Statistical Foundations: Understanding Correlations

Whereas standard deviation shows how risky individual assets are, correlations show how asset risks are interrelated. Correlations are calculated by observing historical comovement in returns and range between –1 and 1.

A correlation of 1 means that returns move together perfectly, whereas a correlation of -1 implies perfect opposite movement. A 0 (zero) correlation implies independence. We generally observe positive correlations within an asset class (for example, equities) and between the major assets classes (for example, stocks and bonds); however, FX prices and commodity prices tend to have lower correlations to other asset classes.

Positive correlation (75%): These stocks generally move in the same direction

Negative Correlation (75%): These stocks generally move opposite each other

Independent: There is no apparent relationship between these stocks r.

Correlations Affect Diversification

Portfolio managers look for assets with low (or even negative) correlations to achieve better diversification.

Correlations are dynamic and often change during volatile market conditions, which may significantly affect portfolio risk.

Correlation vs. Causality

It is important to distinguish between correlation and causality. Causality is result of one event precipitating another event (for example, Thai baht devaluation precipitating an Asian market meltdown), whereas correlation is a statistical measure of observed comovement over a period of time.

Correlations are Dynamic

Correlations can easily change from positive to negative. For example, while we tend to see positive correlations between stocks and bonds (because rising interest rates generally have a negative effect on stock prices and vice versa), you can see that this relationship is not stable. Note in particular how correlation turned negative in October 1997, when there was a high stock market volatility (may be due to flight to safety--people exiting stocks in favor of bonds).