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+ 1

r 2 =0.06+4F 1+ 2

There is a risk free asset which pays 0.03.

a) (5 points) Using only asset 1 and the risk-free asset, compute the portfolio weights and returns for the pure factor portfolio, which has 1 = 1.

b) (5 points). Using only asset 2 and the risk-free asset, compute the portfolio weights and expected returns for the pure factor portfolio, which has 1 = 1.

c) (5 points). What can we say about whether the arbitrage pricing theory holds?

d) (15 points). Suppose that SD( 1) = 0.1,SD( 2) = 0.2, and 1 and 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 1 = 0?