Presentation is loading. Please wait.

Presentation is loading. Please wait.

Lorenzo Coviello and Petros Mol

Similar presentations


Presentation on theme: "Lorenzo Coviello and Petros Mol"— Presentation transcript:

1 Lorenzo Coviello and Petros Mol
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: 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 Trend is your friend
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 pmf b 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 Normalization
stock i over 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 Kernel portfolio 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 Reversal to the mean Trend is your friend
Constant Rebalancing (CRP) Semi-CRP ANTICOR Buy and Hold Histogram Kernel

41 Comparing the winners (w/o Anticor)

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

43 Lorenzo Coviello and Petros Mol
THANKS Lorenzo Coviello and Petros Mol


Download ppt "Lorenzo Coviello and Petros Mol"

Similar presentations


Ads by Google