**Correlation: The Little Statistic That Packs Quite a Punch **
**Correlation is a little understood statistic that plays a huge role in today’s financial markets. It is critical in the calculation of portfolio risk, determining the effectiveness of hedges, forms the basis of some computerized trading systems, greatly impacts the relevance of various investment strategies, and is widely used in economic analysis. This article will briefly discuss the role of correlation in each of these five areas.**
A correlation coefficient is a measure of the linear relationship between two variables. Correlation ranges from -1 to +1 with zero indicating no correlation. Positive correlation means that the two variables change in the same direction, while negative correlation is the opposite. In Excel, the CORREL function calculates correlation. The R2 statistic used in linear regression is the square of the correlation coefficient between the predicted values and the actual values. Scatter plots are a good way to visually see the degree, direction and possible nonlinearity of the correlation between two variables.
While two variables may be correlated for a period of time, it does not imply that one causes the other to change or that there even is a fundamental reason why they should move together. One can correlate any set of variables over a large number of time periods and by chance, there may be some that show high or low correlations. These are so called spurious correlations and mean one should guard against data mining and try to understand the fundamental reasons and mechanism by which the variables should be correlated. Of course, those fundamental reasons can change, sometimes very quickly, which can then quickly change the correlation.
The importance of correlation in modern finance started with Modern Portfolio Theory (MPT) as developed by Harry Markowitz in 1952. The central idea behind MPT is that risk can be reduced for a given level of return by diversifying. Assets such as bonds and stocks can be combined in a theoretically efficient way to produce the highest return for a given level of risk. Correlation underlies MPT since by combining different assets such as stocks and bonds which have correlations of less than +1, risk can be reduced. Risk is defined as variability in returns as measured by standard deviation. Value at Risk is also widely used to measure market risk and it too relies heavily on a correlation grid for all assets in the portfolio. One of the criticisms of VaR is that it greatly underestimates the probability of extreme market moves. In part, this is due to correlations increasing greatly and thereby reducing the diversification benefits exactly during the time they are desperately needed to cushion the blow from a market fall.
Correlations are also used to determine hedge effectiveness, but be careful relying only on correlations. There can be a huge difference between even very high correlations with respect to the degree of spread risk. It is best to chart both assets together and also the difference (basis or spread) to appreciate the risk in the trade. For example, the wheat/corn spread is heavily traded at times and can show remarkably high positive correlation for a long time. It seems like a low risk trade, but it can completely fall apart when one of the crop’s supplies starts to shrink and a larger proportion of the demand is from less price sensitive users.
The degree and behaviour of correlation is dependent on the assets being considered and the time frame. In the physical world, correlations can be very consistent and high such as temperature and altitude above sea level, for example. Correlations measured in many markets are anything but consistent and can exhibit abrupt changes. Correlations in financial markets are greatly impacted by the overall level of stress in the financial system. When markets are trending higher correlations tend to be fairly stable and over time have increased. Financial panic will cause correlations to move to the extremes (most near +1 and some near -1) as investors indiscriminately sell assets and move into lower risk ones such as Treasury Bills. The increasing correlations are accompanied by higher volatility and both can exhibit jumps.
The most infamous case of a failed correlation trade is Long Term Capital Management (LTCM). After operating for a little over 4 years, LTCM lost $4.6 billion in 1998 necessitating the Fed to arrange a takeover of its positions by the major U.S. commercial banks. LTCM traded global credit spreads, among others, which involved buying and selling sovereign debt with trades being entered when the spreads would extend past historical relationships. The expectation was that the spreads would revert to their average within a short period of time resulting in a profit on the trade. This particular strategy is called mean reversion trading or statistical arbitrage and it relies on correlations staying within fairly narrow bounds. LTCM also sold equity volatility which can increase rapidly when markets fall, in effect doubling down on their bet that markets would remain relatively calm. These are classic “blow up trades” in that they are able to produce consistent returns for a number of years (given enough leverage) while enjoying seemingly low risk. At the first sign of market stress, large losses are incurred and forced liquidation into now less liquid markets further exacerbates losses. It is similar to selling far out of the money equity put options.
There are many investment strategies that rely on certain expectations of correlation. Alpha generation is a term used to describe the ability of a fund manager to add value. Alpha is the fund return in excess of its benchmark. If all assets become more highly correlated it becomes increasingly difficult to be a stock picker and generate alpha.
Equity market neutral strategies seek to earn a return on a group of stocks while hedging the overall market risk. Correlations, along with the volatility of the stock and the index, are needed to determine the size of the hedge. The “optimal” hedge ratio is based on historical prices of the stock and the equity index and is really an estimate that can change significantly. Increasing correlations for most assets during a market fall will likely result in the optimal hedge being undersized. Tactical asset allocation involves buying certain asset classes and selling others, such as equity sectors. The appeal of tactical asset allocation is reduced when all sectors become more highly positively correlated during a market downturn.
Finally, correlation is widely used in economic analysis either as a stand alone statistic or in the form of regression analysis. Macroeconomists are fond of analyzing the various economic indicators, such as national income, consumption, unemployment, inflation, savings, trade and investment. By better understanding the relationships among these economic variables, it is hoped that better public policy is formulated such as government spending and central bank policy.
Correlation shows itself in many areas of economics and finance. In many ways, it is a proxy for market stress and trades that rely heavily on a stable correlation are similar to short volatility positions.
**Iebeling Kaastra, CFA FRM** |