This problem explores the idea behind APT and factor models. Suppose the statistical properties of all asset returns are described by a single factor model where the market is the single factor. In particular, you can assume that there is a market portfolio and a risk-free asset that both satisfy the factor model equation.

In parts (a) through (c), consider a well-diversified portfolio A with A = 0.4 and A = 2.0.

a) (7 pts) Combine this portfolio with the market portfolio to form a zero-beta portfolio. Calculate the weightings and alpha of your zero-beta portfolio. [Hint: what are the alpha and beta of the market portfolio?]

b) (7 pts) Calculate the systematic, idiosyncratic and total risk of your zero-beta portfolio in (a)?

c) (6 pts) In light of your answers to (a) and (b), construct a zero-cost (riskless) arbitrage strategy using the zero-beta portfolio and the risk-free asset. [Recall that a zero-cost arbitrage strategy will involve buying one asset and short selling another in equal amounts]. What is the alpha of your zero-cost strategy? How much money would an investor invest in such a strategy?