Lecture Essentials of corporate finance (2/e) – Chapter 11: Risk and return

Chapter 11 introduces you to risk and return. After completing this unit, you should be able to: Know how to calculate expected returns, understand the impact of diversification, understand the systematic risk principle, understand the security market line, understand the risk-return trade-off.

Risk and return Chapter 11 Key concepts and skills • Know how to calculate expected returns • Understand the impact of diversification • Understand the systematic risk principle • Understand the security market line • Understand the risk–return trade-off Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E Allen and Abhay K Singh 11-2 Chapter outline • Expected returns and variances • Portfolios • Announcements, surprises and expected returns • Risk: Systematic and unsystematic • Diversification and portfolio risk • Systematic risk and beta • The security market line (SML) • The SML and the cost of capital: A preview Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E Allen and Abhay K Singh 11-3 Expected returns • Expected returns are based on the probabilities of possible outcomes • In this context, ‘expected’ means average if the process is repeated many times • The ‘expected’ return does not even have to be a possible return E ( R) n pi Ri i • Where: – pi = the probability of state ‘I’ occurring – Ri = the expected return on an asset in state i Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E Allen and Abhay K Singh 11-4 Expected returns—Example • Suppose you have predicted the following returns for shares A and B in three possible states of nature What are the expected returns? E(R) State (i) Recession Neutral Boom E(R) Stock A E(Ra) -20% 15% 35% 25% p(i) 0.25 0.50 0.25 1.00 Stock B E(Rb) 30% 15% -10% 20% n E( R ) pi Ri i Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E Allen and Abhay K Singh 11-5 Expected returns— Example (cont.) E(R) State (i) Recession Neutral Boom E(R) p(i) 0.25 0.50 0.25 1.00 Stock A E(Ra) p(i) x E(Ra) -20% -5.0% 15% 7.5% 35% 8.8% 11.3% Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E Allen and Abhay K Singh Stock B E(Rb) p(i) x E(Rb) 30% 7.5% 15% 7.5% -10% -2.5% 12.5% 11-6 Variance and standard deviation • Variance and standard deviation still measure the volatility of returns • Using unequal probabilities for the entire range of possibilities • Weighted average of squared deviations • Standard deviation = square root of variance σ2 n pi ( Ri E ( R)) i Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E Allen and Abhay K Singh 11-7 Variance and standard deviation (cont.) State (i) Recession Neutral Boom p(i) 0.25 0.50 0.25 1.00 Expected Return Variance Standard Deviation State (i) Recession Neutral Boom p(i) 0.25 0.50 0.25 1.00 Expected Return Variance Standard Deviation E(R) -20% 15% 35% Stock A DEV^2 10% 0% 6% x p(i) 0.0244141 0.0007031 0.0141016 11.3% 0.0392188 19.8% E(R) 30% 15% -10% Stock B DEV^2 3% 0% 5% x p(i) 0.0076563 0.0003125 0.0126563 12.5% Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E Allen and Abhay K Singh 0.0206 14.4% 11-8 Variance and standard deviation—Another example • Consider the following information: State – Boom – Normal – Slow down – Recession Probability 25 50 15 10 KBC Ltd 15 08 04 -.03 • What is the expected return? • What is the variance? • What is the standard deviation? Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E Allen and Abhay K Singh 11-9 Variance and standard deviation—Another example: Solution KBC Ltd State (i) p(i) Boom 0.25 Normal 0.50 Slowdown 0.15 Recession 0.1 E(R) 1.00 Expected Return Variance Standard Deviation E(Ra) p(i) x E(Ra) 15% 3.8% 8% 4.0% 4% 0.6% -3% -0.3% 8.050% 8.05% Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E Allen and Abhay K Singh DEV^2 0.483% 0.000% 0.164% 1.221% p(i)xDEV^2 0.001207563 0.000000125 0.000246038 0.001221025 0.00267475 0.00267475 0.051717985 11-10 Example: Work the Web • Many sites provide betas for companies • Yahoo! Finance provides beta, plus a lot of other information, under its profile link • Click on the information icon to go to Yahoo! Finance – Enter a ticker symbol and get a basic quote Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al – Click on key Slides prepared by David E Allenstatistics and Abhay K Singh 11-34 Total vs systematic risk • Consider the following information: Standard deviation Beta – Security C – Security K 20% 30% 1.25 0.95 • Which security has more total risk? • Which security has more systematic risk? • Which security should have the higher 11-35 expected return? Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E Allen and Abhay K Singh Example: Portfolio betas Consider the example involving four securities on slide 11-13 Portfolio Beta Dollars % of Pf Asset Invested w(j) Double Click $2,000 0.13333 Coca Cola $3,000 0.2 Intel $4,000 0.26667 Keithley Industries $6,000 0.4 $15,000 Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E Allen and Abhay K Singh Beta 4.03 0.84 1.05 0.59 w(j) x Beta( Rj ) 0.53733 0.168 0.28 0.236 1.22133 11-36 Beta and the risk premium • Remember that the Risk premium = Expected return – Risk-free rate • The higher the beta, the greater the risk premium should be • Can we define the relationship between the risk premium and beta so that we can estimate the expected return? – YES! Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E Allen and Abhay K Singh 11-37 Example: Portfolio expected returns and betas Expected Return 30% 25% E(RA) 20% 15% 10% Rf 5% 0% 0.5 1.5 A 2.5 Beta Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E Allen and Abhay K Singh 11-38 Reward-to-risk ratio • Reward-to-risk ratio: E ( Ri ) R f i • = Slope of line on graph • In equilibrium, ratio should be the same for all assets • When E(R) is plotted against β for all assets, the result should be a straight line Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E Allen and Abhay K Singh 11-39 Market equilibrium • In equilibrium, all assets and portfolios must have the same reward-to-risk ratio • Each ratio must equal the reward-torisk ratio for the market E ( R A ) Rf E ( RM Rf ) A Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E Allen and Abhay K Singh M 11-40 Market equilibrium Figure 11.3 Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E Allen and Abhay K Singh 11-41 Security market line • The security market line (SML) is the representation of market equilibrium • The slope of the SML = reward-to-risk ratio: (E(RM) – Rf) / M • Slope = E(RM) – Rf = market risk premium – Since of the market is always 1.0 Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E Allen and Abhay K Singh 11-42 Security market line Figure 11.4 Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E Allen and Abhay K Singh 11-43 Capital asset pricing model • The capital asset pricing model (CAPM) defines the relationship between risk and return • E(RA) = Rf + A(E(RM) – Rf) • If we know an asset’s systematic risk, we can use the CAPM to determine its expected return • This is true whether we are talking about financial assets or physical assets 11-44 Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E Allen and Abhay K Singh Factors affecting expected return E ( Ri ) Rf E ( RM ) R f i • Pure time value of money—measured by the risk-free rate • Reward for bearing systematic risk— measured by the market risk premium • Amount of systematic risk—measured by beta Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E Allen and Abhay K Singh 11-45 Example: CAPM • Consider the betas for each of the assets given earlier If the risk-free rate is 6.15% and the market risk premium is 9.5%, what is the expected return for each? CAPM Example Rf=6.15% Risk Premium=9.5% Expected Return Asset Double Click Coca Cola Intel Keithley Industries Beta 4.03 0.84 1.05 0.59 Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E Allen and Abhay K Singh 44.435 14.13 16.125 11.755 11-46 Quick quiz • How you compute the expected return and standard deviation for an individual asset? For a portfolio? • What is the difference between systematic and unsystematic risk? • What type of risk is relevant for determining the expected return? • Consider an asset with a beta of 1.2, a risk-free rate of 5% and a market return of 13% – What is the reward-to-risk ratio in equilibrium? – What is the expected return on the asset? Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E Allen and Abhay K Singh 11-47 Chapter 11 END 11-48 ... collection of assets • An asset’s risk and return is important in how it affects the risk and return of the portfolio • The risk? ? ?return trade-off for a portfolio is measured by the portfolio expected return. .. systematic and unsystematic risk? • What type of risk is relevant for determining the expected return? • Consider an asset with a beta of 1.2, a risk- free rate of 5% and a market return of 13% – What... the risk? ? ?return trade-off Copyright ©2011 McGraw-Hill Australia Pty Ltd PPTs t/a Essentials of Corporate Finance 2e by Ross et al Slides prepared by David E Allen and Abhay K Singh 11-2 Chapter