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Consider a mutual fund BX, which has a correlation of -0.5 with the market. The annualized expected return on the market is 16% and the annualized standard deviation of the market is 14%. The annualized standard deviation of BX is 22% and the risk-free rate is 4% per year. Assume that the CAPM correctly prices all assets. For simplicity, we assume that BX charges no management fee and has zero expenses.
1. Calculate the maximum Sharpe ratio you could earn with any portfolio.
2. If your coefficient of risk aversion is four, what portfolio should you hold? (Assume that you can trade in BX, the market portfolio, and the risk-free asset).
3. Find the expected return of BX. Interpret.
4. Find the systematic standard deviation of BX.
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