1.) Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 34% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 5%.
Calculate the expected return and variance of portfolios invested in T-bills and the S&P 500 index with weights as follows: (Leave no cells blank - be certain to enter "0" wherever required. Do not enter your answer as a percentage but in a decimal format. Round "Expected Return" to 4 decimal places and the "Variance" to 4 decimal places.)
| W bills |
W index |
Expected return |
Variance |
| 0.2 |
0.8 |
0.1140 |
0.0740 |
| 0.4 |
0.6 |
_______? |
________? |
| 0.8 |
0.2 |
_______? |
________? |
| 1.0 |
0.0 |
_______? |
________? |
| 0.6 |
0.4 |
_______? |
________? |
| 0.0 |
1.0 |
_______? |
________? |
2.) Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $110,000 or $280,000 with equal probabilities of .5. The alternative risk-free investment in T-bills pays 6% per year.
a. If you require a risk premium of 4%, how much will you be willing to pay for the portfolio? (Round your answer to the nearest whole dollar amount. Omit the "$" sign in your response.)
Price $_______??
b. Suppose that the portfolio can be purchased for the amount you found in (a). What will be the expected rate of return on the portfolio? (Round your answer to the nearest whole number. Omit the "%" sign in your response.)
Rate of return ______%??
c. Now suppose that you require a risk premium of 10%. What is the price that you will be willing to pay? (Round your answer to the nearest whole dollar amount. Omit the "$" sign in your response.)
Price $______??