1 A Bayesian Approach to Estimating Mutual Fund

Accurate estimation of mutual fund statistics, such as mean return and standard deviation , can help shedding some light onto whether some mutual funds can consistently outperform the general market. In addition, it can help investors make more sound investment decisions. Because the available sample of returns is often not enough to give suucient conndence in the estimates, we propose a novel Bayesian estimation approach, whereby the priors are obtained from the general market returns (by general market we mean the collection of thousands of available mutual funds). The justiication for this is that any mutual fund is a subset of the general market, and it will therefore inherit some of its statistical properties. The advantages we gain is that we make use of the extensive sample size of the general market returns to ne tune our fund return estimates. The problem we face, however, is that the a priori density of the mean and standard deviation of the general market returns are unknown. The reason is that for an individual fund, the mean and standard deviation of the return can not be obtained exactly, as we can only estimate them from the nite sample available from historical data. In this paper we develop a new algorithm to tackle this estimation problem. We develop an EM-like algorithm that iteratively obtains the desired estimates. In addition, we present an approximate analytical solution to this problem. We use our approach to produce novel rankings of some available mutual funds. Our approach is not limited to mutual fund estimation and can be applied whenever parameters from a group of populations have to be estimated. There has been a raging debate about whether there are trading strategies or money managers that can consistently beat the general stock market. Although the dominant belief now is that the stock market exhibits some predictability, it is not clear whether this predictability oosets the associated risk. Researchers have looked at the performance of mutual funds for evidence. There are funds that consistently produce risk adjusted returns higher than the overall market. However, taking into account that there are over 4000 mutual funds, one cannot rule out the possibility that this is merely due to chance, by sheer number of funds. The topic of data snooping presents an analytical framework for assessing the eeect and bias due to 1. Also holds a position as Research Scientist with Simplex Risk …