Fin Investment Class help
Geoge
BKM_Ess_10e_Ch05_Student1.xlsx5-11
| Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $50,000 or $150,000, with equal probabilities of .5. The alternative riskless investment in T-bills pays 5%. a. If you require a risk premium of 10%, how much will you be willing to pay for the portfolio? b. Suppose the portfolio can be purchased for the amount you found in (a). What will the expected rate of return on the portfolio be? c. Now suppose you require a risk premium of 15%. What is the price you will be willing to pay now? d. Comparing your answers to (a) and (c), what do you conclude about the relationship between the required risk premium on a portfolio and the price at which the portfolio will sell? | |
| Probability | Year end cash flow |
| T-bill return | |
| Solution | |
| a. | |
| Required risk premium = | |
| Expected cash flow = | $ - 0 |
| Portfolio cost = | $ - 0 |
| b. | |
| Expected rate of return = | ERROR:#DIV/0! |
| c. | |
| Required risk premium = | |
| Expected cash flow = | $ - 0 |
| Portfolio cost = | $ - 0 |
5-12
| Assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund. a. What is the expected return and standard deviation of your client’s portfolio? b. Suppose your risky portfolio includes the following investments in the given proportions: Stock A 27% Stock B 33% Stock C 40% What are the investment proportions of your client’s overall portfolio, including the position in T-bills? c. What is the reward-to-volatility ratio (S) of your risky portfolio and your client’s overall portfolio? d. 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 fund’s CAL. | ||
| Expected rate of return on a risky portfolio | ||
| T-Bill rate of return | ||
| Standard deviation | ||
| Fund distribution | ||
| Portfolio of risky assets = | ||
| T-Bill = | ||
| Solution | ||
| a. | ||
| Expected return = | 0.0% | |
| Standard deviation = | 0.0% | |
| b. | ||
| Risky Portfolio distribution | Fund distribution | |
| Stock A | 0.0% | |
| Stock B | 0.0% | |
| Stock C | 0.0% | |
| T-Bills | 0% | 30.0% |
| c. | ||
| Portfolio Sharpe ratio = | ERROR:#DIV/0! | |
| Fund Sharpe ratio = | ERROR:#DIV/0! | |
5-16
| Assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%. You estimate that a passive portfolio invested to mimic the S&P 500 stock index yields an expected rate of return of 13% with a standard deviation of 25%. Your client wonders whether to switch the 70% that is invested in your fund to the passive portfolio. a. Explain to your client the disadvantage of the switch. b. Show your client the maximum fee you could charge (as a percent of the investment in your fund deducted at the end of the year) that would still leave him at least as well off investing in your fund as in the passive one. (Hint: The fee will lower the slope of your client’s CAL by reducing the expected return net of the fee.) | |
| Expected rate of return on a risky portfolio | |
| T-Bill rate of return | |
| Standard deviation | |
| S&P 500 fund expected rate of return = | |
| S&P 500 fund standard deviation = | |
| Solution | |
| b. | |
| Slope of CML = | ERROR:#DIV/0! |
| Maximum fee charged = | ERROR:#DIV/0! |
5-18
| You manage an equity fund with an expected risk premium of 10% and a standard deviation of 14%. The rate on Treasury bills is 6%. Your client chooses to invest $60,000 of her portfolio in your equity fund and $40,000 in a T-bill money market fund. What is the expected return and standard deviation of return on your client’s portfolio? | |
| Equity fund expected risk premium = | |
| Equity fund expected standard deviation = | |
| Treasury bill return = | |
| Investment allocation | |
| Equity fund | |
| Treasury bill | |
| Solution | |
| Expected return on equity fund = | 0.00% |
| Expected return on total investment = | ERROR:#DIV/0! |
| Standard deviation of total investment = | ERROR:#DIV/0! |
