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This paper evaluates Colombia's debt sustainability for the period 1980-2021, using a nonlinear fiscal reaction function approach. We employ a Markov-Switching model with annual data to identify sustainable and unsustainable fiscal regimes. According to this model, we identified an unsustainable fiscal regime during three periods with an average duration of six years - 1980-1985, 1993-1999, and 2015-2021 - while the other periods are identified as a sustainable regime. Although we find evidence of asymmetric behaviour in fiscal responses and the presence of pro-cyclical fiscal policy, Colombia's long-term fiscal sustainability is verified based on a globally-based fiscal sustainability test. In this context, the government reacts appropriately to increases in debt only in the sustainable regime, but the fiscal response is sufficiently robust to stabilise public debt throughout the entire period. Finally, we also highlight concerns regarding the current state of the global economy, particularly due to an inflationary trend and escalating interest rates, which can compromise long-term fiscal sustainability.

En este artículo se implementa un enfoque robusto para la selección óptima de portafolios de inversión, al incorporar los desarrollos del modelo Black-Litterman (BL) y la lógica difusa. Para ello, los retornos esperados, las opiniones del inversor (views) y la matriz de incertidumbre del modelo BL, se redefinen mediante la lógica difusa y se implementa un ejercicio de optimización para un portafolio constituido por acciones del mercado de valores colombiano. Los resultados muestran un desempeño favorable —fuera de muestra— del portafolio, en comparación con el modelo BL tradicional y el modelo media-varianza (MV), lo cual demuestra que el enfoque de lógica difusa permite incorporar información adicional para definir las views y medir la incertidumbre.

In this paper, we implement an integrated framework for constructing ESG-constrained, downside-risk-optimized equity portfolios in the European stock market. Extending traditional mean-variance approaches, we employ downside-oriented risk measures-conditional value at risk (CVaR) and semi-variance-to better capture investors’ asymmetric aversion to losses. ESG scores are introduced as binding constraints based on percentile thresholds, ensuring that portfolios comply with predefined sustainability standards. Semi-variance and CVaR objectives are formulated as convex programs to enable tractable optimization. Using data from Euro Stoxx 50 and Euronext 100 constituents, our empirical analysis reveals that: (i) integrating downside risk measures enhances tail-risk protection and may improve performance for loss-averse investors; but (ii) enforcing ESG constraints, particularly at stricter thresholds, leads to reduced diversification and a decline in risk-adjusted returns (e.g., Sharpe and Sortino ratios). These findings highlight the inherent trade-off between sustainability and financial efficiency, underscoring the importance of moderate ESG integration when balancing performance and ethical objectives.

En este artículo se evalúa la sostenibilidad fiscal en Colombia mediante la utilización de tres metodologías diferentes: pruebas de estacionariedad; estimación de funciones de reacción fiscal —lineal y no lineal— por mínimos cuadrados en dos etapas y por el método generalizado de momentos; y cálculo del indicador sintético de sostenibilidad fiscal propuesto por Mackiewicz-Łyziak y Łyziak, (2019). En el cálculo de este indicador se incorpora el efecto de la tasa de interés de la deuda, la cual se considera como una variable endógena, así como se evalúa la respuesta de la tasa de interés frente a variaciones en el nivel de deuda. Los resultados, aunque muestran el cumplimiento de algunas de las condiciones de sostenibilidad para Colombia hasta el año 2019, también resaltan el riesgo que representa el alto nivel de endeudamiento que alcanzó el país en 2020, producto de la reciente crisis de la pandemia del Covid-19.

In this study, we propose an implementation of the multifactor Heath-Jarrow-Morton (HJM) interest rate model using an approach that integrates principal component analysis (PCA) and Monte Carlo simulation (MCS) techniques. By integrating PCA and MCS with the multifactor HJM model, we successfully capture the principal factors driving the evolution of short-term interest rates in the US market. Additionally, we provide a framework for deriving spot interest rates through parameter calibration and forward rate estimation. For this, we use daily data from the US yield curve from June 2017 to December 2019. The integration of PCA, MCS with multifactor HJM model in this study represents a robust and precise approach to characterizing interest rate dynamics and compared to previous approaches, this method provided greater accuracy and improved understanding of the factors influencing US Treasury Yield interest rates.