An Empirical Study Of Performance Evaluation Of Mutual Funds

Bayesian statistics is widely used in financial econometrics analysis and Bayesianmethod plays an important role in parameter estimation. Traditional frequentist method ofmutual funds performance evaluation is mainly based on history data, neglectinginvestors’ prior beliefs. In contrast, Bayesian method could overcome this drawback,combining the information from different sources. However, current methods of Bayesianmutual funds performance evaluation overlook the impact of the average level of skill inthe universe of fund managers and the variability around that average level for differentfunds on the estimation of individual funds.This paper detailed the basic principles of mutual funds evaluation, constructedBayesian hierarchical learning prior model, and introduced different prior beliefs ofinvestors:diffuse prior and somewhat prior. Considering two cases of the mutual fundsmanagers with skill and without skill, we simulated returns for10funds,100funds,1000funds using Monte Carlo simulation, and applied Markov Chains Monte Carlo method toestimate avearge level of skill, the posterior mean and variation of individual funds. Theresulting estimation is very close to the true value, which demonstrates the precision ofour Bayesian method. In the empirical section of this paper, the Bayesian hierarchicalmodel was constructed. We employed a sample of mutual funds with return observationsfrom2005to2010, aggregated the information from the estimation of the average level ofskill and the variability aroud that average level for different funds, which produced fairlyprecise estimates ofμ αand individual alpha. The results revealed that about35mutualfunds had excellent performance and got excess returns. Under the traditional frequentistmethod, only one fund could gain excess return under statistical significance. The methodof Bayesian hierarchical prior learning model not only demonstrates how the prior beliefscan affect investors’s final decision but also sucessfully solves the limitations of traditionalfrequentist method which is subjected to the precision of data and the significance level.