Portfolio optimization using Mixture Design of Experiments: Scheduling trades within electricity markets

Deregulation of the electricity sector has given rise to several approaches to defining optimal portfolios of energy contracts. Financial tools - requiring substantial adjustments - are usually used to determine risk and return. This article presents a novel approach to adjusting the conditional value at risk (CVaR) metric to the mix of contracts on the energy markets; the approach uses Mixture Design of Experiments (MDE). In this kind of experimental strategy, the design factors are treated as proportions in a mixture system considered quite adequate for treating portfolios in general. Instead of using traditional linear programming, the concept of desirability function is here used to combine the multi-response, nonlinear objective functions for mean with the variance of a specific portfolio obtained through MDE. The maximization of the desirability function is implied in the portfolio optimization, generating an efficient recruitment frontier. This approach offers three main contributions: it includes risk aversion in the optimization routine, it assesses interaction between contracts, and it lessens the computational effort required to solve the constrained nonlinear optimization problem. A case study based on the Brazilian energy market is used to illustrate the proposal. The numerical results verify the proposal's adequacy.