Your mutual fund manager has invested all of your money into a fund whose invest
ID: 1170544 • Letter: Y
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Your mutual fund manager has invested all of your money into a fund whose investment objective is to outperform the Russell 2000 index. The Russell 2000 index includes 2000 stocks that have a small market capitalization, so it it is made up primarily of small size publicly listed companies and as such is not representative of the market portfolio. The reason why your fund manager is benchmarking against this index is that he primarily invests in small size companies too. Your mutual fund manager is very proud to tell you that his fund outperformed his benchmark (Russell 2000) by +1% per year over the last five years as the average return on the mutual fund over the last five year was 20%. The average return on the Russell 2000 over the last five years was 19%. During the last five years, the average return on the Russell 3000 index (the 3000 largest market capitalization stocks, representing 99% of the US stock market and therefore a good proxy for the market portfolio) was 16%, the average risk-free rate was 6%, the standard deviation of the returns for the Russell 3000 was 0.2, the standard deviation of the returns for the Russell 2000 was 0.280, the covariance between the mutual fund and the Russell 3000 was 0.060, the covariance between the mutual fund and the Russell 2000 was 0.0785. Using this information, how would you evaluate the performance of the mutual fund? What is your conclusion? Your mutual fund manager has invested all of your money into a fund whose investment objective is to outperform the Russell 2000 index. The Russell 2000 index includes 2000 stocks that have a small market capitalization, so it it is made up primarily of small size publicly listed companies and as such is not representative of the market portfolio. The reason why your fund manager is benchmarking against this index is that he primarily invests in small size companies too. Your mutual fund manager is very proud to tell you that his fund outperformed his benchmark (Russell 2000) by +1% per year over the last five years as the average return on the mutual fund over the last five year was 20%. The average return on the Russell 2000 over the last five years was 19%. During the last five years, the average return on the Russell 3000 index (the 3000 largest market capitalization stocks, representing 99% of the US stock market and therefore a good proxy for the market portfolio) was 16%, the average risk-free rate was 6%, the standard deviation of the returns for the Russell 3000 was 0.2, the standard deviation of the returns for the Russell 2000 was 0.280, the covariance between the mutual fund and the Russell 3000 was 0.060, the covariance between the mutual fund and the Russell 2000 was 0.0785. Using this information, how would you evaluate the performance of the mutual fund? What is your conclusion?Explanation / Answer
Mutual Fund Return = 20 %, Russell's 3000 Return = 19% and Russell's 2000 Return = 16 %, Risk-Free Rate = 6 %, Standard Deviation of Russell's 3000 = 0.2 and Standard Deviation of Russell's 2000 = 0.28, Covariance between mutual fund and Russell's 3000 = 0.06 and Covariance between mutual fund and Russell's 2000 = 0.0785
Mutual Fund Beta with respect to Russell's 3000 = B1 = Covariance / Russell's 3000 standard deviation^(2) = 0.06 / (0.2)^(2) = 1.5
Mutual Fund Beta with respect to Russell's 2000 = B2 = Covariance / Russell's 2000 standard deviation^(2) = 0.0785 / (0.28)^(2) = 1.0013
Portfolio Performance Evaluation:
Treynor Measure with respect to Russell's 3000 = (Return of Mutual Fund - Risk-Free Rate) / B1 = (0.2-0.06) / 1.5 = 0.0933
Treynor Measure with respect to Russell's 2000 = (0.2 - 0.06) / 1.0013 = 0.1398
As the Treynor measure for the mutual fund is better off with respect to the Russell's 2000 benchmark, it can be safely assumed that the fund manager was being convenient in comparing it to the small cap benchmark instead of the large cap benchmark, as the former posed less risk to mutual fund returns owing to its lower beta. Any comparison with the larger cap benchmark and also the better market proxy will render the manager's boast null and void because even though the fund beat the large cap by a greater margin, the fund's beta (and hence systematic risk) with respect to the large cap benchmark was greater, thereby depressing its Treynor measure.
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