Consider the return generating process (RGP) for three assets G, T, and D. They are affected by two factors, F1,t, the investor confidence and F2,t, changes in interest rates:

RG,t = 0.05-F1,t+2F2,t; RT,t = 0.10+2F1,t; RD,t = -0.005+F1,t-3F2,t

As a portfolio manager, you would like to replicate the performance of the TSX Small Cap Index which has unit exposure to first factor and exposure of 2 to the second factor Assume also the risk-free rate is 0.03.

1. Find the expected returns and the factor betas of the three assets.

2. Determine the tracking portfolio of this TSX Small Cap index using the three assets above. Find its expected return.

3. Find the composition of the two pure factor portfolios, which are by construction well-diversified portfolios. Estimate their expected returns and the factor risk premia. Write their RGPs. Interpret your answer. 

4. Assume that the expected return on the TSX Small Cap Index is 0.10. Determine if there is an arbitrage opportunity. If yes, show in detail how it can be implemented and calculate the arbitrage profit.