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Finding Alphas: A Quantitative Approach to Building Trading Strategies by Igor Tulchinsky

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15 Statistical Arbitrage, Overfitting, and Alpha Diversity

By Zhuangxi Fang

Can alphas direct the stock market? Or, more specifically, can we predict the price of AAPL on 6/29/2030? Unfortunately, we probably cannot. It is the nature of statistical arbitrage that we can only make the prediction in a “statistical” sense.

The key underlying assumption of statistical arbitrage is that the prices of financial instruments are driven by some consistent rules, which can be discovered from the history and applied to the future. As the prices of securities are driven by multiple rules, each of these driving rules may or may not apply with respect to any particular instrument at any given moment. However, a real price-driving rule, or a good alpha based on this price-driving rule, should appear to be predictive with statistical significance when we apply it to the collection of all investigated securities during all available trading days. A simple example is the well-known mean-reversion rule, which states that a stock’s price will tend to move to its average price over time. Within a stock market where this rule holds, it’s still easy to find stocks whose prices keep going up or down in some periods, which divert its average price consistently. Yet, if we examine the collection of N stocks in M trading days, you will find more than 50% of these N × M sample points obeying the mean-reverting rule, which enables us to create potentially profitable alphas based on this driving force. ...

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