Gerhard Tintner · 1960
Gerhard Tintner’s book review presents Harry M. Markowitz’s Portfolio Selection: Efficient Diversification of Investments as a substantial advance in mathematical economics that remains accessible to financial analysts. Its central judgment joins theoretical innovation to practical usefulness: modern mathematical methods make portfolio choice more rigorous, while clear exposition and computational techniques make the resulting analysis usable without extensive prior mathematical preparation.
Tintner begins by mapping the monograph’s four-part structure. Introduction and illustrative analysis lead to the statistical relationships between securities and portfolios, including expected values, variances, diversification across many securities, and long-run returns. The third part treats efficient portfolios through geometry, derivation, and semivariance; the fourth turns to rational choice under uncertainty, encompassing expected utility, choice over time, probability beliefs, and portfolio applications. Appendixes on computation and utility axioms, together with a bibliography he praises, support this progression from examples through formal analysis to decisions.
The review then situates Markowitz within a historical change in economic reasoning. Tintner contrasts classical mathematical economics, grounded in calculus and the differential equations of mechanics, with modern approaches drawing on set theory and algebra. He identifies von Neumann and Morgenstern’s Theory of Games and Economic Behavior as the landmark of this newer orientation.
This book is a very successful attempt to apply some of these ideas to problems of portfolio selection.
This assessment makes portfolio analysis a concrete application of a broader methodological development. Tintner’s decisive conceptual example is efficiency, which relates average return to the dispersion of returns rather than treating either independently:
A key concept is the efficient portfolio. "If a portfolio is efficient, it is impossible to obtain a greater average return without incurring greater standard deviation; it is impossible to obtain smaller standard deviation without giving up return on the average" (p. 22). Standard deviation is here a measure of the dispersion of the return.
The quoted definition establishes a trade-off: improving one dimension requires sacrificing the other. Tintner next translates this conception into a computational problem.
The problem of finding efficient portfolios is a case of non-linear (quadratic) programming.
He notes that Markowitz develops computational methods, provides numerous examples, and suggests electronic computing machines. The closing appraisal returns to accessibility: mathematical and statistical concepts are explained within the text. Tintner therefore recommends the book to analysts and economists, emphasizing the practical promise of its modern methods, especially utility theory. His brief review connects an exact criterion of efficiency, procedures for finding efficient portfolios, and a framework for choice under uncertainty; it endorses these contributions without attempting an independent technical evaluation.
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