Predicting returnsfundmanagers stotz


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Predicting returnsfundmanagers stotz

  1. 1. Original ArticlePredicting returns of equitymutual fundsReceived (in revised form): 18th September 2008Olaf Stotzholds the BHF-BANK Endowed Chair of Private Wealth Management at Frankfurt School of Finance & Management, Germany. Hisresearch interests include wealth management, empirical finance, asset pricing and behavioural finance. His research has beenpublished by various international academic journals, has been discussed in the financial press and is also applied in the financialindustry. Before his academic career he also worked in the fund management industry for several years.Correspondence: Frankfurt School of Finance & Management, Sonnemannstrae 9-11, D-60314 Frankfurt, GermanyABSTRACT This paper investigates 1-year-ahead forecasts of actively managed equitymutual funds. A multifactor forecast model is developed that employs forecasts on themanager’s skill, the fund’s style and the expected factor returns. On the basis of a sample ofGerman equity funds, we show that this forecast model substantially improves forecastpower in relation to a naıve forecast model, which just extrapolates past returns into the ¨future. In particular, the multifactor model reduces the mean-squared error (mean absolute ¨error) by up to 30 per cent compared to the naıve model. More importantly, from theperspective of a mutual fund investor, the return of top-decile funds chosen by the multifactormodel exceeds the average return of all funds by more than 200 basis points per year.Journal of Asset Management (2009) 10, 158–169. doi:10.1057/jam.2009.7Keywords: out-of-sample return forecasting; mutual funds; multifactor modelnaıve investor ¨INDRODUCTION The return of a fund is dependent on twoOver the past few decades, private investors sources. The first source is the return of thehave allocated an increasing amount of fund’s underlying stocks, which can bemoney to mutual funds, thus making this explained by various risk factors. Four factorsfinancial innovation a sweeping success. have been identified by theoretical andMutual fund investors face the problem of empirical research that are successful inhaving to select appropriate funds out of a explaining stock returns (in excess of theuniverse of several hundred individual funds. risk-free rate): market, size, value andFinancial theory guides the investor through momentum (for example Fama and French,this choice by looking at each fund’s 1993; Jegadeesh and Titman, 1993). Theexpected return and risk, as measured by the market factor is based on the capital assetcovariance matrix of returns (Markowitz, pricing model, and predicts that high beta1952). The optimal selection of funds then stocks should produce higher returns thancrucially depends on good estimates of low beta stocks. The size factor refers to theexpected returns (for example Best and empirical observation that, on average, stocksGrauer, 1991; Chopra and Ziemba, 1993). with a small market capitalisation performFinancial theory, however, is silent about the better than stocks with a large marketestimation of expected returns. capitalisation. The value factor captures the 2009 Palgrave Macmillan 1470-8272 Journal of Asset Management Vol. 10, 3, 158–169
  2. 2. Predicting returns of equity mutual fundsdifference in returns between stocks with a valuation ratios (for example book-to-markethigh book-to-price ratio (value stocks) and ratio, dividend yield) are able to predict thestocks with a low ratio (growth stocks). The stock market’s excess return. Predictability ofmomentum effect is related to a stock’s past the remaining three factors (size, value,1-year return. Stocks with a high return in momentum), however, has been rarelythe past year perform better over the next investigated. However, the book-to-marketyear than stocks with a low return do. These ratio seems to predict the return on the sizefactors have been found to explain the cross- and value factor (in addition to the marketsection of stock returns in various countries return), as the empirical evidence of Kothariand over different samples. and Shanken (1997), Pontiff and Schall The second source of a fund’s return is the (1998), Lewellen (1999) and Cohen et aldecision of a fund manager as to which (2003) demonstrates. Therefore, the book-securities she or he holds in a fund. This to-market ratio seems to be an appropriatedecision can be classified into management conditioning variable for predicting factorstyle, selection skill and timing skill. A returns. The management style is anpreference for certain stock characteristics is important issue in fund management (fordescribed by the fund’s management style. example Sharpe, 1992, and Brown andStock characteristics refer to the four factors Goetzmann, 1997). Fund trackingmentioned above. For example, a value companies regularly report the fund’s stylemanager tends to invest in stocks with high (see, for example, the style box created bybook-to-price-ratios (value stocks). Selection Morningstar). Managers tend to hold theskill describes the fund manager’s ability to style of their fund relatively steady over time,find stocks that outperform a benchmark and the style can therefore be derived fromindex on a risk-adjusted basis. Timing skills the correlation between past fund returnscharacterise the ability of whether a fund and factor returns (for example Davis, 2001;manager is able to buy and sell stocks (with Chan et al, 2002). Selection skills are foundcertain characteristics) at favourable times. to be persistent over a horizon of up to 2For example, a fund manager can follow an years (for example Hendricks et al, 1993;active timing strategy by switching between Zheng, 1999; Bollen and Busse, 2004).stocks and cash or between styles (for Therefore, these can also be derived from pastexample, from value to growth). A manager fund returns. Timing decisions, however, dowith good timing skills in value stocks will not seem to enhance the performance ofbuy value stocks before they outperform funds. It is found that parameters measuringgrowth stocks. Management style, selection timing skills are usually not significant (forskills and timing skills then characterise a example Jiang, 2003; Bollen and Busse, 2004),fund manager’s investment decisions. and, in addition, they seem difficult to predict. To predict a fund’s return, an investor has This paper, therefore, will pay particularto forecast the returns on the risk factors and attention to this issue.the investment decisions (management style We combine the prediction of factorand manager’s skills in selection and timing). returns and the information on a fund’s stylePredictability of factor returns has been and a manager’s skills within a multifactorlargely confined to the market return (see, model. We then compare the predictionfor example, Fama and Schwert, 1977; Keim results with that of a naıve forecast, which ¨and Stambaugh, 1986; Campbell, 1987; simply extrapolates the past return into theFama and French, 1988; Lewellen, 1999). In future. We have chosen the naıve model as ¨general, it is found that standard macro- the benchmark model because empiricaleconomic variables (for example term research implies that mutual fund investorsstructure of interest rates, credit spread) and base their estimates of expected returns 2009 Palgrave Macmillan 1470-8272 Journal of Asset Management Vol. 10, 3, 158–169 159
  3. 3. Stotz primarily on past returns. As a result, In specifying equation (1), we rely on investors put more money into funds with a empirical and theoretical research that has high return in the past year than into funds shown that the following four factors with a low return (for example Chevalier and describe the cross-section of stock returns Ellison, 1997; Sirri and Tufano, 1998). (for example Fama and French, 1993; Gruber (1996) shows that newly invested Jegadeesh and Titman, 1993): money slightly outperforms the average the return of the stock market in excess of mutual fund. This outperformance, however, the risk-free rate: market factor ‘MAR’; can be largely attributed to a higher risk of the return of small stocks (small market the fund (Carhart, 1997). Therefore, it seems capitalisation) in excess of large stocks questionable as to whether investors should (large market capitalisation): size factor rely solely on past returns when making ‘SMB’; investment decisions and predict mutual fund the return of value stocks (high book-to- returns. market stocks) in excess of growth stocks This paper is organised as follows. The (low book-to-market stocks): value factor multifactor model is presented in the next ‘HML’; section. Estimation details of the prediction the return of good performing stocks model are discussed in the third section. This (high past-year return) in excess of bad model is then used to predict fund returns. performing stocks (low past-year return): Performance results of the prediction model momentum factor ‘1YR’. are given in the fourth section. The last section concludes. According to the four-factor model, the excess return of stock j is then THE MODEL ~j;t ¼ aj þ bMAR Á ~tMAR þ bSMB Á ~tSMB r r r j j This section derives the multifactor model of fund returns via three steps. The first step þ bHML Á ~tHML þ b1YR Á ~t1YR þ ~j;t : j r j r e relates a stock’s return to various risk factors within a multifactor approach. The second step models the selection decision of stocks by the fund manager. This step also allows the Selection decision of the fund characterisation of the fund’s management manager and management style style. The third step finally introduces the A fund manager now combines various timing strategy of the fund manager. stocks within a fund portfolio, which then yields a return of Multifactor model of stock returns ! The multifactor model states the stock’s X Nt X 4 excess return as ~p;t ¼ r wj;t Á ~ aj þ bk Á ~tk þ ~j;t j r e j¼1 k¼1 X n ! ~j;t ¼ aj þ r bk j Á ~tk r þ ~j;t ; e (1Þ X Nt X Nt X 4 k¼1 ¼ wj;t Á aj þ ~ wj;t Á ~ bk j Á ~tk r j¼1 j¼1 k¼1 where X Nt rj,t ¼ return of stock j in excess of the ˜ þ wj;t Á ~j;t ~ e risk-free rate j¼1 rt k ¼ return of factor k ˜ X 4 aj ¼ risk-adjusted return ¼ ap;t þ ~ r bk Á ~tk þ ~p;t ; e ð2Þ p;t bk ¼ factor loading of stock j to factor k. j k¼1160 2009 Palgrave Macmillan 1470-8272 Journal of Asset Management Vol. 10, 3, 158–169
  4. 4. Predicting returns of equity mutual fundswhere well compared to growth stocks, she or he would buy more stocks with a high load onwj;t ¼ weight of stock j in fund p~ the value factor r t HML, thereby increasing the ˜ ðfund manager’s investment decisionÞ fund’s value beta bHML. As a result, betas are p,tNt ¼ number of stocks in fund p random variables that change taking~p;t ¼ return of fund p in excess of ther expectations of equation (2) as follows: risk free rate X h 4 i  à  à E ~p;tþ1 ¼ ap þ ~ E bk k X Nt r p;tþ1 Á E ~ rtþ1ap;t ¼ wj;t Á aj ¼ risk adjusted return ~ k¼1 (4Þ j¼1 X 4 h i þ ~ cov bk ; ~tþ1 : rk ðmeasures selection skillÞ k¼1 p;tþ1 X Nt~bk ¼ wj;t Á bk ¼ factor loading of fund ~ ~p,t p;t j cov(bk þ 1,rt k 1) then measures the fund ˜þ j¼1 manager’s ability to time the return on factor p to factor k ðmeasures fund’s styleÞ k. We follow Treynor and Mazuy (1966), This four-factor model has also been who assume that the fund’s exposure to theapplied by Carhart (1997) to evaluate the (market) factor depends linearly on theperformance of fund returns, and will be used factor’s return:in this paper to predict fund returns. a1 is ~ bk ¼ bp þ gp Á ~tk : r (5Þ p;tinterpreted as a parameter that measures thestock selection skill of the fund manager. This Then gi characterises the timing skill of kis usually assumed to be constant through time the fund manager. Replacing bp,t þ 1 in(see Christopherson et al, 1998, for an equation (2) with equation (5) yieldsexception). bs are the sensitivities of the fund’s X 4 X 4return on the risk factors, from which the ~p;t ¼ ap þ r bk Á ~tk r þ gk Á ð~tk Þ2 r p pinvestment style of the fund can be deduced. k¼1 k¼1For example, a value manager is characterised þ ep;t: (6Þby a high bHML. In deriving expected fund preturns, we distinguish between a constant Taking expectations then results ininvestment style (bk ¼ const.) and a time- p,tvarying investment style (bk ¼ time-varying). X 4 p,t E½~p;tþ1 Š ¼ ap þ r bk Á E½~tþ1 Š p rkOn the basis of constant selection skill and k¼1investment style, the expected fund return can X 4then be estimated by þ gk Á E½ð~tþ1 Þ2 Š rk p X 4 k¼1  à Âk à E ~p;tþ1 ¼ ap þ r bk Á E ~tþ1 : p r (3Þ X 4 k¼1 ¼ ap þ bk Á E½~tþ1 Š p rk k¼1 X 4Timing decision of the fund þ gk Á ðE½~tþ1 Š2 þ Var½~tþ1 ŠÞ: p rk rk k¼1manager (7ÞHowever, fund managers can vary theexposure of their fund to the four factors in We estimate a fund’s expected return byanticipation of predictable future factor equations (3) and (7). Details of thereturns. For example, if a fund manager determination of each component areexpects value stocks to perform exceptionally described below. We compare the prediction 2009 Palgrave Macmillan 1470-8272 Journal of Asset Management Vol. 10, 3, 158–169 161
  5. 5. Stotz of these models with a naıve estimator that ¨ capitalisation). The return on the factor- uses only information on the past year’s fund mimicking portfolio HML is the return return. This naıve estimator seems to be ¨ difference between a value-weighted applied by mutual fund investors, as portfolio of stocks with the highest book-to- suggested by the mutual fund literature market ratio and a value-weighted portfolio mentioned in the introduction. of stocks with the lowest book-to-market ratio. The return on the factor-mimicking portfolio 1YR is computed as the return ESTIMATION DETAILS difference between a value-weighted portfolio of stocks with the highest past-year Data return and a value-weighted portfolio of We compare the performance of prediction stocks with the lowest past-year return.4 models on the basis of equations (3) and (7) We predict 1-year-ahead returns at the for a large sample of actively managed equity beginning of January of each year from 1991 mutual funds in Germany. The sample is to 2005, inclusive, for each existing fund. taken from the database of BVI Thus, we have 15 prediction periods. As (Bundesverband Investment und Asset funds are closed or newly created, not all 133 Management e.V.),1 and includes all funds funds exist in each prediction period. As a that have an investment objective that is result, 1246 predicted fund return years are focused on German equities. We exclude obtained. Applying equation (3) or (7) for funds that (i) primarily invest in specific return prediction, the following parameters sectors, (ii) have a performance guarantee, have to be estimated: (iii) have a limited duration and (iv) are index Stock selection coefficient alpha: ap funds. This leaves 133 active funds. The Style coefficient beta: bk p sample is free of a survivorship bias, as BVI’s Timing coefficient gamma: gk p database contains surviving and defunct Expected factor returns: E[rt k 1] ˜þ funds.2 Net return data of funds, which Variance of factor returns: Var[rt k 1]. ˜þ account for management and administrative costs, are from Datastream. We use the 1-month LIBOR-offered rate yield as a Alpha, betas and gammas proxy for the risk free-rate, which is The fund’s alpha, betas and gammas are subtracted from net returns to obtain excess estimated by an OLS regression, based on returns. equation (3) and (7). ^, b and ^ then, a ^ l, The return on the market factor is symbolise OLS estimates. The estimation proxied by the return of a stock market index period starts in January 1990 and ends in the in excess of the risk-free rate (MSCI3 month before the prediction date (which is Germany minus 1-month LIBOR-offered the beginning of January of each year). For rate); the returns for the factors size, value example, when returns are forecasted at the and momentum are constructed similarly to beginning of 1995, the estimation period Fama and French (1993). Therefore, factor- covers the period from January 1990 up to mimicking portfolios are computed. For December 1994. This rolling forecasting example, the return on the factor-mimicking scheme uses only lagged information to portfolio SMB is constructed as follows: the predict future returns. If the return series of a value-weighted return of all stocks with the specific fund starts later (because the fund has lowest market capitalisation (below median been created after January 1990), a minimum market capitalisation) minus the value- of 52 weeks are required for parameter weighted return of all stocks with the highest estimation. To obtain precise estimates, market capitalisation (above median market weekly returns are used.162 2009 Palgrave Macmillan 1470-8272 Journal of Asset Management Vol. 10, 3, 158–169
  6. 6. Predicting returns of equity mutual fundsFactor returns We use information variables that areExpected factor returns are estimated both based on the empirical evidence of Kothariunconditionally and conditionally, whereby and Shanken (1997), Pontiff and Schallwe can investigate whether or not fund (1998), Lewellen (1999) and Cohen et almanagers are able to exploit the predictability (2003). They demonstrate that the book-to-of factor returns. In both cases, the market ratio (or spread of the ratio) is able toestimation period starts at the beginning of predict the return in the market, size return1980, and uses yearly returns because 1-year- and value factor. The return of theahead forecasts are made. The unconditional momentum factor will be forecasted on theestimation approach (that is constant factor lagged momentum return becausereturns) uses the average of the realised momentum relies on the notion of returnfactor returns over the estimation period continuation. These assumptions result in theof length T, which is denoted by following information variables:  k à  à 1 X kT ItMAR ¼ logðBMMAR Þ; t E ~tþ1 ¼ AVG rtk ¼ Á r r : (8Þ T t¼1 t ItSMB ¼ logðBMS Þ À logðBMB Þ; t tConditional factor returns are assumed to be ItHML ¼ logðBMH Þ À logðBML Þ and t tlinearly related to information variables It. The It1YR ¼ rtÀ1 : 1YRprediction of each factor’s conditional expectedreturn is then based on the following model: where BMMAR is the book-to-market ratio t of the market index at t, BMS (BMB) is the t t ~tþ1 ¼ f2kÀ1;t þ f2k;t Á Itk þ ~t : rk ~ e (9Þ book-to-market ratio of stocks with a small The estimated OLS regression coefficients (large) market capitalisation, and BMH t^fk,t are used to obtain conditional forecasts of (BML) is the book-to market ratio of value t1-year ahead returns for each factor: (growth) stocks. Âk à Finally, the variance of the factor return is ^ ^ E ~tþ1 jIt ¼ f2kÀ1;t þ f2k;t Á Itk : r (10Þ estimated by the sample variance of realisedTable 1: Details of prediction modelsPrediction Prediction of Consideration of Expected returnmodel factor returns manager’s investment decisions1 Unconditional Management style, P ^k 4 selection skill E½~i;t þ 1 Š ¼ ^i þ r a bi Á AVG½rtk Š k¼12 Conditional Management style, P ^k ^ 4 ^ selection skill E½~i;t þ 1 jIt Š ¼ ^i þ r a bi Á ðfi;2k þ fi;2k þ 1 Á Itk Þ k¼13 Conditional Management style, X4 selection skill, E½~i;t þ 1 jIt Š ¼ ^i þ r a ^ ^ ^ bk Á ðfi;2k þ fi;2k þ 1 Á Itk Þ i timing skill k¼1 X 4 þ ^k Á ððf þ f ^ ^ k 2 ^2 li i;2k i;2k þ 1 Á It Þ þ sk Þ k¼14 — Naıve ¨ E½~i;t þ 1 Š ¼ ri;t r^a: selection coefficient.^b: style coefficient.^l: timing coefficient. ^f: prediction parameter for conditional factor returns.I: information variable for conditionally predicted factor returns.s2: sample variance.^ 2009 Palgrave Macmillan 1470-8272 Journal of Asset Management Vol. 10, 3, 158–169 163
  7. 7. Stotz factor returns, which is denoted by P important (for example Leung et al, 2000). s2 ¼ TÀ1 Á T ðrtk À AVGðr k ÞÞ2 . ^k 1 t¼1 t Therefore, we also calculate the average hit Given these estimation details, Table 1 ratio (HR) as presents an overview of the resulting models ! and their parameters. 1 X 1 X T Mt HR ¼ Á Á hri;tþ1 ; (13Þ T t¼1 Mt i¼1 EVALUATING PREDICTION where (  à MODELS 1 if E ~i;tþ1 Á ri;tþ1 40 r We evaluate the forecast of each model on hri;tþ1 ¼  à the basis of forecast performance (that is 0; if E ~i;tþ1 Á ri;tþ1 p0: r statistical perspective) and investment return HR indicates in how many years the (that is investor’s perspective). The next prediction model will get the correct sign of section presents the statistical perspective the return. and the section after this the investor’s Table 2 summarises the forecast perspective. performance results for each model. As expected, the naıve prediction model 4 ¨ produces the highest prediction error. The Mean absolute error, mean MSE and MAE criteria show an estimation squared error and hit ratio error of 27.47 per cent and 25.21 per cent, The statistical performance of each respectively. This is even higher than the prediction model is evaluated by the average standard deviation of fund returns, difference between the return forecast which is about 22 per cent. The use of and the realised return (that is forecasting information on the fund manager’s error). Hereby, we compute two common investment decisions (management style and statistical measures, the mean absolute selection skill) increases the forecast error (MAE) and the mean-squared error performance. Model 1 reduces the (MSE). The MAE and the MSE are prediction error by about 24 per cent. The defined as the average across individual consideration of management style and funds (Mt denotes the number of available selection skill improves the prediction results funds in t) and over time (T ¼ 15 prediction substantially. periods): If factor returns are predicted vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi conditionally (model 2) instead of u 1 Xu 1 X T t Á Mt unconditionally (model 1), the prediction MSE ¼  ðE½~i;tþ1 Š À ri;tþ1 Þ2 r T t¼1 Mt i¼1 error is reduced by additional 10 per cent. Compared to model 4, the reduction is about (11Þ 30 per cent. Therefore, the conditional and prediction of factor returns seems to improve ! ` the forecast performance vis a vis the 1 X 1 X T Mt E½~i;tþ1 Š À ri;tþ1 : unconditional prediction. However, fund MAE ¼  Á r T t¼1 Mt i¼1 (12Þ Table 2: Forecast performance of prediction models The degree of accuracy of the respective Model MSE(%) MAE(%) HR(%) forecast does not necessarily translate into 1 21.15 19.04 66.89 large investment returns. To achieve large 2 19.85 17.89 67.31 investment returns, the direction of the 3 20.80 18.68 64.49 4 27.47 25.21 57.17 forecast (positive or negative) can be more164 2009 Palgrave Macmillan 1470-8272 Journal of Asset Management Vol. 10, 3, 158–169
  8. 8. Predicting returns of equity mutual fundsmanagers do not seem to be able to exploit performance, which will be investigated inthis predictability. Model 3 – which the next section.models the timing of factor returns of fundmanagers – does not improve forecast Decile portfoliosperformance compared to model 2. This Return forecast are mainly used to guideresult resembles the empirical evidence of investment decisions. Therefore, we furtherother studies that show that fund managers evaluate the forecast models from theare not successful in timing (for example perspective of an investor, and address theChan et al, 2002; Bollen and Busse, 2004). issue of whether forecasts of models 1–3 can Under the HR evaluation criteria, the be translated into investment decisions thatsame conclusions can be drawn. The use of are superior to those of the naıve model 4. ¨information on the fund manager’s selection This issue is investigated with decileskill and the fund’s style in general improves portfolios that are formed on the basis ofthe HR compared to the naıve model 4. ¨ estimates of each model’s expected returns.Furthermore, the conditional prediction of Therefore, for each prediction date, funds arefactor returns enhances the HR. Model 2’s ranked into deciles on the basis of theirHR of 67.31 per cent is slightly higher than expected return. Funds with the highestthe HR of model 1. Accounting for factor (lowest) expected returns are designated totiming by the fund manager (model 3), decile 1 (decile 10). The funds in each decilehowever, worsens the HR. portfolio are held constant for the prediction In summary, model 2 (conditional period (1 year), and are rearranged at theprediction of factor returns and use of next prediction date according to their newinformation on management style and expected returns. In each decile portfolio,selection skill) is the best forecast model, as funds are equally weighted. The yearlyexpected. The prediction error is almost 30 return of each decile portfolio is averagedper cent lower compared to the naıve model 4. ¨ over the 15 prediction periods. If a modelIn addition, model 2 produces an increase in produces good forecasts, the averagethe HR of more than 10 percentage points. return should decrease from decile 1 toThe consideration of these observations decile 10, with a large difference betweenshould result in a better investment decile 1 and 10.Table 3: Investment returns based on decile portfolios of prediction models Decile1 1 2 3 4 5 6 7 8 9 10 10–1Panel A: mean realized return1 9.68 9.64 10.25 9.79 8.91 9.68 7.63 8.40 8.00 6.58 3.102 11.00 10.30 9.79 10.00 9.65 8.86 8.51 8.33 7.73 4.78 6.22*3 9.41 10.47 9.66 9.07 7.96 9.22 9.10 9.34 8.27 6.20 3.214 9.56 9.53 9.54 9.87 8.81 9.20 8.85 8.26 8.35 6.97 2.59ALL 8.88Panel B: Sharpe ratio=(mean realized return–risk-free rate)/standard deviation of realized return1 18.15 22.20 23.80 21.69 18.42 21.97 13.96 17.34 16.11 9.97 8.182 25.55 23.91 22.45 22.30 21.84 18.55 17.38 16.98 14.70 0.79 24.76*3 19.22 25.18 22.68 18.91 14.72 20.75 19.23 21.39 16.91 7.03 12.194 19.15 22.07 23.05 22.55 19.02 20.33 18.46 15.64 17.28 10.01 9.14ALL 18.81* significantly greater than zero at 5% level. 2009 Palgrave Macmillan 1470-8272 Journal of Asset Management Vol. 10, 3, 158–169 165
  9. 9. Stotz Results for average returns of decile consideration of factor timing by the fund portfolios are displayed in Panel A of Table 3. manager, therefore, does not seem to Four main results can be observed from improve investment results. A likely reason Table 3. First, prediction model 2 shows the for this puzzling result seems, to us, to be best investment performance, and, therefore, that either fund managers lack timing skills or reinforces its superiority from the statistical a timing strategy is not being followed by the perspective. For example, decile 1 of fund manager. This notion is consistent with prediction model 2 produces a return, which empirical research that finds that fund returns is the largest of all prediction models (11.00 are not enhanced through timing (for per cent per year). This is about 200 basis example Chan et al, 2002; Bollen and Busse, points higher than the average of all mutual 2004). This issue is explored in more detail funds (symbolised by ‘ALL’), and almost 150 in the next section. basis points better than model 4. In addition, Fourth, the investment results for model 4 the difference between decile 1 and decile 10 are not as bad as suggested by its statistical is also the largest (6.22 per cent per year), and performance. Panel A shows that the naıve ¨ significantly different from zero. The average model 4 is able to select funds that perform return decreases almost uniformly from slightly better than the average fund. For decile 1 to decile 10. Thus, the superior example, decile 1 achieves an average return forecast performance from the statistical of 9.56 per cent per year, whereas the perspective, displayed in the last section, can average mutual fund delivers just 8.88 per also be translated into a superior investment cent per year. The difference between the performance. The use of information on the returns of decile 1 and of decile 10 (displayed fund manager’s selection skill, the fund’s style in the last column) is 2.59 per cent per year, and the conditional prediction of factor which indicates that winner funds returns also results in a good investment outperform loser funds (although the performance. difference is not statistically greater than zero Second, the conditional prediction of at the 5 per cent level). This result indirectly factor returns results in a better investment supports the findings of Elton et al (1996), performance than the unconditional who provide evidence that the performance prediction (model 2 is better than model 1). of newly invested money (that is primarily in The conditional prediction of factor returns funds with high past returns) marginally increases the performance by an additional outperforms money already invested. A likely 132 basis points per year (decile 1). The reason for this observation seems to be a predictability of factor returns translates, positive correlation between alpha and the therefore, into substantial investment gains, past year’s returns. Therefore, the past returns and investors can benefit from the seem to proxy partly the stock selection skill conditional prediction of factor returns by (although not as well as alpha itself). selecting funds that have a high style Panel B shows the corresponding realised coefficient (that is factor loading) for the Sharpe ratios of each decile portfolio. The style that is expected to achieve a high results reinforce the forecast power of return. model 2. For example, decile 1 of model 2 Third, the results of model 3 show that achieves the highest Sharpe ratio, which is fund managers are not able to exploit the substantially larger than the Sharpe ratio of predictability of factor returns. Model 3 – the average fund and of model 4 (naıve ¨ which considers the factor timing of fund model). The Sharpe ratio of model 1 managers – leads to inferior investment decreases uniformly from decile 1 to decile results compared to model 2, and to almost 10, indicating that this model can successfully the same results as model 1. The discriminate good funds from bad funds. On166 2009 Palgrave Macmillan 1470-8272 Journal of Asset Management Vol. 10, 3, 158–169
  10. 10. Predicting returns of equity mutual fundsthe basis of the test statistics of Jobson and decisions. In addition, parameters areKorkie (1981), the difference in the Sharpe estimated with a large estimation error, andratio between decile 1 and decile 10 (last average t-values are small. Only 9 per cent ofcolumn) is significantly greater than zero at all gammas are significantly greater than zerothe 5 per cent level. Therefore, the superior at the 5 per cent level. In contrast, styleinvestment performance reported before parameters’ betas are estimated with a lowerdoes not seem to be the result of a larger risk prediction error, resulting in 59 per cent(measured by the standard deviation of significant betas at the 5 per cent level (notreturns), but instead of superior return reported in Table 4).forecasts. We additionally investigate the stability of estimated timing parameters. A positive relation between past parameters and futureWhy does modelling timing of parameters is a necessary condition to inferfund managers not improve future timing skills from past return data (thatforecasts? is persistency of skills). Therefore, pastResults from the decile analysis summarised parameter estimates are regressed on futurein Table 3 suggest that the modelling of a parameter estimates:fund manager’s factor timing decision does ^i;t ¼ intercept þ slope Á ^i;tÀ1 þ ei;t g gnot improve investment performance. In thissection, we explain this result by We regress past parameters (denoted byinvestigating timing coefficients in more g g ^i,tÀ1) on future parameters (denoted by ^i,t)detail. We obtain two results: first, estimated in a pooled regression approach. Pasttiming parameters are, on average, not parameters are estimated from 1990 to thesignificantly different from zero. This prediction date, and future parameters areindicates that the average mutual fund estimated over the year following themanager is not a good market timer. Second, prediction date. A positive slope thenfuture timing parameters cannot reliably be indicates that timing skills persist. Table 5derived from past returns, as they display a shows that this is partly not the case. Futurelarge degree of instability. gammas are not consistently and positively Table 4 summarises estimates of gamma related to their past estimates. For example,from equation (6) over the full sample the future timing parameter for the marketperiod. Parameters are averaged over all factor is positively related to its past valueindividual funds. Estimated gammas are, on (slope for ^MAR equals 0.256, t-value ¼ gaverage, not significantly different from zero, 4.514), whereas the relation between thewhich indicates that fund managers are not future and past parameter on the momentumsuccessful market timers. Some average factor is negative (slope for ^1YR equals gtiming parameters are even smaller than zero À0.512, t-value ¼ À3.794). These results(size, momentum), indicating that fund suggest that timing is not a persistentmanagers are losing money with their timing management skill, which further explains theTable 4: Results for timing parameter estimates Table 5: Results for parameter stability from pooled regressions MAR SMB HML IYR g ^ g ^ g ^ g ^ ^MAR g ^SMB g ^HML g ^IYR gAverage 0.31 À0.381 0.491 À0.242Average t-value 0.754 À0.565 0.815 À0.241 Intercept 0.058 0.878 0.329 À1.561 t-value 0.372 3.765 1.124 À10.182The table displays estimated timing parameters from Slope 0.256 0.050 À0.104 À0.512equation (6), which are based on the estimation period t-value 4.514 0.876 À1.321 À3.794from 1990 to 2005. 2009 Palgrave Macmillan 1470-8272 Journal of Asset Management Vol. 10, 3, 158–169 167
  11. 11. Stotz bad investment performance of prediction We investigate various models from the models that include timing parameters. In statistical perspective and the perspective of a contrast, stock selection parameters alpha and mutual fund investor. From both style parameters beta display uniformly a perspectives, we found the most successful positive and significant relation between past model to be the one that considers the fund’s and future values with all t-values greater style, the manager’s stock selection skills and than 4 (not reported in Table 5). conditionally estimates the factor returns. These results help to explain the findings This model is able to select funds that of the last sections. Skill and style can be outperform the average mutual fund by more predicted from past returns (and therefore than 200 basis points per year. Moreover, the persist), which leads to good forecast results. prediction error of this model is about 30 per Timing skills cannot be predicted from past cent lower than that of a naıve model that ¨ returns because parameters are (i) not only uses information in the past return. significantly different from zero and (ii) not The skills in timing should not be stable through time, resulting in no considered in the forecast model, as they improvement in investment returns. If mutual lower the forecast power of the respective fund investors want to exploit the predictability model. It seems that fund managers lack of factor returns, they should, therefore, not timing skills. Therefore, fund investors have rely on fund managers’ timing abilities. Instead, to switch between funds with the appropriate they should predict factor returns by style characteristics if they want to exploit themselves, and select funds that have – given the predictability of factor returns. The the conditional return expectations – the empirical results in this study have shown highest expected returns. For example, if the that such a strategy can be beneficial, as it conditional expected return for the factor increases the return of an additional 130 basis HML is exceptionally high, investors should points per year. The gains from conditional select value funds that have a high loading on forecasts of factor returns are, in practice, HML. Therefore, investors should follow an largely neglected. For example, fund- active style-switching strategy (as in model 2) tracking companies, like Morningstar, rank that replaces the non-existent timing abilities of funds according to measures of past fund managers. performance but not by expected returns, thereby neglecting the benefits from factor return predictability, even though these seem CONCLUSION to be an important issue, as shown by the In this paper, a multifactor model for empirical results of this study. predicting mutual fund returns has been investigated. The factor model considers four sources of risk of stock returns: market return, size return, value return and NOTES 1. BVI is the German mutual fund association. momentum return. These risk factors have 2. Survivorship bias is an important issue in mutual fund been found to successfully explain the cross- performance studies, as poorly performing funds disappear section of stock returns, and have been more frequently from the mutual fund universe than good extensively used for evaluating fund returns. performing funds do (for example Brown and Goetzmann, 1995). As a result, performance measures based on samples In terms of mutual fund management, three of surviving funds may be upwardly biased (for example sources from the multifactor model Brown et al, 1992; Malkiel, 1995; Gruber, 1996; Carhart contribute, then, to the expected mutual et al, 2002). 3. MSCI ¼ Morgan Stanley Capital International fund return: the fund’s style, the manager’s 4. As the empirical analysis focuses on the German mutual skills in stock selection and timing and the fund market, the portfolios include all German stocks that predictability of factor returns. are in the database of Datastream.168 2009 Palgrave Macmillan 1470-8272 Journal of Asset Management Vol. 10, 3, 158–169
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