Black–Litterman Portfolio Optimization with Dynamic CAPM via ABC-MCMC

Sebastián Flández, Rolando Rubilar-Torrealba (), Karime Chahuán-Jiménez, Hanns de la Fuente-Mella and Claudio Elórtegui-Gómez
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Sebastián Flández: Departamento de Industrias, Universidad Técnica Federico Santa María, Valparaíso 2090123, Chile
Rolando Rubilar-Torrealba: Departamento de Industrias, Universidad Técnica Federico Santa María, Valparaíso 2090123, Chile
Karime Chahuán-Jiménez: Centro de Investigación en Negocios y Gestión Empresarial, Escuela de Auditoría, Facultad de Ciencias Económicas y Aministrativas, Universidad de Valparaiso, Valparaíso 2340027, Chile
Hanns de la Fuente-Mella: Facultad de Ciencias, Instituto de Estadística, Pontificia Universidad Católica de Valparaíso, Valparaíso 2340031, Chile
Claudio Elórtegui-Gómez: Facultad de Ciencias Económicas y Administrativas, Escuela de Periodismo, Pontificia Universidad Católica de Valparaíso, Valparaíso 2373223, Chile

Mathematics, 2025, vol. 13, issue 20, 1-17

Abstract: The present research proposes a methodology for portfolio construction that integrates the Black–Litterman model with expected returns generated through simulations under dynamic Capital Asset Pricing Model (CAPM) with conditional betas, estimated via Approximate Bayesian Computation Markov Chain Monte Carlo (ABC-MCMC). Bayesian estimation enables the incorporation of volatility regimes and the adjustment of each asset’s sensitivity to the market, thereby delivering expected returns that more accurately reflect the structural state of the assets compared to historical methods. This strategy is applied to the United States stock market, and the results suggest that the Black–Litterman portfolio performs competitively against portfolios optimised using the classic Markowitz model, even maintaining the same fixed weights throughout the month. Specifically, it has been demonstrated to outperform the minimum variance portfolio with regard to cumulative return and attains a Sharpe ratio that approaches the Markowitz maximum Sharpe portfolio, although it does so with a distinct and more concentrated asset allocation. It has been observed that, while the maximum return portfolio attains the highest absolute profit, it does so at the expense of significantly higher volatility.

Keywords: Black–Litterman; ABC-MCMC; optimization; stock market (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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