Portfolio Management

CHAPTER 5Advanced Topics in Asset Allocation

Chapter Outline

1. 5.1 Introduction
2. 5.2 Horizon Effects in the M-V Framework
3. 5.3 Dynamic Programming
4. 5.4 Simulation
5. 5.5 Asset Allocation with Active Managers
6. 5.6 Portfolio Insurance
   1. Summary
   2. Problems
   3. Appendix 1: The Estimated VAR1 Model
   4. Appendix 2: DP Solution of the Mean Reversion Model
   5. Endnotes

5.1 INTRODUCTION

The basic mean–variance (M-V) framework was developed in Chapter 3 in a multi-period context with careful treatment of investment opportunities and investor preferences. Although this was not the simplest approach to the M-V model, it provided a foundation from which we can now generalize and extend our discussion of asset allocation to more advanced issues and methods.

In deriving the M-V model we made several key assumptions. First, investment opportunities are the same in each period. Second, logarithmic returns have a normal distribution. Third, the investor's risk–return preferences are independent of investment horizon and are completely described by constant relative risk aversion (CRRA) with respect to final wealth. Fourth, there are no cash flows into or out of the portfolio before the end of the investment horizon. Given these assumptions, the investor holds the same portfolio in each period and selects that portfolio by maximizing the M-V objective function. Relaxing any of these assumptions will in general cause the investor to adopt an investment strategy that differs from the M-V prescription.

Because one ...