Assume that stock market returns do follow a single-index structure.An investment fund analyzes 500 stocks in order to construct a mean-variance efficient portfolio constrained by 500 investments.They will need to calculate ________ estimates of firm-specific variances and ________ estimate/estimates for the variance of the macroeconomic factor.
A)500; 1
B)500; 500
C)124,750; 1
D)124,750; 500

Question

Quizplus · Accepted Answer

Since the stock market returns follow a single-index structure, the variance of individual stocks can be decomposed into two components: firm-specific variance (unsystematic risk) and market variance (systematic risk). As a result, when constructing a mean-variance efficient portfolio, investment in 500 stocks is equivalent to investing in the market index, hence there is only one macroeconomic factor variance estimate. Therefore, we need to calculate 500 estimates of firm-specific variances and 1 estimate for the variance of the macroeconomic factor. Thus, the correct answer is A.

Assume That Stock Market Returns Do Follow a Single-Index Structure