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Abstract
This paper proposes a concrete theoretical foundation and a new modelling framework that attempts to tackle the issue of market/liquidity risk and economic-capital estimation at a portfolio level by combining two mutual asset market/liquidity risk models. In essence, this study extends research literature related to the assessment of the asset market/liquidity risk by providing a generalized theoretical modelling underpinning that handle, from the same perspective, market and liquidity risks jointly and integrate both risks into a portfolio setting without a commensurate increase of statistical postulations. As such, we argue that market and liquidity risk components are correlated in most cases and can be integrated into one single market/liquidity framework that consists of two interrelated sub-components. The first component is attributed to the impact of adverse price movements and is modelled based on the concept of liquidity-adjusted value-at-risk framework, while the second component focuses on the risk of variation in transactions costs due to the bid-ask spreads and it attempts to measure the likelihood that it will cost more than expected to liquidate the asset position. As such, the model comprises a new approach to contemplating the impact of time-varying volatility of the bid-ask spread and its upshot on the overall asset market/liquidity risk. The modelling framework can be constructive for financial service industries in emerging-economies and particularly in reinforcing rational economic-capital allocation in light of the aftermaths of the sub-prime financial crisis.
Acknowledgements
The author would like to acknowledge the efforts of anonymous referees and the editor in reviewing and providing valuable comments on two earlier versions of this research paper. This work has benefited from a financial support in the form of a summer-grant from the College of Business and Economics (CBE), United Arab Emirates University, Al-Ain, UAE. The usual disclaimer applies.
Notes
Depth is defined as the volume of possible trades without affecting prevailing market prices on order books.
The Basel Capital Accord sets down the agreement among the G-10 central banks to apply common minimum capital standards to their banking institutions. The standards largely address the main risks incurred by banks such as credit, market and operational. Currently, the Basel II accord is embraced by other countries apart from the G-10 countries.
A multiplier that is frequently used by researchers and practitioners is the square root of time. However, it overstates the overall impact of market risk since assets liquidation is not permitted during the close-out (unwinding) period.
Recall that for large sample sizes – large degrees of freedom – the t-distribution converges with the normal distribution.
Economic-capital can be defined as the minimum amount of equity capital a financial entity needs to set aside to absorb worst losses over a certain time horizon with a certain confidence level. This is with the objectives of sustaining its trading operations activities and without subjecting itself to insolvency matters. Economic-capital can be assessed with an internal method and modelling techniques such as L-VaR. Economic-capital differs somehow from regulatory capital, which is necessary to comply with the requirements of Basel II committee on capital adequacy. However, building internal market risk modelling techniques to assess economic-capital can significantly aid the financial entity in complying with Basel II capital adequacy requirements.
It is important to note here that the bid-ask spread could vary over time, but it does not widen at all times, however. In the special case when the bid-ask spread does not widen during the close-out (unwinding) period, it can be assumed with reasonable accuracy that h i = 1. If this is the case, then Equation (25) can be reduced to Equation (18).
Other meaningful operational and/or financial constraints can be set by the risk manager and/or fund manager. For instance, the amount of investment in each trading asset (A i ) or the bid-ask spread widening period (h i ) can be specified as additional constraints on the optimization algorithmic function.
