Defining Correlation
Correlation is a statistical measure of the degree to which two variables move together. In a portfolio context, it describes how the returns of two assets relate to each other over time. Correlation is expressed as a coefficient ranging from +1 to -1.
A correlation of +1 means the two assets move in perfect lockstep: whenever one rises 10%, the other rises exactly 10%; whenever one falls, the other falls by the same proportion. A correlation of -1 means they move in perfect opposition: when one rises, the other falls by the same amount. A correlation of 0 means the movements are statistically independent — knowing what one asset did tells you nothing about what the other did.
In practice, most assets have correlations somewhere between these extremes. Two technology stocks from the same country might have a correlation of 0.85 or higher. A domestic equity index and a domestic government bond index might have a correlation of 0.1 to 0.3 (lower, but usually still positive). Gold and global equities have historically shown low or even slightly negative correlations over many periods.
Covariance vs Correlation
Closely related to correlation is covariance, which measures the extent to which two assets move together in absolute terms. The problem with covariance is that its magnitude depends on the units of measurement — the raw scale of each asset's returns — making it difficult to compare across pairs.
Correlation is the standardised version of covariance. It is calculated by dividing the covariance of two assets by the product of their individual standard deviations. The result is always between -1 and +1 regardless of the underlying scale, making correlations directly comparable. When building portfolios, correlation is the more useful concept.
Why Correlation Determines Portfolio Risk
Harry Markowitz's landmark 1952 paper "Portfolio Selection" established mathematically why correlation — not just individual asset risk — is the key driver of portfolio risk.
The variance (squared standard deviation) of a two-asset portfolio is:
Portfolio variance = w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ₁₂
where w₁ and w₂ are the portfolio weights, σ₁ and σ₂ are the individual asset standard deviations, and ρ₁₂ is the correlation between the two assets. The critical term is the last one: it contains the correlation coefficient directly. When ρ₁₂ is low or negative, this term reduces the portfolio variance substantially below the weighted average of the individual variances.
This is why two assets can each have significant individual risk but combine into a portfolio with lower risk than either asset alone — if their correlation is sufficiently low.
Practical Examples of Correlation
Gold has historically had low or slightly negative correlation with equities. When equity markets fall sharply — particularly in crisis periods — gold has often risen or held its value, providing a partial hedge. This is why gold appears in many diversified portfolios despite its lack of yield or earnings.
Bonds and equities have historically had low or negative correlation during deflationary recessions, when falling interest rates push bond prices up at the same time equity prices are falling. However, this relationship can break down when inflation is the dominant concern, as both bonds and equities can fall simultaneously.
Stocks within the same sector — two pharmaceutical companies, two bank stocks — typically have high positive correlations because they share the same industry-level risks. Diversifying across sectors reduces these within-sector correlations.