1. KUMARAGANESH SUBRAMANIAN XIAOLONG TAN PRABAL TIWAREE DIMITRIOS TSAMIS JUNE 3, 2009 MS&E 444: Investment Practice Short and long-term prediction combination

2. Returns Model

3. Using multiple predictors Assume that alphas are a linear combinations of factors: Estimate B using pooled panel regression Moreover, is a positive definitive matrix of mean-reversion coefficients

4. Transaction Costs Trading shares costs: Assume that

5. Optimization Problem Find the optimal portfolio at each time step by solving the following problem: Use Dynamic Programming!

6. Main result Optimal portfolio is linear combination of previous position and a moving “target portfolio” where and

7. Simplification If then

8. Static model Solve ie fully discount the future Solution:

9. Experiments Use 6 different commodities futures from London Metal Exchange Evaluate based on gross and net SR and cumulative returns Compare optimal, static and no TC strategies Predictors: normalized averages over 5 days, 1 year and 5 years

10. Cumulative Returns

11. Sharpe Ratios Dynamic strategy:0.4707 Static strategy:0.4618

12. Effect of lambda

13. Rebalancing costs

14. Experiments with shares Use predictors provided by EvA Short-term: stat-arb daily predictors Long-term: EMN monthly predictors  interpolate daily values There were 1089 securities common across all data

15. Reduce the size of the portfolio! Using all the securities produces bad results Σis essential to the model, but the quality of the estimator deteriorates as the number of securities increases To evaluate the model try random portfolios and observe their performance

16. Using all securities

17. Cumulative Returns with 20 securities

18. Cumulative Returns with 100 securities

19. Cumulative Returns with 500 securities

20. Best portfolio size: 19 securities

21. Evaluate based on SR

22. Conclusions The strategy works better on commodity data The strategy appears to be self-financing The strategy does not work well on very large portfolios (probably due to parameter estimation errors)