1. Laurent BarrasMcGill University - Faculty of ManagementO. ScailletUniversity of Geneva - HEC; Swiss Finance InstituteRuss WermersUniversity of Maryland - Robert H. Smith School ofBusinessPresentation: Chinbat.DLecture: Dr. Tony Chieh-tse Hou30th May 2011Working Paper No. RHS-06-043

2. CONTENTS page 2 3. Introduction 1952 Harry Markowitz he came with idea fund manager have to look at Risk 1964 Willian Sharpe CAPM introduced a risk-adjusted measure portfolio performance.[Rp-RF]/SD=excess return/risk Then look at definition of Beta measures the volatility a portfolio versus market portfolio Then look at definition of Beta came up it measures the Also managers outperform market return that called alpha if volatility a portfolio versus market portfolio B=1 manager that ability outperform market alpha > 0 positive however manager underperform market alpha< 0 negativeAlpha is a risk-adjusted measure of active managersperformances. the return of a benchmark is subtracted in orderto consider relative performance, which yields Jensen alpha.Footer Text 4. introductionthis working paper lead to False discoveries in Mutualfunds measures a alpha. 2076 fund but it is notsignificant number on this working paperFooter Text12/10/2011 4 5. To control for False discoveries of mutual funds that exhibitsignificant alphas by luck alone.separates fund into 1 Unskilled 2 zero-alpha 3 skilled even dependencies in cross-fund estimated alphas. 75% of Funds a zero-alpha consistent with the Berk and Green 2004 equilibrium. Prior to 1996 find a significant proportion skilled positive alpha but almost none by 2006 also show that controlling for false discoveries substantially improves the ability to find with persistent performance. 6. This paper have new approach to controlling for FD in a multiple fund settingusing a econometric tests Estimated alpha t-statistic /truly negative or positive alphas / Determine the frequency of FD /proportion of zero-alpha/ P-value for individual fund Monte-Carlo experiment accurate partition of mutual fund into zero-alpha unskilled, and skilled funds Cross-sectional dependencies among fund estimated alpha The monthly return of 2076 activelyMeasure estimate managed U.S open-end, domestic-equitymutual funds between 1975-2006 Long-term performance 75.4% are zero- alpha fund managers having stockpicking ability 24.0% are unskilled (true a 0) Berk and Green 2004Footer Text 12/10/2011 6 7. 1.The impact of luck on mutual fund performanceFooter Text 12/10/2011 7 8. the large cross-section of funds in our database makes these estimatedproportions very accurate estimators of thetrue values, even when funds arecross-sectionally correlated. Monte Carlo simulations, that our simpleapproach is quite robust to cross-fund dependencies.High proportion of unskilled funds prior to measure flows These skilled funds are concentrated in the extreme right tail ofcross-sectional estimated alpha distribution which indicates that a very low p-value is accurate of short-run fund manager skill Aggressive Growth Highest proportion of skilled managers Growth& Income No funds exhibit skillsFooter Text 12/10/2011 8 9. To begin suppose that a population of M actively managed mutualfunds is composed of three distinct performance categories, whereperformace is due to stock-selection skills.Footer Text12/10/2011 9 10. Each of the above skill groups from performance estimates forindividual fund? suppose first use the T-statistic as performancemeasureThis procedure, simultaneously applied across all funds is multiple- HypothesisFooter Text 12/10/2011 10 11. Level of 5%, should expect that 5% of these zero-alpha funds will havesignificant estimated alphas-some of them unlucky (0) but all will be FD funds with significant estimated alphas, but zero-alpha trueFooter Text12/10/2011 11 12. Panel a shows the distribution of the fund t-statistic across the tree skill group. The true four factor alpha equal to (-3.2%) and +3.8% per year forthe unskilled and skilled funds are centered at -2.5 and +3the left and right tails of the cross-sectional estimated alpha determine thefrequency of FD the only parameter needed is proportion of zero-alphafunds in population 0.Footer Text12/10/2011 12 13. Does this area consist merelyof skilled funds as definedshaded region in left The above? overestimates the proportion of unskilled The same applies toClearly not because some funds canPanel B displays the very that the positive and significant region the three unskilled The probability exhibitfunds that t-statistic distribution it is a mixture of distribution this example set 75%, -23%, 2% to matchA average estimated valuelucky of the right tail of Panel zero alpha estimated t-stat of skilled fundfunds positive and significant over final 5 years of sample is lower that ti=-1.65 is less thatestimated t-stat0.001%Measure performance with a limited sample data, therefore unskilled and skilled funds cannot easily distinguished from zero-alphaFooter Text12/10/2011 13 14. How do to measure the frequency of FD in cross-sectional t-distribution Using this to determine expected proportion ofskilled fundsing equation that E(F)=3.75 (o) =75% zero-alpha fundsExhibits luck equal expected proportion of/2=10% lucky funds Using a simple Monte-Carlo experiment demonstrate thatapproach provides a much more accurate partition of mutual funds into zero-alpha, unskilled and skilled funds Footer Text 12/10/2011 14 15. this paper-determining the location of truly skilled (or unskilled) funds in the tails of the cross-sectional t-distributioncan only be achieved by evaluating Equations (3) and (4) at several different values of 7. For instance, if themajority of skilled funds lie in the extreme right tail, then increasing the value of 7from 0.10 to 0.20 in Equation (3) would result in a very small increase in E(T+), theproportion of truly skilled funds, since most of the additional significant funds, E(S-), would be lucky funds.Probability of including a zero-alpha in the portfolio equals 2.5% (85%) in population 2*85=1.7, 75*2.5=1.8 the lucky fundsequal to ((1.7/3.5))*3.8=1.8 per year.. Footer Text 12/10/2011 15 16. Measuring luck in a group setting, show as equation (2) is the estimatorof the proportion o, of zero-alpha funds in population The recent estimation approach developed by Storey (2002) called Falsediscovery rate The FDR approach is very straightforward, as its sole input are (two-sided)p-values associated with the (alpha) t-statistic of each of the M funds. FDR uses information from the center of the cross-sectional t-distribution/which dominated by zero-alpha/FDR technique is to estimate these frequencies-from the sample t-statisticsFooter Text12/10/2011 16 17. P-values larger than a sufficientlyhigh threshold =0.6 show in thefigureFooter Text 12/10/2011 17 18. measure the proportion of total area Is close to 75% which is the true valueof 0 Bootstrap procedure introduced by Storey 2002, it minimizes theestimated mean-squared error (MSE) of zero-alpha fundsUsing equation (6) the estimated proportion of unskilled and skilled funds equal to Footer Text 12/10/2011 18 19. Finally estimate the proportions of unskilled and skilled funds in the entire population asThis method is entirely data- driven, some flexibility in choice of*, as long as it sufficiently highSelect with a bootstrap procedure which minimizes the estimated MSE of skilled andunskilled alphas denoted bySimply setting *, to prespecified values0.35-0.45 produces similar estimatesFooter Text12/10/2011 19 20. The previous section has followed two alternativeapproaches when estimating the proportion of unskilledand skilled funds Panel A of figure 1 in the proportions 0,A-,and A+.for each zero-alpha fund the ratio (0.23/2) is held fixedto11.5 in figure 1, to assure that the proportion of skilledfunds remains low compared to the unskilled funds Second uses these sampled t-statistics to estimate theproportion of unlucky, lucky and skilled, unskilled fundsunder each approach First two steps 1000 times then compare the averagevalue of each estimator with true population value. Footer Text 12/10/2011 20 21. Assuming that o=0, the no luck approach consistently underestimates Panel C,D the true value propotion of true proportion of zero-alpha fundsthe unskilled, skilled fundsdecrease by construction when o=75% no luckis higher(large exhibits a o >0) upward bias estimate the total proportion of unskilled, skilled fundsE(T-)+E(T+) underestimatesPanel B are exactly same sinceproportion of true values equalsThe average value of the FDR estimatorThe fulltracks approach which assumes that o=1, closely luck true population valuedenoted by E(F-)Footer Text12/10/2011 21 22. In addition to the bias properties exhibited by FDRestimators, their variability is low because of the largecross-section of funds (M-2,076) Proportion estimator that depends on proportion of p-values higher than significant *, the law of LargeNumbers drives it close to its true value with largesample size *=0.6 threshold and =75%the standard deviation of75% is low as 2.5% with independent p-value Footer Text 12/10/2011 22 23. Mutual funds can have correlated residual if they herd in theirWermers (1999) stockholdings or hold similar industry allocationKTVVW show that a complicated bootstrap 13 necessary to test the significance ofperformance of a fund located at a particular alpha rank, since this test depends on thejoint distribution of all fund estimated alphascross-correlated fund residuals must bebootstrapped simultaneously.However, in order to explicitly verify the properties of our estimators, we run aMonte-Carlo simulation. In order to closely reproduce the actual pairwise correlationsbetween funds in our dataset. we estimate the residual covariance matrix directly fromthe data, then use these dependencies in our simulations. In further simulations, weFooter Text 12/10/2011 23 24. In this case, all fund p-value would be the same, and the p-valuehistogram would not converge to the true p-value distribution, as shown in Figure 2.Clearly, we would make serious errors no matter where we set *.Footer Text12/10/2011 24 25. Footer Text 12/10/2011 25 26. Variable DescriptionR i,t Is month (t) excess return of fund (i) over the riskfreeR m,t Month (t) excess return on (CRSP NYSE/AMEX/NASDAQvalue-weighted market portfolio(Rsmb,t)Month (t) return on zero-investment factor-mimicking(Rhml,t)portfolios for size, book-to-matket, and momentum(Rmom,t)Footer Text 12/10/2011 26 27. Unconditional four factor model for time-varying expose the market portfolio VariableDescription Zt-1Denotes the Jx1 vector of predictive variables measure at the end of month (t) 1975-2006 BIs the Jx1 vector coefficient Four variablesOne month T-bill yield: dividend yield of CRSP Value weighted NYSE/AMEX stock index The term spread, peroxide by the difference between yield on 10-year Treasury and three month T-bill, and the default spread proxied by the yield difference between Moodys Baa-rate and Aaarated corporate bondsFooter Text12/10/2011 27 28. 2076 open-end, domestic equity mutual funds existing for 60 monthsGrowth (1304 funds)Aggressive Growth (388 funds)Growth & Income (384 funds) Two data base are matchedTime periodJanuary 1975 Footer Text December 200612/10/2011 28 29. Estimated annualized alphaPanel A,B estimated alphas for each category are negativefrom -0.45%to-0.60% Aggressive Growth funds tilt toward small capitalization, book-to-market,momentum stockFooter Text12/10/2011 29 30. Footer Text 12/10/2011 30 31. However significant alpha does not always meancomprised of unskilledThat left-tail funds are overwhelmingly and not merely managerskilled fund unlucky funds have a relatively many significant alpha There are long fund life12.7 years on average funds in the right tail 8.2(170funds) in total populationThis is simply due to very lucky outcomes forsmall proportion of the 1565 zero-alpha funds in the populationFooter Text12/10/2011 31 32. Growth funds show similar results to overalluniverse of funds 76.5% have zero-alpha(1565 funds) 23.5% are unskilledLong-termexistence of thisG&I funds consist of largest proportion of category ofunskilled funds (30.7%)actively-managed funds, which includesvalue fundsand corefunds thesepoor results.A-Growth funds, 3,9% of them show true skillsFooter Text 12/10/2011 32 33. Entire period 1975-2006 may not accurately describe theperformance generated by industry before this rapidexpansion At the end of each year from 1989-2006, estimate theproportion of unskilled and skilled funds using the entirereturn history for each fund up to that point time On December 31, 1989 to December 2006 15year funds 1975-1989 (427 funds) basically in 32 years 75-06 (2076funds) Footer Text 12/10/2011 33 34. Unskilled funds rises from 9.2% to 24.0% of the entireuniverse of fund 1989to 2006, skilled fundsdeclines from 14.4% to 0.6%`During the 1990s generate very poor performanceThe growth industry has also affected thethat 24% of them are unskilled, while none are skilled alpha of the older funds created before Jan 1990 During 1997-2006 34.8% of these olderfunds are truly unskilled Panel B shows the yearly count of funds included in the Footer Text estimated proportion 12/10/2011 34 35. To test for short-run mutual fund performance in five years, beginningfrom 1977-1981 ending with 2002-2006 sub period have 60 monthly return observations Five years records together across all time periods to represent the average experience of an investor in randomly chosen fund during a randomly chosen five-year period total of 3311 p-valuesFooter Text 12/10/2011 35 36. Superior performance is rare butdoes exist compare to long-term In left tail unskilled and not merely Almost entirely additionunlucky zero-alpha funds is 5zero-alpha funds are luckytimes in proportion of unluckyCenter of the distribution produces almost no funds additional skilled fundsThe short-term result are similar to the long-termFooter Textresult of left tail funds are truly unskilled. 12/10/2011 36 37. The BG model implies that larger and older funds should exhibit lower alphas,since they have presumably grown (or survived) to the point where theyprovide no superior alphas, net of feespartly due to flows that followed pastsuperior performanceBG also implies that flow should disproportionately move to truly skilled funds and that these funds should exhibit the largest reduction in future skill The result are strongly supportive of BG modelFooter Text12/10/2011 37 38. Previous analysis reveals that only 2.4% of the funds are skilled over short-term Can it detect these skilled funds over time, in order to capture their superior alphas? Expected proportion of lucky funds included in portfolio at significance level :FDR+ target level z+, in persistence test : z+= 10%,20%,50%,70%and 90%Storey (2002) implement the following straightforward estimator of the FDRPortfolio formation date is Dec 1979 to Dec 2005 (5years return observed) 39. Higher FDR target means increase in the proportion of funds includedResult reveal that FDR portfolios successfully detect fund with short- term skillsIR=p-value/STDThe result sharply illustrate the short-term nature of trulyoutperforming fundsFooter Text 12/10/2011 39 40. How the estimate alpha of the portfolio FDR10% evolvesover time using expanding windows. The initial value 1989 Dec 31 yearly of out-of-sample // Measure over the period 1980-1989, Final value, 2006 Dec 31 is the yearly out-of-samplealpha Entire 1980-to-2006 measured over Footer Text12/10/2011 40 41. this performance advantage declines during later years,when the proportion of skilled funds decreasessubstantially, making them much tougher to locate.Therefore, find that the superior performance of the FDRportfolio is tightly linked to the prevalence of skilled fundsin the population. 41 42. This result indicates that only a small fractionof fund managers have stock picking skill /24%to 4.5/ The proportion of pre-expenseunskilled funds remains equal to zero until end 2003Poor skill cannot explainunskilled fundsFooter Text12/10/2011 42 43. F.F model have substantial risk premium over the period /9.4%/ CAPM model have substantial loading on the size and the book-to-market factor positive premium over sample period /3.7% and 5.7%per year/Footer Text12/10/2011 43 44. FRD measure also has natural Bayesian interpretationVariable DescriptionGi Random variable which takes the value of (i) (-1,0+0)FDR+ Fdr+Ti Positive and significant ofFooter Text 12/10/2011 44 45. Gi also provides some relevant information for modeling the fund alpha prior distribution in an empirical Bayes settingWBMW (2001) A full Bayesian estimation of fdr* requires to posit prior distributions for the proportions -1,0 and +1. and for the distribution parameters of Ti for each skill group. This method, based on additional assumptions (including independent p- values) as well as intensive numerical methods, is applied by Tang. Ghosal, and Roy (2007) to estimate the traditional FDR in a genomics study.Footer Text12/10/2011 45 46. FDR technique to show that proportion of skilled fund managers has diminished rapidly over 20 years, while the proportion of unskilled funds has increased substantiallyThis paper also shows that Long-term actively managed mutual fundunderperformance due to long-term survival of truly underperformingfund Most active managed funds provide positive zero net of expense alphas, putting them at least on passive funds. But it is still puzzlingMost key concept is econometric method in this paper work so far unskilled, zero-alpha, skilled in our data decreased by 2006 potentially wide applications in finace. It can be used to control luck in any setting in which a multiple-hypothesis test run and a large sample is availableFooter Text 12/10/2011 46