Correlation

What is correlation?

Correlation is a statistical term that describes the relationship between two variables. In finance, correlation is used to analyse the extent to which the price movements of two assets are coordinated.

If in general, the prices of the two assets move in the same direction at the same time, they have a positive correlation. If they move in opposite directions, they have a negative correlation.

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What you need to know:
• A positive correlation is when two assets move in the same direction at the same time.
• A negative correlation - or inverse correlation - is when two assets move in a different direction at the same time.
• Choosing assets that have a negative correlation to each other can help to reduce portfolio risk. Many investors try to combine instruments that have a low correlation, so that they do not all increase or decrease in price at the same and by the same causes as a means of diversifying their portfolio. It’s important to note that correlation changes over time.
• During periods of heightened market volatility, stocks can become more correlated, even when they are unrelated

Correlation Coefficient

While the concept is called correlation, the number computed is called the correlation coefficient. This takes a value between -1 and +1.

If the prices of the two assets move in the same direction and by the same relative amount at all times, the correlation coefficient is +1.

If the prices of the two assets move in the opposite direction and by the same relative amount at all times, the correlation coefficient is -1.

If the prices of the two assets move in completely unrelated ways, the correlation coefficient is 0.

How is it calculated?

$\small{r_{x,y} = \frac{\sum{(x - \bar{x})(y - \bar{y})}} {\sqrt{\sum{(x - \bar{x})^2}}\sqrt{\sum(y - \bar{y})^2}}}$

where:

If the above formula is daunting, you can also use the "CORREL" function in Excel!

Why should I care?

Choosing assets that have a negative correlation to each other can help to reduce portfolio risk. A common misconception is that combining negatively correlated assets results in flat performance, i.e. that it means that if one asset increases in price, the other will decrease, such that all gains are offset.

While this is true if the correlation coefficient between them is -1 or very close to -1, if they have a relatively low negative correlation, it's possible for them both to increase in value.

The very simplified example below shows this in action. Assets A and B have a correlation coefficient of -0.26, but it's clear that over the time period stated. both have increased in price.

Example Table

DayAsset A PriceAsset B Price
1
40
40
2
50
30
3
60
20
4
70
10
5
80
20
6
90
30
7
80
40
8
60
50
Correlation Coefficient
-0.26

Many investors try to combine instruments that have a low correlation, so that they do not all increase or decrease in price at the same and by the same causes as a means of diversifying their portfolio.

By constructing a pairwise correlation matrix, it's possible to see the combinations of assets that are positively correlated, negatively correlated, or uncorrelated.

The theoretical portfolio below of five assets shows that JPM and KO are quite highly positively correlated, while AAPL has a low correlation to all the other assets except GME, with which it has a significant negative correlation.

Note!

During periods of heightened market volatility, stocks can become more correlated, even when they are unrelated. International markets can also become highly correlated during times of instability. Even in regular market conditions, it’s important to note that correlation changes over time.

It's also important to note that correlation does not imply causation. This means that while the prices of two assets may move together, it does not mean that either one of the asset price changes causes the change in the other, nor that there is a third variable that is driving both sets of prices.