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FRM Part II · FRM Exam Part II · Empirical Properties of Correlation: How Do Correlations Behave in the Real World?

Empirical studies of correlation by volatility regime find that equity correlations are often higher when markets fall sharply than when they rise by the same magnitude. A risk manager wants to capture this feature in a model of joint equity returns. Which modeling choice is most appropriate?

A copula or regime-switching model with stronger lower-tail dependence than the Gaussian best captures correlations that rise in market downturns. A constant-correlation multivariate normal cannot reproduce asymmetric, rising correlation in falling markets, and would understate joint extreme losses.

  1. AA multivariate normal distribution with a single constant correlation
  2. BA copula or regime-based model with greater lower-tail dependence than the GaussianCorrect
  3. CAssuming zero correlation in the tails because extremes are idiosyncratic
  4. DUsing a lower correlation for downside scenarios to be conservative

Explanation

Asymmetric tail dependence requires a model with stronger lower-tail dependence, such as a Student t copula or a regime-switching correlation. A constant-correlation normal model has no tail dependence and symmetric behavior. Lowering the downside correlation would understate risk.

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