Correlation defined
Imagine a flock of birds in the sky, or a school of fish swimming together in the ocean. While each group contains individuals that can make their own decisions, as a group, they tend to move in the same direction almost simultaneously. It is visually striking to watch them move together in near perfect unison as if they were connected by invisible strings. In fact, we can describe the relationship between the birds or the fish as having a nearly perfect correlation. The degree to which the individuals in the group are connected is a function of their correlation.
It is easy to visualize portfolios of individual stocks as being just another example of group behaviour. At times, the individual stocks move together in perfect unison like a flock of birds, and at other times they seem to go in their own direction. Correlation is quantified via a statistic called the Correlation Coefficient, which varies between -1 (moves in opposite directions) and +1 (moves in the same direction). A coefficient of 0 indicates no relationship.
A common misconception is that two securities with a perfect negative correlation will cancel each other out, leaving a portfolio return of zero, but this is not the case. Correlation describes the degree to which two securities deviate in the same direction from their individual average returns. In this way, two securities can be perfectly negatively correlated (coefficient of -1) but also move in the same general direction over time.
Stocks and bonds provide an intuitive example of this phenomenon. Both stocks and government bonds exhibit positive average long-term average returns, but they are negatively correlated over the long-term. In this way, while the average volatility of stocks is 20 percent and the average volatility of bonds is 12 percent, the long-term realized volatility of a 50/50 stock and government bond portfolio is 10.6 percent rather than16 percent, which is the arithmetic average of the two securities (see chart).
In fact, the mathematical relationship between volatility and correlation was the breakthrough that landed Harry Markowitz his Noble Prize in Economics. From this equation it can be demonstrated that portfolio volatility always declines as correlation trends from +1 to -1, and volatility is eliminated entirely when correlation reaches -1 (see table).
In our article on volatility, we demonstrated how managing exposures to individual securities to control volatility resulted in higher absolute and risk-adjusted returns for a variety of asset classes. You can see how correlation and diversification can be applied at the portfolio level by measuring and allocating to assets within portfolios purely on the basis of correlation.
Unfortunately, in practice, most Portfolio Managers make long-term assumptions about correlations between assets. But actual correlations between assets can vary widely over time. Thus, it makes sense to constantly observe the actual correlation over time and adjust the portfolio accordingly. In the chart below, we see the actual historical 60-day rolling correlation between the S&P 500 index and Gold through 2011. Notice that the correlation statistic trends up and down over time, and is persistent over short time periods like days and weeks.
To illustrate, the chart below displays two fictitious portfolios whose investment universe is composed of the 10 major global asset classes ( Commodities, Emerging Markets, Japan, Gold, US Real estate, Europe, International Real Estate, 20-Year Treasuries, Global Equities. ). The red line represents an equal weight portfolio of the asset classes rebalanced monthly. The blue line represents a monthly rebalanced portfolio using a Minimum Correlation algorithm. The method is similar to the Minimum Variance algorithm that has become well-accepted by sophisticated practitioners and academics. While Minimum Variance focuses on minimizing total portfolio risk, the Minimum Correlation algorithm focuses on maximizing diversification by holding non-correlated assets with an optimal weighting scheme.
The returns of the minimum correlation portfolio are 14.54 percent compared to 8.45 percent of the equal weight portfolio. More importantly, the annualized volatility comparison is 8.45 percent versus 12.94 percent respectively. Both the absolute and risk-adjusted returns were substantially improved by harnessing the power of correlation.
All chart sources: Yahoo Finance.
