A History of the Theory of Investments

My Annotated Bibliography

Mark Rubinstein

• Publisher: Wiley
• Year: 2011
• Print ISBN:
  9780471770565
• Edition: 1
• eBook ISBN:
  9781118161098
• Topic: Business
• Subtopic: Finance
• Index: Business

"This exceptional book provides valuable insights into the evolution of financial economics from the perspective of a major player."
-- Robert Litzenberger, Hopkinson Professor Emeritus of Investment Banking, Univ. of Pennsylvania; and retired partner, Goldman Sachs

A History of the Theory of Investments is about ideas -- where they come from, how they evolve, and why they are instrumental in preparing the future for new ideas. Author Mark Rubinstein writes history by rewriting history. In unearthing long-forgotten books and journals, he corrects past oversights to assign credit where credit is due and assembles a remarkable history that is unquestionable in its accuracy and unprecedented in its power.

Exploring key turning points in the development of investment theory, through the critical prism of award-winning investment theory and asset pricing expert Mark Rubinstein, this groundbreaking resource follows the chronological development of investment theory over centuries, exploring the inner workings of great theoretical breakthroughs while pointing out contributions made by often unsung contributors to some of investment's most influential ideas and models.

The Classical Period

1950–1980

1951 John C. Clendenin, “Quality versus Price as Factors Influencing Common Stock Price Fluctuations,” Journal of Finance 6, No. 4 (December 1951), pp. 398–405.

VOLATILITY

Clendenin (1951) may be the first to investigate some of the determinants of stock price volatility. In particular, Clendenin confirms one of the predictions of market rationality: Other things being equal, the volatility of the return of a high-priced stock and the volatility of the return of an otherwise similar low-priced stock should be the same. This finding was later confirmed with a more careful analysis by A. James Heins and Stephen L. Allison in [Heins-Allison (1966)] “Some Factors Affecting Stock Price Volatility,” Journal of Finance 39, No. 1 (January 1966), pp. 19–23. This hypothesis is not to be confused with the suggestion of Black (1976) that the volatility of the return of a given stock typically varies inversely with its stock price. The former is a cross-sectional hypothesis and this latter is a time-series hypothesis.

1952 Harry M. Markowitz, “Portfolio Selection,” Journal of Finance 7, No. 1 (March 1952), pp. 77–91.

1952 Andrew D. Roy, “Safety First and the Holding of Assets,” Econo-metrica 20, No. 3 (July 1952), pp. 431–449.

1959 Harry M. Markowitz, Portfolio Selection: Efficient Diversification of Investments, Cowles Foundation Monograph #16 (New York: John Wiley & Sons, 1959); reprinted in a second edition with Markowitz’s hindsight comments on several chapters and with an additional bibliography supplied by Mark Rubinstein (Malden, MA: Blackwell, 1991).

DIVERSIFICATION, PORTFOLIO SELECTION, MEAN-VARIANCE ANALYSIS, COVARIANCE, RISK AVERSION, LAW OF LARGE NUMBERS, EFFICIENT SET, CRITICAL LINE ALGORITHM, LONG-TERM INVESTMENT, SEMIVARIANCE, MARKET MODEL

The assumption that an investor maximizes the expected return of his portfolio implies that he will place all his eggs in one basket, the single security with the highest expected return, and “watch it”—the advice once given by the industrialist and philanthropist Andrew Carnegie.1 But this leaves unexplained the pervasiveness of diversification. Markowitz (1952/March) is the first mathematical formalization in English of the idea of diversification of investments, the financial version of “the whole is greater than the sum of its parts”: Through diversification, risk can be reduced without changing expected portfolio return. Markowitz postulates that an investor should maximize expected portfolio return (μP) while minimizing portfolio been suggested as a measure of economic risk by Fisher (1906), reprinted in 1965, pp. 406–410. Jacob Marschak in [Marschak (1938)] “Money and the Theory of Assets,” Econometrica 6, No. 4 (October 1938), pp. 311–325 (see in particular p. 320), suggested using the means and the covariance matrix of consumption of commodities as a first-order approximation in measuring utility. Markowitz instead looked directly at the single variable of portfolio return and showed how one could, in practice, calculate the mean-variance efficient set: for each possible level of portfolio expected return, the portfolio with the lowest variance of return.

Probably the most important aspect of Markowitz’s work was to show that it is not a security’s own risk, perhaps as measured by security variance, that is important to an investor, but rather the contribution the security makes to the variance of the entire portfolio—and this was primarily a question of its covariance with all the other securities in the portfolio. This follows from the relation between the variance of the return of a portfolio (σ2P) and the variance of return of its constituent securities (σ2j for j = 1, 2, . . . , m):

where the xj are the portfolio proportions (that is, the fraction of the total value of the portfolio held in security j so that Σjxj = 1) and ρ jk is the correlation of the returns of securities j and k. Therefore, ρjkσjσk is the covariance of their returns. This seems to be the first occurrence of this equation in a published paper on financial economics written in English.

So the decision to hold a security should not be made simply by comparing its expected return and variance to others’, but rather the decision to hold any security would depend on what other securities the investor wanted to hold. Securities cannot be properly evaluated in isolation, but only as a group. This perspective was clearly missing from Williams (1938), from Buffett (1984), and from Graham-Dodd (1934); and even in as late as the revised version of Security Analysis in 1962, it received scant comment. Markowitz’s approach is now commonplace among institutional portfolio managers.

One might ask why Markowitz’s insight had been so long in coming. As noted, Williams (1938) argued that risk could be diversified away and was therefore of modest consequence. In [Hicks (1931)] “The Theory of Uncertainty and Profit,” Economica 0, No. 32 (May 1931), pp. 170–189, John R. Hicks comes tantalizingly close. Hicks argues that diminishing marginal utility suggests that investors will demand extra expected return for bearing risk. But Hicks argues that some risk can be reduced by its transfer to other parties who are more willing to bear risk via insurance or hedging. He also suggests that a key motivation behind firms with many stockholders is to allow the firm to expand while spreading its risk to many investors. And then Hicks falls into the law of large numbers trap, arguing that diversification both across a large number of investments and over time will make the remaining overall risk minimal—a double error:

Finally, it must be asked—what light is thrown by the foregoing on the general question of the influence of risk on the distribution of the National Dividend. . . . Most of the groups of persons whose resources with which we are concerned in the theory of distribution seem to be large enough for nearly all risks they bear to cancel out in a moderate period of time. (p. 187)2

But Hicks qualifies this by writing:

[T]he affairs of a group, large enough and homogeneous enough to be a convenient object of economic discussion, may fail to be independent. . . . The most obvious are changes in the general level of prices. (p. 188)

However, Hicks clearly believes this dependence is a second-order problem and does not pursue its implications. He repeats this reliance on the law of large numbers a second time in [Hicks (1935)] “A Suggestion for Simplifying the Theory of Money,” Economica, New Series 2, No. 5 (February 1935), pp. 1–19 (in particular p. 9).

Contrast this with Markowitz, who states simply:

This presumption that the law of large numbers applies to a portfolio of securities cannot be accepted. The returns from securities are too inter-correlated. Diversification cannot eliminate all variance. (p. 79)3

And this key observation encouraged him to take the next steps that others before him had not seen as necessary.

Markowitz argues that investors dislike variance of portfolio return since they are averse to risk. Hicks, in [Hicks (1962)] “Liquidity,” Economic Journal 72, No. 288 (December 1962), pp. 787–802, his Presidential Address to the Royal Economic Society, instead makes the case that investors dislike variance because it increases the probability that forced selling of securities with significant liquidation costs will be required to meet liquidity needs (that is, consumption), an argument essentially similar to Keynes (1937).

Roy (1952) independently sets down the same equation relating portfolio variance of return to the variances of return of the constituent securities. He develops a similar mean-variance efficient set. Whereas Markowitz left it up to the investor to choose where within the efficient set he would invest, Roy advised cho...

Table of contents

• Cover
• Contents
• Title
• Copyright
• Dedication
• Preface
• The Ancient Period
• The Classical Period
• The Modern Period
• Index of Ideas
• Index of Sources