…I was in the business school, in the library of the business school, reading John Burr Williams’ Theory of Investment Value, and Williams said that the value of a stock, is the present value of its future dividends. I figured dividends are uncertain so he must mean the expected value… I figured, if you only are interested in the expected value of a stock, you must be only interested in the expected value of the portfolio. The way you maximize the expected value of the portfolio is by putting all your money into whatever stock has maximum expected value. That is not right. Everybody knows you are not supposed to put all your eggs in one basket.

Harry Markowitz

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**Harry Max Markowitz**is an American economist, and a recipient of the 1989John von Neumann Theory Prizeand the 1990Nobel Memorial Prize in Economic Sciences.

Harry Markowitz was born to aJewishfamily in 1927, the son of Morris and Mildred Markowitz.During high school, Markowitz developed an interest in physics and philosophy, in particular the ideas ofDavid Hume, an interest he continued to follow during his undergraduate years at theUniversity of Chicago. After high school, Markowitz decided to continue his studies at the University of Chicago, choosing to specialize in economics. There he had the opportunity to study under important economists, includingMilton Friedman,Tjalling Koopmans,Jacob MarschakandLeonard Savage. While still a student, he was invited to become a member of theCowles Commission for Research in Economics, which was in Chicago at the time. Markowitz chose to apply mathematics to the analysis of thestock marketas the topic for his dissertation. Jacob Marschak, who was the thesis advisor, encouraged him to pursue the topic, noting that it had also been a favorite interest ofAlfred Cowles, the founder of the Cowles Commission. While researching the then current understanding of stock prices, which at the time consisted in thepresent valuemodel ofJohn Burr Williams, Markowitz realized that the theory lacks an analysis of the impact of risk. This insight led to the development of his seminal theory ofportfolioallocation under uncertainty, published in 1952 bytheJournal of Finance. In 1952, Harry Markowitz went to work for theRAND Corporation, where he metGeorge Dantzig. With Dantzig's help, Markowitz continued to researchoptimizationtechniques, further developing thecritical line algorithmfor the identification of the optimal mean-variance portfolios, relying on what was later named theMarkowitz frontier. In 1955, he received a PhD from the University of Chicago with a thesis on the portfolio theory. The topic was so novel that, while Markowitz was defending his dissertation, Milton Friedman argued his contribution was not economics.During 1955–1956 Markowitz spent a year at the Cowles Foundation [1], which had moved toYale University, at the invitation of James Tobin. He published the critical line algorithm in a 1956 paper and used this time at the foundation to write a book on portfolio allocation which was published in 1959. Markowitz won theNobel Memorial Prize in Economic Sciencesin 1990 while a professor of finance atBaruch Collegeof theCity University of New York. In the preceding year, he received the John von Neumann Theory Prize from theOperations Research Society of Americafor his contributions in the theory of three fields: portfolio theory; sparse matrix methods; and simulation language programming (SIMSCRIPT). Sparse matrix methods are now widely used to solve very large systems of simultaneous equations whose coefficients are mostly zero. SIMSCRIPT has been widely used to program computer simulations of manufacturing, transportation, and computer systems as well as war games. SIMSCRIPT (I) included theBuddy memory allocationmethod, which was also developed by Markowitz. Markowitz is co-founder and Chief Architect ofGuided Choice, he managed accounts provider and investment advisor. Markowitz’s more recent work has included designing the backbone software analytics for the Guided Choice investment solution and heading the Guided Choice Investment Committee.

**Modern portfolio theory **is a mathematical framework for assembling a portfolio of assets such that theexpected returnis maximized for a given level of risk, defined asvariance.

The main features of modern portfolio theory:

− Risk and expected return;

− Diversification;

− Efficient frontier with no risk-free asset;

− Risk-free asset and the capital allocation line;

− Two mutual fund theorem;

− Systematic risk and specific risk;

− Capital asset pricing model;

− and others.

Harry Markowitz created to be row of first himself modern portfolio theory. **Harry Markowitz model (HM model)**, also known asMean-Variance Modelbecause it is based on the expected returns (mean) and the standard deviation (variance) of different portfolios, helps to make the most efficient selection by analyzing various portfolios of the given assets. It shows investors how to reduce their risk in case they have chosen assets not «moving» together.

Harry Markowitz’s modern portfolio theory assumptions

Modern Portfolio Theory relies on the following assumptions and fundamentals that are the key concepts upon which it has been constructed:

− For buying and selling securities there are no transaction costs. There is no spread between bidding and asking prices. No tax is paid, its only risk that plays a part in determining which securities an investor will buy.

− An investor has a chance to take any position of any size and in any security. The market liquidity is infinite and no one can move the market. So that nothing can stop the investor from taking positions of any size in any security.

− While making investment decisions the investor does not consider taxes and is indifferent towards receiving dividends or capital gains.

− Investors are generally rational and risk adverse. They are completely aware of all the risk contained in investment and actually take positions based on the risk determination demanding a higher return for accepting greater volatility.

− The risk-return relationships are viewed over the same time horizon. Both long term speculator and short term speculator share the same motivations, profit target and time horizon.

− Investors share identical views on risk measurement. All the investors are provided by information and their sale or purchase depends on an identical assessment of the investment and all have the same expectations from the investment. A seller will be motivated to make a sale only because another security has a level of volatility that corresponds to his desired return. A buyer will buy because this security has a level of risk that corresponds to the return he wants.

− Investors seek to control risk only by the diversification of their holdings.

− In the market all assets can be bought and sold including human capital.

− Politics and investor psychology have no influence on market.

− The risk of portfolio depends directly on the instability of returns from the given portfolio.

− An investor gives preference to the increase of utilization.

− An investor either maximizes his return for the minimum risk or maximizes his portfolio return for a given level of risk.

− Analysis is based on a single period model of investment.

Although many applications for MPT exist, the authors conclude that the financial community uses four in particular:

− Most asset managers and financial advisors use MPT in asset allocation implementation by following a top-down approach to develop an optimal portfolio and then selecting different managers with different investment styles (e.g., growth or value).

− In 1963, Sharpe expanded on Markowitz's work by developing the market model, which explains a portfolio's relationship to the market. Factor models can also be used in the analysis of large portfolios. The three main types of factor models used today are statistical, macroeconomic, and fundamental factor models.

− The value-at-risk (VAR) framework for measurement and management of market risk is based on concepts formalized in MPT. Its most useful application is in risk management for sell-side firms and other financial institutions.

− Investors want to manage the active risk associated with their portfolios relative to a benchmark (i. e., tracking error). The authors analyze hypothetical alpha/tracking-error relationships for different large-cap equity managers. With different managers deriving alpha from different sources, investors can use MPT and tracking-error budgeting to determine optimal portfolios.

In conclusion we can say that, Harry Markowitz was the father of the theory of modern portfolio. Through his theories caused development of the sector of investment and a reduction in the risk. Today's modern portfolio theory is based on Markowitz's work.

References:

1. Harry Markowitz & The development of modern portfolio theory by BPV Capital Management. 2015.

2. «Harry M. Markowitz — Facts». Nobelprize.org. Nobel Media AB 2014. Web. September 10, 2015.

3. The Legacy of Modern Portfolio Theory (Digest Summary) by Jonathan Hubbard, CFA. 2003.

4. Hannes Marling and Sara Emanuelsson. The Markowitz Portfolio Theory. 2012.

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