Chapter 7Risk and Return Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver, Australian National University 7-1 Learning Objectives • Understand how risk and return are defined and measured. • Understand the concept of risk aversion by investors. • Explain how diversification reduces risk. • Understand the importance of covariance between returns on assets to determine the risk of a portfolio. • Explain the concept of efficient portfolios. Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver, Australian National University 7-2 Learning Objectives (cont.) • Understand distinction between systematic and unsystematic risk and significance of systematic risk. • Explain the relationship between returns and risk proposed by the capital asset pricing model (CAPM). • Understand the relationship between CAPM and the Fama-French three-factor model. • Explain the development of the Fama-French three-factor model. Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver, Australian National University 7-3 1) 12 0. Assume we can assign probabilities to the possible returns — given the following set of circumstances.09 x 0.11x 0.10 x 2421) 10 0.4 (0. Australian National University 7-4 .1 (0.4) (0.2 (0. the expected return is: Example Solution E R n R P Percentage Return.1 i 1 i i E R 11% Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver.2) 11 0.2 13 0.1) (0.13 x0. Pi 9 0. Ri Probability.12 x 0.Return • There is uncertainty associated with returns on shares. 2 2 0. • Risk measured by variance — how much a particular return deviates from an expected return.000 12 0.Risk • Risk is present whenever investors are not certain about the outcome an investment will produce.10-0. which is simply the square root of the variance: 2 n Ri E R i 1 • 2 Pi Using previous example.11 0.12-0.11 0.11 0.4 0.09-0.095% Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver.1 2 2 = 0. Australian National University 7-5 .11 0.11-0.11 0.1 0.01095 1. risk is given by: Variance: 2 = 0.000 12 Standard Deviation: = 0.2 2 2 0.13-0. Use standard deviation to measure risk. Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver. 175. • Risk-averse investor: (p. 175. investor focuses only on expected return. 175.Risk Attitudes • Risk-neutral investor: (p. Australian National University 7-6 .3) – One who demands compensation in the form of higher expected returns in order to be induced into taking on more risk.3) – One whose utility is unaffected by risk.3) – One who derives utility from being exposed to risk. • Risk-seeking investor: (p. Figure 7. Figure 7. and hence. Figure 7. when chooses to invest. may be willing to give up some expected return in order to be exposed to additional risk. Australian National University 7-7 . – Rather.5 — Risk averse investor) Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver.Risk Attitudes (cont. but may take up on board if compensated with sufficient return. – This does not mean an investor will refuse to bear any risk at all. investors regards risk as something undesirable. trade-off between risk and return. (p. • Investors’ risk preferences – Indifference curve — which represents those combinations of expected return and risk that result in a fixed level of expected utility for an investor. 177. Figure 7.) • The standard assumption in finance theory is all investors are risk averse. • Now concerned about how these individual risks will interact to provide us with overall portfolio risk. Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver.Risk of Assets and Portfolios • We now know that the risk of an individual asset is summarised by standard deviation (or variance) of returns. Australian National University 7-8 . • Investors usually invest in a number of assets (a portfolio) and will be concerned about the risk of their overall portfolio. • Measuring return of portfolio: – Portfolio return (Rp) is a weighted average of all the expected returns of the assets held in the portfolio: n E Rp j 1 where: wjE Rj w j = the proportion of the portfolio invested in asset j n = the number of securities in the portfolio Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver. Australian National University 7-9 .Portfolio Theory • Assumptions: – Investors perceive investment opportunities in terms of a probability distribution defined by expected return and risk. – Investors’ expected utility is an increasing function of return and a decreasing function of risk (risk aversion). Portfolio Risk • Portfolio (comprising two assets) risk depends on : – The proportion of funds invested in each asset (w). Australian National University 7-10 . correlation ( – For a two-asset portfolio the variance is: 2 p 2 2 w1 1 2 2 w2 2 2 w1w2 1. – The relationship between each asset in the portfolio with respect to risk. 2 1 2 where: wi = the proportion of the portfolio invested in asset i i = the standard deviation of asset i ij correlation between asset i and j returns Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver. – The riskiness of the individual assets (2). Portfolio Risk and Return Measurement • Assume 60% of the portfolio is invested in security 1 and 40% in security 2. • The standard deviation is 0.0016 and 0.0036. If variances of security 1 and security 2 are 0. Australian National University 7-11 . respectively.5: Find expected return and risk of portfolio.2) is –0.12 respectively. • The expected returns of the securities are 0.024. Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver.08 and 0. and the correlation (p1. and for this reason is bounded by the range +1 to –1. the other has a propensity to do the same.Relationship Measures • Covariance: – Statistic describing the relationship between two variables. • Correlation coefficient: – Is another measure of the strength of a relationship between two variables? The correlation is equal to the covariance divided by the product of the asset’s standard deviations. the deviations tend to be of an opposite sign. xy cov x. when one of the variables takes on a value above its expected value. – If the covariance is negative. y x y • It is simply a standardisation of the covariance. – If positive. Australian National University 7-12 . Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver. Australian National University 7-13 . • r = –1 If the correlation coefficient is negative. risk is reduced even more. • The degree of risk reduction increases as the correlation between the rates of return on two securities decreases. but this is not a necessary prerequisite for diversification gains. the third term in the portfolio variance equation is reduced. Risk reduction does not occur by combining securities whose returns are perfectly positively correlated. • r = 1. • 0 < r < 1. reducing portfolio risk. Risk reduction occurs by combining securities whose returns are less than perfectly positively correlated. Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver. If the correlation coefficient is less than 1.Gains from Diversification • Diversification gain is related to correlation coefficient value. • r = +1. • With n assets. Australian National University 7-14 . • The key is the correlation between each pair of assets in the portfolio. – The two covariance terms for each pair of assets are identical. • The properties of the variance-covariance matrix are: – It will contain n2 terms.Diversification with Multiple Assets • The more assets we incorporate into the portfolio. Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver. the greater the diversification benefits are. there will be an n × n covariance matrix. – It is symmetrical about the main diagonal that contains n variance terms. Australian National University 7-15 .Diversification with Multiple Assets (cont. • The risk depends largely on the covariances between the returns on the assets. in a 50-asset portfolio there are 50 (n) variance terms and 2450 (n2 − n) covariance terms. – For example. Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver.) • For a diversified portfolio. the variance of the individual assets contributes little to the risk of the portfolio. we should think of risk as comprising: Total Risk = Systematic Risk + Unsystematic Risk • Systematic risk: Component of total risk that is due to economy-wide factors. Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver. (non-diversifiable risk) • Unsystematic risk: Component of total risk that is unique to firm and is removed by holding a well-diversified portfolio. • The returns on a well-diversified portfolio will vary due to the effects of market-wide or economy-wide factors.Systematic and Unsystematic Risk • Intuitively. • Systematic risk of a security or portfolio will depend on its sensitivity to the effects of these market-wide factors. Australian National University 7-16 . p i p • Well-diversified portfolios will be representative of the market as a whole. the relevant measure of risk is the covariance between the return on the asset and the return on the market: Cov Ri .Risk of an Individual Asset • The risk contribution of an asset to a portfolio is largely determined by the covariance between the return on that asset and the return on the holder’s existing portfolio: Cov Ri . R p i . Thus. Australian National University 7-17 . RM Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver. Australian National University 7-18 . Cov(Ri . RM M2 where: RM = return on the market portfolio Ri = return on the particular asset Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver. This is the asset’s beta (i): i Cov Ri . RM) can be scaled by dividing it by the variance of the return on the market. describing the amount of risk contributed by the security to the market portfolio.Beta Beta is a measure of a security’s systematic risk. Australian National University 7-19 . Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver.Construction of a Portfolio • The opportunity set: – The set of all feasible portfolios that can be constructed from a given set of risky assets. Australian National University 7-20 . each investor may prefer a different point along the efficient frontier.) • The efficient frontier: – Investor will try to secure a portfolio on the efficient frontier. – The efficient frontier is determined on the basis of dominance. • Investors are a diverse group and. • Investor risk preferences will determine the preferred portfolio on the efficient frontier. • A portfolio is efficient if: – No other portfolio has a higher return for the same risk. Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver.Construction of a Portfolio (cont. therefore. or – No other portfolio has a lower risk for the same return. can calculate a worst-case scenario. Australian National University 7-21 . Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver. • Using the normal distribution and the standard deviation. • Typically assumes returns are normally distributed. • Defined as ‘the worst loss that is possible under normal market conditions during a given time period’.Value at Risk (VaR) • A relatively new measure of the riskiness of an asset or portfolio. • Requires standard deviation of the return on the asset or portfolio. 29m or an investment value of $6.) • Investment of $10m in Curzon has an estimated return of zero and a standard deviation of 20% ($2m). • VaR was not used effectively by NAB in the foreign exchange scandal — poor implementation and execution. • Worst outcome under normal conditions is a loss of 1. Australian National University 7-22 . Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver.645 (from normal tables) multiplied by standard deviation of $2m. • Worst outcome is loss of $3. • Assume returns are normally distributed and bad market conditions expected 5% of the time.Value at Risk (cont.71m. Australian National University 7-23 . • Investors need to be sufficiently compensated for taking on the risks associated with the investment. Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver.The Pricing of Risky Assets • What determines the expected rate of return on an individual asset? • Risky assets will be priced such that there is a relationship between returns and systematic risk. Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver. Australian National University 7-24 . investors choose an optimal portfolio. • This can be enhanced by introducing a risk-free asset: – The opportunity set for investors is expanded and results in a new efficient frontier — capital market line (CML). • The CML represents the efficient set of all portfolios that provides the investor with the best possible investment opportunities when a riskfree asset is available.The Capital Market Line • Combining the efficient frontier with preferences. • Investors can then vary the riskiness of their portfolio investment by changing weights in the risk-free asset and portfolio M.11.) • The CML links the risk-free asset with the optimal risky portfolio (M): p. 191. • This changes their return according to the CML: E RM R f E R p R f M Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver. Figure 7.The Capital Market Line (cont. Australian National University p 7-25 . RM ) = the covariance between returns on ith risky asset and the market portfolio Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver. is given by the security market line: E RM R f cov Ri . RM E Ri R f M where: E ( Ri ) = the expected return on the ith risky asset Cov( Ri . the expected return on a risky asset i (or an inefficient portfolio). Australian National University 7-26 .The CAPM and the Security Market Line (SML) • In equilibrium. Australian National University 7-27 .RM) is the risk of an asset held as part of the market portfolio.The CAPM and the SML (cont. Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver.12 for graphical depiction of the CAPM and the SML.) • The covariance term is the only explanatory factor in the equation that is specific to asset i. • As Cov(Ri.193. • We can thus write the Security Market Line (SML) as the Capital Assets Pricing Model (CAPM) equation: E Ri • R f i E RM R f See p. Figure 7. and M is the risk of the market portfolio. beta measures the risk of i relative to the risk of the market as a whole. Australian National University 7-28 .Portfolio Beta • The systematic risk (beta) of a portfolio is calculated as the weighted average of the betas of the individual assets in the portfolio: n p wi i i 1 where: n number of assets in the portfolio wi = proportion of the current market value of portfolio p constituted by the i th asset Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver. and concerns have led to introducing new model introduction. – E(Rm): Two ways to calculate: (1) Use average return in share market index over a long period of time. eand E(Rm) – Rf: The government securities current yield whose term to maturity matches the life of the proposed project. number of years and the length of period is significant over which returns are calculated.Implementation of the CAPM • The three components of the CAMP: Rf. test and empirical studies have found problems with CAPM implementation. (2) Estimate market risk premium directly over a long period of time. – e: Use market model to estimate beta by obtaining time series data on the rates of return on shares and market portfolio. Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver. Hence. • However. Australian National University 7-29 . CAPM states the reward for bearing systematic risk is a higher expected return. so capital market will not reward investors for taking this type of firm specific risk. consistent with the idea of higher risk requires higher return. • Unsystematic risk can be diversified away.Risk. • However. Return and the CAPM • The capital market will only reward investors for bearing risk that cannot be eliminated by diversification. Australian National University 7-30 . Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver. given Roll’s critique. CAPM is a useful tool when thinking about asset returns. Australian National University 7-31 . • Most tests of the CAPM can only determine whether the market portfolio used is efficient.Tests of the CAPM • Early empirical evidence was supportive of CAPM in explaining asset pricing. • However. researchers implemented methodological refinements — CAPM seems untestable. • In response. • Roll’s critique (1977) criticised methodology of testing CAPM empirically. Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver. Fama-French Three-Factor Model • Fama and French (1992) provide evidence on factors that explain asset returns — no support for CAPM. a small minus large portfolio factor (SML) and a high minus low market to book portfolio (HML). market factor. • Fama and French (1995) leads to the most common three-factor model: E Rit R ft iM E RMt R ft iS E SMB + ih E HML • Includes the CAPM. BV/MV. support for firm size. though not definitive. Australian National University 7-32 . leverage. Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver. P/E. it suffers from difficult economic interpretation — Why do company size and BV/MV explain asset returns? • The fact that Fama-French includes market factor. • While the three-factor model is empirically robust. Australian National University 7-33 .Fama-French Three-Factor Model (cont.) • This model is supported by Australian data relative to CAPM: Gaunt (2004). along with ambiguity of role of other factors is supportive of CAPM. Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver. • The three-factor model is now very common in empirical research. – Unsystematic risk — can be diversified away. Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver. • CAPM provides the relationship between risk and expected return for risky assets. • Systematic risk of an asset is measured by the asset’s beta. – Diversification works best with negative or low positive correlations between assets and asset classes. Australian National University 7-34 .Summary • Portfolio theory: diversification reduces risk. Risk of asset is relative to market. • Risk can be divided into two categories: – Systematic risk — cannot be diversified away. there is no perfect model. return on a high minus low market to book portfolio. • Although CAPM has its shortfall. Australian National University 7-35 . – Key factors are the market excess return. it does provides some important insights into the link between risk and return.Summary (cont. measured by beta. return on a small minus large portfolio. • Fama–French three-factor model is a contemporary version of the multi-factor (APT) model. Hence.) • CAPM uses asset’s beta and assumes linear relationship between expected return and risk relative to market. Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by Peirson Slides prepared by Farida Akhtar and Barry Oliver.
Report "Peirson Business Finance10e PowerPoint 07"