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## Overview

Modern portfolio theory(MPT) is a theory of investment which tries to maximize return and minimize risk by carefully choosing differentassets. Although MPT is widely used in practice in the financial industry and several of its creators won a Nobel prize for the theory, in recent years the basic assumptions of MPT have been widely challenged by fields such as behavioral economics, and many companies using variants of MPT have gone bankrupt in various financial crises.^{[1}]

MPT is a mathematical formulation of the concept of diversification in investing, with the aim of selecting a collection of investment assets that has collectively lower risk than any individual asset. This is possible, in theory, because different types of assets often change in value in opposite ways. For example, when the prices in the stock market fall, the prices in the bond market often increase, and vice versa. A collection of both types of assets can therefore have lower overall risk than either individually.

More technically, MPT models an asset's return as a normally distributed random variable, defines risk as the standard deviation of return, and models a portfolio as a weighted combination of assets so that the return of a portfolio is the weighted combination of the assets' returns. By combining different assets whose returns are not correlated, MPT seeks to reduce the total variance of the portfolio. MPT also assumes that investors are rational and markets are efficient.

MPT was developed in the 1950s through the early 1970s and was considered an important advance in the mathematical modeling of finance. Since then, much theoretical and practical criticism has been leveled against it. These include the fact that financial returns do not follow a Gaussian distribution and that correlations between asset classes are not fixed but can vary depending on external events (especially in crises). Further, there is growing evidence that investors are not rational and markets are not efficient.

Perhaps the most spectacular example of MPT's shortcomings was the failure of Long Term Capital Management in 1998.

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