Tài chính doanh nghiệp - Chapter 10: Index models

Chapter 10Index ModelsReduces the number of inputs for diversification.Easier for security analysts to specialize.Advantages of the Single Index Modelri = E(Ri) + ßiF + eßi = index of a securities’ particular return to  the factorF= some macro factor; in this case F is unanticipated movement; F is commonly related to security returnsAssumption: a broad market index like the S&P500 is the common factor.Single Factor Model(ri - rf) = i + ßi(rm - rf) + eiaRisk PremMarket Risk Prem or Index Risk Premi= the stock’s expected return if the market’s excess return is zeroßi(rm - rf) = the component of return due to movements in the market index(rm - rf) = 0 ei = firm specific component, not due to market movementsaSingle Index ModelLet: Ri = (ri - rf) Rm = (rm - rf)Risk premiumformatRi = i + ßi(Rm) + eiRisk Premium FormatSecurity Characteristic LineExcess Returns (i)SCL.................................................Excess returnson market indexRi =  i + ßiRm + ei...Jan.Feb...DecMeanStd Dev5.41-3.44..2.43-.604.977.24.93..3.901.753.32ExcessMkt. Ret.ExcessGM Ret.Using the Text Example from Table 10-1Estimated coefficientStd error of estimateVariance of residuals = 12.601Std dev of residuals = 3.550R-SQR = 0.575ß-2.590(1.547)1.1357(0.309)rGM - rf = + ß(rm - rf)Regression ResultsMarket 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 + UnsystematicComponents of Riski2 = i2 m2 + 2(ei) where;i2 = total variancei2 m2 = systematic variance2(ei) = unsystematic varianceMeasuring Components of RiskTotal Risk = Systematic Risk + Unsystematic RiskSystematic Risk/Total Risk = 2 ßi2  m2 / 2 = 2 i2 m2 / i2 m2 + 2(ei) = 2Examining Percentage of VarianceIndex Model and DiversificationRisk Reduction with DiversificationNumber of SecuritiesSt. DeviationMarket RiskUnique Risks2(eP)=s2(e) / nbP2sM2Industry Prediction of BetaMerrill Lynch ExampleUse returns not risk premiumsa has a different interpretationa = a + rf (1-b)Forecasting beta as a function of past betaForecasting beta as a function of firm size, growth, leverage etc.