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                <term xml:lang="en">regulatory capital</term>
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                <term xml:lang="en">systemic risk</term>
                <term xml:lang="en">financial diversification</term>
                <term xml:lang="fr">fonds propres</term>
                <term xml:lang="fr">Diversification financière</term>
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              <p>This article examines the effects of diversification on systemic risk, and its implications for regulatory capital from a macro-prudential perspective. The systemic risk studied is that resulting from a common exposure of banking institutions: when the latter diversify their activities, the compositions of their assets converge, making them therefore susceptible to the same shocks. In this context, the contribution of this article is threefold: firstly, it analyzes the evolution of capital that would compensate for the increased risk of a generalized crisis; secondly, it assumes that the return on banking asset follows a Gumbel distribution, allowing for better modeling of extreme risks (especially on the left tail) than does a gaussian distribution; thirdly, it analyzes arbitrage in terms of regulatory capital for individual risk vs. systemic risk resulting from diversification. We point out that, in this context, the regulator cannot manage individual and systemic risks with a single instrument. Indeed, diversification allows a bank to reduce its individual risk and therefore, from a micro-prudential perspective, to reduce its level of regulatory capital. However, as this strategy leads to an increase in systemic risk, under the macro-prudential regulation, it should hold more. The prudential micro and macro objectives may thus diverge, and thus require two instruments of regulation.</p>
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              <p>Cet article s’intéresse aux effets de la diversification sur le risque systémique, ainsi qu’à ses implications en termes de fonds propres réglementaires dans une optique macroprudentielle. Le risque systémique étudié est celui qui découle d’une exposition commune des établissements bancaires : lorsque ces derniers diversifient leurs activités, les compositions de leur actif convergent, ce qui les rend donc sensibles aux mêmes chocs. Dans ce cadre, l’apport de cet article est triple : premièrement, il analyse l’évolution des fonds propres qui permettrait de compenser l’augmentation du risque d’une crise généralisée ; deuxièmement, il suppose que le rendement de l’actif bancaire suit une loi de Gumbel, ce qui permet de mieux modéliser les risques extrêmes (en particulier sur la queue de distribution gauche) que ne le fait la loi normale ; troisièmement, il analyse l’arbitrage en termes de fonds propres pour risque individuel vs risque systémique résultant de la diversification. Nous pointons ainsi le fait que, dans ce cadre, le régulateur ne peut gérer avec un seul instrument les risques individuel et systémique. En effet, la diversification permet à un établissement bancaire de diminuer son risque individuel et donc, dans une optique microprudentielle, de diminuer son niveau de fonds propres réglementaires. Mais, comme cette stratégie conduit dans le même temps à une augmentation du risque systémique, en vertu de la réglementation macroprudentielle, il devrait en détenir davantage. Les objectifs micro et macroprudentiels peuvent ainsi diverger, et nécessiteraient donc deux instruments de régulation.</p>
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