Economic capital allocation under coherent market liquidity constraints

Abstract

Asset liquidity trading risk arises from the failure to recognize or address changes in market conditions that affect the ability to liquidate trading assets quickly and with minimal loss in value. Yet despite this universal recognition of the phenomena, there exist no precise mathematical definition of liquidity risk and traditional Value at Risk (VaR) models fail to recognize the impact of liquidity trading risk. In this work we do not offer a definitive one either, but we develop measures of certain kinds of liquidity trading risk that is useful for completing the definition of market risk and for predicting liquidity-adjusted VaR (L-VaR) under illiquid market conditions and within a multivariate context. We argue that asset liquidity risk associated with the uncertainty of liquidating multiple-assets over a given holding period, particularly for thinly traded or emerging markets securities under adverse market conditions, is a key factor in formalizing and measuring overall trading risk and is therefore an important component to model. This paper proposes a practical framework for the quantification of asset liquidity risk, and its impact on economic capital allocations, for multiple assets，portfolios. We present a method whereby the holding periods are adjusted according to the particular needs of each trading portfolio; and this can be attained for the entire portfolio or for specific assets within the trading portfolio. This paper extends previous approaches by explicitly modeling the liquidation of trading portfolios, over the holding period, with the aid of an appropriate scaling of the multiple-assets，L-VaR matrix along with GARCH-M technique to forecast conditional volatility and expected return. The key methodological contribution is a different and a less conservative liquidity scaling factor than the conventional root-t multiplier. The proposed liquidity multiplier is a function of a predetermined liquidity threshold, defined as the maximum position which can be unwound without disturbing market prices during one trading day, and is quite straightforward to implement even by very large financial institutions and institutional portfolio managers. Using more than six years of daily return data of emerging Gulf Cooperation Council (GCC) stock markets, we analyze different trading portfolios (of both long and short-sales trading positions) and determine asset liquidity risk exposure and coherent annual economic capital allocations under different illiquid and adverse market conditions and under the notion of different correlation factors and unwinding periods.