Question

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

Answer #1

Risk-free Rate, R_{f} = 5%

Beta_{A} = 0.6

ER_{A} = 8%

Return_{A} = R_{f} +
Beta_{A}*ER_{A} = 0.05 + 0.6*0.08 = 9.8%

Beta_{B} = 0.8

ER_{B} = 10%

Return_{B} = R_{f} +
Beta_{B}*ER_{B} = 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%

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%, while 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
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