Correlation and diversification: why mixing assets reduces risk

Basics8 min read · updated 12 September 2026 · 9 sources

Correlation measures how closely two investments rise and fall together: from −1 (always in opposite directions) through 0 (no relationship) to +1 (always in lockstep). It is the reason why diversification lowers risk without lowering the expected return to the same extent.

How to calculate correlation

Correlation is the covariance of two return series divided by the product of their standard deviations. The covariance measures whether above-average returns of one investment coincide with above-average returns of the other; dividing turns it into a number between −1 and +1 that does not depend on the size of the fluctuations.

Correlation and portfolio volatility

This is the central insight of the portfolio theory of Markowitz (1952): a portfolio's risk is not the average of the individual risks but depends on how the investments interact. The return, by contrast, is simply the weighted average. This is why diversification has often been called the only “free lunch” in investing.

How far diversification goes

For many investments with the same volatility σ and the same pairwise correlation ρ, there is a simple formula. It shows that diversification lowers risk, but not without limit: a residual remains that comes from the risk shared by all the investments.

This calculation explains two things. First, why a broad index ETF has almost the same risk as the market as a whole: more stocks from the same market barely help any more. Second, why genuine diversification needs other sources of risk: bonds, commodities, other currencies or strategies with a low correlation to the stock market. There is also a reason rooted in the distribution of returns: according to Bessembinder (2018), many individual US stocks performed worse over their lifetime than short-term Treasury bills, while a few companies delivered most of the wealth creation. If you hold only a few stocks, you can easily miss the few big winners.

Typical correlations

Correlations are not fixed. In crises, they often rise between risky assets, precisely when diversification is needed most. A rolling correlation over 36 months shows how stable the relationship has been.

Equities and bonds: a changeable relationship

For most portfolios, the most important correlation is the one between equities and government bonds. From about 2000 to 2021, it was mostly negative: in crises, equities fell and investors fled into bonds, whose prices rose. As a result, a 60/40 portfolio was much calmer than its equity half alone.

In 2022 this reversed. As inflation rose and central banks raised interest rates sharply, equities and bonds fell at the same time. The reason makes sense: rising interest rates lower the value of future payments, directly for bonds and, for equities, through a higher discount rate on earnings. Whether the correlation is positive or negative therefore depends on what is currently driving the markets: worries about growth (then bonds help) or worries about inflation and interest rates (then both fall).

For planning, this means that a correlation measured over 20 years of falling interest rates is no guarantee for the next 20. If you want to protect yourself against inflation shocks, you need additional building blocks (such as inflation-linked bonds, short maturities or commodities) and should deliberately look at periods such as the 1970s or 2022 in the Backtest.

What research shows: correlation in crises

Does correlation really rise when it matters? Longin and Solnik (2001) studied international stock markets using methods for extreme events and found a clear asymmetry:

Ang and Chen (2002) found the same pattern for US stock portfolios: in downturns, stocks move together more strongly than in upswings. Forbes and Rigobon (2002) urge caution in measurement: because volatility rises in crises, the correlation coefficient also rises for purely mathematical reasons. After their correction, hardly any increase was left in the 1997 Asian crisis, the 1994 Mexican devaluation and the 1987 crash. But the markets were closely connected at all times. For investors, it comes down to the same thing: stocks from different countries offer each other little protection in a global crash.

Even so, many investors diversify too little. French and Poterba (1991) estimated that investors in Japan held over 98%, in the USA 94% and in the UK 82% of their equity wealth in their own country. This home bias can hardly be explained by costs or regulations; see Home bias.

Measuring diversification properly

• Correlation matrix: all pairs at a glance; values above 0.9 mean that two building blocks do almost the same thing.
• Effective number: how many equally sized, independent positions would give the same diversification? For weights, it is the reciprocal of the sum of the squared weights. For 50/30/20, that is 1 / (0.25 + 0.09 + 0.04) = 2.63 positions. For individual securities, the look-through shows it.
• Diversification ratio: weighted individual volatilities divided by the portfolio volatility. In the 50/50 example with a correlation of 0.3, it is 12.5 / 10.19 = 1.23. Choueifaty and Coignard (2008) build the maximum diversification portfolio on this.
• Principal components: if the first component explains 90% of the variation, the portfolio essentially contains a single risk. Following Kritzman et al. (2011), the share explained by the first components is called the absorption ratio; when it rises, markets are more closely linked.

For advanced readers: the limits of correlation

Pearson correlation measures only linear relationships. Two investments can be uncorrelated in normal times and still crash together. This is exactly what the crisis asymmetry above describes. Rank correlations (Spearman, Kendall) or measures of joint extreme losses are then more informative.

Estimated correlations are also imprecise. Over 36 months, a correlation of 0.3 has a standard error of roughly (1 − 0.3²) / √36 = 0.15. Almost anything between 0 and 0.6 is plausible. With many investments, the estimated matrix also becomes unstable, which leads optimizers to extreme weights. DeMiguel et al. (2009) show that a simple equal weighting often keeps up out of sample; shrinkage estimators help, see covariance estimation.

And finally, currency: for US investors, what counts is the correlation of returns in dollars. A euro bond fund without currency hedging partly behaves in dollars like a bet on the exchange rate via the euro, and its correlation with equities is quite different from what it is in euros.

What diversification cannot do

It lowers the risk of individual investments, not the risk of the market as a whole. A portfolio of 1,500 stocks still moves like the stock market. Genuine diversification comes from different risk drivers: equities, interest rates (duration), commodities, currencies. How much each investment contributes to total risk is shown in the article Risk contribution; what a whole portfolio of weakly correlated building blocks can look like is shown in the article Efficient frontier.

How Portfolio Lab calculates

On the Assets page, Portfolio Lab shows the correlation matrix of the period returns in the base currency over the common period, and rolling correlations for a selectable pair, by default over 36 months or 252 trading days. The principal component analysis works on standardized returns (i.e. on the correlation matrix) and gives the effective number of independent sources of risk (the exponential of the entropy of the explained variance shares) as well as the absorption ratio of the first components. In the look-through, the effective number of individual securities is the square of the sum of the shares divided by the sum of the squared shares. More in the asset analysis methodology.

This article explains a method; it is not investment or tax advice. Worked examples are simplified and rounded. All terms in the glossary.