CFA Society Boston Course

by Richard O. Michaud, Ph.D.

Markowitz (1952) represents the birth of modern finance.  Prior to Markowitz, finance theory was largely security valuation.  Notable examples include Graham and Dodd (1934) and Williams (1938).  There was little attention to the portfolio as an entity or portfolio risk management as the focus of financial theory.   

The Markowitz mean-variance (MV) efficient frontier was invented as a model of institutional investment manager behavior.  Harry Markowitz was a Ph.D. student in the economics department at the University of Chicago in the early 1950s.  He was searching for a thesis on the stock market.  He studied institutional mutual fund companies and noticed that the portfolios they managed were all long only (no short selling) well diversified portfolios that varied by risk level depending on a client’s risk aversion.    Risk-averse clients prefer portfolios with less risky securities and conversely.  While sitting in Chicago’s business library, he had his famous epiphany.  He realized that a linear (equality and inequality) constrained quadratic programming (QP) mathematical optimization program will create a portfolio mathematically like that of a rational informed professional investment manager.  A MV QP framework requires estimates of return with a vague notion of security and portfolio risk conveniently defined as the variance.  In one stroke, Markowitz defined a financial theory of capital markets as well as invented a mathematical procedure to replicate institutional asset management in practice.  Later, Markowitz invented the Critical Line Algorithm (CLA) that made it possible to compute MV efficient frontier portfolios. 

Readers know that the history of financial theory is not based on the Markowitz efficient frontier.  The Capital Asset Pricing Model (CAPM) due to Sharpe (1964), Lintner (1965), Treynor (1961), and Mossin (1966) has been the dominant financial theory of choice since the 1960s.  While CAPM theory is based on Markowitz MV optimization, there is one key omission:  the no-short-selling constraint included in actual institutional fund management was omitted for analytical convenience.  This is because the Markowitz MV QP framework is not analytically solvable with only calculus. 

CAPM has been a very productive financial theory.  With some simple additional assumptions, you can show that the market portfolio is MV efficient, and that a security’s expected return in equilibrium is a linear function of “beta,” or the systematic risk of the security relative to the market.  In addition, beta enables defining “alpha” and the concept of the “active” return of a security or portfolio. 

CAPM is a very popular financial theory.  It spawned a multi-trillion dollar “quantitative” asset management industry.  Academically trained sophisticated professionals started many quant shops in Boston and around the world during the 1970s and beyond, with estimates of beta, alpha, and portfolio risk in order to outperform the market.   

CAPM is not Markowitz theory.  It is not based on an empirical observation of the behavior of informed investment professionals.  It is MV utility preference theory based on Von Neumann and Morgenstern (VM) (1944) game theory rationality axioms.  VM axioms are designed to reflect human rational decision making under uncertainty.  Simple statements such as:  if I like a more than b, and b more than c, then I like a more than c.  There is, of course, great mathematical sophistication to VM game theory.  John von Neumann is one of the greatest mathematical geniuses of the 20^th century.  It is almost impossible to argue that the axioms do not reflect the reasoning of rational informed human thinking.  It was a very convenient set of principles to build a rational social science of financial behavior.  What could possibly go wrong with an expected utility theory of capital markets consistent with VM game theory?

Eventually, red flags started to appear.  The first known dissenter to game theory based finance was Maurice Allais (1953) (Nobel prize 1988).  He was interested in rational low-probability decisions.  He created examples to show that low-probability bets were often not consistent with VM rationality axioms.   Paul Samuelson said of Allais that if he had written in English instead of French the path of modern finance would likely have been very different.  However, many financial economists considered Allais’ examples tricks and the implications of his work were often ignored by American financial economists.   

A second red flag appeared in a Jobson and Korkie (1981) simulation study of unconstrained MV optimized portfolios.   They showed that the CAPM unconstrained MV optimization framework was worse than equal weighting a portfolio.  The study was not widely appreciated as a fundamental critique of the usefulness of CAPM theory for investment management.

However, the third red flag was widely noticed.  The famous Kahneman and Tversky (1979) experiments showed that investors have a consistent bias towards risk aversion that is inconsistent with VM rationality axioms.  Very simply, informed investors do not think like VM and, by implication, CAPM is not a useful framework for practice.   

CAPM is “Finance’s Wrong Turn.” It is what the course given at CFA Society, Boston in March is all about.  It is about returning to the empirically based Markowitz MV efficient frontier framework and resetting financial theory on a more reliable path for practice.  The landscape needs to clear many artifacts of 20^th century theory and practice that have accumulated for more than 50 years.  There is much to talk about and much to think about.  The effort to begin again is solvable. 

I hope to see you all in class.

References

Allais, M.  1953. “Le Comportement de l’Homme Rationel devant le Risque:  Critique des Postulats et Axiomes de l’Ecole Americaine.”  Econometrica 21(4):503-546. 

Graham, Benjamin, 1934.  Security Analysis.  McGraw-Hill, New York. 

Jobson. D. and B. Korkie 1981.  Putting Markowitz Theory to Work.”  Journal of Portfolio Management 7(4):70-74. 

Kahneman, D. and A. Tversky 1979.  Prospect Theory:  An Analysis of Decision under Risk.” Econometrica 47(2):263-269. 

Lintner, J. 1965.  “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.”  The Review of Economics and Statistics 47(1):13-37. 

Markowitz, H. 1952. “Portfolio Selection.” Journal of Finance 7(1): 77-91.

Mossin, J.  1966.  “Equilibrium in a Capital Market.” Econometrica 34(4):768-783. 

Sharpe, William F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk, Journal of Finance, 19 (3), 425–442

Treynor, Jack L. (1961). “Market Value, Time, and Risk,” Unpublished manuscript.

Williams, J.B., The Theory of Investment Value.  Harvard University Press, Boston.

1. This course centers on three issues that explain the crisis in modern finance: finance theory is in error; institutional investment technology is out of date; and capital markets are not well understood.

2. CAPM is based on theoretical assumptions, Markowitz is based on informed investor behavior.

3. From a Markowitz theory perspective, finance is a lot like sociology where a back test is not likely reliable.

4. Unconstrained MV optimization is not useful for practice.

5. Constraints are generally necessary for producing useful results.