Reverse stress testing: Identifying weaknesses to prevent failures - Barroso, Miguel Oliveira dos Reis (2020)
This dissertation uses a methodology for attributing a stock portfolio most likely negative scenarios given a pre-defined loss. Using an extensive dataset spanning from 2007 through 2019, we calculated stock returns and their sample covariance matrix is estimated to obtain the portfolio Value at Risk (VaR). Due to idiosyncratic risk, we aggregate the returns into their corresponding indices to obtain the systematic component (the one explained by the market) and, afterwards, the Systematic Value at Risk was determined. Backward induction is then applied. Considering that returns follow a multivariate normal distribution, we derive the main scenario which could lead to the calculated VaR or even to a worst loss – the decision is up to the user. Reverse Stress Testing should be used as a framework, otherwise the risk manager could simply recalculate the VaR for different confidence intervals and investigate the evolution of the corresponding risk factors. Thus, the objective is to find multiple plausible scenarios –not only the most probable one. Principal component analysis (PCA) is applied to identify additional, less likely scenarios. These scenarios are linked to the basis scenario, which ensures plausibility. The relative likelihood is then defined manually as 0.1, meaning the central scenario is ten times more likely than the less likely one. Consequently, four scenarios were generated along with the calculation of their corresponding likelihoods. Overall, we identify the most probable loss scenarios for our portfolio given an input loss. Additionally, we explore the methodology further to determine scenarios under market extreme volatility events.