Question

We Do Bankruptcies is a law firm that specializes in providing advice to firms in financial distress. It prospers in recessions when other firms are struggling. Consequently, its beta is negative, ?0.3. a. If the interest rate on Treasury bills is 7% and the expected return on the market portfolio is 17%, what is the expected return on the shares of the law firm according to the CAPM? (Enter your answer as a whole percent.) b. Suppose you invested 70% of your wealth in the market portfolio and the remainder of your wealth in the shares in the law firm. What would be the beta of your portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

r_a = r_f + [B_a (r_m-r_f) ]

where:

r_a = Expected return on Security/Asset

r_f = the rate of return for a risk-free security

r_m = the broad market's expected rate of return

B_a = beta of the asset

r_a =7% + [-0.3(17%-7%)]

r_a = 0.07+[-0.3*0.1]

r_a = 0.07-0.03

r_a =0.04

a) Expected return on the shares of the law firm according to the CAPM = 4%

Calculations for b:

Weighted Average Return = [Return from market portfolio* % of investment in market portfolio] + [Return from Law firm * % of investment in law firm]

Weighted Average Return = [17%*70%] + [30%*4%]

Weighted Average Return = 11.9% + 1.2%

Weighted Average Return = 13.1 %

r_a = r_f + B_a (r_m-r_f)

13.1%= 7%+ B_a (17%-7%)

13.1%= 7% + B_a * 10%

13.1% - 7% = B_a * 0.1

6.1/0.1 = B_a

B_a = 0.61