Why does diversification reduce risk?

Because portfolio variance includes a cross term scaled by correlation. Below a correlation of one that term does not fully add, so the combination is less volatile than its parts.

Does it still work in a crash?

Less well. Correlations tend towards one when markets fall together, which is the well-known criticism: the benefit shrinks precisely when it is needed.

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Asset Correlation Calculator

Correlation between two return series and what it does to a portfolio. Any correlation below one reduces portfolio volatility below the weighted average, which is the entire mathematical case for diversification.

Also called: portfolio correlation, diversification benefit.

Correlation

0.99

The two move together with a correlation of 0.99. A 60/40% portfolio has volatility 2.01% against a weighted average of 2.01%, so diversification saves 0% points.

Volatility of the first

2.23%

Volatility of the second

1.69%

Portfolio volatility

2.01%

Weighted average, without the correlation effect

2.01%

Volatility saved by diversifying

Weight on the second

40%

How this is calculated

Method and background

This is what the calculation gives for the numbers you entered. It is an estimate, not advice, and it knows nothing about your situation beyond those numbers. Rules for United States change on a published schedule; the effective date is shown on every rule-based tool.

How this is calculated

Portfolio variance is not the weighted average of the two variances: it includes a cross term scaled by the correlation. When the correlation is below one that term is smaller than it would otherwise be, so the portfolio is less volatile than its parts weighted together. That gap is the diversification benefit, and it is the one free lunch in investing. At a correlation of exactly one it disappears entirely.

portfolio volatility falls below the weighted average whenever the correlation is under one

w: Weights
rho: Correlation

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

two similar series

First series: 2.1, -1.4, 3.2, 0.8, -2.6, 1.9
Second series: 1.8, -0.9, 2.4, 1.1, -1.9, 1.5
Weight on the first: 60%

Correlation0.99

Structural: portfolio volatility must not exceed the weighted average

Open this example

identical series have a correlation of one

First series: 1, 2, 3, 4
Second series: 1, 2, 3, 4
Weight on the first: 50%

Correlation1

boundary: the case where diversification gains nothing

Open this example

Method and limits

What it assumes

Both series cover the same periods in the same order.

What it deliberately does not model

Correlations rise sharply in market stress, which is exactly when the benefit is wanted.
Historical correlation is an unstable estimate of future correlation.

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

Why does diversification reduce risk?: Because portfolio variance includes a cross term scaled by correlation. Below a correlation of one that term does not fully add, so the combination is less volatile than its parts.
Does it still work in a crash?: Less well. Correlations tend towards one when markets fall together, which is the well-known criticism: the benefit shrinks precisely when it is needed.