Question

a.) Consider a one-factor economy. Portfolio A has a beta of 1.0 on the factor, and...

a.) Consider a one-factor economy. Portfolio A has a beta of 1.0 on the factor, and portfolio B has a beta of 2.0 on the factor. The expected returns on portfolios A and B are 11% and 17%, respectively. Assume that the risk-free rate is 6%, and that arbitrage opportunities exist. Suppose you invested $100,000 in the risk-free asset, $100,000 in portfolio B, and sold short $200,000 of portfolio A. What would be your expected profit from this strategy?

b.) Consider the single factor APT. Portfolios A and B have expected returns of 14% and 18%, respectively. The risk-free rate of return is 7%. If Portfolio A has a beta of 0.7 and arbitrage opportunities are ruled out, how much is the beta that portfolio B must have?

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Answer #1

A. Profit from Strategy = Return from Invcestment - Payments for Short Position

Profit from Strategy = $100000 *`6% (risk-free position) + $100,000(0.17) (portfolio B); -$200,000(0.11)(short position, portfolio A)

Profit from Strategy = 1,000 profit.

B.

a.Computation of Risk Premium from Portfolio A

Return = Risk Free Rate + Beta * Risk Premium

14% = 7% + 0.7 * Risk Premium

Risk Premium = 10%

b. Computation of Beta of Portoflio B

18% = 7% + Beta * 10%

Beta of Portfolio B = 1.10

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