Financial Engineering Seminar
February, 6, 2004 (Fri)
3:00 PM - 3:50 PM(8th period),
Weil Hall 307
Meta-heuristics for Portfolio Optimization
Abstract:
The methods used for analyzing and optimizing portfolios in the mean-variance
framework do not carry over easily to other risk concepts like shortfall probability,
expected shortfall etc. Furthermore constraints on the holding size of assets,
trading volume, number of assets in a portfolio etc. result in further complications
for standard optimization tools.
Given the growing need for methods able to solve these complex optimization
tasks and the failure of standard approaches to do so we propose the use of an
optimization heuristic called threshold accepting.
Heuristic optimization methods have proved useful in applications from different
fields like engineering, physics, biomedical sciences etc. They provide
approximate solutions to global optimization problems.
In one set of applications we consider problems where the investor maximizes
the expected return on the portfolio under constraints on downside risk, measured
by shortfall probability, expected shortfall etc. Solutions are constrained by a
number of equalities and inequalities. The decision variables, i.e. the number of
each asset held in the portfolio, are restricted to be integers. Different criteria for
the objective function are experimented. The resulting optimization problem is
complex as it exhibits multiple local extrema and discontinuities. In such situations
classical optimization methods fail to work efficiently and heuristic optimization
techniques can be the only way out.
The second set of applications considers index tracking problems where the
performance of the portfolio is measured against a given benchmark. The optimization
problem consists in minimizing the tracking error between a portfolio
and the benchmark. The objective is to replicate the performance of a given index
upon the condition that the number of stocks allowed in the portfolio is smaller
than the number of stocks in the benchmark index. Transaction costs are incurred
each time that the portfolio is rebalanced.
We find the composition of a portfolio that tracks the performance of the
benchmark during a given period in the past and compare it with the performance
of the portfolio in a subsequent period. We report computational results in the
cases where the benchmarks are market indices tracked by a small number of assets.
We find that the threshold accepting heuristic is an efficient optimization
technique for this problem.
Downloads:
abstract.pdf
abstract.ps