Question

Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $50,000 or $140,000, with equal probabilities of 0.5. The alternative riskless investment in T-bills pays 6%.

a.	If you require a risk premium of 11%, how much will you be willing to pay for the portfolio? (Round your answer to the nearest dollar amount.)

Value of 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? (Do not round intermediate calculations. Round your answer to the nearest whole percent.)

Rate of return

%

c.	Now suppose you require a risk premium of 16%. What is the price you will be willing to pay now?(Round your answer to the nearest dollar amount.)

Value of the portfolio

$

Answer 1

a. E[V_p] = 0.5 * 50000 + 0.5 * 140000 = 95,000 ...(1)

Minimum Risk Premium = Minimum Return - R_f = {(E[V_p] - Price_willing)/Price_willing} - R_f

implies, 0.11 = {(95000-Price_willing)/Price_willing} - 0.06

implies, 0.17 = (95000-Price_willing)/Price_willing

implies, 0.17 * Price_willing = 95000-Price_willing

implies, 1.17 * Price_willing = 95000

implies, Price_willing = $81,196.5812 = $81,197 (nearest dollar)

b. Return = (E[V_p] - 81196.5812) / 81196.5812

Substituting E[V_p] from (1),

Return = (95000 - 81196.5812) / 81196.5812 = 17%

{Intitutionally, R_p = RiskPremium + R_f = 11% + 6% = 17%}

c.

Minimum Risk Premium = Minimum Return - R_f = {(E[V_p] - Price_willing)/Price_willing} - R_f

Substitute E[V_p] from (1)

implies, 0.16 = {(95000-Price_willing)/Price_willing} - 0.06

implies, 0.22 = (95000-Price_willing)/Price_willing

implies, 1.22 * Price_willing = 95000

implies, Price_willing = $77,868.85246 = $77,869 (nearest dollar)