Harry Markowitz is an American economist known for pioneering modern portfolio theory. He developed the concept of the efficient frontier, which shows the set of optimal portfolios that produce the highest expected return for a given level of risk or the lowest risk for a given level of expected return. Markowitz proposed using statistical tools like variance to quantify an investment's risk and using expected returns and correlations between assets to construct portfolios. His work revolutionized the theory and practice of asset management and laid the foundation for much of the subsequent development in financial economics.

1. Harry Markowitz
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Harry Markowitz
Chicago School of Economics
Born
August 24, 1927 (age 84)
Chicago, Illinois, USA
Nationality United States
Institution
Harry Markowitz Company
Rady School of Management at the
University of California at San Diego
Baruch College of the City University of
New York
RAND Corporation

2. Cowles Commission
Field Financial economics
Alma mater University of Chicago (PhD)
Opposed John Burr Williams
Influences
Milton Friedman
Tjalling Koopmans
Jacob Marschak
Oskar Morgenstern
Leonard Savage
John von Neumann
Contributions
Modern Portfolio Theory
Efficient/ Markowitz Frontier
Sparse Matrix Methods
SIMSCRIPT
Awards
John von Neumann Theory Prize (1989)
The Sveriges Riksbank Prize in Economic
Sciences in Memory of Alfred Nobel
(1990)
Information at IDEAS/RePEc
Harry Max Markowitz (born August 24, 1927) is an American economist and a recipient of the
John von Neumann Theory Prize and the Nobel Memorial Prize in Economic Sciences.
Markowitz is a professor of finance at the Rady School of Management at the University of
California, San Diego (UCSD). He is best known for his pioneering work in Modern Portfolio
Theory, studying the effects of asset risk, return, correlation and diversification on probable
investment portfolio returns.

3. Contents
[hide]
 1 Autobiography
 2 Biography
 3 Research
 4 Harry Markowitz Model
o 4.1 Introduction
o 4.2 Determining the Efficient Set
o 4.3 Choosing the best Portfolio
o 4.4 Demerits of the HM Model
 5 Further Reading
 6 Selected publications
 7 See also
 8 References
 9 External links
[edit] Autobiography
"Autobiography of Harry M. Marchoviz, The Sveriges Riksbank Prize in Economic Sciences in
Memory of Alfred Nobel 1990" can be viewed on the official website of The Nobel
Foundation.[1]
[edit] Biography
Harry Markowitz was born on August 24, 1927 in Chicago, to his Jewish parents Morris and
Mildred Markowitz.[1] During high school, Markowitz developed an interest in physics and
philosophy, in particular the ideas of David Hume, an interest he continued to follow during his
undergraduate years at the University of Chicago. After receiving his B.A., 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, including Milton Friedman, Tjalling
Koopmans, Jacob Marschak and Leonard Savage. While still a student, he was invited to become
a member of the Cowles Commission for Research in Economics, which was in Chicago at the
time.
Markowitz chose to apply mathematics to the analysis of the stock market as 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 of Alfred Cowles, the founder of the Cowles
Commission. While researching the then current understanding of stock prices, which at the time
consisted in the present value model of John 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
of portfolio allocation under uncertainty, published in 1952 by the Journal of Finance.[2]

4. In 1952, Harry Markowitz went to work for the RAND Corporation, where he met George
Dantzig. With Dantzig's help, Markowitz continued to research optimization techniques, further
developing the critical line algorithm for the identification of the optimal mean-variance
portfolios, relying on what was later named the Markowitz 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.[3] During 1955–1956 Markowitz spent a year at the Cowles Foundation,[1] which
had moved to Yale 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.[4]
Markowitz won the Nobel Memorial Prize in Economic Sciences in 1990 while a professor of
finance at Baruch College of the City University of New York. In the preceding year, he received
the John von Neumann Theory Prize from the Operations Research Society of America (now
Institute for Operations Research and the Management Sciences, INFORMS) for 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 the Buddy
memory allocation method, which was also developed by Markowitz.
The company that would become CACI International was founded by Herb Karr and Harry
Markowitz on July 17, 1962 as California Analysis Center, Inc. They helped develop
SIMSCRIPT, the first simulation programming language, at RAND and after it was released to
the public domain, CACI was founded to provide support and training for SIMSCRIPT.
In 1968, Markowitz joined Arbitrage Management company founded by Michael Goodkin.
Working with Paul Samuelson and Robert Merton he created a hedge fund that represents the
first known attempt at computerized arbitrage trading. He took over as chief executive in 1970.
After a successful run as a private hedge fund, AMC was sold to Stuart & Co. in 1971. A year
later, Markowitz left the company.[5]
Markowitz now divides his time between teaching (he is an adjunct professor at the Rady School
of Management at the University of California at San Diego, UCSD); video casting lectures; and
consulting (out of his Harry Markowitz Company offices). He currently serves on the Advisory
Board of SkyView Investment Advisors, an alternative investment advisory firm and fund of
hedge funds. Markowitz also serves on the Investment Committee of LWI Financial Inc.
("Loring Ward"), a San Jose, California-based investment advisor; on the advisory panel of
Robert D. Arnott's Newport Beach, California based investment management firm, Research
Affiliates; on the Advisory Board of Mark Hebner's Irvine, California and internet based
investment advisory firm, Index Funds Advisors; and as an advisor to the Investment Committee
of 1st Global, a Dallas, Texas-based wealth management and investment advisory firm.
Dr. Markowitz is co-founder and Chief Architect of GuidedChoice, a 401(k) managed accounts
provider and investment advisor. Dr. Markowitz’s more recent work has included designing the

5. backbone software analytics for the GuidedChoice investment solution and heading the
GuidedChoice Investment Committee. He is actively involved in designing the next step in the
retirement process: assisting retirees with wealth distribution through GuidedSpending.
[edit] Research
A Markowitz Efficient Portfolio is one where no added diversification can lower the portfolio's
risk for a given return expectation (alternately, no additional expected return can be gained
without increasing the risk of the portfolio). The Markowitz Efficient Frontier is the set of all
portfolios that will give the highest expected return for each given level of risk. These concepts
of efficiency were essential to the development of the Capital Asset Pricing Model.
Markowitz also co-edited the textbook The Theory and Practice of Investment Management with
Frank J. Fabozzi of Yale School of Management.
[edit] Harry Markowitz Model
[edit] Introduction
Harry Markowitz put forward this model in 1952. It assists in the selection of the most efficient
by analyzing various possible portfolios of the given securities. By choosing securities that do
not 'move' exactly together, the HM model shows investors how to reduce their risk. The HM
model is also called Mean-Variance Model due to the fact that it is based on expected returns
(mean) and the standard deviation (variance) of the various portfolios. Harry Markowitz made
the following assumption while developing the HM model, which were :[6] [7]
1. Risk of a portfolio is based on the variability of returns from the said portfolio.
2. An investor is risk averse.
3. An investor prefers to increase consumption.
4. The investor's utility function is concave and increasing, due to his risk aversion and
consumption preference.[7]
5. Analysis is based on single period model of investment.[7]
6. An investor either maximizes his portfolio return for a given level of risk or maximum return
for minimum risk. [8]
7. An investor is rational in nature.[7]
To choose the best portfolio from a number of possible portfolios, each with different return and
risk, two separate decisions are to be made :

6. 1. Determination a set of efficient portfolios.
2. Selection of best portfolio out of the efficient set.
[edit] Determining the Efficient Set
A portfolio that gives maximum return for a given risk, or minimum risk for given return is an
efficient portfolio. Thus, portfolios are selected as follows:
(a) From the portfolios that have the same return, the investor will prefer the portfolio with lower
risk, and [6]
(b) From the portfolios that have the same risk level, an investor will prefer the portfolio with
higher rate of return.
Figure 1: Risk-Return of Possible Portfolios
As the investor is rational, they would like to have higher return. And as he is risk averse, he
wants to have lower risk.[6] In Figure 1, the shaded area PVWP includes all the possible
securities an investor can invest in. The efficient portfolios are the ones that lie on the boundary
of PQVW. For example, at risk level x2, there are three portfolios S, T, U. But portfolio S is
called the efficient portfolio as it has the highest return, y2, compared to T and U. All the
portfolios that lie on the boundary of PQVW are efficient portfolios for a given risk level.
The boundary PQVW is called the Efficient Frontier. All portfolios that lie below the Efficient
Frontier are not good enough because the return would be lower for the given risk. Portfolios that
lie to the right of the Efficient Frontier would not be good enough, as there is higher risk for a
given rate of return. All portfolios lying on the boundary of PQVW are called Efficient

7. Portfolios. The Efficient Frontier is the same for all investors, as all investors want maximum
return with the lowest possible risk and they are risk averse ()()
[edit] Choosing the best Portfolio
For selection of the optimal portfolio or the best portfolio, the risk-return preferences are
analyzed. An investor who is highly risk averse will hold a portfolio on the lower left hand of the
frontier, and an investor who isn’t too risk averse will choose a portfolio on the upper portion of
the frontier.
Figure 2: Risk-Return Indifference Curves
Figure 2 shows the risk-return indifference curve for the investors. Indifference curves C1, C2
and C3 are shown. Each of the different points on a particular indifference curve shows a
different combination of risk and return, which provide the same satisfaction to the investors.
Each curve to the left represents higher utility or satisfaction. The goal of the investor would be
to maximize his satisfaction by moving to a curve that is higher. An investor might have
satisfaction represented by C2, but if his satisfaction/utility increases, he/she then moves to curve
C3 Thus, at any point of time, an investor will be indifferent between combinations S1 and S2, or
S5 and S6.

8. Figure 3: The Efficient Portfolio
The investor's optimal portfolio is found at the point of tangency of the efficient frontier with the
indifference curve. This point marks the highest level of satisfaction the investor can obtain. This
is shown in Figure 3. R is the point where the efficient frontier is tangent to indifference curve
C3, and is also an efficient portfolio. With this portfolio, the investor will get highest satisfaction
as well as best risk-return combination. Any other portfolio, say X, isn't the optimal portfolio
even though it lies on the same indifference curve as it is outside the efficient frontier. Portfolio
Y is also not optimal as it does not lie on the indifference curve, even though it lies in the
portfolio region. Another investor having other sets of indifference curves might have some
different portfolio as his best/optimal portfolio.
All portfolios so far have been evaluated in terms of risky securities only, and it is possible to
inclued risk-free securities in a portfolio as well. A portfolio with risk-free securities will enable
an investor to achieve a higher level of satisfaction. This has been explained in Figure 4.

9. Figure 4: The Combination of Risk-Free Securities with the Efficient Frontier and CML
R1 is the risk-free return, or the return from government securities, as government securities have
no risk. R1PX is drawn so that it is tangent to the efficient frontier. Any point on the line R1PX
shows a combination of different proportions of risk-free securities and efficient portfolios. The
satisfaction an investor obtains from portfolios on the line R1PX is more than the satisfaction
obtained from the portfolio P. All portfolio combinations to the left of P show combinations of
risky and risk-free assets, and all those to the right of P represent purchases of risky assets made
with funds borrowed at the risk-free rate.
In the case that an investor has invested all his funds, additional funds can be borrowed at risk-
free rate and a portfolio combination that lies on R1PX can be obtained. R1PX is known as the
Capital Market Line (CML). this line represents the risk-return trade off in the capital market.
The CML is an upward sloping curve, which means that the investor will take higher risk if the
return of the portfolio is also higher. The portfolio P is the most efficient portfolio, as it lies on
both the CML and Efficient Frontier, and every investor would prefer to attain this portfolio, P.
The P portfolio is known as the Market Portfolio and is also the most diversified portfolio. It
consists of all shares and other securities in the capital market.
In the market for portfolios that consists of risky and risk-free securities, the CML represents the
equilibrium condition. The Capital Market Line says that the return from a portfolio is the risk-
free rate plus risk premium. Risk premium is the product of the market price of risk and the
quantity of risk, and the risk is the standard deviation of the portfolio.
The CML equation is :
RP = IRF + (RM - IRF)σP/σM
Where,

10. RP = Expected Return of Portfolio
RM = Return on the Market Portfolio
IRF = Risk-Free rate of interest
σM = Standard Deviation of the market portfolio
σP = Standard Deviation of portfolio
(RM - IRF)/σM is the slope of CML. (RM - IRF) is a measure of the risk premium, or the reward for
holding risky portfolio instead of risk-free portfolio. σM is the risk of the market portfolio.
Therefore, the slope measures the reward per unit of market risk.
The characteristic features of CML are:
1. At the tangent point, i.e. Portfolio P, is the optimum combination of risky investments and the
market portfolio.
2. Only efficient portfolios that consist of risk free investments and the market portfolio P lie on
the CML.
3. CML is always upward sloping as the price of risk has to be positive. A rational investor will
not invest unless he knows he will be compensated for that risk.
Figure 5: CML and Risk-Free Lending and Borrowing
Figure 5 shows that an investor will choose a portfolio on the efficient frontier, in the absence of
risk-free investments. But when risk-free investments are introduced, the investor can can choose

11. the portfolio on the CML (which represents the combination of risky and risk-free investments).
This can be done with borrowing or lending at the risk-free rate of interest (IRF) and the purchase
of efficient portfolio P. The portfolio an investor will choose depends on his preference of risk.
The portion from IRF to P, is investment in risk-free assets and is called Lending Portfolio. In
this portion, the investor will lend a portion at risk-free rate. The portion beyond P is called
Borrowing Portfolio, where the investor borrows some funds at risk-free rate to buy more of
portfolio P.
[edit] Demerits of the HM Model
1. It requires lots of data to be included. An investor must obtain variances of return, covariance
of returns and estimates of return for all the securities in a portfolio.
2. There are numerous calculations involved that are complicated because from a given set of
securities, a very large number of portfolio combinations can be made.
3. The expected return and variance will also have to computed for each securities. [9]
[edit] Further Reading
http://people.orie.cornell.edu/~leventhal/Markowitz.pdf
http://people.maths.ox.ac.uk/~zhouxy/download/mvjump_part2.pdf
http://home.dacor.net/norton/finance-math/problems_w_Markowitz.pdf
[edit] Selected publications
 Markowitz, H.M. (March 1952). "Portfolio Selection". The Journal of Finance 7 (1): 77–
91. DOI:10.2307/2975974. JSTOR 2975974.
 Markowitz, H.M. (April 1952). "The Utility of Wealth". The Journal of Political
Economy (Cowles Foundation Paper 57) LX (2): 151–158. DOI:10.1086/257177.
http://cowles.econ.yale.edu/P/cp/p00b/p0057.pdf.
 Markowitz, H.M. (April 1957). "The Elimination Form of the Inverse and Its Application
to Linear Programming". Management Science 3 (3): 255–269.
DOI:10.1287/mnsc.3.3.255.
 Markowitz, H.M. (1959). Portfolio Selection: Efficient Diversification of Investments.
New York: John Wiley & Sons. http://cowles.econ.yale.edu/P/cm/m16/index.htm.
(reprinted by Yale University Press, 1970, ISBN 978-0-300-01372-6; 2nd ed. Basil
Blackwell, 1991, ISBN 978-1-55786-108-5)
 Markowitz, H.M. (October 1, 1979). Belzer, Jack; Holzman, Albert G.; Kent, Allen. eds.
"SIMSCRIPT", Encyclopedia of Computer Science and Technology. 13. New York and
Basel: Marcel Dekker. pp. 516. ISBN 978-0-8247-2263-0.

12.  Markowitz, H.M. and E. van Dijk (March/April 2003). "Single-Period Mean-Variance
Analysis in a Changing World". Financial Analysts Journal 59 (2): 30–44.
DOI:10.2469/faj.v59.n2.2512.
 Markowitz, H.M. (September/October 2005). "Market Efficiency: A Theoretical
Distinction and So What?". Financial Analysts Journal 61 (5): 17–30.
DOI:10.2469/faj.v61.n5.2752.
http://www.researchaffiliates.com/ideas/pdf/marketEfficiency.pdf.
 Markowitz, H.M. (2009). Harry Markowitz: Selected Works. World Scientific-Nobel
Laureate Series: Vol. 1. Hackensack, New Jersey: World Scientific. pp. 716. ISBN 978-
981-283-364-8. http://www.worldscibooks.com/economics/6967.html.
[edit] See also
 List of economists
 List of Jewish Nobel laureates
 Modern Portfolio Theory
 Capital asset pricing model
 Risk management tools
 Risk
[edit] References
1. ^ a b c Harry M. Markowitz – Autobiography,The Nobel Prizes 1990, Editor Tore Frängsmyr, [Nobel
Foundation], Stockholm, 1991
2. ^ Markowitz, H.M. (March 1952). "Portfolio Selection". The Journal of Finance 7 (1): 77–91.
DOI:10.2307/2975974. JSTOR 2975974.
3. ^ Harry M. Markowitz – Nobel Prize Lecture: Foundations of Portfolio Theory, December 7, 1990 ( PDF
format)
4. ^ Markowitz, H.M. (1959). Portfolio Selection:Efficient Diversification of Investments. New York: John
Wiley & Sons. http://cowles.econ.yale.edu/P/cm/m16/index.htm. (reprinted by Yale University Press, 1970,
ISBN 978-0-300-01372-6; 2nd ed. Basil Blackwell, 1991, ISBN 978-1-55786-108-5)
5. ^ Goodkin, Michael. The Wrong Answer Faster: The Inside Story of Making the Machine that Trades
Trillions. John Wiley & Sons,2012
6. ^ a b c Rustagi, R.P.. Financial Management.India: Taxmann Publications (P.) Ltd.. ISBN 978-81-7194-
786-7.
7. ^ a b c d "Markowitz Model".
http://corporate.morningstar.com/cf/documents/MethodologyDocuments/IBBAssociates/MarkowitzApproa
ch.pdf.
8. ^ "Markowitz". http://dybfin.wustl.edu/teaching/inv/slides/invl3.html.
9. ^ "limitations". http://knowledgebase.abcquant.com/index.php?option=com_kb&task=article&article=59.
[edit] External links
 An Hour with Harry Markowitz: Interviewed by Mark Hebner
 The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, 1990
o Autobiography, The Nobel Prizes 1990, Editor Tore Frängsmyr, [Nobel
Foundation], Stockholm, 1991
o Banquet Speech, December 10, 1990

13. o Nobel Prize Lecture: Foundations of Portfolio Theory, December 7, 1990 ( PDF
format)
 Oral history interview with Harry M. Markowitz, Charles Babbage Institute, University
of Minnesota – Markowitz discusses his development of portfolio theory, sparse
matrices, and his work at the RAND Corporation and elsewhere on simulation software
development (including computer language SIMSCRIPT), modeling, and operations
research.
 History of Finance, interviews, The American Finance Association
 Adjunct Professor of Finance, bio, Rady School of Management, University of California
at San Diego
 1st Global Engages Dr. Harry M. Markowitz, 1st Global
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