# Regression Analysis and Mutual Funds

**Topics:**Regression analysis, Mutual fund, Statistical hypothesis testing

**Pages:**14 (2750 words)

**Published:**December 22, 2012

Introduction

Mutual funds are the name of open-end investment companies, which collect a pool of funds from individual investors to invest in securities such as bonds, stocks or other assets. The main advantages of mutual funds are diversification and professional management. However, if the mangers lack the ability to outperform the market index, individual investors will lose invests. Therefore, it is important for individual investors to evaluate whether the managed portfolio beats the market or not. The propose of this project is to measure the performance of mutual funds and analyse the skills of the manager by producing three models gradually with data from 1968 to 2005. Model discrible

To gain the most suitable model, this project starts conducting model with the basic single factor model-CAPM and then adds other factor premiums such as SMB, HML, mom and TradedLIQ gradually. CAPM describes that the excess return of risk asses is linearly related to its β of market portfolio. Jensen(1968) recommended using the following model as CAPM: Rit-Rft=α+β (Rmt-Rft)+εit

The slope β in CAPM measures the systematic risk of mutual funds compare to the market. A beta less than 1.0 indicates that mutual funds are less risk than market portfolio while a beta more than 1.0 means mutual funds are more volatile than the market. When beta equals to zero, there is no risk. The intercept α, known as Jensen alpha, represents abnormal return of mutual funds, which used to measure the skills of manager. A positive alpha indicates that the mutual funds manager is able to beat the market and a negative alpha suggests the skills of manager are poor. CAPM assumes that the expected return of mutual funds is only explained by market beta. However, Fama and French(1992) found that SMB and HML effect the risk premium of risk asserts. So they added the two risk factors into CAPM model. The Fama-French model can be read as: Rit-Rft=αi+β1 (Rmt-Rft)+β2SMB+β3HML+εi

To better exam the performance of mutual funds, this project adds momentum factor which was put forward by Carhart (1997) and traded liquidity factor suggested by Pastor and Stambaugh (2003) into the Fama-French model. The model is defined as: Rit-Rft=αi+β1 (Rmt-Rft)+ β2SMB+β3HML+β4mom+β5TradedLIQ+εi Regression analysis

Before regress multi-fund asset-pricing models, multicollinearity should be tested. The highly imperfect multicollinearity leads to large variance and covariance of OLS estimators. The t-statistics of OLS estimators tend to not statistically significant and the confidence interval will be wide a lot.Usually there are no highly correlations between all independent variables if the values are less than 0.5. After running the OLS regression, autocorrelation should be tested. Autocorrelation leads to OLS no longer efficient even though OLS still consistent and unbiased and the t-statistic, p-value is not accurate. In this project, Breusch-Godfrey Serial Correlation LM Test used to test autocorrelation. When the probability of chi-square is bigger than 0.5, the null hypothesis is accepted at 5% significance level, that means, there is no autocorrelation in the model. Additionally, if a model has heteroskedasticity, the least squares estimators are still unbiased and consistent while the standard errors of the estimators are biased. Therefore the t-statistic, F-statistic and p-value are not used to accept or reject the null hypothesis. When the white test probability of chi-square is less than 0.05, the model has herteroskedasticity. Even though GLS is the best way to eliminate heteroscedastic, the variance of error term given x is unknown. Therefore, White’s approximate estimator for the variance of the least square used to eliminate heteroskedasticity. The empirical results

Table one: multicollinearity test Correlation | |...

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