Thank you in advance for your time!

Question 12

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

whereRmis 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)

1. Does APT hold for portfolio P?(4 pts)
2. Does an arbitrage opportunity exist in this economy? If so, what would be an arbitragestrategy?(8 pts)
3. Nowsuppose that portfolio P is not well-diversied so that:

r_P=16%+0.5Rm+e_P

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