# Correlation

This page is a summary of correlation as a statistical tool, explaining what it does, which values it can reach and what different values mean, and how correlation can be used in finance and investing.

## Definition

Correlation measures how much two variables (e.g. security returns) tend to move in the same or opposite direction.

## Value Range

Correlation can reach values from -1 to +1.

## Interpretation

• +1 = perfect positive correlation = when one variable declines, the other increases, and vice versa
• Between 0 and +1 = positive correlation = the two variables tend to move in the same direction more often than in the opposite direction
• 0 = no correlation = the two variables move absolutely independently of one another
• Between 0 and -1 = negative correlation = the two variables tend to move in opposite direction more often than in the same direction
• -1 = perfect negative correlation = when one variable rises, the other falls, and vice versa

## Correlation in Finance and Investing

The concept of correlation is widely used in finance and investing, especially for portfolio optimization and risk management purposes. In general, the lower the correlation of two securities, the higher the diversification potential. When two securities are negatively correlated (e.g. typically stocks and government bonds), one usually rises when the other falls and gains on the first offset or reduce the losses on the second. On the contrary, positively correlated markets (e.g. stocks and oil) tend to rise at the same time or fall at the same time, which means high profits or high losses (other things being equal).

As a result, using the examples above, adding government bonds to a stock portfolio tends to diversify the risk, while the diversification effect of oil related securities in a stock portfolio is usually lower.

So far the theory. Practical application is of course much more diffcult, because correlations between securities rarely remain constant over time. We only know correlations from the past, but it's future correlation what actually matters for the risk in our portfolio.

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