1. The Terrapins Investment Fund has a total investment of $500 million in five

Question

1. The Terrapins Investment Fund has a total investment of $500 million in five stocks.

Stock               Investment (millions)   Beta

    1                              $150                   .6

    2                              120                1.2

    3                                  80                3.0

    4                                  90                1.8

    5                                  60                1.0

Total                            $500

What is the fund’s overall, or weighted average, beta?

Refer to the previous problem. If the risk-free rate is 12% and the market risk premium is 6%, what is the required return on the Terrapins Fund?

2. Suppose MGM has a beta of 3.32 and AEP has a beta of 0.28. If the risk-free interest rate = 4.0% and the market risk premium = 10%, according to the CAPM:

What is the expected return of MGM stock?

What is the expected return of AEP stock?

What is the beta of a portfolio that consists of 60% of MGM and 40% of AEP?

What is the expected return of that portfolio with the beta that you found in part c.?

What is the beta of a portfolio that consists of 40% of MGM and 60% of AEP?

Explanation / Answer

1:

Fund beta = (150/500)*0.6 + (120/500)*1.2 + (80/500)*3 + (90/500)*1.8 + (60/500)*1

Fund beta = 1.392

Return on fund = 12 + 1.392*6 = 20.352%

2:

Expected return of MGM = 4 + 3.32*10 = 37.20%

Expected return of AEP = 4 + 0.28*10 = 6.80%

Beta of portfolio (60% MGM, 40% AEP) = 0.6*3.32 + 0.4*0.28 = 2.104

Return on portfolio = 4 + 2.104*10 = 25.04%

Or, Return on portfolio = 0.6*37.20 + 0.4*6.80 = 25.04%

Beta of portfolio (40% MGM, 60% AEP) = 0.4*3.32 + 0.6*0.28 = 1.496

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