Reading 68: LOS j ～ Q6- 10

6.Assume you are considering forming a common stock portfolio consisting of 25 percent Stonebrook Corporation (Stone) and 75 percent Rockway Corporation (Rock). As expressed in the two-factor returns models presented below, both of these stocks’ returns are affected by two common factors: surprises in interest rates and surprises in the unemployment rate.

R_Stone = 0.11 + 1.0F_Int + 1.2F_Un + ε_Stone
R_Rock = 0.13 + 0.8F_Int + 3.5F_Un + ε_Rock

Assume that at the beginning of the year, interest rates were expected to be 5.1 percent and unemployment was expected to be 6.8 percent. Further, assume that at the end of the year, interest rates were actually 5.3 percent, the actual unemployment rate was 7.2 percent, and there were no company-specific surprises in returns. This information is summarized in Table 1 below:

Table 1: Expected versus Actual Interest Rates and Unemployment Rates

What is the expected return for Stonebrook?

A)   11.0%.

B)   13.0%.

C)   13.2%.

D)   17.3%.

The correct answer was A)

The expected return for Stonebrook is simply the intercept return (a_i) of 0.11, or = 11.0%.

7.What is the expected return for Rockway?

A)   11.0%.

B)   13.2%.

C)   13.0%.

D)   17.3%.

The correct answer was C)

The expected return for Rockway is simply the intercept term (a_i) of 0.13, or 13.0 percent.

8.What is the portfolio’s sensitivity to interest rate surprises?

A)   0.85.

B)   0.95.

C)   0.25.

D)   0.75.

The correct answer was A)

The portfolio composition is 25 percent Stonebrook and 75 percent Rockway. The interest rate sensitivities for Stonebrook and Rockway are 1.0 and 0.8, respectively. Thus, the portfolio's sensitivity to interest rate surprises is: (0.25)(1.0) + (0.75)(0.8) = 0.85.

9.What is the portfolio’s sensitivity to unemployment rate surprises?

A)   2.925.

B)   1.775.

C)   2.625.

D)   0.900.

The correct answer was A)

The portfolio composition is 25 percent Stonebrook and 75 percent Rockway. The unemployment rate sensitivities for Stonebrook and Rockway are 1.2 and 3.5, respectively. Thus, the portfolio's sensitivity to unemployment rate surprises is: (0.25)(1.2) + (0.75)(3.5) = 2.925.

10.What is the expected return of the portfolio?

A)   2.75%.

B)   9.75%.

C)   11.5%.

D)   12.5%.

The correct answer was D)     

The portfolio composition is 25 percent Stonebrook and 75 percent Rockway. The expected returns for Stonebrook and Rockway are 11 percent and 13 percent, respectively. Thus, the portfolio’s expected return is (0.25)(0.11) + (0.75)(0.13) = 12.5%.