Rethinking_risk_management.pdf

Rethinking risk management by

René M. Stulz*

Revised, September 1996

*Bower Fellow, Harvard Business School; Reese Chair in Banking and Monetary Economics, The Ohio State University; Research Associate, National Bureau of Economic Research. I am grateful for comments to Steve Figlewski, Andrew Karolyi, Robert Whaley, and participants at a seminar ta McKinsey, at the Annual Meetingof the International Association of Financial Engineers, and at the French Finance Association.

Abstract Empirical evidence shows that the practice of risk management is limited and does not correspond to the prescriptions of the academic literature. In particular, the practice focuses on hedging transactions exposures and a firm’s hedge ratios depend on the views of the managers of that firm. In this paper, we provide a new approach to risk management that is consistent both with the main results of the academic literature but takes into account the factthat firms can have a comparative advantage in bearing some kinds of risks. We examine the implications of this new approach for the management of risk management and for risk measures such as Var.

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1. Introduction. This article explores a paradox in the current practice of risk management. Academic research argues strongly that risk management creates value. Most of the academic research focuses on risk management that decreases variability of firm value or cash flows. Despite this academic literature, however, the practice of risk management is rather limited and it does not seem to correspond to the recommendations of academics. Does this mean that academic theories of risk management are not useful? Is there too little risk management? Is it the right kind of risk management? In the first part of this article, I review some evidence we have about risk management practice. Part of this evidence has to do with the derivative losses of the past few years. What do these losses tell us about practice? Would these losses have occurred if firms had followed modern corporate finance theory? The rest of the evidence consists of survey data. All of the evidence shows that firms let their views about the rewards for bearing hedgeable risks affect their hedge ratios in a significant way. This raises the question of whether such a practice is consistent with modern risk management theory. I present the main elements of this theory. Whereas much of the literature interprets this theory as suggesting that firms should hedge risks to reduce the variance of cash flow, I show that the theory properly interpreted is consistent with some of current practice and can be used to improve current practice. The theory implies that some firms should hedge all risks, that other firms should not worry about risk at all, and finally, that some firms should worry only about some kinds of risks. Some firms have a comparative advantage in taking some types of risks; others do not. I argue that existing risk measures such as VAR or the variance of cash flows cannot be motivated from existing theory. I present a risk measure which has a foundation in modern finance theory and is easy to compute. Finally, I conclude with a discussion of the management of risk management. If risk management is not focused on variance reduction, then much more attention should be devoted to the control, management and evaluation of risk taking and we should develop a better understanding of the agency costs of risk taking. The paper proceeds as follows. Section 2 discusses empirical evidence. Section 3 reviews existing

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academic theories of risk management. Section 4 evaluates the empirical evidence in light of the academic theories. Section 5 makes the argument that firms have comparative advantages in taking some risks. Section 6 discusses why risk-taking differs across firms. Section 7 provides risk measures that are consistent with current practice and academic theories. Section 8 examines how risk management should be organized when it involves exploiting views. Section 9 concludes.

Section 2. Risk management in practice. In one of their papers on Metallgesellschaft, Culp and Miller have a startling footnote: “We need hardly remind readers that most value-maximizing firms do not hedge.” (Culp and Miller (1995), p.122.) Is this really true? How would we know? They refer to survey evidence. The Wharton-Chase study sent questionnaires to 1,999 firms. Of these firms, 530 responded. Only 34.5% of the firms answer “yes” when asked if they buy or sell futures, forwards, options, or swaps. Interestingly, large firms use derivatives a lot more: 65% of the large firms use derivatives, whereas only 13% of the small firms use derivatives. Of the firms that use derivatives, the only uses of derivatives on which more than half the firms using derivatives agree are to hedge contractual commitments and to hedge anticipated transactions taking place within twelve months. About 2/3 of the firms responded that they never use derivatives to reduce funding costs by arbitraging the markets or by taking a view, never use derivatives to hedge the balance sheet, foreign dividends and economic or competitive exposure. The study was updated in 1995 and its results published in 1996 as the Wharton-CIBC Wood Gundy study. Although the 1995 questionnaire was sent to more firms, it received substantially fewer answers than the 1994 questionnaire. Nevertheless, the results of the 1995 confirm the results of the 1994 study. One striking result of the 1995 study is that over a third of all derivative users say that sometimes they actively take positions based on their market views of interest rate and exchange rates. Dolde (1993) also conducted an extensive survey. He sent his questionnaire to Fortune 500 companies. 244 companies responded. 85% said that they were using derivatives to manage financial risks. Almost all

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companies who responded (90%) said that their view would affect the extent to which they hedge. For the companies surveyed, the focus of risk management was mostly on transaction exposures. Another recent study by Price Waterhouse surveys in the first half of 1995 386 leading companies based in 16 countries outside the U.S.1 7% of the companies treat their treasury function as a profit center. In these cases, the firms try to make a profit by actively managing the financial risks of the business and hence do not simply hedge passively. This view of having the treasury operations used to make profits is one that holds frequently within U.S. firms also. Typically, however, the extent to which treasury operations try to make profits is by varying the hedge ratio depending on their expectations. For instance, in some periods, they do not want to be long in a currency because they expect it to depreciate. The bottom line from these surveys and other surveys is that firms do not systematically hedge, that the extent to which they hedge depends on the view they take, and that use of derivatives is greater for large firms than small firms. Many of the well-reported derivative problems of recent years are fully consistent with this survey evidence and make it possible to understand practice better. We briefly review two cases where firms lost large amounts of money as a result of risk management programs.

Metallgesellschaft. The case of Metallgesellshaft has generated strong controversies. Nevertheless, there is general agreement about the facts of the case. MGRM, the oil marketing subsidiary of Metalgesellshaft in the U.S., had contracted to sell 154 million barrells of oil through fixed-price contracts over a period of ten years by the end of 1993. These fixed-price contracts created a large exposure to oil price changes. MGRM therefore decided to hedge. However, it did not do so in a straightforward way. It decided to take positions in short-term contracts, both futures and swaps. One can estimate the minimum-variance hedge position for MGRM in short-term contracts. One such estimate, by Mello and Parsons (1995), is that the minimum-variance hedge position would have 1

See Financial Times, Tuesday October 17, 1995, p.26.

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required the forward purchase of 86 million barrels of oil. According to them, this position would have minimized the variance of the present value of MGRM’s hedged position in oil over the near future and would have needed to be changed over time. Yet, MGRM bought 154 million barrels in short maturity contracts. Hence, in no sense did MGRM use a hedge that minimized the variance of its hedged position in oil. MGRM took the position it did because it thought it could benefit from the typical backwardation of oil futures. Backwardation is the situation where spot prices are higher than futures prices. Over the near future, the long position of 154 million barrels is equivalent to a pure hedge position of 86 million barrels of oil and a speculative position of 58 million barrels of oil. Over the long haul, however, the speculative position taken by MGRM involves a bet on the basis since MGRM has to deliver 156 million barrels of oil to its customers.2 As the oil prices fell, MGRM lost on its futures positions and gained on its cash positions - i.e., the oil it had promised to deliver was worth less. However, the backwardation of oil futures disappeared for a period of time, so that MGRM’s views on the basis proved wrong and generated losses for that period of time.

Daimler-Benz. In 1995, Daimler-Benz reported first-half interim losses of DM1.56 billion. These losses were the largest in the group’s 109 years history. In its explanation, Daimler-Benz attributed the losses to exchange rate losses due to the weakening dollar. One subsidiary of Daimler-Benz, Daimler-Benz Aerospace, has an order book of DM20 billion, 80% of it fixed in dollars. As the dollar fell, Daimler-Benz had to take a provision for losses of DM1.2 billion to cover future losses. Why did Daimler-Benz not hedge? The company explained that it did not hedge because the forecasts it received were too disperse, ranging as they did from DM1.2 to DM1.7 per dollar. Analysts attributed the lack of hedging to Daimler-Benz’s view that the dollar would stay above DM1.55, when instead it fell substantially below that. 3

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See Culp and Miller (1995) for this argument.

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See Risk Magazine, October 1995, p. 11.

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These brief case studies reinforce the conclusion drawn from the survey evidence. For these firms, taking a view was an important determinant of how risk was managed. Risk management did not mean minimizing risk by putting on a minimum-variance hedge. Rather, it meant choosing which risks to bear based on a number of different considerations, including the belief that a particular position would allow the firm to earn abnormal returns. Is such a practice consistent with the modern finance theory of risk management? To answer that question, we first need to review that theory.

Section 3. The perspective of modern finance. The two pillars of modern finance theory are the concepts of efficient markets and diversification. Market efficiency simply states that markets don’t leave money on the table. Information that is freely accessible is incorporated in prices, so that one cannot make profits from it. Yet, most cases of large derivative losses start from having a corporation that wants to take advantage of a view and hence start from the belief that abnormal returns can be earned from exposures. If markets are efficient, this will not be the case. If expected returns look good for a given exposure, it is only because the exposure involves risks rewarded by the market. If shareholders want to bear these risks, they do not need the corporation to do it for them. The corporation has no comparative advantage in bearing these risks and as we will see shortly, it may well have a comparative disadvantage. This does not preclude that management may have information that the market does not have. If it does, taking advantage of this information will benefit shareholders. It suggests, however, that obtaining information that makes it possible to beat the markets is hard. The concept of diversification means that shareholders can diversify the risks of the corporation, except for risks that are common to most corporations, such as business cycle risks. Hence, having the corporation expend real resources to reduce diversifiable risks makes sense only if diversifiable risks impose real costs on the corporation. If these diversifiable risks simply mean that shareholders who are not diversified bear

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diversifiable risks, eliminating these risks will not make shareholders better off because shareholders diversify on their own. Eliminating these risks does not benefit shareholders because they do not bear these risks anyway. In efficient markets, therefore, risk management pays off only if it creates real resource gains for the corporation. What are these gains? The finance literature has identified four types of gains: reductions in bankruptcy and distress costs, reductions in expected tax payments, reductions in expected payments to stakeholders, reductions in costs of raising funds.4 We review these gains in turn.

Bankruptcy costs. Bankruptcy costs provide the simplest example of a real resource cost that can be saved through risk management. Consider a firm where the cash flows fluctuate randomly over time. If the firm has debt, it could happen that with a bad cash flow draw, the firm has to file for bankruptcy. When bankruptcy has real resource costs, such as payments to lawyers and court costs, the present value of these real costs reduces firm value. If the firm can implement a risk management policy that eliminates the risk of bankruptcy, it essentially sets the present value of these real resource costs to zero and increases firm value accordingly. This argument extends to distress costs in general. For instance, as a firm becomes weaker financially, it becomes more difficult for the firm to raise funds, so that it may become unable to undertake profitable investments. The inability to undertake valuable investments is a real resource cost for the firm. To the extent that risk management reduces the risk of financial distress, it reduces the present value of the costs of financial distress and hence increases firm value. Figure 1 shows where the gain from risk management comes from in the presence of bankruptcy costs. We can think of the courts, the lawyers, and other parties who must be paid throughout the bankruptcy process

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The first three gains are analyzed in Smith and Stulz (1985) and the fourth gain is analyzed in Froot, Scharfstein and Stein (1993).

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as holding a put option on a fraction of the firm. Hence, the value of the firm to the debtholders and the shareholders is the present value of the capital cash flows minus this put option. Risk management, by reducing firm volatility, reduces the value of this put option for a given value of the firm and, therefore, increases the present value of capital cash flows. In the case shown in figure 1, hedging changes the distribution of firm value so that default is no longer possible. Consequently, it is no longer possible for firm value before bankruptcy costs to be V and for creditors and shareholders to lose B in the form of bankruptcy costs.

Taxes. Tax rates differ depending on the taxable income. This means that the firm would like more income when its tax rate is low and less income when its tax rate is high. Since tax rates increase with taxable income, a risk management program that reduces the risk of taxable income ends up decreasing expected taxes as well.

Stakeholders. Whereas shareholders can diversify risks, stakeholders who have a large stake in the success of the firm cannot typically do so. Consider workers for instance. If there is a chance that their firm-specific investments might be lost because of financial distress, they will consider jobs in the firm to be less attractive and hence will require a higher wage. They will not be able to create their own risk management program to hedge this risk, because of a lack of economies of scale, but the firm will be able to do so for them. If the firm undertakes a risk management program that reduces financial distress, it will with this reasoning have a lower wage bill.

Costs of raising funds. Consider a firm with a cash flow shortfall. It can offset this shortfall by raising funds on the capital markets. If the firm has a lot of debt capacity, so that it can essentially sell risk-free debt, raising funds will be cheap and easy. For highly levered firms, however, raising funds will be expensive and maybe even impossible.

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As a result, a firm that finds itself in a position where it has to raise funds when highly levered may be unable to undertake projects it would undertake if it had less leverage. In this case, leverage imposes a real cost on the firm when there are bad cash flow realizations. Through efficient risk management, the firm can avoid being in such a situation and hence can insure that it will more often be able to take advantage of good investment opportunities.

Section 4. Who should hedge what and when? Practice versus theory. All the benefits of risk management I just discussed have similar implications for when one would expect risk management to increase firm value. Except for the tax argument, all the other arguments for hedging imply that the firm should manage risks so that the market value of its equity is sufficient to make bankruptcy unlikely, financial distress is unlikely, and the firm can raise funds cheaply when valuable investment opportunities become available. One therefore does not expect firms with low leverage to benefit from hedging. Hence, increases in equity capital are a direct substitute for risk management. It is therefore only to the extent that equity capital is expensive that it pays to have risk management. Through risk management, firms save equity capital. They can have more leverage than otherwise. Equity is the present value of future cash flows to equity. It is not this year’s cash flow. It immediately follows from the modern theory of risk management that one should be concerned about the factors that affect the present value of future cash flows. This is quite different from much of current practice of risk management where one is concerned about hedging transaction risk or the risk of transactions expected to occur in the short run. Risk management is closely connected to valuation. If one can value the firm, one knows how to hedge the firm. This is because in the process of discovering the factors that affect the value of the firm, one learns the factors that are responsible for changes in the value of the firm. Let’s look at a simple example that illustrates the differences between much of current practice and what modern finance theory suggests. Suppose that you wanted to devise an optimal risk management strategy for

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Jaguar as a stand-alone firm - like it was before being acquired by Ford. Half of the sales of Jaguar went to the U.S. Hence, standard practice would focus on the dollar income of Jaguar. If Jaguar sets prices in dollars for the cars it sells in the U.S. for a model year, then Jaguar has an exposure in dollars for the coming year that is welldefined. A more careful analysis indicates however that, even though Jaguar does not export much to Japan or Germany, the pound/DM and pound/yen exchange rates are very important for Jaguar. A depreciation of the pound relative to the DM and the yen improves Jaguar’s competitive position because its competitors are German and Japanese. Since Jaguar’s treasury would hardly see DMs and yen’s, treasury focused risk management would completely ignore these exposures. Risk management built from a firm valuation model would in contrast focus on these exposures. Having figured out its exposures, what should a firm do? Taking its capital structure as given, the firm faces a situation like the one pictured in figure 1. We can then think of three types of firms whose distributions of end-of-period firm value are shown in figure 2. First, consider a firm with a high debt rating. Let’s call it firm AAA. The probability of default is almost nonexistent for this firm. When we look at the distribution of value, the tail of the distribution does not reach the range where low value imposes real costs on the firm. There is no reason for such a firm to hedge based on the theory we have discussed. This firm can always raise funds cheaply. Should the firm take bets? Yes, if it believes that it can make money out of them. A bet that turns out poorly will not affect the firm’s ability to implement its strategy. Let’s consider now a firm that has a lower credit rating but that is not in default. There is some significant probability that the firm could face distress, however. We call it firm B. What should this firm do? Through hedging, this firm could reduce significantly the probability of incurring distress costs. Hence, if management believes that markets are always efficient, this firm should hedge fully assuming that the costs of financial risk management are small. What if management believes that it can identify market inefficiencies? For this type of firm, the cost of having a bet turn sour can be quite substantial, since this would almost certainly imply default. Consequently, one would not expect the management of such a firm to let its views affect the hedge ratio much.

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Finally, let’s consider a firm that is in distress. We call it firm S&L. What should it do? Reducing risk once the firm is in distress is not in the interest of shareholders. If the firm stays in distress and eventually defaults, shareholders would end up with worthless or almost worthless shares. Therefore, if management has the interests of shareholders in mind, it will take bets. In fact, in this case, it would take bets even if it believes that markets are efficient because reducing volatility eliminates the possibility of really good outcomes whereby the firm would get out of distress. Firms that have a lot of capital can make bets without worrying about whether doing so will bring about financial distress. One would therefore not expect these firms to hedge aggressively. If risk management is costly, one would expect such firms to mostly ignore risk management since shareholders are better off without it. The major issue that such firms have to address, though, is whether they have too much capital. In other words, risk management may not be useful to them given their current leverage, but they might be better off increasing leverage and then using risk management. If their leverage is low, however, one would expect them to make bets if they believe to have a comparative advantage in making bets. Obviously, bets do not always turn out to be right, so that losses will sometimes occur. Viewed from this perspective, the losses of Daimler-Benz and Metallgesellschaft are normal outcomes of taking bets. Whereas it seems reasonable to argue that Metallgesellschaft had an information advantage in oil markets, though, it is much harder to argue that DaimlerBenz had an information advantage in currency markets.

Section 5. Comparative advantage in risk-taking and risk management. What kind of risks should firms take? So far, we have seen two useful principles. First, in efficient markets, firms do not make money by taking financial positions based on information that is publicly available. Second, firms should avoid financial positions that could lead them to be financially distressed and unable to implement their overall strategy if they perform poorly. However, by their very activities, firms gather information that is not publicly available. This information gives them a comparative advantage in taking some types of risks

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over their shareholders. Let’s look at a hypothetical example. Consider firm X that produces consumer durables and, in the process of doing so, uses large amounts of a raw material, say copper. As the firm makes sure that it has the appropriate amount of copper on hand, it gathers useful information about the copper market. It knows its demand for copper and knows a lot about the supply of copper. This is information that the shareholders of firm X do not have. If they had that information, they would act on it. In this case, the firm can act for them and make money for them by using its information. This may involve using a variety of financial instruments. For instance, the firm may want to take large long or short positions in futures contracts. There is no reason why the firm should abstain from exploiting its knowledge. There is no conceptual difference between a firm repurchasing its shares because it believes them undervalued and taking futures positions in some commodity because it believes that its price does not reflect the information it has. The information that firm X has need not be about the price of copper, however. The firm could know a lot about the demand and supply of copper, so that it could profit from acting as an intermediary. This would involve taking risks also, but of a different nature. In both cases, however, the trading of firm X in financial markets could enable it not only to make profits out of that trading but also to provide firm X with copper at a lower price. The above example shows that the same activity can lead to different comparative advantages in risk taking for different firms. To understand how important it is for the firm to know what its comparative advantage is, it is useful to think about the sources of profits in a foreign currency trading room. A foreign currency trading room can make a lot of money because of position taking. The firm may have guessed right on changes in exchange rates. In an efficient market, firms can make money out of position taking of this sort only if they have access to some information faster than other firms. This can only happen if the firm is very large, so that its deal flow is informative about general changes in demand for foreign currencies. Hence, some large firms can make money by taking positions in foreign currencies and holding them for a period of time. Other firms, however, have no comparative advantage in gathering information about changes in the value of foreign currencies. The risks

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they take are short-lived. They have a good customer base, so that they know that if a trader buys yens this instant, they can resell them quickly and pocket the bid-ask spread. Braas and Bravler (1990) argue that a large fraction of the profits of a trading room profits can be attributed to this source. If a firm does not understand its comparative advantage in trading currencies, it will not make profits and will endanger its existing comparative advantage. If the source of the profits of the trading room is the customer base of the bank, this means that the bank has to invest in maintaining and increasing its customer base. A bank that mistakenly believes that the source of its profits is position-taking rather than its customer base will take large positions which, on average, will neither make money nor lose money. In the process, though, it will have highly variable trading income, which may worry customers and hurt its customer base. Further, it may choose a compensation system for its traders that rewards profitable position taking rather than emphasizing interactions between traders and sales. Finally, management may be spending its time looking for star traders rather than in devising new marketing strategies and new services. How can a firm figure out where it should take risks and where it should not? The best approach is to implement a risk-taking audit. Think of the risks that the firm takes, both through financial instruments and through operations. What are the risks that are profitable and those that are not? Which risks should be hedged? Which risks should be magnified? Where does the firm’s comparative advantage come from in taking these positions? Where does risk management fit in once a firm has discovered that it has a comparative advantage in taking some risks? Risk management enables the firm to take more of these risks than it would in the absence of risk management. Let’s go back to our example of firm X. This firm has valuable information about the copper market, so that on average it earns profits trading copper. These profits are not a sure thing. Sometimes, the firm makes large losses. The firm’s ability to suffer large losses without endangering its activities depends on its leverage and its general financial health. Through risk management, the firm can increase its ability to take risks by decreasing the volatility of its other activities.

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Section 6. Why firms differ in risk-taking? Why is it that some firms take bets and others do not? One answer is that some firms have a comparative advantage and others have none. This answer is incomplete, however. Incentives matter. Some firms may have no comparative advantage, yet they take risks because doing so is advantageous for those who take the risks. We have little empirical evidence that is convincing on the extent of risk-taking by firms. However, there is one paper that provides striking results for the gold industry by Peter Tufano which is published in the September 1996 issue of the Journal of Finance. In that paper, he examines the ability of various hedging theories to predict the exposure to gold prices of gold mining firms. The bottom line of his study is that the most important determinants of this exposure is managerial ownership of shares and the nature of the managerial compensation contract. If management owns a substantial number of shares, so that the volatility of its wealth is significantly affected by the volatility of the share price, the firm tends to hedge substantially. In contrast, little hedging takes place in gold mining firms where management owns a small stake. Managerial compensation contracts that involve option-like features lead to less hedging because they reward management for taking bets. This is shown in figure 3. With hedging, management’s options are worthless. Without hedging, there is some probability that they will pay off. It is reasonable to believe that if management bears the risk of bets, it will be less likely to take bets and more likely to hedge. It is also reasonable to believe that if management gains more from gains in firm value than it loses from losses in firm value, management will be more willing to take bets. Hence, to understand the extent of hedging, it is important to understand the incentives of management. Consider a firm with a bonus pool that is doing poorly. Managers expect no bonus unless something dramatic happens to profits. One would expect these managers to take positions based on their views. If they have the wrong view, they were not going to get a bonus anyway. If they have the right view, they get a bonus. In contrast, if they already expect to get the maximum bonus, they will not want to take risks to lose some of that money. Management’s incentives will, however,

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always be such that it will want to avoid financial distress. The importance of the relation between the option component of managerial compensation contracts and risk-taking within the corporation is further emphasized in a recent paper on the S&L industry by Schandt and Unal (1995). In that paper, they analyze the risk management changes of S&L’s changing their organizational form from mutual ownership to stock ownership. They find that the S&L’s where management has options end up having greater one-year gaps, hence greater exposure to interest rates. Tufano’s paper also has results showing that managers with options in their compensation contract hedge less. To the extent that risk-taking within the corporation is decentralized, then it is important to understand the incentives of those who take risks. Organizations have lots of people doing a good job. Just doing a good job will not get somebody promoted. There are tremendous incentives to stand out. In many areas of a firm, it is not really possible to take big risks that would affect the firm positively in a big way if they work out. However, the treasury area is certainly one where it is possible to take such risks and succeed. If one views promotions as the outcome of tournaments, it is immediately apparent that they give incentives to take risks. The one with the best outcome wins whereas the others do not get promoted. It would be hard to find supportive empirical evidence for this explanation of risk-taking because the data for such an investigation is not available. It is interesting to note, however, that one area in which evidence is available is in risk-taking by mutual fund managers. In a paper to be published this year in the Journal of Finance, Brown, Harlow and Starks show that mutual fund managers doing poorly relative to other managers increase the volatility of their funds, i.e. take more risks.

Section 7. Managing risks. The academic literature has focused on volatility reduction as a measure of the extent of risk management. This measure does not follow from the theory. In our discussion of comparative advantage in risk-taking, we argued that firms will sometimes hedge some risks so that they can take more of other risks.

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Most of the arguments to practice risk management are arguments to avoid lower tail outcomes. The practice has focused on lower tail outcomes through the use of value-at-risk (VAR). What is VAR? Figure 4 shows a histogram describing the monthly return on the Capital International Morgan Stanley world market portfolio from January 1985 to December 1996. How risky is that portfolio? One measure is the standard deviation of the portfolio. In this case, the standard deviation of the monthly return is 4.3%. You might be concerned, however, about the magnitude of the losses that you make if things go poorly. A measure that would be helpful is one that tells you the loss that you will equal or exceed at some level of probability. An example would be a measure that you the loss that you will equal or exceed with probability of 5%. For monthly data, a probability of 5% corresponds on average to one month over twenty. As an investor, you can then decide whether you are comfortable with such losses. The measure that tells you the loss you can expect to equal or exceed one month out of twenty is the VAR evaluated at the 5% level (1 out of 20 is 5%). This VAR corresponds to a loss of 5.9% (the expected return of 1.23% per month minus 1.65 time the standard deviation of the return). This VAR is represented by the dotted vertical line in Figure 4. At the end of December 1995, the value in dollars of the Morgan Stanley Capital International portfolio was 9,219 billion dollars. A loss of 5.9% corresponds to 444 billion dollars. Hence, the VAR tells us that, on average, one month out of twenty, world equity wealth will fall by $444 billion at least assuming that the return to world wealth is normally distributed.

The VAR is a popular measure of risk among financial institutions, but its use is fast extending beyond financial institutions.5 This measure captures the nature of bad outcomes in a single number. If your wealth is invested in the world market portfolio and it takes you one month to liquidate the portfolio, the VAR tells you that there is one chance out of twenty that you will lose the VAR or more before you can get out of your investment. For a financial institution that trades in liquid markets, the daily VAR is often more useful. It tells

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Sometimes the concept of cash flow at risk is used instead. All of our discussion applies to that concept also.

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the institution that there is one chance in twenty that it will lose at least the VAR before it can get out of its positions. Although extremely attractive, VAR is not consistent with the theory of risk management either. Remember that VAR is the magnitude of the loss that occurs with some probability. The fact that, with probability 0.05, one could have a loss of at least X on a given day or a given month is not useful information when what one is concerned about is that firm value will fall below some critical value. One question one would like to answer is: If we define distress as a situation where we cannot raise funds with a rating of X or where the value of equity falls below some target, what is the probability of distress over a period of time? Another question one would like to answer is: Given that a bad outcome occurred that brought about financial distress, what are the costs incurred by the corporation? VAR by itself answers neither of these two questions. If we know a firm’s VAR and assume the gains and losses are normally distributed, then one can compute the probability of distress over the next day using the VAR. Remember that to compute VAR, one starts with the daily distribution of gains and losses. Having the mean and volatility of that distribution, a 99th percentile VAR is simply the mean minus 2.33 times the volatility. If instead one wants to compute the probability of distress, then one has to know the loss amount that produces distress. One can also compute the expected value of the loss given that the loss is big enough to create distress. The probability of distress over the next day is typically not a very interesting number for a corporation. However, before going on to a more appropriate horizon, it is important to understand two important complications that arise in computing the financial distress probability that are much less important when computing the daily VAR. First, remember that a daily VAR at the 99th percentile is one that occurs one day out of 100. Alternatively, a 95th percentile VAR occurs five days out of 100. It is therefore possible to check empirically whether the model used to compute the daily VAR is reasonable by observing the frequency with which the loss is equal or greater than VAR. Computing VAR over one year at the 99th percentile means that the loss takes place on average one year out of 100. At this point, it becomes much more difficult to figure out

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whether the model used to compute the VAR is sensible. The second problem is the reliance on the normal distribution. When one is especially concerned about tail probabilities (the probabilities of the worst and best outcomes), the assumption made about the statistical distribution of the gains and losses matters a lot. The bottom line from finance research is that the tail probabilities are generally larger than implied by the normal distribution. A simple way to understand this is as follows. Suppose stock returns are normally distributed. In this case, market drops in excess of ten percent in a day would be extremely rare - say once in a million years or less... The fact that such drops happen more often is evidence that the normal distribution does not describe the probability of lower tail events correctly. This is not an important issue for most of finance, but it is one in this context. Because changes in value exhibit fatter tails than with the normal distribution, a probability of distress of 0.01 computed using the normal distribution might actually be 0.05. Using a more relevant horizon of one year, the relevant risk measure for hedging purpose is not the VAR computed at the one year horizon. A VAR computed at the one year horizon at the 95th percentile answers the question: What is the loss that I can expect to occur 5 years out of 100? For hedging purposes, one is concerned about the likelihood of distress during the year which depends on the value of the cumulative loss throughout the year. In other words, one is concerned about the path of firm value during the year rather than the distribution of firm value at the end of the year. Such a probability can be computed from the distribution of cash flows throughout the year. However, one must then pay careful attention to the time-series properties of cash flows. Implicit in all VAR approaches is the notion that the gains and losses are serially independent - experiencing a loss today does not mean that it becomes more likely that a loss will take place tomorrow. This is very unlikely to be correct for a nonfinancial firm’s cash flow. If cash flow is poor today, it is more likely to be poor tomorrow. This property of the distribution of cash flows has to be taken into account carefully when one tries to understand the probability of financial distress.

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Section 8. Managing risk-taking. A hedging strategy that focuses on the probability of distress is consistent with risk-taking. Remember that with such a strategy, one is concerned about the lower-tail outcomes. Hence, it is perfectly feasible for a company to increase its volatility yet reduce the probability of a bad outcome that would create financial distress. For instance, a strategy that levers up the firm but buys way out of the money put options that pay off if the firm does poorly will increase firm value volatility and, if the puts are bought in appropriate numbers, decrease the probability of financial distress. Focusing on lower tail outcomes is also fully consistent with managing economic exposures. Suppose that we are willing to put an explicit cost on an increase in the probability of distress. In that case, the trade-off for taking a bet for the company becomes simple. The bet increases firm value by its expected profit minus the cost of its impact on the probability of distress. A bet that has a positive expected profit and has no impact on the probability of distress is one that the firm should take since it has a positive net present value. If a bet has a positive expected profit but increases the probability of financial distress, it may not be profitable because the adverse effect of a poor outcome is too costly. However, in this case, it makes sense for the firm to think about how it can reduce the impact of a poor outcome on the probability of distress. Consider the situation where the cash flow of that firm is risky, so that if the bet has a poor outcome and cash flow is low the firm will be in distress. The first question the firm should ask is whether it can reduce cash flow risk. It could be that through a hedging program the firm can reduce cash flow risk substantially, so that an adverse outcome of the bet would not create financial distress. After having implemented its hedging program, the firm would then be able to make the profitable bet. When evaluating the bet, however, the appropriate profit is it’s risk-adjusted expected profit. This riskadjusted expected profit is not the expected gain divided by the capital contributed or the expected profit divided by the standard deviation of the bet. Remember that shareholders could take the same risks as the firm and for that risk would receive some compensation from the capital markets. For instance, there is a lot of evidence that

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holding currencies of high interest rate countries earns on average an excess return over the risk-free rate. Most likely, this excess return is compensation for risk. It therefore would not make sense to reward a treasury for earning excess returns this way. The treasury takes on risks when it pursues that strategy. Shareholders want to be compensated for these risks. If all of the expected excess return of this strategy is compensation for risk, on average the excess return earned this way is not a profit for the corporation - it is not an “abnormal return” but compensation for taking a risk that would accrue to anybody who takes on that risk. Consequently, the criterion that should be applied when a corporation makes a bet is whether the compensation it expects from making the bet exceeds what shareholders, without any special information, would expect to receive on their own. A bet will increase firm value only if its expected return exceeds the expected return attributed to it by uninformed investors. When devising a compensation scheme for those managers that can make a bet, it is of crucial importance to provide appropriate incentives so that they only take those bets that increase shareholder wealth. It turns out that the data used to compute VAR provides the way to do that. A firm has many different sources of risk. Consequently, when computing VAR, it is common to focus on the most important sources of risk. Suppose that you have n different sources of risk that you use in the computation of VAR. You can then put a market required return for these risks and hence derive an expected return that must be obtained for a given amount of capital at risk to insure that shareholders benefit. Let’s look at a simple example that makes this clear. Suppose that one source of risk is emerging markets risk. The firm takes exposure to this risk. If shareholders can earn a risk premium of 5% p.a. being exposed to that risk, then managers make money for the firm taking on this risk only if they earn more than 5% on average. Hence, managers should not be compensated for earning more than the risk-free rate. They should be compensated for earning more than what the shareholders could earn without their help. This approach does not completely eliminate the problem that the individual has incentives to take risks because of the reasons discussed earlier. However, it has the advantage that it becomes more difficult for a risktaker to make money by making random bets. If a risk-taker simply receives a bonus for making positive gains,

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he has incentives to take random bets because he gets a fraction of the gains he makes and does not bear the losses. A risk-taker who has to beat the market to make money does not find random bets profitable.

Section 8. Conclusion. In this article, we showed that it is not correct to view modern risk management theory as implying that firms should minimize hedgeable risks. What a firm should do depends on its situation. Taking leverage as given, the lower the leverage, the less valuable risk minimization. If a firm’s management believes that it has identified a market inefficiency, it should seek to exploit it to increase shareholder wealth. However, in this case, it becomes important to evaluate managers’ bets relative to the market. If managers want to behave like money managers, they should be evaluated like money managers. When management believes that it can identify market inefficiencies, it should exploit these inefficiencies paying close attention to the probability that adverse outcomes would put the firm close to or in financial distress. Consequently, an important measure of risk with this view of risk management is the probability that the firm will become financially troubled or will reach a financial situation that is worse than the one that would allow the firm to pursue its overall strategy.

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References

Braas, A., and C.N. Bralver, 1990, An Analysis of trading profits: How trading rooms really make their money, Journal of Applied Corporate Finance 2, Winter, 85-90. Brown, K.C., W.V. Harlow, and L.T. Starks, 1996, Of tournaments and temptations: An analysis of managerial incentives in the mutual fund industry, Journal of Finance, forthcoming. Culp, C., and M.H. Miller, Hedging in the theory of corporate finance: A reply to our critics, Journal of Applied Corporate Finance 8, Spring, 121-127. Dolde, W., 1993, The trajectory of corporate financial risk management, Journal of Applied Corporate Finance 6, Fall, 33-41. Froot, K., D.S. Scharfstein, and J.C. Stein, 1993, Risk management: Coordinating corporate investment and financing policies, Journal of Finance 48, 1629-1658. Mello, A., and J.E. Parsons, 1995, Maturity structure of a hedge matters: Lessons from the Metallgesellschaft debacle, Journal of Applied Corporate Finance 8, Spring, 106-120. Smith, C.W., and R.M. Stulz, 1985, The determinants of firms’ hedging policies, Journal of Financial and Quantitative Analysis 20, 391-405. Schrand, C.M., and H. Unal, 1995, Coordinated risk management: On and off-balance sheet hedging and thrift conversion, unpublished working paper, The Wharton School, University of Pennsylvania, Philadelphia, PA. Tufano, P., 1996, Who manages risk? An empirical examination of the risk management practices of the gold mining industry, Journal of Finance, September.

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