Recent financial debacles have shown the limitations of traditional VaR models. The purpose of this article is to discuss how to complement the VaR analysis with stress tests, one of the most debated topics in finance. We will show why stress testing and scenario analysis are gaining increasing importance in risk management activities, their limitations, and the correct implementation of these tools.
VaR models are based on a set of assumptions regarding the distribution of the returns of market risk factors. Most financial models assume that volatilities and correlations capture the expected variability of returns, and that the estimates are stable over time. The use of the normal distribution makes the randomness of the markets less scary, because it allows us to calculate the probability of any given price move. However, it is essential to include in the risk analysis estimates of future outcomes that can be characterized as unlikely, but possible. Unfortunately, due to the distributional assumptions behind the model, VaR does not deal very well with extreme events (which usually are the risks that result in larger losses).
In practice, market return distributions often have fat tails, which means that high losses with low probabilities (e.g. due to financial crisis, war, stock market crash, etc.) occur more often than what the normal distribution would suggest.
We can think of stress testing and scenario analysis as a series of "what if" questions asked in case assumptions of the model do not hold. Stress tests are a type of fine tuning process to the VaR analysis (e.g. they introduce the human element in the calculations). A risk manager's degree of experience and intuition are key in determining what events to choose, and what each event will mean in actual quantifiable terms. The main contribution of stress tests and scenario analysis is that they can bridge information holes that traditional risk measurement tools may leave wide open.
TYPES OF STRESS TESTS
Historical scenarios: What would have happened to our current portfolio under extreme historical events in the markets? It is usually a good starting point, but by no means sufficient. The main problem is that the number of relevant extreme historical events is very limited by definition. (Gulf War, Summer '98, etc.), and future extreme events are very likely to be different from past events.
Hypothetical scenarios: User-designed scenarios of fluctuations in yield curves, exchange rates, commodity prices, volatilities, correlations. The choice of these scenarios is the key input in this analysis. It is necessary to identify possible events that could result in large losses and quantify its potential impact in certain financial variables.
Mechanical stress tests: "What if" analysis of pre-specified market shocks like parallel and non-parallel shifts in yield curve; exchange rate and equity market changes; changes in volatilities, etc. In each scenario, all current positions are revalued using a specified set of scenarios of market prices and rates. The price and volatility shocks could be an absolute value, a percentage, or a certain number of standard deviations.
In order to conduct stress tests, it is important to determine what are the portfolio's hot spots, and address key vulnerabilities. Once the hot spots have been identified, it is important to choose which risk factors to stress in the different scenarios, as well as the range of possible values to consider and the time horizon of the simulations. Depending on the nature of the positions in the portfolio, we may be interested in stressing individual market risk factors, forward curves, spreads, or combinations of different market risk factors (e.g. forward price curves and forward volatilities), including potential illiquidity and counterparty risks arising from certain market conditions. In this sense, VaRdelta and Component VaR (DW, 5/10, 5/17) offer us a post-covariance analysis of the most sensitive factors of the portfolio, and any stress testing and scenario analysis should include those risk vertices with higher VaR-betas and Component VaR numbers. It is important for fund managers to have a set of risk factors for which stress testing is run on a systematic basis.
The range of possible values should try to cover unlikely but plausible events. If the person/committee deciding the range of stress scenarios exhibits an overactive imagination, that could lead to all types of unrealistic assumptions and scenarios that would not be very meaningful for the firm, and would take time and resources away from the risk management function.
The main benefit of conducting regular stress tests is that it encourages managers to think systematically about how financial shocks can impact business. The frequency of stress tests should be a function of how often the portfolio risk exposures change in nature. The results should be discussed at all levels of the organization that deal with market risk management and distributed to appropriate managers.
Stress tests allow us to answer questions such as "Would certain scenarios be enough to bring down the firm?"; "Are those scenarios likely?"; "What should we do to avoid putting the firm at risk under certain hypothetical situations?". Conducting stress tests regularly may create awareness of the consequences of possible extreme risks that the institution is facing, and provide a tool for the organization to anticipate what would happen under certain events, and whether the firm should take preventive actions.
Let's assume an option currency trader's average profit over the last five years has been USD10 million, without any losing years. However, after stress testing her portfolio, we find out that if the Mexican peso depreciates more than 35%, that trader would lose USD100 million.
* Should the trader worry?
* Should the risk manager worry?
* What should management do?
Risk managers, however, should be aware of some pitfalls with stress tests:
* Mechanical stress scenarios and historical scenarios may
not offer a complete picture of risk. Just because the
results from those tests are not substantial losses, we
should not conclude that we should not conduct other
stress tests.
* The managers in charge of evaluating results do not have
enough authority to reduce the portfolio exposures under
extreme conditions.
* The choice of the "user-defined" scenarios may leave large
risk holes.
* Correlations should be stressed as well, especially for
extreme market moves.
* Stress tests should try to identify the firm's "breaking
point," and what is the probability of reaching that point
after estimating the occurrence of possible future events.
We should point out that risk managers should be fully aware of the limitations of using methodologies such as VaR, even if they include supplemental information from stress tests and scenario analysis, and should never delegate the decision making process on a particular methodology to measure risk. Risk management reports should combine the quantitative results with enough contextual information in order to determine the degree of reliance on the assumptions behind the calculations.
This week's Learning Curve was written by Carlos Blanco, head of global support and eductional services at Financial Engineering Associatesin Berkeley, Calif., and Jose Ramon Aragones, professor of finance at Universidad Complutensein Madrid.
