FRM Part I · FRM Exam Part I · Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)
An analyst builds a Markowitz mean-variance optimization for a universe of 50 risky assets. How many distinct pairwise covariance estimates (excluding the variances) are required as inputs?
The analyst needs 1,225 distinct covariance estimates, calculated as 50 × 49 / 2. Covariance is symmetric, so each pair is counted once, and the 50 variances are excluded. Including the variances would give 1,275 inputs, which is a different count from the one asked for.
- A1,225Correct
- B2,450
- C50
- D1,275
Explanation
The number of distinct pairwise covariances is N(N−1)/2 = 50 × 49/2 = 1,225. The 2,450 option counts both Cov(i,j) and Cov(j,i), though they are identical. The 1,275 option, N(N+1)/2, includes the 50 variances.
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