Question

Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $160,000 or $400,000 with equal probabilities of 50%. The alternative risk-free investment in T-bills pays 5% per year.

a.		If you require a risk premium of 8%, how much will you be willing to pay for the portfolio?
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 12%. 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?

Answer 1

Part (a)

Expected value of year end cash flows, E(C) = p x C1 + (1 - p) x C2 = 50% x 160,000 + (1 - 50%) x 400,000 = $ 280,000

Required return, r = Risk free rate + desired risk premium = 4% + 8% = 12%

Hence, amount you be willing to pay for the portfolio today = PV of expected cash flows = E(C) / (1 + r) = 280,000 / (1 + 12%) = $ 250,000

Part (b)

Expected return = r = 12%

Part (c)

Required return, r = Risk free rate + desired risk premium = 4% + 12% = 16%

Hence, amount you be willing to pay for the portfolio today = PV of expected cash flows = E(C) / (1 + r) = 280,000 / (1 + 16%) = $ 241,379.31

Part (d)

There is an inverse relationship between the two. As the required risk premium on a portfolio increases, the price at which the portfolio will sell decreases. And the vice versa.