Value at Risk in the South African equity market: a view from the tails

C Milwidsky,Eben Mare

doi:10.4102/sajems.v13i3.109

C Milwidsky, Eben Mare

Open Access

https://doi.org/10.4102/sajems.v13i3.109

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Abstract

Traditional parametric Value at Risk (VaR) estimates assume normality in financial returns data. However, it is well known that this distribution, while convenient and simple to implement, underestimates the kurtosis demonstrated in most financial returns. Huisman, Koedijk and Pownall (1998) replace the normal distribution with the Student’s t distribution in modelling financial returns for calculation of VaR. In this paper we extend their approach to the Monte Carlo simulation of VaR on both linear and non-linear instruments with application to the South African equity market. We show, via backtesting, that the t-distribution produces superior results to the normal one.

Highlights

The Value at Risk (VaR) of a portfolio of financial instruments at the confidence level x is given by the smallest number l such that the probability that the loss L exceeds l is no larger than (1–x).1 It is intended to calculate the maximum possible loss on the value of the portfolio over a specific time period with a certain level of confidence (McNeil et al, 2005) and answers the question ‘How much can I lose with x per cent probability over a certain holding period?’ (JP Morgan/Reuters, 1996)
We focus on Daily Value at Risk (DVaR) which is the VaR for a one day holding period
It is commonly accepted that financial returns’ distributions exhibit kurtosis or heavier tails than the normal distribution. We demonstrated that this phenomenon extends to the South African equity market

Summary

Introduction

The Value at Risk (VaR) of a portfolio of financial instruments at the confidence level x is given by the smallest number l such that the probability that the loss L exceeds l is no larger than (1–x). It is intended to calculate the maximum possible loss on the value of the portfolio over a specific time period with a certain level of confidence (McNeil et al, 2005) and answers the question ‘How much can I lose with x per cent probability over a certain holding period?’ (JP Morgan/Reuters, 1996). VaR is appealing in that it attempts to provide a single number summarising the market risk in a portfolio of assets and expresses this directly by assigning a monetary value to the potential losses in the portfolio (Hendricks, 1996; Hull, 2006). It has become a risk measure which is widely-used by financial institutions, both for internal risk management and regulatory reporting purposes and has made its way into the Basel II capital-adequacy framework (Hendricks, 1996; Mc Neil et al, 2005, Van den Goorbergh, 1999). In the former, returns are assumed to mimic a period in the past while the latter methodology assigns an actual probability distribution to the underlying risk factors

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