Correlation, and why diversification fails when you need it

Correlation is a number between minus one and plus one describing how much two things move together. Plus one means identically, zero means unrelated, minus one means opposite. Diversification's entire benefit comes from holding things whose correlations are below one.

The problem is that correlation is not a constant. It is an average over a sample period, and the sample period is usually dominated by ordinary conditions. In stressed markets, correlations across risk assets rise toward one — sometimes dramatically — because in a crisis the dominant driver of every price is the same thing: participants reducing exposure and demanding cash.

The consequence for a diversified portfolio is that its measured diversification benefit is largest exactly when it is not needed and smallest exactly when it is. A portfolio built to have a 12 percent volatility on historical correlations can behave like an 18 percent volatility portfolio in a month when correlations jump, and the leveraged holder discovers this at the trigger level rather than in a spreadsheet.

There is a second-order version specific to lending. Concentration limits and advance rates are set on asset classifications, and a lender may treat two holdings as different asset types while the market treats them as the same trade. Diversification that exists in the classification and not in the correlation gives you the lower haircut and none of the protection.

The honest statement about diversification is that it reduces ordinary volatility reliably and reduces crisis losses much less than the historical numbers suggest.