Optimal portfolios with minimum capital requirements

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 riskadjusted performance of the proposed approach is superior to that of minimum-VaR and minimumstressed VaR portfolios.André A. P. Santos acknowledges financial support from research Projects CNPq 481719/2011 3 and UFSC Funpesquisa 2010/2011 from the Brazilian Government. Francisco J. Nogales is supported by the Spanish Government through Project MTM 2010 16519. Esther Ruiz is supported by the Spanish Government ECO2009 08100Publicad