You manage an equity fund with an expected risk premium of 10% and a standard deviation of 14%. The rate on T-bills is 6%. Your client chooses to invest $60,000 of her portfolio in your equity fund and $40,000 in T-bills. What is the expected return of your client's portfolio? what is the Sharpe ratio for the equity fund?

The expected return is 12% and the Sharpe ratio is 8.4%

Explanation:

In order to calculate the expected return, we have to calculate first the Return on equity fund as follows:

Return on equity fund = risk free rate(= rate on T bill)  + risk premium = 6% + 10% = 16%

Return on T bill money market fund = 6%

Therefore, expected return on portfolio = weight of equity fund x return on equity fund + weight of money market fund x return on money market fund

Expected return on portfolio = (60000/(60000 +40000))*16% + (40000/(60000+40000))*6%

Expected return on portfolio = 60*16% + 40%*6% = 9.6% +2.4% = 12%

In order to calculate the Standard deviation of portfolio we have to use the following formula:

Standard deviation of portfolio = weight of equity fund x standard deviation of equity fund

Standard deviation of portfolio = (60000/(60000+40000))*14%

= 60%*14% = 8.4%

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