ABSTRACT
In this chapter, we develop a theoretical model of portfolio behaviour that is suitable for applying to the behaviour of any investor in general. In subsequent chapters, the model will be applied to the portfolio behaviour of pension funds in particular. (This chapter requires some understanding of modern portfolio theory and stochastic calculus, see, for example, Blake (1990a) and Chow (1979).)
We take a standard mean-variance model of portfolio behaviour and extend it in three important ways. First, we allow the marginal rate of substitution between mean and variance to depend on asset holdings, thereby making the model non-linear in asset quantities, so that the optimal demand for assets is implicit rather than explicit. Second, we allow the mean and variance to be time-varying and forward looking, rather than constants or moving averages determined from the historical sample. Third, we permit dynamic adjustments to the portfolio through an error correction mechanism, thereby allowing the actual portfolio to diverge temporarily from the optimal portfolio.
