Question

3. Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $50,000 with probability 0.6 or $150,000 with probability 0.4. The alternative riskless investment in T-bill pays 5%.

(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 be the expected rate of return on the portfolio?

(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

Answer A) Return on the Portfolio = Risk free return + Risk Premium

= 5% + 10%

= 15%

Expected Value = w₁ x 50000 + w₂ x 150000

= 0.6 x 50000 + 0.4 x 150000

= 30000 + 60000

= 90000

Now let us assume we are paying $X amount for the portfolio , so we will pay

= x * (1 + 15%) = 90000

= 1.15x = 90000

= X = $78260

Answer B) Expected return on the portfolio = ( 90000 - 78260) / 78260

= 11740 / 78260

= 15%

Answer C) Return on the Portfolio = Risk free return + Risk Premium

= 5% + 15%

= 20%

Now let us assume we are paying $X amount for the portfolio , so we will pay

= x * (1 + 20%) = 90000

= 1.20x = 90000

= X = $75000

Answer D) We can conclude that when the return on the portfolio was 15% we were able to sell it at $78260 but when the return on the portfolio increased by 5% i.e. when it became 20% the price at which we can sell reduced by $3260 i.e. it came down to $ 75000.

This means that as the return increases the selling price reduces.