Fast Recursive Portfolio Optimization

Abstract

Institutional equity portfolios are typically constructed via taking expected stock returns and then applying the computationally expensive processes of covariance matrix estimation and mean-variance optimization. Unfortunately, these computational costs make it prohibitive to comprehensively backtest and tune higher frequency strategies over long histories. In this paper, we introduce a recursive algorithm which significantly lowers the computational cost of calculating the covariance matrix and its inverse as well as an iterative heuristic which provides a very fast approximation to mean-variance optimization. Together, these techniques cut backtesting time to a fraction of that of standard techniques. Where possible, the additional step of caching pre-calculated covariance matrices, can result in overall backtesting speeds up to orders of magnitude faster than the standard methods. We demonstrate the efficacy of our approach by selecting a prediction strategy in a fraction of the time taken by standard methods.

Keywords: Portfolio optimization, algorithmic finance, covariance estimation, quadratic optimization, computational finance, mathematical programming, Backtesting