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Source Title: Alternative Decision-Making Models for Financial Portfolio Management: Emerging Research and Opportunities

Copyright: © 2018
|Pages: 40
DOI: 10.4018/978-1-5225-3259-0.ch003

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A little over forty years ago, a University of Chicago graduate student in economics, while in search of a dissertation topic, ran into a stockbroker who suggested that he study the stock market. Harry Markowitz took that advice and developed a theory that became a foundation of financial economics and revolutionized investment practice. His work earned him a share of the 1990 Nobel Prize in Economics. (Paul D. Kaplan, 1998, Vice President and Chief Economist).

In the finance textbooks, investment instrument that can be bought and sold is often called an asset. Asset allocation is a term used to describe the set of weights of broad classes of investment within a portfolio. For an individual investor, asset allocation can be represented by the investment in stocks, bonds, mutual funds and money market investments. Furthermore, the investor decisions are based on his utility function- level of welfare or satisfaction. The key reason for the utility function to be considered as a general approach to a decision making under risk is its sound theoretical basis.

Because future wealth is uncertain, investors attempt to maximize their expected value of utility. The relationship between wealth and the utility of consuming is described by a utility function, U (•). In general, each investor will have a different U (•), and we can write this formally as,

In Markowitz mean-variance portfolio theory (M-V), the rate of return of assets is random variable. The goal is then to choose the portfolio weighting factors optimally. Meaning, the investor’s portfolio achieves an acceptable expected rate of return with minimal volatility. The variance of the rate of return is taken as a proxy for the volatility.

Let us now consider constructing a portfolio consisting of *n* assets. We have an initial budget ** x_{0}**that we wish to assign. The amount that we assign to asset

The returns are also dependent on each other in a certain way and the dependence will be described by the covariance between them. The covariance between the i-th and the j-th return is denoted by,

Note that in this notation, *σ _{ij}* stands for the variance of the return of i-th asset, r

Equation 3 is further simplified to:

Meaning, given a universe of assets with random return *r _{i}, i = 1, . . ., n*, expected return

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