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In this paper, we explore the Loss Distribution Approach (LDA) for computing the capital charge of a bank for operational risk where LDA refers to statistical/actuarial methods for modelling the loss distribution. In this framework, the capital charge is calculated using a Value-at-Risk measure. In the first part of the paper, we give a detailed description of the LDA implementation and we explain how it could be used for economic capital allocation. In the second part of the paper, we compare LDA with the Internal Measurement Approach (IMA) proposed by the Basel Committee on Banking Supervision to calculate regulatory capital for operational risk. LDA and IMA are bottom-up internal measurement models which are apparently different. Nevertheless, we could map LDA into IMA and give then some justifications about the choice done by regulators to define IMA. Finally, we provide alternative ways of mapping both methods together.

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Minimum variance and equally-weighted portfolios have recently prompted great interest both from academic researchers and market practitioners, as their construction does not rely on expected average returns and is therefore assumed to be robust. In this paper, we consider a related approach, where the risk contribution from each portfolio components is made equal, which maximizes diversication of risk (at least on an ex-ante basis). Roughly speaking, the resulting portfolio is similar to a minimum variance portfolio subject to a diversication constraint on the weights of its components. We derive the theoretical properties of such a portfolio and show that its volatility is located between those of minimum variance and equally-weighted portfolios. Empirical applications conrm that ranking. All in all, equally-weighted risk contributions portfolios appear to be an attractive alternative to minimum variance and equally-weighted portfolios and might be considered a good trade-o between those two approaches in terms of absolute level of risk, risk budgeting and diversication.