Bodie Marcus INVESTMENTS Fourth Edition Chapter 6 Single index and Multifactor Models Irwvin/McGrazo-Hill The McGraw-Hill Companies, Inc, 1999
Irwin/McGraw-Hill 10-1 © The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Single Index Single Index and Multifactor Models Multifactor Models Chapter 6 Chapter 6
Bodie Marcus INVESTMENTS Fourth Edition Adyantages of the single index mode Reduces the number of inputs for diversification ■ Portfolio of50 assets 50 expected returns 50 variances 1225 covariance too difficult a task Irwvin/McGrazo-Hill 102 The McGraw-Hill Companies, Inc, 1999
Irwin/McGraw-Hill 10-2 © The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Reduces the number of inputs for diversification. Portfolio of 50 assets ---50 expected returns; 50 variances; 1225 covariance. ---too difficult a task. Advantages of the Single Index Model Advantages of the Single Index Model
Bodie Marcus INVESTMENTS Fourth Edition Single index model (r1:r)=01+B(rm-rt)+e Risk Premium Market risk premium or Index risk premium ai= the stock's expected return if the markets excess return is zero E(rm-r=0 B (rm-r=the component of return due to movements in the market index e;firm specific component, not due to market movements,E(ei=0 Irwvin/McGrazo-Hill 103 The McGraw-Hill Companies, Inc, 1999
Irwin/McGraw-Hill 10-3 © The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus (ri - rf) = i + ßi(rm - rf) + e α i Risk Premium Market Risk Premium or Index Risk Premium i = the stock’s expected return if the market’s excess return is zero ßi(rm - rf) = the component of return due to movements in the market index E(rm - rf) = 0 ei = firm specific component, not due to market movements, E(ei)=0 α Single Index Model Single Index Model
Bodie Marcus INVESTMENTS Fourth Edition sk Premiun format Let: Ri=(r; -rp Risk premium R format m R1=c1+队(Rm)+ Irwvin/McGrazo-Hill 10-4 The McGraw-Hill Companies, Inc, 1999
Irwin/McGraw-Hill 10-4 © The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Let: Ri = (ri - rf) Rm = (rm - rf) Risk premium format Ri = αi + ßi(Rm) + ei Risk Premium Format Risk Premium Format
Bodie Marcus INVESTMENTS Fourth Edition curiO Characteristic li Excess Returns(i SCL Excess returns on market index R:=a: +BR +e Irwvin/McGrazo-Hill 10-5 The McGraw-Hill Companies, Inc, 1999
Irwin/McGraw-Hill 10-5 © The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Security Characteristic Line Security Characteristic Line Excess Returns (i) SCL . . . .. . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Excess returns on market index Ri = α i + ßiRm + ei
Bodie Marcus INVESTMENTS Fourth Edition Using the Text Example orr E xcess Excess GM Ret. Mkt Ret Jan 5.41 7.24 Feb 3.44 93 D ec 243 3.90 Me ean 60 1.75 Std dev 497 3.32 Irwvin/McGrazo-Hill 10-6 The McGraw-Hill Companies, Inc, 1999
Irwin/McGraw-Hill 10-6 © The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Jan. Feb. . . Dec Mean Std Dev 5.41 -3.44 . . 2.43 -.60 4.97 7.24 .93 . . 3.90 1.75 3.32 Excess Mkt. Ret. Excess GM Ret. Using the Text Example Using the Text Example from Table 10 from Table 10-1
Bodie Marcus INVESTMENTS Fourth Edition egression results TGM-r=a+B(rm-re) Estimated coefficient -2.590 1 1357 Std error of estimate (1.547)(0.309 Variance of residuals 12, 601 Std dev of residuals=3.550 R-SQR=0.575 Irwvin/McGrazo-Hill 107 The McGraw-Hill Companies, Inc, 1999
Irwin/McGraw-Hill 10-7 © The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Estimated coefficient Std error of estimate Variance of residuals = 12.601 Std dev of residuals = 3.550 R-SQR = 0.575 ß -2.590 (1.547) 1.1357 (0.309) rGM - rf = + ß(rm - rf) α α Regression Results Regression Results
Bodie Marcus INVESTMENTS Fourth Edition Components of risk a Market or systematic risk: risk related to the macro economic factor or market index a Unsystematic or firm specific risk: risk not related to the macro factor or market index a Total risk- Systematic t Unsystematic Irwvin/McGrazo-Hill 10-8 The McGraw-Hill Companies, Inc, 1999
Irwin/McGraw-Hill 10-8 © The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Market or systematic risk: risk related to the macro economic factor or market index Unsystematic or firm specific risk: risk not related to the macro factor or market index Total risk = Systematic + Unsystematic Components of Risk Components of Risk
Bodie Marcus INVESTMENTS Fourth Edition Measuring components of risk 0 2=B2 0m2+oe) Where 2= total variance B2 0m2=systematic variance oej unsystematic variance Irwvin/McGrazo-Hill 10-9 The McGraw-Hill Companies, Inc, 1999
Irwin/McGraw-Hill 10-9 © The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus σi2 = βi2 σm2 + σ2(ei) where; σi2 = total variance βi2 σm2 = systematic variance σ2(ei) = unsystematic variance Measuring Components of Risk Measuring Components of Risk
Bodie Marcus INVESTMENTS Fourth Edition Examining percentage of variance Total Risk= Systematic Risk Unsystematic Risk Systematic Risk/Total Risk=R2 0m202=R 82n2/(82on2+oe)=R2 Irwvin/McGrazo-Hill 10-10 The McGraw-Hill Companies, Inc, 1999
Irwin/McGraw-Hill 10-10 © The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Total Risk = Systematic Risk + Unsystematic Risk Systematic Risk/Total Risk = 2 ßi2 σ m2 / σ2 = 2 βi2 σm2 / (βi2 σm2 + σ2(ei) )= 2 Examining Percentage of Variance Examining Percentage of Variance R R R
