Liquidity effects on value-at-risk limits: construction of a new VaR model

Sunny B. Walter Madoroba and Jan W. Kruger

Abstract

ABSTRACT

Value-at-risk (VaR) is a common tool applied by market makers to monitor the risk of any trading position. The conventional VaR model assumes a frictionless market, which is seldom the case. The 2008 financial market crisis exposed the inadequacies of VaR limits, which do not factor in liquidity risk. Various liquidity-adjusted VaR models have been created in an attempt to correct this anomaly. Our study presents a new VaR model that incorporates intraday price movements on high-low spreads and adjusts for a trade impact measure, k, a novel sensitivity measure of price movements due to trading volumes. The new VaR model returns violations that are independent and identically distributed for 94% of the trading counters backtested over a one-year period of trading on the Johannesburg Stock Exchange using Kupiec's test of unconditional coverage. The Christoffersen test of independence returns 96% of violations that are neither autocorrelated nor clustered, while the Christoffersen joint test of conditional coverage shows that the average number of violations is correct 93% of the time at 99% significance levels. The new model is valid and robust for the standard VaR backtests conducted.