The variance of returns for a risky asset is 25 percent. The variance of the error term, Var(e), is 8 percent. What portion of the total risk of the asset, as measured by variance, is systematic?
A) 32 percent
B) 8 percent
C) 68 percent
D) 25 percent
E) 75 percent

Question

Quizplus · Accepted Answer

The total variance of the asset can be expressed as the sum of systematic (explained) variance and unsystematic (unexplained) variance: 
Total Variance = Systematic Variance + Unsystematic Variance 
Given: 
Total Variance = 25% 
Unsystematic Variance (Var(e)) = 8% 
Therefore, 
Systematic Variance = Total Variance - Unsystematic Variance 
Systematic Variance = 25% - 8% = 17% 
The portion of the total risk that is systematic can be expressed as a percentage of the total variance: 
Systematic Risk Portion = (Systematic Variance / Total Variance) x 100% 
Systematic Risk Portion = (17% / 25%) x 100% = 68% 
Therefore, the answer is C, 68%.

The Variance of Returns for a Risky Asset Is 25