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PORTFOLIO SELECTION: experimental comparison of Universal and non-universal Algorithms

PORTFOLIO SELECTION: experimental comparison of Universal and non-universal Algorithms. Lorenzo Coviello and Petros Mol. Universal Information Processing, Spring 2011. June 2, 2011. Motivation. Investing money in the stock market How to build a successful portfolio?

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PORTFOLIO SELECTION: experimental comparison of Universal and non-universal Algorithms

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  1. PORTFOLIO SELECTION:experimental comparison of Universal and non-universal Algorithms Lorenzo Coviello and Petros Mol Universal Information Processing, Spring 2011 June 2, 2011

  2. Motivation • Investing money in the stock market • How to build a successful portfolio? • Compare various strategies

  3. Introduction • Universal portfolio selection: provides guarantees on wealth growth rate • Real market: invest in the most profitable way • Compare performance of portfolio selection criteria on real data from the stock market

  4. Rest of the talk • Introduction • Portfolio selection: the model • Methodology • Two approaches • Reversal to the mean • Trend is your friend • Simulations - Comparison

  5. The model – price relatives • Portfolio:m stocks • Trading period: T trading days • Xij: price relative of stock j at day i • Xi often assumed i.i.d. (strong assumption)

  6. The model - wealth • Portfolio at day i • The wealth gain in one day • The overall wealth gain in T days

  7. The model - strategy • How to distribute the wealth among the stocks? • Decision problem: choose a portfolio each day

  8. Rest of the talk • Introduction • Portfolio selection: the model • Methodology • Two approaches • Reversal to the mean • Trend is your friend • Comparison

  9. Methodology • Data Collected from Yahoo! finance • Adjusted close price used • Period: 1996- 2010 • 3778 trading days • No priors on the stocks, no fundamentals • No transaction costs

  10. Portfolio: List of Stocks • Tech(11) : AMD, Apple, AT&T, Cisco, Dell, HP, IBM, Intel, Microsoft, Nokia, Oracle • Finance(7):American Express, Bank of America, Barclay’s, Citigroup, JP Morgan, Morgan Stanley, Wells Fargo • Other (12) : Boeing , BP, Coca-Cola Company, Exxon, Ford, General Electric, J&J, McDonalds, Pfizer, P&G, Wall Mart, Walt Disney

  11. Rest of the talk • Introduction • Portfolio selection: the model • Methodology • Two approaches • Reversal to the mean • Trend is your friend • Comparison

  12. Two main approaches • Reversal to mean • Assume stock growth rates stable in the long run, and • Occasional larger returns followed by smaller rates • CRP, Semi-CRP, ANTICOR • Trend is your friend • Portfolio based on recent stock performance • Histogram portfolio selection, kernel portfolio selection

  13. Buy and hold • Build portfolio once, let the wealth grow • Uniform buy and hold (U-BAH) • Performance guarantees for U-BAH • Best BAH in hindsight: invest on the best stock

  14. Simulation

  15. Rest of the talk • Introduction • Portfolio selection: the model • Methodology • Two approaches • Reversal to the mean • Trend is your friend • Comparison

  16. Reverse to mean approach Assumptions • Stock growth rates stable in the long run • Occasional larger returns followed by smaller rates, and vice versa

  17. Constant rebalancing portfolio • Rebalance portfolio every day according to pmfb • Uniform CRP: • Exponential gain if “reversal to the mean” market • Stock 1: constant value • Stock 2: doubles on odd days, halves on even days • Uniform CRP • Wealth grows of 1/8 every 2 days • Best CRP in hindsight difficult to compute

  18. Semi-constant rebalanced portfolio • Reference: Kalai (1998), Helmbold (1998), Kozat (2009) • Portfolio rebalanced every arbitrary period • Rebalancing period can be fixed • Real market: reduced commissions

  19. Semi-constant rebalanced portfolio • Consider rebalancing every d days • Uniform target distribution • The wealth before rebalancing for the kth time

  20. Semi-CRP with deviation control • Ref. Kozat (2009) • Idea: avoid useless rebalancing • Rebalance only if large distance between target portfolio b and current wealth distribution w

  21. Simulation (with fixed interval)

  22. Simulation (with distance threshold)

  23. ANTICOR algorithm • Reference: Borodin, El-Yaniv, Gogan (2004) • Aggressive “reversal to the mean” • Transfer money from stock i to stock j if • Growth of stock i > growth of stock j over last window • Stock i in second last window and stock j in last window positively correlated

  24. ANTICOR algorithm • Define • Averages of columns of LXk

  25. ANTICOR algorithm • Cross correlation • stock iover the second last window • stock j over the last window • Normalization

  26. ANTICOR algorithm • Transfer money from stock i to stock j if • In an amount proportional to

  27. Simulation (with variable window length)

  28. Simulation (smaller window length)

  29. Simulation (zoom in)

  30. Simulation (zoom in)

  31. Simulation (zoom in)

  32. Rest of the talk • Introduction • Portfolio selection: the model • Methodology • Two approaches • Reversal to the mean • Trend is your friend • Comparison

  33. The trend is your friend • Portfolio based on stock performance • Prefer performing (trendy) stocks • Use the market history to determine the current portfolio

  34. Histogram portfolio selection • Ref: Gyorfi and Schafer (2003) • Rectangular window of width w days • Distribute the wealth uniformly among k best stocks

  35. Simulation (variant window)

  36. Simulation (variable #active stocks)

  37. Kernelportfolio selection • Higher weight to the recent past • Window size of w days • Window shape • Linear • Exponential • Example: score of stock j at day i+1

  38. Kernel portfolio selection • Each day the scores determine the portfolio • Examples • Follow the best stock • Uniform distribution between k best stock • Proportional to score for best k stocks

  39. Simulation

  40. Summary of Cases

  41. Comparing the winners (w/o Anticor)

  42. Conclusion Put all your money in Anticor! But choose the right window!!!

  43. THANKS Lorenzo Coviello and PetrosMol

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