Modern Portfolio Theory: Hierarchical Risk Parity

Abstract

Modern portfolio optimization uses expected return and risk as input variables. Both are unobservable and the associated sample return and sample covariance matrix have huge estimation errors. Risk-based models reduce the error significantly by having only the covariance as input. Hierarchical Risk Parity (HRP) developed by López De Prado uses graph theory and hierarchical clustering to decrease the error even further by improving the estimation of the covariance matrix. This thesis aims to test the performance of HRP compared to the following other non-hierarchical risk-based allocation methods; Minimum-Variance (MV), Inverse-Variance (IV), Equal Risk Contribution (ERC) and Equally-Weighted (EW).

First, the performance and implications of the method are understood through a replication study of the initial simulation by López De Prado. Second, a more simple simulation study is conducted on the dataset 30 Industry Portfolios to analyze the performance of the five allocation methods on empirical data. To nuance this second simulation, an empirical study using Walk-Forward optimization is performed on the same dataset. Finally, it is considered whether a different choice of distance measure could improve the performance of the HRP method.

The combined results indicate that HRP has several favorable properties. The empirical results imply that HRP has the highest cumulative return, Sharpe Ratio and Certainty-equivalent return closely followed by however IV. In addition, the simulation studies indicate that HRP has the lowest out-of-sample risk measure whenever the instability of the covariance matrix is very high. However, both HRP and MV are fairly sensitive to instability in the sample covariance matrix since the methods have a tendency to do error-maximization by allocating large portfolio weights to the most unstable assets signifying the instability. For this reason, it cannot definitively be determined if HRP is preferred over the 4 allocation methods, since IV also has some favorable properties for low-risk averse investors.