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%