Slide 1TopicsSlide 3Beta: Measure of Market RiskRisk Analysis: RecapQuestionBetaPossible Betasb = 1b > 1b < 1Two Known BetasBeta ExamplesBeta from Linear RegressionLinear Regression: ExampleLinear Regression: ExampleBeta FormulaSlide 18The Capital Asset Pricing ModelSecurity Market LineBuilding the SML▪Using the SML▪The CAPM EquationCAPM DataThe CAPM Equation: ExamplesThe CAPM Equation: ExamplesRisk Analysis: RecapProjectExcel: Linear RegressionExcel: Linear RegressionExcel: Linear RegressionExcel: Linear RegressionExcel: Linear RegressionExcel: Linear RegressionExcel: Linear RegressionExcel: Linear RegressionExcel Features: Linear Regression1 of 3711:08 AMTopic 12: Risk and Return IIILarry Schrenk, InstructorFIN 365 Business Finance2 of 3711:08 AMTopics•Measurement of Market Risk•The Capital Asset Pricing Model (CAPM)•Project3 of 3711:08 AMMeasurement of Market Risk4 of 3711:08 AMBeta: Measure of Market Risk•Standard deviation failed–We need a new measure.•Beta (b)•Beta measures–Sensitivity of changes in the return of an asset to changes in the market.5 of 3711:08 AMRisk Analysis: Recap1. Risk Exposure: Market Risk –Not Return Volatility/Total Risk2. Risk Measure: Beta (b)–Not Standard Deviation/Variance3. Risk Price: ???6 of 3711:08 AMQuestion•Measuring of Market Risk•If the market were to go up by 10%, how much would a particular stock approximately change?7 of 3711:08 AMBeta•Measures average change in return to changes in the market•Sensitivity of stock return to market return•‘Multiplier’•Correct approach to step two: Measure risk.8 of 3711:08 AMPossible BetasMarket (b =1)b >1b < 19 of 3711:08 AMb = 1•Return moves with the market•Same sensitivity to market risk as the market as a whole•Average sensitivity to market risk•Implication–Stock return = market return –Stock return = average return on market10 of 3711:08 AMb > 1•Return moves more than the market•Greater sensitivity to market risk than the market as a whole•High sensitivity to market risk•Implication–Stock return > market return –Stock return > average return on market11 of 3711:08 AMb < 1•Return moves less than the market•Less sensitivity to market risk than the market as a whole. •Low sensitivity to market risk•Implication–Stock return < market return –Stock return < average return on market12 of 3711:08 AMTwo Known Betas•The market portfolio has beta of 1– bM = 1–The market moves with itself•Risk free assets have a beta of 0– brf = 0–Risk free  return is pre-determined–Pre-determined  not sensitive to changes in the market13 of 3711:08 AM•IBM 0.76•Wal-Mart 0.20•Disney 1.15•Harley-Davidson 2.33•PEPCO 0.56•Dell 1.35•Microsoft 0.98Beta Examples14 of 3711:08 AMBeta from Linear Regression•Independent variable: Market return•Dependent variable: Stock return•Slope: Beta15 of 3711:08 AMLinear Regression: ExampleSlope = b16 of 3711:08 AMLinear Regression: Example•Intercept 0.02•Coefficient (Beta) 1.20•R20.30•Standard Error 0.0717 of 3711:08 AMBeta Formula•There is also a formula for beta:,2i MiMsbs=bss,2 = Beta of Stock i = Covariance between Stock i and the Market = Variance of the Marketii MM18 of 3711:08 AMThe Capital Asset Pricing Model (CAPM)19 of 3711:08 AMThe Capital Asset Pricing Model•Risk Analysis: Steps 1 & 2 Complete1. Identify Risk: Market Risk2. Measure Risk: Beta•Step 3: Price Risk–What return should an investor expect from a stock with a beta of 0.9?20 of 3711:08 AMSecurity Market Line•Security Market Line (SML)–Graphing the relationship between beta and return•Begin with the two points we know:Return BetaMarket rM1Risk Free Asset rf021 of 3711:08 AMBuilding the SML▪BetaReturnReturnrMrf0 1Risk Free AssetMarketWe know two points.Where would we find portfolios that contain combinations of the risk free asset and the market?22 of 3711:08 AMUsing the SML▪BetaReturnReturnrMrf0 1What would happen if there were a stock below the line?What would happen if there were a stock above the line?Market equilibrium forces all stocks to be on the line, which is called the Security Market Line (SML).SML23 of 3711:08 AMThe CAPM Equation•CAPM equation–Formula for the SML–Firm Data•Beta–Market Data•The risk free rate•The return on the market[ ]( )i f i M fE r r r rb= + -[ ]i fi ME r = Expected Return on Stock i; r = Risk-Free Rateβ = Beta of Stock i; r = Return on the Market24 of 3711:08 AMCAPM Data•Beta –Linear regression–Firm stock return on market return (S&P 500)•Risk free rate–Treasury security –Maturity = CAPM time horizon•Return on the market–Average return on a market portfolio (S&P 500)25 of 3711:08 AMThe CAPM Equation: Examples•Use the following, to find the expected return:•rf = 4.5%•rM = 12.3%–Find the expected return on the following three stocks:• bA = 1.02• bB = 0.89• bC = 1.3426 of 3711:08 AMThe CAPM Equation: Examples[ ]( )[ ]( )[ ]( )[ ]( )0.045 1.02 0.123 0.045 12.46%0.045 0.89 0.123 0.045 11.44%0.045 1.34 0.123 0.045 14.95%i f i M fABCE r r r rE rE rE rb= + -= + - == + - == + - =27 of 3711:08 AMRisk Analysis: Recap1. Risk Exposure: Market Risk –Not Return Volatility/Total Risk2. Risk Measure: Beta (b)–Not Standard Deviation/Variance3. Risk Price: CAPMDone!28 of 3711:08 AM•Data already downloaded•Find the beta for the stock of your firm–Linear regression: Firm versus S&P 500•Calculate the CAPM expected returnProject29 of 3711:08 AMExcel: Linear Regression•Linear regression –Best fit line –beta (b) of a firm’s equity•Example–Beta of MMM –Independent variable (x-axis)•S&P 500 as proxy for the market–Dependent variable (y axis) •Return on MMM30 of 3711:08 AMExcel: Linear Regression1) Returns of the assets arranged in columns:31 of 3711:08 AMExcel: Linear Regression2) Click on Data Analysis under the ‘Tools’ drop-down menu to open the Data Analysis window. Select ‘Regression’…32 of 3711:08 AMExcel: Linear Regression3) Regression box opens33 of 3711:08 AMExcel: Linear Regression4) Enter the cells for the y variable (MMM) and the x variable (S&P 500). Click on ‘Line Fit Plots’ box and ‘OK’.34 of 3711:08 AMExcel: Linear Regression5) A new worksheet will appear with the results and a graph.35 of 3711:08 AMExcel: Linear Regression6) Blue squares are data points and the pink the points on the best-fit line.36 of 3711:08 AMExcel: Linear Regression7) Same graph with a dashed line