ABSTRACT
§ 3-1. Our purpose in this chapter is to examine alternative ways of modelling the relationship between risk and return to those considered in Chapter 2. We begin by demonstrating how one can build asset pricing models in which factors other than beta might be interpreted as important determinants of asset returns. The procedure is implemented by first selecting what is known as an ‘orthogonal’ portfolio. The mean and variance of the return on an orthogonal portfolio always fall on the Markowitz locus. The market portfolio on which the Capital Asset Pricing Model (CAPM) is based is but one example of an infinite number of orthogonal portfolios that lie on the Markowitz locus. Moreover, if one computes asset betas with reference to any of these orthogonal portfolios, there will be a perfectly linear relationship between asset average returns and their betas. Hence, if one wishes to develop a model that appears to demonstrate that there is a direct relationship between asset returns and factors other than beta then one will have to base the calculation of betas on a portfolio with a mean and variance of returns that does not lie on the Markowitz locus. Given this, an important focus of the first part of this chapter is to identify the particular inefficient portfolio that leads to a pre-specified and perfectly linear relationship between the vector of average returns for the assets comprising the sample, the vector of betas based on the inefficient portfolio and such other factors as are deemed to be important in the asset pricing process. This is achieved by first specifying an orthogonal portfolio with certain desirable properties (e.g. a given mean return or variance) and then identifying the inefficient portfolio that mimics these desirable properties associated with the orthogonal portfolio. The proportionate investment weights for the inefficient portfolio are then chosen so as to give a perfectly linear relationship between the asset average returns, the betas based on the inefficient portfolio and such other determining variables as the researcher deems to be important in the asset pricing process. This places the largely ad hoc nature of the asset pricing formulae that characterize the empirical research of this area of the literature onto a similar footing to the CAPM in the sense that there will be a perfectly linear relationship between asset average returns and the variables selected as important determinants in the asset pricing process.
