Time-stamped resampling for robust evolutionary portfolio optimization

Abstract

Traditional mean-variance financial portfolio optimization is based on two sets of parameters, estimates for the asset returns and the variance-covariance matrix. The allocations resulting from both traditional methods and heuristics are very dependent on these values. Given the unreliability of these forecasts, the expected risk and return for the portfolios in the efficient frontier often differ from the expected ones. In this work we present a resampling method based on time-stamping to control the problem. The approach, which is compatible with different evolutionary multiobjective algorithms, is tested with four different alternatives. We also introduce new metrics to assess the reliability of forecast efficient frontiers.

Combining RMT-based filtering with time-stamped resampling for robust portfolio optimization

“…A basic modelling would provide approximations to the efficient frontier that would suffer from the unreliability discussed before, hence our choice of complementing them with a time-stamped resampling strategy. This approach, proposed by García et al 23 , generates sets of likely scenarios, pairs of expected returns and variance-covariance matrices, based on historical data following the nonparametric bootstrap process described in algorithm 1 23 . Each candidate portfolio faces a number of scenarios during the evolution process and the algorithm weeds out those that are too sensitive to deviations in expected returns and variance-covariance matrix.…”

“…We will consider four indicators to measure robustness that mostly capture the divergence between expected results and actual results. These are Estimation Error, Stability, Unrealized Returns, and Extreme Risk 23 . We outline their main features.…”

“…Other efforts regarding the second line were made to introduce robustness in multiobjective optimization 21 . For instance Deb et al 22 launched a robust adaptation for NSGA-II algorithm to optimize portfolios and then Garcia et al 23 dealt with the problem of robustness but using resampling and a third objective as a time-stamp.…”

“…In case the sum of weights per individual is not 1.0, Σ n i=1 w i = 1, the algorithm adjusts the holdings adding or subtracting random amounts up to the required adjustment. These processes are described in detail in 23 .…”

Efficient dynamic resampling for dominance-based multiobjective evolutionary optimization

“…Robustness is often considered through the evolution process as a decision component that favours solutions that are less sensitive to perturbations (Hassan and Clack 2008;García et al 2012). Alternatively, it may be taken into account as an additional objective function, extending the problem with a new objective (Chicano et al 2012).…”