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:

r_P = 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%.

1. Does APT hold for portfolio P?
2. Does an arbitrage opportunity exist in this economy? If so, what would be an arbitrage strategy?
3. Now suppose that portfolio P is not welldiversied so that: r_P = 16% + 0.5Rm + e_P where e_P is unexpected contribution from portfolio specic risk to the return of P. Does an arbitrage opportunity exist? Why? If yes, what is an arbitrage strategy?