How Much Does Low Correlation Reduce Portfolio Risk?
Correlation measures how closely two assets' returns move together. Use a two-asset volatility calculation to understand diversification benefits and the limits of historical correlations.
Holding assets with low correlation can reduce portfolio volatility for given weights and individual volatilities. But correlation alone cannot tell you the size of potential losses or how safe the portfolio is. Correlation measures how returns move together; actual risk also depends on each asset's volatility and portfolio weight.
Use returns at matching intervals rather than price levels
Do not conclude that two stocks have highly correlated returns just because both prices have risen over a long period. Calculate correlation using daily or monthly returns aligned to the same dates. For markets with different trading hours and holidays, the way dates are aligned can affect the result. Mixing dollar returns for one asset with won returns for another also distorts a comparison intended to assess risk for a won-based investor.
Understand the term that creates diversification benefits
For two assets, portfolio variance is the sum of two terms, each equal to a squared weight multiplied by a squared volatility, plus a covariance term equal to twice the product of both weights, both volatilities, and their correlation. Standard deviation is the square root of this variance. A correlation below 1 reduces the covariance term, but overall risk can remain high if a highly volatile asset has a large weight. A correlation of 0 does not mean a zero probability of loss.
Separate average relationships from relationships during crises
A single correlation over a long period can average away episodes when assets fell together during market selloffs. Examine the full period and market downturns separately, and compare how much the figure changes when you shift the period slightly. With fewer observations, the relationship may be coincidental, so do not use it as a precise future coefficient. Even when the statistic is low, examine the business structures for overlapping funding sources or customer bases.
Making large allocation changes based on a new correlation every time data is updated can fit your portfolio to chance patterns in short samples. It is better to show recent and longer periods side by side and see whether the direction of the conclusion holds. If the statistic changes, first check what has changed in company composition, the interest rate environment, or currency hedging. Linking numerical changes to economic causes enables interpretation beyond calculation alone.
Worked example
Hypothetical example: You invest equally in two assets, each with annual volatility of 20%. If their correlation is 1, portfolio volatility is 20%. With a correlation of 0, variance is 0.5²×0.2²+0.5²×0.2²=0.02 and standard deviation is approximately 14.14%. With a correlation of 0.5, variance is 0.03 and standard deviation is approximately 17.32%. These are volatility calculations, not expected returns.
What to check
- Have you aligned returns to the same currency and observation interval?
- Have you also used each asset's volatility and actual weight?
- Have you compared correlations during selloffs with those over the full period?
- Have you avoided interpreting low correlation as a guarantee against losses?
Sources and primary materials
This is educational material about research methods. For an actual company decision, verify the filings and primary sources for the relevant period.