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Suppose that there are two independent economic factors F1 and F2. The risk-free rate is 6%, and all stocks have independent firm-specific components with a standard deviation of 45%. The following are well-diversified portfolios: Portfolio Beta on F1

Beta on F2

A

1.5

2.0

31

B

2.2

-0.2

27

Expected Return

Table 1: Scenarios for 2 stocks with 2 Factors What is the expected return-beta relationship in this economy?

Solution BKM ch. 11, p. 335 # 2 E rp   rf  1, p  E  r1   rf   2, p  E  r2   rf  We need to find the risk premium [rp] for each of the two factors: rp1 = [E(r1)-rf] and rp2 = [E(r2)-rf] To do so, the following system of two equations with to unknowns must be solved: 21 = 6 + 1.5 x rp1 + 2.0 x rp2 27 = 6 + 2.2 x rp1 + (-0.2) x rp2 The solution to this set of equation is rp1 = 10% and rp2 = 5% Thus, the expected return-beta relationship is economicshomeworkhelper.com

E rp   6%  1, p 10%  2, p  5% Question 1) Consider the regression equation: where:

ri - rf = 0g +1g bi 2+ g  e ei 2+ it

ri - rt = the average difference between the monthly return on stock i and the monthly riskfree rate bi = the beta of stock i 2ei = a measure of the nonsystematic variance of the stock i.

If you estimated this regression equation and the CAPM was valid, you would expect the estimated coefficient, g2 to be A) 0 B) 1 C) equal to the risk-free rate of return D) equal to the average difference between the monthly return on the market portfolio and the monthly risk-free rate E) none of the above Ans: A

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Question 2) Consider a well-diversified portfolio, A, in a two-factor economy. The risk-free rate is 6%, the risk premium on the first factor portfolio is 4% and the risk premium on the second factor portfolio is 3%. If portfolio A has a beta of 1.2 on the first factor and .8 on the second factor, what is its expected return?

A) 7.0% B) 8.0% C) 9.2% D) 13.0% E) 13.2% Question 3) Security A has a beta of 1.0 and an expected return of 12%. Security B has a beta of 0.75 and an expected return of 11%. The risk-free rate is 6%. Explain the arbitrage opportunity that exists; explain how an investor can take advantage of it. Give specific details about how to form the portfolio, what to buy and what to sell.

Ans: An arbitrage opportunity exists because it is possible to form a portfolio of security A and the risk-free asset that has a beta of 0.75 and a different expected return than security B. The investor can accomplish this by choosing .75 as the weight in A and .25 in the risk-free asset. This portfolio would have E(rp) = 0.75(12%) + 0.25(6%) = 10.5%, which is less than B's 11% expected return. The investor should buy B and finance the purchase by short selling A and borrowing at the risk-free asset. economicshomeworkhelper.com