IAA Paper on Scenario and Stress Testing – First DRAFTStress testing and scenario analysis in contrast does not require probabilities. It is sufficient to specify the events or sequence

Draft for discussion purposes only – Vienna, October 10, 2010 1

IAA Paper on Stress Testing and Scenario Analysis – THIRD DRAFT

Executive Summary This paper gives guidance on stress testing and scenario analysis. They allow the analysis of the impact of sever events or sequence of events on the financial state of firms. Scenarios are descriptions of consistent future states of the world. They describe plausible and possibly adverse events or sequence of events. Stress scenarios are more extreme scenarios with potentially higher impact. Stress tests and scenario analysis should be seen not only as complements to economic capital models, but also as an essential tool for risk management to for communication with stake holders. Economic capital models require assigning probabilities to the underlying events that are considered. Stress testing and scenario analysis in contrast does not require probabilities. It is sufficient to specify the events or sequence of events sufficiently detailed such that the impact on the firm can be quantified. They are therefore useful as a complement to models to also capture risks that are highly uncertain. Ideally, a firm employs both models, e.g. economic capital models and also stress tests and scenario analysis to capture a wider range of potential risks.

They are also intuitive and useful to communicate with senior managers, board of directors and other stakeholders. Stress tests and scenario analysis are explanatory as they do not only give a loss number or risk measure, but clearly define under which events a firm is in financial stress. They help foster an appropriate risk culture since they expose decision makers to potentially inconvenient truth and forces firms to base their business strategy not only on – often optimistic – forecasts but also on possible adverse scenarios. Stress testing and scenario analysis can foster an appropriate risk culture, but they can also be misused. Specifying weak events, i.e. events with little or no financial impact, can lead to complacency and to a postponement of necessary actions. This is true not only for events used by firms’ risk management, but equally for stress tests and scenario analysis undertaken by supervisory authorities. Defining appropriate events is intellectually equally challenging as developing an economic capital model and requires know-how and experience. It should employ specialists from a fields relevant to the specified events and the firm. Introduction Internal models are becoming more important in the financial services industry worldwide.


Insurance companies, banks and other financial institutions are increasingly studying their financial conditions and capital needs through the use of internal models. Some financial supervisors are actively encouraging companies under their authority to use such models and embed them within the firm’s normal operations1. Indeed, models of this type are currently being used in some regulatory regimes to assist in the determination of regulatory capital requirements2

. Significantly, many stakeholders have expressed clear views that firms can benefit from internal models by helping them develop and refine their corporate strategy and management.

The International Actuarial Association has prepared guidance on the construction and use of internal models3

.

Internal models are usually used to project a firm’s experience over a fixed future period, based on sets of assumptions about the general economy and the specific firm’s operating environment. These assumptions are often outputs from stochastic generators which use parameters based upon past experience. The reliability of these generators depends on the sophistication of the particular underlying distribution chosen and on the data used to fix the parameters of the generator. It is possible that the underlying distribution used does not have ‘sufficiently’ heavy tails (a common trait of many of the most widely used distributions) or that the calibration of the distribution’s parameters is conducted using data from a time period of insufficient length to capture a wide variety of experience. In these cases it is likely that such a generator will fail to replicate situations that are sufficiently extreme so as to cause ‘severe’ stress to the financial institution. This stochastic approach is further unlikely to capture the impacts of very stressful possible situations because such situations are often the result of a complex set of interactions of various risk factors (some of which may not be quantifiable). These interactions are often unique and are therefore not usually embedded in internal models. Although stressful situations may not arise in many stochastic simulations, it is important to investigate them in order to study the financial condition and solvency of an institution and to execute proper risk management. Since one cannot usually depend upon stochastic methods to generate these situations, it is necessary to deterministically construct such situations or scenarios and then project their results using internal models. Deterministic scenarios can also be useful for other purposes such as sensitivity testing, development of management strategy and policy, product development and financial planning. Regulators and supervisors may specify particular scenarios to be tested by all firms operating under their authority in order to gauge the possible impact of systemic risks. This paper provides guidance on the construction and use of deterministic scenarios for insurance companies and other financial institutions. It is best read in conjunction with the IAA paper on Internal Models and on Enterprise Risk Management.

1 Reference FSA’s ICAS, ICA, ICG 2 Reference Solvency II and Basel II for Trading Book 3 Reference the Internal Models Paper


Definitions Often the terms scenarios, stress tests and sensitivities are used interchangeably. In this report, we distinguish between these terms, although the distinctions can become blurred. Scenarios refer to events that impact several risk factors and often go over multiple time periods. Stress tests are severe events that might or might not impact several risk factors and time periods. Sensitivities are weak events that impact few or only one risk factor and are short in nature.

Figure 1: Sensitivities, Stress Tests and Scenarios

A scenario is a description of the potential future evolution of the state of the world. Scenarios can be simple and describe a sudden change in a single variable or risk factor, or quite complex, involving the changes and interactions over time of many factors, perhaps generated by a set of cascading events. Scenarios are tested through projections over time to discover their possible effects on a particular firm or on a national economy. However, in so doing, one is not necessarily assuming that the scenario represents one’s expectation of how the current state of the world is likely to evolve. A forecast is a projection based upon a scenario that is believed to be representative of the likely development of the current state of the world. Forecasts are useful for business planning and for the estimation of expected profits or losses. However, they are not useful for assessing the impact of rare and/or catastrophic future events.


A stress test is an event that is severe in consequence. It can impact many risk factors and its impacts can extend over months or years or it can affect only one or a small number of risk factors and be short in duration.4

A sensitivity test is a slight change of one or several risk factors and the assessment of the financial impact. Sensitivity tests are often used as a tool to calculate volatilities and other quantities by making further assumptions on the underlying probability distributions, e.g. multivariate normality and linearity of the dependency of the profit and loss on the underlying risk factors.

Figure 2: Time Evolution

Sensitivity analysis is concerned with changes in a single variable or risk factor. Generally, several scenarios are projected, each of which involves a different degree of change in the same variable. Changes in a specific variable or risk factor that produce significant unfavourable financial results are a common form of stress tests. A risk manager with a solid understanding of the firm and its activities should have little difficulty in carrying out sensitivity analysis for any variable of interest.

4 In Solvency II, a stress test is defined as the analysis of the impact of single extreme events and scenario analysis as the analysis of the impact of combinations of events. This is consistent with the definitions used in this paper..


While sensitivity analysis is the simplest and perhaps most common form of stress testing, it represents a relatively small part of this field. In this paper, we concentrate on the construction of more complex scenarios that begin with a single disruptive event and give rise to a cascade of effects. A scenario of this type can be illustrated by the financial crisis that began in 2007. This crisis began with a severe weakening of the U.S. housing market, and was followed by the seizing up of the market for securitized financial instruments which, in turn, led to a general credit crisis, a severe drop in equity markets and an economic recession. Such multi-effect scenarios that play out over months and years are caused by the tight coupling between different participants in the financial market. An event led to a loss in some of the market participants. This forced them to sell some of their assets, this lowering the market prices of these assets. Firms holding these or similar assets then also incurred losses even though they might not have been directly exposed to the initial loss. A famous case is the attempted cornering of the silver market by the Hunt brothers during the 1970s. When the price of silver collapsed, the Hunt brothers were forced to sell their holdings in cattle. This also depressed the price of cattle. This demonstrates that it is possible for the financial stress of one part of the financial market (e.g. subprime lenders) can percolate through the entire global financial system and impact investment banks, hedge funds and insurers, even though these participants might not have even held subprime linked investments on their books. These difficulties can extend well beyond the financial community and have large-scale effects on the general economy. Such major catastrophes expose a firm not only to an initial strain but rather to a sequence of effects that can play out over months and years. To only consider the initial event would, in such cases, vastly underestimate the financial stress the firm would experience. However, it is difficult, if not impossible, to think through all the possible ramifications of such an event. Recall that the purpose of using a scenario is less the prediction of a future event than getting a firm to think in advance about certain stylized events and to be prepared if a similar (but not necessarily identical) catastrophe were to occur. It is therefore sufficient that the formulation of the scenario captures the essence of the effects of an initial disruptive event. Some catastrophes may, of course, be limited to only a single initial event. For example, it is unlikely that a bus accident or a hail event will lead to an avalanche of further effects, although both events might be catastrophic for unlucky insurers. Therefore, it is appropriate for stress testing to include such “simpler” scenarios as well. Sensitivities, scenarios and stress tests are all related and there is a continuum ranging from simple sensitivities to very complex stress scenarios.


Figure 3: From Sensitivities to Stress Scenarios

Uses of Scenarios There are a variety of ways in which scenarios can be used within financial institutions and, in particular, within insurance companies. Some of these are described below. Solvency testing (financial condition reporting) The evaluation of a firm’s financial strength is a fundamental issue in financial analysis. The principle issue is to evaluate whether the firm has sufficient financial resources to enable it to meet all of its obligations to policyholders and depositors. More generally, under what conditions will the firm remain solvent? While stochastic generators can provide much useful information here, the complete answer to this question will usually involve sensitivity tests as well as extreme stress tests based upon scenarios. In many cases the analytical models, e.g. the stochastic generators, are not calibrated to take into account rare events and catastrophes and cannot capture the effects of hypothetical events that have not been observed. Stress testing helps to supplement these models. Solvency testing is discussed in greater detail in the IAA publication A Global Framework for Insurer Solvency Assessment.


Solvency testing is often approached from the perspective of satisfying regulatory capital requirements. However, this is far from the only approach to this issue. Another approach is in terms of the firm’s own particular situation and its economic capital requirements. In this case, the emphasis is on how the firm is managed and exactly what type of business it undertakes. The risks considered here include those considered for regulatory capital but may also include others such as new business, the firm’s specific risk exposure that might not be captured by regulatory solvency requirements or the use of a different valuation framework.. Some of these other factors are best treated through scenarios. Some events are so uncertain that it is impossible to assign to them with any confidence probabilities of occurrence. Such events cannot be captured reliably by an economic capital model. Consequently, an economic capital requirement cannot be assigned reliably to such events. Often, it is such events however that prove most disruptive for the financial situation of companies. Scenarios and stress tests allow the analysis of the potential impact of such events and the decision makers can then decide how much capital to put aside to cover these risks. Risk management The task of risk management is to make explicit the risks to which a company or an industry is potentially exposed to and, if appropriate, to propose measures on how to align these risks with the risk appetite of the company. This means that the risk manager should:

• Formulate appropriate scenarios that illuminate the risk exposure of the firm • Evaluate the impact of scenarios, i.e. hypothetical future events, on the financial

position of the company, • Discuss the results of these evaluations with senior management and the board so

as to agree on how they relate to the company’s risk appetite, • Consider what actions the firm could introduce to mitigate the effects of scenarios

that lead to financial difficulty for the company and that are sufficiently likely to occur. Such actions could then be suggested to senior management and the board.

When considering possible mitigating or remedial actions, the risk manager may test the effectiveness of the proposed actions by modifying the relevant basic scenarios so that the actions are then incorporated within the scenarios. For example, if a significant portion of the assets supporting a portfolio of participating life insurance business consists of equities and if one is testing a scenario that involves sharp falls in equity markets, one mitigating action might be to reduce policyholder dividends or bonuses. However, when testing the effectiveness of this action on the firm’s financial condition, one should be somewhat cautious in assuming how quickly management will react and introduce such a reduction. The reason being that scenarios give information over the whole unfolding of the event and this can lead to the unrealistic assumptions on the firm’s management actions. Factors such as company history and


philosophy, competitive position and policyholders’ reasonable expectations can have important effects on the timing of proposed action. The risk manager should take such factors into consideration and disclose the assumptions made when reporting the scenario results. Contingent and mitigating actions, which could be investigated and suggested to senior management and the board include:

• Operational measures such as the strengthening of current processes, • Contingency plans such as, in the example above, adjusting policyholder bonuses

or dividends, • Raising additional capital, • Risk mitigation or transfer; and • Risk elimination.

Analysis of non-quantifiable risks Certain risks an insurance company faces cannot be appropriately quantified, since their likelihood of occurring is highly uncertain or there is no underlying scientific theory. However, they do have quantifiable consequences that can have strong effects on a firm’s financial condition. An example of a risk with highly uncertain probability is reputation risk. The likelihood of financial loss due to loss of reputation depends on the firm’s strategy, the behaviour of its senior management, operational risks etc., However, while it is difficult if not impossible to give a reasonable close estimate of the probability of this occurring, the financial damage once such a reputational loss happens can be expressed numerically. Such damage may affect policyholder behaviour (lapse rates), new business volume, employee turnover or productivity, relations with suppliers, and regulatory actions. All of these effects will have financial consequences. In order to consider the effects of such risk, one must construct a scenario that describes the situation and its impact on various financial elements of the firm’s operations. Also many consider operational risk as not quantifiable. It is not well defined and the definition often used e.g. by Basel II is not sufficiently clear in an insurance context to assign losses clearly to an operational risk event and past data might be not applicable to potential future operational risk losses. Often mathematical models of dubious relevance are used and in general, capital requirements for operational risk are not seen as of the same quality as those for financial market and insurance risk. Scenarios can be a way to define operational risk events that are relevant to a specific firm and that allow for a detailed assessment of the financial impact without having to depend on a – non-existing – sophisticated theory of operational risk. There are many events for which no reasonable estimates for their probability can be arrived at, and it is difficult to exhaustively analyse all of them. However, some of these should be considered if only to give the risk manager, senior management and the board of directors a strong sense of what could happen and what the effects might be.


Evaluating such scenarios, which capture non-quantifiable risks are an essential complement to economic capital models. Communication with senior management and the board One often hears when discussing communication that “a picture is worth a thousand words”. This simple phrase expresses an important idea concerning human comprehension: a clear and graphic view is usually easier to understand than a complicated explanation. A similar situation exists when ideas are expressed in statistical and probabilistic terms: the general listener has a harder time comprehending what is meant than they would have in understanding a concrete example. In this case, the more concrete example is often a scenario. Senior management and board members without a strong mathematical background often understand and respond more easily to results of clearly expressed scenarios than they do to statements expressed in terms of confidence intervals or percentiles. Of course, the audience also requires some estimate of the likelihood that the scenario could actually occur, but this estimate is usually only required up to an order of magnitude and need not be precise. Scenarios thus become an important tool that the risk manager can use in communicating with those who must understand the results of the manager’s work. When scenarios are used as a communication tool, they should be intuitive and understandable, in order that non-specialists can discuss the hypothetical events and their consequences for the firm. It is essential that each scenario should be explained and documented by a narrative that is accessible also to readers who might not have a technical background. The narrative should detail the rationale for the choice of the scenario and should provide a story explaining the history leading up to the event, the actual event, and the event’s impact on the firm. Regulators / supervisors and scenarios Financial supervisors may find it useful to require firms under their jurisdiction to test certain scenarios and to report the results of this testing. There are several approaches to scenario testing that can be taken by supervisors to meet their various needs. The supervisor may be interested in an analysis of systemic risks. In this case the supervisor would create a detailed scenario dealing with a realization of the specific risk and the industry’s resulting experience. The supervisor would require all firms to test the same scenario and to report the test results in a standard form that could be compiled to give a sector-wide picture. Such predefined scenarios should be defined sufficiently narrowly to make the outcomes from different companies comparable. If these scenarios are defined too broadly, different companies might interpret them in different ways, making the outcomes less useful for the assessment of systemic risks. There is however an inherent tension between specifying a scenario very detailed but where it become irrelevant for many insurers and a very general description where the evaluation becomes arbitrary.


The supervisor could also require all firms under its jurisdiction to test specific scenarios designed to assess companies’ exposure to specific risks. Results of these tests would enable the supervisor to assess the relative solvency and financial condition of all firms. Such scenarios are more similar to sensitivity tests in their nature. Each is only likely to involve very few risk factors. Nonetheless, the supervisor, in describing these scenarios, should take care that the scenario descriptions are sufficiently clear and specific so as to produce comparable results across all firms. Given the interconnectedness of globally operating financial firms, stress tests and scenario analysis conducted on a global level should also be contemplated. These would consist of a small number of events that are relevant for the global economy. Such events would likely be global financial catastrophes similar to the Great Depression or the current credit crisis. It could also include a sever pandemic event or a large natural catastrophe (e.g. a Tsunami impacting the eastern seaboard of the US) or a man made catastrophe (e.g. a terrorist attack using nuclear weapons). In order to assess the quality of the risk management and the risk culture of a supervised company, supervisors can ask companies to formulate sufficiently realistic company-specific scenarios, which have the potential to lead to financial distress for the company. This requires the company to formulate scenarios specific to its particular exposure to risk. The formulation of company specific scenarios requires the interaction of different functions within the firm as well as interaction with senior management and the board. The quality of the formulation and the evaluation of such scenarios can be an excellent indicator of the quality of the firm’s risk management and risk culture. A badly formulated scenario may be a sign there is insufficient communication within the firm, and a lack of interest or know-how in the analysis of exposure to risk. Assessment of internal models Scenarios can also be used as a reasonableness check for stochastically driven internal models by providing an assessment of the reasonableness of the outcomes of a given internal model. In particular, scenarios leading to extreme losses can be used to assess whether the internal model assigns reasonable probabilities to such losses. If the likelihood of a particular scenario occurring can be estimated independently and the probability of the outcome of that scenario generated by the internal model is significantly different, one might suspect the internal model contains a significant error. For example, if the evaluation of a given scenario results in a large loss of at least USD 200m with a probability of 1%, but the probability of a corresponding loss as generated by the internal model is only 0.01%, this might indicate that the internal model does not adequately consider such outcomes. The use of scenarios to reality check a given internal model can be useful even if the probability of the scenario cannot be reliably calculated. In the example above, if the internal model allows for a loss of at least USD 200m only once in 1000 years, but such a


loss results from the evaluation of a reasonably probable scenario, then one can assess qualitatively whether this is believed to be a realistic assessment probability of occurrence of the scenario. Such reasonableness checks are important since in most cases, the methodologies and mathematical approaches used in internal models break down in extreme cases. Models are often calibrated (implicitly or explicitly) to normal situations (e.g. parameters based on past experiences without catastrophes, assuming unlimited capital mobility in consolidated models for insurance groups etc.). These details of calibration or these technical assumptions are often not sufficiently clear to the users of models. Scenarios can help find and communicate the limits of these models. Defining the Firm’s Risk Appetite

• Risk appetite must underpin a firm’s strategy and the implementation of an appropriate governance and risk management framework. It is imperative for the board of directors and senior management to have clarity on how to trade potential profit against possible losses. The risk appetite should be defined along multiple dimensions. It is not sufficient to only consider catastrophic risks or the yearly P&L, but different elements should be taken in account in conjunction, e.g., down-grading risks and catastrophic risks at the same time.

Management needs to make a trade-off between these different classes of risks. Does it want to have a smooth yearly P&L while incurring a large catastrophic risk or does it prefer to minimize catastrophic risks while foregoing profits? There is no single correct choice and much depends on the type of business, the firm’s current financial state or risk tolerance, the competitive environment and many other factors. For management to decide on the appropriate strategy, it needs to have information not only on expected but also on possible but less likely future developments. To assess the down-grading risk, events that occur with a likelihood of approximately once every 10 years are relevant. To gain insight into catastrophic risks, rarer and more adverse events are relevant. Here we consider that events that occur once in every 50 to 100 years or even rarer. These risks differ not only quantitatively but are qualitatively different. The type of event is relevant too and different events can impact on the firm differently, even if they cause the same amount of losses in immediate financial terms. For example, a natural catastrophe causing a loss of CHF 1bn for a reinsurer has a very different impact than the same amount lost due to bad investments. The former is likely seen as a normal business occurrence while the latter is seen as a lack of competency leading to a reputational loss. Figure 4 below illustrates this view on the types of losses which might be considered “acceptable” or not from a reputational point of view.


Figure 4: Risk Appetite Therefore, scenarios clearly have a place in assisting in defining the risk appetite of the company. Different scenarios should be formulated which allow for an informed discussion with the board, focusing not only on catastrophic losses but on different magnitudes, and types of losses. Together with an analysis of profit and loss trade-offs and the firm’s risk tolerance, this will result in a clearly defined risk appetite. Constructing Scenarios Types of scenarios There are different types of scenarios with different uses and applications. We distinguish among:

• Reverse Scenarios • Historical Scenarios • Synthetic Scenarios • Company Specific Scenarios • Single-Event Scenarios. • Multi-Event Scenarios • Global Scenarios

Reverse scenarios The purpose of reverse scenarios is to find events, which could give rise to a particular financial loss. For example, what level of mortality could cause a life insurer to become insolvent? Constructing a reverse scenario is equivalent to the construction of an event that leads to the given specified loss. The formulation of reverse scenarios requires a very


good understanding of the potential risks a company faces and of its exposures. Reverse scenarios can also be a powerful tool to conduct a reasonableness check on the result of internal models. Historical scenarios A historical scenario is based on an observed historical event. For example, a scenario might be constructed based on the stock market crash of 2000/2001, on the 1918/1919 Spanish flu pandemic, or on the 1923 Great Kanto earthquake. A major advantage of a scenario based on a historical event is that it can be more easily communicated since the event has actually occurred. As a further advantage, since such a scenario is based on an observed event, data with regards to its short, medium, and long-term impact might be available. In particular, the impact of the event on other risk factors, such as interest rates, equity markets, and inflation can be studied, as can its pre-history, i.e. the history leading up to the event. Clearly, the circumstances surrounding the historical event will be different from the current situation. Therefore, in constructing the scenario, appropriate adjustments need to be applied. For the Spanish flu for instance, these might include increase in population size, increased global mobility and improved medical conditions. In many scenarios, financial values will have to be adjusted for inflation to make the values more consistent with current values. Great care has to be taken when a historical scenario relates to the financial markets. Financial markets are constantly evolving and an event that had little impact in the past might have a big impact now or vice versa Other examples of factors that require adjustment in historical scenarios include:

• Changes in population movement • Medical advances • New technologies, e.g. computers • Globalized and more closely linked financial markets • New asset classes owned by insurers • Management behavior on common incentivisation schemes • Different valuations used, making historical data not directly comparable to

current values Such adjustments cannot realistically consider all differences between the present situation, and that of the historical scenario. The idea is to use historical events as best as possible given the limitations on our information and resources to assist in dictating helpful scenarios for the company. Synthetic scenarios In contrast to historical scenarios, synthetic scenarios describe events which have not yet been observed and which thus can be more easily tailored to a specific situation of


interest. Synthetic scenarios might occur but have not been observed, for instance, because of sheer luck, or because certain risks did not previously exist. Synthetic scenarios require more assumptions than do history-based scenarios. For this reason they are subject to more questioning and can be more difficult to communicate and discuss both within the company and with third parties. Examples of synthetic scenarios include events capturing potential losses due to new technologies, for instance nano-technology; a not-yet observed financial market event; a dirty bomb exploding in a major financial center; etc. Company-specific scenarios Depending on a firm's exposure to risk, very specific events might have a large and unfavourable financial impact. Company-specific scenarios specify events that are tailored to the specific risk exposure of a firm or of a particular portfolio within the firm. For example, if the firm has a unique product or its offerings are highly concentrated in a particular product, then the degree of its exposure to related risks may be significantly different from other similar firms. Single event scenarios Many scenarios can be described by only a single event. For example, a hail storm will likely not lead to a cascade of further events. Such a scenario may be a mild test for most insurers but could be potentially devastating for certain insurers. These scenarios are generally well described by defining the initial event. The evaluation of such scenarios is relatively straightforward as management actions subsequent to the event are not very relevant and not likely to add to the scenario. Multi-event scenarios Some initial events lead to a cascade of relevant further events, possibly over months or years. This is the case particularly for severe initial events that impact a number of financial institutions. Examples are global financial market crises, large natural catastrophes or very severe terror events. For such events, the evaluation of the financial impact on a firm has to take into account the actions management can take during the unfolding of the scenario. Global scenarios Some scenarios affect insurers and other financial institutions on a global level. Examples are the Great Depression of 1929, the Influenza Pandemic of 1918 and the credit crisis that began in 2007. Such scenarios tend to unfold over years and often lead to a substantially changed environment. Global scenarios are particularly useful to assess global interdependencies between financial institutions operating in different regions, the vulnerabilities of different regional markets and the linkages between banks, insurers, pension funds and other market players.


It is likely that in view of the emphasis on systemic risk and the linkages between different economic sectors, global scenarios will play an increasing role in the supervision. The figure below shows an example of a global scenario, detailing the impact of a possible development of the credit crisis on different markets and regions.

Figure 4: Example of a Global Scenario

Cultural issues Courage and fortitude By its very nature, stress testing is focused on situations, which cause some sort of difficulty for the firm. When times are strained, many people, including senior management and boards of directors, are open to considering a variety of troubling scenarios. However, when times are good and have been good for some extended period, memories of bad times fade and optimism dominates. The purpose of scenario analysis is not to predict future events but rather to stimulate the firm and management to be prepared in case a disruptive event occurs. However, when one presents historical evidence of catastrophes (e.g. The Great Depression of 1929 or the Influenza Pandemic of 1918), this is often met with a response that the situation has changed and such events can no longer occur. In good times, such scenarios are not seen as reasonable since they are based upon events in the distant past and do not correspond to the typical experience of management. This typically human behaviour can create a considerable obstacle for the actuary and risk manager. Both are concerned with caution and working to see that the firm has sufficient resources to meet virtually all difficulties. Particularly in good times, their


natural caution and concern with things that could possibly go wrong will often meet with resistance from others and at times, even scorn and ridicule. In such circumstances, a few risk managers and actuaries may pull back and, for fear of being scorned, not present troubling results. But, when the events formulated and evaluated in scenario analysis are so mild as to desensitize senior management to potential risks, the exercise is of little or no value and can actually be harmful as they might cause management to become over-confident. While such behaviour on the part of risk managers might be understandable, it is not consistent with their professional obligations. This discussion points to the need for the risk manager to have a great deal of courage and fortitude. Risk culture Courage and fortitude are particularly required of the risk manager when a firm’s risk culture is not strong. A firm may have a significant risk management organization and may appear to have an appropriate culture. However, if senior management and the board are not active participants and do not consider risk to the firm when taking strategic and tactical decisions, the risk culture cannot be considered satisfactory. In this circumstance particularly, the presentation of results of scenarios that seem to be pessimistic and removed from the current situation may not be well received or taken into consideration in the firm’s planning and operations. Then the perception of the risk manager within the firm becomes rather negative. A risk manager should strive to explain the relevance of scenario testing to those with responsibility for the firm. In these circumstances this may not be easy to do, thus making the need for courage and fortitude all the greater when risk culture is weak. Imagination Scenarios describe hypothetical events, events that are synthetic or are based on historical precedents. They are not meant to be predictions but rather a basis for tests of a firm’s financial strength. Construction of scenarios requires the risk manager to describe events which are troublesome. This requires an appreciation of long term historical experience, an understanding of current trends and developments in the general and firm-specific environments, a keen sense of how things might develop in the future, and a strong imagination. A historical perspective is very important but it must encompass a sufficiently long time-frame. Serious errors in risk management have followed from the use of models and assumptions based upon short time spans that did not include unfavorable experience. For example, many economic models used during the latter part of the twentieth century and the early twenty-first century did not recognize the experience of the Great Depression in the 1930s. Had some of these models been calibrated to data spanning a longer period, they would likely have provided much better guidance for risk managers and financial firms. There is a tendency for financial markets to operate in very long term cycles. While history may not repeat itself exactly, it is the duty of the risk manager


to imagine how the downside of a financial cycle might manifest itself in the current environment. In formulating scenarios, it is important to have a good understanding of recent developments that have had or are likely to have an important influence on the type of risk that can occur or on the likelihood of certain events occurring. An example of this is the increasing effect of technology on society, in particular on the operation of financial markets. The increasing speed with which information is transmitted is another phenomenon that can profoundly affect consequent reaction to significant events and create repercussions that may not have previously existed. Such effects should clearly enter into some scenarios. However, the formulation of scenarios in which these effects emerge in a realistic and convincing way also requires imagination. The risk manager should be open to the liberal exercise of imagination as long as this leads to plausible and relevant scenarios. Interdisciplinary teams Many scenarios involve a chain of related events and reactions to the initial events. In formulating such scenarios, it is advantageous to make use of a multidisciplinary team. In this way, the various aspects of the scenario are more likely to be represented in a more coherent, realistic and believable way. For example, in constructing a pandemic scenario, one could make use of an epidemiologist, a demographer, a financial markets expert and an actuary. It is often a good idea to consult senior management or directors when formulating scenarios since they may have concerns about the future, which deserve to be explored through scenarios. This type of consultation is also likely to increase their receptivity to the stress testing exercise. Formulation of scenarios A scenario needs to be formulated such that the financial impact on the insurer or bank can be calculated. The formulation includes a narrative outlining the initial event as well as the cascade of follow-up events. In order to be able to project the scenario using some form of an internal model, a second step in the formulation consists of the quantification of the relevant risk factors that are impacted by the events (e.g. interest rates, mortality rates etc.). Narrative The first step in formulating a scenario is to explain it in a concise, understandable narrative that outlines the initial event and the potential effects cascading from it. The narrative should explain the key assumptions and simplification that have been made. It should focus on the qualitative aspects of the scenario but also include the major quantitative assumptions. The qualitative formulation describes the effects of the initial event over the duration of the scenario. If relevant, this also includes a description of the effects not only of the risk factors, which affect the firm directly (e.g. mortality rates,


losses, interest rates, etc.) but also the effects on other market participants. This can be relevant if for example the financial position is impacted by counterparties. The narrative should be short and readable; an outline of the scenario would usually consist of not more than two pages. Below is the sketch of a narrative that depicts one possible continuation of the current credit crisis.

Narrative: Credit Crisis Continuation Over time, it becomes evident that the toxic assets are not a problem of liquidity but that they are actually a valuation problem. This leads to losses that have to be realized by financial institutions and governments. This causes the government bailouts to be much more expensive than expected, increasing the burden for tax payers substantially. Firms that betted on a transitory crisis and kept on to their illiquid assets (corporate bonds, structured products etc.) incur high losses and many fail or have to be bailed out. The US government gives up trying to keep the USD the global lead currency and starts printing money to reduce its debt. Consequently, the Chinese government and other owners of US debt start selling US government bonds. This leads to an increasingly fast collapse of the USD. A trade war between the US and countries that saw their foreign reserve reduced commences, and increasingly protectionist measures are implemented. Increasing international tensions and reduced cross-border trade causes ever more corporations to default, leading to generally high spreads and high default rates. Global GDB decreases and oil and commodity consumption is reduced, leading to sharply lower prices. Some sovereigns default, in particular developing countries with high debt and reserves in USD. In a number of Middle Eastern countries, income is massively reduced and – in conjunction with high birth rates and high unemployment – social unrest increases. The European Currency Union decomposes as some EU member cannot cope with the fixed currency rate anymore.


After several years, despite stagnating oil consumption, prices for oil and gas creep up. This is due not only to the social unrest in many of the oil producing countries but also due to the general depletion of the largest oil reserves. Ripple effects spread as food production, transport and heating becomes more expensive and a period of high inflation ensues.

Initial event Most scenarios focus on an initial event which may give rise to a cascade of secondary events. Since there are an infinite number of events, which one could consider, there is no immediately obvious classification system to describe or classify these events. However, it may be useful to think of most events as falling in one of three categories:

• Global events, • Regional events; or • Company-specific events.

Globally disruptive events are more likely to affect most if not all insurers and financial institutions. These events may be economic in nature such as the Great Depression of 1929 or the Credit Crisis of 2007 or related to public health, such as a pandemic. Globally disruptive events are often comprised of a sequence of different events that evolve over time; therefore, a global scenario will expose a firm to a number of related stress events. It follows that a small number of carefully chosen global scenarios should suffice to capture the main effects of a global downturn. Some regional events can affect firms that operate in a specific region or jurisdiction. These can be specific natural catastrophes, e.g. earthquakes, hurricanes or tsunamis, or exposure to public health, legal or regulatory risks. Actual examples of regional disruptive events are the Swedish Banking Crisis, the European Life Insurer Crisis of 2003, the Junk Bond Crisis of 1990 or Hurricane Katrina. Finally, firms might be exposed to idiosyncratic risks from their specific liabilities, assets and strategy. One needs to analyze their portfolios and risk exposures to arrive at appropriate company-specific scenarios. A precondition of such an analysis is detailed knowledge of the firm’s assets and liabilities. Scenario analysis done properly can be time consuming. It is therefore important that the number of events considered is kept reasonably small. The set of scenarios should capture in their totality the major potential risks the firm can face. The objective is less to predict in great detail a potential event, but rather to have a small number of generic scenarios reasonably covering the potential risks. For example, it might be sufficient for covering global financial crises to consider a Japanese style scenario (low interest rates, no growth and deflation) and a high inflation


scenario. Many potential financial crises would of course differ from the two stylized ones, but the essence of the effects is likely captured by the two extreme ones. Time evolution The sequence in which events occur can be of major consequence for the financial impact on the firm. The qualitative description therefore should not only contain the sequence of effects but also a time-line. This is particularly relevant for scenarios, which evolve over months and years or in which the effects of actions that management would take (e.g. de-risking of assets) are to be included in the evaluation of the scenario. The example below shows an illustrative time evolution of a financial market crisis patterned after the credit crisis of 2007.

Figure 5: Evolution of the Credit Crisis

Risk Dependencies Many risk factors, which enter into scenarios exhibit dependencies or relationships. These are often expressed through correlations or other technical devices. When formulating a stress scenario, it is important to incorporate dependencies as they exist in stressful circumstances. Experience has shown that in many situations dependencies under stressed situations are different from dependencies under normal situations. As a simple example, consider the dependency between mortality and the financial market. Normally, mortality and financial markets are uncorrelated. Even if the market drops substantially, this does not normally have a material effect on mortality. However, if mortality increases severely, perhaps due to a pandemic, financial markets may be affected. Since stress situations are relatively rare, historical data are often not relevant when estimating stressed dependencies. Available data might not have been derived from stressed situations, so the implied dependencies would be inappropriate for the scenario. One way of dealing with this issue is to assume that dependencies are given by a copula of a certain shape, e.g. by a copula with upper or lower tail dependency. Examples of such copulas are the Clayton and the Gumbel copula. Both of the latter are one-parameter families. Another approach is to derive dependencies between two risk factors by going one step further down the ladder of causation, trying to find common underlying factors which

Decline in Housing Prices

Collapse of Subprime Industry

Credit CrunchGlobal Recession

Default of Credit Insurers

Default of Reinsurers

Default of Corporates

Financial market entering new equilibrium

…


have an impact on both of the risk factors of interest. If this can be achieved, then the dependency between the risk factors of interest results from their common exposure to the same underlying factors. Ultimately, the final underlying factors would be independent, and all dependencies would be a consequence of common exposure to them. In practice, dependencies under stress will usually not have been observed. It would therefore then be necessary to model them based on informed judgment. Judgment can be informed through a sufficiently detailed narrative, which outlines the expected outcome given an initial event occurs. In real life, the interdependencies are an evolving, expanding web of relationships between risk factors, which might include sudden phase shifts when dependencies suddenly change, time-lagged dependencies, causal linkages and other functional and probabilistic dependencies. Simple correlations or copulas are not necessarily the right tool for defining dependencies as they do not capture the time-dependencies or the underlying causal relationships.

In the following we show stylized depictions of the dependencies of several risk factors over time.

Figure 6: Dependencies over Time

Ripple-Effects

In certain scenarios, an initial event might impact only one or a small number of risk factors. Over time, more and more risk-factors might be affected by the initial event.

Risk Factors

time

Initial Event


Immediate Dependencies

Two or more risk factors, which are causally directly linked. In this instance, a change in one risk factor causes an immediate change in the other risk factor. Examples are a share index and the price of a share that belong to the index

Figure 7: Immediate Dependencies

Time-lagged Dependencies

A risk factor is affected by the change of another risk factor after a certain amount of time. Examples are the default of a financial institution and D&O claims

Figure 8: Time-Lagged Dependencies

Feedback

A change in a risk factor causes a change in a second risk factor, which in turn causes a further change in the first risk factor etc. Examples are the collateral requirements and the market prices of a financial instrument a firm holds.


Figure 9: Feedback

Phase-Shift

A risk factor is affected by the change of another risk factor if and only if the change exceeds a certain threshold. Examples are increases in mortality and changes in equity markets where normally the financial markets are not affected by slight changes in mortality; however a sudden large increase in mortality is likely to negatively affect the financial market.

Figure 10: Phase-Shift

For the construction of a scenario, the different risk factors can be combined to denote the dependencies over time. The figure below illustrates the example of a hypothetical earthquake, which causes loss of life and property losses. The rebuilding leads to a USD depreciation, since the government is selling off its US treasury holdings.


Figure 11: Earthquake Example

Evaluation of Scenarios The evaluation of a given scenario consists in the quantification of its impact on the firm’s balance sheet. The quantification of the impact depends on the valuation framework. In many cases, it is important to gain insight into the firm’s financial state based on different valuation frameworks, e.g. economic valuation, statutory valuation etc. In many cases it might be necessary to analyze the impact not on a single balance sheet, but on several. In particular for events where a firm is in financial stress, it can be important not only to assess the economic loss, but also the impact on the statutory balance sheet, the impact on external ratings etc. For insurance groups, often guarantees and other capital and risk transfer instruments between different legal entities are in place. These instruments are often dependent on different valuations and capital standards. For example, a guarantee between two legal entities might between a parent in the European Union and a subsidiary in the US, specifying that in case the US subsidiary’s RBC ratio drops below a given value, capital will be transferred from the EU parent. In this case, the guarantee depends potentially on the Solvency II market consistent valuation and solvency capital requirements as well as on the US regulatory valuation and capital standard. In case of a material guarantees, the assessment of the impact of the scenario would have to include the evaluation of all relevant valuation and capital standards. If the scenario continues over several years, the evaluation should include the quantification of the effects of the scenario over the entire duration of the event. If the duration of the scenario is more than one year, management actions become more important and should be taken into account on a realistic basis. In the following, we discuss different aspects related to the evaluation of scenarios in more detail. We discuss secondary effects, i.e. consequences of the initial impact the


scenario has on the company, which might for instance lead to further losses. One particular issue concerns capital mobility in the context of insurance groups or conglomerates. Also, secondary effects might depend not only on the loss amount but also on the “nature” of the loss. We consider management actions, i.e. decisions, which can be taken by management while the scenario evolves and thus allow for simulating how a company would react as the scenario plays itself out and what further consequences this might create. Finally, we provide suggestions on the granularity at which a scenario should be evaluated. Secondary Effects The impact of a scenario can lead to secondary effects or even to a cascade of secondary effects. Secondary effects are consequences from the primary effects of an event and often emerge later. For example, a secondary effect of the credit crisis might be sovereign defaults as some countries might not be able to cope anymore with the debt burden imposed by the credit crisis. For example, a loss from a specified event might lead to a ratings down-grade, which in turn might trigger rating-linked debt repayment or collateral calls, or might force the company to exit certain markets etc. This in turn could lead to a liquidity strain, causing further losses, a subsequent further down-grade, lapses of policyholders and so on. As another example, the firm might be forced to sell assets as a consequence of a loss, which could lead – particularly in the case of assets, that are thinly traded – to a decrease in the market value of these assets, forcing the firm to sell even more assets and putting it under additional strain. As a specific form of secondary effects, insurance groups or conglomerates have to consider potential restrictions in capital mobility. In case the insurer incurs material losses, the supervisors of some or all local subsidiaries might require capital injections from the group and might limit capital transfers out of their jurisdiction. In such a situation, the insurer would experience an immediate and potentially devastating liquidity shock. As part of the scenario analysis, the insurer has to assess the legal and regulatory environment in which its major subsidiaries operate and realistically take the situation into account in the case of financial stress. For this it is necessary to take into account how losses flow through the group as a result of an initial loss. Therefore, the assessment of the financial situation of an insurance group or conglomerate can not only be done on group level, but should take into account the group structure and the transfer of capital and risk through the different legal entities of the group. So the initial loss in one subsidiary of the group affects the balance sheet(s) of the legal entity or entities owning the subsidiary and might trigger internal retrocession arrangements or parental guarantees, for instance.


Figure 8: Secondary Effects

It is important for the consideration of secondary impacts that in general they do not solely depend on the loss amount but also on the specifics (or nature) of the loss. For a firm losing a large amount due to an insurance loss (which is part of its accepted risk and aligns with both its business model and the expectations of its various stakeholders), the resulting secondary effect can be very different from a loss of the same magnitude due to bad investments or due to a rogue trader. The former would be seen in the market as an acceptable loss and might actually enhance the firm’s reputation if it were able to speedily pay out the corresponding claims; whereas the latter would be seen as a sign of incompetence and lead to a loss of reputation. Furthermore, the secondary effects of a given loss can depend on how the company reacts to the loss – this topic will be further discussed below under management actions. Another specific feature of the loss, which has a bearing on secondary impacts is the speed with which an insurance loss has to be paid out. This affects the liquidity position of the firm. Exposure to counterparties: In a given scenario, third parties to which the firm is exposed might also be affected by the same event that creates an initial loss to the firm and might then “feedback” as secondary effects, creating additional losses for the firm. This could for instance happen if the firm holds shares in companies which are in financial distress as a result of the event, since the share prices of these companies would then likely fall, leading to a reduction in the asset value of the firm. Other counterparties might be reinsurers to which risks have been ceded; banks to which the firm has exposures, e.g. via posted collateral, etc. Some of these exposures might already be captured by the quantified risk factors that describe the scenario (e.g. spreads or equity prices). For other material exposures, the effect of the scenario might have to be quantified individually.


In the context of secondary effects of a given scenario, the risk manager should therefore consider for example:

• The effect of a ratings down-grade, • Rating triggers, • Collateral requirements, • The liquidity of the firm, • Financial impacts and spill-overs from non-regulated entities of the group or non-

insurance entities (e.g. Banks), • Capital mobility in case of financial distress, • The impact of assets sales, • The impact on the firm’s reputation, • Policyholder lapses, • Impact on new business; and • The effect on increased cost of capital.

Time Evolution For a scenario developing in discrete stages, the financial impact should be assessed for each of the different time steps. The financial impacts during the different stages of the scenario (e.g. due to actual insurance losses, revaluation of assets or liabilities, etc.) should be aggregated to yearly losses in order to assess the yearly solvency. Risk Mitigation The evaluation of a scenario should take into account risk mitigation programs (e.g. hedging, external reinsurance, intra-group retrocession) realistically. If risk mitigation has a material influence on the financial impact of the scenario, special care has to be taken to ensure the risk mitigation will also be effective in case the scenario occurs. For example, in case of a global scenario, reinsurers to which risks have been ceded might also be affected by the event, which might impair their ability to pay out potential losses. Even more significant might be risk ceded to intra group companies. If the firm is in financial stress, the likelihood is great that other legal entities within the group are also in financial problems. Management Actions For scenarios with durations of months or years, management actions can have a material impact on the financial impact on the firm. Assumption on management actions must be realistic and take into account the information available at specific times after the initial event occurred. While the scenario has been formulated and is of course known, clairvoyance should not be assumed when formulating the management actions. It is a natural tendency for management to assume a more optimal strategy to cope with a crisis than what would actually occur. This tendency would be especially pronounced in the case where management would have information on the entire development of the


scenario. In reality, especially in case of scenarios, which play out over long time, there is often a great lack of clarity on how the situation further develops. This uncertainty then often leads to sub-optimal management actions. For this reason, management actions should be subdivided into the different discrete stages of the scenario. At the beginning of each stage, the firm should assume only knowledge of the scenario up to the stage. The firm should calculate at each stage the financial impact taking into account the management action assumed during the stage and without the management action taken. This will allow an analysis of the impact of the action. To be able to implement such an approach, the scenario needs to be sub-divided into discrete intervals and management is then supplied with information only incrementally. Ideally, to make the exercise more realistic, senior management defines the management actions while being informed on the scenario in different steps. In that way, the flow of information to senior management is more realistic and the behaviour of management can be simulated. This approach is not without drawbacks and situations can be envisaged in which senior management's actions were suboptimal, possibly resulting in pressure on the CRO to adjust the numbers and the assumed management actions. Another approach would be to undertake the simulation of management's actions using an external party which would be exposed to less pressure than people reporting to senior management.

Figure 12: Management Actions

Finally, management actions could be defined more realistically by using a “stochastic” scenario. A “stochastic” scenario consists not of a single realization of the initial event and the cascade of effects, but at each stage branches into different possible further


evolutions. Equivalently, this could be considered as a set of different scenarios all emanating from the given initial event. This approach is obviously quite time consuming and complicated and could only be applied to the most relevant scenarios. However, the advantage would be that management and all other player would obtain experience on how to make decisions in a fast changing environment with little or perhaps even conflicting information. Evaluating a scenario together with senior management using a simulation approach as outlined above is potentially the most useful way, as it helps to truly embed risk management within the firm and allows senior management to prepare for potential disruptive events. Such approaches are already used by some companies, although often more of a focus on business planning and on using very simple toy models. They are more common outside of the financial industry, for example in the training of pilots or nuclear power plant operators. Our proposal is to merge scenario analysis and a sophisticated assessment of the financial impact with an interactive senior management simulation program. This puts high demand on the preparation by the CRO and the modeling capability of the firm to have sufficiently fast interactions, i.e. the ability of risk management to quantify the impact of a given management action within a very short time. Example: An insurer analyzes its financial position over the next five year in order to find an optimal asset allocation and risk mitigation strategy. Currently, it has optimized its assets based on its economic forecast. However, the actual development might deviate from the forecast and it also considers a Japanese type scenario and a high-inflation scenario.

Figure 13: Forecast Strategy

The figure above shows that the insurer would fare well under the forecast scenario but would be insolvent eventually under the Japanese and the inflation scenario. Next the insurer considers optimizing its assets for coping with a Japanese scenario by investing in government bonds only.


Figure 14: Japan Scenario Strategy

Given such a strategy, the insurer fares well under the Japanese scenarios, slightly worse under the forecast scenario but very badly under the inflation scenario. Next the insurer optimizes its financial position for all three scenarios by trying to limit the downside under each scenario. For this, it analysis the impact of de-risking its assets partially, and implementing a macro hedge against inflation.

Figure 15: Optimized Strategy

With this strategy, the financial position is acceptable under all scenarios. It foregoes expected profit under the forecast but would not face insolvency under a high inflation or under a Japanese style scenario. Finally, the insurer fine-tunes its strategy by additionally considering intra- and extra-group reinsurance. By putting these additional measures in place, the solvency ratio can be improved for specific situations which would cause a short term financial strain.


Figure 16: Optimized Strategy with Reinsurance

Granularity The evaluation should be sufficiently granular as to allow in the analysis phase to formulate strategies and contingency plans. The following should be seen as a suggestion and the granularity might differ depending on the scenario and the purpose of the scenario analysis.

• Description of the secondary effect considered • Impact

o on assets, split by asset type o on liabilities, split by line of business o of interest rate changes, ideally split by time bucket (often insurers are not

mainly exposed to a parallel shift of the interest rate curve but to more complex movements, e.g. twists)

o of equity changes, ideally split by shares, real estate, hedge funds, private equity

o of FX rate changes o of spreads changes, ideally split by rating class

• Impact of counterparty defaults and rating migrations • The economic balance sheet before and after the scenario • Assumptions the company has made for parameters which have not been

specified • Possible changes to prescribed assumptions • Mapping of the loss (rsp. of the economic balance sheets) to the different legal

entities of the group before and after intra-group retrocession • Description and impact of possible risk mitigation strategies

o External: reinsurance, coinsurance, securitization etc. o Intra-group: guarantees, retrocession,… o Description and impact of management actions assumed

• Description of the assumption on lack of fungibility of capital • Description of where the company

o has deviated from the economic valuation framework


o used simplifications o neglected to take into account some relevant risks

If the scenario evolves over several years, the relevant information has to be split accordingly:

• Losses incurred at the different stages of the scenario • Annual economic balance sheets / losses • Annual solvency ratios • Management actions as they evolve

Analysis The main purpose of a scenario framework is not merely to obtain quantitative results, but to gain insight such that the firm can manage its risk in such a way as to cope with unexpected events. The risk manager should not merely quantify the effects of the scenario but should also formulate contingency plans. These plans can include

• risk mitigation, e.g. via reinsurance, • collateral, contingent capital etc. • risk avoidance, e.g. via change of the business model, • capital increase, • change in assets mix, • etc.

The risk manager should formulate possible management actions, which would mitigate the impact of the effects of the scenario on the firm. Depending on the scenarios considered, it might not be sufficient to consider management actions focused only on a specific scenario but they might also have to take into account other possible scenarios, milder events and the firm’s forecast. The effect of the management actions for the different scenarios should be analysed and quantified. This will allow senior management and the board of directors to decide on the optimal course of action for the firm. Conclusion and Outlook Stress testing and scenario analysis are powerful tools to assess a firm’s exposure to risks. Scenarios are intuitive and allow engaging also non-specialists and people not deeply involved in quantitative modeling. They support the deeper embedding of risk management within the wider firm.


The current credit crisis has shown that often users where not fully aware of the limits of applicability of models that they used to make business decisions. Also the crisis has highlighted the need to have a deeper understanding of systemic risks that affect not only a small number of financial institutions but large parts of the financial market. Regulators will therefore likely supplement their risk based capital requirements increasingly also with stress testing and scenario analysis. While currently stress testing is often seen as a mere complement to economic capital or solvency models, the fact that they allow also the analysis of uncertain and non quantifiable events will likely bring it more to the center. Stress testing can only be a truly powerful too when it is sufficiently embedded and used within a firm. Firms should try to engage different functions and levels of hierarchy in the scenario analysis exercise, from the choice of event, the formulation of the scenario, the evaluation of its impact to the development of contingency plans and risk mitigation strategies.

Ripple-EffectsImmediate DependenciesTime-lagged DependenciesFeedbackPhase-Shift

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IAA Paper on Scenario and Stress Testing – First DRAFTStress testing and scenario analysis in contrast does not require probabilities. It is sufficient to specify the events or sequence