APT

6. 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 diversified portfolio P:

rP = 17% +0.8Rm,

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

return is 10%.

a. Does APT hold for portfolio P?

b. Does an arbitrage opportunity exist in this economy? If so, what would be an arbitrage

strategy?

c. Now suppose that portfolio P is not welldiversified so that

rP = 17% + 0.8Rm + eP

where eP

is unexpected contribution from portfolio specific risk to the return of P. Does an

arbitrage opportunity exist? Why? If yes, what is an arbitrage strategy?