The purpose of this chapter

Chapter 24 will show how to obtain an optimal allocation across the asset classes over which the portfolio manager has a mandate to invest. The result of the optimization will, of course, depend on her choice of utility function. We therefore discuss this important topic in the present chapter. We also make an important distinction between ‘proper’ and what we call ‘reduced-form’ utility functions. The latter should be used with care, but can prove useful in practical applications.

In the next chapter we discuss some alternatives to traditional expected utility maximization (either in its ‘proper’ or in its reduced form). Some of these extensions come from ‘within the theory’ (such as the family of Epstein-Zinn recursive utilities), and some from ‘outside’, such as some forms of Robust-Decision-Making theory. We briefly discuss these topics not because we want to wade into the deep waters of the utility debate – tempting and interesting as doing so might be. Rather we touch on some alternative choice strategies because we find that for our purposes the results provided by ‘straight’ utility maximization display some very undesirable features: in primis, the instability of the optimal allocation weights to small changes in the expected returns. (This feature, as we shall see, is intimately linked to the way utility functions have to be ‘calibrated’.) This instability of the allocation weights is a worrisome feature of virtually any asset-allocation technique based on the maximization of expected utility reasonably calibrated to risk aversion.