Otimização de carteiras no Brasil: aplicação da teoria moderna de Markowitz à gestão de fortunas em multi family offices e evidências comparativas

Abstract

This study develops and applies a quantitative portfolio optimization model based on Markowitz’s Modern Portfolio Theory, implemented using the Python programming language. The main objective is to analyze the performance of theoretical portfolios constructed under the mean–variance framework in the context of the Brazilian market, incorporating realistic operational constraints and distinct risk profiles. The methodology relies on daily return series from multiple asset classes, predominantly represented by market indices, characterizing a passive investment approach, with parameter estimation through rolling five-year windows, covariance matrix shrinkage, multiple optimization initializations, and semiannual portfolio rebalancing. Three risk profiles are defined according to annualized volatility bands: Conservative (up to 3.5%), Moderate (3.5% to 5%), and Aggressive (5.5% to 7.5%). Portfolio performance is assessed using standard risk and return metrics, including annualized return, volatility, Sharpe ratio, and maximum drawdown, and is compared with equal-weight portfolios constructed from exclusive wealth management funds in Brazil, grouped by risk profile and performance quartile. The results show that the optimized portfolios achieved Sharpe ratios approximately between 0.6 and 1.1, depending on the risk profile, while the reference portfolios exhibited, on average, lower values. In terms of returns, the optimized portfolios outperformed the equal-weight benchmarks by approximately 0.5% to 7% per year in the conservative and moderate profiles, reaching values close to 10% to 12% per year in the aggressive profile when compared with lower-performing fund quartiles. Conversely, in some cases involving top-performing fund quartiles, the optimized portfolios underperformed; nevertheless, across the full set of comparisons, they outperformed the majority of the reference portfolios. Additionally, the optimized portfolios exhibited a reduction in maximum drawdown of approximately 2 to 10 percentage points, indicating a more favorable risk–return trade-off over the analyzed period. The findings suggest that the proposed model generates portfolios consistent with predefined risk limits and achieves superior risk-adjusted performance relative to most of the benchmarks considered. Keywords: modern portfolio theory; markowitz; portfolio optimization; multi fam