Question: Consider a risky portfolio. The end-of-year cash flow derived from the

Question

Question: Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $70,000 or $20,0000 with equal probabilities of .5. The alternative risk-free imnvestment in T-bills pays 6% 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?

I need help with Chapter 6, Problem Set #4 of the Investments 11th edition by Bodie, Kane & Marcus. I am having trouble with calculating the answer. Thanks, Scott

Explanation / Answer

(a)

Expected Cash Flow is (0.5*$70,000)+ (0.5*$195,000) =$132,500

With a risk premium of 8% the required rate of return is 12%. Therefore if the value of portfolio is X then to earn an expected return 1.12x= $132,500 Hence the X is $118,304

(b) If the portfolio is purchased at $118,304 and the expected payoff is $132,500, then the expected rate of return E(r), is

$132,500-$118,304/$118,304 =12%

The portfolio price is set to equate the expected return with the required rate of return.

(c) If the risk premium over T-bill is now 12% then the required return is

4%+12%= 16%

The Value of portfolio X must satisfy

X*(1+0.16)=$132,500

X= $114,224

(d) The relationship between the required risk premium on a portfolio and price at which the portfolio will sell is inverse. as the risk premium increased the value of portfolio at which it is sold is reduced.

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