Stephen A. Ross Stephen Ross speaking at the 2017 IAQF/Northfield Financial Engineer Year Award Dinner Financial Analysts Journal | A Publication of CFA Institute In Memoriam: Stephen A. Ross Stephen J. Brown rofessor Stephen A. Ross securities. Unrealistic equilibrium died on 3 March 2017 assumptions of this nature had led Pat his home in Old Lyme, many to view asset pricing theories Connecticut. His death is a great as having few practical applica- loss to his family, to his colleagues tions. Ross argued that the absence at MIT, to the academic com- of arbitrage is a more fundamental munity more generally, and to the concept than equilibrium because world of investment management. only a few rational agents are A preeminent academic, Ross needed to bid away profit oppor- published many papers across a tunities that arise, even in a sea of wide range of subjects in both agents driven by “animal spirits.”3 economics and finance. Moreover, his work—particularly as it relates In the investment manage- to investment management—had ment community, Ross is best an intensely practical focus. As known for his arbitrage pric- he wrote in an article he pub- ing theory, which provides the lished with John Cox in 1976, he had no patience for intellectual basis for factor investing and factor 4 arguments that required the cunning of a currency pricing approaches. His point of reference is a speculator to understand.1 Many of the innovations well-diversified investor. For such an investor, many in the financial markets and the way we think about investment risks can be diversified away, and those those markets in recent decades can be traced to risks that remain must be relatively small in number. his thought and his writings, although he was not Ross provides a very simple and elegant demonstra- especially interested in the ephemera of the markets. tion showing that if the returns investors expect on Rather, his view was that financial transactions are securities, over and above the return on risk-free central to the human experience. A gifted communi- alternative investments, are disproportionate to the cator, Ross delighted in making the most complicated security exposures to those risks, a simple arbitrage ideas transparently simple, even common-sense. is possible. This work did not immediately suggest In this context, he was particularly proud of what these risks might be, and as he observed in a 5 Fundamentals of Corporate Finance,2 an introductory recently published article, the importance of finding text that he published with Randolph Westerfield the right factors explains why this search so absorbs and Bradford Jordan. the attention of the equity investment management profession. His work with Richard Roll and Nai-Fu Many of Ross’s financial market insights were drawn Chen6 proposed several plausible candidates, but the from the understanding that two financial securities or search continues; many factors have been proposed packages of securities that provide the same financial even though we know that the number of pervasive outcomes in the future ought to be offered at the same factors that influence the markets as a whole is price today. If this were not so, simple and profitable necessarily limited.7 arbitrage opportunities would arise. It is not that such arbitrage opportunities do not exist but rather that they The arbitrage pricing theory provides an important are necessarily small and fleeting in a well-organized conceptual foundation for the way many people view securities market. This intensely practical insight lies at the financial markets. In addition, it has profound the heart of his contributions to factor pricing, option implications for portfolio management, spelled out in valuation, and fixed-income analysis. He was not the an article that Richard Roll and Stephen Ross published 8 first to think about these issues. Previous research had in the Financial Analysts Journal in 1984. The practi- assumed that all investors behave rationally in a world cal significance of Ross’s work may be gauged by the in which there is no particular role for the trading of fact that this article is among the 10 most downloaded Volume 73 Number 3 © 2017 CFA Institute. All rights reserved. 5 For Personal Use Only. Not for Distribution. Financial Analysts Journal | A Publication of CFA Institute articles in the history of the Financial Analysts Journal. combining a position in another security with cash It forms the basis for most of the risk factor and smart holdings, then it is possible to define position weights beta approaches prevalent today, and the arbitrage at each point in time that lead to an investment that pricing theory is mentioned in 202 articles subse- has no risk and deserves a riskless rate of return. quently published in the Financial Analysts Journal. These weights are referred to as “risk-neutral prob- abilities.” The idea of valuing financial securities using Developed at the same time and using a similar intu- the derived “risk-neutral” measure has become such 9 ition, Ross’s work with John Cox reduced the com- a standard approach in asset pricing applications that plicated nature and tortuous intuition of the option few people remember that this terminology ultimately pricing mathematics developed by Fischer Black and derives from Ross’s work. It is particularly important Myron Scholes to a matter of simple arithmetic. If in the area of fixed-income analysis. Indeed, with security values can only go up or down, then there John Cox and Jonathan Ingersoll,11 Ross developed must be an intimate relationship between the value the first equilibrium model of the term structure of of options and the value of securities and cash that interest rates. At a theoretical level, it links the pricing leads to the same financial outcome. In their work of fixed-income securities to the process responsible 10 with Mark Rubinstein, Cox and Ross showed that, for interest rate movements; at the practical level, it considering the many ways that security values can provides a basis for valuing fixed-income derivative rise or fall in the course of time, this binomial option securities. In a recent work,12 Ross studied the extent pricing approach can value a wide range of derivative to which one can use risk-neutral probabilities to tease securities and strategies. Each step of the calcula- out from market prices the views that the market has tion involves simple arithmetic, but it is arithmetic about future security returns. repeated many times. Although these contributions are most directly By the time options started trading on the Chicago relevant to the practice of investment management, Board Options Exchange, the Black–Scholes model many of Ross’s other contributions to economic had come into general use, and in 1975, Texas thought also have a bearing on important issues Instruments introduced its new programmable pocket in this field. An example is his development of the calculator that came equipped with a card allowing the economic theory of agency and how to compensate calculation of call values and hedge ratios using this agents appropriately.13 This analysis has particular model. The derivative securities markets have devel- relevance in the context of delegated fund manage- oped since that time. Options and options trading ment. In addition, his thinking has found practical strategies have developed beyond the assumptions application in the series of asset management of Black and Scholes. It would be a number of years companies he founded, including Roll & Ross Asset before computer technology developed to the point Management. More recently, he was a co-founder where it would be a trivial matter to perform the num- of Ross, Jeffrey & Antle LLC, a Connecticut-based ber of calculations necessary to implement the simple, institutional investment firm. common-sense approach that Ross and his coauthors proposed. Now this approach has become the work- Stephen Ross was always a teacher, always a friend. horse of most, if not all, options trading concerns and He was a very warm person, and he and his wife options strategy implementations. As some indication Carol had a particularly wide circle of friends. He was of the relevance for practice, Ross’s work with Cox very proud of his two children, Jonathan and Kate, and Rubinstein has been cited in 67 articles we have and his two granddaughters. On a personal note, he published in the Financial Analysts Journal. was a very important mentor of mine. I remember those wonderful days in the mid-1980s when Stephen The binomial option pricing analysis led to a more fun- would take a few of us to lunch in his new red sports damental insight. If it is possible to replicate the pay- car, driving along the streets of New Haven with the offs of any derivative security—indeed, any asset—by Beach Boys’ music playing. He will be missed by many. Notes 1. John C. Cox and Stephen A. Ross, “A Survey of Some New 2. Stephen A. Ross, Randolph W. Westerfield, and Bradford Results in Financial Option Pricing Theory,” Journal of D. Jordan, Fundamentals of Corporate Finance (New York: Finance, vol. 31, no. 2 (May 1976): 383–402. McGraw-Hill/Irwin, 1991). 6 cfapubs.org Third Quarter 2017 For Personal Use Only. Not for Distribution. In Memoriam 3. Philip H. Dybvig and Stephen A. Ross, “Arbitrage,” in 9. John C. Cox and Stephen A. Ross, “The Valuation of Finance, edited by John Eatwell, Murray Milgate, and Peter Options for Alternative Stochastic Processes,” Journal of Newman (London: Palgrave Macmillan, 1989): 57–71. Financial Economics, vol. 3, no. 1–2 (January–March 1976): 145–166. 4. Stephen A. Ross, “The Arbitrage Theory of Capital Asset Pricing,” Journal of Economic Theory, vol.