Statistical arbitrage involves the simultaneous purchase and sale of two or more assets in order to take advantage of price discrepancies. For example, a trader might buy shares of Company A and sell shares of Company B if the two companies are in the same industry and the price of Company A’s shares is expected to rise relative to Company B’s shares.

Statistical arbitrage strategies often involve the use of algorithms and sophisticated quantitative models in order to identify opportunities and execute trades. These strategies can be deployed on various markets, including stocks, bonds, commodities, and currencies. Statistical arbitrage can also be executed in the non-linear space, for example using equity options. This type of trading is called dispersion trading.

Reference [1] examined dispersion trading strategies based on a statistical index subsetting procedure and applied it to the S&P 500 constituents,

*First, we developed an index subsetting procedure that considers the individual index explanatory power of stocks in the weighting scheme. Therefore, we are in a position to build a replicating option basket with as little as five securities. Second, the large-scale empirical study provides a reliable back-testing for our dispersion trades. Hence, the profitability and robustness of those relative value trades can be examined across a variety of market conditions. Third, we analyzed the added value of our strategies by benchmarking them against a naive index subsetting approach and a simple buy-and-hold strategy. The trading frameworks that employ the PCA selection process outperformed its peers with an annualized mean return of 14.52 and 26.51 percent for PSD and PSU, respectively. The fourth contribution focuses on the conducted deep dive analysis of our selection process, i.e., sector exposure and number of required principal components over time, and the robustness checks. We showed that our trading systems possess superior risk-return characteristics compared to the benchmarking dispersion strategies.*

In short, the authors demonstrated that by using Principal Component Analysis, it is possible to design dispersion trading strategies that deliver superior risk-adjusted returns.

Another implication of the study is that advanced statistical methods can be utilized to efficiently manage risks and improve the stock selection process. We note that Principal Component Analysis is a form of unsupervised machine learning.

**References**

[1] L. Schneider, and J. Stübinger, *Dispersion Trading Based on the Explanatory Power of S&P 500 Stock Returns*, Mathematics 2020, 8, 1627; doi:10.3390/math8091627

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