Harry M. Markowitz

Portfolio Optimization with Factors, Scenarios, and Realistic Short Positions

This paper presents fast algorithms for calculating mean-variance efficient frontiers when the investor can sell securities short as well as buy long, and when a factor and/or scenario model of covariance is assumed. Currently, fast algorithms for factor, scenario, or mixed (factor and scenario) models exist, but (except for a special case of the results reported here) apply only to portfolios of long positions. Factor and scenario models are used widely in applied portfolio analysis, and short sales have been used increasingly as part of large institutional portfolios. Generally, the critical line algorithm (CLA) traces out mean-variance efficient sets when the investors choice is subject to any system of linear equality or inequality constraints. Versions of CLA that take advantage of factor and/or scenario models of covariance gain speed by greatly simplifying the equations for segments of the efficient set. These same algorithms can be used, unchanged, for the long-short portfolio selection problem provided a certain condition on the constraint set holds. This condition usually holds in practice.

Financial Market Simulation

When they want to see how complex systems work, scientists often turn to asynchronous-time simulation models, which allow processes to change sporadically over time, typically at irregular intervals. While rarely used in finance today, such models may turn out to be valuable tools for understanding how markets respond to changes in the participation rates of different types of investors, for example, or to changes in regulatory or investment policies. The asynchronous, discrete-event, stock market simulator described here allows users to create a model of the market, using their own inputs. Users can vary the numbers of investors, traders, portfolio analysts, and securities, as well as their own investing and trading decision rules. Such a simulation may be able to provide a more realistic picture of complex markets.

Efficient Portfolios, Sparse Matrices, and Entities: A Retrospective

In 1989 I was pleased and honored to be awarded the ORSA/TIMS now INFORMS John von Neumann Theory Prize for my work in portfolio theory, sparse matrices, and SIMSCRIPT. The following is a retrospective on my work in these fields.

Harry Markowitz : selected works

Harry M Markowitz received the Nobel Prize in Economics in 1990 for his pioneering work in portfolio theory. He also received the von Neumann Prize from the Institute of Management Science and the Operations Research Institute of America in 1989 for his work in portfolio theory, sparse matrices and the SIMSCRIPT computer language. While Dr Markowitz is well-known for his work on portfolio theory, his work on sparse matrices remains an essential part of linear optimization calculations. In addition, he designed and developed SIMSCRIPT — a computer programming language. SIMSCRIPT has been widely used for simulations of systems such as air transportation and communication networks.

INVITED EDITORIAL COMMENT: How to Represent Mark-to-Market Possibilities with the General Portfolio Selection Model

1. Harry M. Markowitz 1. is the principal of Harry Markowitz Company, San Diego, CA. (harryhmm{at}aol.com) [Jacobs and Levy [2013]][1] state that “conventional mean-variance optimization … does not consider … components of risk that are unique to using leverage. These include the risks

A More Efficient Frontier

In this article, the authors show how a community of investors can provide each of its members with higher expected return for a given standard deviation than any individual member can obtain alone by picking a portfolio from an efficient frontier. The procedure entails pooling the assets of the members into a single community portfolio, then apportioning the gains or losses on this portfolio according to a function depending on the members respective risk-return preferences. Use of such a function makes the pooled risk control procedures equivalent to an “internal risk-free rate” at which conservative investor members lend to more aggressive members. The authors argue, however, that this particular version of pooled procedures is not likely to prevail among investment communities.

Trains of Thought

My essay will be concerned principally with some philosophical views I have held for much of my life. After recounting the sources (for me) and the nature of these views, I will conclude with some brief personal reflections. These philosophical views are on a few related topics. My views on any one topic did not spring instantly to mind, but were the results of a train of thought to which I would return many times over weeks, months and years. It was also important to me that the train of thought on one topic did not contradict that on another.

An Algorithm for Portfolio Selection in a Lognormal Market

Ohlson and Ziemba developed an approximation for the solution of the portfolio problem with lognormally distributed assets when the investor has a power utility function. The approximating problem has been analyzed by Schaible and Ziemba and it may fail to be quasiconcave. In this paper a convergent finite algorithm that finds a global optimum is presented for this problem. The algorithm is an adaption of Markowitzs critical line algorithm for parametric convex quadratic programming.

God, Ants and Thomas Bayes

The editors of this volume have invited me to present here my personal philosophy. But I cannot distinguish between my personal philosophy and my theoretical philosophy. As I explained in my autobiography (Markowitz 1990), when I was in high school I read science at a nontechnical level, like the ABC of Relativity , and the original writings of great philosophers. In particular, I was struck by David Hume’s (1776) argument that even though I release a ball a thousand times and, in every instant, it falls to the floor, that does not prove that it will necessarily fall to the floor the thousand-and-first time. In other words, even though Newton’s law of gravity worked in thousands of instances, that did not prove that it would never fail – such as in explaining the orbit of Mercury! Essentially, my philosophical interest in high school lay in the question “What do we know and how do we know it?” When I entered the Economics Department at the University of Chicago I was naturally drawn to the economics of uncertainty. In particular, the work of Leonard J. Savage (1954) – building on that of von Neumann and Morgenstern (1944) – presented, to me among many others, a convincing axiomatic argument that, in acting under uncertainty, one should maximize expected utility using probability beliefs where objective probabilities are not known. It is a corollary of the latter conclusion that, as information accumulates, one should shift one’s beliefs according to Bayes’s rule, reviewed later in this essay. (Hume, too, said that one should attach probabilities to beliefs but did not specify that Bayes’s rule should be used in response to growing evidence for or against various hypotheses.)