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Portfolio is a financial term denoting a collection of investments held by an investment company, hedge fund, financial institution or individual.^[1]

Definition[link]

Risk/return plot and Pareto-optimal portfolios (in red)

The term portfolio refers to any collection of financial assets such as stocks, bonds and cash. Portfolios may be held by individual investors and/or managed by financial professionals, hedge funds, banks and other financial institutions. It is a generally accepted principle that a portfolio is designed according to the investor's risk tolerance, time frame and investment objectives. The euro amount of each asset may influence the risk/reward ratio of the portfolio and is referred to as the asset allocation of the portfolio. ^[2] When determining a proper asset allocation one aims at maximizing the expected return and minimizing the risk. This is an example of a multi-objective optimization problem: more "efficient solutions" are available and the preferred solution must be selected by considering a tradeoff between risk and return. In particular, a portfolio A is dominated by another portfolio A' if A' has a greater expected gain and a lesser risk than A. If no portfolio dominates A, A is a Pareto-optimal portfolio. The set of Pareto-optimal returns and risks is called the Pareto Efficient Frontier for the Markowitz Portfolio selection problem ^[3].

Description[link]

There are many types of portfolios including the Market Portfolio and the Zero-Investment Portfolio^[4]. A portfolio's asset allocation may be managed utilizing any of the following investment approaches and principles: equally-weighting, capitalization-weighting, price-weighting, Risk parity, Capital asset pricing model, Arbitrage pricing theory, Jensen Index, Treynor Index, Sharpe Diagonal (or Index) model, Value at risk model, Modern Portfolio Theory and others.

There are several methods for calculating portfolio returns and performance. One traditional method is using quarterly or monthly money-weighted returns, however the true time-weighted method is a method preferred by many investors in financial markets. Investment Performance Measurement Errors, accessed 2008-06-29.</ref> There are also several models for measuring the Performance Attribution of a portfolio's returns when compared to an Index or benchmark.

References[link]

1. ^ [1] Investopedia, Portfolio definition and explanation, Retrieved July 2011
2. ^ [2] Investopedia, Portfolio definition and explanation, Retrieved July 2011.
3. ^ Markowitz, H.M. (March 1952). "Portfolio Selection". The Journal of Finance 7 (1): 77-91
4. ^ Momentum Investment Strategies, Portfolio Performance, and Herding: A Study of Mutual Fund Behavior. Mark Grinblatt, Sheridan Titman, Russ Wermers The American Economic Review, Vol. 85, No. 5 (Dec., 1995), pp. 1088-1105

See also[link]

• Investment management
• Infection ratio

External links[link]

• Risk Minimization in Financial Portfolios
• Simultaneous Consumption Planning and Portfolio Management

Look up portfolio in Wiktionary, the free dictionary.

Portfolio ( /pɔərtˈfoʊli.oʊ/) literally means "a case for carrying loose papers," (from Latin, the imperative of portare "to carry" and folium, meaning "a sheet for writing upon").

From about 1930 it has also come to mean a "collection of securities or responsibilities held by an individual"^{[citation needed]} and so may refer to:

• A type of briefcase
• Portfolio (government), the post and responsibilities of a head of a government department
• Portfolio (finance), a collection of investments held by an institution or a private individual
• Career portfolio, an organized presentation of an individual's education, work samples, and skills
• Almerindo Portfolio (1877–1966), Businessman, New York City Treasurer
• Business networking a philosophy of working for several diverse projects directly rather than earning a salary from a regular employer.
• Artist's portfolio, a sample of an artist's work or a case used to display artwork, photographs etc.
• Electronic portfolio, a collection of electronic documents
• Patent portfolio, a collection of patents owned by a single entity
• Product portfolio (business administration), 2D separation of products by their market share and profits or growth rates
• IT Portfolio, in IT portfolio management, the portfolio of large classes of items of enterprise Information Technology (IT)
• Project Portfolio, in Project portfolio management, the portfolio of projects in an organization
• Portfolio: An Intercontinental Quarterly, a cross-disciplinary literary journal published between 1945 and 1947
• Atari Portfolio, a palmtop computer
• Extensis Portfolio, a digital asset manager
• Portfolio.com, a business magazine
• electronic portfolio, a portfolio that has been prepared for distribution online
• Portfolio (Grace Jones album)
• Portfolio (Yolandita Monge album)
• Minister without portfolio

See also[link]

• Port Folio (disambiguation)
• All pages with titles containing "Portfolio"

This disambiguation page lists articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article.

This biographical article needs additional citations for verification. Please help by adding reliable sources. Contentious material about living persons that is unsourced or poorly sourced must be removed immediately, especially if potentially libelous or harmful. (May 2011)

Tom Willett (born 1950) is an American musician, author and entertainment industry executive. He toured and recorded extensively as a bass player during the 1960s and 1970s, served as booking agent and manager for numerous artists in the 1980s, and worked as an artist and repertoire and marketing executive in the 1990s. In the 2000s he co-founded a fully accredited music school for college-aged musicians and entrepreneurs.

Touring and recording bands[link]

Born in Portsmouth, Virginia, Willett moved with his family to the Washington, DC suburbs in the mid-1960s. While attending Thomas Jefferson High School in Fairfax County, VA, he played bass with DC-area Garage Rockers the Keggs, the Uncalled Four, and the Nightcrawlers, which also featured Gerry Beckley, later of the best-selling British ex-pat band, America.

While completing coursework for a B.A. in Psychology at Wake Forest University in Winston-Salem, NC, Willett toured with Brit Rock-Psychedelic outfit Orange, featuring Danny Brubeck, son of legendary Jazz pianist Dave Brubeck, on drums.

After graduation in 1972, Willett recorded and toured with the Sons of Thunder, founded by Blaine Smith in 1968 and the first U.S. Rock act to record a contemporary Gospel album for a major label (Till the Whole World Knows, Zondervan). He also played bass for D.C. Folk-Rocker Scott Wesley Brown.

Early not-for-profit work[link]

While pursuing post-graduate studies in the mid-1970s at a commune in the Maryland suburbs, Willett helped launch both the Cornerstone Study Center (Jim and Lorraine Hiskey) and the C.S. Lewis Institute (James Houston, John R.W. Stott, J. I. Packer).[1] He and Santa Rosa, CA-native Julie Atterbury where married in 1978.

Booking and artist management[link]

Willett returned to the music industry in 1979 when he launched the Chanan Agency to handle booking and management for DC-area talent including musician/author Brian McLaren [2] and college-circuit favorites, Jim and Kim Thomas (the Carpenter’s Tools, Say-So).[3]

In 1980, Willett joined Dharma Artist Agency [4] in Nashville, TN where he served as booking agent for a number of leading artists, including Leon Patillo (Santana), Maria Muldaur, and Richie Furay (Buffalo Springfield, Poco). He later formed Tom Willett Artist Management to provide career direction for John Fischer (Word/A&M), Scott Wesley Brown (Sparrow/EMI), and Marty McCall (MCA Songbird).

Artist and repertoire work in Los Angeles[link]

In 1984, Willett was asked to become executive director of artists and repertoire in Los Angeles for ABC’s Word Records, the world's largest distributor of inspirational music and books. Responsible for signing new artists and overseeing production, Willett managed the creation of more than 50 award-winning CDs and videos, including Grammy and Dove Award winning records by Sam Phillips, The Choir, Dion DiMucci, Philip Bailey (Earth, Wind & Fire), Randy Stonehill and Bryan Duncan.

While in L.A., Willett founded What? Records, a boutique label marketed and distributed by A&M Records. Working with T Bone Burnett, David Miner, John Carter and Lynn Nichols, What? released four critically acclaimed albums: IDeoLa’s ‘’Tribal Opera,’’ Tonio K.’s ‘’Romeo Unchained’’ and ‘’Notes from the Lost Civilization,’’ and Dave Perkins’ ‘’The Innocence.’’

Willett’s A&R work saw him in the studio with such notables as T Bone Burnett, Phil Ramone, Charlie Peacock, Booker T. Jones, Little Richard, Tchad Blake, Bill Schnee and Doug Sax.

Marketing, product management and career development[link]

In 1990, Willett and Epic Record’s Roger Klein brokered a new marketing and distribution relationship for Word with Epic Records and Sony Music Entertainment. After relocating to New York, he, along with Dan Beck (Michael Jackson, Pearl Jam, Indigo Girls, Sade), coordinated the release and marketing of over 250 albums that generated more than $50,000,000 in revenues. While serving as Vice President of Marketing for Word/Epic, Willett and his team spear-headed international marketing campaigns for such artists as Al Green, Deniece Williams, Shirley Caesar, Phil Keaggy, Soul Mission, Sandi Patty, Petra, and Point of Grace. Through their efforts, Word/Epic artists found expanded audiences, while leading mainstream personalities such as Bruce Cockburn, Wynton Marsalis and Garrison Keillor crossed back over into the Gospel marketplace.

In 1995 Willett moved to Virginia, and later, Florida, to pursue writing and independent marketing. He published more than 50 articles in music and arts journals while helping manage the literary estate of Dr. Richard C. Halverson, former Chaplain of the U.S. Senate. With Beck, he formed ADi, a property development and marketing organization focused on creating unique entertainment, character and lifestyle properties. In conjunction with Peacock Papers, Adi’s products found distribution in Hallmark and other leading card and gift shops. Their recording and touring project, The American Soul and Rock & Roll Choir, went on to tour performing arts centers throughout the U.S. Willett and Beck later co-managed Hip-Hop duo, Scratch Track, and artist/writer/filmmaker, Will Gray.

During this period, Willett also founded Creative Development Network, providing career support to Artist/Producer T Bone Burnett (Counting Crows, Wallflowers), recording artist Sam Phillips (Virgin, Nonesuch), and Internet sensation, Boondogs, the first band signed to a major recording contract based solely on consumer voting during the first wave of downloadable .mp3s.

Music industry educator and mentor[link]

In 2000, Willett was asked to spearhead a feasibility study for the creation of a fully accredited, 4-month-long off-campus study experience for college students interested in careers in the music industry. In conjunction with CCCU’s Dr. Richard Gathro and a committee of college presidents, deans and music department chairs, he created a business plan and curriculum that offered developing artists classes and hands-on experience in songwriting, recording and performance, while training young entrepreneurs in artist management, booking, publishing, record company operations and marketing. Established on the Island of Martha’s Vineyard in Massachusetts in the Fall of 2001, Willett and the faculty and staff of the Contemporary Music Center have helped launch the careers of more than 600 students from nearly 100 colleges and universities.

Willett’s work has been cited in ‘’Rolling Stone,’’ ‘’Billboard,’’ ‘’Musician,’’ ‘’The L.A. Times,’’ ‘’Entertainment Weekly,’’ ‘’CMJ’’ and the ‘’Hollywood Reporter,’’ while his articles encouraging excellence in music making and marketing have appeared in ‘’Image,’’ ‘’The Wittenburg Door,’’ ‘’CCM,’’ ‘’Release,’’ ‘’The Other Side’’ and ‘’Prism.’’

Selected credits[link]

Agent, Manager, Career Development

• Boondogs
• Scott Wesley Brown
• T Bone Burnett
• Gary Chapman
• Jamie Owens Collins
• John Fischer
• Richie Furay
• Marty McCall and Fireworks
• Brian McLaren
• Maria Muldaur
• Leon Patillo
• Sam Phillips
• Jim and Kim Thomas
• John and VicciJo Witty

Executive producer and A&R

• Philip Bailey, The Wonders of His Love, A&M
• Philip Bailey, Triumph, A&M (Grammy)
• The Choir, Diamonds and Rain, Word
• The Choir, Chase the Kangaroo, Word
• The Choir, Wide-Eyed Wonder, Word
• The Choir, Circle Slide, Word/Epic
• Bruce Cockburn, Dancing in the Dragon's Jaws, Word
• Dion, Seasons, Word
• Dion, Kingdom in the Streets, Word/A&M
• Dion, Velvet & Steel, Word/A&M
• Bryan Duncan, Anonymous Confessions…, Word
• Bryan Duncan, Mercy, Epic
• John Fischer, Between the Answers, Word
• John Fischer, Casual Crimes, Word
• Mark Heard (iDeoLa), Tribal Opera, What?/A&M
• Benny Hester, Benny from Here, Word
• Benny Hester, Through the Window, Word
• Leon Patillo, I'll Never Stop Loving You, Word
• Leon Patillo, The Sky's the Limit, Word
• Leon Patillo, Love Around the World, Word
• Sam (Leslie) Phillips, Dancing with Danger, Word
• Sam (Leslie) Phillips, Black and White in a Grey World, Word
• Sam (Leslie) Phillips, The Turning, Word/A&M
• Sam (Leslie) Phillips, Recollection, Word
• Rhythm House, (self-titled), Word
• Randy Stonehill, Celebrate This Heartbeat, Word
• Randy Stonehill, Love Beyond Reason, Word
• Randy Stonehill, Wild Frontier, Word
• Randy Stonehill, Can't Buy a Miracle, Word
• Randy Stonehill, Return to Paradise, Word/A&M
• Tonio K., Romeo Unchained, What?/A&M
• Tonio K., Notes from the Lost Civilization, What?/A&M
• Tonio K., Olé, Gadfly
• Various Artists, Adventures in the Land of Big Beats & Happy Feets
• Various Artists, Twelve New Faces
• Various Artists, Voices

Marketing

• Acappella, Acappella America, Epic
• Maia Amada, Maia Amada, Epic
• Anointed, Spiritual Love Affair, Epic (Dove)
• Philip Bailey, Family Affair, Epic
• Philip Bailey, Best of…, Epic
• Helen Baylor, Highly Recommended, Epic
• Helen Baylor, Look A Little Closer, Epic
• Helen Baylor, Start All Over, Epic (Dove)
• Brooklyn Tabernacle Choir, Live with Friends, Epic
• Rev. Milton Brunson and…, Through God's Eyes, Epic (Grammy)
• Shirley Caesar, Stand Still, Epic (Grammy)
• Shirley Caesar, He's Working It Out For You, Epic (Grammy, Dove)
• Glen Campbell, Favorite Hymns, Epic
• Bruce Carroll, Walk On, Epic (Dove)
• The Choir, Circle Slide, Epic
• Bruce Cockburn, Christmas, Columbia
• Bruce Cockburn, Dart to the Heart, Columbia
• Jesse Dixon, I Know What Prayer Can Do, Epic
• O'Landa Draper and the Associates, Above and Beyond, Epic
• Bryan Duncan, Mercy, Epic
• Bryan Duncan, Slow Revival, Epic
• First Call, Human Song, Epic
• First Call, Sacred Journey, Epic
• The Florida Boys, A Taste of Heaven, Epic
• Al Green, One in a Million, Epic
• Al Green, Love Is Reality, Epic
• Guardian, Fire & Love, Epic
• Guardian, Miracle Mile, Epic
• Guardian, Swing Swang Swung, Epic
• Kurt Kaiser, The Lost Art of Listening, Epic
• Phil Keaggy, Beyond Nature, Epic (Dove)
• Phil Keaggy, Blue (Crimson and Blue), Epic
• Garrison Keillor and the Hopeful Gospel Quartet, Sony
• Wynton Marsalis, In This House, Columbia
• Babbie Mason, World of Difference, Epic
• MidSouth, Lessons of Life, Epic
• Mighty Clouds of Joy, Sing and Shout, Epic
• Mighty Clouds of Joy, Pray for Me, Epic (Grammy)
• Cindy Morgan, Real Life, Epic (Dove)
• Michael Omartian, The Race, Epic
• Sandi Patty, Another Time, Another Place, Epic (Grammy, Dove, Gold)
• Sandi Patty, Finest Moments, Epic (Gold)
• Sandi Patty, Le Voyage, Epic (Dove)
• Sandi Patty, Find It On the Wings, Epic (Dove)
• Petra, Unseen Power, Epic (Grammy)
• Petra, Wake-Up Call, Epic (Grammy, Dove)
• Petra, No Doubt, Epic (Dove)
• Point of Grace, The Whole Truth, Epic (Dove, Gold)
• Stephen Soles, Walk by Love, Word
• Soul Mission, Soul Mission, Epic
• Russ Taff, Under Their Influence, Vol. 1, Epic (Grammy)
• The Whites, Doin' It by the Book, Epic
• Deniece Williams, Lullabies to Dreamland, Epic

Publications

• "Archive of a Culture—The Museum of Television and Radio," Prism
• "Artist Representation—A Look at the Heart," Contemporary Christian Music
• "Between Heaven and Earth—Diary of an Artist," Prism
• "Bible Versus®," The Wittenburg Door
• "Burnett Thompson—Artist Profile," Prism
• "Casting the Muse in Feminine Hues—The National Museum of Women in the Arts"
• "Contemporary American Attitudes about God," The Wittenburg Door
• "Down in the Groove," Image
• "Exit Martin—The National Civil Rights Museum," Prism
• "Faith and Activism," Prism
• "Faith and Creation," Prism
• "Faith and Death," Prism
• "Faith and Intellect," Prism
• "Faith and Money," Prism
• "Faith and the Future," Prism
• "Gazing Over the Edge—Activists and Artists Together," The Other Side
• "Giants in the Land—G. K. Chesterton," Prism
• "If Someone Didn't Say It, They Should," The Wittenburg Door
• "Image—A Journal of the Arts and Religion," Prism
• "Jim Hodgson—Artist Profile," Prism
• "Oh Mercy," World Christian
• "Pilgrim at Twenty—Annie Dillard," Prism
• "Simone Weil: Contemporary Saintliness Redux," Prism
• "Slow Train Coming," Washington Arts Group Journal
• "St. Bernard—G. Bernard Shaw," Prism
• "Strong Hand of Love—Mark Heard," Release
• "The Art of Attack—The Armand Hammer Museum of Art and Cultural Center," Prism
• "The Artist: Devotion Plus Creativity," Contemporary Christian Music
• "The Christian and Creativity," Joyful Noise
• "The Gift of Criticism—H. L. Mencken," Prism
• "The State of Christian Media," Prism
• "Toward a Difficult Hope—Albert Camus," Prism
• "Tribute—The Songs of Andraé Crouch," Release
• "Will Horrors Never Cease?—The United States Holocaust Memorial Museum," Prism

External links[link]

• Official Website

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.

Autobiography[link]

"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]

Biography[link]

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]

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 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.

Research[link]

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.

Harry Markowitz Model[link]

Introduction[link]

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 :

1. Determination a set of efficient portfolios.

2. Selection of best portfolio out of the efficient set.

Determining the Efficient Set[link]

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 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[link]

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.

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.

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 :

R_P = I_RF + (R_M - I_RF)σ_P/σ_M

Where,

R_P = Expected Return of Portfolio

R_M = Return on the Market Portfolio

I_RF = Risk-Free rate of interest

σ_M = Standard Deviation of the market portfolio

σ_P = Standard Deviation of portfolio

(R_M - I_RF)/σ_M is the slope of CML. (R_M - I_RF) is a measure of the risk premium, or the reward for holding risky portfolio instead of risk-free portfolio. σ_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 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 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 (I_RF) and the purchase of efficient portfolio P. The portfolio an investor will choose depends on his preference of risk. The portion from I_RF 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.

Demerits of the HM Model[link]

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]

Further Reading[link]

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

Selected publications[link]

• 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. 
• 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. 

See also[link]

• List of economists
• List of Jewish Nobel laureates
• Modern Portfolio Theory
• Capital asset pricing model
• Risk management tools
• Risk

References[link]

External links[link]

• An Hour with Harry Markowitz: Interviewed by Mark Hebner
• The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, 1990
  • Autobiography, The Nobel Prizes 1990, Editor Tore Frängsmyr, [Nobel Foundation], Stockholm, 1991
  • Banquet Speech, December 10, 1990
  • 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