Question 1 :Random returns for two well-diversified portfolios A and B are given by:

rA=0.27+1.6F1+0.8F2

rB=0.16+0.8F1+1.1F2

where F1 AND F2 are unexpected parts of factor 1 and 2 returns,respectively.(One can think that factor one is GDP and factor two is an inflation).The risk free rate is 3%.Assume that the two-factor APT holds.

a.Find the expected returns on factor 1 and factor 2.

b.Construct factor portfolio 1 and factor portfolio 2 by using portfolios A,B,and T-bills.(That is,find the weights of portfolios A,B and T-bills in factor portfolio 1 and the weights of portfolios A,B and T-bills in factor portfolio 2)

Question 2: 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= 19%+1.2RM

where RM is an excess return on the market.The risk free rate is 2% and the expected return on the market is 13%.

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 well-diversified so that

rp=19%+1.2Rm+ep

where ep is unexpected contribution from portfolio specific risk to the return of P. Does an arbitrage opportunity exist in this market?Why? IF yeas,what is an arbitrage strategy?