In this paper, we study the aggregated risk from dependent risk factors under the multivariate Extreme Value Theory (EVT) framework. We consider the heavy-tailness of the risk factors as well a non-parametric tail dependence structure. This allows a large scope of models on the dependency. We...

Analytic solutions to Risk Parity, Maximum Diversification, and Minimum Variance portfolios provide useful perspectives about their construction and composition. Individual asset weights depend on both systematic and idiosyncratic risk in all three risk-based portfolios, but systematic risk...

Striving for maximum diversification we follow Meucci (2009) in measuring and managing a multi-asset class portfolio. Under this paradigm the maximum diversification portfolio is equivalent to a risk parity strategy with respect to the uncorrelated risk sources embedded in the underlying...

We measure the contributions to risk of a set of factors, strategies, or investments, based on "Minimum-Torsion Bets", namely a set of uncorrelated factors, optimized to closely track the factors used to allocate the portfolio. We then introduce a novel definition of contributions to risk, which...

We investigate the out-of-sample diversification benefits of risk parity portfolios by analyzing the properties an asset class has to fulfill in order to be beneficial in a risk parity strategy and compare them with benefits present in other heuristic weighting techniques, especially risk-based...

The current subprime crisis has prompted us to look again into the nature of risk at the tail of the distribution. In particular, we investigate the risk contribution of an asset, which has infrequent but huge losses, to a portfolio using two risk measures, namely Value-at-Risk (VaR) and...

The Basel II Accord requires that banks and other Authorized Deposit-taking Institutions (ADIs) communicate their daily risk forecasts to the appropriate monetary authorities at the beginning of each trading day, using one or more risk models to measure Value-at-Risk (VaR). The risk estimates of...

We discuss risk measures representing the minimum amount of capital a financial institution needs to raise and invest in a pre-specified eligible asset to ensure it is adequately capitalized. Most of the literature has focused on cash-additive risk measures, for which the eligible asset is a...

This paper features an application of Regular Vine copulas which are a novel and recently developed statistical and mathematical tool which can be applied in the assessment of composite financial risk. Copula-based dependence modelling is a popular tool in financial applications, but is usually...

In this paper, we put forth the notion of “Crisis Utility” as a way of estimating the tail risk of an asset or investment strategy. We believe that Crisis Utility is more functional than traditional, narrowly defined definitions of tail risk since it incorporates the concept of...