Evaluation of Optimal and Coherent Risk-Capital Structures Under Adverse Market Outlooks

Abstract

This paper broadens research literature associated with the assessment of modern portfolio risk management techniques by presenting a thorough modeling of nonlinear dynamic asset allocation and management under the supposition of illiquid and adverse market settings. This study analyses, from a fund manager’s perspective, the performance of liquidity adjusted risk modeling in obtaining optimal and coherent economic capital structures, subject to meaningful operational and financial constraints as specified by the fund manager. Specifically, the paper proposes a re-engineered and robust approach to optimal economic capital allocation, in a Liquidity-Adjusted Value at Risk (L-VaR) framework, and particularly from the perspective of trading portfolios that have both long and short trading positions and disallowing both pure long positions and borrowing constraints. This paper expands 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 less conservative liquidity scaling factor than the conventional root-t multiplier. Moreover, in this paper, the authors develop a dynamic nonlinear portfolio selection model and an optimization algorithm which allocates both economic capital and trading assets by minimizing L-VaR subject to the constraints that the expected return, trading volume and liquidation horizon should meet the budget limits set by the fund manager. In addition, the paper illustrates how the modified L-VaR method can be used by an equity trading unit in a dynamic asset allocation framework for reporting risk exposure, optimizing economic capital, and assessing risk reduction alternatives. The empirical results strongly confirm the importance of enforcing financially and operationally meaningful nonlinear and dynamic constraints, when they are available, on the L-VaR optimization procedure.


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