Monte Carlo var under reinvestment risk

Abstract

This study aims to develop a model for calculating the Value at Risk for the Sociedade Gestora dos Fundos de Pensões do Banco de Portugal (SGFPBdP)’s own-asset portfolio using a Monte Carlo simulation-based framework. The primary objective of the model is to incorporate features typically excluded from traditional Value at Risk (VaR) methods, such as the hold-to-maturity assumption for fixed income instruments, reinvestment risk associated with maturing instruments, and eventual expectations regarding future market conditions. A detailed explanation of the Monte Carlo simulation-based framework is provided to clarify the methodology employed. This framework can be applied to calculate VaR over different time horizons. In the report, VaR is calculated and analysed for the following horizons: one business day, 20 business days, and 230 business days. The results are then compared with those obtained from the traditional Parametric method, based on the RiskMetrics framework, to evaluate whether the adjustments introduced by the model deliver the intended improvements. Both models produce similar results over short-term horizons. However, over longer time horizons, the limitations of the traditional Parametric model become increasingly evident. The internal methodology proves to be more accurate and better aligned with real investment conditions, precisely because it successfully delivers the features originally intended in its design: (1) it effectively captures the dynamics of holding fixed income instruments to maturity, including pull-to-par effects and reinvestment risk; and (2) it allows for the incorporation of expectations regarding future market conditions.