Correlation: how co-movement shapes diversification
Interactive bivariate correlation explorer. Slide ρ from −1 to +1, see simulated scatter plots, compare standalone versus portfolio volatility for stocks and bonds or two insurers in one region, and switch to a t-copula to see the joint crashes a single correlation hides.
Diversification works only to the extent that risks do not move together, and correlation (ρ, from −1 to +1) measures how closely they do. For two risks of equal size held 50/50, the portfolio's volatility at ρ = 0 is about 71% of what it would be with no diversification; at ρ = 1 there is no benefit at all; at ρ = −1 the risks cancel. The module shows this with a scatter of 100 simulated paired outcomes and bars comparing each risk's volatility with the portfolio's, for two presets: equities and government bonds (ρ = −0.3 by default) and two insurers writing in the same region (ρ = 0.65).
Correlation is also where risk models fail most expensively. Two insurers writing property in the same region can look weakly correlated in normal years and almost perfectly correlated in the year of the storm. Equity and credit markets behave the same way in a crisis: the scatter tightens into a line exactly when diversification is needed.
Pearson's ρ measures linear co-movement only. A crisis-dependence toggle swaps the normal (Gaussian) dependence for a t-copula with the same ρ: the volatility bars do not move, but the probability that both risks fall into their worst 5% together rises. That is tail dependence, the part of the risk a single correlation number cannot show.
Two-asset portfolio variance
σ_p² = w₁²σ₁² + w₂²σ₂² + 2 w₁ w₂ ρ σ₁ σ₂
w₁ and w₂ are the portfolio weights (50/50 in the explorer), σ₁ and σ₂ the two risks' volatilities, and ρ the Pearson correlation between them; σ_p is the portfolio volatility.
Frequently asked questions
Does zero correlation mean the risks are independent?
No. Zero Pearson correlation rules out linear co-movement only. Two variables can be uncorrelated yet strongly dependent in the tails, which is why insurers and banks model dependence with copulas as well as correlation matrices.
How much does diversification reduce portfolio volatility?
For two equal risks held in equal weights, portfolio volatility relative to the undiversified figure is √((1 + ρ)/2): about 71% at ρ = 0, 87% at ρ = 0.5, and 100% at ρ = 1. The benefit disappears as correlation approaches one.
Why does correlation rise in a crisis?
Common shocks such as a catastrophe or a liquidity squeeze hit every exposure at once, so the shared factor dominates idiosyncratic noise. Models calibrated on calm periods understate joint losses; stress testing and tail-dependence measures address this.
Interactive explorer
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