Basel’s value-at-risk capital requirement regulation: An efficiency analysis

We analyze the optimal portfolio policies of expected utility maximizing agents under VaR Capital Requirement (VaR-CR) regulation in comparison to the optimal policy under exogenouslyimposed VaR Limit (VaR-L) and Limited-Expected-Loss (LEL) regulations. With VaR-CR regulation the agent strategy consists of simultaneous decisions on both the portfolio VaR and on the implied amount of required eligible capital. As a result, the performance of VaR-CR regulation depends on its design (the parameter n) and the agent preferences. We show that an optimal VaR-CR regulation allows the regulator on the one hand, to completely eliminate the exposure to the largest losses, which may jeopardize the existence of the institution, and on the other hand, to restrain the portfolio exposure to all other losses. These results rationalize the current Basel regulations. However, the analysis shows also that there is an optimal level of required eligible capital from the regulator standpoint. Counter-intuitively, any requirement above this optimal level is inefficient as it leads to a smaller amount of actually maintained eligible capital and thereby to a larger exposure to the most adverse states of the world. Unfortunately, the current Basel’s range of required levels (n = 3–4) is within this inefficient range. Moreover, with an inefficient regulation the agent might employ an inefficient reporting and disclosure procedure. 2007 Published by Elsevier B.V. 0378-4266/$ see front matter 2007 Published by Elsevier B.V. doi:10.1016/j.jbankfin.2007.02.007 q The authors acknowledge the helpful comments of the anonymous referees. We also thank the Berliner Prize committee of Tel Aviv University for the grant awarded for ‘‘Best Analytical Research in Risk Management and Insurance, 2006’’ and the Kruger Center for Finance of the Hebrew University for its support. * Corresponding author. Tel.: +972 2 58831011; fax: +972 2 5881341. E-mail addresses: [email protected] (G. Kaplanski), [email protected] (H. Levy). Journal of Banking & Finance 31 (2007) 1887–1906 www.elsevier.com/locate/jbf JEL classification: G11; G18; G28; E58