Can Machine Learning-Based Portfolios Outperform Traditional Risk-Based Portfolios? The Need to Account for Covariance Misspecification

Prayut Jain,Shashi Jain

doi:10.3390/risks7030074

Abstract

The Hierarchical risk parity (HRP) approach of portfolio allocation, introduced by Lopez de Prado (2016), applies graph theory and machine learning to build a diversified portfolio. Like the traditional risk-based allocation methods, HRP is also a function of the estimate of the covariance matrix, however, it does not require its invertibility. In this paper, we first study the impact of covariance misspecification on the performance of the different allocation methods. Next, we study under an appropriate covariance forecast model whether the machine learning based HRP outperforms the traditional risk-based portfolios. For our analysis, we use the test for superior predictive ability on out-of-sample portfolio performance, to determine whether the observed excess performance is significant or if it occurred by chance. We find that when the covariance estimates are crude, inverse volatility weighted portfolios are more robust, followed by the machine learning-based portfolios. Minimum variance and maximum diversification are most sensitive to covariance misspecification. HRP follows the middle ground; it is less sensitive to covariance misspecification when compared with minimum variance or maximum diversification portfolio, while it is not as robust as the inverse volatility weighed portfolio. We also study the impact of the different rebalancing horizon and how the portfolios compare against a market-capitalization weighted portfolio.

Highlights

Many of the present day portfolio optimization techniques are based on the mean-variance optimization framework that was developed by Markowitz (1952)
We have compared the out-of-sample performance of portfolios constructed using traditional risk-based allocation methods with those constructed using machine learning methods
As the forecasted covariance matrix plays an important role in risk-based allocation methods, we first determined whether there were covariance forecasting methods that led to a superior out-of-sample performance of the different portfolio allocation strategies

Summary

Introduction

Many of the present day portfolio optimization techniques are based on the mean-variance optimization framework that was developed by Markowitz (1952). The most well known and common estimator for the forecast of covariance of returns is the sample-based covariance. It is calculated from the time series of historical returns. For a covariance matrix of size N there needs to be at least N ( N + 1)/2 independent and identically distributed (iid) returns observations to estimate the sample-based forecast. In order to construct a covariance matrix of returns for 50 assets, one would ideally need at the least 5 years of daily returns time series, with the hope that they are iid data. There is ample evidence that asset returns exhibit heteroskedasticity with volatility clustering, and that the correlation structures do not remain invariant for such

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