The Principles Of Investment Markowitz
Just how an investor should allocate his resources has long been debated. Classical wisdom suggested that investments should be allocated to those assets yielding the highest returns, without the consideration of correlations. Before the modern formulation of efficient markets, speculators widely acted on the belief that positions should be taken only if they had a competitive advantage in terms of information. A large amount of resources were therefore spent on analyzing financial information. John Maynard Keynes suggested that investors should carefully evaluate all available information and then make a calculated bet. The idea of diversification was anathema to Keynes, who was actually quite a successful investor.
In 1952, Harry Markowitz, then a graduate student at the University of Chicago, and a student member of the Cowles Commission,7 published a seminal article on optimal portfolio selection that upset established wisdom. He advocated that, being risk adverse, investors should diversify their portfolios.8 The idea of making risk bearable through risk diversification was not new: It was widely used by medieval merchants. Markowitz understood that the risk-return trade-off of investments could be improved by diversification and cast diversification in the framework of optimization.
7 The Cowles Commission is a research institute founded by Alfred Cowles in 1932. Originally based in Colorado Springs, the Commission later moved to the University of Chicago and thereafter to Yale University. Many prominent American economists have been associated with the Commission.
8 See Harry M. Markowitz, "Portfolio Selection," Journal of Finance (March 1952), pp. 77-91. The principles in Markowitz's article were then expanded in his book Portfolio Selection, Cowles Foundation Monograph 16 (New York: John Wiley, 1959).
Markowitz was interested in the investment decision-making process. Along the lines set forth by Pareto 60 years earlier, Markowitz assumed that investors order their preferences according to a utility index, with utility as a convex function that takes into account investors' risk-return preferences. Markowitz assumed that stock returns are jointly normal. As a consequence, the return of any portfolio is a normal distribution, which can be characterized by two parameters: the mean and the variance. Utility functions are therefore defined on two variables—mean and variance—and the Markowitz framework for portfolio selection is commonly referred to as mean-variance analysis. The mean and variance of portfolio returns are in turn a function of a portfolio's weights. Given the variance-covariance matrix, utility is a function of portfolio weights. The investment decision-making process involves maximizing utility in the space of portfolio weights.
After writing his seminal article, Markowitz joined the Rand Corporation, where he met George Dantzig. Dantzig introduced Markowitz to computer-based optimization technology.9 The latter was quick to appreciate the role that computers would have in bringing mathematics to bear on business problems. Optimization and simulation were on the way to becoming the tools of the future, replacing the quest for closed-form solutions of mathematical problems.
In the following years, Markowitz developed a full theory of the investment management process based on optimization. His optimization theory had the merit of being applicable to practical problems, even outside of the realm of finance. With the progressive diffusion of high-speed computers, the practice of financial optimization has found broad application.10
9 The inputs to the mean-variance analysis include expected returns, variance of returns, and either covariance or correlation of returns between each pair of securities. For example, an analysis that allows 200 securities as possible candidates for portfolio selection requires 200 expected returns, 200 variances of return, and 19,900 correlations or covariances. An investment team tracking 200 securities may reasonably be expected to summarize their analyses in terms of 200 means and variances, but it is clearly unreasonable for them to produce 19,900 carefully considered correlation coefficients or covariances. It was clear to Markowitz that some kind of model of the covariance structure was needed for the practical application of the model. He did little more than point out the problem and suggest some possible models of co-variance for research to large portfolios. In 1963, William Sharpe suggested the single index market model as a proxy for the covariance structure of security returns ("A Simplified Model for Portfolio Analysis," Management Science (January 1963), pp. 277-293).
10 In Chapter 16 we illustrate one application. For a more detailed discussion, see Frank J. Fabozzi, Francis Gupta, and Harry M. Markowitz, "The Legacy of Modern Portfolio Theory," Journal of Investing (Summer 2002), pp. 7-22.
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