Quantitative portfolio selection: using density forecasting to find consistent portfolios

TL;DR

This paper introduces a methodology to identify regions where ex-post portfolio performance aligns with ex-ante estimates, using density forecasting and an extended Berkowitz statistic, improving portfolio selection accuracy especially in volatile markets.

Contribution

It proposes a novel approach to determine the consistency region in risk-return space and extends ex-post efficient set mathematics to reduce estimation biases.

Findings

Consistency region encloses the ex-post frontier in simulations

Size of the consistency region varies with market volatility

Strategy based on consistent portfolios outperforms traditional methods

Abstract

In the knowledge that the ex-post performance of Markowitz efficient portfolios is inferior to that implied ex-ante, we make two contributions to the portfolio selection literature. Firstly, we propose a methodology to identify the region of risk-expected return space where ex-post performance matches ex-ante estimates. Secondly, we extend ex-post efficient set mathematics to overcome the biases in the estimation of the ex-ante efficient frontier. A density forecasting approach is used to measure the accuracy of ex-ante estimates using the Berkowitz statistic, we develop this statistic to increase its sensitivity to changes in the data generating process. The area of risk-expected return space where the density forecasts are accurate, where ex-post performance matches ex-ante estimates, is termed the consistency region. Under the 'laboratory' conditions of a simulated multivariate normal data set, we compute the consistency region and the estimated ex-post frontier. Over different sample sizes used for estimation, the behaviour of the consistency region is shown to be both intuitively reasonable and to enclose the estimated ex-post frontier. Using actual data from the constituents of the US Dow Jones 30 index, we show that the size of the consistency region is time dependent and, in volatile conditions, may disappear. Using our development of the Berkowitz statistic, we demonstrate the superior performance of an investment strategy based on consistent rather than efficient portfolios.