Portfolio Theory

12 Key excerpts on "Portfolio Theory"

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  eBook - ePub

  Understanding Investments

  Theories and Strategies

  • Nikiforos T. Laopodis(Author)
  • 2012(Publication Date)
  • Routledge

    (Publisher)

  Part III

  Portfolio Theory

  We said that almost all investment instruments (securities) have uncertain or risky outcomes; thus investors must make selections among the various securities (or asset classes) for inclusion in their portfolios. After all, investors should not “put all their eggs in one basket” but diversify among securities. Selecting among the various instruments available for investment is a daunting task. Therefore an investor must ask: What is the optimal (best) combination of securities in my portfolio in order to maximize my expected return for a given level of risk? What are the available asset classes or the asset universe from which the investor chooses securities? Moreover, what if the investor wants to include a risk-free asset in his portfolio? What would that do to its risk and expected return? Or what if the investor wants to borrow on margin? All these questions are known as the portfolio selection problem or Portfolio Theory . Portfolio Theory involves the basic elements of investments: risk and expected return. Harry Markowitz’s seminal contribution to Portfolio Theory, also known as modern Portfolio Theory, was that investors should evaluate potential securities (or portfolios) based on their expected returns and standard deviations (risk).

  One element of modern Portfolio Theory is asset pricing models, such as the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT). Both models are built on the assumption that investors follow the investment approach described above to construct efficient portfolios (offering the highest expected return for a given amount of risk). But what if investors are influenced by fads, rumors, or other investors and act accordingly? In other words, what if some investors are “rational” and others “irrational”? Would their acts still validate the predictions of these models? The answers to these important questions and more fall into the realm of market efficiency and the alternative explanations of investor behavior offered by behavioral finance.

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  Investment Analysis and Portfolio Management

  • Frank Reilly, Keith Brown, Sanford Leeds, Frank Reilly, Keith Brown, Sanford Leeds, (Authors)
  • 2018(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  combining numerous individual securities that have desirable risk–return characteris-tics. Specifically, it has been shown that an investor must consider the relationship among the investments to build the best portfolio to meet the investment objectives. In this chapter we explain Portfolio Theory in detail by introducing the basic portfolio risk formula for combining different assets. When you understand this formula and its implications, you will understand why and how you should diversify your portfolio. 6.1 S OME B ACKGROUND A SSUMPTIONS We begin by clarifying some general assumptions of Portfolio Theory. This includes not only what we mean by an optimal portfolio but also what we mean by the terms risk aversion and risk . One basic assumption of Portfolio Theory is that investors want to maximize the returns from the total set of investments for a given level of risk. To understand such an assumption requires 1 71 certain ground rules. First, your portfolio should include all of your assets and liabilities , not only your marketable securities but also less marketable investments such as real estate, art, and antiques. The full spectrum of investments must be considered because the returns from all these investments interact, and this relationship among the returns for assets in the portfolio is important . Hence, a good portfolio is not simply a collection of individually good investments. 6.1.1 Risk Aversion Portfolio Theory also assumes that investors are risk averse , meaning that, given a choice between two assets with equal rates of return, they will select the asset with the lower level of risk. Evidence that most investors are risk averse is that they purchase various types of insur-ance, including life insurance, car insurance, and health insurance. Buying insurance basically involves an outlay of a known dollar value to guard against an uncertain, possibly larger, outlay in the future.

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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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  Deep Dive into Financial Models

  Modeling Risk and Uncertainty

  • Mathieu Le Bellac, Arnaud Viricel(Authors)
  • 2016(Publication Date)
  • WSPC

    (Publisher)

  Chapter 3

  Portfolio Management Theories

  In this chapter, we take up the point of view of an investor who must select investment among the various possibilities provided by the market. This investor may be an individual, the manager of a regulated fund (pension funds or mutual funds for instance), or of a hedge fund; his goal is to build up a portfolio, that is, to buy various assets which may be stocks, bonds, real estate property, and so forth. This activity is called asset management. As examples, State Street or Blackrock are companies whose main activity is to manage money entrusted by retail or institutional investors.

  Various theories have been developed to guide asset managers. Among them, that of Markowitz, called the modern Portfolio Theory, plays a major role. Developed in the 1950s — see [Markowitz 1952], [Tobin 1958] and [Markowitz 1959] — the theory defines a notion of investment optimality: efficiency. We shall explain this basic notion in the first section and the underlying details of the theory in the second one. In the 1960s, [Sharpe 1964], [Lintner 1965] and [Mossin 1966] have independently used Markowitz’s theory in order to build a model of economic equilibrium, called the Capital Asset Pricing Model (CAPM), which is the subject of our third section. This model has then been widely studied, refined and extended. Next, in the fourth section, we shall turn our attention to a more recent development: the notion of co-integration introduced by [Engle and Granger 1987], which lies at the basis of trading strategies such as pair trading.

  3.1The risk-reward approach

  Before delving into the heart of the subject, it is first necessary to look into the fundamental principle of any investment strategy: the equilibrium between return and risk. Let us consider the theoretical case where investment opportunities are restricted to four assets, A, B, C

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  eBook - ePub

  Property Investment Theory

  • A Macleary, A. Macleary, N. Nanthakumaran(Authors)
  • 2003(Publication Date)
  • Taylor & Francis

    (Publisher)

  CHAPTER 7 Portfolio Theory AND PROPERTY INVESTMENT ANALYSIS

  1 Introduction

  Property is part of an integrated financial market and efficient decisions must be made within this context. This view is important because property has to compete with other sectors of the market when it comes to allocating resources.

  To make significant advances in understanding property it is essential to draw on the rich vein of investment research which has been undertaken in other markets over the last thirty years. This research has had a significant effect on the way investors behave and if applied properly could have the same impact on the property world.

  There can be little doubt that the single most important factor affecting investment has been the development of Portfolio Theory. It is significant because it is at the root of our understanding of the way assets should be priced, how resources should be allocated and the way performance should be measured and analysed.

  The property profession in ths country has been slow to respond to these ideas not only because of the high level of mathematics involved but also because property has in the past been regarded as outside mainstream investment and therefore required a special approach. Fortunately, this position is changing and will no doubt continue to do so as pressure is placed on funds to achieve superior performance.

  This chapter presents a non-technical overview of the most significant develpments in Portfolio Theory and demonstrates their importance to the property sector. It is considered in three parts.

  Part 1 covers the background to Portfolio Theory and its development into capital asset pricing. It stresses the importance of market risk and shows that investors are not compensated for all the risk they take on.

  Part 2 develops the ideas in Part 1 and shows that rational investors will wish to maximise net present value and that this approach is wholly consistent with the concept of utility maximisation. The correct valuations of assets are shown to be present values and the quality of a valuation depends on the available subset of information. The implications of this approach on market efficiency are also discussed.

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  eBook - ePub

  Islamic Capital Markets

  Theory and Practice

  • Noureddine Krichene(Author)
  • 2012(Publication Date)
  • Wiley

    (Publisher)

  Chapter 2

  Portfolio Theory and Risk–Return Tradeoff

  The purpose of this chapter is to analyze risk–return tradeoff and capital asset pricing in the context of portfolio diversification theory. The chapter describes market uncertainty and its measurement. It presents the portfolio diversification theory; it describes the mean-variance efficiency frontier, the investor’s risk preferences, and the portfolio diversification model. It addresses portfolio diversification in a model of two risky assets, and a model of a riskless asset and a risky market portfolio. The chapter defines the capital market line and exposes the two-fund theorem. It defines the notions of diversifiable and nondiversifiable risk and presents the capital asset pricing model (CAPM). It discusses the concepts of market security line and the characteristic line.

  Diversification is a main foundation of risk–return analysis. A highly diversified portfolio of assets reduces risk. Diversification does not seek to increase return irrespective of risk or minimize risk irrespective of return. Instead, it aims at maximizing expected return for a target risk or minimizing risk for a target expected return, or equivalently selecting a portfolio on the mean-variance efficiency frontier. The CAPM involves a tradeoff between risk and return; higher return may require higher risk. The CAPM, based on diversification theory, determines the required expected return of a stock and depends on three main variables, which are the risk-free return, the expected return of a market portfolio, and the beta risk of the stock. The latter is defined as the contribution of a stock to the risk of a market portfolio and could be positive or negative. A main feature of the CAPM is that investors use only beta risk of a stock, and not the standalone risk, to price a stock. Diversifiable risk does not affect stock price. The expected return of a stock is equal to the risk-free rate plus a risk premium that depends on the market price of risk and the beta risk. The higher the beta risk of a stock, the higher the risk premium required by investors to buy the stock.

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  eBook - ePub

  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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  eBook - PDF

  Quantitative Equity Portfolio Management

  Modern Techniques and Applications

  • Edward E. Qian, Ronald H. Hua, Eric H. Sorensen(Authors)
  • 2007(Publication Date)
  • Chapman and Hall/CRC

    (Publisher)

  23 C H A P T E R 2 Portfolio Theory T he traditional objective of active portfolio management is to consistently deliver excess return against a benchmark index with a given amount of risk. The benchmark in question could be one of the traditional market indices, such as the Standard & Poor’s (S&P) 500 Index and the Russell 2000 Index, or a cash return, such as Treasury bill rate, or LIBOR, in the case of market-neutral hedge funds. To be successful, quantitative equity managers must rely on four key components to their investment process. First and foremost on the list is an alpha model, which predicts the relative returns of stocks within a specified investment. The sec-ond component is a risk model that estimates the risks of individual stocks and the return correlations among different stocks. The third piece is a portfolio construction methodology to combine both return forecasts and risk forecasts to form an optimal portfolio. Lastly, one must have the port-folio implementation process in place to execute the trades. We present the portfolio construction methodology in this chapter. Risk models, alpha models, and portfolio implementations are introduced in later chapters. Ever since the seminal work by Markowitz (1959), the mean–variance optimization has served as the workhorse for many areas of quantitative finance, including asset allocation, equity, and fixed income portfolio management. It finds the appropriate portfolio weights by solving an opti-mization problem. There could be several versions of this optimization: one to maximize expected portfolio return for a given level of risk, and another to minimize portfolio variance for a required expected return. Yet another version is to maximize an objective function, that is, the expected portfolio return minus a multiple (risk-aversion parameter) of < Quantitative Equity Portfolio Management the portfolio variance.

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  eBook - PDF

  Openend Investment Fund

  • D. C. Corner, D C Corner(Authors)
  • 2019(Publication Date)
  • Taylor & Francis

    (Publisher)

  3 Portfolio Theory and Investment Funds I. INTRODUCTION Although investment funds particularly those of the closed-end variety, have been about for over a century, it is only during the last two decades that a substantial volume of theoretical justification for their existence has come into being. In essence, their justification as a medium of investment, particularly for small investors, is that purchase of a share in an investment fund enables the investor both to achieve a higher rate of return and to run less risk than he might otherwise do. Risk reduction is achieved through the existence of many shares in the fund's portfolio. The principle of balancing rate of return and risk is basic to the whole process of investment decisions in the world's capital markets. Maximum diversifi-cation would clearly be achieved by holding some of every share in the capital market; but, in the case of the world's major capital markets, this is obviously impossible for the bulk of investors, be they individuals or institutions. Indeed, such a portfolio, with share-holdings weighted according to their market capitalisation, would give precisely the market rate of return. With portfolios comprising a mixture of liquid assets (say cash) and all securities, there would be a reduction in both the rate of return, since none can be achieved by holding cash, and the risk of the portfolio as a whole, since, in the absence of inflation cash is a riskless asset. Indeed, it is by 'going liquid' and holding part of the fund's assets in cash that portfolio managers attempt to reduce the risk of asset loss during a bear market. It is as well then, in setting out to examine the portfolio behaviour of · investment funds, to consider just how diversification may reduce risk.

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  eBook - ePub

  The Investment Advisor Body of Knowledge + Test Bank

  Readings for the CIMA Certification

  • (Author)
  • 2015(Publication Date)
  • Wiley

    (Publisher)

  Fundamental factor models use company and industry attributes and market data as raw descriptors. Examples are price/earnings ratios, book/price ratios, estimated economic growth, and trading activity. The inputs into a fundamental factor model are stock returns and the raw descriptors about a company. Those fundamental variables about a company that are pervasive in explaining stock returns are then the raw descriptors retained in the model. Using cross-sectional analysis, the sensitivity of a stock's return to a raw descriptor is estimated. There are several fundamental factor models available from vendors.

  Summary

  This part explains the implications of modern Portfolio Theory as formulated by Markowitz (1952), a theory that deals with the construction of Markowitz efficient portfolios by rational risk-averse investors. Once a risk-free asset is introduced, the new efficient frontier is the capital market line, which represents a combination of a risk-free asset and the market portfolio. The capital asset-pricing model is an economic theory that describes the relationship between risk and expected return, or, equivalently, it is a model for the pricing of risky securities. The CAPM asserts that the only risk that is priced by rational investors is systematic risk, because that risk cannot be eliminated by diversification. Essentially, the CAPM says that the expected return of a security or a portfolio is equal to the rate on a risk-free security plus a risk premium. The risk premium in the CAPM is the product of the quantity of risk times the market price of risk.

  The beta of a security or portfolio is an index of the systematic risk of the asset and is estimated statistically. Historical beta is calculated from a time series of observations on both the asset's return and the market portfolio's return. This assumed relationship is called the characteristic line and is not an equilibrium model for predicting expected return, but rather a description of historical data.

  There have been numerous empirical tests of the CAPM, and, in general, these have failed to fully support the theory. Roll (1977) criticized these studies because of the difficulty of identifying the true market portfolio. Furthermore, Roll asserts that such tests are not likely to appear soon, if at all.

  The arbitrage pricing theory is developed purely from arbitrage arguments. It postulates that the expected return on a security or a portfolio is influenced by several factors. Proponents of the APT model cite its less restrictive assumptions as a feature that makes it more appealing than the CAPM. Moreover, testing the APT model does not require identification of the “true” market portfolio. It does, however, require empirical determination of the factors because they are not specified by the theory. Consequently, the APT model replaces the problem of identifying the market portfolio in the CAPM with the problem of choosing and measuring the underlying factors.

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  Investments

  Analysis and Management

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

    (Publisher)

  The relevant risk of an individual stock is its contribution to the riskiness of a well-diversified portfolio. The return that should be expected on the basis of this contribu-tion can be estimated by the capital asset pricing model, which we consider in Chapter 9. Summary • Markowitz Portfolio Theory provides a means to select optimal portfolios based on using the full information set about securities. • The expected returns, standard deviations, and correlation coefficients are inputs in the Markowitz analysis. Therefore, the portfolio weights are the vari-able manipulated to determine efficient portfolios. • An efficient portfolio has the highest expected return for a given level of risk, or the least risk for a given level of expected return. • The Markowitz analysis determines the set of efficient portfolios, all of which are equally desirable. The efficient set is an arc in expected return—standard deviation space. • The efficient frontier captures the optimal potential portfolios that exist from a given set of securities. Indifference curves express investor preferences. • The optimal portfolio for a risk-averse investor occurs at the point of tangency between the investor’s highest indifference curve and the efficient set of port-folios. Total risk Risk of portfolio (standard deviation of return) Unsystematic risk Systematic risk 0 10 20 30 40 Number of securities in portfolio 50 1990s 1960s FIGURE 8.6 Diversification and the number of securities Source : From “How Much Diversification is Enough!” by Burton Malkiel from the CFA Institute Conference and Pro-ceedings EQUITY PORTFOLIO CONSTRUCTION. Copyright © 2002, CFA Institute. Reproduced and Republished from Equity Portfolio Construction with Permission from CFA Institute. All Rights Reserved.

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  Portfolio Theory and Performance Analysis

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

    (Publisher)

  If investors want a portfolio with a low level of total risk, then only a small amount of active management is used. As investors in- crease their tolerance for risk, more active management can be used in the portfolio. Portfolio 204 Portfolio Theory and Performance Analysis optimisation takes place in two steps. First, a long-run benchmark portfolio is chosen based on the risk–return relationships for bearing systematic risk. Then, a decision is made on how to structure the portfolio using a combination of passive and actively managed strategies. We also find the same idea in the core–satellite portfolio described in Scherer (2002). Core– satellite investing involves separating portfolio management into a passive part, called the core of the portfolio, and an active part, made up of one or more satellites of active managers. The optimal allocation between the core and the satellites will depend on the level of risk tolerance. The case of international portfolios 9 In the case of international investment, asset allocation involves, above all, dividing the portfolio between the different countries. This decision, which determines the largest share of portfolio performance, is based on market indices representing each country and the levels of exchange rates between the different countries. Exchange rate forecast models were presented in Chapter 2. Observing the differences compared with the equilibrium values, along with the predicted evolution of macroeconomic variables such as inflation, growth and interest rates, allows us to forecast the evolution of the currency markets and determine, for a given period, the most favourable markets. The methods for allocating the asset classes, presented in the national case, are then applied for each country. The investment decisions on assets and currencies can be dissociated from each other, which leads, depending on the case, to portfolios that are globally hedged, unhedged, or partially hedged against exchange rate risk.

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