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 risk-free investment in T-bills pays 8% per year.
(a) If you require a risk premium of 10%, how much will you be willing to pay for the portfolio now? Hint: the present value of a portfolio equals its expected value divided by (1+the required rate of return); the required rate of return is the sum of the risk premium and the risk-free rate.
(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?
(c) Now suppose that you require a risk premium of 6%. What is the price that you will be willing to pay?
(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?