An investigation into reference-day risk-free metrics in the context of modern portfolio theory on the JSE

Modern portfolio theory (MPT), asset pricing models and broader financial modelling are dependent upon the accuracy of input parameters. For example, the accuracy of expected returns, standard deviations and correlations as an input into MPT will result in a more efficient selection of the optimal portfolio. These metrics are exposed to reference-day risk which is the variation in input estimation due to the selection of initial reference-day in calculations. This paper examines whether a change in reference-day, the day on which a metric is calculated, significantly affects estimates of risk-return metrics on the Johannesburg Stock Exchange (JSE). Thereafter, it applies these findings to the asset allocation problem of constructing a maximum Sharpe portfolio. The objective of this paper is to further prior research through the evaluation of an alternative simulation method and an extension of the range of tested metrics. The advancement of this prior research is achieved through the use of the Cholesky decomposition and a nonparametric bootstrapping procedure to generate reference-day risk-free estimates for average returns, standard deviations, correlations and betas. Furthermore, this paper applies the reference-day risk-free metrics to the construction of optimal multi-asset portfolios in the mean-variance framework. The findings suggest that through the use of a five-year period of monthly returns, the selection of a reference-day materially affects risk-return metrics and the subsequent portfolio characteristics that are based upon these metrics. The performance of portfolios, optimised on each reference day, ranged between 10% during the out-of-sample period. Additionally, using traditional end of month data resulted in underperformance of out-of-sample, overstated average returns, understated standard deviations and lower correlations between asset classes. Based on these findings we propose an alternative bootstrapping method for calculating reference-day risk-free metrics which reduces the effect of reference-day risk. The purpose of this methodology is to use these estimates for portfolio construction, risk management and asset pricing. The results of this paper indicate that reference-day risk makes a material difference in portfolio construction.

Grantor

Department of Finance and Tax

Year dc:date.issued

2019

Author dc:creator

• Feinstein, Samuel G

Advisor dc:contributor.advisor

• Rajaratnam, Kanshukan

• Finance and Tax

Handle dc:identifier.uri

http://hdl.handle.net/11427/31380

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/31380