Robust portfolio optimization : a stochastic evaluation of worst-case scenarios

This article presents a new approach for building robust portfolios based on stochastic efficiency analysis and periods of market downturn. The empirical analysis is done on assets traded on the Brazil Stock Exchange, B3 (Brasil, Bolsa, Balcão). We start with information on the assets from periods of market downturn (worst-case) and we group them using hierarchical clustering. Then we do stochastic efficiency analysis on these data using the Chance Constrained Data Envelopment Analysis (CCDEA) model. Finally, we use a classical model of capital allocation to obtain the optimal share of each asset. Our model is able to accommodate investors who exhibit different risk behaviors (from conservatives to risky investors) by varying the level of probability in fulfilling the constraints (1-αi) of the CCDEA model. We show that the optimal portfolios constructed with the use of information from periods of market downturns perform better for the Sharpe ratio (SR) in the validation period. The combined use of these approaches, using also fundamentalist variables and information on market downturns, allows us to build robust portfolios, with higher cumulative returns in the validation period, and portfolios with lower beta values.