portfolio selection: experimental comparison of universal and non-universal algorithms lorenzo...
Post on 29-Dec-2015
217 Views
Preview:
TRANSCRIPT
PORTFOLIO SELECTION:EXPERIMENTAL COMPARISON OF UNIVERSAL AND
NON-UNIVERSAL ALGORITHMS
Lorenzo Coviello and Petros Mol
June 2, 2011
Universal Information Processing, Spring 2011
2
Motivation
• Investing money in the stock market
• How to build a successful portfolio?
• Compare various strategies
3
• 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
Introduction
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 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• 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
Conclusion
Put all your money in Anticor!
But choose the right window!!!
THANKSLorenzo Coviello and Petros Mol
top related