Financial professionals frequently refer to correlation when talking about investments.  The term is taken from statistics and refers to the strength of a relationship between two or more variables.

Examples of correlation are all around us: people with higher education tend to have higher incomes and kids who watch more TV have lower grade point averages. 

For the purposes of illustration, I created some data about education and income to illustrate how a statistician would use correlation to understand the relationship between these two variables.

In this example, there are ten people whose income is measured on the bottom of the chart, compared to the number of years of their education, on the chart axis.  

In general, we see that people with more years of education have higher levels of income.  This isn’t true for every data point, but we see a strong connection between these two factors. 

Of course, it’s important to note that this relationship isn’t necessarily causal, meaning that more education doesn’t necessarily cause higher incomes in the same way we wouldn’t say that a higher income causes more years of education.  What we are measuring is the strength of the relationship between the two variables.

The relationship that we see graphically above can be distilled into a single number, known as the correlation coefficient.  In this case, the correlation is approximately 0.80.  Two series of data that are perfectly correlated have a correlation of 1 and a 0.80 correlation means that there is a high degree of correlation.

Conversely, correlations can be negative.  Consider the example of grades compared to hours of TV watching per week.  We would expect that the greater levels of TV watching lead to lower grades.  Unlike education and income where more education was related to more income, more TV watching leads to lower grades.  Something that is perfectly negatively correlated has a correlation coefficient of -1. 

The range from -1 to 1 shows the strength of the relationship.  A correlation of zero, (the half way mark between -1 and 1) means that there is no relationship between the two variables.  The image below is copied from Wikipedia and does a nice job of helping visualize various levels of correlation between -1 and 1.

In finance, correlation is very important because it is the key factor in diversification of investment portfolios.  For example, if two assets with similar risk/return characteristics are perfectly correlated and move in complete lockstep with each other, then it doesn’t make sense to own both of the assets – one would suffice. 

We frequently see people ‘diversify’ by owning ten large cap stock funds, but since the risk return characteristics are basically the same and they are all highly correlated with each other, there is not much diversification benefit.

More importantly, though, is the impact of correlation on two assets with different risk/reward characteristics.  For purposes of example, let’s assume that stocks have an average return of 10 percent and an average standard deviation of 20 percent.  Next month I will address standard deviation, but for now, all you need to do is recognize that a higher standard deviation is more volatile, or riskier. 

Let’s also assume that bonds have an expected return of four percent and a standard deviation of five percent.  In this example, stocks earn 2.5 more than bonds but are four times as volatile.

Now, let’s assume five different levels of correlation: -1, -0.5, 0, 0.5 and 1, which are all displayed on the chart on the previous page.

The dark blue line to the right shows the portfolio allocation choices between stocks and bonds if the correlation between them is 1, or a perfect correlation.  The bottom point represents a portfolio that is 100 percent bonds and no stocks, and the top point represents a portfolio of 100 percent stocks and no bonds. 

Because the correlation is perfect in this example, there is no benefit from diversification.  When stocks go up, bonds go up proportionally and the risk/return properties change proportionally as the asset mix changes.  Therefore, with the standard deviation for bonds at five percent and the standard deviation for stocks at 20 percent and perfect correlation, an investor who wants a 50/50 stock bond mix, would have a portfolio with a 12.5 percent standard deviation and a return of 7%.

On the other hand, if stocks and bonds were perfectly negatively correlated, a -1 correlation, as depicted by the light blue line on the left, there is a major benefit of diversification.  Using the same stock/bond assumptions, it is theoretically possible to have a portfolio with zero volatility. 

Obviously, in the real world it isn’t possible to create portfolio of stocks and bonds with no volatility.  In theory, though, a -1 correlation mix with a 20/80 mix of stocks/bonds would be expected to grow at 5.2 percent without any volatility.  That’s because whenever stocks lost, bonds would rise and perfectly offset that loss and when bonds lost, stocks would serve in the same capacity.

When evaluating asset allocation choices, the correlation assumption is one of the most important to consider.  Unfortunately, it is also the most difficult since correlations are not static, they are constantly changing.  They differ depending on the time periods evaluated and they change over time. 

At Acropolis, we measure and evaluate the annual correlation between approximately 50 different asset classes over 25 years to help identify the long-term relationships among them.  In our view, 25 years allows enough time to see how different asset classes react to each other in a variety of different market environments but still allow new data to have the same impact as older data to try and capitalize on the changing nature of correlation.  Using this information we are able to build portfolios with a mix of asset classes, large cap, mid cap, international, bonds, etc.  that maximizes returns for a prescribed  amount of risk.

It’s often said in finance that diversification is the only free lunch.  That may well be true and correlation (or the lack thereof) is the key ingredient.