Homework; Diversification & CAPM

Assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%. You estimate that a passive portfolio invested to mimic the S&P 500 stock index yields an expected rate of return of 13% with a standard deviation of 25%. a. What is the slope of the CML? (Round your answer to 2 decimal places.)

.24 +- 1

What must be the beta of a portfolio with E(rP) = 20%, if rf = 5% and E(rM) = 15%? (Round your answer to 1 decimal place.)

1.5

The standard deviation of the market-index portfolio is 20%. Stock A has a beta of 1.5 and a residual standard deviation of 30%. a. Calculate the total variance for an increase of .15 in its beta. (Do not round intermediate calculations. Round your answer to the nearest whole number.) b. Calculate the total variance for an increase of 3% in its residual standard deviation. (Do not round intermediate calculations. Round your answer to the nearest whole number.)

1,989 ± 1 1,989 ± 1

Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $50,000 or $150,000, with equal probabilities of .5. The alternative riskless investment in T-bills pays 5%. a. If you require a risk premium of 10%, how much will you be willing to pay for the portfolio? (Round your answer to the nearest dollar amount.) 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? (Do not round intermediate calculations. Round your answer to the nearest whole percent.) c. Now suppose you require a risk premium of 15%. What is the price you will be willing to pay now? (Round your answer to the nearest dollar amount.)

86957 15% 83333

Investors expect the market rate of return this year to be 10%. The expected rate of return on a stock with a beta of 1.2 is currently 12%. If the market return this year turns out to be 8%, how would you revise your expectation of the rate of return on the stock? (Do not round intermediate calculations. Round your answer to 1 decimal place.)

9.6%