Assume that the single index model holds for all securities and an investor comes up with the following equation for the return of the well diversied portfolio P:

rP = 16% + 0.5Rm

where Rm is an excess return on the market. The risk-free rate is 2% and the market expected return is 10%.

(Tips: Rules on expectation: E(a) = a ; E(x + a) = E(x) + a; where a is a constant)

• Does APT hold for portfolio P? (4 pts)

• Does an arbitrage opportunity exist in this economy? If so, what would be an arbitrage strategy? (8 pts)

• Now suppose that portfolio P is not welldiversied so that:

rP = 16% + 0.5Rm + eP

where eP is an unexpected contribution from portfolio specic risk to the return of P. Does an arbitrage opportunity exist? Why? If yes, what is an arbitrage strategy? (2 pts)