Corporate finance chapter 013 the capital asset pricing model

Chapter 13: The Capital Asset Pricing Model Objective •The Theory of the CAPM •Use of CAPM in benchmarking • Using CAPM to determine correct rate for discounting Chapter 13 Contents 13.1 The Capital Asset Pricing Model in Brief 13.2 Determining the Risk Premium on the Market Portfolio 13.3 Beta and Risk Premiums on Individual Securities 13.4 Using the CAPM in Portfolio Selection 13.5 Valuation & Regulating Rates of Return Introduction • CAPM is a theory about equilibrium prices in the markets for risky assets • It is important because it provides – a justification for the widespread practice of passive investing called indexing – a way to estimate expected rates of return for use in evaluating stocks and projects Specifying the Model • We also observed that in the limit as the number of securities becomes large, we obtained the formula σ portfioio = σ exemplar ρ exemplari ,exemplarj – This formula tells us that the correlations are of crucial importance in the relationship between a portfolio risk and the stock risk CAPM Formula µ m − rf µr = σ r + rf σm µ m − rf slope = σm 13.2 Determining the Risk Premium on the Market Portfolio • CAPM states that – the equilibrium risk premium on the market portfolio is the product of • variance of the market, σ2M • weighted average of the degree of risk aversion of holders of risk, A µ rm − rf = Aσ M Example: To Determine ‘A’ µ rM = 0.14, σ rM = 0.20, rf = 0.06, µ rM − rf = Aσ rM µ rM − rf ⇒ A= σ rM 0.14 − 0.06 A= = 2 0.20 CAPM Risk Premium on any Asset • According the the CAPM, in equilibrium, the risk premium on any asset is equal the product of – β (or ‘Beta’) – the risk premium on the market portfolio µ ri − rf = ( µ m − rf ) β i ⇒ µ ri = rf + ( µ m − rf ) β i Security Prices 70 60 Value 50 40 30 20 Market_Price Stock_Z_Price 10 0.000 0.083 0.167 0.250 0.333 0.417 0.500 0.583 0.667 0.750 0.833 0.917 1.000 Years Table of Prices month 10 11 12 Mkt_Price Z_Price hpr_Mkt hpr_Z 50.00 30.00 hpr_Mkt hpr_Z annual_cont_mkt annual_cont_z reg_line 55.84 33.87 11.68% 12.90% 132.55% 145.56% 176.82% 52.87 33.65 -5.32% -0.64% -65.59% -7.75% -64.54% 58.19 39.19 10.07% 16.47% 115.15% 182.98% 155.62% 60.33 41.30 3.66% 5.38% 43.19% 62.90% 67.97% 56.97 38.93 -5.57% -5.74% -68.71% -70.89% -68.35% 51.52 34.20 -9.56% -12.15% -120.56% -155.40% -131.50% 52.80 35.88 2.47% 4.91% 29.32% 57.54% 51.08% 55.04 38.24 4.24% 6.56% 49.83% 76.22% 76.06% 55.76 40.64 1.32% 6.28% 15.70% 73.08% 34.48% 62.20 46.26 11.55% 13.83% 131.12% 155.46% 175.09% 56.84 41.01 -8.62% -11.34% -108.23% -144.43% -116.49% 55.30 39.54 -2.71% -3.58% -32.93% -43.78% -24.76% an_an_fact 1.105934 1.318151 an_cont_rate 0.10069 0.27623 mu sig rho beta 10.07% 27.62% 0.259099 0.325796 0.968777 1.218157 10 Regression of Returns of Z on Market 200% 150% Return on Z 100% 50% 0% -150% -100% -50% 0% 50% -50% -100% -150% -200% Market Return 11 100% 150% Model and Measured Values of Statistical Parameters µm σm µz σz ρ β modl 15% 20% 12% 25% 90% 1.13 Meas 10% 26% 28% 33% 97% 1.22 12 Market Portfolio Security Market Line 20% Expected Risk Premium 15% 10% 5% 0% -2.0 -1.5 -1.0 -0.5 0.0 0.5 -5% -10% -15% -20% Beta (Risk) 13 1.0 1.5 2.0 The Beta of a Portfolio • When determining the risk of a portfolio – using standard deviation results in a formula that’s quite complex σ w1r1 + w2 r2 + + wn rn  =  ∑ wiσ ri  i =1,n ( ) ( + 2∑ wi w jσ ri σ r j ρ i , j i> j )     – using beta, the formula is linear β w1r1 + w2 r2 + + wn rn = w1 β r1 + w2 β r2 + + wn β rn = ∑ wi β ri i 14 Computing Beta • Here are some useful formulae for computing beta σ i , M σ iσ M ρ i , M σ i ρ i , M β i = β i,M = = = σM σM σM µ ri − rf βi = µ M − rf 15 Valuation and Regulating Rates of Return • Assume the market rate is 15%, and the riskfree rate is 5% • Compute the beta of betaful’s operations β company = wequity β equity + wbond β bond β company = 0.80 *1.3 + 0.20 * β company = 1.04 16 Valuation and Regulating Rates of Return • Beta of betaful’s operations is equal to the beta of our new operation • To find the required return on the new project, apply the CAPM µ r = rf + β ( rm − rf ) = 0.05 + 1.04( 0.15 − 0.05) = 15.4% 17 Valuation and Regulating Rates of Return • Assume that your company is just a vehicle for the new project, then the beta of your unquoted equity is β company = wequity β equity + wbond β bond 1.04 = 0.60 * β equity + 0.40 * β equity = 1.73 18 Valuation and Regulating Rates of Return • Assume that your company has an expected dividend of $6 next year, and that it will grow annually at a rate of 4% for ever, the value of a share is D1 p0 = = = $52.63 r − g 0.154 − 0.04 19 [...]... Regulating Rates of Return • Beta of betaful’s operations is equal to the beta of our new operation • To find the required return on the new project, apply the CAPM µ r = rf + β ( rm − rf ) = 0.05 + 1.04( 0.15 − 0.05) = 15.4% 17 Valuation and Regulating Rates of Return • Assume that your company is just a vehicle for the new project, then the beta of your unquoted equity is β company = wequity β equity... 2 – using beta, the formula is linear β w1r1 + w2 r2 + + wn rn = w1 β r1 + w2 β r2 + + wn β rn = ∑ wi β ri i 14 Computing Beta • Here are some useful formulae for computing beta σ i , M σ iσ M ρ i , M σ i ρ i , M β i = β i,M = 2 = = 2 σM σM σM µ ri − rf βi = µ M − rf 15 Valuation and Regulating Rates of Return • Assume the market rate is 15%, and the riskfree rate is 5% • Compute the beta of betaful’s... -150% -200% Market Return 11 100% 150% Model and Measured Values of Statistical Parameters µm σm µz σz ρ β modl 15% 20% 12% 25% 90% 1.13 Meas 10% 26% 28% 33% 97% 1.22 12 Market Portfolio Security Market Line 20% Expected Risk Premium 15% 10% 5% 0% -2.0 -1.5 -1.0 -0.5 0.0 0.5 -5% -10% -15% -20% Beta (Risk) 13 1.0 1.5 2.0 The Beta of a Portfolio • When determining the risk of a portfolio – using standard... equity + 0.40 * 0 β equity = 1.73 18 Valuation and Regulating Rates of Return • Assume that your company has an expected dividend of $6 next year, and that it will grow annually at a rate of 4% for ever, the value of a share is D1 6 p0 = = = $52.63 r − g 0.154 − 0.04 19