Assume the assumptions of Arbitrage Pricing Theory hold and a three-factor model describes the realized returns. All other risk is diversifiable. Assume that factors are normalized so that [ 1 ] = [ 2 ] = [ 3 ] The risk-free rate is rf = 2% = 0.02 and you are given the multi-factor representation of three risky assets:

= 0.05 + 1 + = 0.02 1 + 2 + = 0.085 0.5 1 + 2 + 3 +

where risks , , are diversifiable/idiosyncratic.

a) Assume the 3-factor Arbitrage Pricing Theory applies. What are the risk-premia for holding factors 1,2,3?

b) Assume the 3-factor Arbitrage Pricing Theory applies. What is the expected return of an asset that has loading 0.75 on factor 1, 0.2 on factor 2, and -0.4 on factor 3?

c) Suppose there is an asset with loadings of 1 on each of the factors. The asset has an expected return of 10%. If there arbitrage? If so, construct the arbitrage strategy.