Factor Representing Portfolios in Large Asset Markets

We discuss the properties of factor representing portfolios in an intertemporal APT model, in which the conditional mean and covariance matrix of asset returns change through time in an interdependent manner. We use a signal extraction approach and relate the properties of basis portfolios with (possibly) time-varying weights to mean square error minimisation. We prove that many basis portfolios converge to the factors as the number of assets increases, but show that those generated by the Kalman filter are the best possible for any conditional distribution of returns. We also discuss practical ways of modelling the time variation in the covariance matrix of return innovations. 

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