A Comparison of Stochastic Search Heuristics for Portfolio Optimization

Modern portfolio theory is based on a rational investor choosing the proportions of assets in a portfolio so as to minimize risk and maximize the expected return. In this paper, we investigate the applicability of different stochastic search heuristics to the problem of finding the optimum portfolio. We compare their performance on two problems with known solutions. 1. Portfolio Optimization Given a set of assets, what is the optimum proportion of each that is required to achieve an investment objective? Modern portfolio theory is based on a rational investor choosing these proportions so as to minimize risk and maximize the expected return. If risk is measured in terms of the variance of the resulting portfolio, then portfolio optimization is reduced to a “means-variance paradigm” — the optimal portfolio can be derived by knowing the expectations of returns and correlations of returuns for all assets. Using vector notation from linear algebra, in its simplest form, the portfolio problem is to Find a vector w = (w1, ...wn) that maximizes the return/risk ratio [r • w]_________ (wT • C • w)1/2 subject to constraints mk = wk = Mk, k=1,...,n and ( |w1| + |w2| + ... + |wn| ) = 1 The vector w defines the portfolio: the set of weights that represent the proportion of each asset. Vector r is the vector of expected returns for the assets. C is a symmetric n-by-n matrix that represents the covariance beteween the returns: c(i,j) is the return covariance between the returns of asset i and asset j: