Lecture notes Risk Management

Risk Management
Dr.NaveenBansal Profile Pic
Published Date:25-10-2017
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CHAPTER 1 Introduction 1.1 LESSONS FROM A CRISIS I began the first edition of this book with a reference to an episode of the television series Seinfeld in which the character George Costanza gets an assignment from his boss to read a book titled Risk Management and then give a report on this topic to other business executives. Costanza finds the book and topic so boring that his only solution is to convince someone else to read it for him and prepare notes. Clearly, my concern at the time was to write about financial risk management in a way that would keep readers from finding the subject dull. I could hardly have imagined then that eight years later Demi Moore would be playing the part of the head of an investment bank's risk management department in a widely released movie, Margin Call. Even less could I have imagined the terrible events that placed financial risk management in such a harsh spotlight. My concern now is that the global financial crisis of 2007–2008 may have led to the conclusion that risk management is an exciting subject whose practitioners and practices cannot be trusted. I have thoroughly reviewed the material I presented in the first edition, and it still seems to me that if the principles I presented, principles that represented industry best practices, had been followed consistently, a disaster of the magnitude we experienced would not have been possible. In particular, the points I made in the first edition about using stress tests in addition to value at risk (VaR) in determining capital adequacy (see the last paragraphs of Section 7.3 in this edition) and the need for substantial reserves and deferred compensation for illiquid positions (see Sections 6.1.4 and 8.4 in this edition) still seem sound. It is tempting to just restate the same principles and urge more diligence in their application, but that appears too close to the sardonic definition of insanity: “doing the same thing and expecting different results.” So I have looked for places where these principles need strengthening (you'll find a summary in Section 5.4). But I have also reworked the organization of the book to emphasize two core doctrines that I believe are the keys to the understanding and proper practice of financial risk management. The first core principle is that financial risk management is not just risk management as practiced in financial institutions; it is risk management that makes active use of trading in liquid markets to control risk. Risk management is a discipline that is important to a wide variety of companies, government agencies, and institutions—one need only think of accident prevention at nuclear power plants and public health measures to avoid influenza pandemics to see how critical it can be. While the risk management practiced at investment banks shares some techniques with risk management practiced at a nuclear facility, there remains one vital difference: much of the risk management at investment banks can utilize liquid markets as a key element in risk control; liquid markets are of virtually no use to the nuclear safety engineer. My expertise is in the techniques of financial risk management, and that is the primary subject ofthis book. Some risks that financial firms take on cannot be managed using trading in liquid markets. It is vitally important to identify such risks and to be aware of the different risk management approaches that need to be taken for them. Throughout the book I will be highlighting this distinction and also focusing on the differences that degree of available liquidity makes. As shorthand, I will refer to risk that cannot be managed by trading in liquid markets as actuarial risk, since it is the type of risk that actuaries at insurance companies have been dealing with for centuries. Even in cases that must be analyzed using the actuarial risk approach, financial risk management techniques can still be useful in isolating the actuarial risk and in identifying market data that can be used as input to actuarial risk calculations. I will address this in greater detail in Section 1.2. The second core principle is that the quantification of risk management requires simulation guided by both historical data and subjective judgment. This is a common feature of both financial risk and actuarial risk. The time period simulated may vary greatly, from value at risk (VaR) simulations of daily market moves for very liquid positions to simulations spanning decades for actuarial risk. But I will be emphasizing shared characteristics for all of these simulations: the desirability of taking advantage of as much historical data as is relevant, the need to account for nonnormality of statistical distributions, and the necessity of including subjective judgment. More details on these requirements are in Section 1.3. 1.2 FINANCIAL RISK AND ACTUARIAL RISK The management of financial risk and the management of actuarial risk do share many methodologies, a point that will be emphasized in the next section. Both rely on probability and statistics to arrive at estimates of the distribution of possible losses. The critical distinction between them is the matter of time. Actuarial risks may not be fully resolved for years, sometimes even decades. By the time the true extent of losses is known, the accumulation of risk may have gone on for years. Financial risks can be eliminated in a relatively short time period by the use of liquid markets. Continuous monitoring of the price at which risk can be liquidated should substantially lower the possibility of excessive accumulation of risk. Two caveats need to be offered to this relatively benign picture of financial risk. The first is that taking advantage of the shorter time frame of financial risk requires constant vigilance; if you aren't doing a good job of monitoring how large your risks are relative to liquidation costs, you may still acquire more exposure than desired. This will be described in detail in Chapter 6. The second is the need to be certain that what is truly actuarial risk has not been misclassified as financial risk. If this occurs, it is especially dangerous—not only will you have the potential accumulation of risk over years before the extent of losses is known, but in not recognizing the actuarial nature, you would not exercise the caution that the actuarial nature of the risk demands. This will be examined more closely in Sections 6.1.1 and 6.1.2, with techniques for management of actuarial risk in financial firms outlined in Section 8.4. I believe that this dangerous muddling of financial and actuarial risk was a key contributor to the 2007–2008 crisis, as I argue in Section 5.2.5. Of course, it is only an approximation to view instruments as being liquid or illiquid. The volume of instruments available for trading differs widely by size and readiness of availability. This constitutes the depth of liquidity of a given market. Often a firm will be faced with a choice between the risks of replicating positions more exactly with less liquid instruments or less exactly with moreliquid instruments. One theme of this book will be the trade-off between liquidity risk and basis risk. Liquidity risk is the risk that the price at which you buy (or sell) something may be significantly less advantageous than the price you could have achieved under more ideal conditions. Basis risk is the risk that occurs when you buy one product and sell another closely related one, and the two prices behave differently. Let's look at an example. Suppose you are holding a large portfolio of stocks that do not trade that frequently and your outlook for stock prices leads to a desire to quickly terminate the position. If you try selling the whole basket quickly, you face significant liquidity risk since your selling may depress the prices at which the stocks trade. An alternative would be to take an offsetting position in a heavily traded stock futures contract, such as the futures contract tied to the Standard & Poor's™ S&P 500 stock index. This lowers the liquidity risk, but it increases the basis risk since changes in the price of your particular stock basket will probably differ from the price changes in the stock index. Often the only way in which liquidity risk can be reduced is to increase basis risk, and the only way in which basis risk can be reduced is to increase liquidity risk. The classification of risk as financial risk or actuarial risk is clearly a function of the particular type of risk and not of the institution. Insurance against hurricane damage could be written as a traditional insurance contract by Metropolitan Life or could be the payoff of an innovative new swap contract designed by Morgan Stanley; in either case, it will be the same risk. What is required in either case is analysis of how trading in liquid markets can be used to manage the risk. Certainly commercial banks have historically managed substantial amounts of actuarial risk in their loan portfolios. And insurance companies have managed to create some ability to liquidate insurance risk through the reinsurance market. Even industrial firms have started exploring the possible transformation of some actuarial risk into financial risk through the theory of real options. An introduction to real options can be found in Hull (2012, Section 34) and Dixit and Pindyck (1994). A useful categorization to make in risk management techniques that I will sometimes make use of, following Gumerlock (1999), is to distinguish between risk management through risk aggregation and risk management through risk decomposition. Risk aggregation attempts to reduce risk by creating portfolios of less than completely correlated risk, thereby achieving risk reduction through diversification. Risk decomposition attempts to reduce a risk that cannot directly be priced in the market by analyzing it into subcomponents, all or some of which can be priced in the market. Actuarial risk can generally be managed only through risk aggregation, whereas financial risk utilizes both techniques. Chapter 7 concentrates on risk aggregation, while Chapter 8 primarily focuses on risk decomposition; Chapter 6 addresses the integration of the two. 1.3 SIMULATION AND SUBJECTIVE JUDGMENT Nobody can guarantee that all possible future contingencies have been provided for—this is simply beyond human capabilities in a world filled with uncertainty. But it is unacceptable to use that platitude as an excuse for complacency and lack of meaningful effort. It has become an embarrassment to the financial industry to see the number of events that are declared “once in a millennium” occurrences, based on an analysis of historical data, when they seem in fact to take place every few years. At one point I suggested, only half-jokingly, that anyone involved in risk management who usedthe words perfect and storm in the same sentence should be permanently banned from the financial industry. More seriously, everyone involved in risk management needs to be aware that historical data has a limited utility, and that subjective judgment based on experience and careful reasoning must supplement data analysis. The failure of risk managers to apply critical subjective judgment as a check on historical data in the period leading to the crisis of 2007–2008 is addressed in Section 5.2.5. This by no means implies that historical data should not be utilized. Historical data, at a minimum, supplies a check against intuition and can be used to help form reasoned subjective opinions. But risk managers concerned with protecting a firm against infrequent but plausible outcomes must be ready to employ subjective judgment. Let us illustrate with a simple example. Suppose you are trying to describe the distribution of a variable for which you have a lot of historical data that strongly supports a normal distribution with a mean of 5 percent and standard deviation of 2 percent. Suppose you suspect that there is a small but nonnegligible possibility that there will be a regime change that will create a very different distribution. Let's say you guess there is a 5 percent chance of this distribution, which you estimate as a normal distribution with a mean of 0 percent and standard deviation of 10 percent. If all you cared about was the mean of the distribution, this wouldn't have much impact—lowering the mean from 5 percent to 4.72 percent. Even if you were concerned with both mean and standard deviation, it wouldn't have a huge impact: the standard deviation goes up from 2 percent to 3.18 percent, so the Sharpe ratio (the ratio of mean to standard deviation often used in financial analysis) would drop from 2.50 to 1.48. But if you were concerned with how large a loss you could have 1 percent of the time, it would be a change from a gain of 0.33 percent to a loss of 8.70 percent. Exercise 1.1 will allow you to make these and related calculations for yourself using the Excel spreadsheet MixtureOfNormals supplied on the book's website. This illustrates the point that when you are concerned with the tail of the distribution you need to be very concerned with subjective probabilities and not just with objective frequencies. When your primary concern is just the mean—or even the mean and standard deviation, as might be typical for a mutual fund—then your primary focus should be on choosing the most representative historical period and on objective frequencies. While this example was drawn from financial markets, the conclusions would look very similar if we were discussing an actuarial risk problem like nuclear safety and we were dealing with possible deaths rather than financial losses. The fact that risk managers need to be concerned with managing against extreme outcomes would again dictate that historical frequencies need to be supplemented by informed subjective judgments. This reasoning is very much in line with the prevailing (but not universal) beliefs among academics in the fields of statistics and decision theory. A good summary of the current state of thinking in this area is to be found in Hammond, Keeney, and Raiffa (1999, Chapter 7). Rebonato (2007) is a thoughtful book-length treatment of these issues from an experienced and respected financial risk manager that reaches conclusions consistent with those presented here (see particularly Chapter 8 of Rebonato). The importance of extreme events to risk management has two other important consequences. One is that in using historical data it is necessary to pay particular attention to the shape of the tail of the distribution; all calculations must be based on statistics that take into account any nonnormality displayed in the data, including nonnormality of correlations. The second consequence is that allcalculations must be carried out using simulation. The interaction of input variables in determining prices and outcomes is complex, and shortcut computations for estimating results work well only for averages; as soon as you are focused on the tails of the distribution, simulation is a necessity for accuracy. The use of simulation based on both historical data and subjective judgment and taking nonnormality of data into account is a repeated theme throughout this book—in the statement of general principles in Section 6.1.1, applied to more liquid positions throughout Chapter 7, applied to positions involving actuarial risk in Section 8.4, and applied to specific risk management issues throughout Chapters 9 through 14. EXERCISE 1.1 The Impact of Nonnormal Distributions on Risk Use the MixtureOfNormals spreadsheet to reproduce the risk statistics shown in Section 1.3 (you will not be able to reproduce these results precisely, due to the random element of Monte Carlo simulation, but you should be able to come close). Experiment with raising the probability of the regime change from 5 percent to 10 percent or higher to see the sensitivity of these risk statistics to the probability you assign to an unusual outcome. Experiment with changes in the mean and standard deviation of the normal distribution used for this lower- probability event to see the impact of these changes on the risk statistics.CHAPTER 2 Institutional Background A financial firm is, among other things, an institution that employs the talents of a variety of different people, each with her own individual set of talents and motivations. As the size of an institution grows, it becomes more difficult to organize these talents and motivations to permit the achievement of common goals. Even small financial firms, which minimize the complexity of interaction of individuals within the firm, must arrange relationships with lenders, regulators, stockholders, and other stakeholders in the firm's results. Since financial risk occurs in the context of this interaction between individuals with conflicting agendas, it should not be surprising that corporate risk managers spend a good deal of time thinking about organizational behavior or that their discussions about mathematical models used to control risk often focus on the organizational implications of these models. Indeed, if you take a random sample of the conversations of senior risk managers within a financial firm, you will find as many references to moral hazard, adverse selection, and Ponzi scheme (terms dealing primarily with issues of organizational conflict) as you will find references to delta, standard deviation, and stochastic volatility. For an understanding of the institutional realities that constitute the framework in which risk is managed, it is best to start with the concept of moral hazard, which lies at the heart of these conflicts. 2.1 MORAL HAZARD—INSIDERS AND OUTSIDERS The following is a definition of moral hazard taken from Kotowitz (1989): Moral hazard may be defined as actions of economic agents in maximizing their own utility to the detriment of others, in situations where they do not bear the full consequences or, equivalently, do not enjoy the full benefits of their actions due to uncertainty and incomplete or restricted contracts which prevent the assignment of full damages (benefits) to the agent responsible. . . . Agents may possess informational advantages of hidden actions or hidden information or there may be excessive costs in writing detailed contingent contracts. . . . Commonly analyzed examples of hidden actions are workers' efforts, which cannot be costlessly monitored by employers, and precautions taken by the insured to reduce the probability of accidents and damages due to them, which cannot be costlessly monitored by insurers. . . . Examples of hidden information are expert services—such as physicians, lawyers, repairmen, managers, and politicians. In the context of financial firm risk, moral hazard most often refers to the conflict between insiders and outsiders based on a double-edged asymmetry. Information is asymmetrical—the insiders possess superior knowledge and experience. The incentives are also asymmetrical—the insiders have anarrower set of incentives than the outsiders have. This theme repeats itself at many levels of the firm. Let's begin at the most basic level. For any particular group of financial instruments that a firm wants to deal in, whether it consists of stocks, bonds, loans, forwards, or options, the firm needs to employ a group of experts who specialize in this group of instruments. These experts will need to have a thorough knowledge of the instrument that can rival the expertise of the firm's competitors in this segment of the market. Inevitably, their knowledge of the sector will exceed that of other employees of the firm. Even if it didn't start that way, the experience gained by day-to-day dealings in this group of instruments will result in information asymmetry relative to the rest of the firm. This information asymmetry becomes even more pronounced when you consider information relative to the particular positions in those instruments into which the firm has entered. The firm's experts have contracted for these positions and will certainly possess a far more intimate knowledge of them than anyone else inside or outside the firm. A generic name used within financial firms for this group of experts is the front office. A large front office may be divided among groups of specialists: those who negotiate transactions with clients of the firm, who are known as salespeople, marketers, or structurers; those who manage the positions resulting from these negotiated transactions, who are known as traders, position managers, or risk managers; and those who produce research, models, or systems supporting the process of decision making, who are known as researchers or technologists. However, this group of experts still requires the backing of the rest of the firm in order to be able to generate revenue. Some of this dependence may be a need to use the firm's offices and equipment; specialists in areas like tax, accounting, law, and transactions processing; and access to the firm's client base. However, these are services that can always be contracted for. The vital need for backing is the firm's ability to absorb potential losses that would result if the transactions do not perform as expected. A forceful illustration of this dependence is the case of Enron, which in 2001 was a dominant force in trading natural gas and electricity, being a party to about 25 percent of all trades executed in these markets. Enron's experts in trading these products and the web-enabled computer system they had built to allow clients to trade online were widely admired throughout the industry. However, when Enron was forced to declare bankruptcy by a series of financing and accounting improprieties that were largely unrelated to natural gas and electricity trading, their dominance in these markets was lost overnight. Why? The traders and systems that were so widely admired were still in place. Their reputation may have been damaged somewhat based on speculation that the company's reporting was not honest and its trading operation was perhaps not as successful as had been reported. However, this would hardly have been enough to produce such a large effect. What happened was an unwillingness of trading clients to deal with a counterparty that might not be able to meet its future contractual obligations. Without the backing of the parent firm's balance sheet, its stockholder equity, and its ability to borrow, the trading operation could not continue. So now we have the incentive asymmetry to set off the information asymmetry. The wider firm, which is less knowledgeable in this set of instruments than the group of front-office experts, must bear the full financial loss if the front office's positions perform badly. The moral hazard consists of the possibility that the front office may be more willing to risk the possibility of large losses in which it will not have to fully share in order to create the possibility of large gains in which it will have a full share. And the rest of the firm may not have sufficient knowledge of the front office's positions, due tothe information asymmetry, to be sure that this has not occurred. What are some possible solutions? Could a firm just purchase an insurance contract against trading losses? This is highly unlikely. An insurance firm would have even greater concerns about moral hazard because it would not have as much access to information as those who are at least within the same firm, even if they are less expert. Could the firm decide to structure the pay of the front office so that it will be the same no matter what profits are made on its transactions, removing the temptation to take excessive risk to generate potential large gains? The firm could, but experience in financial firms strongly suggests the need for upside participation as an incentive to call forth the efforts needed to succeed in a highly competitive environment. Inevitably, the solution seems to be an ongoing struggle to balance the proper incentive with the proper controls. This is the very heart of the design of a risk management regime. If the firm exercises too little control, the opportunities for moral hazard may prove too great. If it exercises too much control, it may pass up good profit opportunities if those who do not have as much knowledge as the front office make the decisions. To try to achieve the best balance, the firm will employ experts in risk management disciplines such as market risk, credit risk, legal risk, and operations risk. It will set up independent support staff to process the trades and maintain the records of positions and payments (the back office); report positions against limits, calculate the daily profit and loss (P&L), and analyze the sources of P&L and risk (the middle office); and take responsibility for the accuracy of the firm's books and records (the finance function). However, the two-sided asymmetry of information and incentive will always exist, as the personnel in these control and support functions will lack the specialized knowledge that the front office possesses in their set of instruments. The two-sided asymmetry that exists at this basic level can be replicated at other levels of the organization, depending on the size and complexity of the firm. The informational disadvantage of the manager of fixed-income products relative to the front office for European bonds will be mirrored by the informational disadvantage of the manager of all trading products relative to the manager of fixed- income products and the firm's CEO relative to the manager of all trading products. Certainly, the two-sided asymmetry will be replicated in the relationship between the management of the firm and those who monitor the firm from the outside. Outside monitors primarily represent three groups—the firm's creditors (lenders and bondholders), the firm's shareholders, and governments. All three of these groups have incentives that differ from the firm's management, as they are exposed to losses based on the firm's performance in which the management will not fully share. The existence of incentive asymmetry for creditors is reasonably obvious. If the firm does well, the creditors get their money back, but they have no further participation in how well the firm performs; if the firm does very badly and goes bankrupt, the creditors have substantial, possibly even total, loss of the amount lent. By contrast, the firm's shareholders and management have full participation when the firm performs well, but liability in bankruptcy is limited to the amount originally invested. When we examine credit risk in Section 13.2.4, this will be formally modeled as the creditors selling a put option on the value of the firm to the shareholders. Since all options create nonlinear (hence asymmetric) payoffs, we have a clear source of incentive asymmetry for creditors. It is less clear whether incentive asymmetry exists for shareholders. In principle, their interests are supposed to be exactly aligned with those of the firm's management, and incentives for management based on stock value are used to strengthen this alignment. In practice, it is always possible that management will take more risk than shareholders would be completely comfortable with in the hopeof collecting incentive-based compensation in good performance years that does not have to be returned in bad performance years. Kotowitz (1989) quotes Adam Smith from Wealth of Nations: “The directors of such companies, however, being managers rather of other people's money than of their own, it cannot well be expected, that they should watch over it with the same anxious vigilance with which the partners in a private company frequently watch over their own.” Government involvement arises from the asymmetric dangers posed to the health of the overall economy by the failure of a financial firm. If an implicit government guarantee is given to rescue large financial firms from bankruptcy (the notion of “too big to fail”), then moral hazard is created through management's knowledge that it can try to create profit opportunities, in which the government has only limited participation through taxes, by taking risks of losses that will need to be fully absorbed by the government. If the government is not willing to prevent the failure of large financial firms, then it will want to place restrictions on the externalities that those firms can create by not having to bear their share of the cost to the overall economy of a firm's potential bankruptcy. In all three cases of moral hazard involving outside monitors, the information asymmetry is even more severe than when the information asymmetry takes place wholly inside the firm. Senior management and its risk monitors are at least on the premises, are involved in day-to-day business with more junior managers, and can utilize informal measures, such as the rotation of managers through different segments of the firm, to attempt to diffuse both incentives and knowledge. Outside monitors will have only occasional contact with the firm and must rely mostly on formal requirements to obtain cooperation. Let us look at some of the outside monitors that creditors, shareholders, and governments rely on: In addition to their own credit officers, creditors rely on rating agencies such as Moody's Investors Service and Standard & Poor's (S&P) to obtain information about and make judgments on the creditworthiness of borrowers. Shareholders and creditors rely on investment analysts working for investment bankers and brokerage firms to obtain information about and make judgments on the future earnings prospects and share values of firms. Although neither rating agencies nor investment analysts have any official standing with which to force cooperation from the firms they analyze, their influence with lenders and investors in bonds and stocks gives them the leverage to obtain cooperation and access to information. Governments can use their regulatory powers to require access to information from financial firms and employ large staffs to conduct examinations of the firms. For example, for the U.S. government, the Federal Reserve System and the Comptroller of the Currency conduct examinations of commercial banks. A similar function is performed by the Securities and Exchange Commission (SEC) for investment banks. Creditors, shareholders, and governments all rely on independent accounting firms to conduct audits of the reliability of the financial information disclosures that are required of all publicly held firms. Over the years, many critical questions have been raised about how truly independent the judgment of these outside monitors really is: Credit rating agencies have been accused of being too slow to downgrade ratings in response to adverse changes in a firm's financial condition because their source of revenue comes from thefirms whose debt they rate. Similarly, independent auditors have been suspected of being too deferential to the firms they monitor since these firms are the ones who pay their audit fees and hire them for consulting services. The fear is that the desire for more revenue will blunt objections to companies choosing accounting methods that cast their results in a favorable light. Investment banks have a built-in conflict of interest from competing for the business of the firms whose performance their investment analysts are monitoring. It has long been noted that analysts' buy recommendations far outnumber sell recommendations. Accusations have been leveled that government regulatory agencies are more concerned with protecting the interests of the firms being monitored than with protecting the public interest. These charges have particular force when personnel flow freely between employment in the regulatory agencies and in the firms they regulate. All of these criticisms seemed to be coming to a head in 2002 amid the scandals involving the now- defunct auditing firm of Arthur Andersen, Enron's declaration of bankruptcy only a week after being rated investment grade, and the massive declines in the stock values of technology firms highly touted by investment analysts. Some useful reforms have been undertaken, such as forbidding auditing firms to sell consulting services to firms they audit and not allowing the bonuses of investment analysts to be tied to investment banking fees collected from clients whose stocks they cover. However, the basic sources of conflict of interest remain, and investors and lenders will continue to need to employ a skeptical filter when utilizing input from outside monitors. Although the conflicts between insiders and outsiders due to the two-sided asymmetry of moral hazard cannot be eliminated, a frank understanding by both sides can lead to a cooperative relationship. In a cooperative relationship, insiders will acknowledge the need to have outsiders exercise controls and will voluntarily share information and knowledge with outsiders. In a cooperative relationship, outsiders will acknowledge their need to learn from the insiders and will ease controls in response to a track record of openness, although both must recognize the need to always have some level of controls (the ancient folk wisdom states that “I trust my grandmother, but I still cut the cards when she deals”). A lack of understanding of moral hazard can lead to an uncooperative relationship fueled by mutual resentments between an insider, such as a trader or structurer, with an outsider, such as a corporate risk manager or regulator. An insider who does not understand the purely situational need to have someone less knowledgeable “look over my shoulder” will attribute it to an insulting lack of personal trust, an arrogant assumption of more knowledge than the other possesses, or a simple desire by the outsider to create a job or grab power (which is not to say that some of these motivations do not exist in reality, mixed in with the need to control moral hazard). The insider's response will then probably be to withhold information, obfuscate, and mislead, which will drive the outsider to even closer scrutiny and more rigid controls, which is clearly a prescription for a vicious circle of escalation. An outsider who lacks an understanding of the situation may defensively try to pretend to have more knowledge than he actually has or may denigrate the knowledge of the insider, which will only exacerbate any suspicions of the process the insider has. Moral hazard has long been a key concept in the analysis of insurance risks. A typical example would be an insurance company's concern that an individual who has purchased insurance against auto theft will not exercise as much care in guarding against theft (for example, parking in a garagerather than on the street) as one who has not purchased insurance. If the insurance company could distinguish between individuals who exercise extra care and those who don't, it could sell separate contracts to the two types of individuals and price the extra losses into just the type sold to those exercising less care. However, the information advantage of an individual monitoring his own degree of care relative to the insurance company's ability to monitor it makes this prohibitively expensive. So the insurance company needs to settle for cruder measures, such as establishing a deductible loss that the insured person must pay in the event of theft, thereby aligning the interests of the insured more closely with the insurer. It has become increasingly common for moral hazard to be cited in analyses of the economics of firms in general, particularly in connection with the impact of the limited liability of shareholders willing to take larger gambles. The shareholders know that if the gamble succeeds, they will avoid bankruptcy and share in the profits, but will suffer no greater loss in a large bankruptcy than in a smaller one. To quote W. S. Gilbert: You can't embark on trading too tremendous, It's strictly fair and based on common sense, If you succeed, your profits are stupendous, And if you fail, pop goes your eighteen pence. (from Gilbert and Sullivan's Utopia, Limited) A firm's creditors can exercise some control over their actions and might be able to forbid such gambles, assuming they have sufficient knowledge of the nature of the firm's investments. This is where the informational advantage of the managers over the creditors with respect to the firm's investments comes in. What sort of actions can we expect from a trader based on the concept of moral hazard? We can certainly expect that the trader may have a different degree of risk aversion than the firm's management, since traders' participation in favorable results exceeds their participation in downside results. Taleb (1997, 66) refers to this as the trader “owning an option on his profits” and states that in such circumstances “it is always optimal to take as much risk as possible. An option is worth the most when volatility is highest.” This will probably become even more noticeable if the trader has been having a poor year. Knowing that she is headed toward a minimal bonus and possible dismissal may incline the trader to swing for the fences and take a large risk. The trader knows that if the risk turns out favorably, it might be enough to reverse previous losses and earn a bonus. If it turns out poorly, then “you can't get less than a zero bonus” and “you can't get fired twice.” (You can damage your reputation in the industry, but sharing information about a trader's track record between competitor firms cannot be done that efficiently—more information asymmetry.) For this reason, firms may severely cut the trading limits of a trader having a poor year. Beyond the differences in risk aversion, moral hazard can even result in the perverse behavior (for the firm) of having a trader willing to increase risk exposure when faced with a lower expected return. Consider the following advice to traders from Taleb (1997, 65): How aggressive a trader needs to be depends highly on his edge, or expected return from the game: When the edge is positive (the trader has a positive expected return from the game, as is the case with most market makers), it is always best to take the minimum amount of risk and letcentral limit slowly push the position into profitability. This is the recommended method for market makers to progressively increase the stakes, in proportion to the accumulated profits. In probability terms, it is better to minimize the volatility to cash-in on the drift. When the edge is negative, it is best to be exposed as little as possible to the negative drift. The operator should optimize by taking as much risk as possible. Betting small would ensure a slow and certain death by letting central limit catch up on him. The mathematics and economic incentives that this advice is based on are certainly sound. It is advice that is known to every gambler (or ought to be) and is well founded in statistical theory. When the odds are in your favor, place many small bets; when the odds are against you, place one large bet. Essentially, when the odds are against you, you are attempting to minimize the length of time you are playing against the house since you are paying a tax, in the form of an expected loss, for the privilege of playing. However, although this makes perfect economic sense from the viewpoint of the individual trader, it is hardly the strategy the firm employing these traders would want to see them follow. The firm, whose P&L will be the sum of the results of many traders, would like to see traders with a negative expected return not take any positions at all rather than have these be the traders taking on the most risk. To the extent the firm's management can figure out which traders have a negative edge, it will restrict their risk taking through limits and the replacement of personnel. However, the individual traders have the information advantage in knowing more than the firm about their expected returns. They also have the asymmetrical incentive to take larger risks in this case, even though doing so will probably hurt the firm. The traders will not derive much benefit from the firm doing well if they do not contribute to that result, but they will benefit if they do increase their risk and win against the odds. Moral hazard helps to explain the valuation that investors place on the earnings volatility of financial firms. You could argue that firms should worry just about the expected value and not about volatility, since the market should place a risk premium only on risk that it cannot hedge away (an investor who wants less risk will just take the stock with the highest expected return and diversify by mixing with government bonds). However, empirical evidence shows that the market places a stiff discount on variable trading earnings. The reason may be information asymmetry. It is hard for outsiders to tell whether a firm is taking sound gambles to maximize expected value or is maximizing its insiders' option on one-way bets. Perold (1998) states: I view financial intermediaries as being special in several ways: First, these firms are in credit- sensitive businesses, meaning that their customers are strongly risk-averse with respect to issuer default on contractually promised payoffs. (For example, policyholders are averse to having their insurance claims be subject to the economic performance of the issuing firm, and strictly prefer to do business with a highly rated insurer.) The creditworthiness of the intermediary is crucial to its ability to write many types of contracts, and contract guarantees feature importantly in its capital structure. Second, financial firms are opaque to outsiders. They tend to be in businesses that depend vitally on proprietary financial technology and that cannot be operated transparently. In addition, the balance sheets of financial firms tend to be very liquid, and are subject to rapid change. Financial firms, thus, are difficult to monitor, and bear significant deadweight costs ofcapital. Guarantors face costs related to adverse selection and moral hazard. . . . Third, financial firms are also internally opaque. Information tends to be private at the business unit level, or even at the level of individual employees such as traders. Efficient management of these firms thus involves significant use of performance-related compensation to mitigate against monitoring difficulty. Moral hazard can create a battleground over information between insiders and outsiders. Insiders are fearful that any information obtained by outsiders will be used as a tool to tighten controls over insiders' actions. Insiders can be expected to have an inherent bias against tighter controls, partly because narrowing the range of actions available leads to suboptimal solutions and partly because incentive asymmetry makes riskier action more rewarding to insiders than to outsiders. One of the most common ways in which insiders can mislead outsiders about the need for controls is termed a Ponzi scheme. 2.2 PONZI SCHEMES In its original meaning, a Ponzi scheme is a criminal enterprise in which investors are tricked into believing that they will receive very high returns on their investments, but the early investors are paid out at high rates of return only with the payments coming from the cash invested by later investors. The illusion of high returns can be pretty convincing. After all, you can actually see the early investors receiving their high returns in cash, and the con men running these schemes can produce very plausible lies about the purported source of the returns. As a result, the pace of new investment can be intense, enabling the illusion of profit to be maintained over a fairly long time period. It's a vicious cycle—the eagerness of new investors to place money in the scheme leads to the heightened ability to make investments appear highly profitable, which leads to even greater eagerness of new investors. However, ultimately, any Ponzi scheme must collapse, as there is no ultimate source of investment return (in fact, investment return is quite negative, as the flow of new investment must also be partially diverted to the criminals profiting from it). Ponzi schemes are also sometimes called pyramid schemes and bear a close resemblance to chain letter frauds. When I wrote the immediately preceding paragraph for the first edition of this book in 2003, I felt the need to thoroughly explain what a Ponzi scheme is. Today, it is probably not necessary, as Bernie Madoff has regrettably given us all an exhaustive lesson in how a Ponzi scheme is run. The original meaning of Ponzi schemes has been broadened by risk managers to include situations in which firms are misled as to the profitability of a business line by the inadequate segregation of profits on newly acquired assets and returns on older assets. Let's consider a typical example. Suppose a trading desk has entered into marketing a new type of path-dependent option. The desk expects substantially more customer demand for buying these options than for selling them. They intend to manage the resulting risk with dynamic hedging using forwards and more standard options. As we will see when discussing path-dependent options in Section 12.3, it is very difficult to try to estimate in advance how successful a dynamic hedging strategy for path-dependent options will be. In such circumstances, the pricing of the option to the client must be based on an estimate of the future cost of the dynamic hedging, applying some conservatism to try to cover the uncertainty. Let'sassume that a typical trade has a seven-year maturity, and that the customer pays 8 million and the firm pays 5 million to purchase the initial hedge. Of the remaining 3 million, we'll assume that the desk is estimating dynamic hedging costs of 1 million over the two years, but the uncertainty of these costs leads to setting up a 2 million initial allowance (or reserve) to cover the hedging costs, leaving 1 million to be booked as up-front profit. Suppose the trading desk has made a serious error in predicting the hedging costs, and the hedging costs actually end up around 5 million, leading to a net loss of 2 million on every transaction booked. You may not be able to do anything about deals already contracted, but you would at least hope to get feedback from the losses encountered on these deals in time to stop booking new deals or else raise your price to a more sustainable level. This should happen if P&L reporting is adequately detailed, so you can see the losses mounting up on the hedging of these trades (this is called hedge slippage). However, it is often difficult to keep track of exactly how to allocate a day's trading gains and losses to the book of deals being hedged. You want to at least know that trading losses are occurring so you can investigate the causes. The most severe problem would be if you didn't realize that trades were losing money. How could this happen? If P&L reporting is not adequately differentiated between the existing business and new business, then the overall trading operation can continue to look profitable by just doing enough new business. Every time a new deal is booked, 1 million goes immediately into P&L. Of course, the more deals that are booked, the larger the hedging losses that must be overcome, so even more new trades are needed to swamp the hedging losses. The resemblance to a Ponzi scheme should now be obvious. One key difference is that in its original meaning, the Ponzi scheme is a deliberate scam. The financial situation described is far more likely to arise without any deliberate intent. However, those in the front office, based on their close knowledge of the trading book, will often suspect that this situation exists before any outsiders do, but may not want to upset the apple cart. They would be jeopardizing bonuses that can be collected up front on presumed earnings. They may also be willing to take the risk that they can find a way to turn the situation around based on their greater participation in future upside than future downside. They may choose to hide the situation from outsiders who they suspect would not give them the latitude to take such risks. So moral hazard can turn an accidentally originated Ponzi scheme into one that is very close to deliberate. As a historical footnote, the Ponzi scheme derives its name from Charles Ponzi, a Boston-based swindler of the 1920s (though it was not the first Ponzi scheme—William “520 Percent” Miller ran one in Brooklyn around 1900; an excellent 1905 play by Harley Granville-Barker, The Vosey Inheritance, which has been revived frequently over the past decade, revolves around a lawyer specializing in trusts and estates trying to train his son to take over the management of his Ponzi scheme). The following account of Charles Ponzi is drawn from Sifakis (1982): Ponzi discovered he could buy up international postal-union reply coupons at depressed prices and sell them in the United States at a profit up to 50 percent. It was, in fact, a classic get-rich-slowly operation, and as such, it bored Ponzi. So he figured out a better gimmick. Ponzi figured out that telling people he was making the money and how he could make it was just as good as actually making it. He advertised a rate of return of 50 percent in three months. It was an offer people couldn't refuse, and money started to come rolling in.When Ponzi actually started paying out interest, a deluge followed. On one monumental day in 1920, Ponzi's offices took in an incredible 2 million from America's newest gamblers, the little people who squeezed money out of bank accounts, mattresses, piggy banks, and cookie jars. There were days when Ponzi's office looked like a hurricane had hit it. Incoming cash had to be stuffed in closets, desk drawers and even wastebaskets. Of course, the more that came in, the more Ponzi paid out. As long as new funds were coming in, Ponzi could continue to make payments. However, as with all pyramid schemes, the bubble had to burst. A newspaper published some damaging material about his past, including time spent in prison. New investors started to hesitate. Ponzi's fragile scheme collapsed, since it required an unending flow of cash. His books, such as they were, showed a deficit of somewhere between 5 and 10 million, or perhaps even more. No one ever knew for sure. 2.3 ADVERSE SELECTION Let's return to the situation described previously. Suppose our accounting is good enough to catch the hedge slippage before it does too much damage. We stop booking new deals of this type, but we may find we have booked a disturbingly large number of these deals before the cutoff. If our customers have figured out the degree to which we are underpricing the structure before we do, then they may try to complete as many deals as they can before we wise up. This pattern has frequently been seen in the financial markets. For example, the last firms that figured out how to correctly price volatility skew into barrier options found that their customers had loaded up on trades that the less correct models were underpricing. A common convention is to label this situation as adverse selection as a parallel to a similar concern among insurance firms, which worry that those customers with failing health will be more eager to purchase insurance than those with better health, taking advantage of the fact that a person knows more about his own health than an insurance company can learn (Wilson 1989). So adverse selection is like moral hazard since it is based on information asymmetry; the difference is that moral hazard is concerned with the degree of risk that might be taken based on this asymmetry, whereas adverse selection is concerned with a difference in purchasing behavior. In 2001, George Ackerlof, Michael Spence, and Joseph Stiglitz won the Nobel Prize in economics for their work on adverse selection and its application to a broad class of economic issues. Concern about the risk from adverse selection motivates risk managers' concern about the composition of a trading desk's customer base. The key question is: What proportion of trades is with counterparties who are likely to possess an informational advantage relative to the firm's traders? As a general rule, you prefer to see a higher proportion of trades with individuals and nonfinancial corporations that are likely trading to meet hedging or investment needs rather than seeking to exploit informational advantage. Alarm is raised when an overwhelming proportion of trades is with other professional traders, particularly ones who are likely to see greater deal flow or have a greater proportion of trades with individuals and nonfinancial corporations than your firm's traders. Seeing greater deal flow can give a firm an informational advantage by having a more accurate sense of supply-and-demand pressures on the market. A greater proportion of customers who are not professional traders yields two further potential informational advantages:1. At times you work with such customers over a long period of time to structure a large transaction. This gives the traders advance knowledge of supply and demand that has not been seen in the market yet. 2. Working on complex structures with customers gives traders a more intimate knowledge of the structure's risks. They can choose to retain those risks that this knowledge shows them are more easily manageable and attempt to pass less manageable risks on to other traders. Traders may tend to underestimate the degree to which their profitability is due to customer deal flow and overestimate the degree to which it is due to anticipating market movements. This can be dangerous if it encourages them to aggressively take risks in markets in which they do not possess this customer flow advantage. A striking example I once observed was a foreign exchange (FX) trader who had a phenomenally successful track record of producing profits at a large market-making firm. Convinced of his prowess in predicting market movements, he accepted a lucrative offer to move to a far smaller firm. He was back at his old job in less than year, confessing he simply had not realized how much of his success was due to the advantages of customer deal flow. A pithy, if inelegant, statement of this principle was attributed to the head of mortgage-backed trading at Kidder Peabody: “We don't want to make money trading against smart traders; we want to make money selling to stupid customers.” Of course, stupid needs to be understood here as macho Wall Street lingo for informationally disadvantaged. It's the sort of talk that is meant to be heard only in locker rooms and on trading floors. An unfriendly leak resulted in his quote appearing on the front page of the Wall Street Journal. It is delightful to imagine the dialogue of some of his subsequent conversations with the firm's customers. 2.4 THE WINNER'S CURSE In response to the risks of adverse selection, traders may exhibit confidence that this is not something they need to worry about. After all, adverse selection impacts only those with less knowledge than the market. It is a rare trader who is not convinced that she possesses far more knowledge than the rest of the market—belief in one's judgment is virtually a necessity for succeeding in this demanding profession. Whether the firm's management shares the trader's confidence may be another story. However, even if it does, the trader must still overcome another hurdle—the winner's curse, the economic anomaly that says that in an auction, even those possessing (insider) knowledge tend to overpay. The winner's curse was first identified in conjunction with bidding for oil leases, but has since been applied to many other situations, such as corporate takeovers. My favorite explanation of the mechanism that leads to the winner's curse comes from Thaler (1992): Next time you find yourself a little short of cash for a night on the town, try the following experiment in your neighborhood tavern. Take a jar and fill it with coins, noting the total value of the coins. Now auction off the jar to the assembled masses at the bar (offering to pay the winning bidder in bills to control for penny aversion). Chances are very high that the following results will be obtained: 1. The average bid will be significantly less than the value of the coins. (Bidders are risk averse.)2. The winning bid will exceed the value of the jar. In conducting this demonstration, you will have simultaneously obtained the funding necessary for your evening's entertainment and enlightened the patrons of the tavern about the perils of the winner's curse. When applied to trading, the winner's curse is most often seen in market making for less liquid products, where opinions on the true value of a transaction may vary more widely. Market makers are in competition with one another in pricing these products. The firm that evaluates a particular product as having a higher value than its competition is most likely to be winning the lion's share of these deals. Consider a market for options on stock baskets. As we will discuss in Section 12.4, a liquid market rarely exists for these instruments, so pricing depends on different estimates of correlation between stocks in a basket. The firm that has the lowest estimate for correlation between technology stocks will wind up with the most aggressive bids for baskets of technology stocks and will book a large share of these deals. Another firm that has the lowest estimate for correlation between financial industry stocks will book the largest share of those deals. An anecdotal illustration comes from Neil Chriss. When Chriss was trading volatility swaps at Goldman Sachs, they would line up five or six dealers to give them quotes and would always hit the highest bid or lift the lowest offer. The dealers knew they were doing this and were very uneasy about it, limiting the size of trades they would accommodate. One dealer, on winning a bid, told Chriss, “I am always uncomfortable when I win a trade with you, as I know I was the best bid on top of five other smart guys. What did I do wrong?” Adverse selection can be controlled by gaining expertise and increasing the proportion of business done with ultimate users rather than with other market makers. However, the winner's curse can be controlled only by either avoiding auction environments or adequately factoring in a further pricing conservatism beyond risk aversion. It provides a powerful motivation for conservatism in pricing and recognizing profits for those situations such as one-way markets (see Section 6.1.3) in which it is difficult to find prices at which risks can be exited. We demonstrate the mechanism of the winner's curse with a simple numerical example involving a market with only three firms, two buyers, and one seller. The results are shown in Table 2.1. TABLE 2.1 The Winner's CurseWe consider two different situations. In the first, direct negotiation occurs on the price between the seller and a single buyer. In the second, both buyers participate in an auction. There are 10 transactions that the seller might sell to the buyers. Neither the buyers nor the seller is certain of the true value of these transactions (for example, they might depend on future dynamic hedging costs, which depend on the evolution of future prices, which different firms estimate using different probability distributions). After the fact, we know the true realized value of each transaction, as shown in column 2 of the table. Buyer 1's knowledge of this market is superior to buyer 2's, and both have superior knowledge compared to the seller. This can be seen by the correlations between realized value and each party's estimate of transaction value (83.3% for buyer 1, 72.2% for buyer 2, and 63.2% for the seller). The consequences of this informational advantage are that both buyer 1 and buyer 2 make a profit at the expense of the seller in direct negotiations, and that buyer 1's profit in this situation is higher than buyer 2's profit. In the direct negotiation situation, we assume that the buyer, being risk averse, has successfully biased his bids down to be on average lower than the realized value, and the seller, being risk averse, has successfully biased his asked prices up to be on average higher than realized value. We assume no transaction takes place if the buyer's bid is lower than the seller's asked. If the buyer's bid exceeds the seller's asked, we assume the transaction takes place at the average price between these two prices. As a result, buyer 1 has a total P&L of +1.09, and buyer 2 has a total P&L of +0.55. Now consider what happens in the auction when the buyers have to compete for the seller'sbusiness, a situation very typical for market making firms that must offer competitive price quotations to try to win customer business from other market makers. The seller no longer relies on his own estimate of value, but simply does business at the better bid price between the two firms. Even though both firms continue to successfully bias their bids down on average from realized values, both wind up losing money in total, with buyer 1 having a P&L of –0.86 and buyer 2 having a P&L of –0.84. This is because they no longer have gains on trades that they seriously undervalued to balance out losses on trades that they seriously overvalued, since they tend to lose trades that they undervalue to the other bidder. This illustrates the winner's curse. The spreadsheet WinnersCurse on the course website shows the consequences of changing some of the assumptions in this example. 2.5 MARKET MAKING VERSUS POSITION TAKING An important institutional distinction between participants in the financial markets that we will refer to on several occasions throughout this book is between market making and position taking: Market making (also called book running or the sell side) consists of making two-way markets by engaging in (nearly) simultaneous buying and selling of the same instruments, attempting to keep position holdings to a minimum and to profit primarily through the difference between (nearly) simultaneous buy and sell prices. Position taking (also called market using, price taking, speculation, or the buy side) consists of deliberately taking positions on one side or the other of a market, hoping to profit by the market moving in your favor between the time of purchase and the time of sale. Positions may be taken on behalf of a firm (in which case it is often labeled proprietary trading) or on behalf of an individual client or a group of clients, such as a mutual fund, hedge fund, or managed investment account. Some time lag nearly always occurs between the purchase and sale involved in market making. Depending on the length of time and degree of deliberate choice of the resulting positions, these may be labeled position-taking aspects of market making. Market making almost always involves risk because you cannot often buy and sell exactly simultaneously. The market maker makes a guess on market direction by its posted price, but the bid-ask spread can outweigh even a persistent error in directional guess as long as the error is small. (In Exercise 9.1, you'll be asked to build a simulation to test out the degree to which this is true.) The experience and information gained from seeing so much flow means you most likely will develop the ability to be right on direction on average. However, the position taker has the advantage over the market maker of not needing to be in the market every day. Therefore, the position taker can stay away from the market except when possessed of a strong opinion. The market maker cannot do this; staying away from the market would jeopardize the franchise. The different objectives of market makers and position takers tend to be reflected in different attitudes toward the use of models and valuation techniques. A position taker generally uses models as forecasting tools to arrive at a best estimate of what a position will be worth at the conclusion of a time period tied to an anticipated event. The position taker will pay attention to the market price of the position during that time period to determine the best time to exit the position and to checkwhether new information is coming into the market. However, a position taker will generally not be overly concerned by prices moving against the position. Since the position taker is usually waiting for an event to occur, price movements prior to the time the event is expected are not that relevant. A frequently heard statement among position takers is: “If I liked the position at the price I bought it, I like it even better at a lower price.” By contrast, a market maker generally uses models to perform risk decomposition in order to evaluate alternative current prices at which a position can be exited. The market maker will pay close attention to current market prices as the key indicator of how quickly inventory can be reduced. The direction in which prices will move over the longer term is of little concern compared to determining what price will currently balance supply and demand. An amusing analogy can be made to gambling on sports. Position takers correspond to the gamblers who place their bets based on an analysis of which team is going to win and by what margin. Market makers correspond to the bookmakers whose sole concern is to move the odds quoted to a point that will even out the amount bet on each side. The bookmaker's concern is not over which team wins or loses, but over the evenness of the amounts wagered. Close to even amounts let the bookmakers come out ahead based on the spread or vigorish in the odds, regardless of the outcome of the game. Uneven amounts turn the bookmaker into just another gambler who will win or lose depending on the outcome of the game. As explained in Section 1.1, the focus of this book is on the active use of trading in liquid markets to manage risk. This view is more obviously aligned with market making than with position taking. In fact, the arbitrage-based models that are so prominent in mathematical finance have been developed largely to support market making. Position takers tend more toward the use of econometric forecasting models. In Section 6.1.7, we will further discuss the issue of the extent to which position takers should adopt the risk management discipline that has been developed for market makers. Some authors distinguish a third type of financial market participant besides market makers and position takers—the arbitrageurs. I believe it is more useful to classify arbitrage trading as a subcategory of position taking. Pure arbitrage, in its original meaning of taking offsetting positions in closely related markets that generate a riskless profit, is rarely encountered in current financial markets, given the speed and efficiency with which liquid prices are disseminated. What is now labeled arbitrage is almost always a trade that offers a low but relatively certain return. The motivations and uses of models by those seeking to benefit from such positions are usually closely aligned with other position takers. A good example is merger arbitrage (sometimes misleadingly called risk arbitrage). Suppose that Company A and Company B have announced a forthcoming merger in which two shares of A's stock will be traded for one share of B's stock. If the current forward prices of these stocks to the announced merger date are 50 for A and 102 for B, an arbitrage position would consist of a forward purchase of two shares of A for 100 and a forward sale of one share of B for 102. On the merger date, the two shares of A purchased will be traded for one share of B, which will be delivered into the forward sale. This nets a sure 2, but only if the merger goes through as announced. If the merger fails, this trade could show a substantial loss. Merger arbitrageurs are position takers who evaluate the probability of mergers breaking apart and study the size of loss that might result. They are prototypical forecasters of events with generally little concern for market price swings prior to the occurrence of the event.

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