Suppose that the world is described by a one-factor model, so stock returns depend on one systematic risk factor, F ̃1, which has mean 0.

 r ̃1 =0.05+2F ̃1+ε ̃1 

r ̃2 =0.06+4F ̃1+ε ̃2

 

There is a risk free asset which pays 0.03.

a)  Using only asset 1 and the risk-free asset, compute the portfolio weights and returns for the pure factor portfolio, which has β1 = 1. 

b) Using only asset 2 and the risk-free asset, compute the portfolio weights and expected returns for the pure factor portfolio, which has β1 = 1. 

c) What can we say about whether the arbitrage pricing theory holds? 

d)  Suppose that SD(ε ̃1) = 0.1,SD(ε ̃2) = 0.2, and ε ̃1 and ε ̃2 are uncorrelated. Using assets 1, 2, and the risk-free asset, what is the highest Sharpe ratio that you can attain, using a portfolio with β1 = 0?