Lesson 1 of 25 · 6 min

Why a count of holdings measures nothing on its own

Two portfolios of twelve names can carry 13.3 percent volatility and 24.8 percent, and the statement looks the same.

A holdings page reports a count, and the count is the one fact about diversification that carries no information by itself. It is not a weak signal or a rough guide. Without a second number beside it, it is consistent with almost any level of risk the portfolio could have.

Track 4 lesson 15 established that correlations measured in calm markets are not the correlations you get in stressed ones, and Track 7 lesson 10 showed that a group of correlated names is entitled to be treated as fewer names. This track starts from both results and does the work they imply: it treats correlation as the unit in which diversification is measured, computes it, and computes what happens to it when the market stops being ordinary.

Here is the count's failure in one comparison. Two portfolios, twelve equally weighted holdings each, every holding with 29 percent annualised volatility. In the first the average pairwise correlation is 0.14; in the second it is 0.71. Using the arithmetic Track 7 lesson 10 set out — one-twelfth, plus eleven-twelfths of the correlation, then the square root, times 29 percent — the first portfolio carries 13.34 percent volatility and the second carries 24.85 percent. Eleven and a half points apart, on identical counts and identical single-name volatilities.

The count is not merely uninformative; it can point the wrong way. Six holdings at an average correlation of 0.20 carry less risk than thirty holdings at 0.55, and the thirty-line statement is the one that looks prudent.

Diversification is a statement about how many different things can go wrong, not about how many lines are printed. The two are related only through a number that appears on no statement.

Key terms

Average pairwise correlation: The average of the correlations between every possible pair of holdings in a portfolio. One number standing in for the whole grid of them.
Holdings count: How many separate positions appear on a statement. It bounds diversification from above and says nothing about how much of that bound is reached.
Single-name volatility: How much one holding moves on its own, usually annualised. The starting point every diversification calculation works down from.

Worked example

Twelve holdings, twice, with different answers

Two portfolios of twelve equally weighted holdings, every holding at 29% annualised volatility. Average pairwise correlation 0.14 in one and 0.71 in the other. Illustrative figures.

Bracket at 0.14 correlation: 0.2117
Portfolio volatility at 0.14: 13.34%
Bracket at 0.71 correlation: 0.7342
Portfolio volatility at 0.71: 24.85%
Difference: 11.51 percentage points
Difference visible on either statement: None

Same count, same single-name volatilities, nearly double the risk. The count was not a rough guide to the answer; it was silent about it.

Check yourself

Portfolio A holds six equally weighted names at an average pairwise correlation of 0.20. Portfolio B holds thirty at 0.55. Every holding in both has 26% volatility. Which portfolio carries less risk?

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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.