Evaluate the below unit trusts for performance evaluation. The risk-free return during the sample period is 6%, and the average return on the market portfolio is 8%. The average returns, standard deviations and betas for the three funds are given below.Unit trustAverage returnStandard deviationBetaFund Alpha10%0.050.4Fund Beta12%0.151.0Fund Sigma15%0.101.2 Determine the fund with the highest Sharpe measure.Select one:a.Fund Betab.Fund Alpha and Sigma are tiedc.Fund Sigmad.Fund Alpha
Question
Evaluate the below unit trusts for performance evaluation. The risk-free return during the sample period is 6%, and the average return on the market portfolio is 8%. The average returns, standard deviations and betas for the three funds are given below.Unit trustAverage returnStandard deviationBetaFund Alpha10%0.050.4Fund Beta12%0.151.0Fund Sigma15%0.101.2 Determine the fund with the highest Sharpe measure.Select one:a.Fund Betab.Fund Alpha and Sigma are tiedc.Fund Sigmad.Fund Alpha
Solution
The Sharpe ratio is a measure for calculating risk-adjusted return, and this ratio has become the industry standard for such calculations. It is calculated as follows:
Sharpe Ratio = (Rx - Rf) / StdDev Rx
Where: Rx = Expected portfolio return Rf = Risk-free rate StdDev Rx = Standard deviation of portfolio return (aka: Total Risk)
Let's calculate the Sharpe ratio for each fund:
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Fund Alpha: Sharpe Ratio = (10% - 6%) / 5% = 0.8
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Fund Beta: Sharpe Ratio = (12% - 6%) / 15% = 0.4
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Fund Sigma: Sharpe Ratio = (15% - 6%) / 10% = 0.9
So, the fund with the highest Sharpe measure is Fund Sigma. Therefore, the correct answer is c. Fund Sigma.
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