Abstract
Traditionally, financial risk management has mainly focused on the types of risk that can be identified and measured. Many actuarial and statistical theories and models have been developed in the past, to quantify such risks. However, high-profile events such as Black Monday, the Asian financial crisis, 9/11 terrorist attacks, the Enron scandal, and more recently the global financial crisis, has repeatedly proven to the financial world that risks which matter to the stability of financial firms are often immeasurable and unidentifiable. Hence, simply focusing on the measurable risks is inadequate for a sound management of financial risks. In this paper, we develop a holistic framework to identify (if possible), measure (if possible), and manage the measurable, as well as the immeasurable, and the unidentifiable risks. We identify four realms of financial uncertainties and point out that each realm possesses a unique set of challenges to risk management. Moreover, we show that the tools needed to grapple each realm of uncertainty are fundamentally different, therefore stressing the importance of the need for awareness of these separate realms of uncertainty. The paper provides a discussion of methods available for assessing and managing each realm of uncertainty, and their limitations, by drawing from risk management techniques used in various fields of science and other industries.
1. Introduction
…there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – the ones we don’t know we don’t know.–Donald Rumsfeld, Defense Department Briefing 12/02/2002
Recent events, such as the 9/11 terrorist attacks, US banking crisis, global financial crisis (GFC), and the European debt crisis, which had unanticipated surprise effects on the global economy, made many people question the reasonability and adequacy of the way we look at financial risks. It is quite obvious now that simply focusing on only measurable risk is not enough to ensure the solvency of a firm. The uncertainties that matter to the solvency of a firm are almost always the immeasurable and unidentifiable ones. Hence, a much broader view of risk is needed for sound management of financial uncertainties.
The goal of this paper is to broaden the understanding of different types of financial uncertainties and develop a holistic framework to identify and manage them. In Section 2 we will start off with discussing different realms of uncertainty. Section 3 will introduce the proposed framework. Sections 4–7 will outline the challenges faced by risk managers when dealing with different realms of uncertainty and the tools available to grapple them, and finally Section 8 will conclude the paper with a general discussion.
2. Risk and beyond
Although humans have been dealing with risk since the dawn of the mankind, we have still failed to come up with a consensus definition for risk (see Gross, 2010; Rosa, 2003, for different definitions of risk). Rosa (2003: 55) points out that at one extreme, there is the positivist view that considers risk as an objective property which can be measured by probabilities, and at the other extreme there is the constructivist view which considers risk as the subjective perception of individuals, based on their personal experience and culture. 1 Under both views, our understanding of what is knowledge plays a crucial role in defining the nature of risk. Risk, whether it is objective or subjective can only be identified if and only if we have knowledge about the possible future states of the environment. In addition, the extent of our knowledge about the process that creates the risk will dictate whether the risk can be measured or not. For example, before the discovery of the AIDS virus, the risk it possessed on life insurance contracts was unidentifiable. Even after its discovery, the risk of death due to contraction of AIDS remained immeasurable, until knowledge about how it is contracted, longevity after contraction, and possible treatment methods were established. In other words, our knowledge, which is based on our experience, history, and culture, dictates what we identify and perceive as risk, and whether the identified risk can be measured.
One of the earliest attempts to distinguish measurable and immeasurable risk is the work of Knight (1921). Knight (1921) claimed that risk and uncertainty are not the same. According to Knight (1921), risk applies to situations where we possess knowledge about the possible set of future outcomes and their underlying probability distribution, whereas uncertainty applies to situations where knowledge exists about the possible set of future outcomes, but knowledge does not exist about their precise underlying probability distribution. A similar classification can be found in Oberkampf et al. (2004), where the authors classify uncertainty into two categories: Aleatory uncertainty and Epistemic uncertainty. Aleatory uncertainty is defined as the ‘inherent variation associated with the physical system or the environment under consideration’ (Oberkampf et al., 2004: 12). It applies to situations where future outcomes follow a particular known probability distribution. Thus, remaining uncertainty is inherent to the system or the environment and cannot be reduced by increasing knowledge. Hence, Aleatory uncertainty is also sometimes referred to as irreducible uncertainty, inherent uncertainty, and stochastic uncertainty. Aleatory uncertainty is a concept similar to Knight’s definition of risk. Epistemic uncertainty is defined as the uncertainty derived from ‘some level of ignorance of the system or the environment’ (Oberkampf et al., 2004: 14). Unlike Aleatory uncertainty, Epistemic uncertainty can be reduced by investing in activities that increase knowledge about the system or the environment. Epistemic uncertainty is similar to the concept of Knightian uncertainty. The distinction between Knightian risk and Knightian uncertainty is important, since people would rather face a quantifiable risk than an unquantifiable uncertainty, as shown by the Ellsberg paradox (Ellsberg, 1961). The implication of this is that the expected reward under Knightian risk and Knightian uncertainty are fundamentally different from one another. In addition, Knightian risks can be transferred through insurance, whereas Knightian uncertainty is difficult to transfer, simply because an insurer would be reluctant to take on an unquantifiable uncertainty. Furthermore, from a regulatory point of view, the capital requirement should be different for each of them as well.
Borrowing the taxonomy from Donald Rumsfeld’s quote presented at the beginning of the paper, we (Ganegoda and Evans, 2008) extended the idea of Knightian risk and Knightian uncertainty to form a conceptual framework to measure operational risk in banks, by categorizing the operational risk into three domains: known/known—the risks that we know exist and know how to model, Known/Unknown—the risks that we know exist but do not know how to model (or are difficult to model), and Unknown/Unknown—risks that we are unaware of. Although our work focuses on operational risk, the framework can be easily extended to any type of financial risk.
A similar framework has been proposed by Diebold et al. (2010), by using knowledge as measurement and knowledge as theory. The authors categorize risk into three domains—‘known’, ‘unknown’, and ‘unknowable’—which they denote using the acronym
The discussion, so far, has only been limited to the two situations where possible future outcomes are well defined (i.e., Knightian risk and Knightian uncertainty,
Although often ignored, Ambiguity is an important source of indeterminacy, which is difficult to measure and manage like risk, and it cannot be reduced by investing in knowledge as in uncertainty. A primary source of Ambiguity is the ability to understand something more than one way and respond differently. For example, even a simple term such as ‘prudent person’, which is set out in the standards of trustees, will introduce a multiple of interpretations and intersubjectivity. The difference in interpretations could be quite significant among individuals operating in different countries and cultures. Hence, the Ambiguity in terms of how each individual would interpret and respond to the situation will bring upon indeterminacies to the system or the environment in consideration. Such situations are quite common in regulatory and legal environments, emerging markets, operational, and governance processes of large financial institutions with international activities, and so forth. Best (2008: 365) states ‘Ambiguity poses genuine challenges and possibilities for the practice of governance’. Best identifies three different relationships between Ambiguity and governance. According to the author, the slipperiness of communication and openness to multiple interpretations creates governance ambiguity, and on the other hand openness to multiple interpretations can serve as a strategic asset for those who wish to exploit ambiguity to govern through ambiguity. Thirdly, Ambiguity will always act as a limit to governance.
Examples of ambiguous situations are plentiful in financial markets. For example, when board members of a firm make decisions on corporate governance, the manner in which these decisions would propagate down towards the line managers is ambiguous. It is quite possible that the final outcome could be very different than what the board members expected, simply because junior staff interpreted the decision in a different way. A classic example of how poor interpretations can lead to disastrous outcomes is the highly publicized controversial credit rating system of asset-backed securities (ABSs), which served as a catalyst to the recent subprime mortgage crisis and the consequent global market meltdown. The originate-to-distribute lending model of the banking industry, which has been partly blamed for the subprime mortgage crisis, heavily depended on the ability of rating agencies such as Moody’s to accurately value ABSs. Rating agencies used a scale similar to the ones they used to rate bonds to rate the probabilities of default on ABSs. This led investors and analysts to treat ABS tranches as being rated, say BBB the same way as a BBB-rated bond (Hull, 2009: 342). It was only later that it was realized that although a BBB-rated tranche of an ABS may have the same expected loss as a BBB-rated bond, the loss distribution of the two are significantly different. In fact, the probability of losing all the capital in the BBB-rated tranche of an ABS was significantly higher than for a BBB bond. Hull (2009: 342) points out that the fact that ABSs usually promised a higher return than a similar rated bond should have provided a signal to investors of the higher risk in ABSs. However, most market participants failed to notice this due to the Ambiguity created by similarities in the notation of the rating systems. If rating agencies used a different notation than the one they have being using for the bonds, investors might have not made the false interpretation.
Wynne (1992) points out that risk and uncertainty could only be defined by betting on the existing knowledge being correct. In other words, our interpretations of events, and the theories and models that we develop based on them, are inherently intersubjective in nature. This raises the important issue that what we consider as knowledge itself is ambiguous. To illustrate this point, we give the example of the problems created by misusing the Li’s (2000) Gaussian copula model to price collateralized debt obligations (CDOs). In early 2000, Li proposed a method to price CDOs using Gaussian copulas. Although Li himself had cast doubt on the theoretical justification of his model, bankers started using the model fiercely simply because everyone else was using it. Due to this high social commitment to the model, the method ascended to a level of paradigm to price CDOs within a small period of time. During this time many international organizations, such as the International Monetary Fund (IMF) and World Bank, have been actively supporting securitization, believing that it would deepen the financial markets and make the markets more efficient (Best, 2008). Best (2008: 369) states that ‘central to this drive to securitize was the assumption that markets were only subject to risk and uncertainty—not to Ambiguity—and that such risks were manageable’. It was around 2008 that everyone started to notice the limitations of Li’s model, which eventually paved the way to a financial crisis. The Financial Times even called the model ‘The formula that felled Wall St’ (Jones, 2009). However, if financial institutions had paid more attention to the intersubjective nature of the process that the model ascended to a paradigm, they would have understood the limitations of the model much better. Thus, overcommitment to the model could have being avoided. As the example points out, social commitment itself can ascend a model to become a paradigm without giving much thought to the underlying theoretical justification. If such ambiguities are not explicitly treated, consequences could be disastrous.
Wynne (1992: 116) states that ‘science can define a risk, or uncertainties, only by artificially ‘freezing’ a surrounding context which may or may not be this way in real-life situations’. The risk and uncertainties ignore the self-fulfilling nature of the market participants’ perception. As Shubik (1954) points out, when dealing with the future, the forecaster himself can have an influence on the outcome. For example, a stock market prediction may influence the perception of the market participants and change their intended actions, in turn making the prediction a reality. The collective belief of market participants can create asset bubbles without any underlying justification of price increments. However, when fundamentals finally catch up, the bubble will burst, surprising everyone. Best (2008: 370) states that ‘misplaced faith and over-optimism are a common feature of capitalist economies, because of their intersubjective and often self-fulfilling character’. Yet such market ambiguities are ignored consistently. This self-fulfilling character is also common to economic theory, as pointed out by MacKenzie and Millo (2003: 107). The authors study the use of the Black–Scholes option pricing theory, which they state is the ‘crown jewel’ of neoclassical economics. They state that the model ‘succeeded empirically not because it discovered pre-existing price patterns but because markets changed in ways that made its assumptions more accurate and because the theory was used in arbitrage’. Counterfactual reasoning makes us wonder what would have happened if the Black–Scholes option pricing theory had different underlying assumptions. Will the financial markets behave differently today?
3. A framework to assess uncertainty in financial markets
Extending from the discussion of the previous section, we propose a conceptual framework to analyze financial uncertainty, by defining four realms of uncertainty: (1) Knightian risk; (2) Knightian uncertainty; (3) Ambiguity; and 4) Ignorance. The proposed framework is an extension of our previous work (Ganegoda and Evans, 2008) and the
The main difference of the proposed framework, from the previous work, is that here we explicitly consider the Ambiguity in financial markets as a separate realm of uncertainty. In contrast, the
The great Greek philosopher Socrates (469–399 BC) once said ‘I know that I am intelligent, because I know that I know nothing’. We can reasonably assume that Socrates did not necessarily believe that he did not know anything. The premise of the statement is that what we consider as scientific knowledge today can be very well be proven as a fallacy tomorrow. Socrates was humble enough to admit that what he considers as correct could probably be proven wrong. As Wynne (1992) points out, risk and uncertainty are defined by betting on current knowledge being correct. The example given in Section 2, on misusage of Gaussian copula for pricing CDOs, illustrates how a model that has ascended to a status of paradigm can later be found to be flawed. Hence, a type of risk that we may believe belongs to the realm of Knightian risk may later be proven as belonging to the realm of Knightian uncertainty. Therefore, we emphasize the importance of taking a cautious attitude towards current scientific models and theories, rather than blindly considering them as absolute truth. Drawing from Wynne (1992), we postulate that Knightian risk, Knightian uncertainty, Ambiguity, and Ignorance can exist contemporaneously, in such a manner that each realm of uncertainty is overlaid on upon the other, expressing the social commitment towards knowledge (see Figure 1). In other words, we reject the notion that uncertainty exists in an objective scale from small (Knightian risk) to large (Ignorance). We postulate all other realms of uncertainty are overlaid on the realm of Ignorance. Thus, completely escaping from ignorance is almost impossible, which emphasizes the fact that current scientific knowledge can be found to be wrong in the future.
Different realms of uncertainty.
We also postulate that the realm of Knightian risk and Knightian uncertainty are overlaid on the realm of Ambiguity. The reason for this is that knowledge itself is ambiguous, as we pointed out earlier. Therefore, the models and tools we use in the realm of Knightian risk, as well as the subjective estimates we use in methods such as scenario analysis, logic tree analysis, etc. (see Section 5 for details) in the realm of Knightian uncertainty, are subject to Ambiguity.
We believe that the main advantage of the proposed framework is that it would enhance the awareness of the challenges possessed by different realms of uncertainty. This would allow risk managers to make better decisions in terms of choosing the appropriate risk management tools, understanding their limitations, and developing new tools. As it turns out, the boundaries of each realm of uncertainty are fuzzy and subject to change. Thus, a proper understanding and use of the framework should motivate not only knowledge about financial and economic theory, but also meta-knowledge about those theories. The emphasis of each realm being overlaid on another points out that ignorance will always lurk in any sort of analysis and cannot be completely removed. Therefore, special emphasis is given to crisis management in addition to risk management to manage unavoidable black swan events (see Section 7 for details).
It is important to point out that the boundaries of each realm of uncertainty will depend on the individual’s own knowledge, as well as their commitment towards the knowledge. In other words, different individuals (as well as firms) will construct different frameworks depending on the individual circumstances. For example, financial institutions with adequate expertise (i.e., knowledge) to model credit risk and high confidence in their internal models will classify credit risk as belonging to the realm of Knightian risk. In contrast, financial institutions that do not have adequate expertise and low confidence in their internal models may classify credit risk as belonging to the realm of Knightian uncertainty. Thus, one could argue that the proposed framework motivates firms to assess their capabilities, as well limitations, in terms of measuring and managing risk.
In the subsequent sections, we will present some of the tools available to measure and manage each realm of uncertainty. From this point onwards, we will use the terms Knightian risk and Knightian uncertainty to refer to Knight’s definition of risk and uncertainty. In all other instances, risk and uncertainty refer to its general usage.
4. Dealing with Knightian risk
Knightian risk refers to situations where we have a good understanding of possible future states of the world, and great confidence in the models and theories that can be used to quantify the underlying probabilities of these states. Therefore, quantifying and managing uncertainty in this realm is far easier than in other realms. Since the loss distribution is known, financial institutions can price their products accordingly, to cover the expected losses and then hold capital or buy (re)insurance to safeguard against unexpected losses (ULs). In the realm of Knightian risk it is easy to arrange insurance by pooling idiosyncratic risk, given that contracts can be designed to remove adverse selection and moral hazard. Any defaults of institutions in the realm of Knightian risk are not informational failures, but rather the result of inadequate economic capital (Diebold et al., 2010).
Market risk for banks, and certain business lines such as automobiles, fire, and life insurers, falls under the realm of Knightian risk (Kunreuther and Pauly, 2010; Kuritzkes and Schuermann, 2010). For these types of risk, the models are well developed, and financial institutions have large amounts of data at their disposal to estimate the loss distribution (or the return distribution) with a high level of confidence. Once the loss distribution is estimated, then the firm can use methods such as value-at-risk (VaR) or conditional value-at-risk (CVaR) to determine the required economic capital.
To illustrate this with an example, consider an insurer who underwrites automobile insurance and fire insurance for homes. Usually, a large number of policies are sold for automobile and fire insurance. Therefore, the insurer will have a rich set of data to comfortably estimate the frequency and severity of claims for each business line with satisfactory accuracy. In normal circumstances it is reasonable to assume that the two lines of business are independent. By using the independent assumption, one could easily combine the loss distributions of the business lines by using techniques, such as Monte Carlo simulations, to obtain the aggregate loss distribution for the insurer as given in Figure 2. Finally, the VaR can be computed by taking the percentile of the aggregate loss distribution at the desired confidence level. It is usual to take confidence levels in the range of 97–99% and higher (Basel II recommends using 99.9% for banks). The UL is defined as the difference between the VaR and the expected loss (EL). The insurer can adjust the prices of his contracts to cover the expected losses, and then hold economic capital or take up reinsurance to buffer against ULs.
Aggregate loss distribution.
Holding capital is expensive and therefore financial institutions only hold enough economic capital to ensure survivability up to a certain pre-determined probability (say 99%). If the estimated tail of the aggregate loss distribution is fatter than that of the true distribution, the firm will be holding more capital than it needs. This would be inefficient, as the firm could have invested the extra capital elsewhere for higher returns. If the estimated tail is thinner than the true distribution, the firm will be holding less capital than it should. This would increase the financial distress costs for the firm. In order to hold the correct amount of economic capital, the firm needs to be able to estimate the tail of the distribution accurately. However, in most instances, this is a challenging task. In the previous example, although it is reasonable to assume the two business lines are independent under general conditions, the assumption can be violated as we move towards the tail of the aggregate loss distribution. For example, during the 9/11 terrorist attacks many insurance lines, which are generally considered independent, such as workers’ compensation, life, health, disability, and general liability insurance, were triggered simultaneously. Hence, as we move along the distribution to its tail region, standard statistical relationships may fall apart, moving us out from the realm of Knightian risk and into the other realms of uncertainty. The challenges and the tools needed to deal with these realms are quite different. These are discussed in subsequent sections.
5. Dealing with Knightian uncertainty
As we move out from the realm of Knightian risk to Knightian uncertainty, life tends to become harder. In this realm, we have knowledge about possible future states, but cannot measure their underlying probabilities with accuracy. There are many reasons why one might fail to estimate the underlying probability distribution. They include insufficient data, limitations of theory and models, wild randomness, and high-degree unique events.
Insufficient data is one of the major reasons behind not being able to estimate the underlying probability distribution. This is often the case with low-frequency–high-severity (LF/HS) events such as natural disasters. Lack of well-developed theories and models is another reason for not being able to estimate the underlying probability distribution. This is the case with operational risk and certain applications of credit risk. Measuring the risk of tsunamis is a classic example of the challenges posed by both insufficient data and limited theory. Measuring the risk of tsunamis is difficult, since it requires modeling of complex multiphase (water, air, solid) interactions in three-dimensional space. A publication by the National Research Council of the United States (2011: 50–51) states that ‘some hydrodynamic fundamentals (e.g., turbulence) remain unsolved’, and therefore ‘… there is inherent uncertainty in the models and the accuracy of topographic and bathymetric data that precludes the possibility of a completely accurate and precise tsunami inundation model’. This publication further points out the challenges created by lack of data. For example, scientists still do not have bathymetric data with appropriate resolution for certain coastal regions, such as Alaska, to carry out inundation modeling (National Research Council (U.S.), 2011: 50).
Many types of risk, such as market risk, operational risk, and natural perils, follow heavy-tailed distributions. For heavy-tailed risks, an extreme single observation can disproportionately impact the aggregate outcome. Mandelbrot and Taleb (2007) call this phenomena wild randomness. Since aggregate outcome for heavy-tailed risks is driven by few extreme observations, uncertainty of a given risk measure for a heavy-tailed risk is much greater than for a light-tailed risk. To illustrate this, let us first explain the concept of mild randomness, as defined by Mandelbrot and Taleb (2007). Mild randomness applies to situations in which few extreme observations cannot impact the aggregate disproportionately. In other words, the risk events follow a light-tailed distribution, such as Normal or Gamma distribution. An example is the longevity risk handled by a life insurance business. In this particular situation, although it is possible for an individual to live up to an amazing age of (say) 130 years, the insurer can confidently rule out an extreme observation of an individual surviving for a few hundred years. Hence, the inability to accurately measure the probabilities of extreme events does not necessarily increase the Knightian uncertainty for light-tailed risks, as those events can be disregarded as outliers from the analysis. The implication of this is that insurer can accurately estimate a risk measure, such as mean or standard deviation of age at death, either by analyzing a large enough portfolio or by simply ignoring the outliers. Here, the standard statistics, such as mean, standard deviation, and correlation, remain useful in describing the longevity risk. In contrast, for wild random variables, an extreme event that is a few thousand times larger than the average cannot be ruled out from the analysis. Therefore, standard statistical measures, such as mean, standard deviation, and correlation, will no longer provide a meaningful description of the risk. 4 An example is the long-term market risk of investing in an index fund. Using daily returns of the S&P500 index, Estrada (2008) shows that the average daily return of the index for the sample period of 1927–2006 was 0.03%, but the maximum daily return for the period was 16.6% (55,233.3% larger than the average), and the minimum was ™22.61% (−68,333.3% smaller than the average). The aggregate outcome, in this particular example the long-term performance of the investment, is largely determined by just a few extreme observations. Therefore, the mean and standard deviations hardly provide any useful information. In fact, for an investment made from 1927 to 2006 in the S&P500 index, the author shows that by not being invested in the best 10 days of the market, the terminal wealth would decrease by 64%, whereas by avoiding the worst 10 days of the market, the terminal wealth would increase by 202.5%, relative to a passive investment strategy. This demonstrates the disproportionate impact of the extreme events on the aggregate outcome and the importance of properly accounting for those extreme events. In other words, in contrast to light-tailed risks, the uncertainty of risk measure for a heavy-tailed risk would be largely determined by the ability to accurately estimate the probabilities of the extreme events. Estimating the probabilities of those few extreme events, which determines the aggregate outcome, using conventional statistical techniques is impossible, since it would require observing thousands of years of data. A method to overcome the problem is to develop a catastrophic (CAT) model, by modeling the process that creates the extreme events. Such models have been developed by boutique companies, such as Risk Management Solutions Inc. (RMS) and EQECAT, to estimate insurance losses from natural perils by using the latest developments in seismological and meteorological sciences, to model how a natural catastrophe may arise. Such models do not require past observations in order to estimate a loss from natural catastrophes. Although CAT models provide valuable insights, there are still many uncertainties involved with these models due to the limited understanding of the underlying risk processes, and the limitations of the theories on which the models are based. Therefore, CAT models can be considered as useful tools to reduce the Knightian uncertainty of heavy-tailed risks, but they are not a complete solution to the estimation problem.
Another area that falls under the realm of Knightian uncertainty is high-degree unique events. Probabilities of high-degree unique events are difficult or even impossible to quantify, because the circumstances that lead up to the event and surrounds it are so unique that it is unlikely that particular exact set of circumstances would prevail again in the future. Such events are frequently met in operational risk. To illustrate this point we give an example of a record-setting fine imposed by Britain’s Financial Services Authority (FSA) on J.P. Morgan Securities Ltd In 2010, the FSA imposed a £33.32 million (US$49.12 million) fine on J.P. Morgan Securities Ltd, for not segregating the client funds held by its futures and options business with the firm’s own funds, following a merger (FSA, 2010). The FSA ruled that J.P. Morgan Securities Ltd had not committed any deliberate misconduct nor incorrect financial reporting. The firm self-reported the issue as soon as it was discovered and immediately remedied the situation. Taking these factors into account, the £33.32 million fine included a 30% discount, or otherwise the fine would have been £47.6 million. Although a similar incident could occur in another securities firm in the future, the circumstances surrounding the incident could turn out be quite different from those of J.P Morgan Securities Ltd. The fact that this regulatory breach had persisted for several years without been detected, despite correct financial reporting and no deliberate misconduct, is quite a unique situation. Furthermore, the large fine imposed by the FSA also means that, in the future, an identical incident would probably not occur, as the large fine has sent a warning message to the industry.
To cope with Knightian uncertainty one needs to use a different set of tools than the ones used for Knightian risk. The main challenge in the realm of Knightian uncertainty arises from lack of knowledge. Thus, the pursuit of activities that leads to the evolution of theories and understanding of our surroundings is vital. Furthermore, in terms of assessing the uncertainty, even if one is unable to measure the exact probabilities of possible future events, one could still use methods such as stress testing and logic trees to quantify the possible impact of uncertain events. In addition, problems of inadequate data can be solved by drawing from different sources of information, such as external databases and expert opinions. These topics are discussed next.
5.1. Investing in knowledge
One of the obvious methods to deal with Knightian uncertainty is to invest in knowledge. This could include, for example, collecting data, investing in research (e.g., for better understanding of natural hazards), and collaboration between financial institutions to develop better models and share their experience. Although such activities would improve our understanding of the possible future and move us away from the realm of Knightian uncertainty towards Knightian risk, there are many barriers to increasing knowledge.
For certain types of risk, collecting data can be quite difficult or even impossible. For example, collecting data on LF/HS events necessitates waiting for long periods of time until such events occur, or an insurer who provides protection for a nuclear plant would need data on nuclear explosions, which would be almost impossible to obtain. In such situations other methods need to be considered, as collecting historical losses is not an option. There are also situations in which collecting data is simply too expensive. Referring to our earlier example on modeling tsunamis, collecting bathymetric data on coastal areas with appropriate resolution is quite expensive and might even need government funding, as well as government approval. Unless the industry receives government backing, no single insurer would be able to undertake such a task.
Investing in internal research and development (R&D) activities is an essential requirement for better risk management. A collaborative working environment between financial institutions, academics, and regulators is needed for successful research and knowledge sharing. However, there are many barriers for R&D activities in the financial services industry. Firstly, academics and financial institutions find it difficult to collaborate, due to conflict of interest. Academia prefers to publish new-found knowledge as soon as possible, while firms prefer to use it for comparative advantage. Collaboration between financial institutions is also difficult, as they do not want to share information about their proprietary models and confidential data. Furthermore, cost is also a significant barrier for R&D, as many small-to-medium size firms might find it too costly to run their own R&D programs. Sands (2011) reports that many US banks had invested in R&D before the GFC, but R&D budgets fell immediately after the crisis.
5.2. Fractal market analysis
Traditional asset pricing models, such as the Capital Asset Pricing Model (CAPM), Arbitrage Pricing Theory (APT), Black–Scholes option pricing model, and risk models such as the Merton model for credit risk, are based on the assumptions of Normal distributions and Brownian motions. The use of Normal distributions and Brownian motions are usually justified by the Efficient Market Hypothesis (EMH). However, as discussed earlier, most of the variables found in the financial world do not adhere to the Gaussian assumption, particularly those risk processes exhibiting wild randomness. Hence, one would need to look beyond the traditional models and the assumptions they are based on in order to reduce the Knightian uncertainty involved with extreme events such as market crashes, large insurance losses, liquidity black holes, etc.
The recent advancements in fractal statistics and other mathematical theories, such as chaos theory, has led to the development of new theories and tools to better model systems and processes that exhibit wild randomness.
5
The Fractal Market Hypothesis (FMH) (Jain and Gupta, 1987; Peters, 1994) is an alternate theory that has been put forward to address the shortcomings of the traditional EMH. The FMH focuses on the liquidity of the financial markets. In contrast to the EMH, which makes the overly simplified assumption of rational and homogenous investors, the FMH assumes markets consist of heterogeneous investors with different investment horizons who help markets to stay liquid and stable. Peters (1994: 47) states that: As long as investors with different investment horizons are participating, a panic at one horizon can be absorbed by the other investment horizons as a buying (or selling) opportunity. However, if the entire market has the same investment horizon, then the market becomes unstable. The lack of liquidity turns into panic.
In contrast to the EMH, the FMH implies that the markets follow a Stable Pareto distribution with high peaks and fat tails. Extreme price movements caused by discontinuous jumps and turbulences are not uncommon under the FMH. Hence, the FMH provides a more realistic representation of the wild randomness observed in the financial markets than the EMH. Furthermore, the FMH hypothesizes that financial markets exhibit a fractal structure, which provides a natural statistical framework to model the conflicting local randomness and global determinism tied to economic cycles observed in financial markets. The fractality of the markets implies that history plays an important role in determining the future states of the markets and markets are at least partially predictable. The FMH also emphasizes the importance of modeling the behavior of the market agents. Under the FMH, information is valued differently by investors with different investment horizons. How each group of investors will react to the information will dictate the stability of the market. The central argument in the FMH is that the market is stable when it maintains a fractal structure. Certain behaviors of market participants that make the investment horizons of all investors become fairly uniform will lead to a loss in the fractal structure. Hence, the FMH stresses the importance of explicitly accounting for the Ambiguity of the behavior of market participants in a risk management framework (this topic is discussed in detail in Section 6.1).
The FMH provides the theoretical grounds to go beyond the traditional concepts to model financial variables with wild randomness. Hence, fractal market analysis may provide a better understanding of the extreme events observed in the financial markets and reduce the Knightian uncertainty involved with wild random variables. However, use of the FMH means a change in the fundamental way we look at financial markets. Therefore, a move from the traditional Gaussian environment to a Stable Paretian environment would require changes to the underlying assumptions in the CAPM, APT, Black–Scholes option pricing model, Merton model, etc. In other words, although fractal analysis may account for the extreme outliers, it comes at the cost of discounting the current paradigms of economic and finance theory.
5.3. Scenario analysis and stress testing
It has been argued that, when faced with uncertainty, agents will make choices which would maximize the expected utility under the worst case scenario (Gilboa and Schmeidler, 1989). Therefore, well-articulated stress testing procedures are a natural way of incorporating Knightian uncertainty in modeling. Stress testing involves examining the health of a financial institution under various extreme market scenarios. Usually, scenarios used for stress testing are LF/HS events that are hard to quantify in probability. Stress testing does not require the exact probabilities of the scenarios; it will focus on whether, if the scenario occurs, can the institution remain solvent?
The most challenging part of stress testing is to generate plausible future scenarios. The obvious starting point is to use historical extreme scenarios. For example, an Australian insurance company may stress test against a tsunami similar in magnitude to the 2004 Indian Ocean tsunami hitting the coasts of Sydney. The insurer can decide not to include such a scenario in the analysis if there are scientific reasons to believe a tsunami with a similar magnitude hitting the coasts of Sydney is impossible. However, other than for a scientific reason, one should not remove a scenario from the analysis just because it has not happened in the past, since even an extremely unlikely event will eventually occur given enough time. This in fact is a statistical law (Rootzén and Klüppelberg, 1999: 551).
If the risk of a catastrophe tomorrow is greater than p percent (where p may be as small as 0.1% or even smaller) every day, then the catastrophe will happen (sooner or later).
Ignoring possible catastrophic events because the probability of their occurrence is low can have serious consequences. A classic example of this is the 2004 Indian Ocean tsunami. Before 2004, the only major tsunami to hit the Indian subcontinent was the Krakatoa eruption in 1883. Therefore, the subcontinent did not have a tsunami warning system prior to 2004, as the authorities ignored the threat of such an event because of its low probability. As there was no warning system, nearly all the victims were taken by complete surprise, despite the fact that the tsunami took several hours to hit the shores after the underwater earthquake. A number of lives could have been saved had the authorities monitored the threat despite its low probability.
Usually, when one changes a variable in a system by a significant degree, the other variables also change. This should be taken into account when designing scenarios. When using historic scenarios, it is possible to allow for contemporaneous changes of variables by setting all the variables in the system to historic values. For example, a bank that wishes to stress test against extreme daily equity market movements may set the changes in all market variables equal to those changes on 20 October 20 1987, when the ASX Ordinaries Accumulation index fell by 25%. If hypothetical scenarios are considered, one may separate the core variables and peripheral variables in the system, and regress the peripheral variables on core variables to obtain forecasts for the peripheral variables under stressed conditions (Hull, 2009: 356; Kupiec, 2002). This method is known as conditional stress testing.
In certain applications, such as analyzing path-dependent financial instruments (e.g., barrier options), the volatility of the variables is an important consideration. Typically, during market turmoil, the volatility of variables such as interest rates and exchange rates tends to rise. Furthermore, regular correlation relationships between asset classes tend to break down, as was proven during the GFC. Construction of successful scenarios requires taking into account the breakdown of relationships between variables, increased correlation between assets/perils, and increased volatility. For example, an insurer selling motor insurance and boat insurance needs to relax the assumption that the two lines are independent, when stress testing against a catastrophic hurricane.
A market shock may lead to flight to quality and create shortage of liquidity, as happened in 2007. Hull (2009: 356) points out that such knock-on effects resulting from different financial firms reacting similarly to the shock need to be taken into account when developing scenarios. Only focusing on the immediate effect of a shock would be unrealistic. Knock-on effects are sometime difficult to determine due to Ambiguity of post-crisis social behavior. For example, it has been theorized by Epstein and Schneider (2008) that under Knightian uncertainty agents react asymmetrically to information by discounting good news and overreacting to bad news. This has been confirmed by Williams (2009) by using US data. However, using Australian data Bird and Yeung (2012) show that during times of low Knightian uncertainty and positive market sentiment asymmetry in market response may reverse such that agents may overreact to good news and discount bad news. The authors argue that the market sentiment has an opposite effect than the one Knightian uncertainty has on how investors react to information. In other words, Bird and Yeung’s (2012) results indicate that agents may not deal with Knightian uncertainty consistently as expected. In such situations, Ambiguity of the behavior of the market participants needs to be explicitly accounted for when creating scenarios. We shall discuss the methods to deal with Ambiguity in more detail later, in Section 6.
An alternative way to generate scenarios for stress testing is reverse stress testing. Reverse stress testing involves utilizing search algorithms to find scenarios which will lead to a loss that is large enough to make the firm insolvent. Reverse stress testing asks the question: ‘How much should the market move in order for the firm to become insolvent?’ Hull (2009: 357) points out that reverse stress testing has the disadvantage of generating totally unreasonable scenarios. Nevertheless, the scenarios generated by the search algorithm can be useful for the stress testing committee, as a starting point for building plausible scenarios.
5.4. Use of logic trees and simulation techniques
The distribution of possible future events cannot be estimated when there are larger uncertainties surrounding the underlying model. The uncertainty of the model could be due to uncertain parameter values of the model or competing alternative mathematical relationships. In such situations, logic trees are a useful tool to assess the uncertainty, by obtaining confidence bounds. There are many different types of logic trees available, depending on need. Some of them include fault trees, success trees, attack trees, event trees, probability trees, and decision trees. To analyze uncertainty, fault trees, success trees, attack trees, and event trees are generally used. Decision analysis is generally carried out using probability trees and decision trees (Dillon-Merrill et al., 2008). The two basic components of logic trees are nodes and branches. Nodes are input points of the uncertain parameters (or mathematical relationships). The branches connect nodes by representing the possible alternative input values. The alternative sets of input values are assigned relative weights by experts, based on their assessment of the credibility of the input. Then the output is computed by evaluating all possible paths along the logic tree.
To illustrate how logic trees can be used when there are large uncertainties surrounding the underlying model, we present the following simple example of quantifying the possible loss from a residential mortgage-backed security (RMBS). Let us assume that we are uncertain about the quality of the underwriting standard of the underlying mortgages. There are two possible underwriting standards: prime and subprime. The default rate for the two standards is fundamentally different. Furthermore, there is the possibility of the housing market collapsing in the near future, which in turn will impact differently on the default rate (di) and the recovery rate (ri) for the prime mortgages and the subprime mortgages. To make things further complicated, there are two competing models, M1 and M2, to compute the expected loss by using alternative dependence structures of the mortgages. To analyze the situation, we can construct a logic tree, as given in Figure 3. The first branch of the tree presents the two possible underwriting standards with weights w1 and (1-w1) . In the second branch, the possible default rates and the recovery rates are set based on the condition of the housing market. The final branch feeds the inputs into the two alternative models. The output of this simple example is eight expected loss calculations based on alternative assumptions and models. The range of these values quantifies the uncertainty in the estimates.
An application of logic trees.
It is also possible to incorporate Monte Carlo simulations for branches of the logic tree, so that uncertain parameters are sampled from a distribution. In our example, it is possible to include a Monte Carlo step in the second branch, to sample default rates and recovery rates from two probability distributions. Using the Monte Carlo method, one could obtain a range of outputs in order to obtain a confidence band on possible losses.
Logic trees are popular in modeling situations with uncertainty, as they are tractable, can easily extend to incorporate alternative assumptions and parameters, and are a useful tool in communicating modeling assumptions to different stakeholders. Logic trees have been found to be quite useful in modeling natural catastrophes. A detailed exposition of the use of logic trees in catastrophic modeling and a simple example demonstrating the use of logic trees to quantify the housing structural damage by an earthquake based on alternative assumptions of slip rates, underlying soils, and empirical attenuation models can be found in Grossi et al. (2005: 74).
The main drawback of logic trees is that they rely heavily on the subjective weights provided by the experts. Subjective estimates of the experts are ambiguous, due to the possibility that they are contaminated with cognitive biases (this topic is discussed in detail in Section 6.1). Therefore, the final results still contain some uncertainty.
5.5. Combining different data sources
Inadequate data is one of the reasons why underlying probability distribution of certain perils cannot be quantified. Situations of inadequate data can occur when firms have not been collecting data out of unawareness (e.g., financial institutions started collecting operational loss data only recently, as they were not previously aware of the degree of threat they possessed), when dealing with LF/HS events, and when new business lines and products are introduced. Although firms may prefer to use internal data for their analysis, in most cases their own experience will not be adequate to obtain a holistic understanding of the uncertainty faced by an institution. In such instances, one of the solutions is to combine internal data with external data and expert opinion. The critical role of external data sources has been increasingly recognized by the industry, as well as by the regulators, in the recent past. Both Basel II for banks and Solvency II for insurers have stressed that external data should be considered when quantifying certain categories of risk, such as operational risk.
Use of external data can complement internal data to reduce parameter uncertainty in the models and as inputs for scenario analysis. The process of combining internal data with external data is an exercise that requires due diligence. If not properly combined, external data may distort parameter estimates and eventually lead to perverse estimates of economic capital (Baud et al., 2002). Wilson (2007) points out there are three types of biases inherent to external data that may lead to poor estimates:
reporting bias—occurs when different thresholds have been used by institutions to report losses to the external database;
control bias—occurs when data is collected from institutions with different control systems, underwriting standards, etc.
scale bias—occurs when data is collected from organizations of different sizes.
Many techniques have been suggested by various authors to correct for each type of bias.
The reporting bias of external data can be seen as a randomly truncated data problem. Techniques for analyzing randomly truncated data can be found in Amemiya (1984), Greene (2012), Maddala (1983), and many other sources. De Fontnouvelle et al. (2006) demonstrate how a stochastic truncation model can be used to correct the reporting bias in an external database with unknown loss reporting thresholds, where they treat each institution’s loss reporting threshold as an unobserved random variable. An alternative and simpler method has been proposed by Guillen et al. (2007) to estimate the true underlying distribution of external data based on expert opinion. In their method, experts are asked to provide subjective estimates of the probabilities of losses at different sizes being reported to a public database. These estimates are then used to derive an underreporting function, which in turn can be combined with the external data to obtain the true underlying loss distribution.
In contrast to correcting for reporting bias, correcting for control bias is much harder, since data vendors usually collect data on an anonymous basis, making it difficult to obtain information about factors such as the quality of governance and control structure of the institution from which data is derived. Given that factors such as the control structure will dictate the severity and frequency of losses, regulators require firms to only use ‘relevant’ external data in their models. However, deciding which data is relevant is open to subjectivity. Khan et al. (2006) argue that by trying to select relevant data one would often introduce distortions. They state that if objective scores of the control structure could not be obtained, one should refrain from attempting to do subjective scaling of losses to account for the differences in the controls. Furthermore, the authors state that analysts should avoid asking the question ‘Could this loss happen to me, given my internal control structure?’, since fundamentally anything can go wrong in a firm. Rather, the analyst should ask the question ‘What is the relative probability of a loss of this size taking place in my business in relation to other losses of different sizes?’ The authors point out that since it is difficult to give subjective estimates of relative probabilities, it is best not to attempt to pick relevant individual data points. A better approach is to use all external data to obtain the loss distribution for an ‘average’ firm in the industry, and then adjust it to match the unique characteristics of the particular firm, so that relative probabilities of different loss sizes are preserved. However, under certain circumstances, the analyst may sometimes be able to obtain information regarding the quality of the control structure of the firms contributing to the external database (perhaps through an external auditor). In such instances, the authors state that it is reasonable to select relevant data from firms that may have identical operations and risk profiles as the own firm. However, the authors note that this should be ‘done for whole data sets (groups of firms), not individual data points’.
The third type of bias in the external data is the scale bias. When combining data, it is best to combine data coming out from institutions with a similar operational volume and scale. For example, an insurance company that uses external data to complement the internal data, in order to increase the accuracy of their estimates of the tail of the loss distribution of an insurance peril, needs to take into account the average size of the coverage they provide. Similarly, a bank that uses external data to model operational losses should consider its average transaction volume as well as the transaction size, since the larger the volume, the greater the likelihood of a large number of losses, and the larger the transaction, the more likelihood of large losses. There are several techniques available to account for the scaling bias. Most of them make use of some sort of a regression analysis to model the scaling properties of the loss distribution with respect to explanatory variables, such as the size of the firm, location of the firm, and transaction volume, and then use those results to adjust the loss distribution of the external data to make it relevant to the own firm. Recent work carried out to resolve the scaling problem can be found in Cope and Labbi (2008), Dahen and Dionne (2010), and Wei (2007).
6. Dealing with Ambiguity
The third realm of uncertainty in our framework is Ambiguity. As explained earlier, financial markets are inherently ambiguous due to the human factor. In environments where agents have the free will to make their own decisions and respond accordingly, possible future states of the environment are more or less vaguely defined. To analyze such situations, traditional probabilistic approaches are inadequate.
In Section 6.1 we consider how human cognitive process may create financial Ambiguity. The cognitive biases of humans, fuelled by their fear and greed, can make them irrational, which in turn can make financial markets become irrational, unpredictable, and deviate from the traditional finance and economic theory. Some of the financial market phenomena, such as formations of asset bubbles, market crashes, and long-term mispricing of assets, have been blamed on the cognitive biases of humans. In such situations behavioral economics proves to be useful to understand the possible future behavior of market participants.
The game theory is another useful tool that can be used in ambiguous environments. In Section 6.2, we discuss the use of game theory in modeling terrorist risk and legal risk, where agents with free will interact with one another to maximize their own utility.
6.1. Behavioral economics and finance
Traditional finance theories, such as the EMH, assume that markets are rational and competition between rational investors drives prices to their ‘correct’ values. However, there is compelling evidence that markets do not always behave rationally (Barberis and Thaler, 2003: 1059). Hence, in order to provide a more realistic representation of the financial markets, the FMH (see Section 5.2) characterizes market participants as agents with limited cognition capabilities who may behave irrationally from time to time. By using two building blocks – cognitive psychology, which take into account the irrational behavior of humans, and limits to arbitrage, which argues that in some cases markets can be inefficient, as rational market participants will not be able to undo the disruptions caused by less rational market participants – behavioral economists attempt to bridge the gap between traditional finance and the real-world financial markets (Barberis and Thaler, 2003: 1052). In other words, behavioral economics and finance can be considered as the study of how the psychology of market participants affects financial markets.
Cognitive psychologists have studied the behavioral traits of humans, such as herding, framing, mental accounting, loss aversion, overconfidence, conservatism, anchoring, etc. These behavioral traits can often assist to explain (maybe even to predict) market anomalies and events, such as bubble formations, erratic trading activities, and overreaction to information. A risk manager who pays attention to the cognitive behavior of market participants will have a better chance of understanding financial markets and their future direction. The findings of behavioral economics show that financial markets and their participants may not always behave rationally. Hence, it is always a good idea to perform a scenario analysis by relaxing the ‘rational’ assumption of traditional finance theory, to see what can happen when market participants behave irrationally. In the following sections we present a few of the well-known cognitive biases that affect the market psychology and decision process. The discussion below is not intended to be a complete or comprehensive discussion about cognitive biases or behavioral economics. Rather, it is an illustration of the importance of cognitive psychology in risk management. Readers interested in more in-depth treatment of this subject are referred to Thaler (1993), Shiller (2000), and Shefrin (2001). An interesting discussion of how cognitive biases observed in Asian markets are different from what is observed in Western markets can be found in Kim and Nofsinger (2008).
6.1.1. Overconfidence
Being overconfident about one’s abilities and knowledge is probably one of the most common and biggest mistakes. There are many interesting and sometimes amusing experiments carried out to illustrate the overconfident nature of human beings. Weinstein (1980) reports that the degree of desirability, greater perceived probability through ‘availability’ (see Section 6.1.3 for details), personal experience, egocentric tendency of seeing things as controllable, and stereotype salience, leads people to believe that they have much more likelihood of experiencing positive events and less likelihood of experiencing negative events than their peers. Overconfidence can lead to overestimation, as well as underestimation, of probabilities. In fact, events people consider certain to happen only occur approximately 80% of the time, while events they assume impossible to occur happen approximately 20% of the time (Barberis and Thaler, 2003). Furthermore, various studies have shown that the confidence intervals individuals attach to their estimates are often too narrow. If people are well calibrated, their estimates of 90% confidence interval should contain the true value 90% of the time. However, empirical evidence shows that the true value of the quantity falls in the estimated confidence region only about 30–60% of the time (McKenzie et al., 2008; Van De Venter and Michayluk, 2008, and the references there in).
Overconfidence can lead to overcommitment to current knowledge or beliefs. Cialdini (2007: 51) states ‘once a stand is taken, there is a natural tendency to behave in ways that are stubbornly consistent with the stand’. Various studies have shown that once someone makes a commitment to a choice his confidence in that choice enhances. Using a study of racetrack betting, Knox and Inkster (1968) found that punters become much more confident about the chances of their horse winning right after they place their bets. Although fundamentals about the race have not changed, the fact that the punter has made a commitment by purchasing the ticket increased his subjective estimates of the probability of the particular horse winning. Cialdini (2007: 43) states that ‘once we have made a choice or taken a stand, we will encounter personal and interpersonal pressures to behave consistently with that commitment’. Once a commitment is made, information that is consistent with the commitment is processed easily and reinforces the current belief, and information that is inconsistent with the existing beliefs tends to be overlooked (Heuer, 1999).
The two case studies given in Section 2, on the rating problem of ABSs and the misuse of the Gaussian copula model to price CDOs, are examples of how overconfidence and overcommitment to current knowledge can lead to nasty outcomes in the financial markets. In the example of rating problem of ABSs, although there was direct evidence to imply that the credit rating of the ABSs and the bonds are not comparable, investors overlooked the evidence due to their commitment to their beliefs. In the example of pricing CDOs, due to firms been overcommitted to the model they could not see the limitations of their model, even if the creator of the model himself had cast doubt on the model. Both examples illustrate the Ambiguity of the correctness of current knowledge/beliefs due to the problem of overconfidence.
There are several cognitive strategies to debias oneself against overconfidence. Providing accelerated feedback, which enhances meta-knowledge, say from actuarial control cycles (Arkes et al., 1987; Lichtenstein and Fischhoff, 1980), counter-argumentation and devil’s advocacy (Koriat et al., 1980; Mussweiler et al., 2000; Soll and Klayman, 2004), analyzing paths to trouble using techniques such as fault trees (Russo and Schoemaker, 1992), and analyzing alternative scenarios (Russo and Schoemaker, 1992), can assist in reducing overconfidence. Larrick (2004) argues that group decision making can reduce overconfidence arising from ‘availability’ (see the definition in Section 6.1.3) simply because a group would increase the sample size of experience used to make a decision. However, the author states that in order for group decisions to work better, group members must have diverse experience and training, and each member must formulate their hypotheses, judgments, and estimates independently of one another, before working in the group. In a separate study by Plous (1995) where individuals were asked to provide confidence intervals, it was found that groups with 3–4 members working independently, and later combining their highest and lowest estimates to create the confidence intervals, outperformed individual decision makers as well as interactive groups.
Overconfidence of experts, which leads to ambiguous subjective estimates of parameters, can have serious implications for methods such as scenario analysis and logic trees, which we outlined in Section 5.4 to deal with Knightian uncertainty. In an interesting study carried out by McKenzie et al. (2008) it was found that compared to novices, experts tend to provide interval estimates with midpoints closer to the true value of the parameter, but with too narrow intervals, which reduces the hit rate. The net effect of this was that novices, as well as the subject experts, were both found to be equally overconfident. Authors conclude ‘experts are good at reporting relatively narrow intervals centred on true values, but they are no better than novices at reporting well calibrated, high confidence intervals’ (McKenzie et al., 2008: 188). In a separate study, by comparing foreign exchange (FX) forecasts made by professionals and sophisticated amateurs, Önkal et al. (2003) reported that professionals were able to outperform the amateurs in providing accurate point estimates and directional forecasts, but not so much in interval forecasts. Drawing from the previous works of several authors, McKenzie et al. (2008: 188) argue that ‘experts are indispensable for measuring variables and discovering new ones, but they are poor at combining diverse sources of information in order to arrive at a single predictive judgment’. The poor ability of subject experts to make predictions has been termed process-performance paradox by Camerer and Johnson (1997). As it turns out, cognitive biases can seriously impair the accuracy of expert opinion. Thus, it is important to understand how these biases may affect the experts’ opinion, methods to debias them, and which estimates to rely on and which estimates not to. Evidence from behavioral studies suggest that it is usually better to ask a subject expert for point estimations (Önkal et al., 2003), or for a probability evaluation for predefined intervals (Winman et al., 2004), rather than to ask for interval estimations.
6.1.2. Anchoring
When people make estimates they usually start off with an initial estimate (could be arbitrary) and adjust it by moving away from it. Using experimental evidence, Tversky and Kahneman (1974) state that often the adjustments are insufficient due to individuals anchoring themselves in the initial estimate. In the context of financial markets, market participants can often anchor themselves to past perceptions, historical prices, recently purchased prices, initial data, etc. Such behavior can sometimes create Ambiguity. For example, credit ratings given by rating agencies for firms and countries heavily rely on the subjective assessments of the analysts. These subjective assessments can be biased, due to the rating analyst being anchored to past information about the firm or the nation being rated. Hence, when interpreting the credit ratings one needs to consider the possibility of anchoring bias. However, one cannot know to what extent the rating has been contaminated from anchoring. Thus, the rating given by a credit rating agency becomes ambiguous. A number of such apparent rating discrepancies have been reported by Bain (2011)
The effects of anchoring can have serious consequences on financial firms. Dougal et al. (2011) have found evidence that the interest rates paid by firms for syndicated bank loans are strongly influenced by anchoring. They report that the interest rates paid by firms depend highly on the previous borrowing rates, even if the credit market conditions have drastically changed. Rao (2009: 140) discuss the anchoring in the context of price cognition. 6 The author provides several examples of how anchoring may affect the investment decisions of firms as well as their sales. It is worth pointing out that even the most astute investors can make wrong judgments due to anchoring. For example, the veteran investor Warren Buffet once admitted that it cost Berkshire Heathway around US$10 billion when he did not buy enough Wal-Mart shares because he got anchored at a previous price (Berkshire Hathaway, 2004).
6.1.3. Availability
When asked to make subjective estimates of the probability of an event, people do so often by searching their memory for similar occurrences. Tversky and Kahneman (1974) state that certain memories are more easily ‘available’ than the others, thus creating a bias in the subjective estimates. The authors state that recent memories, salient memories, and familiar events are easily retrievable. Furthermore, estimates can be biased due to illusionary correlations, and limitations of imagination in situations which own memory does not have stored occurrences.
Quite often risk managers need to consider the likelihood of possible future scenarios (e.g., when developing scenarios for stress testing). In such instances, it is possible that management may become biased towards recent events, and those events they find salient and familiar. The likelihood of events that have occurred in the distant past, or events that they themselves did not have a firsthand experience of, but read in a newspaper or a journal, might be underestimated simply because those scenarios are not as easily ‘available’. Thus, availability makes subjective estimates made by the experts ambiguous, as one cannot determine to which extent the estimates are biased towards the expert’s own experience.
People tend to underestimate low probability events when they haven’t happened recently, and overestimate them when they have.—Warren Buffet, Berkshire Hathaway Annual Meeting (May 1, 2004).
6.1.4. Framing
Framing is a cognitive bias that refers to the manner in which the way concepts and information are presented may affect the decision of an agent. Tversky and Kahneman (1981) demonstrated that people can switch from being risk averse to risk loving, depending on the frame in which the information is presented to them. Authors provide a series of experimental examples to illustrate that people’s decisions are not always consistent or coherent. Thus, the decisions made by market participants has to be treated as ambiguous, if one is uncertain about the decision framework they are using. Any analysis carried out by making the traditional financial assumptions of market participants being rational and their decisions being consistent should be treated with caution. If analysis is carried out assuming a certain framing, it is always prudent to test the results in an alternative framing to confirm them.
6.1.5. Herding
Herding refers to the human (as well as animal) tendency to form into groups and mimic each other. Herding can occur in financial markets when market participants look into each others’ activities to infer information, when everybody is following the same models and data (e.g., models prescribed by the regulator), when everybody pursues similar actions (say, flight to quality), and when they share similar sentiments and fads. Herding can make financial markets behave irrationally and become unstable (Brunnermeier, 2001: 165; Hirshleifer and Teoh, 2003; Scharfstein and Stein, 1990; Shiller, 2000). However, herding does not necessarily mean individual market participants are irrational. Brunnermeier (2001: 147) states that even rational agents may participate in herd behavior when payoff externalities and information externalities are present. In such instances, even if individual behavior is rational, group behavior can be irrational, thus leading rational individuals astray. This has been illustrated by Shiller (2000: 151) with a fine example.
Various studies have found empirical evidence to support the herding behavior of financial markets. For example, Hwang and Salmon (2004) find empirical evidence supporting herding in the US and South Korean stock markets; Iihara et al. (2001), Nakagawa (2008) and Nakagawa et al. (2012) find evidence of herding in financial markets in Japan, and, in particular, Nakagawa et al. (2012) find empirical evidence to support that the deterioration of the Japan’s real economy in the 1990s was partly caused by the herding behavior of the country’s financial markets. Chang (2010) examines the herding behavior surrounding qualified foreign institutional investors (QFIIs) using data from the Taiwan stock exchange and finds evidence that the herding may have a destabilizing effect on emerging markets. Many similar studies have also reported evidence of herding in the financial markets and how it may lead to asset bubbles, frenzies, and market crashes (see, for example, Bikhchandani and Sharma, 2000; Brunnermeier, 2001; Jain and Gupta, 1987). Given that herding can dictate the direction of the financial markets, a good understanding of social behavior is needed in order to decide when to ride the herd and when to become a contrarian. As mentioned in Section 5.2, when carrying out scenario analysis one needs to take into account social behaviors such as herding. In particular, post-crisis knock-on effects can be highly influenced by herding behavior. In most instances, institutions tend to underestimate the severity of herding. For example, during the subprime mortgage crisis, herding of investors for liquidity created a liquidity black hole almost overnight in the markets for securitize products in August 2007. The speed with which liquidity dried up came as a surprise for most bankers, as they had underestimated the power of the herding effect earlier.
6.2. Applications of game theory
For many years, game theory has been used to model ambiguous situations where the actions of two or more agents affect each other’s payoffs. Game theory is capable of handling an array of complex situations, such as corporative and non-corporative agents, perfect information and imperfect information, repetitive situations, and bounded rationality. For this reason, it has found applications in a diversity of fields, including economics, political science, evolutionary biology, and computer science.
One of the promising applications of game theory in risk management is to assess insurance losses from terrorist risk. Several recent studies, including Woo (2002), Major (2002), Fricker (2006), Banks and Anderson (2006), and Ezell et al. (2010), have demonstrated applications of game theory on terrorist risk. Woo (2002) points out that although modeling a loss from a terrorist attack, in principle, is quite similar to modeling a natural catastrophe (which requires complex engineering to model the dynamics of energy dissipation, vulnerability of engineering constructions, etc.), measuring the likelihood of a terrorist attack is quite different from a natural peril, due to the attack being intentional. Terrorists need to maximize their utility by attacking high-profile locations while maximizing the number of casualties. But at the same time, they face the challenges of limited resources and increased security. This would mean terrorists have to adapt new strategies and targets for their attacks. Hence, a location that was previously considered as low risk can become high risk due to political and counter-terrorist responses made by the governments. 7 The result of this is that a terrorist risk cannot be measured as any other type of catastrophic risk, by simply analyzing past data or by the use of the techniques that we outlined in Section 5 to deal with the Knightian uncertainty. The Ambiguity of the human factor requires terrorist risk to be modeled using methods such as game theory, where possible future attacks can be modeled by considering the actions and counteractions of the terrorist organizations and the relevant governments, as players engaged in a strategic game. An industry example of such a model is the terrorist risk model developed by RMS (2004). RMS monitors terrorist activities through a network of international experts on terrorism, to understand operational and behavioral characteristics of terrorist organizations and their target patterns. Then, using game theory, these dynamics are analyzed against increased security and counter-terrorism measures, to assess the probable threat, attack capability, and target prioritization. RMS considers a range of attack modes, from conventional attacks to plausible chemical, biological, radiological, and nuclear attacks on credible targets. In addition to the probabilities, the RMS model also provides high-resolution estimates of insurance losses stemming from damage to life, property, and business disruptions (Insurance Journal, 2002).
Another area of risk for which game theory is useful is the quantification of legal risk. In order to quantify legal risk, one needs to take into account strategic decisions made by lawyers. The outcome of a lawsuit can end up with a trial, an outside court settlement, or a withdrawal of the case. During the process of the lawsuit, each party may threaten, bluff, corporate, or adapt many other strategies to maximize their utility. The final outcome is uncertain, as it is ambiguous how the lawyers of each party would respond to the strategies of the other. Often in such situations, game theory can provide insight to possible outcomes. P’ng (1983) provides a game theoretic analysis of a simple legal settlement where the plaintiff is unaware of whether the defendant is at fault or not. The author demonstrates how each party can choose an optimal strategy of either to go to trial, reach an outside settlement, or withdraw the case, depending on the different parameterizations of the model. Rasmusen (2007) demonstrates, with examples, how game theory can be used to model the behavior of agents under certain legal contracts. These games are useful to analyze situations with moral hazard and adverse selection.
7. Dealing with ignorance
The great Chinese philosopher Confucius (551–479 BC) once said that Real knowledge is to know the extent of one’s ignorance.
Knowing the limitations of one’s own knowledge, as well as being humble enough to admit ignorance, are two important traits a risk manager should possess. Very few would disagree if someone says that what we know about our surrounding is insignificant compared to what we do not know. Therefore, we are almost always unaware of some of the possible future states of the world simply because we are ignorant that those states could exist. This ignorance makes it impossible to identify the threats these future states might engender, let alone to quantify them, thereby making them unavoidable. Some of these unknowable events can have a significant impact on the course of the future. Taleb (2007) famously defines such events as black swan events. According to Taleb, black swan events have three characteristics: (1) they occur as a complete surprise; (2) they have a major impact; and (3) once the event has occurred people tend to convince themselves that the event is explainable in hindsight. Taleb points out that almost all of the consequential events in history are black swans. For example, World War I, the invention of the aircraft, the fall of the USSR, and the creation of the Internet, can be considered as black swan events that dramatically changed the course of history.
Although black swan events are almost impossible to pre-identify, this does not necessarily mean that we cannot prepare for unforeseen hazards. Diebold et al. (2010) point out that although crisis events may have unique and unanticipated causes, most of the time the required post-crisis responses are often quite similar. Thus, readiness for a known possible crisis can become useful in responding to a surprise crisis situation. For example, several experts have pointed out that the system redundancies developed in New York city, in anticipation of the Y2K bug (which never materialized), became indispensable for the fast recovery of the city’s transportation and telecommunication systems after the 9/11 attacks (Slavin, 2002; Woodworth, 2002). The lesson here is that even if one cannot anticipate the nature of a possible black swan event, it is still possible to have some sort of contingent plan in place to assist in a crisis situation. Diebold et al. (2010) emphasize the importance of having dedicated systems and teams to manage a possible crisis. Using the 1982 cyanide scare with the Tylenol product at Johnson & Johnson, the authors point out that ‘sound management of crises can not only mitigate their impact, but also generate new knowledge’ and secure competitive advantage (Diebold et al., 2010: 12). Sheffi (2005) provides a wonderful case study on how corporate culture and an innovative crisis management team assisted Nokia to deal with a supply chain crisis. Although not a financial firm, the lessons learnt from this case study are relevant to the financial industry as well, to develop strategies to deal with a crisis. Therefore, a summary of the case is provided below. A detailed analysis of the case can be found in Sheffi (2005) and Mukherjee (2008).
7.1. Nokia–Ericsson supply chain crisis
Both Nokia and Ericsson, two of the giants in the mobile phone industry in the late 1990s, relied on Philips Electronics to supply chips for their mobile phones. On 17 March 2000, one of the Philips plants at Albuquerque, NM, caught fire. At first, employees at Philips estimated the damage from the fire as minor, and they thought they would be able to make the plant operational again in a week’s time.
Meanwhile, at a Nokia plant outside Helsinki, a production planner who was following a well-articulated process of monitoring supplies noted an anomaly in the system. Shipments of some Phillip chips seem to have been delayed. Although it was not unusual for a shipment to be delayed, the employee informed the plant manager of the situation. Following an established corporate process, the plant manager reported the situation to Tapio Markki, Nokia’s chief component purchasing manager. Mr Markki immediately put the affected parts on a special watch list. Nokia made daily enquiries to Philips to find out about the evolving situation at the Philips plant. They even offered assistance to Philips to get the plant back to normal.
Eventually, Philips realized that the damage of the fire was far more severe than they had initially estimated. The smoke and soot from the fire, and dirt from fire fighters, had contaminated the clean rooms and had ruined wafers in almost every stage of production, destroying millions of mobile phones’ worth of chips. It would take weeks to get the plant back into operation. On 31 March, Philips informed Nokia and Ericsson that they had initially underestimated the situation and would need at least six weeks to get the plant back into operation.
Nokia responded by immediately creating a crisis response team consisting of supply chain managers, chip designers, and executives. The team searched for alternative supply sources for the chips. They found three of the five affected parts could be purchased from other suppliers. But two of the parts came only from Philips. Therefore, Nokia started negotiating with Philips to find solutions to the crisis. At this stage the CEO of Nokia also became involved in the negotiations with Philips, to convey the importance of the issue. Nokia demanded to know details of Philips’ other plants, to examine the possibility of rerouting their capacities to build the necessary parts. Philips agreed to reroute some of the capacity at their Eindhoven and Shanghai plants to meet the demand by Nokia. Engineers at Nokia developed new methods to boost the production at the Albuquerque plant once it got back on line. The goal was for Nokia and Philips to work as one company until the crisis is solved. With these extraordinary efforts and an intensive collaboration with Philips, Nokia was able to steer through the crisis successfully.
In contrast, the story evolved quite differently at Ericsson. The lower-level employees did not communicate the delays in the component to their senior management until the last moment. The head of the consumer division did not find out about the problem until several weeks after the fire. Even after been informed by Philips about the situation, Jan Warby, the head of Ericsson’s mobile phone division, did not get involved until early April. By the time Ericsson’s senior management responded, Nokia had already secured other sources of suppliers as well as the excess capacity of Philips. By then Ericsson had very few options left. The shortage of millions of chips meant shortage of millions of high-end mobile phones for Ericsson. They ended up with the wrong product mix in a fast-moving market. The affect lasted for several quarters, with Ericsson posting a loss of US$2.34 billion at the end of 2000. The setback at Ericsson had a positive effect on Nokia. Nokia’s mobile phone market share increased by 3%, while Ericsson lost its market share by 3% and eventually announced a retreat from the mobile phone market.
The Nokia–Ericsson case study provides several lessons on crisis management. The main lesson is that the ability to steer through a crisis depends more on the decisions made before the crisis rather than the decisions made in the midst of it. In addition, it is possible to identify the following four reasons for Nokia’s success in crisis management. Firstly, Nokia was able to identify the crisis much earlier than Ericsson, since they had a system already in place that assisted the production planner at Helsinki to identify the anomaly in the supply of chips. This emphasizes the importance of having an established process to monitor near-miss events for the early detection of a problem. A near-miss event is defined as an unanticipated event that did not cause a serious loss but had the potential to do so. Many industries, such as the aviation, nuclear, and chemical industries, monitor near-miss events regardless of their impact, since they provide a better understanding of possible catastrophic events, as well as provide useful information on how to improve the process or the system to avoid catastrophes. Having an established process to monitor near misses can benefit financial firms as well. In particular, management of near-miss losses can greatly benefit financial firms to avoid and contain operational losses, as discussed by Muermann and Oktem (2002). The second reason for Nokia’s success was the nature of corporate culture, which encourages bad news to travel fast. A corporate culture that encourages the reporting of problems rather than the habit of hiding them is vital in detecting a crisis at the early stage. As in the Nokia–Ericsson example, the early involvement of senior management would help to take the required actions quickly, in order to contain the crisis. Thirdly, Nokia had a flexible organizational structure and a team of experts who were highly adaptable. This flexibility in the organizational structure allowed Nokia to free up their engineers to assist Philips and to collaborate to get the plant back on production. Furthermore, engineers were able to adapt to the situation by developing new methods to boost Philips’ production within a short period of time. Kleindorfer (2010) points out the parallels between the Darwinian evolution of species and the importance of adaptability and innovation for survivability of financial firms. Similar to species, firms that cannot innovate and adapt to the changes in the environment will face extinction. In the context of financial firms, this means having a flexible corporate structure that allows adaptation and innovation to survive a crisis situation, and has excess capital and liquidity for a rainy day through dedicated credit lines, reinsurance arrangements and contingent capital facilities. The fourth reason for Nokia’s success is the close relationship it maintained with Philips. The magnitude of the collaboration was enormous. In any crisis situation, firms will need to maintain good public relations and collaborate with the relevant parties. Unless firms develop cooperative relationships with their partners, they will not get preferential assistance during either a crisis or an opportunity.
8. General discussion
In this article we have discussed various realms of uncertainty in financial markets. In particular, we identified four realms of uncertainty: (1) Knightian risk—situations in which we can confidently identify possible future events and their underlying probabilities; (2) Knightian uncertainty—situations in which we can only identify possible future events, but not the probabilities; (3) Ambiguity—situations in which possible future events are vaguely defined due to the ambiguous nature of interactions and behavior of agents with free will; and (4) Ignorance—situations in which possible future events are unknown. We pointed out that each of these realms possesses a unique set of challenges to risk managers. In particular, to grapple with the unknowns and unknowable of ever-changing financial markets and the Ambiguity of human behavior, one would require techniques that go beyond traditional statistical methods. Recognizing these needs, we believe treating the four realms as a framework to analyze financial market uncertainty can improve the decision-making process of risk managers. Furthermore, the proposed framework would provide a holistic view of uncertainty in the financial world, and assist risk managers to identify the unique challenges of each realm of uncertainty and the appropriate theories and models to deal with them, while simultaneously maintaining awareness of their limitations.
The proposed framework can be considered as an extension of our previous work (Ganegoda and Evans, 2008) and the
Another feature of the proposed framework is that we take the stance that Knightian risk, Knightian uncertainty, Ambiguity, and Ignorance can exist contemporaneously, in such a manner that each realm of uncertainty is overlaid upon another, expressing the social commitment towards current knowledge. Thus, our framework emphasizes the incidence of ignorance on all realms of uncertainty. This line of thinking highlights the unavoidable nature of black swan events, hence stressing the importance of having a crisis management system in place, and a flexible and adaptable corporate structure. We have discussed the advantages of having a good crisis management team and how a properly managed crisis may even provide a comparative advantage over rival firms.
Footnotes
Date of acceptance of final transcript: 16 August 2012.
Accepted by Associate Editor, Tom Smith (Finance).
Funding
This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.