Out-of-sample performance-based estimation methods for portfolio selection

Abstract

The modern portfolio theory plays an important role in finance. The construction of a portfolio typically involves two stages: first estimate the mean and covariance matrix of asset returns, and second obtain the optimal portfolio weight by solving a mean-variance optimization. However, due to the estimation errors in the first stage given a limited set of historical asset returns, the portfolio constructed using sample mean and maximum likelihood covariance matrix usually leads to poor out-of-sample performance. This thesis aims to propose new estimators of mean returns and covariance matrix to achieve better out-of-sample portfolio performance.

First, we provide a framework for obtaining the estimator of expected asset returns for portfolio selection. The framework relies on a linear model where the expected returns are the coefficients to be estimated. The model is fitted to a synthetic dataset by Bayesian regression. The estimator is computed using a Gibbs sampler; it is consistent and asymptotically efficient when the size of the synthetic dataset grows to infinity. An empirical study shows that, under appropriate conditions, mean-variance portfolios constructed using this estimator yield better out-of-sample average returns and Sharpe ratios than benchmark portfolios, with or without a norm constraint.

Second, we provide a framework for obtaining the estimator of asset return covariance matrix for portfolio selection. A linear model is developed based on the estimates of out-of-sample portfolio variances, where the elements of covariance matrix are the coefficients to be estimated. The model is fitted by two-stage least squares regression to a synthetic dataset generated from a set of historical asset returns over a limited time horizon, where the lagged variables are used as instrumental variables. Although the set of historical asset returns is finite, the proposed estimator converges to the population covariance matrix as the size of the synthetic dataset grows to infinity. An empirical study shows that under appropriate conditions, the global minimum-variance portfolios constructed using this estimator produce better out-of-sample average returns and Sharpe ratios than benchmark portfolios.

(326 words)