# Introduction to Stress Testing

In the modern risk management practices, the statistical tools and models play a significant role in measuring risk. These statistical models are used to estimate the distribution of future possible outcome, such as that of interest rates, stock prices, etc. One of the most popular measures of risk is Value-at-risk. VaR is defined as the predicted worst-case loss with a specific confidence level (for example, 95%) over a period of time. One shortcoming of VaR is that it does not capture all the possible outcomes. For example, it does not capture sudden, dramatic changes in the financial markets, such as some of the recent financial crisis that we have seen.

In order to overcome this shortcoming, risk managers use the tool called “Stress Testing”.

A very basic definition of stress testing:

Stress testing is a form of testing that is used to determine the stability of a given system or entity. It involves testing beyond normal operational capacity, often to a breaking point, in order to observe the results.

In terms of financial risk management, it involves stressing the portfolio with extreme conditions to see how it will perform. A stress test is a scenario that measures risk under unlikely but plausible events in abnormal markets. For example, what will happen if the interest rates become extremely high, or if there is an unexpected change foreign exchange. The stress testing can be done using many such plausible events or changes in financial variables. While such events of extreme changes will not affect the VaR, the stress testing using such events will tell us more about the expected losses in the given time horizon.

Most banks and financial institutions use stress tests as a complement to value-at-risk. Stress test are more common for portfolios that require managing market risk. The portfolios most suitable for stress testing are the ones that include interest rates, equity, foreign exchange, and commodity-related instruments.

There are two types of stress tests: sensitivity tests, and scenario tests.

Sensitivity analysis identifies how portfolios respond to shifts in relevant economic variables or risk parameters. Scenarios assess the resilience of financial institutions and the financial system to severe but plausible scenarios.

The following is an excerpt from the JP Morgan Chase 2010 annual report describing how they use stress tests:

Economic value stress testing

While VaR reflects the risk of loss due to adverse changes in markets using recent historical market behavior as an indicator of losses, stress testing captures the Firm’s exposure to unlikely but plausible events in abnormal markets using multiple scenarios that assume significant changes in credit spreads, equity prices, interest rates, currency rates or commodity prices. Scenarios are updated dynamically and may be redefined on an ongoing basis to reflect current market conditions. Along with VaR, stress testing is important in measuring and controlling risk; it enhances understanding of the Firm’s risk profile and loss potential, as stress losses are monitored against limits.

Stress testing is also employed in cross-business risk management. Stress-test results, trends and explanations based on current market risk positions are reported to the Firm’s senior management and to the lines of business to allow them to better understand event risk–sensitive positions and manage risks with more transparency.

Earnings-at Risk Stress Testing

The Firm manages interest rate exposure related to its assets and liabilities on a consolidated, corporate-wide basis. Business units transfer their interest rate risk to Treasury through a transferpricing system, which takes into account the elements of interest rate exposure that can be risk-managed in financial markets. These elements include asset and liability balances and contractual rates of interest, contractual principal payment schedules, expected prepayment experience, interest rate reset dates and maturities, rate indices used for repricing, and any interest rate ceilings or floors for adjustable rate products. All transfer-pricing assumptions are dynamically reviewed.

The Firm conducts simulations of changes in net interest income from its nontrading activities under a variety of interest rate scenarios. Earnings-at-risk tests measure the potential change in the Firm’s net interest income, and the corresponding impact to the Firm’s pretax earnings, over the following 12 months. These tests highlight exposures to various rate-sensitive factors, such as the rates themselves (e.g., the prime lending rate), pricing strategies on deposits, optionality and changes in product mix. The tests include forecasted balance sheet changes, such as asset sales and securitizations, as well as prepayment and reinvestment behavior.

Immediate changes in interest rates present a limited view of risk, and so a number of alternative scenarios are also reviewed. These scenarios include the implied forward curve, nonparallel rate shifts and severe interest rate shocks on selected key rates. These scenarios are intended to provide a comprehensive view of JPMorgan Chase’s earnings at risk over a wide range of outcomes.

JPMorgan Chase’s 12-month pretax earnings sensitivity profiles as of December 31, 2010 and 2009, were as follows.

The change in earnings at risk from December 31, 2009, resulted from investment portfolio repositioning, assumed higher levels of deposit balances and reduced levels of fixed-rate loans. The Firm’s risk to rising rates was largely the result of widening deposit margins, which are currently compressed due to very low short-term interest rates.