Establishing the risk denominator in a Sharpe ratio framework for share selection from a momentum investment strategy approach

Chris Van Heerden

doi:10.4102/sajems.v23i1.3467

Abstract

Background: Based on the static mean-variance portfolio optimisation theory, investors will choose the portfolio with the highest Sharpe ratio to achieve a higher expected utility. However, the traditional Sharpe ratio only accounts for the first two moments of return distributions, which can lead to false portfolio performance diagnostics with the presence of asymmetric, highly skewed returns. Aim: With many criticising the standard deviation's applicability and with no consensus on the ascendency of which other risk denominator to consult, this study contributes to the literature by validating the importance of consulting value-at-risk as the more commendable risk denominators for the Johannesburg Stock Exchange. Method: These results were derived from a novel index approach that produces a comprehensive risk-adjusted performance evaluation score. Results: Of the 24 Sharpe ratio variations under evaluation, this study identified the value-at-risk Sharpe ratio as the better variation, which led to more profi table share selections for long-only portfolios from a one-year and five-year momentum investment strategy perspective. However, the attributes of adjusting for skewness and kurtosis exhibited more promise from a three-year momentum investment strategy perspective. Conclusion: The results highlighted the ability to outperform the market, which further emphasised the importance of active portfolio management. However, the results also conrfimed that active and more passive equity portfolio managers will have to consult different Sharpe ratio variations to enhance the ability to outperform the market and a buy-and-hold strategy.

Highlights

Common practice in selecting suitable portfolio compositions comprises the characterising of the different assets under consideration, where the desired properties in terms of reward and risk are evaluated (Markowitz 1952)
This study proved that from a risk-adjusted performance perspective it matters which risk denominator is considered to be admissible for the Sharpe ratio framework
The standard deviation exhibited poor evidence as a risk denominator, the results suggested that variations of the traditional Sharpe ratio may be more advisable in order to enhance the ability to make more profitable share selections

Summary

Introduction

Common practice in selecting suitable portfolio compositions comprises the characterising of the different assets under consideration, where the desired properties in terms of reward and risk are evaluated (Markowitz 1952). Roy (1952) considered the implications of minimising the upper bound of the chance of losses, if information is confined to only the first and second order moments This implies that investors tend to be more protective of portfolio wealth against the possibility of making losses and not necessarily interested in how share prices deviate around a profitable mean. From this argument Markowitz (1959) was inspired to introduce the downside risk measure, named semi-variance, replacing the ordinary variance to include a downside risk measure for the first time in portfolio selection. The traditional Sharpe ratio only accounts for the first two moments of return distributions, which can lead to false portfolio performance diagnostics with the presence of asymmetric, highly skewed returns

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Methods

Results

Conclusion