Assume that you manage a risky portfolio with an expected rate of return of 15% and a standard deviation of 40%. The T-bill rate is 5%.

Your client has a total investment budget of $1,800,000. She decides to invest in your risky portfolio a proportion of her total investment budget with the remainder in a T-bill money market fund so that her overall portfolio will have an expected rate of return of 13%.

Required

1- What is the amount invested in your risky portfolio?

2. What is the standard deviation of your clients portfolio?

3- Calculate the amount of the expected net gain of your client (in dollars), if you require a commission of 3.8%.

4. What is the reward-to-volatility ratio of your risky portfolio and your client's overall portfolio?

5. Draw the CAL of your portfolio on an expected return/standard deviation diagram. What is the slope of the CAL? Show the position of your client on your funds CAL.

6. You estimate that a passive portfolio invested to mimic the S&P 500 stock index provides an expected rate of return of 12% and a standard deviation of 34%.

• Draw the CML and your funds CAL on an expected return/standard deviation diagram.
• Explain in one short paragraph the advantage of your fund over the index fund.

7. Your client is considering adopting a passive strategy. She prefers investing in the market portfolio a proportion (y) that maximizes the expected return on the overall portfolio subject to the constraint that the overall portfolio standard deviation will not exceed 32%.

Explain to your client the disadvantage of the swich. Support your answer with relevant calculations.