FRM Part II · FRM Exam Part II · Empirical Properties of Correlation: How Do Correlations Behave in the Real World?
Equity correlations are estimated in two regimes. A risk manager finds that the average correlation is substantially higher when markets fall than when they rise by a similar magnitude. What is the most appropriate implication for VaR computed with a single constant correlation matrix estimated over a full sample?
A single full-sample correlation matrix may understate portfolio risk in downturns. It blends calm-period and stressed-period correlations, so it is lower than the correlations actually seen in sell-offs. The result is too much assumed diversification and a VaR that is too low when it matters most.
- AIt may understate portfolio risk in downturns because it blends calm and stressed correlationsCorrect
- BIt will overstate risk in all market conditions
- CIt is unbiased because average correlation equals the true correlation in every regime
- DIt affects only expected shortfall, not VaR
Explanation
A full-sample correlation averages regimes, so it is lower than the stressed correlation seen in sell-offs. Using it in a downturn understates co-movement and thus portfolio VaR for long-only positions. It is not unbiased conditionally, and VaR is affected too.
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