Multiple-Factor models Two-Factor models Assume that the return-generating process contains two factors. =a; +b,F1+b,2 F2t +eir r=a+b,GDi+b2INF +et
Multiple-Factor Models • Two-Factor Models – Assume that the return-generating process contains two factors. it i i t i t it r = a +b F +b F + e 1 1 2 2 t t t t r = a + b GDP + b INF + e 1 2
Multiple-Factor models k The second equation provides a two-factor model of a company's stock, whose returns are affected by expectations concerning both the growth rate in gdP and the rate of inflation K Page 301: Figure 11.2 K To this scatter of points is fit a two- dimensional plane by using the statistical technique of multiple-regression analysis
Multiple-Factor Models «The second equation provides a two-factor model of a company’s stock, whose returns are affected by expectations concerning both the growth rate in GDP and the rate of inflation. «Page 301: Figure 11.2 «To this scatter of points is fit a twodimensional plane by using the statistical technique of multiple-regression analysis
Multiple-Factor models Four parameters need to be estimated for each security with the two-factor model: a, bil, bi2, and the standard deviation of the random error term For each of the factors, two parameters need to be estimated. These parameters are the expected value of each factor and the variance of each factor. Finally, the covariance between factors
Multiple-Factor Models – Four parameters need to be estimated for each security with the two-factor model: ai , bi1, bi2, and the standard deviation of the random error term. – For each of the factors, two parameters need to be estimated. These parameters are the expected value of each factor and the variance of each factor. Finally, the covariance between factors