Hierarchical Risk Parity (HRP)

Hierarchical Risk Parity for Portfolio Allocation in the Latin American NUAM Market ArXiv ID: 2509.03712 “View on arXiv” Authors: Gonzalo Ramirez-Carrillo, David Ortiz-Mora, Alex Aguilar-Larrotta Abstract This study applies the Hierarchical Risk Parity (HRP) portfolio allocation methodology to the NUAM market, a regional holding that integrates the markets of Chile, Colombia and Peru. As one of the first empirical analyses of HRP in this newly formed Latin American context, the paper addresses a gap in the literature on portfolio construction under cross-border, emerging market conditions. HRP leverages hierarchical clustering and recursive bisection to allocate risk in a manner that is both interpretable and robust–avoiding the need to invert the covariance matrix, a common limitation in the traditional mean-variance optimization. Using daily data from 54 constituent stocks of the MSCI NUAM Index from 2019 to 2025, we compare the performance of HRP against two standard benchmarks: an equally weighted portfolio (1/N) and a maximum Sharpe ratio portfolio. Results show that while the Max Sharpe portfolio yields the highest return, the HRP portfolio delivers a smoother risk-return profile, with lower drawdowns and tracking error. These findings highlight HRP’s potential as a practical and resilient asset allocation framework for investors operating in the integrated, high-volatility markets like NUAM. ...

A Comparative Study of Portfolio Optimization Methods for the Indian Stock Market ArXiv ID: 2310.14748 “View on arXiv” Authors: Unknown Abstract This chapter presents a comparative study of the three portfolio optimization methods, MVP, HRP, and HERC, on the Indian stock market, particularly focusing on the stocks chosen from 15 sectors listed on the National Stock Exchange of India. The top stocks of each cluster are identified based on their free-float market capitalization from the report of the NSE published on July 1, 2022 (NSE Website). For each sector, three portfolios are designed on stock prices from July 1, 2019, to June 30, 2022, following three portfolio optimization approaches. The portfolios are tested over the period from July 1, 2022, to June 30, 2023. For the evaluation of the performances of the portfolios, three metrics are used. These three metrics are cumulative returns, annual volatilities, and Sharpe ratios. For each sector, the portfolios that yield the highest cumulative return, the lowest volatility, and the maximum Sharpe Ratio over the training and the test periods are identified. ...

A Comparative Analysis of Portfolio Optimization Using Mean-Variance, Hierarchical Risk Parity, and Reinforcement Learning Approaches on the Indian Stock Market ArXiv ID: 2305.17523 “View on arXiv” Authors: Unknown Abstract This paper presents a comparative analysis of the performances of three portfolio optimization approaches. Three approaches of portfolio optimization that are considered in this work are the mean-variance portfolio (MVP), hierarchical risk parity (HRP) portfolio, and reinforcement learning-based portfolio. The portfolios are trained and tested over several stock data and their performances are compared on their annual returns, annual risks, and Sharpe ratios. In the reinforcement learning-based portfolio design approach, the deep Q learning technique has been utilized. Due to the large number of possible states, the construction of the Q-table is done using a deep neural network. The historical prices of the 50 premier stocks from the Indian stock market, known as the NIFTY50 stocks, and several stocks from 10 important sectors of the Indian stock market are used to create the environment for training the agent. ...