A Primer on Portfolio Theory
Application in Mean–Variance Investing
Frictional Costs of Diversification
Incorporating Deviations from Normality: Lower Partial Moments
Portfolio Resampling and Estimation Error
Robust Portfolio Optimisation and Estimation Error
Bayesian Analysis and Portfolio Choice
Testing Portfolio Construction Methodologies Out-of-Sample
Portfolio Construction with Transaction Costs
Portfolio Optimisation with Options: From the Static Replication of CPPI Strategies to a More General Framework
Core–Satellite Investing: Budgeting Active Manager Risk
Removing Long-Only Constraints: 120/20 Investing
Performance-Based Fees, Incentives and Dynamic Tracking Error Choice
Long-Term Portfolio Choice
Risk Management for Asset-Management Companies
Valuation of Asset Management Firms
Tail Risk Hedging
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