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Generalized marginal risk
An important aspect of portfolio risk management is the analysis of the overall risk with respect to the assets' allocations. Marginal risk is the traditional tool, however, this metric is only meaningful when a position is levered or when the proceeds from the sale of a position are put in the cash account. This paper proposes an extension of the traditional marginal risk approach as a means of overcoming this defficiency. The new concept addresses situations where the change in a position results in changes to other positions as well. An illustration is provided for synthetic and real-world portfolios.
Fully flexible extreme views
We extend the entropy pooling generalization of the Black-Litterman approach to effectively handle extreme views on the tails of a distribution. First, we provide a recursive algorithm to process views on conditional value-at-risk which cannot be handled directly by the original implementation of entropy pooling. Second, we represent both the prior and the posterior distribution on a grid instead of using Monte Carlo scenarios. This way it becomes possible to parsimoniously cover even the far tails of the underlying distribution. Documented code is available to download.