Backtesting historical simulation value-at-risk for a selected portfolio of South African bonds

Abstract

As financial asset portfolios have become more complex, it has become more difficult for the management of financial institutions to obtain a useful, yet practical measure of market risk. Since modern portfolios contain more derivative instruments, simple linear measures such as standard deviation and duration are inappropriate. Due to this need a market risk measurement technique called Value-at-Risk (VaR) was developed. VaR can be defined as the predicted maximum potential adverse loss of a single financial asset, or portfolio of assets, over a target horizon, within a given confidence interval. A backtesting procedure was designed to compare realized trading results of a selection of representative bonds with model generated risk measures in order to evaluate the accuracy of the VaR model. The backtesting procedure used in this study involves the comparison between the number of times the VaR model under-predicted the subsequent day's loss, versus the number of times such an under-prediction is expected. The empirical results from this study illustrates that VaR underestimated risk during periods of high volatility and overestimated VaR during periods of low volatility, thus rendering it useless as a measure of extreme market movement. The purpose of this study is not to test the validity of VaR, but to illustrate the shortcoming of VaR, in that it measures only market risk. Practitioners should always bear in mind that VaR is a market risk measurement technique and does not warn of extreme market movements.