Global Credit–Equity Risk Dynamics: Empirical Analysis of the Impact of Exogenous Defaults in Heterogeneous Stock Portfolios

Abstract

The ever-evolving landscape of global financial markets has been subject to unprecedented challenges throughout history, with market stakeholder institutions facing critical credit and liquidity obstacles on a regular basis. At times, these challenges escalate to the point where there is a heightened risk of default, a situation that is mirrored in equity markets. In this thesis, we empirically analyze the impact of downward jumps in equity prices across three portfolios in the US, Europe, and Asia where jumps are triggered by defaults of exogenous entities, i.e. firms which are not included in the portfolios that are being affected by the negative jumps. We take inspiration from Herbertsson (2023b), building our study on the tractable solutions developed by Herbertsson for the stock price movement and for risk management tools such as Value at Risk (VaR) which assesses potential losses at a specified confidence level and a time period. We perform VaR calculations for our selected portfolios under two different methods by treating our portfolios to be heterogeneous and homogeneous in nature while modelling the default times of our exogenous entities using two separate credit portfolio models. The calibration of the credit risk parameter is done based on techniques outlined in B. Smits W. Heynderickx (2016) to ensure accuracy in applying real-world data to Herbertsson’s credit-equity hybrid model. Generally, VaR estimations for our three heterogeneous portfolios follow a similar pattern to that of numerical examples of homogeneous portfolios provided in Herbertsson (2023b). Further, VaR is observed to be higher for a portfolio having a higher drift and even higher for a portfolio having a negative drift. Interestingly, portfolios dominated by stocks with negative drifts seem to produce VaR values higher than the initial portfolio value in cases with higher default correlation and when default times are driven by Clayton copula, a dependency modelling technique capable of capturing extreme events. We show that during the first wave of Covid-19 pandemic in spring 2020, there was a 0.1% probability that our US portfolios would lose around 25% of the total portfolio value within 10 days using a rolling window VaR estimation. In addition, the relative difference between VaR in the Black-Scholes model without jumps and our estimated rolling window VaR in the Herbertsson setting reached a maximum of 6,430% in the Asian portfolio at a confidence level of 99.9%. Our study identified Herbertsson’s jump-diffusion model as highly sensitive to input parameters.