Consider the following statement to answer Questions i-iv: You manage a risky portfolio with an expected rate of return of 17% and a standard deviation of27%. The Treasury-bill rate is 7%. (i) One of your clients chooses to invest 70% of a portfolio in your fund and 30% in a T-bill moneymarket fund. What is the expected value and standard deviation of the rate of return on yourclientâs portfolio?(2 marks) (ii) Suppose that your client decides to invest in your portfolio a proportion y of the total investmentbudget so that the overall portfolio will have an expected rate of return of 15%. (a) What is the proportion y? (Hint: Use CAPM formula) (b) Further suppose that your risky portfolio includes the following investments in the givenproportions: Stock A (27%), Stock B (33%), and Stock C (40%). What are your clientâsinvestment proportions in your three stocks and the T-bill fund?(2 marks) (iii) Now suppose that your client prefers to invest in your fund a proportion ythat maximizes theexpected return on the overall portfolio subject to the constraint that the overall portfolioâsstandard deviation will not exceed 20%. (a) What is the investment proportion, y? (b) What is the expected rate of return on the overall portfolio?(2 marks) (iv) Suppose that your clientâs degree of risk aversion is A = 3.5. What proportion, y, of the totalinvestment should you suggest that he invest in your fund?(2 marks) (v) The market price of a security is $40. Its expected rate of return is 13%. The risk- free rate is 7%and the market risk premium is 8%. What will be the market price of the security if itscovariance with the market portfolio doubles (and all other variables remain unchanged)?Assume that the stock is expected to pay a constant dividend in perpetuity.(2 marks) QUESTION 2: OMEGA Currently Omega Corporationâs shares are selling at $60 per share and company is paying $5 per share dividend. Dividends are expected to grow at an annual rate of 3% for foreseeable future. Required rate of return for investors is 12% At the same time, Heller Corporationâs shares are selling at $58 per share and company is paying $4 per share dividend. Dividends are expected to grow at an annual rate of 5% for foreseeable future. Required rate of return for investors is 12% a) Calculate the current value of each stock on the basis of Dividend Discount Model. b) On the basis of above calculation, determine either each stock is overvalued or undervalued. (5 marks)
Consider the following statement to answer Questions i-iv: You manage a risky portfolio with an expected rate of return of 17% and a standard deviation of27%. The Treasury-bill rate is 7%. (i) One of your clients chooses to invest 70% of a portfolio in your fund and 30% in a T-bill moneymarket fund. What is the expected value and standard deviation of the rate of return on yourclientâs portfolio?(2 marks) (ii) Suppose that your client decides to invest in your portfolio a proportion y of the total investmentbudget so that the overall portfolio will have an expected rate of return of 15%. (a) What is the proportion y? (Hint: Use CAPM formula) (b) Further suppose that your risky portfolio includes the following investments in the givenproportions: Stock A (27%), Stock B (33%), and Stock C (40%). What are your clientâsinvestment proportions in your three stocks and the T-bill fund?(2 marks) (iii) Now suppose that your client prefers to invest in your fund a proportion ythat maximizes theexpected return on the overall portfolio subject to the constraint that the overall portfolioâsstandard deviation will not exceed 20%. (a) What is the investment proportion, y? (b) What is the expected rate of return on the overall portfolio?(2 marks) (iv) Suppose that your clientâs degree of risk aversion is A = 3.5. What proportion, y, of the totalinvestment should you suggest that he invest in your fund?(2 marks) (v) The market price of a security is $40. Its expected rate of return is 13%. The risk- free rate is 7%and the market risk premium is 8%. What will be the market price of the security if itscovariance with the market portfolio doubles (and all other variables remain unchanged)?Assume that the stock is expected to pay a constant dividend in perpetuity.(2 marks) QUESTION 2: OMEGA Currently Omega Corporationâs shares are selling at $60 per share and company is paying $5 per share dividend. Dividends are expected to grow at an annual rate of 3% for foreseeable future. Required rate of return for investors is 12% At the same time, Heller Corporationâs shares are selling at $58 per share and company is paying $4 per share dividend. Dividends are expected to grow at an annual rate of 5% for foreseeable future. Required rate of return for investors is 12% a) Calculate the current value of each stock on the basis of Dividend Discount Model. b) On the basis of above calculation, determine either each stock is overvalued or undervalued. (5 marks)
Related questions
Assume that you manage a risky portfolio with an expected rate of return of 14% and a standard deviation of 38%. The T-bill rate is 5%. Your client chooses to invest 85% of a portfolio in your fund and 15% in a T-bill money market fund.
a. What is the expected return and standard deviation of your client's portfolio? (Round your answers to 2 decimal places.)
| Expected return | % per year |
| Standard deviation | % per year |
b. Suppose your risky portfolio includes the following investments in the given proportions:
| Stock A | 22% |
| Stock B | 31% |
| Stock C | 47% |
What are the investment proportions of your clientâs overall portfolio, including the position in T-bills? (Round your answers to 2 decimal places.)
| Security | Investment Proportions | |
| T-Bills | % | |
| Stock A | % | |
| Stock B | % | |
| Stock C | % | |
c. What is the reward-to-volatility ratio (S) of your risky portfolio and your client's overall portfolio? (Round your answers to 4 decimal places.)
| Reward-to-Volatility Ratio | |
| Risky portfolio | |
| Clientâs overall portfolio | |
| A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.8%. The probability distributions of the risky funds are: |
| Expected Return | Standard Deviation | |||
| Stock fund (S) | 19 | % | 48 | % |
| Bond fund (B) | 9 | % | 42 | % |
| The correlation between the fund returns is .0762. |
| Suppose now that your portfolio must yield an expected return of 17% and be efficient, that is, on the best feasible CAL. |
| a. | What is the standard deviation of your portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places.) |
| Standard deviation | % |
| b-1. | What is the proportion invested in the T-bill fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.) |
| Proportion invested in the T-bill fund | % |
| b-2. | What is the proportion invested in each of the two risky funds? (Do not round intermediate calculations. Round your answers to 2 decimal places.) |
| Proportion Invested | |
| Stocks | % |
| Bonds | % |
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