Stress Testing in Value at Risk: Overview, Calculations

Generally speaking, the financial industry does not have a standard stress testing method for Value at Risk, or VaR measures.

There are different VaR methods, such as Monte Carlo simulations, historical simulations and parametric VaR, that one can stress test in different ways. Most VaR models assume away extremely high levels of volatility. This makes VaR particularly poorly adapted, yet well-suited, for stress testing.

Ways to Stress Test

Stress testing involves running simulations under crises for which a model was not inherently designed to adjust. The purpose of it is to identify hidden vulnerabilities, especially those based off of methodological assumptions.

The literature about business strategy and corporate governance identifies several approaches to stress testing. Among the most popular are stylized scenarios, hypotheticals, historical scenarios.

In a historical scenario, the business, or asset class, portfolio, or individual investment is run through a simulation based on a previous crisis. Examples of historical crises include the stock market crash of October 1987, the Asian crisis of 1997, and the tech bubble bursting in 1999-2000.

A hypothetical stress test is normally more firm-specific. For example, a firm in California might stress test against a hypothetical earthquake or an oil company might stress test against the outbreak of a war in the Middle East.

Stylized scenarios are a little more scientific in the sense that only one or a few test variables are adjusted at once. For example, the stress test might involve the Dow Jones index losing 10% of its value in a week. Or it might involve a rise in the federal funds rate of 25 basis points.

VaRisk Calculations and Monte Carlo Simulations

A company's management, or investor, calculates VaR to assess the level of financial risk to the firm, or investment portfolio. Typically, VaR is compared to some predetermined risk threshold. The concept is to not take risks beyond the acceptable threshold.

Standard VaR equations have three variables:

  1. Probability of loss
  2. Amount of potential loss
  3. Time frame that encompasses the probable loss

A parametric VaR model employs confidence intervals to estimate the probability of loss, profit, and maximum acceptable loss. Monte Carlo simulations are similar, except they involve thousands of tests and probabilities.

One of the variable parameters in the VaR system is volatility. The more volatile a simulation, the greater the chance for loss beyond the maximum acceptable level. The purpose of a stress test is to increase the volatility variable to an extent consistent with a crisis. If the probability of extreme loss is too high, the risk might not be worth assuming.

Some financial industry experts consider stress testing and VaR as competing concepts. They also view stress testing, which uses fixed horizons and specific risk factors, as incompatible with true Monte Carlo simulations that use random scenarios.

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