Consider the single-index model applied to a stock (or a portfolio of stock) S: RS,t = S + S RM,t + eS,t. For this exercise, we are going to ignore the factors SMB and HML (alternatively, you can think that you run the Fama-French 3-factor model and you obtained S,SML = 0 and S,HML = 0). Your estimates for the single-index model are S = 2% (and statistically different from zero), S = 0.6, V (eS,t) = 0.09. In addition, E (RS,t) = 6.8%, E (RM,t) = 8%, V (RM,t) = 0.0625. The risk-free rate is rf = 1% and lets assume that rf is constant over time. 1. Build the portable alpha portfolio Z. That is, compute the weights wS and wM such that the portfolio Z has zero load on the market factor.