Characterise the behaviour of equity correlations and of correlation volatilities across different states of the economy.
The idea
Equity correlations are not constant: they depend on the state of the economy. Empirically, average pairwise correlations between stocks are lowest in expansions and highest in recessions and sell-offs. Common systematic factors then swamp firm-specific news, so diversification weakens exactly when it is needed. Correlation volatility, the standard deviation of changes in correlation over time, is also higher in recessions, so correlation is both higher and less stable in stress. Correlations also mean-revert: after a spike they drift back towards a long-run level. The practical consequence is that a correlation matrix estimated in calm markets understates portfolio risk in a downturn. VaR and hedge ratios therefore need stressed correlation inputs. Exam point: recession means higher correlation and higher correlation volatility. Do not confuse the level of correlation with its volatility.
A practice question
Which statement best characterises how average equity correlations behave across states of the economy?
- Equity correlations are highest in expansions, when stocks respond to firm-specific news, and lowest in recessions.Why not: Reverses the empirical pattern: common systematic factors dominate in recessions, so correlations rise there.
- Equity correlations are higher in recessions than in expansions, and they tend to drift back towards a long-run level after a spike. - correct
- Equity correlations are essentially constant over the economic cycle, so a single estimate is enough.Why not: Treats correlation as a stable parameter and ignores its dependence on the state of the economy.
- Equity correlations are lowest in recessions because investors spread money across many sectors.Why not: Confuses investor diversification behaviour with the common-factor driven co-movement that pushes correlations up in stress.
Empirically equity correlations are lowest in expansions and highest in recessions, and they mean-revert. Diversification therefore weakens in downturns.
A harder one
A portfolio holds 10 equally weighted stocks, each with annual volatility 30%. The average pairwise correlation is 0.25 in an expansion and rises to 0.50 in a recession. Using the average-correlation formula, portfolio volatility = sigma x sqrt(1/n + (1 - 1/n) x rho), the portfolio volatility under recession conditions is closest to:
- 22.2% - correct
- 17.1%Why not: Uses the expansion correlation of 0.25, ignoring that correlations rise in a recession.
- 21.2%Why not: Drops the 1/n term and computes sigma x sqrt(rho), which treats the portfolio as if it had infinitely many stocks.
- 4.9%Why not: Reports the portfolio variance (0.0495) rather than taking the square root to get volatility.
Variance factor = 1/10 + 0.9 x 0.50 = 0.55; volatility = 30% x sqrt(0.55) = 22.2%. In expansion (rho 0.25) it would be only 17.1%, so recession correlation lifts risk.
The hardest tier
A desk hedges a stock A with a sector index future B using the minimum-variance hedge ratio h = rho x sigma_A / sigma_B. In an expansion sigma_A = 20%, sigma_B = 15% and rho = 0.30. In a recession the volatilities are sigma_A = 35% and sigma_B = 28%, and the correlation rises to 0.60. The hedge ratio recalibrated to recession conditions is closest to:
- 0.40Why not: Keeps the stale expansion inputs, ignoring that both correlation and volatilities change with the economic state.
- 0.48Why not: Inverts the volatility ratio, using sigma_B / sigma_A instead of sigma_A / sigma_B.
- 0.80Why not: Combines the recession correlation with expansion volatilities, mixing inputs from two states.
- 0.75 - correct
h = 0.60 x 35 / 28 = 0.75, against 0.40 in the expansion. A hedge calibrated in calm markets under-hedges when correlation and volatility jump.
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