Beta in Finance

11 Key excerpts on "Beta in Finance"

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  eBook - PDF

  Introduction to Finance

  Markets, Investments, and Financial Management

  • Ronald W. Melicher, Edgar A. Norton(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  Under the CAPM, beta (β) is the measure of an asset’s systematic risk. It is important to note that beta is a measure of relative risk and is not an absolute or total risk measure such as standard deviation. A total risk measure allows a comparison between risk and the range of probable returns. Recall the normal distribution (Figure 12.2) and the return distributions shown in Table 12.2. If we know the aver- age return and standard deviation, we can estimate the range of returns based on probabilities. Using beta, all we know is the asset’s risk relative to the market; we can’t measure the risk of the asset’s returns in an absolute sense. A beta of, say, 0.8, doesn’t give us the ability to generate a range of returns at different probability levels, as we did in Table 12.2. Beta measures the volatility or variability of an asset’s returns relative to the market portfolio. For example, if an asset’s returns are one-half as volatile as those of the market portfolio, its beta will be 0.5. That means that if the market portfolio changes in value by 10%, on average the asset’s value changes by 0.5, or 5%. If an asset’s beta equals 1.4, then the asset’s returns are 40% more volatile than the market. When the market changes in value by 10%, the asset’s value changes, on average, by 1.4 times 10%, or 14%. With this definition of beta, the beta of the market portfolio, β MKT , is 1.0. By defi- nition, the market is exactly as volatile as itself. Assets that are more volatile than the market, or equivalently, those that have greater systematic risk than the market, have betas greater than 1.0. What ever the market return, these assets’ average returns are larger in absolute value. Assets that are less volatile than the market (i.e., those with less systematic risk) have betas less than 1.0. These assets’ returns, on average, are less in absolute value than those of the market. Table 12.8 lists the historic betas for some stocks.

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  Postmodern Portfolio Theory

  Navigating Abnormal Markets and Investor Behavior

  • James Ming Chen(Author)
  • 2016(Publication Date)
  • Palgrave Macmillan

    (Publisher)

  40

  According to historians and philosophers of science, “the eminence of a scientist” can be measured “by the length of time that he holds up progress in his field.”41 By that standard, beta’s dead hand still grips mathematical finance. For a statistic that many academics dismiss as “economically meaningless,” beta remains “intensively employed” by financial professionals.42 “The CAPM is widely viewed as one of the two or three major contributions of academic research to financial managers during the postwar era.”43 Despite all the opprobrium and disqualifying evidence adduced against “standard deviation and its variations” (including beta) as measures of risk “in … non-normal distributions,” “relatively little effort has been made” to devise “a better risk measure that might resolve … dispute[s]” over the vitality of the CAPM.44 Even today, “the concept of beta risk” arguably remains “the single most important contribution of academic researchers to the financial community.”45

  Throughout the 1970s and 1980s, financial scholarship identified significant departures from capital asset pricing based exclusively on beta. Small firms (defined as firms with modest market capitalization)46 and firms with a high ratio of book value to market value47 offered returns in excess of those predicted solely by beta. In a comprehensive synthesis of these insights, Eugene Fama and Kenneth French declared in 1992 that “the relation between β and average return … is weak, perhaps nonexistent.”48 One line of scholarship, which now dominates financial literature, pursues the small size and book-to-market ratio factors that Fama and French identified as the most significant deviations from the conventional CAPM.49 Their work arguably comprises the dominant paradigm in contemporary financial literature, the Fama–French three-factor model, which explains asset prices as a function of market risk, size, and value.50

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  Finance

  A Fine Art

  • Michel Fleuriet(Author)
  • 2003(Publication Date)
  • Wiley

    (Publisher)

  On the other hand, the value of a portfolio has to include remuneration for the investor of an amount in proportion to the degree of systematic risk. 100 THE FUTURE IS THE FIELD OF PLAY Market risk is attributable to the ongoing evolution of financial assets; it dictates the fluctuation of a given security. Some stocks react strongly to market movements; others do not. The degree of sensitivity to overall market fluctuation proper to a given security is known as the beta coefficient (the estimated coefficient of independent variables in a regression equation). It historically measures the systematic risk proper to a given security on the basis of comparison between the price fluctuations of the security and the fluctuations of the financial market taken as a whole. A security with a 1.0 beta presents the same risk as the market. With a beta lower than 1.0, its risk is also lower than that of the overall market; the security attenuates market fluctuations. With a beta higher than 1.0, the security tends to amplify market fluctuations. With a beta of 2.0, the instrument moves twice as much as the market. If the market rises by 10 percent, it goes up by 20 percent; when the market falls, it goes just as precipitately down. Yet for a given security, the beta does not necessarily hold steady. In other words, it takes on different values in accordance with the periods for which it is measured. On the other hand, the beta value of a market portfolio shows more stability over the course of time. It measures the responsiveness of this portfolio to market fluctuations; it quantifies its volatility. The CAPM establishes a logical relationship between expected rate of returns and portfolio volatility. The greater the latter, the greater should be the mathematical expectancy of high returns.

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  Investments

  An Introduction

  • Herbert Mayo(Author)
  • 2016(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  When an individual constructs a well-diversified portfolio, the unsystematic sources of risk are diversified away. That leaves the systematic sources of risk as the relevant risks. A beta coefficient is a measure of systematic risk; it is an index of the volatility of the individual asset relative to the volatility of the market. The beta coef -ficient for a specific security ( b i ) is defined as follows: b i 5 Standard deviation of the return on stock i 3 Correlation coefficient between the return on the stock and the return on the market 5.6 Standard deviation of the return on the market Thus, beta depends on (1) the variability of the individual stock’s return, (2) the vari -ability of the market return (both measured by their respective standard deviations), and (3) the correlation between the return on the security and the return on the mar -ket. (The computation of beta is illustrated in the section on regression analysis in the appendix to this chapter.) The ratio of the standard deviations measures how variable the stock is relative to the variability of the market. The more variable a stock’s return (i.e., the larger the standard deviation of the stock’s return) relative to the variability of the market’s return, the greater the risk associated with the individual stock. The correlation coef -ficient indicates whether this greater variability is important. The impact of different numerical values for the standard deviation of the stock’s return and for the correlation coefficient on the beta coefficient is illustrated in Exhibituni00A05.2. The exhibit has two parts. In the first, the stock return moves exactly with the market, so the correlation coefficient between the return on the stock and the return on the market is 1.0. Since the correlation coefficient is equal to 1.0, there is a strong, positive relationship between the return on the market and the return on the stock.

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  Risk Management for the Future

  Theory and Cases

  • Jan Emblemsvag(Author)
  • 2012(Publication Date)
  • IntechOpen

    (Publisher)

  Section 4 Finance and Economics 0 Risk, Return and Market Condition: From a Three-Beta to a Functional-Beta Capital Asset Pricing Model Zudi Lu 1 and Yuchen Zhuang 2 1 Section of Statistics, School of Mathematical Sciences, The University of Adelaide 2 Department of Mathematics and Statistics, Curtin University of Technology, Perth Australia 1. Introduction In this chapter, we are concerned with how a time-varying beta is linked to market condition in capital asset pricing model (CAPM). This is a question that is related to the recent interest in these large and unexpected swings in asset values, revived after the publication of Taleb’s (2007) book, “The Black Swan: The Impact of the Highly Improbable, to explore the merits of beta in the presence of large market fluctuations (c.f., Estrada and Vargas 2011). It is well known that capital asset pricing model due to (Sharpe 1964) and (Lintner 1965) conveys important information that individual securities are priced so that their expected return will compensate investors for their expected risk. Symbolically, CAPM can be expressed in a general non-expected form as R i = α i + β i R m + ε i , (1) where R i is the return on security i , R m is the return on the market portfolio and β i is the measure of security i ’s non-diversifiable risk relative to that of the market portfolio. Here the return on individual security R i can be decomposed into the specific return, including expected specific return α i and random specific return ε i , and the systematic return, β i R m , owing to the common market return R m . In this model, the quantity β i is of particular importance, which is an alternative measure of the risk that an investor has to bear owing to the systematic market movement. In the traditional CAPM, β i is assumed to be constant. This assumption has been widely documented to be untrue in the literature.

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  eBook - ePub

  Security Analysis, Portfolio Management, and Financial Derivatives

  • Cheng-Few Lee, Joseph Finnerty, John Lee, Alice C Lee, Donald Wort(Authors)
  • 2012(Publication Date)
  • WSPC

    (Publisher)

  Table 9.1 it is clear that IBM is an offensive stock while J&J is a defensive stock.

  The CAPM has illustrated the concept that risks are associated with portfolios where the relevant (systematic) risk of an individual security is dependent upon the security’s effect on portfolio risk. Therefore, the CAPM equation represents a description of how rates of return are established in the marketplace assuming investors behave according to the assumptions of the model. Thus a stock’s beta measures its contributions to the risk of the portfolio and is therefore a measure of the stock’s riskiness relative to the market.

  In the previous section it was found that the rates of return of stock i are presumed to bear a linear relationship with the market rate of return as defined in Equation (9.11 ). Equation (9.11 ) is a fixed-coefficient market model. Following Fabozzi and Francis (1978), Sunder (1980), and Lee and Chen (1980), a random-coefficient market model can be defined as Equation (9.15a ) or Equation (9.15b ):

  in which represents the random fluctuation associated with the beta coefficient. Using the random-coefficient market model, the total risk can be decomposed into three components, as defined in Equation (9.16 ):

  in which represents an interaction risk between the market and the random fluctuation of the beta. Equation (9.16 ) is a generalized case of Equation (9.12

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  eBook - PDF

  Basic Finance

  An Introduction to Financial Institutions, Investments, and Management

  • Herbert Mayo, , , (Authors)
  • 2018(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  One measure of risk, the standard deviation , emphasizes the extent to which the return differs from the average or expected return. An alternative measure of risk, a beta coefficient , is an index of the return on an asset relative to the return on a portfolio of assets (for example, the return on a stock relative to the return on the Standard & Poor’s 500 stock index). This section con-siders the standard deviation as it is used to measure risk, while beta coefficients are explained later in the chapter. The standard deviation measures the dispersion around an average value. As applied to investments, it considers an average return and the extent to which indi-vidual returns deviate from the average. If there is very little difference between the average return and the individual returns, the dispersion will be small. If there is a Purchasing power risk Uncertainty that future inflation will erode the purchasing power of assets and income Exchange rate risk Risk of loss from changes in the value of foreign currencies Sovereign risk Risk associated with a government defaulting on its debt obligations Standard deviation Measure of dispersion around an average value; a measure of risk Beta coefficient Index of systematic risk; measure of the volatility of a stock’s return relative to the market return Copyright 2019 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 116 PART 2 Financial Tools large difference between the average return and the individual returns, the disper-sion will be large. The larger this dispersion, the greater the risk associated with the investment.

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  An Introduction to Stock Exchange Investment

  • Janette Rutterford, Marcus Davison(Authors)
  • 2017(Publication Date)
  • Red Globe Press

    (Publisher)

  A perhaps more transparent term would be enterprise beta , because this draws atten-tion to the fact that it derives from the market sensitivity of the business enterprise itself rather than from the incidental circumstances of the enterprise’s financing. If we let V = the market value of the company or enterprise E = the market value of the equity D = the market value of the debt, Such that V = E + D then we can readily capture the idea of the concentration of risk on to the shareholders’ interest in a leveraged company with the equation (7.18) In the example given in Table 7.4, we have initially assumed no leverage, and so the equity beta is equal to the asset beta, and is equal to 1. Now suppose that the company is financed instead with 50 per cent equity and 50 per cent debt, so that V/E = 2. The asset beta, reflect-ing the business risk, does not change. But the equity beta, reflecting both business and financial risk, will rise. From equation 7.18 we can estimate the revised equity beta: β E = β A × V E = 1.0 × 2 β E = 2.0 β E = β A × V E The Capital Asset Pricing Model 245 Equities 246 Adding debt to the capital structure has increased the required rate of return on equity through a higher equity beta. We can estimate the revised expected rate of return on equity: E ( R i ) = R F + β E ( E ( R M ) – R F ) = 5% + 2.0(12%) E ( R i ) = 29% The required rate of return on the company’s shares has risen from 17% to 29% to reflect the higher financial risk. Conversely, if all we have is the value of the leveraged beta, we can use the same equation to calculate the underlying unleveraged beta of a company: As we stated earlier, this simple relationship depends on our assumption that the company borrows at the risk-free rate and that its debt has no market risk at all: that is, that its debt has a beta of zero. In practice this is seldom if ever the case, so we need to modify the above equation to take account of this added complexity.

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  eBook - ePub

  Cost of Capital

  Applications and Examples

  • Shannon P. Pratt, Roger J. Grabowski(Authors)
  • 2014(Publication Date)
  • Wiley

    (Publisher)

  Studies discussed earlier suggest that rates of return are a function of more risk factors than just beta. One measure of total risk, total beta, has been discussed relative to the cost of capital for closely held businesses. We discuss total beta in Chapter 27. Adjusted Beta for Company Size and Company-specific Risk Assume that one is using the modified CAPM (Formula 10.6) to estimate the cost of equity capital. The analyst now needs to estimate the effect of modifying the CAPM model in, say, an option pricing model. The effect of adding risk premiums for company size and company-specific risk is equivalent to increasing the variability of returns, as risk is no longer measured by beta alone. The analyst can adjust beta in this way to get a modified beta or B e (beta adjusted from the modified CAPM): (Formula 13.9) where: E (R) = Expected rate of return R f = Rate of return on a risk-free security B L = Levered beta for (equity) capital RP m = Risk premium for the market RP s = Risk premium for small stocks RP c = Risk premium for company-specific risk attributable to the specific company B e = Modified or expanded beta (equity) Modified beta incorporates both the small-company risk and company-specific risk. Assuming that any other factors (which many would consider to be classified as nondiversified risk factors) are small, we can then derive variance of returns for use in option pricing models as follows: (Formula 13.10) where: σ 2 = Variance of returns for subject company stock = Variance of the returns on the market portfolio (e.g., S&P 500) = Variance of error terms Substituting modified beta B e for B L and assuming is close to zero, we get: (Formula 13.11) where σ 2 takes into account the entirety of the effect of all risk factors used in the expanded CAPM. Downside Risk Conduct a survey of the man on the street, and the common concept of risk is loss below some threshold

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  Financial Decision Making Under Uncertainty

  • ANDERSON ANDERSON WEBSTER, ANDERSON WEBSTER(Authors)
  • 2014(Publication Date)
  • Academic Press

    (Publisher)

  Part III PORTFOLIO ANALYSIS AND CAPITAL MARKET THEORY This page intentionally left blank THE CAPITAL ASSET PRICING MODEL A Multi-Beta Interpretation William F. Sharpe Stanford University I. Introduction In recent years, considerable attention has been accorded the Capital Asset Pricing Model of Sharpe [10], Lintner [4], and Mossin [7]. It suggests that in equilibrium the expected excess return on a security over and above the pure interest rate will equal some constant times its ex ante risk, measured by the security's so-called beta coefficient. The latter equals the covariance of the security's return with that of the market portfolio (consist-ing of all assets, each in proportion to total value outstanding) divided by the variance of the return on the market portfolio, where all measures refer to ex ante probability distributions. Many have used these ideas for practical investment policies. Moreover, a number of tests have been performed to determine the extent to which ex post results conform to the relationships predicted by the theory for ex ante values. In the light of empirical work to date, Black [1] has suggested a I am indebted to Professor Marcus C. Bogue of Carnegie-Mellon University for a number of suggestions on this subject. Helpful comments were also provided by Professors Paul Cootner and Robert Litzenberger of Stanford University and Professor Alan Kraus of the University of British Columbia. 127 128 William F. Sharpe zero-beta model, while Blume and Friend [3] have argued in favor of an unspecified model of market segmentation. Given this interest, it seems worthwhile to examine carefully the nature of the beta measure of risk. The following section shows that a security's beta relative to the market portfolio can be expressed as a weighted average of beta values relative to any desired number of portfolios, the collection of which equals the market portfolio.

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  Advanced Modelling in Finance using Excel and VBA

  • Mary Jackson, Mike Staunton(Authors)
  • 2006(Publication Date)
  • Wiley

    (Publisher)

  7 Asset Pricing We move from examining individual investors (a micro view) to the markets for assets and looking at the behaviour of all investors (a macro view). The crucial difference is the move from making statements about individuals to the drawing of conclusions about the behaviour of investors as a whole. It is this different focus that allows us to make statements about the pricing of financial assets. The capital asset pricing model (CAPM) was developed in the sixties by finance academics. It developed out of the mean–variance portfolio analysis described in the previous chapter. An important conclusion was that market prices reflect only part of a portfolio’s risk. The part that is priced, the market-related risk, is measured by beta. The background to the CAPM is extensively discussed in Bodie et al. (1996), Chapter 8. This chapter opens with the single-index model and illustrates the calculation of associ-ated risk measures, in particular the estimation of betas and variance–covariance matrices from the returns of individual assets. The central numerical technique is regression, which is applied to estimate the beta of an asset, i.e. the return on the asset relative to the return on the market. The betas for a set of assets are useful in their own right to describe the rela-tive responsiveness of assets to the market. However, they also facilitate the calculation of covariances via the single-index model. The EQUITY2.xls workbook contains imple-mentations of the various estimation procedures and a range of user-defined functions have been developed to reduce the computational burden of the procedures. In the previous chapter, we developed the mean–variance model of Markowitz assuming a utility function to describe the preferences of individual investors. In that analysis, the distribution of asset returns was ignored.

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