WP-AD 2011-14 On downside risk predictability through liquidity and trading activity : a quantile regression approach

Most downside risk models implicitly assume that returns are a sufficient statistic with which to forecast the daily conditional distribution of a portfolio. In this paper, we address this question empirically and analyze if the variables that proxy for market liquidity and trading conditions convey valid information to forecast the quantiles of the conditional distribution of several representative market portfolios. Using quantile regression techniques, we report evidence of predictability that can be exploited to improve Value at Risk forecasts. Including tradingand spread-related variables improves considerably the forecasting performance. Keywords: Value at Risk, Basel, Liquidity, Trading Activity. * We would like to thank David Abad, Jos van Bommel, Lucía Cuadro, Christian Riis Flor, Angel León, Antonio Machado, Simone Manganelli, Manuel Moreno, Alfonso Novales, Alberto J. Plazzi, Gonzalo Rubio, Allan Timmerman, Ross Valkanov, participants in XVII Finance Forum (Madrid, Spain), EFMA 2010 Meeting (Aarhus, Denmark), EAA 2010 Meeting (Istanbul, Turkey), 2010 ASEPELT Meeting (Alicante, Spain) and seminar attendants at University of Valencia for their valuable comments and suggestions to previous versions of this paper. Any error is our own responsibility. Financial support from the Spanish Department of Science and Innovation through ECO2008-02599 project and Ivie is gratefully acknowledged. A. Rubia: University of Alicante. L. Sanchis-Marco: University of Castilla-La Mancha. Corresponding author: lidia.sanchis@uclm.es. 1 Introduction Implementing risk control and monitoring systems requires quantitative procedures to capture the level of underlying uncertainty and make accurate predictions. The Basel Committee on Banking Supervision (BCBS) has contributed greatly to the popularization of certain international standards, known as Basel I and II Accords, in the nancial services industry. This regulatory setting entitles eligible nancial institutions to use internal models based on the Value-at-Risk (VaR) measure for meeting market risk capital requirements. It is agreed that, without the e¤orts made to comply with the BCBS standards, the nancial industry would likely be facing a deeper crisis. The depth of the economic turmoil has shown the necessity for new standards to achieve greater banking sector resilience and the need to improve the existing procedures for quantifying market risk.1 The present paper is motivated by this concern. The existing literature has suggested a number of procedures for forecasting downside risk, mainly VaR, which largely di¤er in their degree of sophistication: From the simple EWMA approach popularized by RiskMetrics to the more advanced probabilistic settings based on the Extreme Value Theory; see Manganelli and Engle (2004) and McNeil et al. (2005) for a review. Remarkably, a number of empirical studies have revealed that most of these methods do not seem to perform successfully in practice under standard backtesting techniques (e.g., Kuester et al., 2006), which underlines the practical complexity that lies behind the simple notion of VaR. Why is accurate VaR forecasting so elusive? Whereas most of the previous literature has attempted to address this question on the grounds of model misspeci cation, in this paper we adopt an alternative view within the framework of model risk and analyze the important role played by the set of conditioning information. In spite of the large methodological di¤erences, the existing methodologies to model market risk share a common characteristic: They all rely exclusively on the information conveyed by historical returns. Naturally, this may turn out to be unnecessarily restrictive for practical purposes, since the conditional loss function of a portfolio may exhibit non-trivial links with the state variables that characterize the market environment and trading conditions and which may help forecasting bursts in volatility and illiquidity, particularly, in times of stress.2 1The BCBS is currently carrying out a reform program that aims to enhance Basel II towards a new regulatory setting on the basis of higher supervisory standards (Basel III), and which is expected to be completed by the end of 2010. The BCBS has issued several consultative documents in the interim outlining the main features of the new regulatory setting. It is interesting to note that, despite its limitations, the VaR paradigm is still a pillar in the internal model approach for market risk adopted in Basel III, although further re nements, such as stressed VaR and stress tests, will also be required to provide a complementary risk perspective. 2The implicit belief that returns subsume all the relevant information to forecast downside risk may be originated in a conservative interpretation of the E¢ cient Market Hypothesis. This