Modern Portfolio Theory TThe factor models and The Arbitrage Pricing Theory Chapter 8 By ding zhaoyong
Modern Portfolio Theory The Factor Models and The Arbitrage Pricing Theory Chapter 8 By Ding zhaoyong
Return-generating Process and factor models Return-generating process Is a statistical model that describe how return on a security is produced. The task of identifying the Markowitz efficient set can be greatly simplified by introducing this process. The market model is a kind of this process, and there are many others
Return-generating Process and Factor Models • Return-generating process – Is a statistical model that describe how return on a security is produced. – The task of identifying the Markowitz efficient set can be greatly simplified by introducing this process. – The market model is a kind of this process, and there are many others
Return-generating Process and factor models Factor models These models assume that the return on a security is sensitive to the move ments of various factors or indices In attempting to accurately estimate expected returns, variances, and covariances for securities multiple factor models are potentially more useful than the market model
Return-generating Process and Factor Models • Factor models – These models assume that the return on a security is sensitive to the movements of various factors or indices. – In attempting to accurately estimate expected returns, variances, and covariances for securities, multiplefactor models are potentially more useful than the market model
Return-generating Process and factor models Implicit in the construction of a factor model is the assumption that the returns on two securities will be correlated only through common reactions to one or more of the specified in the model. Any aspect of a security's return unexplained by the factor model is uncorrelated with the unique elements of returns on other securities
Return-generating Process and Factor Models – Implicit in the construction of a factor model is the assumption that the returns on two securities will be correlated only through common reactions to one or more of the specified in the model. Any aspect of a security’s return unexplained by the factor model is uncorrelated with the unique elements of returns on other securities
Return-generating Process and factor models A factor model is a powerful tool for portfolio management. It can supply the information needed to calculate expected returns, variances, and covariances for every security, which are the necessary conditions for determining the curved markowitz efficient set k It can also be used to characterize a portfolios sensitivity to movement in the factors
Return-generating Process and Factor Models – A factor model is a powerful tool for portfolio management. «It can supply the information needed to calculate expected returns, variances, and covariances for every security, which are the necessary conditions for determining the curved Markowitz efficient set. «It can also be used to characterize a portfolio’s sensitivity to movement in the factors
Return-generating Process and factor models Factor models supply the necessary level of abstraction in calculating covariances The problem of calculating covariances among securities rises exponentially as the number of securities analyzed ncrease Practically, abstraction is an essential step in identifying the markowitz set
Return-generating Process and Factor Models • Factor models supply the necessary level of abstraction in calculating covariances. – The problem of calculating covariances among securities rises exponentially as the number of securities analyzed increase. – Practically, abstraction is an essential step in identifying the Markowitz set
Return-generating Process and factor models Factor models provide investment managers with a framework to identify important factors in the economy and the marketplace and to assess the extent to which different securities and portfolios will respond to changes in these factors a primary goal of security analysis is to determine these factors and the sensitivities of security return to movements in these factors
Return-generating Process and Factor Models • Factor models provide investment managers with a framework to identify important factors in the economy and the marketplace and to assess the extent to which different securities and portfolios will respond to changes in these factors. – A primary goal of security analysis is to determine these factors and the sensitivities of security return to movements in these factors
One-Factor models The one-factor models refer to the return generating process for securities involves a single factor These factors may be one of the followings: The predicted growth rate in GDP The expected return on market index The growth rate of industrial produc tion etc
One-Factor Models • The one-factor models refer to the returngenerating process for securities involves a single factor. These factors may be one of the followings: – The predicted growth rate in GDP – The expected return on market index – The growth rate of industrial production, etc
One-Factor models An example Page 295: Figure 11.1 =a+ gDP+e, Where r= the returnon widgetin period t GDP= the predictedrate of returnin gdP in period t e, the unique oe specific return on Widget in period t b= sensitivity of widget to predictedgDP growth a= the zero factor for gdp
One-Factor Models • An example Page 295: Figure 11.1 the zero factor for GDP sensitivity of Widget to predictedGDP growth the unique oe specific returnon Widget in period t the predictedrate of returnin GDP in period t the returnon Widget in period t where: = = = = = = + + a b e GDP r r a bGDP e t t t t t t
One-Factor models Generalizing the example +bi F+ Assumptions The random error term and the factor are uncorrelated (Why <The random error terms of any two securities are uncorrelated. ( why?
One-Factor Models • Generalizing the example – Assumptions «The random error term and the factor are uncorrelated. (Why?) «The random error terms of any two securities are uncorrelated. (Why?) it ai bi Ft eit r = + +