Article Detail

Measuring Market Liquidity Risk – Which Model Works Best?

Journal 35: Zicklin-Capco Institute Paper Series in Applied Finance

Cornelia Ernst, Sebastian Stange, Christoph Kaserer

Market liquidity risk, the difficulty or cost of trading assets in crises, has been recognized as an important factor in risk management. The literature has already proposed several models to include liquidity risk in the standard Value-at-Risk framework. While theoretical comparisons between those models have been conducted, their empirical performance has yet to be benchmarked. This paper performs comparative back-testings of daily risk forecasts for a large selection of liquidity risk models. In a comprehensive 5.5-year stock sample we show which model provides the most accurate results and provide detailed recommendations about which model is most suitable in a specific situation.

That assets cannot be liquidated as previously thought seems to frequently come as a surprise in crisis situations. The discussion always flourishes after stock market crashes. But liquidity is a continuous problem for financial institutions. Trading strategies and investments that yield high profits often invest in less-liquid assets like private equity, emerging markets or low capitalization stocks. In crash situations, those asset positions often cannot be traded at anywhere close to fair prices, because scarce liquidity is consumed by the concerted sales of many market participants. Yet, market liquidity risk often remains unaddressed in many risk management systems.

Several liquidity risk models have already been proposed in the literature. While overarching theoretical discussions and summaries already exist, empirical testing is indispensable. All models must necessarily use simplifying assumptions. But which most distort the overall result? Only the empirical evaluation of model accuracy and relative performance will clarify which simplification is most detrimental. To the best of our knowledge, extensive comparative testing of these models has not been conducted.

This paper adds to the existing literature by extensively back-testing some of the most important liquidity risk models on the basis of a large stock data set. This data set includes daily prices on the 160 largest listed stocks in Germany, i.e. the constituent stocks of the four major German stock indexes DAX, MDAX, SDAX and TecDAX over the period July 2002 to December 2007. Price, volume and bid-ask spread data is taken from Thomson Financial Datastream. Moreover, the dataset is enriched by order book data published under the label Xetra Liquidity Measure (XLM) by Deutsche Börse.

Specifically, we examine the models proposed by Bangia et al. (1999), Berkowitz (2000a), Cosandey (2001), Francois-Heude and van Wynendaele (2001), Giot and Grammig (2005), Stange and Kaserer (2011) and Ernst et al. (2012). On the basis of these results we provide recommendations about which model is most suitable in practice. Purely theoretical models without obvious empirical specifications, as well as models requiring intraday data, remain outside the scope of this analysis.

Our main results can be summarized as follows. First and not surprisingly, we find that data availability is the main driver for the precision of risk forecasts. Models based on limit order data generally outperform models based on bid-ask spread or volume data. More specifically, the Kupiec (1995) acceptance rate is in the range of 10 to 30% for those models that use transaction data only, while it increases to more than 70%, if models build on limit order book data. Even when bid-ask spread data is used, acceptance rates stay below 50%. Hence, models based on bid-ask spread or volume data are highly approximate and should only be used if no other data is available. Second, if limit order book data is available, an approach based on empirical or t-distributed net returns [Stange and Kaserer (2011) or Giot and Grammig (2005)] as well as the modified addon model adapted from Ernst et al. (2012), all show satisfactory results. Ernst et al. (2012) with limit order data show the best performance by achieving an acceptance rate of 74%. Third, if only bid-ask spread data can be obtained, the modified add-on model with bid-ask spreads by Ernst et al. (2012) is recommended, even though the acceptance rate is only 44%. Fourth, on the basis of volume data only, Cosandey (2001) provides the best results with an acceptance rate of 32%.

In the rest of the paper we proceed as follows: We start by defining liquidity risk in a general framework, outlining different liquidity risk models in detail and sketching our implementation approach. Afterwards we evaluate and compare all liquidity risk models based on the precision of their risk forecasts. Finally, we summarize the results.

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