Question

Consider a one factor economy where the risk free rate is 5%, and Portfolios A and...

Consider a one factor economy where the risk free rate is 5%, and Portfolios A and B are well diversified portfolios.

Portfolio A has a Beta of 0.6 and an expected return of 8%

Portfolio B has a Beta of 0.8 and an expected return of 10%

Is there an arbitrage opportunity in this economy? If yes, how could you exploit it?

Please explain the steps

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Homework Answers

Answer #1

Risk-free Rate, Rf = 5%

BetaA = 0.6

ERA = 8%

ReturnA = Rf + BetaA*ERA = 0.05 + 0.6*0.08 = 9.8%

BetaB = 0.8

ERB = 10%

ReturnB = Rf + BetaB*ERB = 0.05 + 0.8*0.1 = 13%

So, there is clearly an arbitrage opportunity.

Sell Portfolio A and pay expected return of 9.8% on this portfolio.

From the Amount received by selling Portfolio A, purchase portfolio B.

Earn 13% return on Portfolio B and from this return pay 9.8% to the buyer of Portfolio A.

Through this arbitrage, earn a profit of 3.2%

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