatage of oolig data with hierarchical ael data odels to arrive at ore recise araeter estiates. Quarterly reveue volatility shows excetioally high levels for a idustry that has bee erceived as a auity busiess. Table 1 Statistical Proerties of Reveue Growth Data fro 24 Q2 to 21 Q1 The table rovides ea (ad -value uder the ull hyothesis of zero reveue growth), volatility, skew, kurtosis, JARQUE/BERA orality test (ad -value uder the ull hyothesis of orality) for quarterly reveue growth of 17 US asset aageet coaies fro Q2 to 21 Q1. Aedix C exlais the abbreviatio for each asset aager ad discusses the data sources. All data rovided by Kliek Advisors. Asset Maager Mea -value Volatility Skew Kurtosis JB-test -value AB.65.8 12.64 -.37.97 1.5.47 AMG 2.7.23 1.67 -.97.55 4.1.13 BAM 9.49.15 31. 1.3 2.32 9.62.1 BEN 2.72.18 9.64-1.32 2.71 14.25. BLK 15.19.11 44.89 4.14 18.91 426.9. DHIL 19.8.2 35.72 2.11 5.61 49.23. EV 2.55.8 6.88-1.3 1.77 7.37.3 FIL.35.74 4.98 -.62.89 2.34.31 GBL 1.6.71 2.51.92.36 3.5.17 GROW 12.69.13 39.29 -.18 -.53.41.81 IVZ 21.16.29 94.9 3.5 8.67 112.36. JNS.19.93 1.74-1.49 4.42 28.39. LM 3.6.43 18.74.75 3.3 11.42. SMHG 3.92.38 21.37.64.77 2.21.33 TROW 2.85.9 7.98-1.89 5.68 46.63. WDR 2.58.1 7.32-1.34 3.4 18.72. WHG 6.42.16 21.79.5 5.64 32.83. 4
This suorts our rior that asset aageet risk cotais a large fractio of arket risk, directly built ito fee cotracts. 6 The relatioshi betwee average reveue growth ad reveue volatility is liear ad excetioally strog with a adjusted R-square of.76 ad a t-value of 6.2 o volatility whe regressed agaist ea returs. 7 Figure 1 rovides suort that a coo factor (geeratig the sae retur er uit of risk) rus through the asset aageet idustry ad differet firs exhibit differet exosure (leverage) to this factor. Reveue risk is highly o-oral for alost all firs with large egative skew (siilar to arket risks). Figure 1 Average Reveue Growth versus Reveue Volatility The figure lots average reveue growth versus the volatility of reveue growth for the data i Table 1. A regressio of average reveue growth versus reveue volatility suggests a adjusted R-squared of.76..225.2.175.15 Average reveue growth.125.1.75.5.25...25.5.75 1. Reveue volatility I cobiatio with high oerative leverage (high fixed costs relative to variable costs) this risk characteristic creates a risky ositio ost asset aagers have boxed theselves ito. If fiacial regulatio would force ivestet aageet firs to set regulatory caital aside to cover otetial losses fro arket risk, we should see a ore careful use of ecooic caital. 2.2 Market Data Next, we relate reveue risk to arket risk. The Russell 1 i USD is used as a roxy for stock arket returs. 8 R1t However istead of calculatig a sile quarter ed retur r = R1-1, t-1 we use the average value of the Russell 1 over the quarter as uerator, i.e. the quarterly ercetage chages i average rice relative to rices at the start of the quarter, r av, t. We cojecture the latter to better rereset the ature of asset based fees as asset based fees are calculated as a fractio of average assets uder aageet for a give eriod. Aedix A 6 - We ca aroxiate the reveue volatility of assed based fees by usig v/ 3 where v is the volatility of bechark returs. This aroxiatio is based o a geoetric average that will be close to the arithetic average (average AUM) that uderlies fee calculatios. Give that the MSCI WORLD retur i this eriod was about 2%, it is clear that additioal (ad ossibly correlated) factors are at work. I other words, asset aager secific risk is cosiderable. Cliets ight chage fro risky high fee busiess to safe low fee assets, cliet grous ight disaear or articular roducts becoe out of favor. 7 - Ruig a robust regressio (MAD) istead, the t-value icreases to alost eight with a alost idetical sloe. However give our data iclude both outliers as well as ifluetial observatio (the leverage value for IVZ is 6 ties larger tha the average leverage value) just robustifyig agaist outliers ight ot be sufficiet. I ay case reovig IVZ as ost likely the wackiest data oit will ot chage our results. 8 - This choice is likely to uderestiate the aout of beta exosure i reveue streas as the busiess ix of asset aageet firs differ. It agai akes our result very coservative as we could easily fid higher systeatic arket exosure by data iig for the best i sale fittig arket becharks. 5
roves that the regressio beta of year ed stock arket returs agaist reveue growth will lead to isleadig stock arket sesitivities. Uder fairly stadard assutios fee sesitivities b rev i a OLS regressio will coverge agaist half the asset class beta, b, as averagig becoes cotiuous ( " 3), i.e. b rev 1 2 1 ^1 2 bv b 1 2 b = + - h ^ + - h 2 2 = v "3 = 2 2 where v deotes bechark volatility. I other words: the averagig rocess for fee icoe hides arket exosure. Low betas result fro the averagig rocess ad are ot a idicatio of low arket exosure. The averagig rocess effectively decoules asset returs ad fees eve though there is a deteriistic oe to oe relatioshi. Fially, we eed to allow for the ossibility that reveue streas react differetly to u ad dow arkets. Bear arkets lead to fallig reveues as assets uder aageet fall both due to arket iact or to cliet rebalacig to less risky (cash, fixed icoe) but less rofitable ivestet roducts. Aecdotic evidece suggests that this rebalacig o the dowside was articularly aiful i 28. The reduced ability to take risks by istitutioal ivestors also eat that cliets did ot restock their ortfolios of risky assets leadig to a asyetric resose. We therefore estiate (1) u revit= bi i urav t idr d + b + b av t + f,,,,,, it, (2) d d Here rav, t = i^rav, t, h ad rav, t = ax^rav, t, h. We ca use this forulatio to test : b which is the secificatio used by SCHERER (21). Table 2 suarizes the results. H q iu, = bi, d, Table 2 Idividual OLS Regressios Reveues for each asset aageet fir are regressed agaist u ad dowside average arket returs accordig to (2). We erfor sigificace tests usig robust stadard errors (HAC adjustet with 3 autocorrelatio lags). Asset i, Maager b t t val - iu, b t t val - id, b t t- val H : b t iu, = b t q i, d Rr 2 ^- valueh AB -.1 (-.45) 2.18 (3.29) 1.49 2.95.48 57.37% AMG.5 2.47.65 1.24 2.6 5.15.7 62.8% BAM.6.68 3.26 1.43 1.56.9.61 16.11% BEN.6 2.86 -.46 -.77 1.7 3.7.2 39.72% BLK.16 1.27 1.68.48 2.7 1.2.84 7.69% DHIL.22 2.21 1.17.44 3.12 1.53.62 13.43% EV.5 3.38 -.13 -.34 1.32 4.36.2 48.98% FIL..25 -.1 -.2..1.98.% GBL.1.25 1.57 1.6 1.72 1.52.94 18.93% GROW.19 1.64-1.5 -.48 2.6.87.43 3.71% IVZ.25.89 1.59.21 4.18.73.81 3.44% JNS..23 1.45 3.9 1.83 5.12.57 7.59% LM.7 1.24-1.1 -.69 1.6.95.34 4.87% SMHG.3.5 1.92 1.25 1.62 1.38.89 19.22% TROW.4 5.41 1.6 6.9 1.65 12.41.3 92.61% WDR.3 2.89.78 2.5 1.38 5.81.19 72.7% WHG..4 1.88 1.12-1.53-1.2.17 8.97% 6
There is a clear idicatio that b t iu, < b t i, d (for 12 out of 17 asset aagers), although agai oe of the tests show statistical sigificace at the 99% cofidece level. Oly results for TROW, BEN ad EV are sigificat at the 95% cofidece level. More iterestigly adjusted Rr 2 s show a large variatio. The exlaatory ower of the odel is largest for stable (o recet M&A activity) ad diversified asset aageet firs like TROW, JNS ad AB. For those firs arket risks are the doiat source of reveue volatility, questioig the covetioal wisdo, that the biggest risks i asset aageet are oerative risks. A Rr 2 of 93% - as i the case of TROW - leaves little roo for iterretatio. Oly 7% of reveue volatility could otetially arise fro oerative risks. O the other side, saller ad id size firs do ot exlai risks sufficietly, ad soe egative u arket betas are difficult to uderstad (for exale FIL, WHG ad GROW). 2.3 Ecooetric Model Our objective is to estiate arket risks ilicit i asset aageet reveues. I extesio to SCHERER (21), we distiguish betwee u- ad dow-arket exosures (betas). Iitial calculatios i the revious sectio have show, that the sall sale (24 observatios, 21 degrees of freedo) cobied with volatile data roves to be a challege for the statistical sigificace of each searate regressio odel. While a fully ooled odel assues that all asset aageet firs scatter aroud the sae regressio lie, the ature of our data set ight require us to relax this assutio. Firs differ i size, cliet set, roduct ix, brad ad asset gatherig facilities. A atural way to deal with this heterogeeity i great flexibility (without iosig a solutio) is to exted (2) with a hierarchical rior for each regressio coefficiet. This also allows us to take advatage of a larger data set. To be ore recise I assue R V b JR V i, b N S W KS W O bi = Sb W id, ~ NKSb W d, XbbO = N^b, Xbbh (3) S K O b W S iu, b W u T X LT X P Idividual exosures, b i, are orally distributed aroud b(3# 1 vector) with covariace X bb. 9 If the uer left had eleet i X bb is large (sall), the (3) allows uch (little) variatio aroud the first eleet of b (autooous reveue growth) across idividuals. The above secificatio results fro the followig hyer-riors (all rior iforatio eterig the odel is arked by. X b~ N^b, R bb h = Wv ^, X -1-1, bb bb h (4) (5) Here W stads for the Wishart distributio ad v is ofte used as a sale equivalet. If v -1, = 1, this would ea that our rior X bb has the sae recisio as if it was calculated fro a (hyothetical) observed sale of 1 data oits. Fially, I assue a Gaa rior o the recisio h(1/variace of residuals) h~ G^s,, -2 x h (6) for the roduct of all N idividual likelihood fuctios (with idividual araeter vectors b i). I essece (3) states that the idividual araeters for each fir are (costraied to be) draw fro a coo ool. This ool i tur is govered by (4) ad (5). Coutatioally, I use GIBBS salig to derive the distributio for each b i as well as the ool ea b. All calculatios are detailed i Aedix B. I effect, our odel allows every asset aageet coay to be 9 - Note, that it does ot atter whether this is really the case. All that is required is that the decisio aker does ot ossess additioal iforatio. 7
differet. To iose soe coo structure (otherwise we could ru idividual regressios) our hierarchical riors cotrol the way firs are allowed to differ. At the higher level (3) I assue that idividual betas are best described by a ultivariate oral distributio, i.e. a vector of eas ad a atrix of covariates. At the lower level, I assue that, give idividual betas, reveue growth is drive by a liear regressio. Iitial oolig estiates are estiated for each asset aageet uit to rereset a startig oit for the GIBBS saler. The stregth of this Bayesia rado coefficiets odel with hierarchical rior odel 1 is its flexibility, both i estiatio ad testig. It allows us to iose differet views (beliefs) o how siilar or dissiilar the ivestigated asset aageet coaies are i.e. o the oolability of our data set. I additio, aggregate estiatio odels cofoud heterogeeity ad oise by odelig idividuals rather tha a average relatio. The searatio of sigal (heterogeeity) fro oise leads to ore stable odels. Draws (relicates) for each fir rovide a rich source of iforatio for ore accurately coductig statistical tests 3 Estiatio Results This sectio discusses our estiatio results. I set rior ea ad recisio for the ea of the ooled desity (3) as uiforative. More recisely ~ N 1H, 1 3 3 3 b f> > H (7) I other words, I do ot iose ay structure about the true idustry wide odel for reveue risks i (3). This is the relatioshi we fially wat to estiate. It should therefore ot be heavily iflueced by the choice of a secific rior. However, we eed to iose soe structure to beefit fro our Bayesia aroach. If we set all riors to be uiforative, our results would oly be hilosohically differet fro a sile rado coefficiet odel. Hece, we set the araeters for the (iverse) Wishart rior o the variace of the ool fro which the idividual coefficiets are draw i (5) to 1 R bb = > 25. H. 25. (8) Our ratioale is to allow estiates for the autooous reveue growth to vary with a stadard deviatio of 1 (square root of 1) across uits which is still quite uiforative give the eirical distributio of autooous growth i Table 2. For idividual betas, we iose a soewhat tighter rior. 8 1 - The rado coefficiet odel has bee otivated by SWAMY (197) ad is essetially a atrix weighted GLS estiator that will weight regressio coefficiets deedig o the quality (residual variace) of each regressio ad usually alied whe the data aear to be o ool-able. This is siilar to ractitioers that weight regressio coefficiets based o their t-values.
Table 3 Bayesia Rado Coefficiet Model This table reorts the results for our Bayesia rado coefficiet odel usig GIBBS salig. Idividual beta estiates, t-value ad -values directly follow fro the osterior distributio of regressio coefficiets. Asset i, Maager b t t val - iu, b t t val - id, b t t- val Hq : b t = b t iu, i, d ^- valh AB.1.25 1.4 1.49 1.65 2.76.25 AMG.4.67.94 1.34 1.68 2.79.21 BAM.1 1.84 1.11 1.84 1.69 2.83.26 BEN.4.68.85 1.22 1.61 2.7.21 BLK.16 2.88 1.3 1.46 1.79 2.98.21 DHIL.2 3.63 1.1 1.44 1.82 3..19 EV.3.62.86 1.23 1.57 2.6.22 FIL.1.21.84 1.2 1.42 2.35.26 GBL.2.45.99 1.42 1.67 2.79.24 GROW.14 2.48.79 1.12 1.62 2.71.18 IVZ.22 4.2 1.6 1.52 1.95 3.19.17 JNS.1.19.99 1.42 1.68 2.81.23 LM.4.73.79 1.12 1.53 2.53.22 SMHG.5.85 1.2 1.46 1.67 2.77.25 TROW.4.66.95 1.36 1.64 2.74.23 WDR.3.61.93 1.34 1.6 2.67.23 WHG.7 1.21.93 1.33 1.29 2.16.34 All Firs.7.37.95 1.85 1.64 4.31.22 Whatever the ea of the ooled desity will look like, y rior belief is that idividual betas should - with 95% cofidece - differ fro their hierarchical beta by oe (. 196. : 2). This is a crucial odel iut. The tighter we set this rior, the closer will our results reseble a oolig solutio. The reverse is true for uiforative riors. I the case of totally uiforative riors we revert back to searate OLS regressios. First, we reset results for the idividual regressio odels whe cofroted with a hierarchical rior i Table 3. The GIBBS saler is started fro the idividual regressio estiates. Slittig our sale of 2 salig ito two halfs (after reovig the first 4 bur i observatios) the GEWEKE z-score is well below 1. 9
Figure 2 Hierarchical u ad dow arket beta fro GIBBS salig for Bayesia rado coefficiet odel The grah shows 6 rado draws fro GIBBS salig (after discardig the first 4 observatios) for our Bayesia rado coefficiet odel described i Aedix B. 4 Siulated values fro GIBBS saler 3 2 1-1 Dow arket beta U arket beta -2 217 248 279 31 341 372 43 434 465 496 527 558 Siulatio ru Figure 3 Distributio of u- ad dow- arket beta for 2 GIBBS saligs This grah shows a histogra of differeces betwee u ad dow arket betas for 2 GIBBS saligs. While there is evidece of higher dow tha u arket beta (78% of the distributio of osterior returs lie below zero) it is ot sigificat at covetioal cofidece levels..5.4.3 Desity.2.1. -5. -2.5. 2.5 5. Differece i u ad dow arket beta fro GIBBS saler 1 Give the flaky relatioshis (isigificat regressios with low exlaatory ower) fro sigle regressios it is little surrisig that our rado coefficiet odel suggests shrikage towards the hierarchical odel. Secod, we show the siulated osterior idustry wide reveue betas i Figure 2. We use the ter idustry wide as our odel assues that idividual u- ad dow- betas are rado draws fro latet idustry betas give i (3). While u-arket betas are ersistetly lower tha dow-arket betas, u-arket betas also exhibit arkedly higher volatility i their siulatios. This is the reaso, why we do ot fid a sigificat differece i
arket exosure for asset aageet firs i u- ad dow- arkets i Figure 3. The above results so far oit us i the directio of a sile oolig odel as idividual differeces are hardly sigificat. Desite leavig cosiderable freedo o how idividual betas ight vary across asset aageet uits, the idividual estiates scatter arrowly aroud coo values. For coarative uroses, I therefore estiate a sile ooled OLS regressio u revt = b urav, t dr d + b + b av, t + f t (9) All data are stacked o to of each other (idividual subscrit i is droed) ad a sigle regressio equatio is ru, essetially eforcig the sae araeters across all uits. The results are suarized i Table 4. Table 4 Poolig Regressio Model The table shows the estiates of a ooled OLS regressio. The test statistic for a Chow for oolability versus a rado coefficiets odel takes a value of.18 ad is distributed as F(31,374). Variable Estiate Stadard Error t-statistic value OLS b.7.2 3.32. OLS b u.94.57 1.64.1 OLS b d 1.64 1.64 3.72. All estiates are rearkably close to our first stage hierarchical relatio described by (3) ad show i the last row (deoted by all firs) i Table 3. While the statistical sigificace for uad dow- arket betas is siilar it is sigificatly higher for autooous reveue growth. The reaso for this lies i the very uiforative rior for b that ilies a large ucertaity about the true beta. OLS igores this ad hece arrives at a high t-value. We ca use this setu to test the assutios of hoogeeity across asset aageet firs. This is usually addressed by a CHOW F-test of the for 11 F = RSSCP - RSS RSSSR SR df CP dfsr - df SR = Fdf ^ -df, df CP SR SR Here RSS CP is the residual su of squares for the oolig odel, RSS SR is the residual su of squares fro searate regressios (su of each regressios residual risk ultilied by uber of observatios) ad dfcp, dfsr are the degrees of freedo for each odel. The test statistic is.18 ad distributed as F(31,374). The zero hyothesis of classical oolig odel is ot rejected. 12 h (1) While the Bayesia rado coefficiet odel is cocetually uch ore geeral tha a aive ooled regressio a researcher aiig for less sohisticatio (OCCAMS razor) ight further OLS OLS silify the estiatio rocess. I fact, we ca ot reject the ull hyothesis that bu = bd (-value of.3 for a stadard F-test). This leads to a eve siler odel secificatio where we ake o differece betwee u- ad dow- arket betas. OLS rev t = b OLS + bav r av, t+ f t (11) 11 - See BALTAGI (25). 12 - Alteratively oe could estiate a SUR odel for all firs ad test the coefficiet restrictios usig a WALD test. 11
Table 5 suarizes these results. Table 5 Silified Poolig Model The table shows the estiates of a ooled OLS regressio where o attet has bee ade to distiguish betwee u- ad dow- arket betas. We ca ot reject the ull hyothesis, that H : OLS b av = 1 (the corresodig t-test shows a -vale of oly.15). Variable Estiate Stadard Error t-statistic value OLS b.5.1 3.91. OLS bav 1.36.25 5.29. Our results show that asset aageet coaies do ot hedge arket risks desite their beig echaically built ito their reveue strea. This is surrisig give that arket risks arise fro cliet becharks choice. Asset aageet coaies have little cotrol over this. I fact those reveue risks are icidetal to the asset aagers roductio rocess which cosists of the creatio of value added relative to a cliet chose bechark. 13 Why should (or should ot) asset aageet firs hedge their fees at risk ad what drives the to igore this? This is addressed i the ext two sectios. 4 The Case for Asset Maagers Hedgig Beta Risk Market or beta risk exosures create a uber of otetial costs for asset aageet coaies that rereset beefits fro hedgig these risks. 14 Market risks directly affect asset aager fees through their iact o returs. Both asset- ad erforace-based fees are affected ad they corresod roughly to beta (geeral ecooic ad arket exosure) ad alha (outerforace versus a risk-adjusted bechark) risks. 15 Coittig caital with the ai of roducig alha is oe of the core coetecies of a asset aageet fir ad, to the extet the fir is cofidet i its ow caabilities, reresets a ositive-npv ivestet. For ost log-oly asset aagers, however at least those that do t rofess to have arket-tiig skills the takig of beta risk is geerally a icidetal cosequece of takig alha risk. I the attet to roduce alha, ost log-oly asset aagers, whether they ackowledge it or ot, ed u bearig cosiderable aouts of beta risk. Beta, or broad stock arket, risks affect asset aagers ot oly directly by their otetial to reduce AUM, but also by resultig i systeatic caital outflows fro the coay across a rage of roducts. Durig a severe equity dow arket, retail ivestors will shift their asset allocatio out of fee-itesive equity fuds ad ito oey arket fuds or goveret guarateed deosits. At the sae tie, istitutioal cliet redetios could be otivated by their ow fiacial distress; for exale, the cliet ay eed to raise cash or de-risk its asset allocatio, or regulatory costraits ay be bidig i the case of isurace coaies. Cooudig the 12 13 - Ideally oe would wat to show i a cross sectioal regressio that firs that are hedgig their fees at risk receive higher arket valuatios (after cotrollig for factors that ake firs differet). However give that virtually all asset aageet firs do ot hedge there is o variatio i the ideedet variable (degree of hedgig). 14 - A geeral review of the beefits of risk aageet ca be foud i DOHERTY (2). 15 - How ca we hedge asset aageet fees? The easiest way to hedge asset based fees is ot to offer the. This follows the idea of duality i risk aageet. We ca either root out the cause (variability i arkets) or the effect (offer fixed fees). There are however liits to this arguet. First, this sily shifts risks to cliets. If assets fall, ercetage fees rise. Secod, oerative risks are still roortioal to assets uder aageet. A ure flat fee would ot reflect this. Also flat fees are ot suitable where liited caacity exists (which is less a issue for ure beta exosure). How do we ractically ileet a hedge rogra aied at isulatig a asset aagers P&L fro arket iduced variatios of its average assets uder aageet for a give tie eriod? A sile way would be to sell futures with oe year aturity o the uderlyig assets with a otioal i $ A, where i reresets the asset based ercetage fee ad A the assets uder aageet at the begiig of the eriod. If assets icrease i value the hedge (igorig carry) creates a loss of - i $ DA while asset aageet fees rise by a offsettig + i $ DA. I other words: How do we hedge a 5bs fee o a 1 Millio USD adate? We go short 5. USD i the futures arket. If the arket goes u 1% you will loose 5. USD o this hedge, but you will get a equal aout back fro rise fees (5bs o ow 11 illio USD will rovide 55. USD i fee icoe). I total you locked i 5. USD i fees at the begiig of the year.
redetio roble for fud aagers is that it is at recisely these ties whe bak fudig also dries u. I other words, there is a high correlatio betwee reveue (or caital arket) risks ad fudig risks. 16 Hedgig the beta risk exosure of its P&L could beefit asset aagers, first of all, by reservig the liquidity ecessary to fiace ew rojects--icludig ew roducts, eole, or IT latfors-- 17 at a tie whe losses have reduced iteral caital ad exteral caital has becoe exesive. Hedgig rotects costly liquidity ad debt caacity. 18 If a asset aageet fir chooses ot to hedge its asset-based fees, it will be ecessary to hold additioal cash i reserve agaist P&L risks. But erhas equally iortat, the hedgig of a log-oly asset aager s beta risk should also rovide the fir s curret ad rosective cliets with a clearer sigal of whether its aagers are succeedig i the fir s issio of geeratig alha. What s ore, by isolatig aager erforace, hedgig ca facilitate ore effective icetive coesatio liked to shareholder value creatio. This has two additioal beefits: (1) it should otivate greater effort to geerate alha because erforace is rewarded o a relative basis; ad (2) it should hel attract skilled talet ore caable of geeratig alha (while ecouragig those aagers who ilicitly relied o beta exosure to leave). 5 Why Do Asset Maagers Not Hedge their P&Ls? Few coaies i the asset aageet idustry hedge arket risk, which eas that alost all suffered a large loss i reveue because of the 5% dro i stock rices durig the worst of the fiacial crisis. Log-oly asset aagers usually give a few geeral reasos for ot hedgig. The ost coo is that by hedgig, asset aagers would forgo the exected icrease i fee icoe that coes fro a risig arket. I other words, it would eliiate the uside otio that such fees rereset for a covetioal asset aageet fir. But uless a asset aager has a distictive advatage i arket tiig, ad cites that advatage i its raisig caital fro ivestors, it s ot clear that ivestors are willig to ay asset aagers just for bearig beta risk. Ad if oe evaluates a asset aager as a log-ru ecooic eterrise, the questio becoes: Do the beefits of bearig risk (aily i the for of higher fees durig u eriods) outweigh the costs of trouble durig the dow eriods? The aswer rovided by ost ecooists would be o. While fud aagers ay beefit fro the uside otio, the value of a asset aageet fir i theory reflects its log-ru rosects i creatig value for its cliet ad value is ot created sily by ridig a risig arket. 19 Viewed i that light, those log-oly asset aagers that choose to liit their arket exosure as art of their ivestet strategy uch like arket-eutral hedge fuds are akig a very differet value roositio both to their ivestor cliets ad, i cases where the asset aager is ublicly traded, to their stockholders. The other coo objectio to hedgig beta risk is the difficulty of exlaiig hedgig losses ad arket udererforace durig u arkets. This difficulty ca be aaged through clarity ad ersistece i couicatig the fir s objectives ad arket-eutral stace to its ivestor cliets ad, agai, i the case of ublicly traded asset aagers, the fir s stockholders. 16 - GATZERT/SCHMEISER/SCHUCKMANN (28) aalyze strogly related risk cocetratio i fiacial firs. 17 - U-hedged swigs i fee icoe will also icrease the value of the tax otio the goveret holds agaist the asset aageet coay. Taxes have to be aid if rofits are ade, but with liited carry forwards ad backwards, o equal aout is received if losses are ade. The larger these swigs, the higher the value of this otio. This arguet obviously deeds whether the tax otio is at the oey. 18 - See MELLO/PEARSONS (2). 19 - As ROSS (25, 71) has argued, sice the fee is cotiget o asset value, as a cotiget clai its curret value is ideedet of exected rates of returs. 13
6 Practical Ilicatios We have show that asset aageet reveues carry substatial arket risks. This challeges both the acadeic view i the risk aageet literature about the redoiace of oerative risks as well as the curret idustry ractice of ot hedgig arket risks that are systeatically built ito the reveue geeratio rocess. As these risks are icidetal to the roductio rocess (alha geeratio, roduct develoet, asset gatherig) fiacial theory suggests that these risks eed to be eliiated. For asset aageet coaies to retur to a auity odel, this is ierative. Shareholders do ot wat to get exosure to arket beta via holdig asset aageet coaies, rather they wat to articiate i their alha geeratio ad fud gatherig exertise as fiacial iterediaries. At the very iiu, asset aageet coaies eed to rethik their risk aageet fuctios. They eed to ove fro a ex-ost fiduciary risk easureet reortig aroach to a aagig a firs reveue risks. Literature BALTAGI B. (25), Ecooetric Aalysis of Pael Data, 3rd Editio, Wiley BASU N. (21), Treds i cororate diversificatio, Joural of Fiacial Markets ad Portfolio Maageet, v241,. 87-12. CHEVALIER J. ad G. ELLISON (1997), Risk takig by utual fuds as a resose icetives, Joural of Political Ecooy, v15, 1997,. 1167-12. DOHERTY N. (2), Itegrated Risk Maageet, McGraw Hill (2) GATZERT N., SCHMEISER H., SCHUCKMANN S. (28), Eterrise risk aageet i fiacial grous: aalysis of risk cocetratio ad default risk, Joural of Fiacial Markets ad Portfolio Maageet, v223,. 241-258. HULL J. (27), Risk Maageet ad Fiacial Istitutios, Pretice Hall MELLO A. ad J PEARSON (2), Hedgig ad Liquidity, Review of Fiacial Studies, v131,.127-153. ROSS S. (25), Neoclassical Fiace, Priceto Uiversity Press SIRRI E. ad P. TUFANO (1998), Costly search ad Mutual Fud Flows, Joural of Fiace, Vol. 53,. 1589 1622 SCHERER B. (29), Fees at Risk, EDHEC Workig Paer SCHERER B. (21), A Note o Asset Maageet ad Market Risks, Fiacial Markets ad Portfolio Maageet, 21, vol. 24, o3,. 39-32. STULZ R. (23), Rethikig Risk Maageet, i: STERN J. ad D. CHEW, The Revolutio i Cororate Fiace, Blackwell ublishig, 4th editio. VERBEEK M. (24), Moder Ecooetrics, Wiley ZIMMERMANN H. ad J. SCHULTZ (1989), Risikoaalyse schweizerischer Aktie: Stabilität ud Progose vo Betas, Joural of Fiacial Markets ad Portfolio Maageet, v33,. 196-29. 14 Aedix A Market Beta for Asset Based Fees Asset based fees are based o average rices over a year, while arket sesitivities are calculated usig year ed rices, igorig the iddle art of the stock rice ath over a year. How will this affect estiated stock arket sesitivities? How do the returs for the arket ortfolio ad returs o average fud rices ove together? We start fro our defiitio of arket sesitivity b rev = -1 / i Cov S i = 1 e, S S S Var S c S o (A1)
where S i (S i ) deotes the arket (ortfolio) level at tie i Without loss of geerality we set S = S = 1. Assue that ortfolio ad arket rices follow S = S + S / D i, i = 1 S = S + D / Si where Var^D S h = v 2 such that = 1 i Var S Var S 2 2 ^ h = ^/ D i h = Var^DSh = v. i = 1 We ca ow work out the covariace betwee average ortfolio rices over days ad the fial arket rice at day. Cov^ -1 / i = 1 S i, S -1 Cov S S1 S S1 S2, S Si ; + D + + D + D + f + D ; E i = 1 14243 144424443 E S1 S2 h = / (A2) (A3) Let us assue further that DS i = bds i + f i. Cov^ S i, S ^-1h ^-^-1hh = Var^bDS1 h+ Var^bDS2h+ f + Var^bDS h -1 / = ^1 + i = 1 hbv -1 2 2 h = (A4) Substitute (A4) ad (A2) ito (A1) ad we arrive at b rev 1 2 1 1 2 bv b 1 2 b = + - - ^ h ^ + h 2 2 = = v " 3 2 Eve though asset based fees i the above exale are deteried by arket returs, regressio betas will equal half the arket beta as a result of the averagig rocess. Aedix B GIBBS Salig for Rado Coefficiet Model with Hierarchical Prior We ca erfor the followig calculatios for our odel (3) to (6) i the below (arbitrary) order. To iitialize the first calculatio i a Markov chai the issig araeters eed soe assutios. Deedig o how lucky we are with our iitial assutios, this ight ea that early siulatios arrive at ulikely values. It is therefore coo ractice to discard the first uber of draws (so called bur i eriod). GIBBS salig cosists of a large uber of cycles though the followig set of equatios. First, we sale the idividual exosures fro (A5) X bb i i N bi + ^bi, X bb h i i = ^h61 r u av r d av@ l61 r u av rav@ + X h d -1-1 bb bi = X ^h6 1 r u av r d av@ lrevi + X bb i i -1 bb h (B1) (B2) (B3) A obvious way to iitialize the Markov chai would be to use equatio by equatio OLS to arrive at a iitial estiate for bi, X bb i i. Note that all osterior values (araeters calculated reeatedly throughout the chai for statistical iferece) are arked with, while all riors (our iut) are arked with. Next, we draw the ool araeters accordig to our hierarchical rior structure. b + N^b, S bb h (B4) 15
1 N -1, -1 b = Rbb ^XbbRi = 1bi + Rbb b h R = ^NX + R 1-1, -1 bb bb bb -1 Wv, vw -1 X b + ^ ^ bbh h h (B5) (B6) v = N+ v w bb = At i = 1 ^bi-bh^bi- bhl + X bb (B7) Fially we draw the osterior for the error recisio fro - h + G^s 2,, x h (B8) s x = TN + x N u rev,,, r,, r u u / ^ it-bi i u av t id av, t revit, i, i, urav, t id, r u -b -b hl^ -b -b - b av, th+ x s i 1 = x - 2, = All rado draws oly ivolve either oral, gaa or Wishart distributio ad as such are easy to erfor with stadard software Aedix C Data Descritio BLOOMBERG CODE COMPANY WEBSITE AB:US ($) AlliaceBerstei Holdig LP www.alliaceberstei.co AMG:US ($) Affiliated Maagers Grou Ic www.ag.co BAM:US ($) Brookfield Asset Maageet Ic www.brookfield.co BEN:US ($) Frakli Resources Ic www.frakliteleto.co BLK:US ($) BlackRock Ic www.blackrock.co DHIL:US ($) Diaod Hill Ivestet Grou Ic www.diaod- hill.co EV:US ($) Eato Vace Cor www.eatovace.co FII:US ($) Federated Ivestors Ic www.federatedivestors.co GBL:US ($) GAMCO Ivestors Ic www.gabelli.co GROW:US ($) US Global Ivestors Ic www.usfuds.co IVZ:US ($) Ivesco Ltd www.ivesco.co JNS:US ($) Jaus Caital Grou Ic www.jaus.co LM:US ($) Legg Maso Ic www.leggaso.co SMHG:US ($) Saders Morris Harris Grou Ic www.shgrou.co TROW:US ($) T Rowe Price Grou Ic trow.cliet.shareholder.co WDR:US ($) Waddell & Reed Fiacial Ic www.waddell.co WHG:US ($) Westwood Holdigs Grou Ic www.westwoodgrou.co DATA SOURCES: Coay reorts ad ress releases; Blooberg; Caital IQ; Google Fiace; Yahoo Fiace 2, (B9) 16