Question

Consider a single factor of APT. Portfolio A has a beta of 1.2 and an expected return of 14%. Portfolio B has a beta of 0.7 and an expected return of 9%. The risk-free rate of return is 5%. If you ____ $1000 of portfolio B, your arbitrage profit is ____.

Answer 1

Expected return = Risk free rate + (Beta x Risk premium)

Portfolio A:

Expected return = Risk free rate + (Beta x Risk premium)
14% = 5% + (1.2 x Risk premium)
1.2 x Risk premium = 14% - 5%
1.2 x Risk premium = 9%
Risk premium = 9% / 1.2
Risk premium = 7.5%

Portfolio B:

Expected return = Risk free rate + (Beta x Risk premium)
9% = 5% + (0.7 x Risk premium)
0.7 x Risk premium = 9% - 5%
0.7 x Risk premium = 4%
Risk premium = 4% / 0.7
Risk premium = 5.71%

Short position A.

If you short $1000 of Portfolio B, your arbitrage profit is $14.

short; $14