We show how to mix machine learning signals such as kernel smoothing and fuzzy memberships via the Entropy Pooling approach by Meucci (2008). We illustrate a case study, where we overlay an exponentially time-decayed prior to a pseudo-Gaussian kernel that emphasizes market scenarios where...

Expected returns should not only include rewards for accepting the risk of a potential downside loss, but also discounts for potential upside gains. Since investors care differently about upside gains versus downside losses, they require a risk premium for bearing the relative downside risk. We...

Propagating causal stress-tests or contagion on selected risk factors to all the risk drivers is a challenging task. We use Entropy Pooling by Meucci (2008) to address this issue. Our causal stress-tests comprise, but are not restricted to, stress-testing Bayesian networks. We detail the theory...

We extend the Fully Flexible Views 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 the conditional value at risk, which cannot be handled directly by the original...

In the paper we introduce an empirical approximation of the log-optimal investment strategy that guarantees an almost optimal growth rate of investments. The proposed strategy also considers the effects of portfolio rearrangement costs on growth optimality and advises a suboptimal portfolio for...

We introduce "factors on demand", a modular, multi-asset-class return decomposition framework that extends beyond the standard systematic-plus-idiosyncratic approach. This framework, which rests on the conditional link between flexible bottom-up estimation factor models and flexible top-down...

We present a simple method to generate scenarios from multivariate elliptical distributions where the sample mean and covariances match the respective population moments. This methodology easily applies to large numbers of scenarios and large-dimensional distributions. We show an application to...

We introduce the multivariate Ornstein-Uhlenbeck and discuss how it generalizes a vast class of continuous-time and discrete-time multivariate processes. Relying on the simple geometrical interpretation of the dynamics of the Ornstein-Uhlenbeck process we introduce cointegration and its...

By default, most investors equate a passive investment such as a traditional market capitalisation based index with a welldiversified investment. However, “diversified” and “passive” should not a priori be considered as synonymous. We have attempted to show that “passive” should not...

The article focuses on the categorisation of indexing methods in equity space. Based on the theoretical concepts of the various index methods, we first conduct a qualitative categorisation. In a second step, we try to validate it with a formal statistical analysis. We conclude that many indexing...