Managing Risk, Reaping Rewards

By Stavros A. Zenios

Thales, the philosopher from the island of Milos, once used his knowledge of astronomy to predict a particularly favorable season for olive production. He proceeded to lease all the olive-presses on the island and "made a killing" when the islanders paid high prices for processing their abundant crops. Having thus demonstrated to his fellow citizens that philosophy could be put to practical use, he returned to the pursuit of more lofty ideas. He did not go on to develop options pricing theory.

Farmers today sign future contracts to protect themselves from price fluctuations. Owners of ski and beach resorts and utility companies take positions in weather derivatives to protect their business from inclement weather. Dutch farmers — and speculators — of the 17th century bought options on the prices of tulip bulbs. Thousands of miles away Japanese feudal lords would sell their rice in the cho-ai-mai market under contracts that protected them from bad weather and war.

What separates the old financial world from the new? And what does operations research have to do with this change?

Peter Bernstein gives an answer to the first question in his book "Against the gods: the remarkable story of risk." According to the author, the revolutionary idea that defines the boundary between modern times and the past is the mastery of risk: the notion that the future is more than a whim of the gods and that men and women are not passive before nature. Business globalization, rapid technological changes and increased volatility in the financial markets change dramatically the risk profiles of many companies. Firms are responding by embracing the concept of enterprise-wide risk management. Today it is widespread corporate practice to take steps in understanding the firm's risk exposure in a global economy, and take active measures to neutralize undesirable risk exposures.

An answer to the question "What does operations research have to do with the changing financial world?" is given in this article. We will see, first, that operations research provides some indispensable tools to support financial decision-making. Then we will argue that the value-added proposition of operations research to risk management goes beyond "tools" toward the development of a new paradigm. We will illustrate with several examples that the new paradigm of integrative enterprise-wide risk management adds value to financial decision-making. But a fresh outlook is needed to develop enterprise risk management solutions. That is where we perceive significant opportunities for intellectual arbitrage: by bringing together the tools and techniques of operations research with contemporary theories of financial economics. It is worth noting that a search by researchers at Algorithmics Inc., one of the leading providers of enterprise risk management solutions, identified the first article on the topic of integrative enterprise risk management to be a paper in Operations Research titled "The productivity of financial intermediation and the technology of financial product management."

Enterprise-Wide Risk Management


Enterprise-wide risk management (ERM) is defined as the strategy that aligns the firm's business with the risk factors of its environment in the pursuit of strategic objectives. It consists of the conceptual framework, organizational approaches, and tools that integrate market, credit, liquidity, operational, and business risks in achieving the organization's objectives.

Four key functions are the pillars on which enterprise risk management strategies rest. We discuss them briefly here, in order to place on a concrete footing our analysis of the role of operations research in supporting ERM.

Pricing. To properly align the risks one first has to measure them. Options pricing has come a long way since Thales negotiated the lease of Milos' olive-presses. The celebrated Black-Scholes-Merton formula for options pricing is recognized today as the most successful mathematical model of any economic activity, standing shoulder-to-shoulder with mathematical models of physical phenomena. Thanks to mathematical models, analysts can price all sorts of exotic financial instruments and derivative securities. A long list of new derivative products has been added to the early options that motivated the work of Black, Scholes and Merton: Barrier options, Bermuda, Asian, Russian options, cliquets, swaptions, etc., etc. These options offer, at a price, protection from the risks of some underlying asset. The underlying risky asset could be a stock, a commodity, or even the weather and other uncertain events such as earthquakes for weather-derivatives and catastrophe-bonds. Additional innovative derivative products offer protection from the risks of a trading strategy or of a broad market segment. Such is the case with look-back options and guaranteed products.

Securitization. Properly priced risks can be securitized into new financial products that cater to the risk-management needs of diverse businesses. Mortgages, credit cards, bank loans and bond portfolios are re-packaged, securitized and re-sold. By securitizing and selling some of their risk exposures corporations can avoid risk concentration arising from their core business. In this way they free regulatory capital, thus improving efficiency. The risks are transferred where they can be managed best and the overall risk exposure of the economy is reduced. The alphabet soup of securitized products with names such as MBS, CLO, CBO, CMO, IO/PO is a good cure for risk.

Asset and liability management. Whatever financial risk is eventually retained by a business, it must be diversified and properly aligned with the firm's obligations. Harry M. Markowitz showed the way with his doctoral dissertation that introduced mean-variance analysis for optimizing portfolio diversification. This work laid the foundation for the development of market equilibrium theories, and it was later extended to include liabilities. In 1989, Markowitz was awarded the von Neumann Prize in Operations Research Theory. The Swedish Academy recognized the significance of this work a year later with the awarding of a Nobel Prize in Economics. It is noteworthy that Markowitz's motivation for the pursuit of his dissertation topic was the application of mathematical programming techniques to the stock market.

Indexation. Market equilibrium theories that followed from the mean-variance analysis posed a challenging problem for the management of financial assets. The theory tells us that it is impossible to do any better than the market. But what exactly defines the "market"? The day-to-day management of financial risk exposures requires availability of a market benchmark. Broadly defined market indices provide the necessary benchmarks and guide managers in assessing how well their business manages its own risks vis-à-vis the markets. Tracking market indices is a widely adopted strategy for portfolio management: If one can not beat the market, the best it can do is to track it closely. An estimated $1 trillion in index funds are currently managed to replicate Standard & Poor's indices.

Operations research provides essential tools to support these key functions of enterprise risk management. The pricing of complex path-dependent options — whose prices depend on a history of asset prices and not just the asset value on exercise — requires Monte Carlo simulation methods. For several derivatives the decision whether to exercise the option, or not, follows from the solution of an optimization problem. Theoretical models of the price evolution of the risky assets must be linked with dynamic programming algorithms to arrive at options prices resulting from optimal exercise strategies.

When the exercise strategy is not optimal, the resulting prices will create arbitrage opportunities; arbitrageurs push the market toward optimal strategies, although they do not do so with the explicit use of optimization algorithms. Furthermore, pricing in incomplete markets requires specification of preference assumptions that can only be resolved in an optimization framework. Linear programming and linear complementarily problems are prevalent in options pricing. Some times the operations research models appear as alternative formulations to other options pricing formulas, enjoying some computational advantages. In other instances they provide the only formulations.

Securitization with the design of innovative financial products and the re-packaging of financial risks can be made more effective with the use of optimization models. Like engineers — who routinely use optimization techniques to optimize structural designs for safety, stability, cost or fuel efficiency — financial engineers use optimization models to achieve their design goals along the competing dimensions of risk and reward.

The management of assets and liabilities using the principles of diversification relies on quadratic optimization models. Significant developments since Markowitz's pioneering contribution in the 1950s — derivative securities that violate assumptions on normality of returns, long time horizons of complex liability structures, increasing transaction costs for derivative securities — ushered a new generation of multi-period portfolio optimization models. Dynamic financial analysis was developed to go beyond the single-period decisions of mean-variance analysis to the optimization of dynamic strategies. These strategies adapt with the arrival of new information. Stochastic programming for planning under uncertainty provides a versatile tool for dynamic financial analysis, and its use in finance has been gaining popularity since the 1980s.

Finally, portfolio indexation and portfolio compression relies on the combination of pricing and simulation models with optimization models.

The risk factors of the index are simulated and optimization models create portfolios that respond to the risk factors in a way that mimics the market's response. When the risk factors are properly identified and correctly simulated, the optimized portfolio will closely track the index.

We have focused thus far on the use of operations research in managing financial risks. What remains yet unexplored is the interplay of financial risks with operational decisions. Indeed, in enterprise risk management this interaction is of paramount importance. Risks can be eliminated or controlled not only through the use of financial tools but also through operational decisions. For instance, the decision to delay capacity expansion could buffer demand or price uncertainty. Decisions to outsource production could eliminate some of the effects of exchange rate uncertainty. The field of real options — options on non-traded underlying assets — brings together the finance literature on options valuation with the operations management literature on flexibility. In addition to the value added to risk management by linking operational decisions with financial decisions, this link makes it also possible to communicate operational decisions to a firm's financial officers.

Finally, we explore the role of operations research tools in the support of regulatory requirements. Financial institutions are carefully regulated in their risk management practices. The Basel Accords, for instance, stipulate practices that should be followed by banks in the management of their risks. They are the bible for supervisory authorities worldwide. In an interesting development, recent Basel Accords allow institutions to develop internal models that, properly audited, are used to report risk exposures for regulatory compliance. Value-at-Risk (VaR) has become the standard of measurement in establishing an institution's long-term financial health. VaR is a quantile of the loss distribution of a position as illustrated in Figure 1. Extremely large values of VaR, say at the 95 percent level, signal potential disaster once every 20 days (i.e., 5/100) and require action.



Figure 1: The Value-at-Risk of the loss distribution of a portfolio is a right quantlie of extreme losses at a given confidence interval. At the 95 percent level, for instance, losses will not exceed VaR on the average 95 out of 100 trading dates. CVaR estimates the expected losses for the remaining 5 days.

Institutions are required to monitor their VaR and set aside adequate regulatory capital to cover extreme movements. The estimation of VaR requires Monte Carlo simulations, while the optimization of an institution's VaR can be achieved with models of global optimization. When the VaR calculations are flawed the results can be catastrophic. The managers of Long Term Capital Management, of Orange County (Calif.) or ENRON learned this lesson the hard way, at a large cost to shareholders.

Recently, operations researchers have pointed out that optimizing the expected losses conditioned on losses exceeding VaR can be formulated as a linear program. Minimization of expected shortfall, also known as Conditional Value-at-Risk (CVaR), is a simple linear program, while minimization of VaR is a global optimization problem. A debate that started on technical arguments (linear programming or global optimization?) brought to the surface an intriguing policy issue: Optimizing VaR is to the best interest of shareholders, but not of the public that regulators must serve. Shareholders do care about extreme losses (VaR) that may drive their institution into bankruptcy. But limited liability protects them if the institution goes into bankruptcy. Regulators and the public, on the other hand, are left with the burden of bailing out failing institutions. They have to absorb the expected losses once an institution is in distress. The cost to the public is the failing institution's CVaR and not its VaR. The question "To VaR or to CvaR" is contributing to the debate on the adoption of the new Basel Accord.

The Value Added Proposition of Operations Research to Enterprise Risk Management


We have seen that operations research tools have a significant role to play in enterprise risk management. The use of these tools has been constantly on the rise since the introduction of quadratic programming for portfolio management half a century ago. However, "tools" is not the value-added proposition of operations research to the brave new world of enterprise risk management. Several other disciplines — physics, probability and statistics, numerical mathematics, fluid dynamics — are contributing significant tools to finance.

The value-added proposition of operations research to enterprise-wide risk management is as follows: To align efficiently the firm's business with the risk factors of its environment, corporations must take a global view of the risks they are exposed to and an integrated view of the risk management process. As concurrent engineering calls for the integration of engineering design, manufacturing and marketing of products in a seamless process, similarly enterprise risk management calls for the integration of the design, pricing, capitalizing, marketing and funding of financial products. These functions are clearly interdependent as illustrated in Figure 2. When multiple financial products are offered by an institution there is the additional problem of managing the business portfolio. Determining the appropriate product mix and allocating the firm's capital should again take an integrated view of the risks and returns of competing lines of business.


Figure 2: The management of a firm's portfolio necessitates the study of enterprise risk management functions as integrated processes and the efficient alignment of these processes.

Taking a global view of an enterprise requires a multidisciplinary systems approach that has been the cornerstone of operations research since its early World War II days. And the integration of the risk management process requires tools that integrate risk measurement with risk management over long-time horizons. Stochastic programming with large-scale optimization provides a powerful tool to integrate the risk-management process. In conclusion, operations research offers a unique perspective and the required technical tools for taking both a global and an integrated view of risk management.

Figures 3, 4 and 5 illustrate the value-added when adopting an integrative approach in diverse settings such as international portfolio management, the management of insurance liabilities and the management of credit risk.



Figure 3: The frontier of risk vs. reward of international portfolio managers is pushed out, and efficiency is improved, when integrating interest rate and exchange rate risk.(A. Consiglio and S.A. Zenios, Math. Prog., 89:311-339, 2001.)



Figure 4: Scenario analysis pushes out the frontier of risk vs. reward of insurance managers with complex liabilities offering guaranteed returns and bonuses. (A. Consiglio, F. Cocco, S.A. Zenios, Journal of Risk Finance., 1-11, Spring 2001.)


Figure 5: Integrating interest rate and credit risk allows portfolio managers to add value to a portfolio of government bonds and closely track a market index.(N. Jobst and S.A. Zenios, HERMES Working Paper 01-04, 2001.)

Conclusions and Caveats


Operations research has a significant role to play in the world of modern finance. It has both a support role, in providing tools from the traditional toolkit of operations research, and a main role in shifting the risk management paradigm from a compartmentalized approach toward an enterprise-wide view. But unlike other systems of human activity where operations research is applied — logistics, transportation, military — there is a rich theory describing the behavior of the financial system. Finance is a relatively new field of formal scientific inquiry. But it provides us with a well-developed body of theory that describes the financial world, as we see it. Those who wish to engage in intellectual arbitrage between finance and operations research should be well versed in both areas. Otherwise they run the risk of being at the paying side of financial arbitrage trades.



HERMES European Center of Excellence on Computational Finance and Economics




Recognizing the significance of a multidisciplinary approach to enterprise risk management, the European Commission selected the HERMES Center on Computational Finance and Economics of the University of Cyprus as a European Center of Excellence. This is one of about 20 centers established in the European Union pre-accession states to advance know-how and develop technology in areas of critical importance to European integration. The Center's faculty, graduate students and visitors engage in the study of both the supply and demand sides of financial services. In a broad research agenda that brings together economists, business administration faculty, mathematicians and computer scientists, they study household behavior, monitor accounting data to predict financial distress, develop simulations to integrate disparate sources of risk and optimize risk profiles, and use real options to mitigate business risks through enhanced managerial flexibility.

The inaugural Conference of the Center attracted a world-wide cast of leading operations research and finance scholars from European Union countries, the United State and Canada, and EU pre-accession states. (For more information visit www.hermes.ucy.ac.cy)

The founder of modern portfolio theory and Economics Nobel laureate Harry M. Markowitz honored the launching of the Center with his plenary talk. He was awarded an Honorary Doctorate by the School of Economics and Management of the University of Cyprus.

In his remarks Professor Markowitz compared the questions individuals ask ("Will the market go up or down" and "What is a hot tip?") with the questions professional money managers ask ("What are the characteristics of the probability distribution of market returns?" and "Can I hire anybody who can outperform the indices, the benchmarks, in delivering performance in any one of the asset classes?") He traced his analysis to Samuelson's classic 1972 paper that properly anticipated prices fluctuate randomly to make his point that we cannot know the answers to the questions we tend to ask as individuals. But we can think hard about the questions we ask as professional money managers, give answers to these questions, and use the techniques of portfolio optimization to guide investment decisions.

Professor Markowitz then turned to the book by David Swinston, the chief investment officer for Yale University, to draw some lessons on the challenges in implementing successful portfolio strategies. He admitted that he does not use portfolio theory in his own investment as it is too complicated for him to do anything about it, but he follows some principles that are common sense.

He concluded with the following remark, which made headline news in the local newspapers as the Cyprus stock market had the dubious distinction of holding a world record for market bubbles with its spectacular collapse: "If you're sitting next to me after the speech and have the urge to know whether the market is going to go up or down and what's a hot tip, you now know I don't know and probably nobody knows. But if you want to save for your retirement or your children's education, as permitted, I think you should consider a broadly diversified portfolio of equities and remember it fluctuates from year to year. Just stick with it."





References


- R.S. Dembo, A.R. Aziz, D. Rosen and M. Zerbs, "Mark-to-Future: A framework for measuring risk and reward," Algorithmics Publications, Algorithmics Inc., Toronto, May 2000.
- M. Holmer and S.A. Zenios, "The productivity of financial intermediation and the technology of financial product management," Operations Research, Vol. 43, pgs. 970-982, 1995.
- S.A. Zenios, "Financial Optimization," Cambridge University Press, Cambridge, England, 1993.
- W.T. Ziemba and J.M. Mulvey, "Worldwide asset and liability modeling," Cambridge University Press, Cambridge, England, 1998.



Stavros A. Zenios is director of the HERMES Center on Computational Finance and Economics at the University of Cyprus, and director of RiskLab (Cyprus), a joint venture between the Cyprus International Institute of Management and Algorithmics Inc. of Canada. He was formerly on the faculty of the Wharton School at the University of Pennsylvania, where he is currently a Senior Fellow with the Wharton Financial Institutions Center.