Liquidity adjusted value-at-risk based on the components of the bid-ask spread

Abstract

This paper proposes a method of calculating a Liquidity Adjusted Value-at-Risk (L-VaR) measure. Traditional VaR approaches assume perfect markets, where an investor can buy or sell any amount of stock without causing a significant price change. Such a hypothesis is seldom verified in practice, especially in emerging markets, consequently underestimating the VaR risk measure. An attempt is made to remedy this shortcoming by first estimating the bid–ask spread components in order to calculate accurately both the endogeneous and the exogenous liquidity risk. Under this framework, the liquidation price of a position will not be the spread midpoint, but at most the bid price. The Madhavan et al. ( 1997 Madhavan, A , Richardson, M and Roomans, M . 1997. Why do security prices change? A transaction-level analysis of NYSE stocks. Review of Financial Studies, 10: 1035–64. [Crossref], [Web of Science ®] [Google Scholar] ) model is extended by incorporating the traded volume and find that liquidity risk, for an emerging stock market, displays an inverse U-shape pattern throughout the day. For the high-priced, high-capitalization stocks of the Athens Stock Exchange, it represents 3.40% of total market risk, while for the low capitalization ones, it is even higher at 11%. VaR measures are then adjusted for such spread variation since, neglecting such effect, leads so serious failure of VaR backtesting.