Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $70,000 or $200,000 with equal probabilities of .5. The alternative risk-free investment in T-bills pays 6% per year. Required:
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 id. what do you conclude about the relationship between the required risk premium on a portfolio and the price at which the portfolio will sell?

(a) $118,421 (b) $135,000 (c) $114,407 (d) The portfolio that has a risk higher will sell at a lower price rate. The discount additional value is regarded as a risk of consequence

Explanation:

Solution

(a) If you require a risk premium of 8%, the total return expected on the risky portfolio is given as follows:

E(r) =Risk premium + rf

= 8% + 6% = 14%

Thus

The portfolio is given as follows:

Probability   Return

0.5                $70,000

0.5                $200,000

Hence the dollar return that is expected is computed as follows:

E(r) =∑p(s)r(s)

=Now,  0.5 x 70,000 + 0.5 x 200,000

=$135,000

Now,

we want  135,000 to be 14% of our initial investment, so, the portfolio present value is:

Present value = $135,000/1.14

=$118,421

(b)The expected rate of return on the portfolio, suppose that the portfolio can be bought or the amount 118,421

Then

The expected rate of return =[ E(r) ] = $118,421 * [ 1 +  E(r)]

= $118,421 *(1+ 0.14) = $135,000

(c) The price that you are willing to pay when the premium is 12%, then the risk free rate is given by 6%

Thus,

E(r) =Risk premium + rf

=12% + 6% = 18%

The dollar expected return is stated as follows:

E(r) =∑p(s)r(s)

Now, 0.5 x 70,000 + 0.5 x 200,000

=$135,000

we want  135,000 to be 18% of our initial investment, so, the portfolio present value is:

Present value = $135,000/1.18

= $114,407

(d) The portfolio that has a risk higher will sell at a lower price rate. The discount additional value is regarded as a risk of consequence.

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