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

Question

Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $95,000 or $240,000 with equal probabilities of .5. The alternative risk-free investment in T-bills pays 6% per year.

a. If you require a risk premium of 6%, how much will you be willing to pay for the portfolio? (Round your answer to the nearest whole dollar amount. Omit the "$" sign in your response.) Price?

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? (Round your answer to the nearest whole number. Omit the "%" sign in your response.) Rate of return %

c. Now suppose that you require a risk premium of 12%. What is the price that you will be willing to pay? (Round your answer to the nearest whole dollar amount. Omit the "$" sign in your response.) Price $

Explanation / Answer

a.)

Risk premium refers to the amount that the expected value of an investment must be

above the risk-free rate to compensate an invester for the riskiness of the investment. Thus,

the investment must provide an expected return equal to the risk free rate plus the risk

premium for us to be willing to hold it (that is

E[R] = 6% + 8% = 14%)

E[R] = 0.14 = (E[P(t+1)] - Pt)/Pt = (E[P(t+1)/Pt) - 1

(0.5*95,000 + 0.5*240,000)/Pt = 1.14

So Pt = $146,929.82

b.) E[R] = 6% + 8% = 14%

c.) E[R] = 6% + 12% = 18%

E[R] = 0.18 = (E[P(t+1)] - Pt)/Pt = (E[P(t+1)/Pt) - 1

(0.5*95,000 + 0.5*240,000)/Pt = 1.18

So Pt = $141,949.15

d.)

The higher the risk premium, the lower the price at which the portfolio will sell. Given

that the payoff structure remains the same, the more risk averse the investor is, the lower

the price they will be willing to pay for the portfolio

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