The optimal asset allocation for South African real return investors

Van Zyl, Barry

The optimal asset allocation for South African real return investors

Master Thesis

2019

Abstract

This research aims to establish the optimal asset allocations for targeting specific real returns over short, medium and long-term investment horizons. The joint returns are modelled with data-centric methods that are empirical and non-parametric in nature, and are able to capture the dependencies of returns over time. The asset classes that are considered are South African (SA) equities, SA bonds, SA cash, SA property, global equities, global bonds, global cash, and global property. The returns of each asset class are modelled, each class with its own empirical distribution based on monthly returns from 1972 to 2017. The monthly returns are grouped in a block of rolling periods of varying block lengths in order to attempt to capture dependencies across time. These blocks of data are resampled in order to simulate the distributions of returns of portfolios with their own unique empirical distribution. The optimal portfolios are derived using a genetic algorithm, showcasing how these extremely versatile optimisation tools can be used in combination with resampling methods to find the optimal portfolio for virtually any criterion. A comparison is also made to the traditional mean-variance optimal portfolios, yielding an estimate of the bias in mean-variance optimisation’s (MVO) optimal weights. It is investigated how these optimal portfolios are influenced by the choice of risk criterion and investment horizon. The effect of the most important and consequential nuisance parameter in this research’s model, the block length, is discussed. The relationships established between the characteristics of optimal portfolios and investment horizon and risk criterion and the comparisons with classic MVO should be of interest to investors and investment professionals alike. Economic and market regimes are “identified” on the basis of economic and market data, consequently the resampling probabilities will be unequal. The optimal weights conditional on regimes are derived. Both static and changing regimes are considered. Lastly, an out-of-sample backtest of the performance of the optimal portfolios conditional on the regime across time at six month intervals is conducted from 1983 to 2017. It shows that out of the three block lengths tested for a single investment horizon of 36 months, a block length of 24 months yielded the best overall risk-adjusted performance, on average. Conditioning for regimes is shown to generally outperform the unconditional approach. The improvements are marginal and further research is recommended to investigate the performance for longer investment horizons and other values of the two tuning parameters, block length and tactical pressure. The higher level aim of this work is to present a broad sense of how data-driven nonparametric methods can be used in conjunction with metaheuristic procedures. The objective of combining these techniques is to find optimal portfolios under very general conditions and with very few assumptions regarding the underlying distributions.

Keywords

Statistical Sciences

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