RECOMMENDED READING

A5.4 RECOMMENDED READING

9.9 RECOMMENDED READING

Berkowitz (2001); Blanco and Ihle (1998); Christoffersen (1998); Crnkovic and Drachman (1996); Deans (2000); Hendricks (1996); Kupiec (1995); Lopez (1998, 1999); Tilman and Brusilovskiy (2001).

10

Stress Testing

This chapter examines stress testing — procedures that attempt to gauge the vulnerability of our portfolio to hypothetical events. Financial institutions have used stress testing in some form or an- other for many years, particularly for gauging their exposure to interest-rate risk. Early stress tests were often little more than ‘back of the envelope’ exercises, but the methodology has improved over the years, thanks in large part to improvements in spreadsheet technology and computing power and, though still limited in many respects, modern stress testing is much more sophisticated than its predecessors.

There has in the past often been a tendency to see stress testing as secondary to other methods of risk estimation, such as those based on Greek parameter estimation in the derivatives field or VaR more generally. This is due in part to the fact that the methodology of stress testing is not as developed as risk measurement methodologies in the proper sense of the term. Prior to 1996, most stress testing was also done at the desk level, and relatively few firms carried out stress testing at the corporate-wide level. However, since then, corporate-wide stress testing has become much more common and more sophisticated, and stress tests are now routinely applied to credit and liquidity shocks, as well as market ones.¹As Schachter points out:

The events of October 1997 represent a watershed of sorts for stress testing. The attention given to stress tests by regulators and banks has increased dramatically since that event. In some respects, the event has kindled a love affair with stress testing. Yet the theory behind stress testing is still ill developed, more so than value at risk, which itself is an immature risk management tool.

(Schachter (1998, p. 5F-10)) So stress testing is now getting much more attention, fuelled in large part by the belated recognition that good stress testing might have helped institutions to avoid some of the painful losses of recent years.²

Stress testing is particularly good for quantifying what we might lose in crisis situations where

‘normal’ market relationships break down and VaR and ETL risk measures can be very misleading.

Stress tests can identify our vulnerability to a number of different crisis phenomena:

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Breakdowns in ‘normal’ correlation relationships. In crises, correlations often swing to extreme values, and losses can be much greater than suggested by VaR estimates based on ‘normal’ corre- lation assumptions.

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Sudden decreases in liquidity. Markets can suddenly become very illiquid in crisis situations, bid–

ask spreads and order execution times can increase dramatically, and risk management strategies

1The current state of the art in stress testing is reflected in a BIS survey of leading financial institutions’ stress testing procedures, carried out on May 31, 2000. For more on this survey and its results, see Bank for International Settlements (2000) or Fender and Gibson (2001).

2The importance of stress testing is also recognised in the Amended Basle Accord on bank capital adequacy requirements.

This specifies that banks that seek to have their capital requirements based on their internal models should also have in place a ‘rigorous and comprehensive’ stress testing programme, and this programme should include tests of the portfolio against past significant disturbances and a bank’s own stress tests based on the characteristics of its portfolio.

(e.g., such as those based on dynamic trading) can become unhinged, leading to much bigger losses than anticipated.

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Concentration risks. Stress tests can sometimes reveal that we might have a much larger exposure to a single counterparty or risk factor than we had realised, taking into account the unusual conditions of a crisis. VaR or ETL measures can overlook such concentration risks because they tend not to pay much attention to crisis conditions.

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Macroeconomic risks. Stress tests are also better suited for gauging our exposure to macroeconomic factors such as the state of the business cycle, the economic condition of a particular country, and so on.

Although the principles behind stress testing are straightforward, there are a huge variety of dif- ferent categories of stress test depending on thetype of event(i.e., normal, extreme, contingent, sea change, liquidity, etc.), thetype of riskinvolved (market risk, liquidity risk, credit risk, and combina- tions of these risks), therisk factors(e.g., equity risks, yield curve risks, FX risks, default risks, etc.), thecountry or region(e.g., North America, Japan, etc.), the stress testmethodology(i.e., scenario analysis, factor push, maximum loss optimisation, etc.), the model assumptions(e.g., relating to yield curves, the distributions of risk factors, default parameters, etc.), thebook(i.e., trading book, banking book, off-balance sheet), theinstrumentsconcerned (e.g., basic equities or bonds, futures, options, etc.), thelevelof the test (desk level, business-unit level, or corporate level), data require- ments (e.g., desk-level data, corporate-wide data, etc.) and thecomplexity of our portfolio. Stress testing is thus simple in principle but complex in practice.

Stress testing is a natural complement to probability-based risk measures such as VaR and ETL.

Recall that the VaR gives us the maximum likely loss at a certain probability, but gives us no idea of the loss we might suffer in ‘bad’ states where we would get a loss in excess of VaR. ETL is a little better because it gives us the expected value of a loss in excess of VaR, but even ETL tells us nothing else about the distribution of ‘tail losses’ other than the expected value. By contrast, stress testing can give us a lot of information about bad states — and, indeed, stress testing is explicitly designedto give us information about losses in bad states. However, stress testing does not (usually) tell us, and is not as such designed to tell us, thelikelihoodof these bad states. So VaR and ETL are good on the probability side, but poor on the ‘what if’ side, whereas stress tests are good for ‘what if’ questions and poor on probability questions. The two approaches — the probabilistic approaches, VaR and ETL, and stress tests — are therefore natural complements to each other, each highlighting what the other tends to miss.

Broadly speaking, we can distinguish between two main approaches to stress testing:

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Scenario analyses, in which we evaluate the impact of specified scenarios (e.g., such as a particular fall in the stock market) on our portfolio. The emphasis is on specifying the scenario and working out its ramifications.

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Mechanical stress tests, in which we evaluate a number (and often a large number) of mathemat- ically or statistically defined possibilities (e.g., such as increases and decreases of market risk factors by a certain number of standard deviations) to determine the most damaging combination of events and the loss it would produce.

We will consider these presently, but we begin by looking at the benefits and difficulties of stress testing.

Box 10.1 Using Stress Tests

In the right hands, stress testing can be a very important and useful risk management tool, and stress tests can be used for risk management in at least three ways. The first is as a source of information, and the results of stress tests can be disseminated to all levels of management or decision-makers. Stress test results can be a particularly effective means of communicating risk information because the underlying conceptual experiment — i.e., what if . . . happens? — is easy to understand and free of any dependence on the probability notions that are inescapable when using VaR or ETL risk measures. However, it is important not to swamp recipients with unnecessary data, so it is best to give each level of manager or decision-maker only the stress test information relevant to them. When used in this way, stress tests can help to assess risks in the context of the firm’s risk appetite, as well as identify major contributors to the firm’s overall exposure and reveal hidden sources of risk that might not otherwise be apparent. If they are to provide up-to-date information, stress tests also need to be carried out on a reasonably frequent basis (e.g., every week or month).

The second main use of stress tests is to guide decision-making and, in particular, to help with setting position limits, allocating capital, and managing funding risks. The usefulness of stress tests for setting positions and allocating capital is self-evident, and stress tests can help manage funding risks by identifying the circumstances in which firms might get bad headlines and run into funding problems, so that managers can take appropriate pre-emptive action.

The third use of stress testing is to help firms design systems to protect against bad events — for example, to provide a check on modelling assumptions, to help design systems to protect against stress events (e.g., to protect the firm’s liquidity in a liquidity crisis), and to help with contingency planning.