Stress testing in risk management process.

Stress testing is an important part of the risk management process.
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P1: TIX/b P2:c/d QC:e/f T1:g JWBT668-c19 JWBT668-Hull March 7, 2012 8:35 Printer: Courier Westford CHAPTER 19 Scenario Analysis and Stress Testing tress testing involves evaluating the impact of extreme, but plausible, scenarios that are not considered by VaR models. If there is one lesson to be learned from the S market turmoil that started in the summer of 2007, it is that more emphasis should be placed on stress testing and less emphasis should be placed on the mechanistic application of VaR models. VaR models are useful, but they are inevitably backward looking. Risk management is concerned with what might happen in the future. This chapter considers the different approaches that can be used to generate scenarios for stress testing and how the results should be used. It explains that the financial crisis of 2007 and 2008 has caused bank supervisors to require banks to conduct more stress testing. Indeed, supervisors themselves have sometimes devel- oped stress tests for financial institutions to determine the ability of the financial sector as a whole to withstand shocks. 19.1 GENERATING THE SCENARIOS The most popular approach for calculating VaR is the historical simulation approach covered in Chapter 14. This approach assumes that data from the last few years is a good guide to what will happen over the next 1 to 10 days. But if an event has not occurred during the period covered by the data, it will not affect the VaR results when the basic VaR methodology in Section 14.1 is used. We have discussed a number of ways VaR calculations can be modified so that they reflect more than the simple assumption that the future short term movements in market variables will be a random sample from the recent past. In particular: 1. Volatility updating (see Section 14.3) can lead to more extreme outcomes being considered when the market is highly volatile. 2. Extreme value theory (see Section 14.5) provides a way of extending the tails of the loss distribution obtained from historical data. 3. Calculating stressed VaR (see Section 13.1) considers the impact of a particularly bad period of 250 days that has occurred in the past. But the nature of a VaR calculation is that it is backward looking. Events that could happen, but are quite different from those that occurred during the period covered by the data, are not taken into account. Stress testing is an attempt to overcome this weakness of the VaR measure. 413P1: TIX/b P2:c/d QC:e/f T1:g JWBT668-c19 JWBT668-Hull March 7, 2012 8:35 Printer: Courier Westford 414 RISK MANAGEMENT AND FINANCIAL INSTITUTIONS Stress testing involves estimating how the portfolio of a financial institution would perform under scenarios involving extreme market moves. Sometimes, the extreme market moves are measured in standard deviations, as was the case for our exchange rate example in Table 10.2. If daily changes are normally distributed, a five-standard-deviation daily change in a market variable happens about once every 7,000 years. But in practice, it is not uncommon to see a five-standard-deviation move once or twice every 10 years. (This emphasizes that the assumption that variables are normally distributed is not a good one in risk management.) A key issue in stress testing is the way in which scenarios are chosen. We now consider alternative procedures. Stressing Individual Variables One approach is to use scenarios where there is a large move in one variable and other variables are unchanged. Examples of scenarios of this type that are sometimes considered are: 1. A 100-basis-point parallel shift (up or down) in a yield curve. 2. Increasing or decreasing all the implied volatilities used for an asset by 20% of current values. 3. Increasing or decreasing an equity index by 10%. 4. Increasing or decreasing the exchange rate for a major currency by 6%. 5. Increasing or decreasing the exchange rate for a minor currency by 20%. The impact of small changes in a variable is measured by its delta, as explained in Chapter 7. The impact of larger changes can be measured by a combination of delta and gamma. Here we are considering changes that are so large that it is likely to be unreliable to estimate the change in the value of a portfolio using Greek letters. Scenarios Involving Several Variables Usually, when one market variable shows a big change, others do as well. This has led financial institutions to develop scenarios where several variables change at the same time. A common practice is to use extreme movements in market variables that have occurred in the past. For example, to test the impact of an extreme movement in U.S. equity prices, a company might set the percentage changes in all market variables equal to those on October 19, 1987 (when the S&P 500 moved by 22.3 standard deviations). If this is considered to be too extreme, the company might choose January 8, 1988 (when the S&P 500 moved by 6.8 standard deviations). Other dates when there were big movements in equity prices are September 11, 2001, when terrorists attacked the World Trade Center in New York, and September 15, 2008, when Lehman Brothers declared bankruptcy. To test the effect of extreme movements in UK interest rates, the company might set the percentage changes in all market variables equal to those on April 10, 1992 (when 10-year bond yields moved by 8.7 standard deviations). Another approach is to magnify what has happened in the past to generate ex- treme scenarios. For example, we might take a period of time when there were mod- erately adverse market movements and create a scenario where all variables move byP1: TIX/b P2:c/d QC:e/f T1:g JWBT668-c19 JWBT668-Hull March 7, 2012 8:35 Printer: Courier Westford Scenario Analysis and Stress Testing 415 three or five times as much as they did then. The problem with this approach is that correlations increase in stressed market conditions and increasing the movements in all market variables by a particular multiple does not increase correlation. Some historical scenarios are one-day shocks to market variables. Others, partic- ularly those involving credit and liquidity, involve shocks that take place over several days, several weeks, or even several months. It is important to include volatilities in the market variables that are considered. Typically, extreme movements in mar- ket variables such as interest rates and exchange rates are accompanied by large increases in the volatilities of these variables and large increases in the volatilities of a wide range of other variables. Some scenarios are likely to involve big movements in commodity prices. On September 22, 2008, oil posted its biggest one-day price increase ever. On September 27–28, 1999, the price of gold increased by 15.4%. Some scenarios are likely to involve a situation where there is a flight to quality com- bined with a shortage of liquidity and an increase in credit spreads. This was what happened in August 1998 when Russia defaulted on its debt and in July and August 2007 when investors lost confidence in the products created from the securitization of subprime mortgages (see Chapter 6). Scenarios Generated by Management History never repeats itself exactly. This may be partly because traders are aware of past financial crises and try to avoid making the same mistakes as their prede- cessors. The U.S. mortgage market led to the credit crisis that started in 2007. It is unlikely that future credit crises will be a result of mortgage-lending criteria being relaxed—but it is also likely that there will be credit crises in the future. In many ways, the scenarios that are most useful in stress testing are those generated by senior management or by the economics group within a financial in- stitution. Senior management and the economics group are in a good position to use their understanding of markets, world politics, the economic environment, and current global uncertainties to develop plausible scenarios that would lead to large losses. Sometimes, the scenarios produced are based on things that have happened in the past, but are adjusted to include key features of the current financial and economic environment. One way of developing the scenarios is for a committee of senior management to meet periodically and “brainstorm” answers to the simple question: “What can go wrong?” Clemens and Winkler (1999) have done studies to investigate the optimal 1 composition of a committee of this type. Their conclusions are that (a) the committee should have three to five members, (b) the backgrounds of the committee members should be different, and (c) there should be a healthy dialogue between members of the committee. It is important that members of the committee are able step back from their day-to-day responsibilities to consider the big picture. It is not always the case that senior management’s thinking has to be highly innovative in order for it to come up with relevant scenarios. In 2005 and 2006, many commentators realized that the U.S. housing market was experiencing a bubble 1 See R. Clemens and R. Winkler, “Combining Probability Distributions from Experts in Risk Analysis,” Risk Analysis 19, no. 2 (April 1999): 187–203.P1: TIX/b P2:c/d QC:e/f T1:g JWBT668-c19 JWBT668-Hull March 7, 2012 8:35 Printer: Courier Westford 416 RISK MANAGEMENT AND FINANCIAL INSTITUTIONS and that sooner or later the bubble would burst. It is easy to be wise after the event, but one reasonable scenario for the stress-testing committee to propose during that period would have been a 10% or 20% decline in house prices in all parts of the country. It is important that senior management and the board of directors understand and recognize the importance of stress testing. They have the responsibility for taking strategic decisions based on the stress-testing results. One advantage of involving senior management in the development of the scenarios to be used in stress testing is that it should naturally lead to a “buy in” by them to the idea that stress testing is important. The results generated from scenarios that are created by individuals who have middle management positions are unlikely to be taken as seriously. Core vs. Peripheral Variables When individual variables are stressed or scenarios are generated by management, the scenarios are likely to be incomplete in that movements of only a few (core) market variables are specified. One approach is to set changes in all other (periph- eral) variables to zero, but this is likely to be unsatisfactory. Another approach is to regress the peripheral variables on the core variables that are being stressed to ob- tain forecasts for them conditional on the changes being made to the core variables. These forecasts (as point forecasts or probability distributions) can be incorporated into the stress test. 2 This is known as conditional stress testing and is discussed by Kupiec (1999). Kim and Finger (2000) carry this idea further by using what they call a “broken ar- row” stress test. In this, the correlation between the core variables and the peripheral variables is based on what happens in stressed market conditions rather than what 3 happens on average. Making Scenarios Complete Scenarios should be carefully examined in an attempt to make sure that all the adverse consequences are considered. The scenarios should include not only the immediate effect on the financial institution’s portfolio of shock to market variables, but also any “knock-on” effect resulting from many different financial institutions being affected by the shock in the same way and responding in the same way. Many people have said that they recognized the real estate bubble in the United States would burst in 2007, but did not realize how bad the consequences would be. They did not anticipate that many financial institutions would experience losses at the same time with the result that there would be a flight to quality with severe liquidity problems and a huge increase in credit spreads. Another example of knock-on effects is provided by the failure of Long-Term Capital Management (LTCM) in 1998 (see Business Snapshot 19.1). LTCM tended 2 P. Kupiec, “Stress Testing in a Value at Risk Framework,” Journal of Derivatives 6 (1999): 7–24. 3 See J. Kim and C. C. Finger, “A Stress Test to Incorporate Correlation Breakdown,” Journal of Risk 2, no. 3 (Spring 2000): 5–19.P1: TIX/b P2:c/d QC:e/f T1:g JWBT668-c19 JWBT668-Hull March 7, 2012 8:35 Printer: Courier Westford Scenario Analysis and Stress Testing 417 BUSINESS SNAPSHOT 19.1 Long-Term Capital Management’s Big Loss Long-Term Capital Management (LTCM), a hedge fund formed in the mid- 1990s, always collateralized its transactions. The hedge fund’s investment strategy was known as convergence arbitrage. A very simple example of what it might do is the following. It would find two bonds, X and Y, issued by the same company promising the same payoffs, with X being less liquid (i.e., less actively traded) than Y. The market always places a value on liquidity. As a result, the price of X would be less than the price of Y. LTCM would buy X, short Y, and wait, expecting the prices of the two bonds to converge at some future time. When interest rates increased, the company expected both bonds to move down in price by about the same amount so that the collateral it paid on bond X would be about the same as the collateral it received on bond Y. Similarly, when interest rates decreased, LTCM expected both bonds to move up in price by about the same amount so that the collateral it received on bond X would be about the same as the collateral it paid on bond Y. It therefore expected that there would be no significant outflow of funds as a result of its collateral- ization agreements. In August 1998, Russia defaulted on its debt and this led to what is termed a “flight to quality” in capital markets. One result was that investors valued liquid instruments more highly than usual and the spreads between the prices of the liquid and illiquid instruments in LTCM’s portfolio increased dramatically. The prices of the bonds LTCM had bought went down and the prices of those it had shorted increased. It was required to post collateral on both. The company was highly leveraged and found it difficult to make the payments required under the collateralization agreements. The result was that positions had to be closed out and there was a total loss of about 4 billion. If the company had been less highly leveraged it would probably have been able to survive the flight to quality and could have waited for the prices of the liquid and illiquid bonds to become closer. to have long positions in illiquid securities and short positions in liquid securi- ties. Its failure was caused by a flight to quality following Russia’s default on its debt. Many investors were only interested in buying liquid securities. Spreads be- tween liquid and illiquid securities increased. LTCM contends that it had done stress tests looking at the impact of flights to quality similar to those that had oc- curred pre-1998. What it did not allow for was the knock-on effect. Many hedge funds were following similar trading strategies to those of LTCM in 1998. When the flight to quality started, they were all forced to unwind their positions at the same time. Unwinding meant selling illiquid securities and buying liquid securities, reinforcing the flight to quality and making it more severe than previous flights to quality.P1: TIX/b P2:c/d QC:e/f T1:g JWBT668-c19 JWBT668-Hull March 7, 2012 8:35 Printer: Courier Westford 418 RISK MANAGEMENT AND FINANCIAL INSTITUTIONS Scenarios should ideally be dynamic so that the response to the shock of the financial institution doing the stress test, as well as the response of other financial institutions, are considered. Consider, for example, the situation where a financial institution has sold options dependent on an underlying asset and maintains delta neutrality. A shock where there is a large increase or decrease in the asset price will lead to an immediate loss on the option position (see Section 7.7). To maintain delta neutrality large amounts of the asset will have to be bought or sold. The cost of subsequent delta hedging is liable to depend on the path followed by the asset price. The worst-case scenario, which should be the one considered by stress testers, is that the asset price experiences wild swings (i.e., large increases and decreases) before it settles down. Reverse Stress Testing Reverse stress testing involves the use of computational procedures to search for sce- narios that lead to large losses and has become an important tool in risk management. EXAMPLE 19.1 As a simple example of reverse stress testing, suppose a financial institution has positions in four European call options on an asset. The asset price is 50, the risk-free rate is 3%, the volatility is 20%, and there is no income on the asset. The positions, strike prices, and times to maturity are as indicated in the table below. The current value of the position (in 000s) is −25.90. The DerivaGem Application Builder can be used to search for one-day changes in the asset price and the volatility that will lead to the greatest losses. Some bounds should be put on the changes that are considered. We assume that the asset price will not decrease below 40 or increase above 60. It is assumed that the volatility will not fall below 10% or rise above 30%. Position (000s) Strike Price Life (years) Position Value (000s) +250 50 1.0 1176.67 −125 60 1.5 −293.56 −75 40 0.8 −843.72 −50 55 0.5 −65.30 Total −25.90 Using the DerivaGem Application Builder in conjunction with Solver, the worst loss is found to be when the volatility decreases to 10% and the asset price falls to 45.99. The loss is 289.38. Reverse stress testing therefore shows that the financial institution is most exposed to a reduction of about 8% in the asset price combined with a sharp decline in volatility. This might seem to be an unreasonable scenario. It is unlikely that volatility would go down sharply when the asset price declines by 8%. Solver could be run again with the lower bound to volatility being 20% instead of 10%. This gives a worst-case loss occurring when the volatility stays at 20% and the asset price falls to 42.86. The loss (in 000s) is then 87.19.P1: TIX/b P2:c/d QC:e/f T1:g JWBT668-c19 JWBT668-Hull March 7, 2012 8:35 Printer: Courier Westford Scenario Analysis and Stress Testing 419 Searching over all the market variables to which a financial institution is exposed in the way indicated in Example 19.1 is in practice usually not computationally feasible. One approach is to identify 5 to 10 key market variables and assume that changes in other variables are dependent on changes in these variables. Another way of simplifying the search process is to impose some structure on the problem. A principal components analysis (see Section 8.8) can be carried out on the changes in market variables (ideally using data from stressed market conditions) and then a search can be conducted to determine the changes in the principal components that generate large losses. This reduces the dimension of the space over which the search is conducted and should lead to fewer implausible scenarios. An alternative approach is for the risk management group to impose a structure on scenarios. For example, management might be interested in a scenario similar to one that has occurred in the past where interest rates rise, stock prices fall, and a particular exchange rate weakens. An analyst could then search to find what multiplier must be applied to the changes observed in the past for a particular loss level to be reached. Reverse stress testing can be used as a tool to facilitate brainstorming by the stress-testing committee. Prior to a meeting of the stress-testing committee, analysts can use reverse stress testing to come up with several scenarios that would be dis- astrous to the financial institution. These scenarios, along with others they generate themselves, are then considered by the stress-testing committee. They use their judg- ment to eliminate some of the analysts’ scenarios as implausible and modify others so that they become plausible and are retained for serious evaluation. 19.2 REGULATION The Basel Committee requires market risk calculations that are based on a bank’s internal VaR models to be accompanied by “rigorous and comprehensive” stress testing. Similarly, banks using the IRB approach in Basel II (advanced or foundation) to determine credit risk capital are required to conduct stress tests to determine the robustness of their assumptions. In May 2009, the Basel Committee issued the final version of its recommen- dations on stress-testing practices and how stress testing should be supervised by 4 regulators. The recommendations emphasize the importance of stress testing in de- termining how much capital is necessary to absorb losses should large shocks occur. They make the point that stress testing is particularly important after long periods of benign conditions because such conditions tend to lead to complacency. The recommendations stress the importance of top management and board in- volvement in stress testing. In particular, top management and board members should be involved in setting stress-testing objectives, defining scenarios, discussing the re- sults of stress tests, assessing potential actions, and decision making. It makes the point that the banks that fared well in the financial crisis that started in mid-2007 were the ones whose senior management as a whole took an active interest in the 4 See “Principles for Sound Stress-Testing Practices and Supervision,” Basel Committee on Banking Supervision, May 2009.P1: TIX/b P2:c/d QC:e/f T1:g JWBT668-c19 JWBT668-Hull March 7, 2012 8:35 Printer: Courier Westford 420 RISK MANAGEMENT AND FINANCIAL INSTITUTIONS development and operation of stress testing, with the results of stress testing serving as an input into strategic decision making. Stress testing should be conducted across all areas of the bank. It should not be the case that each area conducts its own stress test. The Basel recommendations make the point that many of the scenarios chosen pre-2007 were based on historical data and much less severe than what actually happened. Specific recommendations for banks are: 1. Stress testing should form an integral part of the overall governance and risk management culture of the bank. Stress testing should be actionable, with the results from stress-testing analyses impacting decision making at the appropriate management level, including strategic business decisions of the board and senior management. Board and senior management involvement in the stress-testing program is essential for its effective operation. 2. A bank should operate a stress-testing program that promotes risk identification and control, provides a complementary risk perspective to other risk manage- ment tools, improves capital and liquidity management, and enhances internal and external communication. 3. Stress-testing programs should take account of views from across the organiza- tion and should cover a range of perspectives and techniques. 4. A bank should have written policies and procedures governing the stress-testing program. The operation of the program should be appropriately documented. 5. A bank should have a suitably robust infrastructure in place, which is suffi- ciently flexible to accommodate different and possibly changing stress tests at an appropriate level of granularity. 6. A bank should regularly maintain and update its stress-testing framework. The effectiveness of the stress-testing program, as well as the robustness of major individual components, should be assessed regularly and independently. 7. Stress tests should cover a range of risks and business areas, including at the firm-wide level. A bank should be able to integrate effectively across the range of its stress-testing activities to deliver a complete picture of firm-wide risk. 8. Stress-testing programs should cover a range of scenarios, including forward- looking scenarios, and aim to take into account system-wide interactions and feedback effects. 9. Stress tests should feature a range of severities, including events capable of gen- erating most damage whether through size of loss or through loss of reputation. A stress-testing program should also determine what scenarios could challenge the viability of the bank (reverse stress tests) and thereby uncover hidden risks and interactions among risks. 10. As part of an overall stress-testing program, a bank should aim to take account of simultaneous pressures in funding and asset markets, and the impact of a reduction in market liquidity on exposure valuation. 11. The effectiveness of risk mitigation techniques should be systematically chal- lenged. 12. The stress-testing program should explicitly cover complex and bespoke prod- ucts such as securitized exposures. Stress tests for securitized assets should con- sider the underlying assets, their exposure to systematic market factors, relevantP1: TIX/b P2:c/d QC:e/f T1:g JWBT668-c19 JWBT668-Hull March 7, 2012 8:35 Printer: Courier Westford Scenario Analysis and Stress Testing 421 contractual arrangements and embedded triggers, and the impact of leverage, particularly as it relates to the subordination level in the issue structure. 5 13. The stress-testing program should cover pipeline and warehousing risks. A bank should include such exposures in its stress tests regardless of their probability of being securitized. 14. A bank should enhance its stress-testing methodologies to capture the effect of reputational risk. The bank should integrate risks arising from off-balance-sheet vehicles and other related entities in its stress-testing program. 15. A bank should enhance its stress-testing approaches for highly leveraged coun- terparties in considering its vulnerability to specific asset categories or market movements and in assessing potential wrong-way risk related to risk-mitigating techniques. The recommendations for bank supervisors are: 16. Supervisors should make regular and comprehensive assessments of a bank’s stress-testing programs. 17. Supervisors should require management to take corrective action if material deficiencies in the stress-testing program are identified or if the results of stress tests are not adequately taken into consideration in the decision-making process. 18. Supervisors should assess and, if necessary, challenge the scope and severity of firm-wide scenarios. Supervisors may ask banks to perform sensitivity analysis with respect to specific portfolios or parameters, use specific scenarios or to evaluate scenarios under which their viability is threatened (reverse stress-testing scenarios). 19. Under Pillar 2 (supervisory review process) of the Basel II framework, supervisors should examine a bank’s stress-testing results as part of a supervisory review of both the bank’s internal capital assessment and its liquidity risk management. In particular, supervisors should consider the results of forward-looking stress testing for assessing the adequacy of capital and liquidity. 20. Supervisors should consider implementing stress-test exercises based on common scenarios. 21. Supervisors should engage in a constructive dialogue with other public authori- ties and the industry to identify systemic vulnerabilities. Supervisors should also ensure that they have the capacity and the skills to assess banks’ stress-testing programs. Scenarios Chosen by Regulators Bank regulators require banks to consider extreme scenarios and then make sure they have enough capital for those scenarios. There is an obvious problem here. Banks want to keep their regulatory capital as low as possible. They therefore have 5 “Pipeline and warehousing” risks refer to risks associated with assets that are awaiting securitization, but might not be securitized if market conditions change. These risks led to losses during the onset of the crisis.P1: TIX/b P2:c/d QC:e/f T1:g JWBT668-c19 JWBT668-Hull March 7, 2012 8:35 Printer: Courier Westford 422 RISK MANAGEMENT AND FINANCIAL INSTITUTIONS no incentive to consider extreme scenarios that would lead to a bank supervisor telling them that their capital requirements need to be increased. There is there- fore a natural tendency for the scenarios they consider to be “watered down” and fairly benign. One approach to overcoming this problem is for regulators themselves to provide the scenarios (see Recommendations 18 and 20). This creates a lot of additional work for regulators, but it is obviously attractive for them to use the same set of scenarios for all banks. The banks are then compared using a common benchmark and systemic risk problems might be identified (see Business Snapshot 12.1 for an explanation of systemic risk). U.S. regulators used this approach in 2009 when they carried out stress tests of 19 financial institutions and found that 10 of them needed a total of 74.6 billion of additional capital. The European Banking Authority announced the results of a similar stress test in 2011 and found that 9 out of 91 financial insitutions failed the test. (Banks failed the test when their core Tier 1 capital ratio fell below 5%.) By choosing scenarios themselves, regulators are able to focus the attention of banks on issues that are of concern to regulators. In particular, if regulators see many banks taking positions with similar risks, they could insist that all banks consider a particular set of scenarios that gave rise to adverse results for the positions. The downside of regulators generating scenarios themselves is that part of the reason for the increased focus by supervisors on stress testing is that they want to encourage financial institutions to spend more time generating and worrying about potential adverse scenarios. If supervisors do the work in generating the scenarios, this may not happen. A compromise might be to insist on both management-generated scenarios and supervisor-generated scenarios being evaluated. Systems put in place by regulators do not always have the results one expects. Business Snapshot 19.2 explains that, when Danish regulators defined key scenarios for life insurance companies and pension funds in Europe, some of those companies responded by hedging against the particular scenarios used by regulators, and only 6 against those scenarios. This is not what regulators intended. Each scenario used in stress testing should be viewed as representative of a range of things that might happen. Financial institutions should ensure that their capital will be in good shape not just for the specified scenarios, but also for other similar or related scenarios. An extreme form of hedging against the red light scenario in Business Snapshot 19.2 would be to buy a security that pays off only if there is a decline in equity prices between 11% and 13% combined with a decline in interest rates between 65 and 75 basis points. This security would presumably cost very little and would be a ridiculous hedge, but could ensure that the financial institution passes the regulator-generated stress tests. Mechanistic hedging against particular adverse scenarios, whether generated by regulators or in some other way, is not desirable. It is important for the financial institution to understand the range of risks represented by each stress scenario and to take sensible steps to deal with them. Risk management should not be a game between regulators and financial institutions. 6 The information in Business Snapshot 19.2 is from P. L. Jorgensen, “Traffic Light Options,” Journal of Banking and Finance 31, no. 12 (December 2007): 3698–3719.P1: TIX/b P2:c/d QC:e/f T1:g JWBT668-c19 JWBT668-Hull March 7, 2012 8:35 Printer: Courier Westford Scenario Analysis and Stress Testing 423 BUSINESS SNAPSHOT 19.2 Traffic Light Options In June 2001, the Danish Financial Supervisory Authority (DFSA) introduced a “traffic light” solvency stress-testing system. This requires life insurance companies and pension funds to submit semiannual reports indicating the impact on them of certain predefined shocks. The “red light scenario” involves a 70-basis-point decrease in interest rates, a 12% decline in stock prices, and an 8% decline in real estate prices. If capital falls below a specified critical level in this scenario, the company is categorized with “red light status” and is subject to more frequent monitoring with monthly reports being required. The “yellow light scenario” involves a 100-basis-point decrease in interest rates, a 30% decline in stock prices, and a 12% decline in real estate prices. If capital falls below the critical level in this scenario, the company is categorized with “yellow light status” and has to submit quarterly reports. When the company’s capital stays above the critical levels for the red and yellow light scenarios, the company has a “green light status” and is subject to normal semiannual reporting. Some other countries in Europe have adopted similar procedures. Investment banks have developed products for helping life insurance and pension funds keep a green light status. These are known as traffic light options. They pay off in the traffic light scenarios so as to give a boost to the financial institution’s performance when these scenarios are considered. Rather than hedge against interest rates, equities, and real estate prices in the usual way, the financial institution buys a hedge that pays off only when the traffic light scenario specified for one or more of these variables occurs. This is much less expensive. (In practice, most of the financial institutions being regulated had very little exposure to real estate and the big moves that led to a payoff involved only interest rates and equity prices.) 19.3 WHAT TO DO WITH THE RESULTS The biggest problem in stress testing is using the results effectively. All too often, the results of stress testing are ignored by senior management. A typical response is, “Yes, there are always one or two scenarios that will sink us. We cannot protect ourselves against everything that might happen.” One way of trying to avoid this sort of response is to involve senior management in the development of scenarios, as outlined earlier. A better response on the part of senior management would be, “Are the risks associated with these scenarios acceptable? If not, let’s investigate what trades we can put on to make these types of risks more acceptable.” The problem for both senior management and the risk management group is that they have two separate reports on their desks concerning what could go wrong. One report comes from VaR models, the other from stress testing. Which one should they base their decision making on? There is a natural tendency to take the VaR results more seriously because they impact regulatory capital in a direct way.P1: TIX/b P2:c/d QC:e/f T1:g JWBT668-c19 JWBT668-Hull March 7, 2012 8:35 Printer: Courier Westford 424 RISK MANAGEMENT AND FINANCIAL INSTITUTIONS Integrating Stress Testing and VaR Calculations Berkowitz (2000) suggests that stress testing will be taken more seriously if its 7 results are integrated into the calculation of VaR. This can be done by assigning a probability to each stress scenarios that is considered. Suppose that a financial institution has considered n stress scenarios and the total probability assigned to the s stress scenarios is p. Assume further that there are n VaR scenarios generated using v historical simulation in the usual way. An analyst can assume that there are a total of n + n scenarios. The n stress scenarios have probability p and the n historical s v s v scenarios have probability 1 − p. Unfortunately human beings are not good at estimating a probability for the occurrence of a rare event. To make the task feasible for the stress-testing committee, one approach is to ask the stress-testing committee to allocate each stress scenario to categories with preassigned probabilities. The categories might be: 1. Probability = 0.05%. Extremely unlikely. One chance in 2,000. 2. Probability = 0.2%. Very unlikely, but the scenario should be given about the same weight as the 500 scenarios used in the historical simulation analysis. 3. Probability = 0.5%. Unlikely, but the scenario should be given more weight than the 500 scenarios used in the historical simulation analysis. EXAMPLE 19.2 Suppose that, in the example in Section 14.1, five stress scenarios are considered. They lead to losses (in 000s) of 235, 300, 450, 750, and 850. The probabilities assigned to the scenarios are 0.5%, 0.2%, 0.2%, 0.05%, and 0.05%, respectively. The total probability of the stress scenarios is, therefore, 1%. This means that the probability assigned to the scenarios generated by historical simulation is 99%. Assuming that equal weighting is used, each historical simulation scenario is assigned a probability of 0.99/500 = 0.00198. Table 14.4 is therefore replaced by Table 19.1. The probabilities assigned to scenarios are accumulated from the worst scenario to 8 the best. The VaR level when the confidence level is 99% is the first loss for which the cumulative probability is greater than 0.01. In our example this is 282,204. Rebonato (2010) suggests a more elaborate approach to assessing probabilities of scenarios involving a careful application of a well known result in statistics, Bayes’ 9 theorem, and what are known as Bayesian networks. The probability of a scenario consisting of two events is equal to the probability of the first event happening 7 See J. Berkowitz, “A Coherent Framework for Stress Testing,” Journal of Risk 2, no. 2 (Winter 1999/2000): 5–15. 8 This is the same procedure that we used when weights were assigned to historical simulation scenarios. (See Table 14.5 in Section 14.3.) 9 See Riccardo Rebonato, “Coherent Stress Testing: A Bayesian Approach to Financial Stress,” (Chichester, UK: John Wiley & Sons, 2010).P1: TIX/b P2:c/d QC:e/f T1:g JWBT668-c19 JWBT668-Hull March 7, 2012 8:35 Printer: Courier Westford Scenario Analysis and Stress Testing 425 TABLE 19.1 Losses Ranked from Highest to Lowest Scenario Loss (000s) Probability Cumulative Probability s5 850.000 0.00050 0.00050 s4 750.000 0.00050 0.00100 v494 477.841 0.00198 0.00298 s3 450.000 0.00200 0.00498 v339 345.435 0.00198 0.00696 s2 300.000 0.00200 0.00896 v349 282.204 0.00198 0.01094 v329 277.041 0.00198 0.01292 v487 253.385 0.00198 0.01490 s1 235.000 0.00500 0.01990 v227 217.974 0.00198 0.02188 v131 205.256 0.00198 0.02386 v238 201.389 0.00198 0.02584 ... ... ... ... ... ... ... ... ... ... ... ... For Example 19.2 s1, s2,... are the stress scenarios; v1, v2,... are the VaR historical simulation scenarios. times the probability of the second event happening conditional on the first event having happened. Similarly the probability of a scenario consisting of three events is the probability of the first event happening times the probability of the second event happening conditional that the first event has happened times the probability of the third event happening conditional that the first two events have happened. Rebonato’s approach provides a way of evaluating the conditional probabilities. Subjective vs. Objective Probabilities There are two types of probability estimates: objective and subjective. An objective probability for an event is a probability calculated by observing the frequency with which the event happens in repeated trials. As an idealized example of an objective probability, consider an urn containing red balls and black balls in an unknown proportion. We want to know the probability of a ball drawn at random from the urn being red. We could draw a ball at random, observe its color, replace it in the urn, draw another ball at random, observe its color, replace it in the urn, and so on, until 100 balls have been drawn. If 30 of the balls that have been drawn are red and 70 are black, our estimate for the probability of drawing a red ball is 0.3. Unfortunately, most objective probabilities calculated in real life are usually less reliable than the probability in this example, because the probability of the event happening does not remain constant for the observations that are available and the observations may not be independent. A subjective probability is a probability derived from an individual’s personal judgment about the chance of a particular event occurring. The probability is not based on historical data. It is a degree of belief. Different people are liable to have different subjective probabilities for the same event.P1: TIX/b P2:c/d QC:e/f T1:g JWBT668-c19 JWBT668-Hull March 7, 2012 8:35 Printer: Courier Westford 426 RISK MANAGEMENT AND FINANCIAL INSTITUTIONS The probabilities in historical simulation are objective whereas the probabilities assigned to the scenarios in stress testing are subjective. Many analysts are uncom- fortable with subjective probabilities because they are not based on data. Also, it is unfortunately the case that political considerations may play a part in a financial institution’s decision to focus on historical data. If you use historical data and things go wrong, you can blame the data. If you use subjective judgments that have been provided by a group of people, those people are liable to be blamed. However, if it is based only on objective probabilities, risk management is in- evitably backward looking and fails to capitalize on the judgment and expertise of senior managers. It is the responsibility of those managers to steer the financial institution so that catastrophic risks are avoided. SUMMARY Stress testing is an important part of the risk management process. It leads to a financial institution considering the impact of extreme scenarios that are ignored by a traditional VaR analysis, but that do happen from time to time. Once plausible scenarios have been evaluated, the financial institution can take steps to lessen the impact of the particularly bad ones. One advantage of a comprehensive stress-testing program is that a financial institution obtains a better understanding of the nature of the risks in its portfolio. Scenarios can be generated in a number of different ways. One approach is to consider extreme movements in just one market variable while keeping others fixed. Another is to use the movements in all market variables that occurred during periods in the past when the market experienced extreme shocks. The best approach is to ask a committee of senior management and economists to use their judgment and experience to generate the plausible extreme scenarios. Sometimes financial institutions carry out reverse stress testing where algorithms are used to search for scenarios that would lead to large losses. Scenarios should be as complete as possible and include the impact of knock-on effects as well as the initial shock to market variables. The market turmoil starting in summer 2007 shows that, in some cases, the knock-on effect can be significant and include a flight to quality, an increase in credit spreads, and a shortage of liquidity. Regulators require financial institutions to keep sufficient capital for stress sce- narios. Sometimes regulators themselves develop a common set of stress scenarios to be used by all financial institutions themselves. This helps to identify those financial institutions with insufficient capital and may uncover systemic risk problems. If subjective probabilities are assigned to the extreme scenarios that are consid- ered, stress testing can be integrated with a VaR analysis. This is an interesting idea, but was not one of the approaches outlined in the Basel Committee consultative document published in January 2009. FURTHER READING Alexander, C., and E. A. Sheedy. “Model-Based Stress Tests: Linking Stress Tests to VaR for Market Risk.” Working Paper, Macquarie Applied Finance Center, 2008.P1: TIX/b P2:c/d QC:e/f T1:g JWBT668-c19 JWBT668-Hull March 7, 2012 8:35 Printer: Courier Westford Scenario Analysis and Stress Testing 427 Aragones, J. R., C. Blanco, and K. Dowd. “Incorporating Stress Tests into Market Risk ´ Modeling.” Derivatives Quarterly 7 (Spring 2001): 44–49. Aragones, J. R., C. Blanco, and K. Dowd. “Stress Tests, Market Risk Measures, and Extremes: ´ Bringing Stress Tests to the Forefront of Market Risk Management.” In Stress Testing for Financial Institutions: Applications, Regulations, and Techniques,editedbyD.Rosch ¨ and H. Scheule. London: Risk Books, 2008. Basel Committee on Banking Supervision. “Principles for Sound Stress-Testing Practices and Supervision.” May 2009. Berkowitz, J. “A Coherent Framework for Stress Testing.” Journal of Risk 2, no. 2 (Winter 1999/2000): 5–15. Bogle, J. C. “Black Monday and Black Swans.” Financial Analysts Journal 64, no. 2 (March/April 2008): 30–40. Clemens, R., and R. Winkler. “Combining Probability Distributions from Experts in Risk Analysis.” Risk Analysis 19, no. 2 (April 1999): 187–203. Duffie, D. “Systemic Risk Exposures: A 10-by-10-by-10 Approach.” Working Paper, Stanford University, 2011. Hua, P., and P. Wilmott. “Crash Courses.” Risk 10, no. 6 (June 1997): 64–67. Kim, J., and C. C. Finger. “A Stress Test to Incorporate Correlation Breakdown.” Journal of Risk 2, no. 3 (Spring 2000): 5–19. Kupiec, P. “Stress Testing in a Value at Risk Framework.” Journal of Derivatives 6 (1999): 7–24. Rebonato, R. Coherent Stress Testing: A Bayesian Approach to the Analysis of Financial Stress. Chichester, UK: John Wiley & Sons, 2010. Taleb, N. N. The Black Swan: The Impact of the Highly Improbable. New York: Random House, 2007. PRACTICE QUESTIONS AND PROBLEMS (ANSWERS AT END OF BOOK) 19.1 Explain three different ways that scenarios can be generated for stress testing. 19.2 What is reverse stress testing? How is it used? 19.3 Why might the regulatory environment lead to a financial institution under- estimating the severity of the scenarios it considers? 19.4 What are traffic light options? What are their drawbacks? 19.5 Why is it important for senior management to be involved in stress testing? 19.6 What are the advantages and disadvantages of bank regulators choosing some of the scenarios that are considered for stress testing? 19.7 Explain the difference between subjective and objective probabilities. 19.8 Suppose that, in the example in Section 14.1, seven stress scenarios are con- sidered. They lead to losses (in 000s) of 240, 280, 340, 500, 700, 850, and 1,050. The subjective probabilities assigned to the scenarios are 0.5%, 0.5%, 0.2%, 0.2%, 0.05%, 0.05%, and 0.05%, respectively. What is the new one-day 99% VaR that would be calculated using the procedure discussed in Section 19.3? 19.9 Suppose that the positions in the four options in Example 19.1 are changed to 200, −70, −120, and −60. Use the DerivaGem Application Builder and Solver to calculate the worst-case scenario for a daily change. Consider asset prices between 40 and 60 and volatilities between 10% and 30%.P1: TIX/b P2:c/d QC:e/f T1:g JWBT668-c19 JWBT668-Hull March 7, 2012 8:35 Printer: Courier Westford 428 RISK MANAGEMENT AND FINANCIAL INSTITUTIONS FURTHER QUESTIONS 19.10 What difference does it make to the worst-case scenario in Example 19.1 if (a) the options are American rather than European and (b) the options are barrier options that are knocked out if the asset price reaches 65? Use the DerivaGem Applications Builder in conjunction with Solver to search over asset prices between 40 and 60 and volatilities between 18% and 30%. 19.11 What difference does it make to the VaR calculated in Example 19.2 if the exponentially weighted moving average model is used to assign weights to scenarios as described in Section 14.3?P1: TIX/b P2:c/d QC:e/f T1:g JWBT668-c20 JWBT668-Hull March 7, 2012 8:39 Printer: Courier Westford CHAPTER 20 Operational Risk n 1999, bank supervisors announced plans to assign capital for operational risk in the new Basel II regulations. This met with some opposition from banks. The I chairman and CEO of one major international bank described it as “the dopiest thing I have ever seen.” However, bank supervisors persisted. They listed more than 100 operational risk losses by banks, each exceeding 100 million. Here are some of those losses: Internal fraud: Allied Irish Bank, Barings, and Daiwa lost 700 million, 1 bil- lion, and 1.4 billion, respectively, from fraudulent trading. External fraud: Republic New York Corp. lost 611 million because of fraud committed by a custodial client. Employment practices and workplace safety: Merrill Lynch lost 250 million in a legal settlement regarding gender discrimination. Clients, products, and business practices: Household International lost 484 mil- lion from improper lending practices; Providian Financial Corporation lost 405 million from improper sales and billing practices. Damage to physical assets: Bank of New York lost 140 million because of damage to its facilities related to the September 11, 2001, terrorist attack. Business disruption and system failures: Salomon Brothers lost 303 million from a change in computing technology. Execution, delivery, and process management: Bank of America and Wells Fargo Bank lost 225 million and 150 million, respectively, from systems inte- gration failures and transaction processing failures. Most banks have always had some framework in place for managing operational risk. However, the prospect of new capital requirements has led them to greatly increase the resources they devote to measuring and monitoring operational risk. It is much more difficult to quantify operational risk than credit or market risk. Operational risk is also more difficult to manage. Financial institutions make a conscious decision to take a certain amount of credit and market risk, and there are many traded instruments that can be used to reduce these risks. Operational risk, by contrast, is a necessary part of doing business. An important part of operational risk management is identifying the types of risk that are being taken and which should be insured against. There is always a danger that a huge loss will be incurred from taking an operational risk that ex ante was not even recognized as a risk. 429P1: TIX/b P2:c/d QC:e/f T1:g JWBT668-c20 JWBT668-Hull March 7, 2012 8:39 Printer: Courier Westford 430 RISK MANAGEMENT AND FINANCIAL INSTITUTIONS It might be thought that a loss such as that at Societ ´ eG ´ en ´ erale ´ (SocGen, see Business Snapshot 5.5) was a result of market risk because it was movements in market variables that led to it. However, it should be classified as an operational risk loss because it involved fraud. (Jer ´ ome ˆ Kerviel created fictitious trades to hide the big bets he was taking.) Suppose there was no fraud. If it was part of the bank’s policy to let traders take huge risks, then the loss would be classified as market risk. But, if this was not part of the bank’s policy and there was a breakdown in its controls, it would be classified as operational risk. The SocGen example illustrates that operational risk losses are often contingent on market movements. If the market had moved in Kerviel’s favor, there would have been no loss. The fraud and the breakdown in SocGen’s control systems might then never have come to light. There are some parallels between the operational risk losses of banks and the losses of insurance companies. Insurance companies face a small probability of a large loss from a hurricane, earthquake, or other natural disaster. Similarly, banks face a small probability of a large operational risk loss. But there is one important difference. When insurance companies lose a large amount of money because of a natural disaster, all companies in the industry tend to be affected and often premiums rise the next year to cover losses. Operational risk losses tend to affect only one bank. Because it operates in a competitive environment, the bank does not have the luxury of increasing prices for the services it offers during the following year. 20.1 WHAT IS OPERATIONAL RISK? There are many different ways in which operational risk can be defined. It is tempting to consider operational risk as a residual risk and define it as any risk faced by a financial institution that is not market risk or credit risk. To produce an estimate of operational risk, we could then look at the financial institution’s financial statements and remove from the income statement (a) the impact of credit losses and (b) the profits or losses from market risk exposure. The variation in the resulting income would then be attributed to operational risk. Most people agree that this definition of operational risk is too broad. It includes the risks associated with entering new markets, developing new products, economic factors, and so on. Another possible definition is that operational risk, as its name implies, is the risk arising from operations. This includes the risk of mistakes in processing transactions, making payments, and so on. This definition of risk is too narrow. It does not include major risks such as the risk of a “rogue trader” such as Jer ´ ome ˆ Kerviel. We can distinguish between internal risks and external risks. Internal risks are those over which the company has control. The company chooses whom it employs, what computer systems it develops, what controls are in place, and so on. Some peo- ple define operational risks as all internal risks. Operational risk then includes more than just the risk arising from operations. It includes risks arising from inadequate controls such as the rogue trader risk and the risks of other sorts of employee fraud. Bank regulators favor including more than just internal risks in their definition of operational risk. They include the impact of external events such as natural disasters (for example, a fire or an earthquake that affects the bank’s operations), political andP1: TIX/b P2:c/d QC:e/f T1:g JWBT668-c20 JWBT668-Hull March 7, 2012 8:39 Printer: Courier Westford Operational Risk 431 regulatory risk (for example, being prevented from operating in a foreign country by that country’s government), security breaches, and so on. All of this is reflected in the following definition of operational risk produced by the Basel Committee on Banking Supervision in 2001: The risk of loss resulting from inadequate or failed internal processes, people, and systems or from external events. Note that this definition includes legal risk but does not include reputation risk and the risk resulting from strategic decisions. Some operational risks result in increases in the bank’s operating cost or de- creases in its revenue. Other operational risks interact with credit and market risk. For example, when mistakes are made in a loan’s documentation, it is usually the case that losses result if and only if the counterparty defaults. When a trader exceeds limits and misreports positions, losses result if and only if the market moves against the trader. 20.2 DETERMINATION OF REGULATORY CAPITAL Banks have three alternatives for determining operational risk regulatory capital. The simplest approach is the basic indicator approach. Under this approach, operational risk capital is set equal to 15% of annual gross income over the previous three 1 years. Gross income is defined as net interest income plus noninterest income. A slightly more complicated approach is the standardized approach. In this, a bank’s activities are divided into eight business lines: corporate finance, trading and sales, retail banking, commercial banking, payment and settlement, agency services, asset management, and retail brokerage. The average gross income over the last three years for each business line is multiplied by a “beta factor” for that business line and the result summed to determine the total capital. The beta factors are shown in Table 20.1. The third alternative is the advanced measurement approach (AMA). In this, the operational risk regulatory capital requirement is calculated by the bank internally using qualitative and quantitative criteria. The Basel Committee has listed conditions that a bank must satisfy in order to use the standardized approach or the AMA approach. It expects large internationally active banks to move toward adopting the AMA approach through time. To use the standardized approach a bank must satisfy the following conditions: 1. The bank must have an operational risk management function that is responsible for identifying, assessing, monitoring, and controlling operational risk. 2. The bank must keep track of relevant losses by business line and must create incentives for the improvement of operational risk. 3. There must be regular reporting of operational risk losses throughout the bank. 1 Net interest income is the excess of income earned on loans over interest paid on deposits and other instruments that are used to fund the loans (see Section 2.2).P1: TIX/b P2:c/d QC:e/f T1:g JWBT668-c20 JWBT668-Hull March 7, 2012 8:39 Printer: Courier Westford 432 RISK MANAGEMENT AND FINANCIAL INSTITUTIONS TABLE 20.1 Beta Factors in Standardized Approach Business Line Beta Factor Corporate finance 18% Trading and sales 18% Retail banking 12% Commercial banking 15% Payment and settlement 18% Agency services 15% Asset management 12% Retail brokerage 12% 4. The bank’s operational risk management system must be well documented. 5. The bank’s operational risk management processes and assessment system must be subject to regular independent reviews by internal auditors. It must also be subject to regular review by external auditors or supervisors or both. To use the AMA approach, the bank must satisfy additional requirements. It must be able to estimate unexpected losses based on an analysis of relevant internal and external data, and scenario analyses. The bank’s system must be capable of allocating economic capital for operational risk across business lines in a way that creates incentives for the business lines to improve operational risk management. The objective of banks using the AMA approach for operational risk is analogous to their objectives when they attempt to quantify credit risk. They would like to produce a probability distribution of losses such as that shown in Figure 20.1. Assuming that they can convince regulators that their expected operational risk cost Expected 99.9% operational worst-case risk loss loss Capital Operational risk loss over one year FIGURE 20.1 Calculation of VaR for Operational Risk

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