Upload
muhammad-mubasher-rafique
View
216
Download
0
Embed Size (px)
Citation preview
7/30/2019 Makowitz
1/11
BornAugust 24, 1927 (age 85)
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
Cowles Commission
Field Financial economics
Alma mater University of Chicago, (PhD)
Opposed John Burr Williams
http://en.wikipedia.org/wiki/Chicagohttp://en.wikipedia.org/wiki/Illinoishttp://en.wikipedia.org/wiki/United_Stateshttp://en.wikipedia.org/wiki/Rady_School_of_Managementhttp://en.wikipedia.org/wiki/University_of_California_at_San_Diegohttp://en.wikipedia.org/wiki/Baruch_Collegehttp://en.wikipedia.org/wiki/City_University_of_New_Yorkhttp://en.wikipedia.org/wiki/City_University_of_New_Yorkhttp://en.wikipedia.org/wiki/RAND_Corporationhttp://en.wikipedia.org/wiki/Cowles_Commissionhttp://en.wikipedia.org/wiki/Financial_economicshttp://en.wikipedia.org/wiki/University_of_Chicagohttp://en.wikipedia.org/wiki/John_Burr_Williamshttp://en.wikipedia.org/wiki/File:Markowitz_1.jpghttp://en.wikipedia.org/wiki/John_Burr_Williamshttp://en.wikipedia.org/wiki/University_of_Chicagohttp://en.wikipedia.org/wiki/Financial_economicshttp://en.wikipedia.org/wiki/Cowles_Commissionhttp://en.wikipedia.org/wiki/RAND_Corporationhttp://en.wikipedia.org/wiki/City_University_of_New_Yorkhttp://en.wikipedia.org/wiki/City_University_of_New_Yorkhttp://en.wikipedia.org/wiki/Baruch_Collegehttp://en.wikipedia.org/wiki/University_of_California_at_San_Diegohttp://en.wikipedia.org/wiki/Rady_School_of_Managementhttp://en.wikipedia.org/wiki/United_Stateshttp://en.wikipedia.org/wiki/Illinoishttp://en.wikipedia.org/wiki/Chicago7/30/2019 Makowitz
2/11
Influences
Milton Friedman
Tjalling Koopmans
Jacob Marschak
Leonard Savage
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
Introduction
Harry Markowitz was born on August 24, 1927 in Chicago, to his Jewish parents Morris andMildred Markowitz.[1]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 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. Therehe had the opportunity to study under important economists, including Milton Friedman, Tjalling
Koopmans, Jacob Marschakand 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 thetime.
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 ofAlfred 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 ofJohn Burr Williams, Markowitz realized that the theorylacks an analysis of the impact of risk. This insight led to the development of his seminal theory
ofportfolio allocation under uncertainty, published in 1952 by the Journal of Finance.
http://en.wikipedia.org/wiki/Milton_Friedmanhttp://en.wikipedia.org/wiki/Tjalling_Koopmanshttp://en.wikipedia.org/wiki/Jacob_Marschakhttp://en.wikipedia.org/wiki/Leonard_Savagehttp://en.wikipedia.org/wiki/Modern_Portfolio_Theoryhttp://en.wikipedia.org/wiki/Modern_portfolio_theory#The_efficient_.28Efficient.2F_Markowitz.29_frontierhttp://en.wikipedia.org/wiki/SIMSCRIPThttp://en.wikipedia.org/wiki/John_von_Neumann_Theory_Prizehttp://en.wikipedia.org/wiki/The_Sveriges_Riksbank_Prize_in_Economic_Sciences_in_Memory_of_Alfred_Nobelhttp://en.wikipedia.org/wiki/The_Sveriges_Riksbank_Prize_in_Economic_Sciences_in_Memory_of_Alfred_Nobelhttp://en.wikipedia.org/wiki/The_Sveriges_Riksbank_Prize_in_Economic_Sciences_in_Memory_of_Alfred_Nobelhttp://ideas.repec.org/e/pma73.htmlhttp://en.wikipedia.org/wiki/Research_Papers_in_Economicshttp://en.wikipedia.org/wiki/Harry_Markowitz#cite_note-autobiography-1http://en.wikipedia.org/wiki/Harry_Markowitz#cite_note-autobiography-1http://en.wikipedia.org/wiki/Harry_Markowitz#cite_note-autobiography-1http://en.wikipedia.org/wiki/David_Humehttp://en.wikipedia.org/wiki/University_of_Chicagohttp://en.wikipedia.org/wiki/Milton_Friedmanhttp://en.wikipedia.org/wiki/Tjalling_Koopmanshttp://en.wikipedia.org/wiki/Tjalling_Koopmanshttp://en.wikipedia.org/wiki/Jacob_Marschakhttp://en.wikipedia.org/wiki/Leonard_Savagehttp://en.wikipedia.org/wiki/Cowles_Commission_for_Research_in_Economicshttp://en.wikipedia.org/wiki/Stock_markethttp://en.wikipedia.org/wiki/Alfred_Cowleshttp://en.wikipedia.org/wiki/Present_valuehttp://en.wikipedia.org/wiki/John_Burr_Williamshttp://en.wikipedia.org/wiki/Portfolio_(finance)http://en.wikipedia.org/wiki/Journal_of_Financehttp://en.wikipedia.org/wiki/Journal_of_Financehttp://en.wikipedia.org/wiki/Journal_of_Financehttp://en.wikipedia.org/wiki/Portfolio_(finance)http://en.wikipedia.org/wiki/John_Burr_Williamshttp://en.wikipedia.org/wiki/Present_valuehttp://en.wikipedia.org/wiki/Alfred_Cowleshttp://en.wikipedia.org/wiki/Stock_markethttp://en.wikipedia.org/wiki/Cowles_Commission_for_Research_in_Economicshttp://en.wikipedia.org/wiki/Leonard_Savagehttp://en.wikipedia.org/wiki/Jacob_Marschakhttp://en.wikipedia.org/wiki/Tjalling_Koopmanshttp://en.wikipedia.org/wiki/Tjalling_Koopmanshttp://en.wikipedia.org/wiki/Milton_Friedmanhttp://en.wikipedia.org/wiki/University_of_Chicagohttp://en.wikipedia.org/wiki/David_Humehttp://en.wikipedia.org/wiki/Harry_Markowitz#cite_note-autobiography-1http://en.wikipedia.org/wiki/Research_Papers_in_Economicshttp://ideas.repec.org/e/pma73.htmlhttp://en.wikipedia.org/wiki/The_Sveriges_Riksbank_Prize_in_Economic_Sciences_in_Memory_of_Alfred_Nobelhttp://en.wikipedia.org/wiki/The_Sveriges_Riksbank_Prize_in_Economic_Sciences_in_Memory_of_Alfred_Nobelhttp://en.wikipedia.org/wiki/The_Sveriges_Riksbank_Prize_in_Economic_Sciences_in_Memory_of_Alfred_Nobelhttp://en.wikipedia.org/wiki/John_von_Neumann_Theory_Prizehttp://en.wikipedia.org/wiki/SIMSCRIPThttp://en.wikipedia.org/wiki/Modern_portfolio_theory#The_efficient_.28Efficient.2F_Markowitz.29_frontierhttp://en.wikipedia.org/wiki/Modern_Portfolio_Theoryhttp://en.wikipedia.org/wiki/Leonard_Savagehttp://en.wikipedia.org/wiki/Jacob_Marschakhttp://en.wikipedia.org/wiki/Tjalling_Koopmanshttp://en.wikipedia.org/wiki/Milton_Friedman7/30/2019 Makowitz
3/11
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, furtherdeveloping 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 wasnot economics.[3]During 19551956 Markowitz spent a year at the Cowles Foundation, which
had moved to Yale University, at the invitation ofJames Tobin. He published the critical line
algorithm in a 1956 paper and used this time at the foundation to write a book on portfolioallocation which was published in 1959.
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 hiscontributions in the theory of three fields: portfolio theory; sparse matrix methods; and
simulation language programming (SIMSCRIPT). Sparse matrix methods are now widely usedto 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 tothe 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 yearlater, Markowitz left the company.
Markowitz now divides his time between teaching (he is an adjunct professor at the Rady Schoolof 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 ofSkyView 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 basedinvestment advisory firm, Index Funds Advisors; and as an advisor to the Investment Committee
of1st Global, a Dallas, Texas-based wealth management and investment advisory firm.
Markowitz is co-founder and Chief Architect ofGuidedChoice, a 401(k) managed accounts
provider and investment advisor. Markowitzs more recent work has included designing the
http://en.wikipedia.org/wiki/RAND_Corporationhttp://en.wikipedia.org/wiki/George_Dantzighttp://en.wikipedia.org/wiki/George_Dantzighttp://en.wikipedia.org/wiki/Optimization_(mathematics)http://en.wikipedia.org/w/index.php?title=Critical_line_algorithm&action=edit&redlink=1http://en.wikipedia.org/wiki/Modern_portfolio_theoryhttp://en.wikipedia.org/wiki/Harry_Markowitz#cite_note-nobellecture-3http://en.wikipedia.org/wiki/Harry_Markowitz#cite_note-nobellecture-3http://en.wikipedia.org/wiki/Harry_Markowitz#cite_note-nobellecture-3http://en.wikipedia.org/wiki/Yale_Universityhttp://en.wikipedia.org/wiki/James_Tobinhttp://en.wikipedia.org/wiki/Nobel_Memorial_Prize_in_Economic_Scienceshttp://en.wikipedia.org/wiki/Baruch_Collegehttp://en.wikipedia.org/wiki/City_University_of_New_Yorkhttp://en.wikipedia.org/wiki/Operations_Research_Society_of_Americahttp://en.wikipedia.org/wiki/Institute_for_Operations_Research_and_the_Management_Scienceshttp://en.wikipedia.org/wiki/INFORMShttp://en.wikipedia.org/wiki/SIMSCRIPThttp://en.wikipedia.org/wiki/Buddy_memory_allocationhttp://en.wikipedia.org/wiki/Buddy_memory_allocationhttp://en.wikipedia.org/wiki/CACI_Internationalhttp://en.wikipedia.org/wiki/Michael_Goodkinhttp://en.wikipedia.org/wiki/Paul_Samuelsonhttp://en.wikipedia.org/wiki/Robert_C._Mertonhttp://en.wikipedia.org/w/index.php?title=SkyView_Investment_Advisors&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Loring_Ward&action=edit&redlink=1http://en.wikipedia.org/wiki/Robert_D._Arnotthttp://en.wikipedia.org/wiki/Newport_Beach,_Californiahttp://en.wikipedia.org/wiki/Research_Affiliateshttp://en.wikipedia.org/wiki/Research_Affiliateshttp://en.wikipedia.org/w/index.php?title=1st_Global&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=GuidedChoice&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=GuidedChoice&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=1st_Global&action=edit&redlink=1http://en.wikipedia.org/wiki/Research_Affiliateshttp://en.wikipedia.org/wiki/Research_Affiliateshttp://en.wikipedia.org/wiki/Newport_Beach,_Californiahttp://en.wikipedia.org/wiki/Robert_D._Arnotthttp://en.wikipedia.org/w/index.php?title=Loring_Ward&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=SkyView_Investment_Advisors&action=edit&redlink=1http://en.wikipedia.org/wiki/Robert_C._Mertonhttp://en.wikipedia.org/wiki/Paul_Samuelsonhttp://en.wikipedia.org/wiki/Michael_Goodkinhttp://en.wikipedia.org/wiki/CACI_Internationalhttp://en.wikipedia.org/wiki/Buddy_memory_allocationhttp://en.wikipedia.org/wiki/Buddy_memory_allocationhttp://en.wikipedia.org/wiki/SIMSCRIPThttp://en.wikipedia.org/wiki/INFORMShttp://en.wikipedia.org/wiki/Institute_for_Operations_Research_and_the_Management_Scienceshttp://en.wikipedia.org/wiki/Operations_Research_Society_of_Americahttp://en.wikipedia.org/wiki/City_University_of_New_Yorkhttp://en.wikipedia.org/wiki/Baruch_Collegehttp://en.wikipedia.org/wiki/Nobel_Memorial_Prize_in_Economic_Scienceshttp://en.wikipedia.org/wiki/James_Tobinhttp://en.wikipedia.org/wiki/Yale_Universityhttp://en.wikipedia.org/wiki/Harry_Markowitz#cite_note-nobellecture-3http://en.wikipedia.org/wiki/Modern_portfolio_theoryhttp://en.wikipedia.org/w/index.php?title=Critical_line_algorithm&action=edit&redlink=1http://en.wikipedia.org/wiki/Optimization_(mathematics)http://en.wikipedia.org/wiki/George_Dantzighttp://en.wikipedia.org/wiki/George_Dantzighttp://en.wikipedia.org/wiki/RAND_Corporation7/30/2019 Makowitz
4/11
backbone software analytics for the GuidedChoice investment solution and heading the
GuidedChoice Investment Committee. He is actively involved in designing the next step in theretirement process: assisting retirees with wealth distribution through GuidedSpending.
Research
AMarkowitz Efficient Portfolio is one where no added diversification can lower the portfolio's
riskfor a given return expectation (alternately, no additional expected return can be gainedwithout 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 textbookThe Theory and Practice of Investment Managementwith
Frank J. Fabozzi ofYale School of Management.
Harry Markowitz Model
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 :
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.
5. Analysis is based on single period model ofinvestment.
6. An investor either maximizes his portfolio return for a given level of risk or maximum return
for minimum risk.
7. An investor is rational in nature.
To choose the best portfolio from a number of possible portfolios, each with different return and
risk, two separate decisions are to be made :
http://en.wikipedia.org/wiki/Diversification_(finance)http://en.wikipedia.org/wiki/Riskhttp://en.wikipedia.org/wiki/Modern_portfolio_theoryhttp://en.wikipedia.org/wiki/Capital_Asset_Pricing_Modelhttp://en.wikipedia.org/wiki/Frank_J._Fabozzihttp://en.wikipedia.org/wiki/Yale_School_of_Managementhttp://en.wikipedia.org/wiki/Meanhttp://en.wikipedia.org/wiki/Variancehttp://en.wikipedia.org/wiki/Standard_deviationhttp://en.wikipedia.org/wiki/Portfoliohttp://en.wikipedia.org/wiki/Consumption_(economics)http://en.wikipedia.org/wiki/Utility_functionhttp://en.wikipedia.org/wiki/Investmenthttp://en.wikipedia.org/wiki/Investmenthttp://en.wikipedia.org/wiki/Utility_functionhttp://en.wikipedia.org/wiki/Consumption_(economics)http://en.wikipedia.org/wiki/Portfoliohttp://en.wikipedia.org/wiki/Standard_deviationhttp://en.wikipedia.org/wiki/Variancehttp://en.wikipedia.org/wiki/Meanhttp://en.wikipedia.org/wiki/Yale_School_of_Managementhttp://en.wikipedia.org/wiki/Frank_J._Fabozzihttp://en.wikipedia.org/wiki/Capital_Asset_Pricing_Modelhttp://en.wikipedia.org/wiki/Modern_portfolio_theoryhttp://en.wikipedia.org/wiki/Riskhttp://en.wikipedia.org/wiki/Diversification_(finance)7/30/2019 Makowitz
5/11
1. Determination a set of efficient portfolios.
2. Selection of best portfolio out of the efficient set.
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
(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. 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 thatlie 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
http://en.wikipedia.org/wiki/File:Risk-Return_of_Possible_Portfolios.jpghttp://en.wikipedia.org/wiki/File:Risk-Return_of_Possible_Portfolios.jpghttp://en.wikipedia.org/wiki/File:Risk-Return_of_Possible_Portfolios.jpghttp://en.wikipedia.org/wiki/File:Risk-Return_of_Possible_Portfolios.jpg7/30/2019 Makowitz
6/11
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.
Choosing the best Portfolio
For selection of the optimal portfolio or the best portfolio, the risk-return preferences areanalyzed. An investor who is highly risk averse will hold a portfolio on the lower left hand of the
frontier, and an investor who isnt too risk averse will choose a portfolio on the upper portion ofthe 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 adifferent 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 curveC3 Thus, at any point of time, an investor will be indifferent between combinations S 1 and S2, or
S5 and S6.
http://en.wikipedia.org/wiki/Indifference_curvehttp://en.wikipedia.org/wiki/Utilityhttp://en.wikipedia.org/wiki/File:Risk-Return_Indifference_Curves.jpghttp://en.wikipedia.org/wiki/File:Risk-Return_Indifference_Curves.jpghttp://en.wikipedia.org/wiki/File:Risk-Return_Indifference_Curves.jpghttp://en.wikipedia.org/wiki/File:Risk-Return_Indifference_Curves.jpghttp://en.wikipedia.org/wiki/Utilityhttp://en.wikipedia.org/wiki/Indifference_curve7/30/2019 Makowitz
7/11
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 curveC3, 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. PortfolioY 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
include 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.
http://en.wikipedia.org/wiki/Indifference_curvehttp://en.wikipedia.org/wiki/File:The_Efficient_Portfolio.jpghttp://en.wikipedia.org/wiki/File:The_Efficient_Portfolio.jpghttp://en.wikipedia.org/wiki/File:The_Efficient_Portfolio.jpghttp://en.wikipedia.org/wiki/File:The_Efficient_Portfolio.jpghttp://en.wikipedia.org/wiki/Indifference_curve7/30/2019 Makowitz
8/11
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. Thesatisfaction 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 madewith 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 onboth 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 rateplus risk premium. Risk premium is the product of the market price of risk and thequantity of risk, and the risk is the standard deviation of the portfolio.
The CML equation is :
RP = IRF + (RM - IRF)P/M
Where,
http://en.wikipedia.org/wiki/Governmenthttp://en.wikipedia.org/wiki/Capital_markethttp://en.wikipedia.org/wiki/File:The_Combination_of_Risk-Free_Securities_with_the_efficient_frontier_and_CML.jpghttp://en.wikipedia.org/wiki/File:The_Combination_of_Risk-Free_Securities_with_the_efficient_frontier_and_CML.jpghttp://en.wikipedia.org/wiki/File:The_Combination_of_Risk-Free_Securities_with_the_efficient_frontier_and_CML.jpghttp://en.wikipedia.org/wiki/File:The_Combination_of_Risk-Free_Securities_with_the_efficient_frontier_and_CML.jpghttp://en.wikipedia.org/wiki/Capital_markethttp://en.wikipedia.org/wiki/Government7/30/2019 Makowitz
9/11
RP = Expected Return of Portfolio
RM = Return on the Market Portfolio
IRF = Risk-Free rate ofinterest
M = Standard Deviation of the market portfolio
P = Standard Deviation of portfolio
(RM - IRF)/M 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. M 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 themarket 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 willnot 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 ofrisk-free investments. But when risk-free investments are introduced, the investor can choose the
http://en.wikipedia.org/wiki/Interesthttp://en.wikipedia.org/wiki/Standard_Deviationhttp://en.wikipedia.org/wiki/Markethttp://en.wikipedia.org/wiki/File:CML_and_Risk-free_lending_and_borrowing.jpghttp://en.wikipedia.org/wiki/File:CML_and_Risk-free_lending_and_borrowing.jpghttp://en.wikipedia.org/wiki/File:CML_and_Risk-free_lending_and_borrowing.jpghttp://en.wikipedia.org/wiki/File:CML_and_Risk-free_lending_and_borrowing.jpghttp://en.wikipedia.org/wiki/Markethttp://en.wikipedia.org/wiki/Standard_Deviationhttp://en.wikipedia.org/wiki/Interest7/30/2019 Makowitz
10/11
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 ofefficient 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 ofportfolio P.
Demerits of the HM Model
1. It requires lots of data to be included. An investor must obtain variances of return, covarianceof 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 ofsecurities, a very large number of portfolio combinations can be made.
3. The expected return and variance will also have to computed for each securities
The contribution for which Harry Markowitz now receives his award was first published
in an essay entitled "Portfolio Selection" (1952), and later, more extensively, in his book,
Portfolio Selection: Efficient Diversification(1959). The so-called theory of portfolio
selection that was developed in this early work was originally a normative theory for
investment managers, i.e., a theory for optimal investment of wealth in assets which
differ in regard to their expected return and risk. On a general level, of course,
investment managers and academic economists have long been aware of the necessityof taking returns as well as risk into account: "all the eggs should not be placed in the
same basket". Markowitz's primary contribution consisted of developing a rigorously
formulated, operational theory for portfolio selection under uncertainty - a theory which
evolved into a foundation for further research in financial economics.
Markowitz showed that under certain given conditions, an investor's portfolio choice can
be reduced to balancing two dimensions, i.e., the expected return on the portfolio and
its variance. Due to the possibility of reducing risk through diversification, the risk of the
portfolio, measured as its variance, will depend not only on the individual variances of
the return on different assets, but also on the pairwise covariances of all assets.
Hence, the essential aspect pertaining to the risk of an asset is not the risk of each
asset in isolation, but the contribution of each asset to the risk of the aggregate portfolio.
However, the "law of large numbers" is not wholly applicable to the diversification of
risks in portfolio choice because the returns on different assets are correlated in
7/30/2019 Makowitz
11/11
practice. Thus, in general, risk cannot be totally eliminated, regardless of how many
types of securities are represented in a portfolio.
In this way, the complicated and multidimensional problem of portfolio choice with
respect to a large number of different assets, each with varying properties, is reduced to
a conceptually simple two-dimensional problem - known as mean-variance analysis. In
an essay in 1956, Markowitz also showed how the problem of actually calculating the
optimal portfolio could be solved. (In technical terms, this means that the analysis is
formulated as a quadratic programming problem; the building blocks are a quadratic
utility function, expected returns on the different assets, the variance and covariance of
the assets and the investor's budget restrictions.) The model has won wide acclaim due
to its algebraic simplicity and suitability for empirical applications.
Generally speaking, Markowitz's work on portfolio theory may be regarded as having
established financial micro analysis as a respectable research area in economicanalysis.
