Overview

• Regime conditional reverse stress tests help identify hidden scenarios that could have an adverse effect on a diversified multi-asset portfolio in different states of the economy.
• Reverse stress tests identify plausible asset class return outcomes given a specified adverse portfolio event and can complement traditional stress tests which reveal portfolio exposure to specific shocks.
• Conditional or stressed covariance matrices can be integrated into reverse stress test analysis. An example of how a reverse stress test can be used to extract scenarios is explored here by sampling data from historical periods of elevated inflation.

Stress tests have become an integral component of risk management (see [2] for a discussion of flexible risk platforms). Stress tests are more transparent and intuitive than risk estimates and are, therefore, essential complements to risk model analysis. Though risk models provide useful decompositions of portfolio risk, stress tests overcome the shortcomings of risk models by estimating the impact of adverse market movements on a portfolio, capturing volatility jumps and changing correlation structures, and incorporating liquidity shifts.

Reverse stress tests (RSTs) provide a complementary analysis to regular or traditional stress tests. Under a traditional stress test, risk factor shifts (scenarios) are specified as inputs and the loss of the portfolio is computed. Instead, reverse stress tests work in the opposite direction. Under a reverse stress test, we specify the portfolio loss as an input, and then find scenarios that can generate this loss (see Figure 1 for an illustration). For instance, what plausible combination of asset return outcomes would correspond with a total multi-asset portfolio loss of 10%?

It should be noted that regulators have endorsed RST analysis because of its ability to identify hidden risk factor scenarios that could threaten the survival of an institution (see [4] and [5]). While regulators and financial institutions placed more focus on stress testing after the Global Financial Crisis, reverse stress testing has gained widespread acceptance as an important risk management methodology. According to a report from the Basel Committee on Banking Supervision [4], reverse stress testing is conducted as a complimentary stress test by two-thirds of the institutions that they surveyed.

In this note we explore an example of how RSTs can be used to extract scenarios from a high inflation environment. The inflation example builds from the work in the recent PGIM Quant paper Portfolio Implications of a Higher US Inflation Regime. In this paper, the authors acknowledge that there is a non-trivial probability that inflation could stay elevated for the next few years. In addition, they discuss the drivers and implications of higher inflation across different asset classes such as equities, bonds, commodities, and real estate and demonstrate that real assets can mitigate inflation risk. Here we utilize a conditional covariance matrix of asset returns extracted from high inflation periods.