Risk Parity Portfolios with Skewness Risk: An Application to Factor Investing and Alternative Risk Premia

Machine Learning Optimization Algorithms & Portfolio Allocation

“…Let π i be the probability of choosing the coordinate i at the iteration k. The simplest approach is to consider uniform probabilities: π i = 1/n. A better approach consists in pre-specifying probabilities according to the Lipschitz constants 11 :…”

“…where Y is the n × 1 vector, X is the n × p design matrix, β is the p × 1 vector of coefficients and ε is the n × 1 vector of residuals. In this model, n is the number of observations and p 11 Nesterov (2012) assumes that f (x) is convex, differentiable and Lipschitz-smooth for each coordinate:…”

The multivariate mixture dynamics model: shifted dynamics and correlation skew

“…If we replaced the drift parameters μ with historical returns, leaving aside the fact that these are known to be difficult to estimate in a satisfactory way, we would immediately obtain a mixture dynamics under the physical measure. Gaussian mixtures for multivariate returns have been considered in the risk premia literature for risk parity portfolios, see for example Bruder at al. (2016) and references therein.…”

“…(2016) and references therein. In further work we could try to connect our approach to frameworks such as the mixture models used in Bruder at al. (2016).…”

Alternative Risk Premia: Is the Selection Process Important?

“…One can cite for instance the article of Roncalli and Weisang [2016] that discusses factor investing and risk parity. One can think about the article of Bruder et al [2016] who introduce skewness risk to risk parity solution, or that of Brandt and Santa-Clara [2009] who compute portfolio weights using the assets' characteristics. Finally, one can find articles that use the idea of ARP and factor investing to replicate hedge fund returns, such as Fung and Hsieh [2004], Maeso and Martellini [2017], or Tancar and Viebig [2008].…”