Value at risk (VaR) backtesting 'Evidence from a South African market portfolio'
Date
2014-03-18
Authors
Katsenga, Gerald Z
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Abstract
Value at Risk (VaR) has emerged as one of the most prominent risk measurement techniques
in finance. It is a measure that quantifies the worst expected loss over a given confidence level
and target horizon, under normal market conditions. In this thesis, the concept of VaR as an
invaluable tool for financial risk management is explained, and a theoretical but detailed description
of some of the methods of VaR computation are presented, with a key emphasis on the
assumptions and shortcomings of these models. A discussion that is preceded by a presentation
on the calculation of portfolio returns and the choice of VaR parameters as key determinants in
the choice of an appropriate VaR model.
In light of the shortcomings to VaR measures, a number of backtesting techniques that examine
the accuracy of VaR estimates are presented and reviewed. The review of these VaR
validation methods is both from a theory and practice perspective. The unconditional coverage,
independence property and the conditional coverage property are defined and their relation to
backtesting methods discussed. The backtesting techniques presented are classified by whether
they test for the unconditional coverage property, independence property or the conditional
coverage (joint) property of a VaR measure.
The backtesting methods presented and discussed in this work are then utilized in empirically
validating the accuracy of one of the most widely used VaR method in South Africa, the historical
simulation. The examination of VaR estimates from this model is applied on an ‘actual’
interest rate portfolio. The outcome of the statistical backtests show positive results of accurate
performance of the model at lower confidence levels, and an underestimation of risk at
higher VaR confidence levels. However, when hedge positions are excluded from the portfolio
the model’s performance in accurately estimating VaR is questionable.