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Modern Portfolio Theory And Investment Analysis [NEW]



The Modern Portfolio Theory (MPT) refers to an investment theory that allows investors to assemble an asset portfolio that maximizes expected return for a given level of risk. The theory assumes that investors are risk-averse; for a given level of expected return, investors will always prefer the less risky portfolio.




Modern Portfolio Theory and Investment Analysis



The following 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).


MPT works under the assumption that investors are risk-averse, preferring a portfolio with less risk for a given level of return. Under this assumption, investors will only take on high-risk investments if they can expect a larger reward.


At every point on the Efficient Frontier, investors can construct at least one portfolio from all available investments that features the expected risk and return corresponding to that point. A portfolio found on the upper portion of the curve is efficient, as it gives the maximum expected return for the given level of risk.


So how did this play out in the Great Recession of 2008? According to Markowitz, investors that limited risk during the recession kept a percentage of their portfolios in lower-risk U.S. Treasure bonds; these investments were top performers, while stocks and corporate bonds took a dive.


Modern Portfolio Theory and Investment Analysis, 9th Editionexamines the characteristics and analysis of individual securities, as well as the theory and practice of optimally combining securities into portfolios. It stresses the economic intuition behind the subject matter while presenting advanced concepts of investment analysis and portfolio management.


  • Martin J. Gruber is Professor Emeritus and Scholar in Residence at the Leonard N. Stern School of Business of New York University where he previously served as Professor of Finance for 45 years.He is a director and a member of the investment committee of the National Bureau of Economic Research. He is a fellow of the American Finance Association, the Financial Management Association, and the Institute for Quantitative Research in Finance. He is past president of the American Finance Association and served as Finance Department Chairman at NYU for nine years.The ninth edition of his book, Modern Portfolio Theory and Investment Analysis, is one of the leading texts in graduate schools of business. In addition, he has published six other books in investment analysis and portfolio management. Professor Gruber has written over 100 articles which have appeared in the Journal of Finance, Review of Economics and Statistics, Journal of Financial Economics, Journal of Business, Management Science, Journal of Financial and Quantitative Analysis, Operations Research, Oxford Economic Papers and the Journal of Portfolio Management. A collection of his pre-1996 articles has been published as a two-volume anthology by The MIT Press entitled Investments. A collection of his post-1996 articles has been published by World Scientific Publishing Company. He was formerly co-managing editor of the Journal of Finance, Department editor for Finance of Management Science, a member of the Advisory Board of the European Finance Review and an Associate Editor of the Journal of Banking and Finance. He has been a director of both the Computer Applications Committee, and the Investment Technology Symposium of the New York Society of Security Analysts, and an Associate Editor of the Financial Analysts Journal. He has also been a director of the European Finance Association and a founding member of the Asian Finance Association.Professor Gruber was named a distinguished scholar by the Eastern Finance Association, has received the Graham and Dodd Award for research in investments and in 2004 was awarded the prestigious James R. Vertin Award by AIMR in recognition of his research notable for its relevance and enduring quality to investment professionals. He has served as a consultant in the areas of investment analysis and portfolio management with many major financial institutions in the United States, Asia, and Europe. Professor Gruber has been a Director of the Singapore Equity Fund Inc., The Thai Equity Fund and chairman of the board of the Japan Equity Fund Inc. He has been chairman of the Equity Committee and a member of the DWS Mutual Funds New York Board. He has served as a member of the board of trustees of TIAA, a member of the board of CREF, chairman of the board of CREF, and a member of the board of the S.G. Cowen Funds. Professor Gruber holds an S.B. degree in Chemical Engineering from MIT and both an MBA in Production Management and a Ph.D. in Finance and Economics from Columbia University. He also was awarded the degree of Docteur "honoris causa" by the University of Liege, Belgium. Research Interests General equilibrium theory

  • Expectations and their role in security price formation

  • Mutual funds

  • Pension funds

  • Courses Taught Executive Education Courses on Mutual Funds and Portfolio Management

Academic Background Ph.D., Finance and Economics, 1965 Columbia University


Modern Portfolio Theory And Investment Analysis is a comprehensive book for undergraduate finance students. The book covers the subject of modern portfolio theory, teaching students about minimizing risk in the field of investments for a given level of expected return, by carefully choosing the proportions of various assets. The book explains how to analyse financial markets and enterprises and how to estimate their security. It also explains how to assess opportunities under risk, and how to delineate efficient portfolios. Readers learn how to estimate portfolios for risk, and how to understand the various pricing models which are used in the industry. It is an essential resource for all commerce students.


\r \tModern Portfolio Theory And Investment Analysis is a comprehensive book for undergraduate finance students. The book covers the subject of modern portfolio theory, teaching students about minimizing risk in the field of investments for a given level of expected return, by carefully choosing the proportions of various assets. The book explains how to analyse financial markets and enterprises and how to estimate their security. It also explains how to assess opportunities under risk, and how to delineate efficient portfolios. Readers learn how to estimate portfolios for risk, and how to understand the various pricing models which are used in the industry. It is an essential resource for all commerce students.


Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. It is a formalization and extension of diversification in investing, the idea that owning different kinds of financial assets is less risky than owning only one type. Its key insight is that an asset's risk and return should not be assessed by itself, but by how it contributes to a portfolio's overall risk and return. It uses the variance of asset prices as a proxy for risk.[1]


The MPT is a mean-variance theory, and it compares the expected (mean) return of a portfolio with the standard deviation of the same portfolio. The image shows expected return on the vertical axis, and the standard deviation on the horizontal axis (volatility). Volatility is described by standard deviation and it serves as a measure of risk.[3] The return - standard deviation space is sometimes called the space of 'expected return vs risk'. Every possible combination of risky assets, can be plotted in this risk-expected return space, and the collection of all such possible portfolios defines a region in this space. The left boundary of this region is hyperbolic,[4] and the upper part of the hyperbolic boundary is the efficient frontier in the absence of a risk-free asset (sometimes called "the Markowitz bullet"). Combinations along this upper edge represent portfolios (including no holdings of the risk-free asset) for which there is lowest risk for a given level of expected return. Equivalently, a portfolio lying on the efficient frontier represents the combination offering the best possible expected return for given risk level. The tangent to the upper part of the hyperbolic boundary is the capital allocation line (CAL).


One key result of the above analysis is the two mutual fund theorem.[8][9] This theorem states that any portfolio on the efficient frontier can be generated by holding a combination of any two given portfolios on the frontier; the latter two given portfolios are the "mutual funds" in the theorem's name. So in the absence of a risk-free asset, an investor can achieve any desired efficient portfolio even if all that is accessible is a pair of efficient mutual funds. If the location of the desired portfolio on the frontier is between the locations of the two mutual funds, both mutual funds will be held in positive quantities. If the desired portfolio is outside the range spanned by the two mutual funds, then one of the mutual funds must be sold short (held in negative quantity) while the size of the investment in the other mutual fund must be greater than the amount available for investment (the excess being funded by the borrowing from the other fund).


Modern portfolio theory has also been criticized because it assumes that returns follow a Gaussian distribution. Already in the 1960s, Benoit Mandelbrot and Eugene Fama showed the inadequacy of this assumption and proposed the use of more general stable distributions instead. Stefan Mittnik and Svetlozar Rachev presented strategies for deriving optimal portfolios in such settings.[13][14][15] More recently, Nassim Nicholas Taleb has also criticized modern portfolio theory on this ground, writing: 041b061a72


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