Liquidity and the Value at Risk

Abstract

We introduce an intuitive method of enhancing low-frequency volatility measures used to compute Value-at-Risk (VaR) by incorporating intradaily liquidity information from the limit order book. Using the quote slope of Hasbrouck and Seppi (2001), a compound liquidity measure comprising the dimensions of bid-ask spread and log depths, as a proxy for latent liquidity, we assign states of liquidity that the asset instantaneously resides in to allow only extremal liquidity shocks to influence volatility. To forecast the liquidity states, we use the autoregressive conditional multinomial model of Liesenfeld et al. (2006). We test the method on a number of stocks and find that (1) for stocks in financial and technological sectors, only the extremal shocks to liquidity affect volatility significantly and such a liquidity-state adjusted volatility is likely to improve VaR forecasts; (2) the volatility of stock returns in most other sectors are less affected by extremal shocks to liquidity but the continuous liquidity proxy is able to explain some of the dynamics of volatility and (3) the inclusion of liquidity in VaR becomes increasingly important as the quantile under consideration becomes more extreme.