An Online Algorithm for Multi-Strategy Trading
Utilizing Market Regimes
Hynek Mlnǎŕık 1
Subramanian Ramamoorthy 2
Rahul Savani 1
1Warwick Institute for Financial Computing
Department of Computer Science
University of Warwick
2School of Informatics
University of Edinburgh
The Portfolio Allocation Problem
Dynamically allocate working capital in a portfolio of instruments
– over time, as market conditions continually change.
Classic problem with established theory, e.g., mean-variance
optimization and modern extensions.
Traditional techniques are “model-based” - one makes
assumptions (e.g., model of expected returns) that may turn out
to be troublesome.
This issue spurred research into “model-free” approaches.
“Model-free” Portfolio Allocation
Point of departure: Classic work on optimal bet sizing (Kelly
1956, Breiman 1961) - how much to bet given odds?
Constantly rebalanced portfolios (Thorp 1971, Markovitz 1976,
Bell+Cover 1988, Algoet+Cover 1988) - keep relative allocation
of capital constant (still assuming known market return
Universal portfolio (Cover 1991) - Sequential portfolio allocation
to match the best constantly rebalanced portfolio in hindsight
(for an arbitrary market process).
Many extensions and follow-on work: multiplicative updates
(Helmbold et al. 1998), efficient online computation (Kalai et al.
2002), Anticor (Borodin et al. 2004), kernel-weighted allocation
(Györfi et al. 2006).
Utilizing Market Context
Market processes are not entirely arbitrary – how to utilize odds
without overly restrictive assumptions?
Statistical view of Universal Portfolios (Belentepe 2005):
Weights (constrained to a partition of unity) are conditional
expectation of a multivariate normal distribution,
w ∼ N
Unconstrained version is the standard log-optimal investment.
Major contribution of universal algorithms is an online procedure
to solve this problem, within a target portfolio class.
We seek online procedures that also allow us to utilize context in
the spirit of (non-pa