Estimating Market Expectations for Portfolio Selection Using Penalized Statistical Models

The portfolio selection problem can be viewed as an optimization problem that maximizes the risk–return relationship. It consists of a number of elements, such as an objective function, decision variables and input parameters, which are used to predict expected returns and the covariance between the said returns. However, the real values of these parameters cannot be directly observed; thus, estimations based on historical data are required. Historical data, however, can often result in modelling errors when the parameters are replaced by their estimations. We propose to address this by using some regularization mechanisms in the optimization. In addition, we explore the use of implicit information to improve the portfolio performance, such as options market prices, which are a rich source of investor expectations. Accordingly, we propose a new estimator for risk and return that combines historical and implicit information in the portfolio selection problem. We implement the new estimators for the mean-VAR and mean-VaR2 problems using an elastic-net model that reduces the risk of all estimations performed. The results suggest that the model has a good out-of-sample performance that is superior to models with pure historical estimations.