Defesa – Dissertação de Kevin Pergher

Aluno(a): Kevin Gabriel Ramisch Pergher
Orientador(a): Jacob Scharcanski

Título: Orthogonal Hierarchical Risk Parity Methods for Portfolio Allocation in the Brazilian Stock Market
Linha de Pesquisa: Aprendizado de Máquina, Representação de Conhecimento e Raciocínio

Data: 29/09/2026
Hora: 10:30
Local: Esta banca ocorrerá de forma presencial na sala 218 (43412) do Instituto de Informática/UFRGS.

Banca Examinadora:
-Vitor Venceslau Curtis (ITA)
-Eduardo Fonseca Mendes (FGV)
-Leandro Krug Wives (UFRGS)

Presidente da Banca: Jacob Scharcanski

Resumo: Portfolio allocation methods based on hierarchical clustering, such as Hierarchical Risk Parity (HRP), avoid the instability of covariance matrix inversion but remain sensitive to the estimation noise that contaminates sample correlations, especially in large, volatile, and sector-concentrated equity universes. This dissertation proposes and validates two allocation methods designed for such conditions, using the Brazilian stock market as the empirical setting. The first method, Orthogonal Hierarchical Risk Parity (OHRP), projects asset returns into a lower-dimensional orthogonal subspace that preserves data locality before the hierarchical clustering and risk allocation stages, with projection parameters optimized in-sample at every rebalancing period. The second method, Sectoral OHRP (SOHRP), generalizes OHRP by restricting the locality graph to intra-sector connections, thereby injecting an economic prior into the learned representation, and by unifying the in-sample selection into a ?·F framework that supports the minimization or maximization of arbitrary portfolio objectives, including the Sharpe ratio. This work also introduces the Sectoral Gini Index (SGI), a concentration measure defined over sector-level aggregate weights. The methods are evaluated out of sample against equally weighted, risk parity, and HRP benchmarks, on 158 Brazilian stocks spanning January 2011 to February 2026, across estimation windows from 0.2 to 5 years, under a unified backtesting protocol with transaction costs and Wilcoxon signed-rank testing. OHRP achieves statistically significant lower volatility, smaller drawdowns, and lower Pain Index than all benchmarks at every window length, together with the best composed Sharpe ratios at most long windows. S-OHRP delivers the best risk-adjusted performance of the entire study at the one-year estimation window, with a composed Sharpe ratio of 0.381, where the sectoral prior regularizes the locality topology without destroying signal. The SGI reveals that the orthogonal methods concentrate allocations within few sectors despite asset-level diversification, a dimension of risk invisible to classical concentration measures.

Palavras-Chave: Portfolio allocation; Hierarchical risk parity; Orthogonal projections; Brazilian stock market; Machine learning