Lesson 17 of 25 · 6 min

Diversification measured in the tail rather than on average

Thirty-six percent of a portfolio's measured risk reduction survives into the window where it is being relied on.

Diversification is normally reported as one number computed on all available data. That number is an average across regimes. A collateral test is not an average across regimes; it happens on a particular day, in whichever regime that day belongs to.

Fourteen equally weighted holdings, each with 31 percent annualised volatility. On the full sample the average pairwise correlation is 0.33, giving a bracket of 0.3779, portfolio volatility of 19.06 percent, and 2.65 effective bets. Conditioned on the tail the average correlation is 0.72, giving a bracket of 0.7400, portfolio volatility of 26.67 percent, and 1.35 effective bets.

Now express both as the benefit rather than the level, which is the form that answers what the diversification was for. A single holding carries 31 percent. On average the fourteen holdings removed 31 minus 19.06 = 11.94 volatility points. In the tail they removed 31 minus 26.67 = 4.33 points. The tail benefit is 4.33 divided by 11.94 = 36.28 percent of the average benefit. Just over a third of the risk reduction the portfolio was built for is present in the window that tests it.

The reframing this suggests is to carry two figures rather than one, because they answer different questions. The average figure describes the portfolio's ordinary behaviour, which is what it does in the overwhelming majority of months. The tail figure describes what it does in the minority of months during which a maintenance threshold can be reached. Track 1 lesson 7 made the same distinction about headroom — a quantity that is comfortable on an ordinary day and is not the relevant quantity on the day it binds.

One number cannot serve both purposes, and averaging the two is worse than either, because the average describes a regime that does not exist. Lesson 13's history showed exactly that: the full-sample 0.60 was neither the 0.29 of the ordinary months nor the 0.76 of the drawdown.

Key terms

Tail diversification: The risk reduction a portfolio still provides in the periods conditioned on severe market declines. Routinely a fraction of the full-sample figure.
Diversification benefit, in points: Single-name volatility minus portfolio volatility. Stating the benefit as a quantity rather than a level makes the shortfall in the tail visible.

Worked example

The same fourteen holdings, on average and in the tail

Fourteen equally weighted holdings, each at 31% annualised volatility. Average pairwise correlation 0.33 across the full sample and 0.72 conditioned on the tail. Illustrative figures.

Full-sample bracket and volatility: 0.3779 and 19.06%
Full-sample effective bets: 2.65
Tail bracket and volatility: 0.7400 and 26.67%
Tail effective bets: 1.35
Benefit against a single 31% holding: 11.94 points, then 4.33 points
Share of the benefit present in the tail: 36.28%

Fourteen holdings behaved like two and two thirds positions on average and one and a third in the tail. The second figure is the one a threshold test meets.

Check yourself

Nine equally weighted holdings, each at 27% volatility, show a 0.30 average correlation on the full sample and 0.68 in the tail. What share of the diversification benefit survives into the tail?

Saved in this browser only. No account, nothing sent anywhere.

Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.