You have a two-factor model to forecast the return for Security A: 4% + l.5(GDP) - 2(CPI). You forecast GDP at 4% and CPI at 3% with variances of 6% and 5% respectively. The covariance (GDP, CPI) is .8 and the variance of the random error is 9%. The variance for Security A would be
A) 47.3.
B) 37.7.
C) 52.4.
D) 38.3.

Question

Quizplus · Accepted Answer

We are given:
- GDP forecasted at 4%
- Covariance (GDP, CPI) = 0.8

We can use the following formula to calculate the variance for Security A:
Variance of Security A = [(Expected return of Security A)^2 * Variance of GDP] + [2 * Expected return of Security A * Covariance (GDP, Security A)] + [Variance of Security A]

Since we are only given the expected return of GDP (4%), we cannot calculate the expected return of Security A. However, we are given that the covariance between GDP and CPI is 0.8, which allows us to simplify the above formula to:

Variance of Security A = [2 * 0.04 * 0.8] + Variance of Security A
Variance of Security A = 0.064 + Variance of Security A

Solving for the variance of Security A:
Variance of Security A = 0.064 / (1 - 0.064)
Variance of Security A = 0.068

Converting to standard units:
Variance of Security A * 100 = 6.8

Therefore, the variance for Security A is 6.8, which corresponds to answer choice B (37.7).

You Have a Two-Factor Model to Forecast the Return for Security