Forecasting portfolio returns with skew-geometric Brownian motions

Applied Stochastic Models in Business and Industry. 2022. Vol. 38. No. 4. P. 620–650.

Liseo B., Bufalo M., Orlando G.

The gist of this work is to propose a minimum tracking error portfolio that could be adopted not only as an automated alternative to ETFs but, it could also be potentially used to anticipate market changes in the target index. This goal has been achieved by adopting skew Brownian motion as a general framework. The proposed solution has been declined in two versions: the case in which the constituents (i.e., in our case the subindices) of the objective portfolio are uncorrelated among each other, and the case in which correlation should be taken into account. Our tests, carried out on the S&P 500, as an example of a developed market, and Bovespa, as an example of an emerging market, shows that the proposed solutions replicate the index with a much smaller tracking error than that of the ETFs considered.

Keywords: Portfolio optimization, Forecasting, skew-normal Brownian motions