Multiple Regression Model Averaging and the Focused Information Criterion With an Application to Portfolio Choice

Abstract

We consider multiple regression (MR) model averaging using the Focused Information Criterion (FIC). Our approach is motivated by the problem of implementing a mean-variance portfolio choice rule. The usual approach is to estimate parameters ignoring the intention to use them in portfolio choice. We develop an estimation method that focuses on the trading rule of interest.Asymptotic distributions of submodel estimators in the MR case are derived using a localization framework. The localization is of both regression coefficients and error covariances. Distributions of submodel estimators are used for model selection with the FIC. This allows comparison of submodels using the risk of portfolio rule estimators. FIC model averaging estimators are then characterized. This extension further improves risk properties. We show in simulations that applying these methods in the portfolio choice case results in improved estimates compared with several competitors. An application to futures data shows superior performance as well.

Optimal portfolio choice: a minimum expected loss approach

“…They proposed the naive portfolio as a shrinkage target. Other strategies to mitigate estimation error are based on robust portfolios [28,29], and transforming the optimal weight estimation problem into linear regressions [30,31]. In the former approach, parameter uncertainty is taken into account in the optimization procedure.…”

“…In the latter approach, Li [30] proposed a sparse and stable methodology based on lasso and ridge regressions with similar statistical characteristics than shrinkage estimators. Klimenka and Wolter [31], also proposed a regression framework that uses the focused information criterion [32], which is based on the trading strategy, and model averaging to take model uncertainty into account.…”

“…Our proposal has some characteristics from previous proposals due to being based on a Bayesian setting [2,3,16,17] under a decision theory framework focused on the final inferential goal [6,31]. However, our proposal is based on minimizing the posterior expected loss function rather than the frequentist risk function, and our loss function is based on the trading strategy rather than the utility function.…”