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FRM Part II · FRM Exam Part II · Portfolio Risk: Analytical Methods

A risk manager decomposes a portfolio's variance using a multifactor model and finds that 70% of variance is explained by common factors. The manager then adds many additional, uncorrelated positions to diversify the portfolio. Which outcome is most likely?

The residual share of variance falls and the factor-explained share rises. Adding many positions with uncorrelated residuals diversifies away idiosyncratic risk, but exposure to common factors remains. Systematic risk is not eliminated by diversification, so it becomes a larger proportion of total variance.

  1. AResidual variance share falls and factor-explained share risesCorrect
  2. BFactor-explained share falls as factor betas shrink to zero
  3. CBoth residual and systematic variance fall in equal proportion
  4. DSystematic variance is eliminated while residual variance remains

Explanation

Diversification across positions with independent residuals shrinks idiosyncratic variance toward zero, while factor exposure (systematic risk) cannot be diversified away. Hence the factor-explained share of total variance rises. The other options contradict this asymmetry.

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