1. Statistical Arbitrage in the U.S. Equities Market

2. ETF approach: Using industries A diverse set of ETFs can be used to explain the returns of a stock Multiple regression model will be of the form:

3. The PCA approach Principle Component Analysis to extract factors from the return data Eigenvectors are the principle components of the data and its corresponding eigenvalues are its variance. Each principle components are a linear combination of all the stocks in the data and can be regarded as an eigenportfolio The returns of each eigenportfolio can be used in the multiple regression analysis

4. Differences between PCA and ETF approaches ETF approach requires some prior understanding of the economical situation to know the “appropriate” set of ETFs needed PCA factor loadings is more intuitive than for ETF ETF gives more weight to large capitalization companies, whereas PCA has no a priori capitalization bias

5. Trading Signals Using the OU parameters, we can obtain the mean and variance of X and define the dimensionless variable: Above equation is known as the s-score which measures the distance to equilibrium of the co-integrated residual in units of standard deviations. The signals are as follow: buy to open if s i < −s bo sell to open if s i > +s so close short position if s i < +s bc close long position s i > −s sc

6. Results from using PCA approach The stock MCK gives the best result. The trading strategy performs well throughout the 3-year period with a profit of almost $754,000 at the end of the trading period. The optimized trading levels s bo, s bo, s bc, s sc obtained are 1, 0.25, 1, 0.25 respectively.

7. Results from using PCA approach Second best performing stock is “IP” with an Omega of 1.33. The P&L over the three year period is shown below. A profit of almost $811,000 at the end of the trading period. The optimized trading levels are same as before.

8. Results from using ETF approach Among the 100 stocks, NRG gives the best results. The trading strategy performs well throughout the 3-year period with a profit of almost $1,730,000 at the end of the trading period. The optimized trading levels s bo, s bo, s bc, s sc obtained are 1, 0.25, 1, 0.25 respectively.

9. Results from using ETF approach Second best performing stock is “ATI” with an Omega of 1.47. The P&L over the three year period is shown below. A profit of almost $1,590,000 at the end of the trading period. The optimized trading levels are same as before. Video of P&L using ETF Approach

10. Backtest: Bootstrapping

12. Backtest: Outsample Test

13. New Findings We find that the optimized trading levels s bo, s bo, s bc, s sc obtained are 1, 0.25, 1, 0.25 respectively as opposed to what is being proposed in the paper For the optimized set of parameters we got very good profit in both the approaches (ranging above 80%) Omega achieved from out-sample testing was not good enough to support the strategy This is further cemented by the results from bootstrapping Please run ‘main_ETF.m’ to see the results.