Risk Management (posted 22 Feb 99)

The complexity of our modern lives and the numerous decisions we are able to take are only made possible by our ability to manage risks - the risk of house fire; the risk of losing a job; the risk to the entrepreneur who invests in a business; the risk to the farmer who plants a crop that will have an uncertain yield and be sold at an uncertain price in several months time; the risk to the investor in the stock market; and so on.

For each of these problems, society has found solutions. For example, most people agree that house insurance and unemployment insurance increase social well-being. The role of futures markets in insuring farmers against commodity price uncertainty is also understood to increase welfare. Equally, the role of the stock market in enabling the risks of businesses to be shared is now well understood - as indeed is the role of diversification in enabling investors to achieve the minimum risk for the returns generated on their portfolios.

But such widespread public acceptance is almost certainly not true of derivatives, and their role as a means for managing risk through the financial markets is frequently misunderstood. This may, in part, be due to the idiosyncratic nature of the instruments themselves, as illustrated by a number of controversial episodes: the failure of portfolio insurance in the 1987 stock market crash; their misuse in the cases of Barings, Gibson Greetings Cards, Metallgesellschaft, Orange County, California, and Procter and Gamble; and the near failure of Long Term Capital Management (LTCM) whose board included the pioneers of option pricing, 1997 Nobel Laureates for economics, Robert Merton and Myron Scholes.

Yet these instruments - futures, options and a multitude of variations on these themes - are packages of the basic components of risk: they more than anything else traded come close to the theoretically ideal instruments for the trading of risk. On the one hand, insurance can be a cost borne to eliminate a negative occurrence, accidental or structural, an outcome you cannot tolerate. On the other hand, it becomes a tool to shape a risk-return relationship, unique to each investor, from quite common investment alternatives. Derivatives can turn stocks into bonds and vice versa. And derivatives can pinpoint very precisely specific risks and returns that are packaged within a complex structure.

Gurus of risk management: Fischer Black, Robert Merton and Myron Scholes

Over the past twenty-five years, financial futures and options have established themselves as an integral part of the international capital markets. While futures and options originated in the commodities business, the concept was applied to financial securities in the United States in the early 1970s. Currency futures grew out of the collapse of the Bretton Woods fixed exchange rate system, and heralded the growth of a wide variety of financial instruments designed to capture the advantages or minimize the risks of an increasingly volatile financial environment. Now these products are traded around the world by a wide variety of institutions.

The quantitative tools which brought derivatives into common use were the invention of the late Fischer Black and Myron Scholes in what is called the Black-Scholes option pricing model. Their sometime collaborator Robert Merton took the work further into a form for everyday application by applying his notions of continuous time relationships in security pricing. Merton's modifications made the leap from the theory to a practical tool.

As Peter Bernstein's excellent books on risk and 'capital ideas' recount, having been rejected by two academic journals, the original Black-Scholes paper was eventually published in the University of Chicago's Journal of Political Economy. It is said that the option formula can be derived from the heat transform formula and that while wrestling with the problem, Black was inspired by a conversation after a game of tennis. Apparently, his playing partner, an engineer, saw the analogy with his own field.

Of the three developers of options theory (and its earlier roots date back to work done in 1900 by Louis Bachelier in Paris), two - Black and Scholes - moved full-time into investment practice. Merton moved from MIT to Harvard, a short distance upriver, though he too was involved with LTCM. Thus, the widespread application of academic theory from the early 1970s influenced investments but also the course of the lives of the developers.

The partnership of academia and investments is emphatically illustrated by the integration of derivatives into the everyday work of investment people. Some extracts from the Nobel citation for Merton and Scholes from the Royal Swedish Academy of Sciences provide a useful overview of their work and its many practical applications:

'Risk management is essential in a modern market economy. Financial markets enable firms and households to select an appropriate level of risk in their transactions, by redistributing risks towards other agents who are willing and able to assume them. Markets for options, futures and other so-called derivative securities have a particular status. Futures allow agents to hedge against upcoming risks; such contracts promise future delivery of a certain item at a certain price. As an example, a firm might decide to engage in copper mining after determining that the metal to be extracted can be sold in advance at the futures market for copper. The risk of future movements in the copper price is thereby transferred from the owner of the mine to the buyer of the contract.'

'Due to their design, options allow agents to hedge against one-sided risks; options give the right, but not the obligation, to buy or sell something at a pre-specified price in the future. An importing British firm that anticipates making a large payment in US dollars can hedge against the one-sided risk of large losses due to a future depreciation of sterling by buying call options for dollars on the market for foreign currency options.'

'Effective risk management requires that such instruments be correctly priced. Black, Merton and Scholes made a pioneering contribution to economic sciences by developing a new method of determining the value of derivatives. Their innovative work in the early 1970s, which solved a longstanding problem in financial economics, has provided us with completely new ways of dealing with financial risk, both in theory and in practice. Their method has contributed substantially to the rapid growth of markets for derivatives in the last two decades. Fischer Black died in his early fifties in August 1995.'

'The Chicago Board Options Exchange introduced trade in options in April 1973, one month before publication of the option pricing formula. By 1975, traders on the options exchange had begun to apply the formula - using especially programmed calculators - to price and protect their option positions. Nowadays, thousands of traders and investors use the formula every day to value stock options in markets throughout the world.'

'Such rapid and widespread application of a theoretical result was new to economics. It was particularly remarkable since the mathematics used to derive the formula were not part of the standard training of practitioners or academic economists at that time.'

'The ability to use options and other derivatives to manage risks is quite valuable. For instance, portfolio managers use put options to reduce the risk of large declines in share prices. Companies use options and other derivative instruments to reduce risk. Banks and other financial institutions use the method developed by Black, Merton and Scholes to develop and determine the value of new products, sell tailor-made financial solutions to their customers, as well as to reduce their own risks by trading in financial markets.'

Counterpoint

Until the collapse of Barings in February 1995, derivatives were rarely mentioned beyond narrow professional financial circles. At that point, they became infamous, labeled the 'wild card of international finance'. James Morgan nicely captured their ambiguous role in an article in the Financial Times: 'A derivative is like a razor. You can use it to shave yourself and make yourself attractive for your girlfriend. You can slit her throat with it. Or you can use it to commit suicide.'

There is still some dispute in the academic world as to whether hedging using options is necessarily a good thing. Some argue that our ability to price these instruments unambiguously is primarily restricted to environments in which they are redundant securities and therefore cannot add to welfare. In other words, if we need them we cannot price them but if we can price them we do not need them.

Stephen Eckett of Numa sees dangers in the quest for a 'correct' price or value for a derivative. He comments: 'I think the search for this (apart from all sorts of demand reasons) comes from investors traditionally being able to value their other investments - such as stocks - and being in the mindset to do the same with derivatives. But with the rise of the internet - and high-tech in general - many of those traditional value tools are looking shaky even for stocks.'

'Because of this, I regard the Black-Scholes model as one of the most dangerous inventions of the twentieth century. This is not to blame Black and Scholes obviously: the danger is always in the application. But what happened was that one simple equation - and mathematically, the model is simple - seemed to offer the possibility of quickly 'understanding' and controlling derivatives risk. This encouraged thousands of banks to employ bright mathematicians, who had little knowledge of the financial markets but nonetheless started furiously programming their spreadsheets on which billions of dollars were gambled.'

Certainly, it is by no means clear that much of the use of derivatives by non-financial corporations is strictly necessary. Indeed, in some cases, it appears that firms use derivatives not so much for risk management as for trading opportunities - they are selective hedgers, opting not to hedge when they think they are in a winning position, and treating their treasuries as profit centers. Firms as prominent as Proctor and Gamble have sustained enormous losses through derivatives, in large part by gambling on the chance of reducing small losses.

Derivatives in their 'over-the-counter' form (as opposed to options and futures listed on exchanges) are based on the notion that investments can be designed to fit the investor not the issuer. Thus, you do not take the investor's intention and find the suitable investment, but you make it. And every time you do you get a investment banking fee. Furthermore, the designer of the derivative instrument has a superior pricing skill than the buyer so there is a trading fee.

It is also possible that hedging leaves society worse off than it would be if unhedged since it can make markets more volatile than they otherwise would be. During the crash of 1987, for example, a strategy called portfolio insurance, which aimed to use futures to reduce losses in a market decline, was blamed for driving the market down. And the rescue of LTCM by a consortium of banks after its near failure in September 1998 indicates that there were real fears that the liquidation of its positions would threaten the entire financial system. Derivatives flourish in an environment when the ability to pay is optimistic, where the creditworthiness of the chain of issuers is not in doubt. This is clearly a bull market condition only.

Much of the early success of LTCM was a result of the credibility of Merton and Scholes, which attracted heavyweight investors, lenders and trading partners to the firm, and their ideas, which provided potentially profitable trading opportunities. But for all the brilliance of their theory, it was based on 'expected volatility', which implicitly assumes that history repeats itself, that the future movements of asset prices will mirror their past movements. Unexpected events in the real world - in this case, Russia's debt default and currency devaluation in August 1998 - can wreak havoc with such models.

In the past five years, a new and extremely important field of asset management has emerged called risk control. At many financial institutions, a risk control manager sits at the center of all of the position managers and asset managers to ensure that the diversification and covariances are in place so that dire results will not occur. But the risk control management process has to be severely challenged with the story of LTCM. Indeed, all the models that are being used for risk control and to buy assets on the basis of small increments using extraordinary leverage must be challenged.

It is far from clear that we have risk control in hand simply by looking at the past and thinking that the correlations are stable. They are not: when you get out to the tails of events, they do not behave like multiples of the means. In such circumstances, risk control by linear standards becomes non-linear and we have disasters like LTCM. Risk control, in the first instance, needs to be challenged, and we may have to go back to such old-fashioned practices as just not taking as much risk of loss.

Where next?

The Nobel citation for Merton and Scholes points out the impact their work has had on the markets: 'Financial institutions employ mathematicians, economists and computer experts who have made important contributions to applied research in option theory. They have developed databases, new methods of estimating the parameters needed to value options and numerical methods to solve partial differential equations.'

The citation also refers to the extension of options pricing to the world beyond the financial markets: 'Black, Merton and Scholes' contribution extends far beyond the pricing of derivatives. Whereas most existing options are financial, a number of economic contracts and decisions can also be viewed as options: an investment in buildings and machinery may provide opportunities (options) to expand into new markets in the future. Their methodology has proven general enough for a wide range of applications. It can thus be used to value not only the flexibility of physical investment projects but also insurance contracts and guarantees.'

It is said that before Black-Scholes, the government was amazed by what they saw as the stupidity of oil companies. These firms continually paid significantly more than the expected present value of oil when bidding for leases in government auctions. Looked at as options (the oil firms were not required to drill), these payments for the leases were easier to explain. The market managed to price these without the Black/Scholes formula. Indeed, Black-Scholes is only a model: the market still prices some options differently than the Black-Scholes value, and there is little convergence until close to expiry.

MIT's Sloan School is the location of much exciting work on the future of risk management. Professor Stephen Ross, for example, has coined the term 'forensic finance' to describe a process he recommends: going back to some of the great disasters of risk management as a 'financial pathologist', and poring over them carefully to find out what went wrong and what lessons we can learn. 'Learning the lessons of our past errors is what risk control is all about.', Ross writes, 'Practicing good risk control, particularly employing serious scenario analysis and stress testing, is just practicing financial safe sex.'

And Ross's colleague Professor Andrew Lo (see FINANCIAL ENGINEERING) is working on the concept of 'total risk management', integrating probabilities, prices and preferences into risk analysis in both the financial and non-financial worlds.

Read on

In print

Peter Bernstein, Against the Gods: The Remarkable Story of Risk
Peter Bernstein, Capital Ideas: The Improbable Origins of Modern Wall Street
Fischer Black and Myron Scholes, The Pricing of Options and Corporate Liabilities, Journal of Political Economy, 1973 - the original article
Robert Merton, Continuous Time Finance
Robert Merton and Zvi Bodie, Finance

Online

web.mit.edu/lfe/www - the website of the Laboratory of Financial Engineering directed by Andrew Lo - includes his paper 'The Three P's of Total Risk Management'
www.nobel.se - website for the Nobel Prizes, including the citations for recent economics laureates
www.numa.com and www.global-investor.com - excellent derivatives websites and online bookstores run by Stephen Eckett