Consider the three stocks: stock X, stock Y and stock Z, that have the following factor loadings (or factor betas)

Stock	Factor 1 Loading	Factor 2 Loading
X	-0.8	1.4
Y	-0.1	1.5
Z	1.3	1.1

The zero-beta return (F₀) = 1%, and the risk premia are F₁(Inflation) = 3%, F₂ (GDP) = 7%.

Assume that all three stocks are currently priced at $40.

a) Calculate the expected returns for stock X, stock Y, and stock Z (based on the APT model)

E(Rx) =

E(Ry) =

E(Rz) =

b) Calculate the expected prices one year from now for stocks X, Y and Z

P1(X) =

P1(Y) =

P1(Z) =

c) If you know that the actual prices one year from now for ALL stocks are $45 per share, then which of stocks X, Y, and Z should you buy today?

d) How could the factor 1 loading for some stocks be negative (e.g. Stocks X and Y) and for other stocks it can be positive (e.g. Stock Z)?