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Optimal and coherent economic-capital structures: evidence from long and short-sales trading positions under illiquid market perspectives

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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. 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-sales trading positions. 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. 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 subject to some selected financial and operational rational constraints. The empirical results strongly confirm the importance of enforcing financially and operationally meaningful nonlinear and dynamic constraints, when they are available, on economic capital optimization procedure. The empirical results are interesting in terms of theory as well as practical applications and can aid in developing robust portfolio management algorithms that financial entities could consider in light of the aftermath of the latest financial crisis.

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Notes

  1. Economic capital (or risk 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 modeling 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 an internal market risk modeling techniques to assess economic capital can significantly aid the financial entity in complying with Basel II capital adequacy requirements.

  2. In this paper, the concept of coherent market portfolios refers to rational portfolios that are contingent on meaningful financial and operational constraints. In this sense, coherent market portfolios do not lie on the efficient frontiers as defined by Markowitz (1959), and instead have logical and well-structured long/short asset allocation proportions.

  3. For an excellent survey of recent contributions to robust portfolio strategies from operations research and finance to the theory of portfolio selection, one can refer to Fabozzi et al. (2010).

  4. In a related approach, Elliott and Siu (2010) provide a verification theorem for the Markovian regime-switching HJB solution of the stochastic differential game corresponding to the risk-minimizing problem.

  5. In this class of models (that is, GARCH-M), the conditional variance enters into the conditional mean equation as well as the usual error variance part. As such, when the return of a security is dependent on its volatility, one can use the GARCH-M model formulation. Indeed, the GARCH-M model implies that firstly there exists serial correlation in the return series and secondly these serial correlations are introduced by the volatility process due to a risk-premium.

  6. In this paper, severe or crisis market conditions refer to unexpected extreme adverse market situations at which losses could be several-fold larger than losses under normal market situation. Stress-testing technique is usually used to estimate the impact of unusual and severe events.

  7. An interesting issue for further research would be the implementation of advanced asymmetric GARCH models that allow for asymmetry in both the conditional mean and the variance equations. As such, it is suggested that future research on the topic could focus on the modified models developed by Glosten et al. (1993) and Gonzalez-Rivera (1998), the sign and volatility-switching ARCH (SVSARCH) model by Fornari and Mele (1997), the Markov switching volatility ARCH (MSVARCH) model by Hamilton and Susmel (1994) and the asymmetric non-linear smooth-transition generalized autoregressive conditional heteroskedasticity (ANST-GARCH) model (Anderson et al. 1999; Nam et al. 2001). Furthermore, there are new members to the extended GARCH models family which can be focused on as well in future research, such as, the dynamic conditional correlation (DCC) GARCH model of Engle (2002) and the asymmetric generalized dynamic conditional correlation (AG-DCC) model (Cappiello et al. 2006), which permits conditional asymmetries in correlation dynamics and accounts for heteroskedasticity directly by estimating correlation coefficients using standardized residuals.

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Correspondence to Mazin A. M. Al Janabi.

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Al Janabi, M.A.M. Optimal and coherent economic-capital structures: evidence from long and short-sales trading positions under illiquid market perspectives. Ann Oper Res 205, 109–139 (2013). https://doi.org/10.1007/s10479-012-1096-3

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