# Trading Noncorrelated Systems in Small Accounts

Many individuals are drawn to trading thinking they won’t have to do math. This belief is rarely held by successful traders, and few actually succeed in modern trading without some math skills. It is possible to win at trading without understanding any math, but that is the exception rather the rule. Fortunately, it doesn’t take an understanding of calculus or advanced statistical modeling to become a winning trader. Just a few simple concepts will usually be enough.

Correlation is one of those concepts that can offer a great deal of help to traders. The basic idea is that correlation quantifies the relationship between different data sets. Mathematicians can argue that this is a very imprecise definition, and they’re right but this is from a trading perspective so we want to cover the least amount of math detail possible. In the end, we want to come up with a way to use correlations in a good enough way, rather than in a way that ensures we get an ‘A’ in math class. Ideally, we can employ correlation in trading without needing a spreadsheet.

In a slightly more precise expression, correlation is a statistical measure of how two sets of data move in relation to each other. Correlation is usually calculated in terms of the correlation coefficient, which is expressed as a value between -1.0 and +1.0. Applying the idea to two stocks, a perfect positive correlation, calculated as a correlation coefficient of +1, would mean that the two securities move in the same direction and with the same percentage change all the time. This type of correlation would be seen between the S&P 500 index and the SPY exchange traded fund (ETF) which tracks the index.

On the other hand, perfect negative correlation, a correlation coefficient of -1, means that if one security moves in either direction the security that is perfectly negatively correlated will move in the opposite direction by the same percentage amount. This is the concept behind inverse ETFs, but their track record shows that profits can be hard to capture from correlations. The classic example is oil and some of the inverse funds which track the price of oil, with both long and short funds managing to close down in 2008. This result is because the funds traded as designed and tracked daily changes only and tracking long term correlations is not their objective.

If the correlation coefficient is 0, the movements of the securities are said to have no correlation and their relationship is completely random. A trend in one will not have any impact on the other. This is what would be found if markets were truly a random walk as many academics propose, but in reality is rarely seen. The overall trend of the market has an impact on almost all stocks. Nobel Prize winning economist William Sharpe found that the general trend in the stock market accounts for about 70% of the returns in any individual stock.

Correlations can also be applied across different markets. The ill-fated hedge fund Long Term Capital Management applied this idea. They could determine what the expected relationship between Danish mortgage bonds and the US 10-year Treasury note looked like. When the correlation moved significantly away from the trend, they could take a position in Danish mortgages. They eventually discovered that they were the largest investor in that very illiquid market and had no one to trade with when they wanted to exit the position. While this exact scenario isn’t likely to occur for individual traders, liquidity should always be a concern. Lumber futures are a strongly trending market and test very well in many systems, but with very light volume the individual trader may pay a heavy price to get in and out of a trade.

Individual traders can visually test for correlation by looking at the performance of two stocks, or two different markets, on the same graph. It is very important to set up the y-axis to be in percentage terms, rather than price units. Sequential price changes tend to display autocorrelation and looking at the raw price data of two different series will almost always show a strong positive correlation.

Visual analysis formed the basis of the first popular discussion of correlation for traders. John Murphy created interest in the subject with his 1991 book, “Intermarket Technical Analysis.”  He demonstrated that stocks and bonds had a negative correlation, a relationship that held throughout the 1980s but is now less useful as markets and the economy have evolved. With deflation a primary driver of emotions in the bond market, the long-standing and easily understood correlation with stocks has broken down.

While correlations between markets change, correlations between trading systems are fairly stable over time. This allows traders to achieve steadier profits.

Trading systems can usually be classified in broad terms as trend following or mean reverting. Trend following systems make money on the occasional big trade, enduring frequent small losses. Mean reverting systems take advantage of the idea that markets only trend a short amount of the time. Mean reversion means that prices tend to move back and forth in a relatively narrow range most of the time. To picture this, view any chart with a moving average and prices can be seen rising above and falling back below the average. In this example, the moving average is the mean and prices tend to move back (revert) to the mean after they move away from it.

Noncorrelation of the two system types is rooted in the basic difference between the two strategies. Using the two different strategies together, in a single account, can help traders realize a steadily increasing equity curve. In a trending market, mean-reversion strategies suffer and trend following strategies profit. In non-trending markets, strategies designed to take advantage of the trend will generate losses. This is how the systems are designed.

In practice, a diversified portfolio is best. Multiple strategies with multiple securities offer the greatest profit potential in backtesting. In reality, traders often trade only a single system and focus on a single market because they don’t have large trading accounts. It is also true that most small traders fail to make a profit.

Small traders can diversify and improve their odds for success with some careful planning. Futures offer leverage and with proper risk management offer the best odds of success to the small trader. It is definitely possible at an online broker to trade at least two markets with an account size of \$10,000. Day trading can be done with even less, with some brokers allowing margins as small as \$500 per contract provided the trades are closed each day. This isn’t the ideal trading account, but it’s an option for the small trader with the time to pursue day trading, a subject we’ll take up next.

By Michael J. Carr, CMT