Mar 9, 2006 - (2000) use CART to partition assets into outperforming and .... Feb99 Aug99 Feb00 Aug00 Feb01 Aug01 Feb02 Aug02 Feb03 Aug03 Feb04 ...
Portfolio selection with classification trees M. Gilli
E. K¨ellezi
I. Roko
University of Geneva
Mirabaud & Cie
University of Geneva
CCFEA, University of Essex March 9, 2006
1
Motivation Classical approach balances risk and return, static, relies on past information, unable to capture variations in investment opportunities How to overcome these inconveniences? • Model future of the time-varying behavior of mean returns, variances and covariances • Factor models ◦ statistical (black box) ◦ macroeconomic ◦ fundamental Gilli, K¨ellezi and Roko
CART – 2
Outline • Factor models for portfolio selection • Decision trees • Application S&P technology (1999–2005) • Conclusions Gilli, K¨ellezi and Roko
CART – 3
Fundamental factor models Returns on assets ri explained by characteristics ( z1 , z2 , . . . ) of individual assets: • • • • •
Balance sheet average Liquidity Market capitalization Price/earning ratio Earnings growth
How to model r
i,
t+1
= f (z
1
t
,z
2
t
, . . .)
Linear models will generally not work. Gilli, K¨ellezi and Roko
CART – 4
2
Modelling approaches If rit are discrete (discretized) we can use: • • • •
Ordered logistic or Probit regression Artificial Neural Networks (ANN) Genetic algorithms Recursive partitioning algorithms CART ( C lassification A nd R egression T rees) Breiman et al. (1984)
Able to handle highly nonlinear models. Gilli, K¨ellezi and Roko
CART – 5
Advantages of decision trees • Provide interpretable rules and logic statements • No assumptions about the statistical distributions of variables • Provides a clear indication which variables are most important for classification • Robust with noisy data – outliers, errors, etc. Gilli, K¨ellezi and Roko
Decision trees • • • • •
CART – 6
(applications)
Medicine: identification of factors influencing myocardial infarction, drug testing, etc. Artificial intelligence (machine learning) Internet engine Database screening Management and finance: • •
Frydman et al. (1985): default risk personal loans, credit rating, asset allocation, stock screening
Gilli, K¨ellezi and Roko
CART – 7
Decision trees for portfolio selection • Kao and Shumaker (1999) use CART to explain relationships between macroeconomic variables and performance of timing strategies based on market, size, and style. • Sorensen et al. (2000) use CART to partition assets into outperforming and underperforming assets. Portfolio composed by uniformly weighted outperforming assets. • Albanis and Batchelor (2000) compare different techniques to distinguish outperforming and underperforming assets and demonstrate the efficency of CART. Gilli, K¨ellezi and Roko
CART – 8
3
Decision trees for portfolio selection
(contd.)
We build on Sorensen et al. (2000) • Use a moving window to build successive classification trees • Construct portfolios and analyse their performance including non-convex transaction costs Gilli, K¨ellezi and Roko
CART – 9
Building a classification tree y
Recursive partitioning algorithm
variable by building a binary decision tree according to some splitting rule based on discrete or continuous predicting variables Data separated into: learning and testing samples
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