博迪第八版投资学第十章课后习题答案(3)

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5. The expected return for Portfolio F equals the risk-free rate since its

beta equals 0.

For Portfolio A, the ratio of risk premium to beta is: (12 6)/1.2 = 5

For Portfolio E, the ratio is lower at: (8 – 6)/0.6 = 3.33

This implies that an arbitrage opportunity exists. For instance, you

can create a Portfolio G with beta equal to 0.6 (the same as E’s) by combining Portfolio A and Portfolio F in equal weights. The expected

return and beta for Portfolio G are then:

E(r G ) = (0.5 12%) + (0.5 6%) = 9%

G = (0.5 1.2) + (0.5 0) = 0.6

Comparing Portfolio G to Portfolio E, G has the same beta and higher

return. Therefore, an arbitrage opportunity exists by buying Portfolio

G and selling an equal amount of Portfolio E. The profit for this

arbitrage will be:

r G– r E =[9% + (0.6 F)] [8% + (0.6 F)] = 1%

That is, 1% of the funds (long or short) in each portfolio.

6. Substituting the portfolio returns and betas in the expected return-

beta relationship, we obtain two equations with two unknowns, the risk-free rate (r f ) and the factor risk premium (RP):

12 = r f + (1.2 RP)

9 = r f + (0.8 RP)

Solving these equations, we obtain:

r f = 3% and RP = 7.5%

7. a. Shorting an equally-weighted portfolio of the ten negative-alpha

stocks and investing the proceeds in an equally-weighted portfolio

of the ten positive-alpha stocks eliminates the market exposure and

creates a zero-investment portfolio. Denoting the systematic market

factor as R M , the expected dollar return is (noting that the

expectation of non-systematic risk, e, is zero):

$1,000,000 [0.02 + (1.0 R M )] $1,000,000 [(–0.02)

+ (1.0 R M )]

= $1,000,000 0.04 = $40,000

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