Assume that you manage a risky portfolio with an expected rate of return of 19%
ID: 1225621 • Letter: A
Question
Assume that you manage a risky portfolio with an expected rate of return of 19% and a standard deviation of 33%. The T-bill rate is 7%.
Your risky portfolio includes the following investments in the given proportions:
Suppose that your client decides to invest in your portfolio a proportion y of the total investment budget so that the overall portfolio will have an expected rate of return of 16%.
What is the proportion y? (Round your answer to the nearest whole number. Omit the "%" sign in your response.)
What are your client’s investment proportions in your three stocks and the T-bill fund? (Do not round intermediate calculations. Round your answers to 2 decimal place. Omit the "%" sign in your response.)
What is the standard deviation of the rate of return on your client’s portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal place. Omit the "%" sign in your response.)
Assume that you manage a risky portfolio with an expected rate of return of 19% and a standard deviation of 33%. The T-bill rate is 7%.
Explanation / Answer
1. Suppose that your client decides to invest in your portfolio a proportion y of the total investment budget so that the overall portfolio will have an expected rate of return of 16%.
Mean return on portfolio = Rf + (Rp - Rf)y = 7% + (19% - 7%)y = 7% + 12%y
If the mean of the portfolio is equal to 16%, then solving for y we will get:
16% = 7% +12%y
=> y = (16% - 7%)/12% => y = 0.75
Thus, in order to obtain a mean return of 16%, the client must invest 75% of total funds in the risky portfolio and 24.25% in Treasure bills.
2. Investment proportions of the client’s funds:
• 24.25% in T-bills
• 0.75 x 29% = 21.75% in Stock A
• 0.75 x 36% = 27% in Stock B
• 0.75 x 35% = 27% in Stock C
3. Standard deviation = 0.70 x 33% = 23.1% per year