Optimal Portfolios with Minimum Capital Requirements

55 Pages Posted: 4 May 2010 Last revised: 17 Jul 2012

See all articles by Andre A. P. Santos

Andre A. P. Santos

CUNEF Universidad

Francisco J. Nogales

Universidad Carlos III de Madrid - Department of Statistics; Institute of Financial Big Data UC3M-BS

Esther Ruiz

Charles III University of Madrid - Department of Statistics and Econometrics

Dick J. C. van Dijk

Erasmus University Rotterdam - Erasmus School of Economics - Econometric Institute; ERIM

Date Written: May 2, 2010

Abstract

We propose a novel approach to active risk management based on the recent Basel II regulations to obtain optimal portfolios with minimum capital requirements. In order to avoid regulatory penalties due to an excessive number of Value-at-Risk (VaR) violations, capital requirements are minimized subject to a given number of violations over the previous trading year. Capital requirements are based on the recent Basel II amendments to account for the ‘stressed’ VaR, that is, the downside risk of the portfolio under extreme adverse market conditions. An empirical application for two portfolios involving different types of assets and alternative stress scenarios demonstrates that the proposed approach delivers an improved balance between capital requirement levels and the number of VaR exceedances. Furthermore, the risk adjusted performance of the proposed approach is superior to that of minimum-VaR and minimum stressed VaR portfolios.

Keywords: Multivariate GARCH, Convex Optimization, Out-Of-Sample Evaluation

JEL Classification: G11, G32

Suggested Citation

A. P. Santos, Andre and Nogales, Francisco J. and Ruiz, Esther and van Dijk, Dick J.C., Optimal Portfolios with Minimum Capital Requirements (May 2, 2010). Journal of Banking and Finance, Vol. 36, No. 7, 2012, Available at SSRN: https://ssrn.com/abstract=1599266 or http://dx.doi.org/10.2139/ssrn.1599266

Andre A. P. Santos (Contact Author)

CUNEF Universidad ( email )

Calle de los Pirineos 55
Madrid, 28040
Spain

Francisco J. Nogales

Universidad Carlos III de Madrid - Department of Statistics ( email )

Avda. de la Universidad, 30
Leganes, Madrid 28911
Spain
+34 916248773 (Phone)

HOME PAGE: http://www.est.uc3m.es/Nogales

Institute of Financial Big Data UC3M-BS ( email )

CL. de Madrid 126
Madrid, Madrid 28903
Spain

Esther Ruiz

Charles III University of Madrid - Department of Statistics and Econometrics ( email )

c/ Madrid 126
Getafe (Madrid), 28903
Spain

Dick J.C. Van Dijk

Erasmus University Rotterdam - Erasmus School of Economics - Econometric Institute

P.O. Box 1738
3000 DR Rotterdam
Netherlands

ERIM ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands
+31 10 408 1263 (Phone)
+31 10 4089162 (Fax)

HOME PAGE: http://people.few.eur.nl/djvandijk

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