2 Introduction

If a risk-averse investor wants to construct portfolios with desirable properties, they would ideally want to find allocations that offer an attractive risk-reward trade-off. Markowitz (1952) developed modern portfolio theory and introduced the mean-variance optimal portfolio as a quantitative solution to this asset allocation problem. However, the reward derived from this portfolio has to be estimated from sample data and is often difficult to accurately predict - which, in turn, leads to Markowitz’s mean-variance portfolio being highly sensitive to the estimated portfolio inputs.

As an alternative, risk-based investing provides an avenue for finding portfolios for which expected returns do not need to be estimated, and therefore resolves the portfolio expected return sensitivity problem. Examples of risk-based portfolios commonly seen in practice are the global minimum variance portfolio, the equal risk contribution portfolio, and the equal weight portfolio. These three portfolios are optimal for investors that prioritise weight diversification, risk diversification, or a specific combination of both.

Nevertheless, risk-based portfolios remain sensitive to covariance matrix estimation and hence estimation risk. Improving risk-based estimation is done in three ways in this research. The first improvement alters the covariance estimation procedure by accounting for differences in the sample data. These changes include grouping to account for both non-normality and state-based inhomogeneity. The second involves penalising the optimisation to limit the range of admissable portfolios, which increases the investor’s odds of choosing a well-estimated portfolio. The final enhancement changes the implementation methodology entirely by performing the portfolio optimisation on subsets of assets and then resampling to find an aggregate portfolio.

This research aims to bring together useful elements of risk-based portfolio estimation and construction methodology into a single flexible framework. The general structure allows a choice of risk-based portfolio as well as estimation risk reduction technique to improve the out-of-sample portfolio performance. Once we have established a framework, the specific portfolio and estimation technique, examples are developed theoretically. All of these reforms will be hollow without being applied to actual financial data. Therefore, the various estimation techniques and risk-based portfolio pairs are back-tested using South African equity data in an experiment, with the results being measured by standard performance methodologies.

This research is built on the work of several different authors. Firstly - as with nearly all portfolio construction research - this dissertation hinges on the modern portfolio theory of Markowitz (1952). It then considers the particular case of risk-based investing and makes use of the generalised frameworks introduced by Jurczenko, Michel, and Teiletche (2013) and Richard and Roncalli (2015). Finally, in terms of improving the estimation and optimisation processes, we make use of the ideas investigated by Flint and Du Plooy (2018), Kinn (2018), and Shen and Wang (2017).

The rest of this dissertation is set out as follows. Chapter 2 outlines a general framework for constructing risk-based portfolios and estimating them in a robust manner. Chapter 3 gives an overview of the specific risk-based portfolios considered in this work. Chapter 4 presents several techniques for reducing estimation risk, exploring their theoretical underpinnings and providing general intuition. Chapter 5 then considers the empirical application of these techniques, highlighting several technicalities. Chapter 6 then applies the flexible risk-based framework to SA equity data, providing an empirical comparison of different implementations. Chapter 7 concludes the research and provides avenues for further research.

References

Flint, Emlyn James, and Simon Du Plooy. 2018. “Extending Risk Budgeting for Market Regimes and Quantile Factor Models.” Available at SSRN 3141739.

Jurczenko, Emmanuel, Thierry Michel, and Jerome Teiletche. 2013. “Generalized Risk-Based Investing.” Available at SSRN 2205979.

Kinn, Daniel. 2018. “Reducing Estimation Risk in Mean-Variance Portfolios with Machine Learning.” arXiv Preprint arXiv:1804.01764.

Markowitz, Harry. 1952. “Portfolio Selection.” The Journal of Finance 7 (1): 77–91.

Richard, Jean-Charles, and Thierry Roncalli. 2015. “Smart Beta: Managing Diversification of Minimum Variance Portfolios.” In Risk-Based and Factor Investing, 31–63. Elsevier.

Shen, Weiwei, and Jun Wang. 2017. “Portfolio Selection via Subset Resampling.” In Thirty-First Aaai Conference on Artificial Intelligence.