Question

Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $40,000 or $135,000, with equal probabilities of 0.5. The alternative riskless investment in T-bills pays 4%.
a.If you require a risk premium of 10%, 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?

Answer 1

Answer:

a. $76,754

.38

b. 14%

c. $73,529

Explanation:

a. The computation of portfolio is given below:-

Risk Premium

= Required return - Risk free rate

= 10% + 4%

= 14%

Expected value of the payoff

= $40,000 × 1 ÷ 2 + $135,000 × 1 ÷ 2

= $87,500

Value of portfolio = $87,500 ÷ (1 + 14%)

= $76,754.39

b. The calculation of expected rate of return on the portfolio is shown below:-

= ($87,500 - $76,754.39) ÷ $76,754.39

= 14%

c. The calculation of risk premium is shown below:-

Risk premium = Required return - Risk free rate

Required return = 15%+4% = 19%

Expected rate of the payoff

= $40,000 × 1 ÷ 2 + $135,000 × 1 ÷ 2

=$87500

Value of portfolio

= $87,500 ÷ (1 + 19%)

= $73,529