One-Factor models Expected return ri=atb. F Variance 22 b2 or+O Covariance pp
One-Factor Models – Expected return – Variance – Covariance ri = ai + bi F 2 2 2 2 i = bi F + ei 2 ij = bi bj F
One-Factor models Two important features of one-factor model The tangency portfolio is easy to get k The returns on all securities respond to a single common factor greater simplifies the task of identifying the tangency portfolio. The common responsiveness of securities to the factor eliminates the need to estimate directly the covariances between the securities k The number of estimates: 3N+2
One-Factor Models • Two important features of one-factor model – The tangency portfolio is easy to get. «The returns on all securities respond to a single common factor greater simplifies the task of identifying the tangency portfolio. «The common responsiveness of securities to the factor eliminates the need to estimate directly the covariances between the securities. «The number of estimates: 3N+2
One-Factor models The feature of diversification is true of any one-factor model. Factor risk: (bi02 K Nonfactor risk k Diversification leads to an averaging of factor risk k Diversification reduces nonfactor risk
One-Factor Models – The feature of diversification is true of any one-factor model. «Factor risk: «Nonfactor risk: «Diversification leads to an averaging of factor risk «Diversification reduces nonfactor risk ( ) 2 2 bi F 2 ei
One-Factor models OD=bDO+O where X:b X ∑() oD1+oe2 +o2
One-Factor Models + + + = = = = = + = = = N N N b X b X b e e eN N i ep ei N i ep i ei N i p i i p p F ep 2 2 2 2 1 1 2 2 2 1 2 2 2 1 2 2 2 2 1 1 where:
Multiple-Factor models The health of the economy effects most firms, but the economy is not a simple, monolithic entity. Several common influences with pervasive effects might be identified The growth rate of gDP The level of interest rate The inflation rate The level of oil price
Multiple-Factor Models • The health of the economy effects most firms, but the economy is not a simple, monolithic entity. Several common influences with pervasive effects might be identified – The growth rate of GDP – The level of interest rate – The inflation rate – The level of oil price