We will shock you: a coherent Bayesian approach for stress testing

João Vinícius França Carvalho and Filipi Sanguino

Abstract

The stress testing technique is used to understand the financial consequences of unlikely but plausible scenarios. The importance of this exercise is accentuated in highly unstable and volatile markets, such as Brazilian equities. We develop a coherent Bayesian stress test methodology that preserves the mathematical properties of the risk measures, using dynamic Bayesian networks as our method and arbitrage pricing theory as the theoretical basis. The former provides the interdependence topology of the variables, considering the temporal dynamics and the possibilities of contagion propagation, while the latter captures the effects of shocks on the returns of the Ibovespa index, the main performance indicator for Brazilian equities, between January 1995 and July 2021. Our results indicate that the Ibovespa index is more sensitive to risk factors linked to international investors (foreign exchange and Standard & Poor’s 500) than to domestic elements (inflation and Certificado de Depósito Interbancário (CDI) overnight rate). Finally, we simulate extreme shocks on the Ibovespa index and compute the risk measures as value-at-risk and tail value-at-risk. Our results suggest that a declining Standard & Poor’s 500 rate, a positive exchange rate and a neutral Índice Nacional de Preços ao Consumidor Amplo (IPCA) inflation rate is a consistently aggressive combination that could lead to heightened economic volatility or uncertainty, with a significative probability mass function.