Post-modern Approaches for Portfolio Optimization

Abstract

25.1 Introduction The search for alpha is the major challenge for both traditional equity managers and hedge funds. The assets under management only in hedge fund industry rose from about $500 billion to over 1 trillion for the period 2001−2005 and are ex-pected to grow to 2.5 trillion over the next 4 years; the number of hedge funds approaches ten thousands. This highly competitive environment challenges dis-coveries of scalable strategies that can effectively attract and utilize new invest-ments. Besides, the market itself calls for increased sophistication demonstrating pronounced asymmetry in financial returns, heavy-tails and other phenomena. It is clear that in this new environment the traditional portfolio optimization methods based on the minimization of the standard deviation or tracking error can no longer present a viable portfolio construction mechanism and portfolio managers are forced to shift from what is now known as modern portfolio management and revise some key concepts in their practices. The research for improved portfolio construction approaches has four directions: a. constructing better alpha models b. searching for an alternative risk measure which possesses better properties than the classical standard deviation c. realistic models for assets returns d. combining the three above into a nice practical optimization framework In the current chapter we will skip the item a) considering it a special domain of knowledge of portfolio managers often being the most subjective part of the port-folio construction process and will concentrate on the other three. The motivation behind item b) relates to the well known fact that the traditional standard deviation used as a proxy of risk measure has numerous disadvantages. One is that it penalizes profit and loss symmetrically while a true risk measure should be asymmetric as risk is associated with potential, future loss only.