When diversification fails

What happens during market crashes, how correlations spike in times of stress, and why diversified portfolios can still suffer large losses.

Play with it

Diversification and portfolio risk. Mix two assets, trace the efficient frontier, then switch on a crisis and watch correlations jump.

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Weight in asset A60% A, 40% B

Correlation between A and B-0.20

A volatility18%

B volatility7%

A expected return8.0%

B expected return3.5%

Portfolio volatility10.6%

Expected return6.2%

If risk just added up13.6%no diversification

Where the portfolio's variance comes from

Risk from A

117

Risk from B

Interaction

-12

Total variance

112

Variance in squared percentage points. Negative interaction cancels risk.

Holding 60% in A and 40% in B gives volatility of 10.6%, not the 13.6% you'd get if risks simply added up. The interaction term is negative, so the two risks partly cancel out. The lowest-risk mix holds 18% in A.

Try this

Set correlation to +1. The curve becomes a straight line: no free reduction in risk.
Set it to −1 and find the weight where portfolio volatility drops to zero.
Start at 100% in B (bonds) and add a little A (stocks). Does risk go up or down at first?
Any point below the lowest-risk dot is inefficient: more risk for less return.

The math

\sigma_p^2 = w^2\sigma_A^2 + (1-w)^2\sigma_B^2 + 2w(1-w)\,\rho\,\sigma_A\sigma_B

$w$: weight in asset A
$\sigma_A, \sigma_B$: each asset's volatility
$\rho$: their correlation
$2w(1-w)\rho\sigma_A\sigma_B$: the interaction term

Quick check

Two questions to see if it clicked. Answers explain themselves.

What tends to happen to correlations during a market panic?

Why can liquidity make crashes worse?