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UK Mutual Fund Performance: Genuine Stock-Picking Ability or Luck Keith Cuthbertson1 Tanaka Business School Imperial College London Dirk Nitzsche1 Tanaka Business School Imperial College London Niall O’ Sullivan1,2 Department of Economics University College Cork, Ireland (email:niall.osullivan@ucc.ie) May 2004 Abstract We use a bootstrap technique to construct a distribution of abnormal performance among UK equity mutual funds under a null hypothesis of zero abnormal performance. Such a distribution of random sampling variation around no abnormal performance is employed as an estimate of, or proxy for, luck in mutual fund performance. Actual performance is then compared against this luck distribution. Using a number of alternative risk adjustment performance models, we find that a small proportion of funds in the positive tail of a cross-sectional performance distribution produce a level of performance in excess of that which may be explained by good luck. Poor performance is generally found to be worse than bad luck. Please do not quote or reproduce without author permission. 1. The authors are grateful to Micropal for providing the mutual fund data set used in the analysis. 2. The author wishes to gratefully acknowledge financial support from the Arts Faculty Research Fund at University College Cork, Ireland. 1 Section 1. Introduction This study examines the performance of open-end mutual funds investing in UK equity (Unit Trusts and Open Ended Investment Companies (OEICs)) during the period April 1975 to December 2002. A data set of 1,596 funds is examined. This represents almost the entire UK equity mutual fund industry at the end of the sample period. In contrast to the US mutual fund industry, there have been comparatively few studies of the performance of UK unit trusts. Studies of UK unit trusts have, for the most part, examined issues such as overall fund performance relative to a benchmark market index, survivor bias and performance persistence. A discussion of the literature on both the UK and US mutual fund industries is provided in section 2. This study advances the literature on UK mutual funds by explicitly controlling for random sampling variability in the performance measure using a bootstrap procedure. By constructing a distribution of sampling variability under a null hypothesis of zero abnormal performance one can estimate the distribution of performance which is simply due to random chance or ‘luck’. This provides a means of determining whether the performance of funds with the best records is simply due to good luck or whether there is genuine stock picking talent on the part of the manager(s). Likewise, it is possible to evaluate whether the performance of the worst funds lies within the boundaries of random chance. Many studies of UK equity mutual fund performance1 rank fund performance and examine whether there is persistence in this performance among the top and bottom funds in subsequent periods throughout the sample period. Performance may be based on raw returns or on a risk adjusted measure which controls for the return premia accruing to the risk characteristics of the stockholdings within the fund. However, while these methods correct for common variation in fund returns, they do not correct for idiosyncratic 1 A UK equity mutual fund is a fund in which at least 80% of the fund’s capital is invested in UK equity, as defined by the Investment Management Association (IMA), formerly the Association of Unit Trusts and Investment Funds (AUTIF). The fund is not necessarily operated from within the UK. Of the 1,596 UK equity funds examined in this study 305 are operated from outside the UK. 2 variation. This is important because with such a large number of mutual funds in existence one would expect that a number of funds will exhibit strong performance simply due to chance. However, the extant literature on UK fund performance does not explicitly model the role of luck in performance. The role of luck in mutual fund performance among US equity fund managers was first directly addressed by Kosowski, Timmermann, Wermers and White (2003). Kosowski et al apply a bootstrap technique to establish the sampling variation in the performance measures under a null hypothesis of zero abnormal (risk adjusted) performance and compare the actual distribution of US fund performance against this bootstrapped distribution. A common difficulty in examining fund performance is that of survivor bias. Excluding funds which have failed to remain in existence throughout the sample period and drawing inferences about overall mutual fund performance based only on surviving funds can induce a potentially serious bias in such findings. This study controls for survivor bias by including 450 nonsurviving funds among the 1,596 funds which are examined. This study also comprehensively examines UK equity unit trusts by evaluating their performance using a greater number of alternative models of performance measurement than identified in the extant literature. Performance measurement models are extended to include conditional risk factor loadings and conditional abnormal performance as well as conditional market timing models. The momentum effect in stock returns is also examined as a source of cross-sectional variation in unit trust performance. In addition, the sample period under investigation in this study is the longest among similar studies. Examining such a wide range of performance measurement methods over a relatively long sample period reduces the risk that findings could be model or sample period specific. 3 Fund performance may also be influenced by the investment objective of the fund. In this study funds are classified by their self-declared investment objective. These include growth stock funds, income stock funds, general equity funds (income and growth) or small company stock funds. One cannot be certain that these investment style characteristics of the fund are adequately controlled by standard risk adjustment measures. Therefore, in order to investigate whether stock picking skills vary across funds with different investment objectives, this study also carries out the bootstrap analysis separately among funds with these four different investment styles. Kosowski et al (2003) find that many of the US funds with apparent stock picking ability, or fund “stars”, are those with growth oriented investment strategies. This study will identify whether such findings transfer to the UK mutual fund industry. In addition, by examining the stock picking skills of funds which specialize in small company stocks, this study investigates the claim that the market for small company stocks is less efficient and is therefore more easily exploited by small company mutual funds. This study proceeds as follows: Section 2 describes the literature on performance measurement and persistence in performance among international studies, the vast majority of which are studies of the UK and US mutual fund industry. Section 3 describes the bootstrap methodology used to provide an estimate of luck in performance. Section 4 describes models of performance measurement and applies these models to the sample of UK equity mutual funds in this study from which a number of ‘best-fit’ models are selected for the bootstrap analysis. Section 5 provides a description of the data set of mutual funds and other variables used to measure performance. In section 6 the findings from the bootstrap analysis are reported while section 7 concludes. 4 Section 2: Literature Review Available on Request. Section 3. Methodology Many approaches to estimating mutual fund performance rely on estimating hypothesised models of equilibrium security returns in order to measure abnormal (risk-adjusted) performance. In turn, inferences regarding the statistical significance of abnormal performance are often based on standard statistical tests of measures such as alpha (Jensen’s alpha, Carhart’s alpha etc). There are two central difficulties with these approaches. First, for their statistical validity these tests require that the alpha performance measure be normally distributed. However, as will be seen in section 4 the residuals from Jensen, Carhart and other equilibrium model regressions are highly non-normal for around 70% of the mutual funds in the sample under investigation in this study. Hence the vector of model random disturbances may be poorly approximated by multivariate normality and in turn the distribution of alpha may not in fact be normal as required. Furthermore, it is also found that high variance non-normal residuals are far more prevalent in the top and bottom performing funds relative to the middle ranking funds and it is the former group of funds which are of most interest. Second, with such a large number of UK equity mutual funds in existence, 1,596 in this study, one would expect that some funds will appear to exhibit abnormal performance simply due to chance alone. Therefore, the question arises as to how genuine stock picking ability may be distinguished from simple ‘good luck’. Likewise, how may true inferior performance be distinguished from bad luck? Following from Kosowski et al (2003), the bootstrap procedure in this study is an attempt to establish the boundaries of performance (good and bad) that is explicable by chance. Observed performance in excess of this is deemed to be superior/inferior. 5 Adopting the Kosowski et al (2003) methodology, this study bootstraps the abnormal performance measure, (alpha or the t-statistic of alpha), under a null hypothesis of abnormal performance equal to zero. This allows a sampling distribution of fund performance to be constructed where ‘true’ abnormal performance is not present among funds. The procedure is to simulate the fund return under the null hypothesis (say 1,000 times) for each fund in the sample. In each simulation the performance model is reestimated and the cross-section of performance measures are ranked from highest to lowest. Over 1,000 simulations this provides 1,000 best alphas, 1,000 second best alphas etc to 1,000 worst alphas, ie a distribution of performance is constructed under the null hypothesis at each point/percentile in the ranked cross-sectional distribution of performance. These bootstrap distributions represent random sampling variability in the performance measure at each point in the performance distribution around a ‘true’ value of zero, ie they are estimates of random chance or ‘luck’. We then compare the cross-sectional ranked measures of actual fund abnormal performance against the empirical bootstrap distribution of fund alphas under the null hypothesis at each point in the performance distribution. For example, we compare the highest ranked actual fund alpha against the distribution of performance under the null hypothesis at the extreme top end of the performance distribution. Similarly, we compare the second highest ranked fund alpha against the bootstrap distribution of performance at the second highest point in the performance distribution etc. The bootstrap p values indicate the probability of observing the actual observed level of performance simply due to random sampling variability in the performance measure around a true value of zero, ie the probability of observing this actual performance due to random chance or ‘luck’. The estimate of luck is based on the (large) sample of peer group funds. Alternatively, for any given level of performance, good or bad, one can identify how may funds in the sample one would expect to achieve this level of performance by chance and compare this to how many funds actually achieve or exceed this performance. 6 Equally, one can evaluate the bootstrap distribution of the t-statistic of alpha under the null hypothesis of zero abnormal performance, Ho: αi = 0, and compare this bootstrap distribution to the observed t-statistic of alpha. Using t-statistics has more reliable statistical properties. Funds with fewer observations may be estimated with higher variance and less precision and will in consequence tend to generate outlier alphas. There is a risk therefore that these funds will disproportionately occupy the extreme tails of the actual and bootstrapped alpha distributions. The t-statistic provides a correction by scaling alpha by its estimated precision. The distribution of bootstrapped t-statistics for extreme values of the unmodified return t-statistics is likely to have fewer problems with high variance relative to the bootstrap distribution of alpha at that percentile in the performance distribution. For this reason in this study, the t-statistic of alpha is employed as the measure of abnormal performance and the bootstrap methodology described above is implemented for the t-statistic of alpha. All t-statistics are based on Newey-West heteroscedasticity and autocorrelation adjusted standard errors. The bootstrap procedure has the advantage that it provides a nonparametric approach to statistical inference about performance as it makes no assumptions about the shape of the true distribution of performance measures. As such the bootstrap technique provides an improved picture of the ‘empirical’ distribution of the performance measures such as alpha. To further improve the precision of performance estimates one can impose a minimum number of observations requirement for a fund to be included in the analysis. As indicated, an insufficient number of observations in the estimation is likely to increase the sampling variability of the resulting estimates which affects the tails of the actual and bootstrap performance distribution. In this study a minimum of 60 monthly observations is set as the requirement for the inclusion of funds in the analysis. The disadvantage with this approach, however, is that it may impose a certain survivor bias by restricting the examination to funds which have been skilled or lucky enough to survive for five years. 7 To examine the significance of this issue the sensitivity of the bootstrap results can be tested for a number of alternative minimum observations specifications. In order to provide a comprehensive study of performance and to test the robustness of results, the bootstrap test is applied to alternative performance measurement models, ie both single and multi-factor models with unconditional and conditional factor loadings and alphas. Performance measurement models commonly applied in the literature are now described in the next section. Section 4. Performance Measures and Model Selection 4.1 Performance Measurement An appropriate method of adjusting for risk is required when examining mutual fund performance. The performance measure depends on the asset pricing model chosen to represent the cross section of expected returns. The most common measures that appear in the literature and the measures that will be bootstrapped in this study are presented in this section. First, the theoretical basis for the performance measurement models is discussed. All models are then applied to the data set of UK mutual funds with a view to selecting subsets of appropriate models with which to perform the computationally intensive bootstrap analysis. 4.1.1 Jensen’s Alpha Measure The Jensen (1968) measure represents abnormal performance based on a single risk factor model, ie the CAPM specification (4.1) (Rit-Rf) = αi + βi(Rmt-Rf) + εit where Rit is the expected return on fund i in period t, Rmt is the expected return on a market proxy portfolio, Rf is a risk free rate, typically proxied in empirical work by the return on a treasury bill. If the CAPM is the correct model of equilibrium returns then the 8 portfolio should lie on the Security Market Line and the value of alpha should be zero. Therefore, a positive and statistically significant value of alpha is hypothesised to indicate superior risk adjusted performance or stock picking skills (selectivity) on the part of the fund manager. That is, a positive alpha indicates that the portfolio has performed better than a random selection buy-and-hold strategy. Alpha may be estimated empirically from least squares regression of (4.1). Similarly, a statistically significant negative value of alpha is taken to indicate inferior risk adjusted performance. 4.1.2 Carhart’s Alpha Measure The Carhart (1997) measure is the alpha estimate from a four-factor model which is an extension of (4.1) and includes additional risk factors for fund exposure to size, book-tomarket value and momentum strategies to model expected fund returns: (4.2) (Rit-Rf) = αi + β1i(Rmt-Rf) + β2i(SMBt) + β3i(HMLt) + β4i(PR1YRt)+ εit where SMBt, HMLt and PR1YRt are risk factor mimicking portfolios for size, book-tomarket value and one-year momentum effects respectively in the stock holdings of the mutual funds. Carhart’s alpha may be estimated empirically from (4.2). The four-factor model is largely based on the empirical findings of Fama and French (1992 and 1993) and Carhart (1995). Fama and French (1992 and 1993) find that a three-factor model including market, size and book-to-market value risk factors provides significantly greater power than the CAPM alone in explaining common variation in stock returns. Fama and French (1992) report a strong negative relationship between stock returns and size: smaller firms tend to have higher average returns (the authors report a spread of 0.74% per month on average based on their size rankings). The size factor, SMB (‘small minus big’), is a measure of the difference between the returns on small versus big stocks2. The economic rational underpinning the specification of a size risk factor is related to relative prospects. The earnings prospects of small firms may 2 The calculation of SMB and the other risk factors in (4.2) is described in Section 5. 9 be more sensitive to economic conditions with a resulting higher probability of distress during economic downturns. There is also the concern that small firms embody greater informational asymmetry for investors than large firms. Both these factors imply a risk loading for size and a higher required return by investors. Fama and French (1992) also report a strong positive relationship between stock returns and the book-to-market value ratio: stocks with high book-to-market ratios have higher average returns than low book-to-market value stocks (the authors report a spread of 1.5% per month between the highest and lowest book-to market stocks in their study). The book-to-market value factor, HML (‘high minus low’), is a measure of the difference between the returns on high versus low book-to-market stocks. As Fama and French outline, if stock prices are rational the book-to-market value ratio should reflect firms’ relative prospects. A high book-to-market ratio firm indicates low earnings on assets relative to low book-to-market firms. Consequently, there is a high book-to-market or ‘value’ premium. Alternatively, if stock prices are irrational the cross-section of book-tomarket ratios may be the result of market overreaction to the relative prospects of firms. High (low) book-to-market ratios represent firms whose prices have ‘overshot’ on the downside (upside) and therefore the ratio predicts the cross-section of stock returns. The fourth risk factor, PR1YR, in (4.2) is an additional factor capturing Jegadeesh and Titman’s (1993) one year momentum anomaly. The PR1YR variable is the difference in returns between a portfolio of previously high performing stocks and previously poor performing stocks. Its specification in (4.2) captures a fund’s sensitivity to following a zero-investment strategy of investing in past strong performing ‘momentum’ stocks and short-selling stocks with low past returns. Carhart’s main motivation for examining momentum effects is due to the inability of the Fama and French three-factor model to explain cross-sectional variation in ranked portfolio returns. Carhart finds that the momentum variable explains almost half of the spread in returns between the top and bottom decile portfolios of funds ranked by raw return. In a sense, the momentum factor is specified due to an ex-poste hypothesis that it ‘must be’ providing a proxy for a risk factor that explains a significant amount of common variation in fund returns. However, 10