Question

Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $120,000 or $300,000 with equal probabilities of 0.5. The alternative risk-free investment in T-bills pays 5% per year.

Required:
a. If you require a risk premium of 8%, 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?

Answer 1

a. If you require a risk premium of 8%, how much will you be willing to pay for the portfolio?

the expected value of our portfolio = ($120,000 x 50%) + ($300,000 x 50%) = $210,000

the current market price of the investment = $210,000 / 1.13 = $185,840.71

discount rate = 5% + 8% = 13%

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?

13%, it should be equal to the discount rate

c. Now suppose you require a risk premium of 15%. What is the price you will be willing to pay now?

the current market price of the investment = $210,000 / 1.21 = $175,000

discount rate = 5% + 15% = 20%

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?

the higher the risk premium, the lower the market price of the portfolio