Modern Portfolio Theory

12 Key excerpts on "Modern Portfolio Theory"

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  Proximity Bias in Investors' Portfolio Choice

  • Ted Lindblom, Taylan Mavruk, Stefan Sjögren(Authors)
  • 2017(Publication Date)
  • Palgrave Macmillan

    (Publisher)

  Fig. 2.1 From savings to investment: the asset transformation process 12 T. Lindblom et al. The Modern Portfolio Theory (MPT) developed and first formalized by Markowitz (1952) is an important cornerstone of financial economic thinking. This theory explains how wealth-optimizing investors (house- holds and their representatives) behave when making their investments on ef ficient financial markets. It also provides the financial market a tool for optimal portfolio diversification. The origin of the MPT involved many academics and researchers, including Nobel laureates, such as Harry M. Markowitz himself, James Tobin, William F. Sharpe, Joseph E. Stiglitz, Daniel Kahneman, Robert J. Shiller, and Eugene F. Fama, all acknowl- edged and famous for making important contributions to our under- standing of investors’ portfolio choice. According to Markowitz (1999), who is often referred to as the father of the portfolio theory, the development of MPT can be divided into two parts. The first part is the groundbreaking work of Markowitz himself published in the Journal of Finance in the early 1950s. This stage focused on how a rational risk-averse investor should behave when optimizing her or his wealth. In that respect, the MPT can be thought of as being normative. The theory formalizes what investors already knew intuitively: That it is better to invest in portfolios than in single securities.

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  Wealth

  How the World's High-Net-Worth Grow, Sustain, and Manage Their Fortunes

  • (Author)
  • 2010(Publication Date)
  • Wiley

    (Publisher)

  CHAPTER 5

  The Doctrine of Asset Allocation

  ENHANCING RETURNS WITH Modern Portfolio Theory (MPT)

  One day in 1951, Harry Markowitz, a graduate student in mathematics at the University of Chicago, was sitting outside his thesis advisor’s office waiting to discuss the subject of his doctoral dissertation. His field of research was linear programming, a discipline that employs complex mathematical models to maximize output for a given level of cost or to minimize cost for a given level of output. One of the most common applications of linear programming is a mathematical equation by which auto manufacturers seek to determine how many cars should optimally be built when constrained by specific amounts of materials and worker hours.40

  Fortunately for the future development of the fine art of risk management, the mathematics professor was not immediately free to see Markowitz. While cooling his heels in the waiting room, Markowitz struck up a conversation with a stockbroker also waiting to see one of the professors in the department. Strictly to kill time, the broker asked Markowitz to describe his field of research. After listening intently for a few minutes, the broker casually observed that a promising application of linear programming might be for a young mathematician to tackle the challenges inherent in forecasting and tracking fluctuations in financial portfolios.

  And so, the discipline of asset allocation—the most critical conceptual component of the now-widely-accepted doctrine known as Modern Portfolio Theory (MPT)—was born. Intellectually stimulated by the notion of applying his arcane tool kit to such a hitherto virgin field of research, Markowitz began by drawing what turned out to be a stunningly fruitful analogy between desired output as a manufacturer might define the term and desired output as an investor might define it. For investors, the desired output of a well-managed portfolio would be an above-average rate of return over time. In his linear analysis, Markowitz defined costs as the level of volatility to which any particular portfolio might be exposed in order to generate an above-average rate of return.41

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  R Programming for Actuarial Science

  • Peter McQuire, Alfred Kume(Authors)
  • 2023(Publication Date)
  • Wiley

    (Publisher)

  155 8 Modern Portfolio Theory Peter McQuire library(dplyr) 8.1 Introduction In 1952 Harry Markovitz published his paper “Portfolio Selection” in the Journal of Finance. The paper proposed a methodology which allowed investors to analyse the balance between risk and returns between various asset portfolios. The theory became popularly known as “mean-variance portfolio theory,” “Modern Portfolio Theory (MPT),” “mean-variance optimisation,” or even “Markovitz Portfolio Theory”. In this chapter we discuss the key aspects of this theory. We proceed to calculate the expected returns and variance of returns from various combinations of assets, comparing our results from portfolios which consist of a range of risky and risk-free assets (we will define exactly what is meant by “risk” under MPT shortly). We will do this by writing our own code rather than use one of the many functions within R already available, which should aid the learning process. An Appendix is included which describes a method to determine efficient portfolios using Lagrange multipliers. Remark 8.1 There are various packages in R which are related to the material in this chapter, such as fPortfolio and PortfolioAnalytics. The reader may wish to review these in due course. MPT allows an investor, at least in theory, to choose a particular portfolio of assets which is expected to provide the greatest investment return subject to an acceptable level of risk which the investor is willing to take. Thus our calculations may provide a wide range of potential portfolios from which the investor can choose, each with a different risk/return profile; the portfolio chosen by the investor will depend on the level of risk which is most desirable to them. R Programming for Actuarial Science, First Edition. Peter McQuire and Alfred Kume. © 2024 John Wiley & Sons Ltd. Published 2024 by John Wiley & Sons Ltd. Companion Website: www.wiley.com/go/rprogramming.com.

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  Portfolio Construction and Analytics

  • Frank J. Fabozzi, Dessislava A. Pachamanova(Authors)
  • 2016(Publication Date)
  • Wiley

    (Publisher)

  Part Three Three Portfolio Theory Passage contains an image

  Chapter 8 Asset Diversification

  The concepts of portfolio risk management and diversification have been instrumental in the development of modern financial decision making. These breakthrough ideas originated in an article by Harry Markowitz that appeared in 1952. Before Markowitz's publication, the focus in the investment industry was on identifying and investing in “winners”—stocks that appear undervalued relative to some measure of their potential or promise sustainable growth, that is, stocks with high expected returns. Markowitz reasoned that investors should decide based on both the expected return from their investment, and the risk from that investment. He defined risk as the variance of future returns. The idea of incorporating risk in investment decisions and applying a disciplined quantitative framework to investment management was novel at the time.1 Originally, this investment philosophy generated little interest, but eventually, the finance community adopted it. Over the years, the theory of portfolio selection formulated by Markowitz has been extended and reinvented based on a modification of the assumptions made in the original model that limited its application. It has also introduced a whole new terminology, which is now the norm in the investment management community. Markowitz's investment theory is popularly referred to as mean-variance analysis, mean-variance portfolio optimization, and Modern Portfolio Theory (MPT). In 1990, Markowitz was awarded the Nobel Memorial Prize in Economic Sciences in recognition of his seminal work.

  As we will see in this chapter, the definition of risk as the variance of returns leads to the conclusion that diversification

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  Property Investment

  • David Isaac, John O'Leary(Authors)
  • 2011(Publication Date)
  • Bloomsbury Visual Arts

    (Publisher)

  11.2 Modern Portfolio Theory Early work by Markowitz (1952, 1959 and 1991) regarding share portfolios led to Modern Portfolio Theory which in common with all theoretical models is based upon some reasoned assumptions. Thus it is assumed that investors are risk averse in that they rationally expect a higher rate of return to compensate them for taking greater risks. It was also assumed that risk can be measured by analysing the likely divergence between the returns from a portfolio and its expected return. When considering whether or not to buy an asset, investors were also assumed to be concerned about the effect of the decision on their overall portfolio and thus would not consider the risk of the asset in isolation from other assets held. Markowitz suggested that investors should select assets for inclusion in their investment portfolios on the basis of mean variance or alternatively mean and semi-variance. Semi-variance seemed the more plausible measure of risk but posed greater computational difficulties. Markowitz suggested that assets in a portfolio can be combined to provide an efficient portfolio that will give the highest possible level of return for any level of portfolio risk as measured by the variance or standard deviation. The risk-and-return trade-off for investments in a portfolio can be described graph-ically as an ‘efficient frontier’ as shown in Figure 11.1. Investments which have a combination below this efficient frontier will not be achieving an efficient trade-off in the light of an investor’s preference. Given an efficient frontier, investors have to choose where their preferences lie on the frontier and that choice will depend on attitudes to risk. Some investors will wish to minimize risk at the expense of return, while others will be prepared to take a higher risk to potentially achieve a higher return.

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  Real Estate Appraisal

  From Value to Worth

  • Sarah Sayce, Judy Smith, Richard Cooper, Piers Venmore-Rowland(Authors)
  • 2009(Publication Date)
  • Wiley-Blackwell

    (Publisher)

  Following that, the issues that are raised and that question the validity of MPT are assessed in the light of the implications for property portfolios. In particular, the application of expected return factor models is considered. 12.2 The nature of risk in financial assets Before explaining the concepts of MPT and portfolio optimisation, a definition of risk is provided. Risk can be defined as the degree of likelihood that an expected outcome will not hap-pen. It is therefore a measure that can be linked to probability. The higher the risk, the less able we are to predict the outcome. With an individual asset the classic measure of risk, as was explained in Chapter 8, is in relationship to standard deviation. The more closely clustered outcomes are around the average outcome, the lower the standard deviation and hence the lower the risk. Intuitively, investors seeking a lower than average level of risk will accept a lower than average return; conversely, to achieve a higher than aver-age return, intuitively an investor will have to accept a higher level of risk. However, where groups of assets are considered the very act of combining the assets may affect the level of risk. It will depend on both the type of risk and the risk profile of each asset. The aim of the theorists has been to devise models that can enable investors to build portfolios of risk-prone investments that, when combined, decrease the overall exposure to risk without an equivalent reduction in expected returns. The attempts collectively are known as portfolio theory. Fundamental to these theories is an appreciation of the types of risk that affect assets. These can be divided into two main types: • systematic (market-related) risk; and • non-systematic (specific) risk. 12.2.1 Systematic risk Systematic risk is typically perceived as market risk, and is driven by general sentiment; it is therefore a risk that an individual investor cannot independently control.

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  Portfolio Diversification

  • Francois-Serge Lhabitant(Author)
  • 2017(Publication Date)
  • ISTE Press - Elsevier

    (Publisher)

  2

  Modern Portfolio Theory and Diversification

  Abstract

  Portfolio construction and diversification were for a long time more of an art than a science. Investors were intuitively aware of the notion of return and risk, but had no mathematically consistent framework to model and build portfolios. In addition, the question of the underlying common characteristic along which some assets may be diverse had never been formally addressed. Thus, there had been no analysis on how to measure the benefits of diversification with respect to this characteristic. Markowitz was the first to formalize the measurement of portfolio risk and return in a mathematically consistent framework, which he subsequently expanded in Markowitz. Acknowledging that measuring portfolio risk and portfolio return was only the first step, Markowitz introduced a methodology for assembling portfolios that considers the expected returns and risk characteristics of the underlying assets as well as the investor’s appetite for risk. The result, usually referred to as the Modern Portfolio Theory, pushed portfolio construction toward a science and away from being an art.

  Keywords

  Approximation risk; Constraints on the weights; Empirical applications; Estimation risk; Markowitz portfolios; Modeling returns as random variables; Modern Portfolio Theory; Optimal and efficient portfolios; Return and risk statistics

  Portfolio construction and diversification were for a long time more of an art than a science. Investors were intuitively aware of the notion of return and risk, but had no mathematically consistent framework to model and build portfolios. In addition, the question of the underlying common characteristic along which some assets may be diverse had never been formally addressed. Thus, there had been no analysis on how to measure the benefits of diversification with respect to this characteristic. Markowitz [MAR 52] was the first to formalize the measurement of portfolio risk and return in a mathematically consistent framework, which he subsequently expanded in Markowitz [MAR 56 , MAR 59 ]. Acknowledging that measuring portfolio risk and portfolio return was only the first step, Markowitz introduced a methodology for assembling portfolios that considers the expected returns and risk characteristics of the underlying assets as well as the investor’s appetite for risk. The result, usually referred to as the Modern Portfolio Theory, pushed portfolio construction toward a science and away from being an art1

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  Investments

  Analysis and Management

  • Gerald R. Jensen, Charles P. Jones(Authors)
  • 2019(Publication Date)
  • Wiley

    (Publisher)

  Unfortunately, when it comes to investing in finan- cial assets, the assumption of statistically independent returns is unrealistic. In practice, most stocks are positively correlated with each other; that is, the movements in their returns are related, not independent. We call the variation in returns that is attributable to general market moves, market risk. While total risk can be reduced, it cannot be eliminated because market risk cannot be eliminated. Unlike firm-specific risk, common sources of risk (market risk) affect all firms and cannot be diversified away. For example, an increase in interest rates affects most firms adversely because most firms borrow funds to finance part of their operations. Diversification Another major implication of MPT is that there are two general sources of risk, firm-specific and market risk. Because the sources of risk are not entirely independ- ent, adding securities reduces the firm-specific risk, but not the market risk. The process of adding securities to a portfolio to reduce firm-specific risk is referred to as diversification. • Diversification is the key to managing portfolio risk because it allows investors to significantly lower portfolio risk without adversely affecting return. We consider two forms of portfolio diversification, beginning with random diver- sification and moving to efficient portfolio diversification, which is based on MPT principles. Random diversification Random or naive diversification refers to the act of ran- domly diversifying without regard to how security returns are related to each other. An investor simply selects a relatively large number of securities randomly—the The risk of a portfolio declines quickly as more securities are added. Using Equation 7-8 and assuming that each security’s standard deviation is 20 percent, the risk of a 100-security portfolio is reduced to 2.0 percent: p 20 100 2 0 1 2 / . % EXAMPLE 7.5

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  Investments

  Analysis and Management

  • Gerald R. Jensen, Charles P. Jones(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  Unfortunately, when it comes to investing in finan-cial assets, the assumption of statistically independent returns is unrealistic. In practice, most stocks are positively correlated with each other; that is, the movements in their returns are related, not independent. We call the variation in returns that is attributable to general market moves, market risk. While total risk can be reduced, it cannot be eliminated because market risk cannot be eliminated. Unlike firm-specific risk, common sources of risk (market risk) affect all firms and cannot be diversified away. For example, an increase in interest rates affects most firms adversely because most firms borrow funds to finance part of their operations. Diversification Another major implication of MPT is that there are two general sources of risk, firm-specific and market risk. Because the sources of risk are not entirely independ-ent, adding securities reduces the firm-specific risk, but not the market risk. The process of adding securities to a portfolio to reduce firm-specific risk is referred to as diversification. • Diversification is the key to managing portfolio risk because it allows investors to significantly lower portfolio risk without adversely affecting return. We consider two forms of portfolio diversification, beginning with random diver-sification and moving to efficient portfolio diversification, which is based on MPT principles. Random diversification Random or naive diversification refers to the act of ran-domly diversifying without regard to how security returns are related to each other. An investor simply selects a relatively large number of securities randomly—the The risk of a portfolio declines quickly as more securities are added. Using Equation 7-8 and assuming that each security’s standard deviation is 20 percent, the risk of a 100-security portfolio is reduced to 2.0 percent: p 20 100 2 0 1 2 / . % EXAMPLE 7.5

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  Portfolio Theory and Performance Analysis

  • Noel Amenc, Veronique Le Sourd(Authors)
  • 2005(Publication Date)
  • Wiley

    (Publisher)

  The Markowitz theory does not speak of efficient markets, but of efficient portfolios. An efficient portfolio is defined as a portfolio with minimal risk for a given return, or, equivalently, as the portfolio with the highest return for a given level of risk. The complete set of these portfolios forms the efficient frontier, which constitutes the convex envelope of all the portfolios that can be produced. Each investor uses his own forecasts and deduces his efficient frontier from these. Two investors who use different forecasts will not therefore have the same efficient frontier. We shall see in Chapter 4 that we only consider that all investors make the same forecasts within the framework of the CAPM. The Markowitz model is based on the following assumptions. Individuals construct their portfolios in order to maximise the expected utility of their terminal wealth. Their utility func- tion is an increasing function of their wealth and they are risk averse. They make their choice based only on the first two moments of the random distribution of their wealth: the expecta- tion and the variance. Since the final wealth is determined by the return on the investment, it is therefore equivalent to basing it on the expected portfolio return and the variance of the The Basic Elements of Modern Portfolio Theory 81 portfolio return. The expected utility of an individual’s terminal wealth is therefore a function of the mean and the variance of the portfolio return. Portfolios that result from maximising the investor’s utility are, by definition, efficient portfolios. The Markowitz approach is described as a mean–variance approach because it only takes those two parameters, mean return and return variance, into account, i.e. the first two moments of their distribution, to characterise the investor’s portfolio. This is the same as assuming that higher order moments are null.

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  Investments

  Analysis and Management

  • (Author)
  • 2016(Publication Date)
  • Wiley

    (Publisher)

  AFTER READING THIS CHAPTER YOU WILL BE ABLE TO: ▶ Understand capital market theory as an extension of portfolio theory. ▶ Recognize the capital market line, which applies to efficient portfolios, and the security market line, which applies to all portfolios as well as individual securities. ▶ Understand beta and the capital asset pricing model (CAPM) and use CAPM to calculate the required rate of return for a security. ▶ Recognize alternative theories of how assets are priced, the arbitrage pricing theory and multifactor models. 1 Much of this analysis is attributable to the work of Sharpe. See William Sharpe, “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk,” The Journal of Finance , 19 (September 1964): 425–442. John Lintner and Jan Mossin developed a similar analysis. Capital Market Theory 223 Capital Market Theory Capital market theory (CMT) is a positive theory in that it hypothesizes how investors do behave rather than how investors should behave, as in the case of Modern Portfolio Theory (MPT). It is reasonable to view CMT as an extension of portfolio theory, but it is important to understand that MPT is not based on the validity, or lack thereof, of CMT. The specific equilibrium model of interest to many investors is the capital asset pricing model, typically referred to as the CAPM. It allows us to assess the relevant risk of an individual security and the relationship between risk and expected return. The CAPM is attractive as an equilibrium model because of its simplicity and its implications. As a result of serious chal-lenges to the model, however, several alternative models have been developed. The primary alternatives to the CAPM are arbitrage pricing theory (APT) and other multifactor models. The output from an asset pricing model, whether it be the CAPM or a multifactor model, is an asset’s expected or required return.

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  Portfolio Management under Stress

  A Bayesian-Net Approach to Coherent Asset Allocation

  • Riccardo Rebonato, Alexander Denev(Authors)
  • 2014(Publication Date)
  • Cambridge University Press

    (Publisher)

  Part III Diversification and subjective views In the previous parts of this book we have argued the merits of causal over an association-based way of dealing with stress events, and we have tried to put our proposed approach in the context of some well-known ways to look at extreme events and outliers. In this part we look at the similarities and differences between what we propose and some better established ways to deal with diversification and to assign sub- jective scenarii. Not surprisingly, Modern Portfolio Theory, pioneered by Markowitz half a century ago, is the best place to start. We also look, however, at the approaches by Black–Litterman, Meucci and Doust, because of their relevance to the assignment of subjective views. In Part III we also introduce for the first time the topic of stability (of the allocation weights). Achieving stability will be one of the underlying themes of our book, and we shall therefore return to the topic in the later parts. 7 Diversification in Modern Portfolio Theory The approach to asset allocation pioneered by Markowitz in the late 1950s and devel- oped over the next five decades truly changed the investment landscape. As we men- tioned in our Introduction, it was not much earlier that asset allocation and stock-picking were fundamentally equivalent with identifying the investment opportunity with the highest expected return (see, e.g., Williams 1938). There are two distinct insights in the Markowitz’s approach: the first is that, for most plausible ‘utility functions’ (i.e., behavioural responses to certain and uncertain changes in consumptions), risk and return are inextricably linked. 1 The second insight points to the importance of diversification in appraising a given investment opportunity given the available universe of investable assets.

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