Modeling Liquidity Risk, with Implications for Traditional Market Risk Measurement and Management

Abstract

Market risk management has traditionally focussed on the distribution of portfolio value changes produced by changes in the midpoint of bid and ask prices. Hence market risk is traditionally assessed under the assumption of an idealized market with a negligible bid-ask spread. In reality, however, spreads can be both wide and variable; hence a superior approach would recognize that positions will not be liquidated at the mid-price, but rather at the mid-price less the uncertain bid-ask spread. Liquidity risk associated with the uncertainty of the spread, particularly for thinly traded or emerging market securities under adverse market conditions, is an important part of overall market risk and is therefore important to model. We do so, proposing a simple liquidity risk methodology that can be easily and seamlessly integrated into standard value-at-risk models. We show that ignoring the liquidity effect can produce underestimates of market risk in emerging markets by as much as thirty percent. Furthermore, we show that because the BIS is already implicitly monitoring liquidity risk, banks that fail to model liquidity risk explicitly and capitalize against it will likely experience surprisingly many violations of capital requirements, particularly if their portfolios are concentrated in emerging markets.

We thank Steve Cecchetti, Edward Smith and two anonymous referees for helpful comments and suggestions. All remaining errors are ours. This paper was written while the second author visited the Stern School of Business, New York University, whose hospitality is gratefully appreciated. An abridged version was published as “Liquidity on the Outside,” Risk Magazine, 12, 68–73, 1999.

“Portfolios are usually marked to market at the middle of the bid-offer spread, and many hedge funds used models that incorporated this assumption. In late August, there was only one realistic value for the portfolio: the bid price. Amid such massive sell-offs, only the first seller obtains a reasonable price for its security; the rest lose a fortune by having to pay a liquidity premium if they want a sale…. Models should be revised to include bid-offer behavior.”

Nicholas Dunbar (“Meriwether’s Meltdown,” Risk, October 1998, 32–36)