Exhibit 7-8
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
Consider the three stocks, stock X, stock Y and stock Z, that have the following factor loadings (or factor betas) $$\begin{array} { c c c }
\text { Stack } & \text { Factor 1 Loading } & \text { Factor 2 Loading } \
\hline \mathbf { X } & - 0.55 & 1.2 \
\mathbf { Y } & - 0.10 & 0.85 \
\mathbf { Z } & 0.35 & 0.5
\end{array}$$
The zero-beta return (λ₀) = 3%, and the risk premia are λ₁ = 10%, λ₂ = 8%. Assume that all three stocks are currently priced at $50.
-Refer to Exhibit 7-8. If you know that the actual prices one year from now are stock X $55, stock Y 52, and stock Z $57, then
A) stock X is undervalued, stock Y is undervalued, stock Z is undervalued.
B) stock X is undervalued, stock Y is overvalued, stock Z is overvalued.
C) stock X is overvalued, stock Y is undervalued, stock Z is undervalued.
D) stock X is undervalued, stock Y is overvalued, stock Z is undervalued.
E) stock X is overvalued, stock Y is overvalued, stock Z is undervalued.

Question

Exhibit 7-8
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
Consider the three stocks, stock X, stock Y and stock Z, that have the following factor loadings (or factor betas) $$\begin{array} { c c c } 
\text { Stack } & \text { Factor 1 Loading } & \text { Factor 2 Loading } \
\hline \mathbf { X } & - 0.55 & 1.2 \
\mathbf { Y } & - 0.10 & 0.85 \
\mathbf { Z } & 0.35 & 0.5
\end{array}$$ 
The zero-beta return (λ₀) = 3%, and the risk premia are λ₁ = 10%, λ₂ = 8%. Assume that all three stocks are currently priced at $50.
-Refer to Exhibit 7-8. If you know that the actual prices one year from now are stock X $55, stock Y 52, and stock Z $57, then
A) stock X is undervalued, stock Y is undervalued, stock Z is undervalued.
B) stock X is undervalued, stock Y is overvalued, stock Z is overvalued.
C) stock X is overvalued, stock Y is undervalued, stock Z is undervalued.
D) stock X is undervalued, stock Y is overvalued, stock Z is undervalued.
E) stock X is overvalued, stock Y is overvalued, stock Z is undervalued.

Quizplus · Accepted Answer

To determine if the stocks are overvalued or undervalued, we calculate the expected return using the formula: $$E(R) = \lambda_0 + \beta_1\lambda_1 + \beta_2\lambda_2$$ and compare it to the actual return. For each stock:- Stock X: $E(R) = 3\% + (-0.55 \times 10\%) + (1.2 \times 8\%) = 3\% - 5.5\% + 9.6\% = 7.1\%$. Actual return = $\frac{55 - 50}{50} = 10\%$. Since the actual return is higher than expected, stock X is undervalued.- Stock Y: $E(R) = 3\% + (-0.10 \times 10\%) + (0.85 \times 8\%) = 3\% - 1\% + 6.8\% = 8.8\%$. Actual return = $\frac{52 - 50}{50} = 4\%$. Since the actual return is lower than expected, stock Y is overvalued.- Stock Z: $E(R) = 3\% + (0.35 \times 10\%) + (0.5 \times 8\%) = 3\% + 3.5\% + 4\% = 10.5\%$. Actual return = $\frac{57 - 50}{50} = 14\%$. Since the actual return is higher than expected, stock Z is undervalued.

Exhibit 7-8 USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)

Exhibit 7-8
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)