1. Optimal Trading of a Mean-Reverting Process Shih-Arng (Tony) Pan, Wei Wang, Chen Tze Wee, Ren Fung Yu MS&E 444, Spring 2008

2. Introduction X t is the spread between two correlated stocks: To maximize power utility of wealth at T, the optimal position of X t to hold is:

3. Choosing correlated stocks Stocks were chosen from the S&P 100 index Chose stock pairs with the highest correlation of daily returns (>0.75). Examples: –International Paper/Weyerhauser –Merrill Lynch/Morgan Stanley –Chevron/Exxon Mobil –Baker Hughes/Schlumberger

4. Unadjusted Adjusted

5. Parameters Parameters k and σ were estimated using MLE using January 2003 to December 2004 data. The strategy was implemented after January 2005, out of sample. Power Utility parameter: γ= -0.1 Transaction cost: 0.15% of initial wealth (constant)

6. Maximize Immediate Utility w/ Scaled Margins Chevron-Exxon (k=5.51, σ=6.47)

7. Moving Window (of 1.5 years) Baker Hughes - Schlumberger

8. Moving Window (of 1.5 years) Citigroup – Lehman Brothers

9. Annual Return Histogram (18 pairs) Moving Window: Return = 1.0764 Volatility = 0.3428 No Moving Window: Return = 1.0418 Volatility = 0.5511

10. Conclusion Theoretical strategy too risky for market conditions. Maximizing immediate utility w/ scaled margin strategy shows promise. Moving Window parameter estimation improves returns, but not enough to beat market. Better stock pairs, or a process with even more memory is required.