Incorporating Deviations from Normality: Lower Partial Moments

Bernd Scherer

This chapter deals with non-normality, a prominent shortcoming of traditional portfolio analysis. We first review key issues that arise when we are faced with non-normality in data series. The main focus of the chapter, however, is the application of lower partial moments as one way of dealing with asymmetric return distributions. A second, more general method will be presented in Chapter 8.

6.1 NON-NORMALITY IN RETURN DATA

6.1.1 Single-period returns: visualising and testing for non-normality

This and the next two sections will deal with non-normality (which was identified in Chapter 1 as a potential shortcoming of the traditional Markowitz framework) and its impact on portfolio choice. We will not attempt to arrive at some definitive “cookbook recipe” for constructing a portfolio but, rather, attempt to establish the following key issues to keep in mind when doing so.

• Are returns normal?

• Are deviations from normality statistically significant?

• Are these deviations stable, ie, forecastable?

• Will non-normality vanish over time?

• Can we model a simple non-normal alternative?

Most of these questions are covered in this section, though the last two are