Multifactor Models of Risk and Return

1.Under the following conditions, what are the expected returns for stocks X and Y?

l⁰ = 0.04

b_x,1 = 1.2

k₁ = 0.035

b_x,2 = 0.75

k₂ = 0.045

by,1_,1 = 0.65

by_,2 = 1.45

2.Under the following conditions, what are the expected returns for stocks Y and Z?

l⁰ = 0.05

b_y,1 = 0.75

k₁ = 0.06

b_y,2 = 1.35

k₂ = 0.05 b_z,1 = 1.5

b_z,2 = 0.85

3.Under the following conditions, what are the expected returns for stocks A and B?

l⁰ = 0.035

b_a,1 = 1.00

k₁ = 0.05

b_a,2 = 1.40

k₂ = 0.06

b_b,1 = 1.70

b_b,2 = 0.65

4.Consider a two-factor APT model where the first factor is changes in the 30-year T-bond rate, and the second factor is the percent growth in GNP. Based on historical estimates you determine that the risk premium for the interest rate factor is 0.02, and the risk premium on the GNP factor is 0.03. For a particular asset, the response coefficient for the interest rate factor is -1.2, and the response coefficient for the GNP factor is 0.80. The rate of return on the zero-beta asset is 0.03. Calculate the expected return for the asset.

Exhibit 9.2

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)

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

-0.55

1.2

Y

-0.10

0.85

Z

0.35

0.5

The zero-beta return (l₀) = 3%, and the risk premia are l₁ = 10%, l₂ = 8%. Assume that all three stocks are currently priced at $50.

5.Refer to Exhibit 9.2. The expected returns for stock X, stock Y, and stock Z are?

6.Refer to Exhibit 9.2. The expected prices one year from now for stocks X, Y, and Z are?

7.Refer to Exhibit 9.2. If you know that the actual prices one year from now are stock X $55, stock Y $52, and stock Z $57, then which stock is overvalued, and which stock is undervalued?

8.Refer to Exhibit 9.2. Assume that you wish to create a portfolio with no net wealth invested. The portfolio that achieves this has 50% in stock X, -100% in stock Y, and 50% in stock Z. The weighted exposure to risk factor 1 for stocks X, Y, and Z are?

9.Refer to Exhibit 9.2. Assume that you wish to create a portfolio with no net wealth invested and the portfolio that achieves this has 50% in stock X, -100% in stock Y, and 50% in stock Z. The net arbitrage profit is?

10.Refer to Exhibit 9.2. The new prices now for stocks X, Y, and Z that will not allow for arbitrage profits are?