Review of Finance(2007)11:359–400hold it against me
doi:10.1093/rof/rfm018
Advance Access publication:25August2007
hotdogImproved Forecasting of Mutual Fund Alphas and Betas∗
HARRY MAMAYSKY1,MATTHEW SPIEGEL2and HONG ZHANG3 1Old Lane LP;2Yale School of Management;3INSEAD
Abstract.This paper propos a simple back testing procedure that is shown to dramatically improve a panel data model’s ability to produce out of sample forecasts.Here the procedure is ud to forecast mutual fund alphas.Using monthly data with an OLS model it has been difficult to consistently predict which portfolio managers will produce above market returns for their investors.This paper provides empirical evidence that sorting on the estimated alphas populates the top and bottom deciles not with the best and worst funds,but with tho having the greatest estimation error.This problem can be attenuated by back testing the statistical model fund by fund.The back test ud here requires a statistical model to exhibit some past predictive success for a particular fund before it is allowed to mak汽车打蜡步骤
e predictions about that fund in the current period.Another estimation problem concerns the u of a single statistical model for all available mutual funds.Since no one statistical model is likely tofit every fund,the result is a great deal of misspecification error.This paper shows that the combined u of an OLS and Kalmanfilter model increas the number of funds with predictable out of sample alphas by about60%.Overall,a strategy that us very modest ex-antefilters to eliminate funds who parameters likely derive primarily from estimation error produces an out of sample risk-adjusted return of over4%per annum.
JEL Classification:G12,G13
Over the last20years the mutual fund industry has grown at an incredible rate,and this has naturally attracted a lot of attention from the academic and financial community.One area of particular interest has been whether or not it is possible to identify fund managers with skills that investors can capitalize
六级怎么算分*We thank David Musto who critique of an earlier paper lead to the creation of the eight-factor model ud in this one.Additional thanks go to Jonathan Berk,Mark Carhart,Joshua Coval,Wayne Ferson,William Goetzmann,Peter Starr,Peter Bossaerts(the editor),and three referees for their comm
ents.Finally,we thank minar participants at INSEAD,Rutgers,the University of Michigan at Ann Arbor,the University of Calgary,and the University of Alberta and conference participants at the2005Winter Finance Summit,the2005Meetings of the Western Finance Association,and the2005Meetings of the European Finance Association. The Author2007.Published by Oxford University Press on behalf of the European Finance Association.
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360HARRY MAMAYSKY et al. on.The approach taken in this literature has been to apply a single statistical model to every available fund.But at any one time funds exhibit substantial differences in their strategies and holdings(Brown and Goetzmann(1997)). This makes it likely that any one statistical model will be incorrectly specified for at least some funds in the data pool.Also,as noted by Timmermann and Granger(2004),behavioral changes over time can cau a model that fits a subject in one time interval to fail in another.As a result many of the estimated parameter values ud to forecast fund returns(especially tho in the extreme deciles)may reflect misspecification error rather than reality. This paper propos a very simple back testing procedure to help alleviate this problem.The results indicate that with back testing even simple ordinary least squares(OLS)models,which have previously been found to exhibit little predictive power,produce u
ful forecasts for large subts of funds.Back testing is also shown to generate substantial improvements for the nonlinear models tested here.Overall,back testing,along with a combination of models, can produce portfolios encompassing over15%of the mutual fund population that yield economically and statistically significant predictable above market performance in any one period.
In general,the problem with using a single model for every fund in a time ries panel databa is that sorting on the estimated alphas(or any other attribute)may simultaneously sort on misspecification errors.If this happens, then models may not lect funds with predictable superior performance as ‘‘best’’but rather tho with the poorest parameter estimates,as the will tend to be the most extreme.1One possible way to help identify possible misspecification errors,and the one pursued here,is the following algorithm: prior to using a model to forecast a particular subject’s performance in the current period it mustfirst generate acceptable out of sample forecasts in the recent past.This helps to avoid using the model’s in sample attributes to determine if it will do well out of sample.Intuitively,if one wishes to u a model tofind funds that will produce future above(or below)market returns it ems natural to require at least some past success in this regard.If an extreme high alpha fund underperforms in the recent past,one might strongly suspect that there may be some problem with the model’s forecasting ability,at least for the moment.The same should be tru
e for an extreme low alpha fund that overperforms.Conquently,the back test propod here requires a model to correctly predict the sign of a fund’s excess return in the previous month before 1This argument is similar to the size anomaly critique found in Berk(1995).There he argues that mistimated betas will lead to the appearance that smallfirms outperform large ones on a risk-adjusted basis.Roughly,all el equal,higher discount rates lead to smaller market capitalizations.To the degree that a model mistimates beta,thefirm’s market capitalization will then proxy for the true cashflow risk.
FORECASTING OF MUTUAL FUND ALPHAS AND BETAS361 allowing it to make predictions about the fund’s future behavior.Applying even this simple criterion yields a dramatic improvement of the risk-adjusted return for top mutual fund deciles lected by either the one or Carhart’s four–factor OLS model.Monthly returns jump from initial values of−8basis points(bps)and18bps to the economically and statistically significant values of21bps and37bps,respectively.武汉出国
Beyond that,this paper also shows the benefits of simultaneously using multiple models.Back testing implies that any one model will not be ud to generate forecasts for every single subject.Thus,by using multiple models the t of funds for which one might produce uful forecasts potentially widens. To illustrate the point a dynamic Kalmanfilter model is tested along with the standard rolling
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OLS model.2The models provide a good pairing as they offer very different costs and benefits and(with the help of back testing to clean out misspecification errors)capture different types of managerial skills.Rolling OLS models are simple to estimate.But they require that a portfolio’s parameters drift slowly over time,if at all.If a fund actively trades curities during the(typically)estimated5year window,the resulting parameter estimates may not accurately reprent the current situation.3A Kalmanfilter model can potentially adapt itlf to such changes and avoid this problem.4
Similar to the OLS ca,with back testing the Kalmanfilter models successfully lect funds with out of sample risk-adjusted abnormal returns in excess of3.5%per annum.More importantly,each model lects a relatively unique t of funds with an overlap of only about a third.This implies that it is possible tofind a remarkably wide variety of funds with positive(or negative)predictable risk-adjusted returns if one is willing to employ a variety of models.Hence,instead of running a hor race among different models and picking a‘‘winner,’’this paper demonstrates the benefit of simultaneously using more than one model.By going from one model to two,the t of funds with predictable super normal returns increas by about50%.Meanwhile, 2See Mamaysky et al.(2007)for a detailed derivation of the Kalman model bad on dynamic lection ability.
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3One solution can be found in Grinblatt and Titman(1994).The methodology they u avoids a direct comparison against a specific portfolio,and instead us an‘‘endogenous’’benchmark. However,their technique requires knowledge of the fund’s actual composition,which may not always be available.Ferson and Khang(2002)extend the technique to condition the portfolio betas on exogenous variables such as macro economic data.
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4Grinblatt and Titman(1989)also propo a technique that can detect market timing abilities that ari from a fund’s dynamic ast allocation strategy,and implement it in their1994paper. However,as Ferson and Schadt(1996)point out,correlations between factor loadings and market returns may also be due to predictable changes in time varying expected returns,and thus implement a technique for handling this ca.
362HARRY MAMAYSKY et al. funds jointly lected by the OLS and Kalman models within the top decile, presumably the funds run by managers with more than one type of managerial talent,can have risk-adjusted returns as high as6.0%per annum.
Whether or not statistical models can identify fund managers who will produce positive risk-adjusted returns for their investors has implications regarding the general functioning of markets.If such skills
joondo not exist then this calls into question the value of fundamental analysis and active management,at least for mutual fund investors.On the other hand,if such skills do exist,but are somehow bid away when discovered,then this offers support for the Berk and Green(2004)hypothesis regarding fund returns in an efficient competitive environment.5Overall,this paper’sfindings offer support for at least part of their thesis:managerial skill exists but its benefit to mutual fund investors is short lived.
Carhart’s(1997)paper documents how momentum returns can make it appear that some managers can,at least temporarily,appear to produce positive alphas going forward even when they cannot.In order to get around hisfindings,performance studies have since tried using more comprehensive data ts and/or improved methodologies.One approach has been to u the underlying holdings data,as in Chen et al.(2000),Cohen et al.(2005),and Kacperczyk et al.(2005a),and Baker et al.(2004).Another has been to u Bayesian models as in Avramov and Wermers(2005)and Bus and Irvine (2005),or daily data as in Bollen and Bus(2004).Recently,Kosowski et al. (2007)looked at whether it may be possible to detect the existence of funds that have outperformed the market by dropping the assumption of normality associated with classic t tests and instead using boot strapped standard errors. Theyfind that boot strapped standard errors indicate that some managers are able t
o produce positive alphas.However,out of sample their results are similar to Carhart(1997).Top deciles funds yield alphas of0.08%per month.With the boot strapped standard errors this is statistically significant while under the standard t test it is not.This paper can be en as both complementing and extending this literature.The simple back test propod here allows even the one factor OLS model to reliably identify funds that will produce above market returns of economic significance using classic t tests. This obrvation suggests that misspecification error is conceivably the main impediment preventing traditional models from identifying superior funds.It also suggests that it is perhaps too early to give up on traditional models and 5The published model excludes the cost of arching for funds with superior managers and thus states that investors literally earn zero excess returns from their mutual fund investments. However,as discusd later on in this paper,with positive arch costs well designed strategies should be profitable.
FORECASTING OF MUTUAL FUND ALPHAS AND BETAS363 data ,Hendricks et al.(1993),Brown and Goetzmann(1995))in the quest tofind managerial talent ex-ante.
someThe back testing procedure suggested here can also potentially strengthen thefindings and methodologies within the above and other related papers. Indeed,this has started happening.Kacperczyk et al.(2005b)u a variant of the back test propod here to improve their mo
del’s ability to forecast fund returns bad on the difference between obrved returns and tho calculated from the reported holdings data.6Future rearch will undoubtedly show that other(better)back testing procedures can be employed.Still,it should be emphasized that the goal here is not to produce an‘‘optimal’’estimator or back test.Rather,the goal of this paper is to develop an effective and simple procedure that is likely to be robust across a variety of possible situations and thus potentially a heuristic for future rearch.Having said that,it is not obvious that more complexfilters alone will in fact yield better results.The difficulty is that misspecification errors can influence the values generated by any statistical model in a variety of ways and thus,to the degree,more complex filters are less robust they may yield inferior results.In fact,this paperfinds just that.When the estimated betas are ud as part of the back test the resulting portfolios exhibit poorer performance.Alternatively,one might think to u a model’s diagnostics,like the estimated alpha’s t statistic.However,this too yields inferior results relative to simply using the model’s forecasting success in the previous period.
The paper’s negativefinding regarding more complex back testing methodologies may be due to the possibility that misspecification errors lead not only to large parameter estimates but also to erroneously good in sample diagnostics.The problem is that admitting that a model may be misspeci
fied is tantamount to admitting‘‘we do not know what we do not know.’’This can be en in the negative results generated by Bossaerts and Hillion(1999)and Goyal and Welch(2006).Both studies try various model switching criteria andfind no out of sample predictability regarding the equity premium(Goyal and Welch evenfind it degrades the resulting portfolio’s performance).Both studies also suggest that‘‘model instability,’’which is a form of misspecification error,may be to blame.Thus,as indicated here, simpler(and potentially more robust)tests may in the end produce the best results.
Since mutual funds u‘‘closing prices’’to calculate end of day net ast values(NAV),any model may appear to lect funds with positive abnormal 6They cite this paper as the source for the procedure.
