April 1997 € Volume 24 € Number 2

Money Matters

By C.S. Venkatakrishnan

In recent years, the financial service industry has become a career haven for many operations researchers and others with quantitative training. Some see this as the result of a "greedy algorithm," with graduates, dismayed by the relative paucity of career options in their own fields of training, flocking to where the jobs are. There is perhaps some truth to this. However, finance is also not a short-term refuge -- indeed, few who enter leave. Rather, as one who initially had a career in operations research before entering finance, I strongly believe it to be an industry with excellent long-term career prospects for OR professionals.

I can suggest three reasons for this. First, as I shall aim to illustrate in this article, is that finance offers a dynamic and invigorating work environment which provides tremendously challenging projects, along all dimensions of an operations research training. Second, these projects tend to have a direct and immediate relevance to the business of the firms, and there is perhaps unique scope in finance for operations researchers to be a valued and integral part of the enterprise. Third, finance is ipso facto a highly numerate profession, and management is quite attuned to realizing the value of quantitative and analytical contributions. All of which can, of course, make for a brilliant career.

This article aims to give the reader a sense of the type of career an OR professional can expect in finance, with some guidance on how to get there. To that end, I shall survey some areas of interest in quantitative financial research. Then I shall turn to the career development issue for operations researchers, with some thoughts for those who may be interested in finance as a career. First, though, a sketch of the field in which these endeavors take place.


Overview of Industry
The financial industry ranges from the consumer-oriented bank branches, credit card companies, brokerages and mortgage lending agencies on "Main Street" to the large corporate treasuries, banks, investment managers and securities houses throughout the country and on Wall Street. The major capital markets -- stock exchanges, futures exchanges and over-the-counter bond markets -- serve as clearinghouses where buyers and sellers of financial instruments balance their desire for return with their appetite for risk. The large institutional buyers and sellers in the major capital markets are primary employers of quantitative researchers who study and model the risks and returns inherent in the instruments that are traded.

In the major capital markets, the institutional participants divide themselves into two groups -- the "buy side" and the "sell side" -- though both obviously do buying and selling at any given time. The sell side consists of the major securities houses that take firms public and sell their stock, that structure bond offerings for companies, and create derivatives that allow investors to offset risks in underlying stocks, bonds, currencies and commodities.

The buy side consists of corporate treasuries, who invest on their own behalf, and investment management firms which invest cash, on their own behalf or on behalf of other investors, in portfolios of securities. These portfolios may comprise "vanilla" stocks and bonds, as well as derivatives and other non-traditional instruments. Both the buy and sell side employ quantitative research.

The sell side tends to be more focused on shorter term trading and hedging of portfolios of instruments within one sector or "book" (e.g. mortgage backed securities). The buy side, on the other hand, looks to longer term returns, typically against benchmarks, using portfolios often comprised of instruments from different sectors. There are, of course, some large companies, like the one for which I work, which operate on both the sell side and the buy side.

In choosing three areas of quantitative financial research to describe, I wish to emphasize the mathematical techniques that are employed and illustrate how they play to the strengths of an OR training. These examples will depict the use of stochastic modeling, statistics and optimization, respectively. Further, in discussing the business context for these areas of research, I hope to convey a sense of the importance of the models that are developed and the extent of their usage.

Two caveats at the outset. First, a short piece cannot do justice to the full range and scope of quantitative problems in finance. Indeed, my choice of examples will be colored by my experience and interests -- investment management (the buy side) and, within that, fixed income -- at J.P. Morgan. The second caveat is that, though I shall be focusing on model development, quantitative training such as OR is also valuable to the users of models. This is because, relatively speaking, in finance, the end-users tend to be closer, in my view, to the models and underlying methodology, both in understanding and appreciation, than is the case in other disciplines.


Term Structure Models and Interest Rate Derivatives
Fixed income securities are those that pay their holders a specified amount periodically. Typical examples are bonds which pay their holder a coupon every six months. In the absence of any embedded derivatives, the value of such an instrument at a given time can be calculated relatively easily with reference to the interest provided at the same time by comparable U.S. government securities. Frequently, however, fixed income securities contain embedded derivatives.

A "derivative," often referred to as an option, is defined as an instrument whose value is derived from the value of another instrument. For instance, an issuer of a corporate bond at a particular coupon (or rate of interest) may prefer to have an option to recall the issue and refinance the debt if rates fall below their levels at issuance. Such a bond is said to be callable. Likewise, in a mortgage pass-through security, which provides the holder with the principal and interest from a pool of individual home mortgages, there is an embedded option: the homeowner has the right to "prepay" the loan. He may either pay more than his monthly due or, more seriously, refinance his entire remaining mortgage if interest rates were to fall below the levels at which the loan was first financed. In either case, the option -- a right, but not an obligation -- to recall the bond or prepay the mortgage takes its value from the worth of the underlying instrument itself, as well as the set of possible future interest rates and their likelihood of occurrence.

From an investment point of view there are a few fundamental questions about such securities with embedded interest rate derivatives, or indeed about any fixed income instrument. First, given its market price, what is its "spread" or relatively higher yield to a "comparable" U.S. government obligation (which by definition has zero risk)? The spread is typically defined as the additional interest rate, compared to U.S. government bonds, by which all the income from the instrument has to be discounted. The second question is to measure the sensitivity of the price of the instrument to changes in interest rates. In either case, an instrument has to be priced given a sample spread (to find the true spread, one then iterates to find the particular value that results in the computed price being equal to the market price).

As an operations researcher would recognize, computing the price of an instrument, given a spread, would involve simulating a range of possible future interest rate states, determining the cash flows from the instrument given the interest rate state (itself not an easy task, as the next section will discuss), and then discounting the cash flows by the appropriate interest rate (plus spread). The information would finally have to be distilled into one number, typically an expected present value of future cash flows. An OR person will also recognize many familiar elements of this process: constructing a parsimonious but realistic mathematical model for interest rate movements (called a "term structure model" in finance), effectively simulating interest rate movements based on this model, numerically computing the cash flows along simulated paths, and having the process converge to an answer. Lastly, a theoretically minded OR person would wonder if there exists an overarching methodological framework in which such models can be constructed, and whether there are special cases for which the evaluation is simpler. It does, and there are.

Term structure models are typically stochastic models of interest rate movements employing drift terms and Wiener process based diffusion terms. There is a vast body of work in finance, some of it contributed by (once and future?) operations researchers, on developing term structure models with desirable theoretical and computational properties. Further, much work has been done, in academia and industry, on calibrating these models to market conditions. However, as markets evolve and computational capabilities advance, there is a constant effort to improve upon models of the term structure. Since these models are the bedrock of fixed income analytics of any reasonable complexity, there is always scope for persons with solid training in stochastic processes, simulation and numerical methods: skills that have never been in short supply in the OR community.


Prepayment Modeling
Suppose we are given a term structure model of interest rates on the basis of which we can simulate paths of future interest rates. There is still the question for some securities of what the actual cash flow will be at a given point in time along a particular interest rate path. For securities with path-dependent payoffs, the actual payoff at any point in time may be uncertain because it depends to some degree on human behavior. A classic example is the mortgage backed security.

Consider a security backed by a pool of identical fixed rate mortgages. (A "pass-through security," created when one or more holders of mortgages form a collection, or pool, of mortgages and sell shares or participation certificates in the pool.) An investor holding such an instrument typically receives a higher yield compared to a "similar" (a term I will leave loosely defined) U.S. government or high grade corporate bond. The reason is that the investor has written an option to the homeowner (or mortgagor) who can refinance his home if interest rates drop below his rate of original financing. If rates fall, and the mortgagor does refinance and repay his outstanding loan balance early, the investor would have to reinvest the proceeds at less favorable terms than they were originally lent. Hence the prepayment option can be costly to the lender (or investor). In return for the risk of this option underwritten to the mortgagors, the investor expects a higher return. But what should the higher return be? It depends on the likelihood of circumstances arising in which homeowners in a given pool will find it profitable to refinance and the extent to which, on average, they do so. The cash flow at a point along an interest rate path is the sum of the scheduled interest and principal payments and the unscheduled prepayments.

The extent of prepayments on average in a given interest rate scenario is typically assessed with statistical models of prepayment behavior. Consider the pool of mortgagors whose loans comprise the instrument being held. Some fraction of them may not follow interest rates as closely as others and may be less aware of opportunities to refinance. Such borrowers contribute to the "burnout" component of prepayment models: the expected proportion of homeowners who resolutely resist the blandishments of lower interest rates. Even among those who do follow interest rates closely, there will be greater and lesser degrees of financial sophistication and strategy. Some may refinance immediately if it is advantageous to do so; others may play a waiting game. Indeed, for some sophisticated mortgage structures (with adjustable rates, for instance) a doctoral training in OR may be a prerequisite to evaluating the refinancing decision. Even without interest rate-based refinancings, there may be prepayments in the natural course of time. These would be due to people moving from one house to another for a variety of reasons (termed "relocations"). There is a strong seasonal component to relocations: more people move in the summer than in the winter.

The statistical modeling of prepayments, then, is a mainstay of methods to value mortgage-backed securities. It is a problem of tremendous importance and deep complexity. Advanced models have been developed for pass-through securities based on loans guaranteed by certain federal agencies created by Congress to increase the supply of capital to the residential mortgage market. These "agency" pass-throughs form 98 percent of the pass-through market [1]. Even in this well-studied market, modelers have to continually focus on particular aspects of prepayment behavior that can help identify mispricings in securities. Should one disaggregate prepayments by geographic origin of loans? What weight should be given to data on prepayment behavior in a previous interest rate cycle as against the last few months? What is it worth if the mortgages underlying the security provide strong incentives against refinancings in the first few years (a "lockout" period) of the loan?

Beyond these agency pass-throughs, the modeling of prepayments is extending to whole new classes of securities backed by other types of residential loans, such as adjustable rate mortgages or home equity loans, and even non-residential ones such as auto loans, credit card borrowings and the like. Clearly, as long as there is securitization of new types of consumer loans, and innovations in security underwriting based on these loans, there is great scope and need for prepayment modeling.

For an operations researcher with a statistical bent, prepayment modeling is a vast arena in which to develop, calibrate and apply sophisticated behavioral models based on rich seams of empirical data. There is tremendous value and applicability to the findings, and one must be assiduously watching and learning from the data.


Portfolio Optimization
Lastly, I will focus on an example in optimization, a skill perhaps more closely associated with operations research than with any other field. The challenge here is less one of developing new methodologies, though that may be the case in certain instances. Rather, it is to help identify good methods to construct portfolios, to gather the data to support an optimization and to decipher the results. Both in fixed income and in equities, the portfolio construction paradigm has been fairly well established. Broadly speaking, it is to identify an efficient frontier to capture the tradeoff between risk and return and to find ways in which to adjust a given portfolio to move it close to this risk-return frontier.

In highly evolving financial markets, there is a constant search for greater return by investing in non-traditional asset classes or non-traditional markets (e.g. emerging markets). A disciplined investor will try to understand, however, how returns in these new markets are correlated to those in markets or asset classes which already exist in his portfolio. The aim is to measure the additional return from exposure to new instruments in the context of the additional risk taken on by this exposure.

In this context, one can consider a set of assets which one wishes to combine in a portfolio. Assume one is given a vector of expected returns over a certain time horizon and a matrix of correlations (or covariances) between the individual asset returns. Typically, both the returns and the covariances in return are inferred from data -- a challenging task in itself. The problem then is to maximize expected returns over a time horizon subject to a certain maximum volatility in returns. The optimization is typically performed using standard packages, though these naturally take advantage of technological improvements. The challenge, though, is to be able to understand and explain the answers in the context of the portfolio construction, including the interpretation of results in terms of marginal analyses with respect to the new asset class. This clearly is the bread and butter of an operations researcher and an area where OR skills would be of great advantage.


Finding a Financial Career
Suppose then that you are an operations researcher nearing the end of your studies, or about to embark upon them, and you wish to have a career in finance. What do you do? What skills should you establish? I would have to respond with three pieces of advice:

1. Diversify your portfolio of skills. In pursuing a methodological concentration, it can be valuable not to neglect the broad-based OR training. One can develop a career in any of the three areas I outlined above, and indeed in many others. Wall Street encourages specialization. However, there can be great scope for those who can easily cross boundaries of methodology. Operations researchers may be able to take advantage of their broad methodological training to be effective in a variety of projects.
2. Mark the markets. It is important, though by no means indispensable, to have had some exposure to finance in either coursework or experience. Most firms do expect to have to train new employees, but would prefer those who are more, rather than less, conversant with economics and finance.
3. Pay attention to performance. A historical strength of OR has been its close attention to practical problems with an engineer's approach to solving them. This has meant strong computer programming skills and a facility with data and empirical work. In any business setting, a results-oriented approach is valued, and a record of such work appreciated.

In conclusion, I hope to have conveyed a sense of how valuable OR skills are in finance, not only in modeling and research but in portfolio construction and management. The financial world is constantly evolving, and it tends to be in the forefront of using information technology. There is a continual search for improvement in pricing and analysis, and even minor improvements can be richly rewarded by the large volume of transactions. It is a place where people with an OR training have made valued contributions and should continue to do so. Indeed, for some operations researchers, finance may well be déjà vu all over again.


References

1. "Capital Markets: Institutions and Instruments," Frank Fabozzi and Franco Modigliani, Prentice-Hall, 1991.

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