# Primer: taking correlations out of the black box

2 May 2016

One of the most frequently used and misused statistics in investing is correlation. We tend to look at correlations where it is easiest to find data rather than look at the relationships we care most about. Overcoming these shortcomings requires a more discerning approach, we argue. The resulting impact on a portfolio can be significant.

A fuller understanding of correlations requires an understanding of covariance. The correlation of any two series is their covariance divided by the product of the volatility of each series. Covariance measures how each series varies around its average value. So the covariance (and therefore the correlation) measures the average relationship between two variables over some period, a relationship based on the frequency of the data and the average value of each series over that period at that frequency. That’s a very important sentence and one that deserves further investigation:

Correlation is mostly used in investment to say something about how two assets will behave relative to each other in the future. If the future looks like the past and the relationship between the two assets is very stable, then the correlation will function as we hoped. But if the correlation is not stable, as is often the case, then the near-term future may look very different from the average of the past.

The relationship that is measured by the correlation compares two assets against their respective average values over the selected time period at the chosen data frequency. As the time period and/or the data frequency change, so the correlation is likely to change, leading in part to the instability just mentioned.

In Figure 1 below, the left-hand chart plots a very simple example of two series where the correlation is a perfect +1.0. The right-hand chart adds one more data point to each series. This flips the correlation from +1.0 to almost -1.0, highlighting the instability of correlations and their susceptibility to outlier data.

Figure 1: Guess the correlation

For illustrative purposes only. Source: Schroders.

To extract better information from our correlations, we need to think harder both about what we expect them to be in the future and the data we use to calculate them. Our analysis will improve if we first answer some questions:

• At what frequency do we care about the relationship between two assets?
• What periods in the past are most representative of the period in the future we care about?
• How much data do we have to crunch, given our frequency of interest and the number of historical periods similar to our expected future?

The missing – and vital – ingredient from this analysis is an understanding of what drives asset returns. We have to be ready to use our knowledge of the impact of the economic environment if we are to put correlations to good use. But ultimately, we also have to recognise their limitations. At best they distil complex relationships into an average over a selected period at a certain frequency of observation. To get the best out of correlations, we need to step out of our black-box mindset and think a little harder about what we want from them and how that will affect what we actually get from them.

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### Primer: taking correlations out of the black box5 pages | 717 kb

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