Risk Parity Models for Portfolio Optimization: A Study of the Toronto Stock Exchange

It has been more than 60 years since the development of Mean-Variance (MV) framework and inception of Modern Portfolio theory. Despite its wide acceptance and applicability, it suffers from few limitations. This paper addresses two issues of MV framework: (i) estimation errors of mean-variance model, and (ii) instability of covariance matrix. Risk parity models, robust statistics and robust optimization minimize the effects of estimation errors of parameters of MV framework. The paper presents two such risk parity models for portfolio optimization, namely, (a) Hierarchical Risk Parity model based on Historical correlation (HRP-HC), and (b) Hierarchical Risk parity model based on Gerber statistics (HRP-GS). The models are tested and analysed using stocks comprising the TSX complete index for a time period of 10 years ranging from 2007 to 2016. Results suggest that the proposed HRP-GS model outperforms HRP-HC model. This is due to the fact that the HRP-GS model integrates the advantages of a risk parity model (i.e. HRP) and robust statistics (i.e. Gerber statistics).