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Mathematical Trading Strategies

Many trading strategies are based on perceived relationships between the prices of different assets. Some of these relationships are based on fundamental relationships e.g. when oil goes up oil companies do better but transportation companies like airlines do worse. Most of the strategies based on fundamental relationships have been exploited to the point where they are no longer profitable. Using methods developed by Robert Engle and Steve Grainger (for which they received the Nobel Memorial Prize) on can find portfolios of stocks whose aggregate price is mean reverting and one can trade such a portfolio very profitable. The problem is to discover these stock portfolios and determine when these relationships end and the strategy breaks down. We describe an algorithm to search for pairs and successfully trade them. A very important part of the strategy is to determine when to exit and we discuss some possible ways to determine this point.