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