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%, 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 exploit it?

For an Arbitrage Opportunity, there should be 2 Portfolios with SAME BETA.

In this case, Beta of A is 0.6 and Beta of B is 0.8

Therefore, By Weight of 1 to Portfolio A will have a Beta of 0.6*1 = 0.6 and Weight of 0.75 to Portfolio B will have a Beta of 0.8*0.75 = 0.6

Now, we have 2 Portfolios as follows:

1) 1 unit of A, which has an Expected Return of 8% and Beta of 0.6

2) 0.75 of B, which has an Expected Return of 10*0.75 = 7.5% and Beta of 0.6

Therefore, To make an Arbitrage Gain, Portfolio (1) should be BOUGHT and Portfolio (2) should be SOLD. Arbitrage Profit = 8%-7.5% = 0.5%

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