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Optimal Trading of a Mean-Reverting Process

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

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Optimal Trading of a Mean-Reverting Process

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

  2. Introduction • Xt is the spread between two correlated stocks: • To maximize power utility of wealth at T, the optimal position of Xt 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 MarginsChevron-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.

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