Lesson 10 of 25 · 7 min

Correlated names are one name for haircut purposes

Counting holdings measures nothing useful; what a schedule counts is how many independent things are present.

Six holdings sound like six exits. They are six exits only if the six can fall for six different reasons, and when they cannot, a schedule is entitled to treat them as fewer.

The arithmetic is compact. For equally weighted holdings sharing one pairwise correlation, portfolio volatility depends on the count and the correlation together, and the correlation term dominates as soon as it is large.

portfolio volatility = single-name volatility × square root of (1/n + (1 − 1/n) × correlation)

portfolio volatility: The volatility of the equally weighted group taken as one collateral block.
single-name volatility: The volatility each holding has on its own.
n: The number of equally weighted holdings.
correlation: The pairwise correlation shared by every pair in the group, from 0 to 1.

Six holdings, each at 34 percent volatility, correlated 0.85 with each other. The bracket is 1/6 + (5/6 × 0.85) = 0.1667 + 0.7083 = 0.8750, and 34 × the square root of 0.875 = 34 × 0.9354 = 31.80 percent. One holding alone was 34 percent. Six holdings bought 2.2 points of reduction. Drop the correlation to 0.15 and the bracket becomes 0.1667 + 0.1250 = 0.2917, giving 34 × 0.5401 = 18.36 percent.

The reciprocal of the bracket is the useful summary: it is the effective number of independent holdings. At 0.85 correlation, 1 ÷ 0.875 = 1.14, so six names are worth 1.14 names of diversification. At 0.15 correlation, 1 ÷ 0.2917 = 3.43. The count on your statement said six in both cases. Track 4 lesson 15 adds the sting: correlations rise in stressed markets, so the effective count falls exactly when the exit is needed.

Key terms

Pairwise correlation: How closely two holdings move together, from 0 for unrelated to 1 for identical behaviour.
Effective number of holdings: How many genuinely independent positions a group behaves like. Six highly correlated names can behave like barely more than one.
Grouped exposure: Several holdings a lender treats as one for concentration purposes because they respond to the same events.

Worked example

Six holdings, counted two ways

Six equally weighted holdings, each with 34% volatility. Compare a pairwise correlation of 0.85 with one of 0.15. Illustrative figures.

Bracket at 0.85 correlation: 0.8750
Group volatility at 0.85: 31.80%
Effective number of holdings at 0.85: 1.14
Bracket at 0.15 correlation: 0.2917
Group volatility at 0.15: 18.36%
Effective number of holdings at 0.15: 3.43

The same six positions were worth 1.14 independent holdings in one case and 3.43 in the other. The count never changed.

Check yourself

Four equally weighted holdings each have 30% volatility and a pairwise correlation of 0.70. What is the group's volatility, and how many independent holdings does it behave like?

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.