CHAPTER 4Asset Allocation Inputs

Chapter Outline

  1. 4.1 Sensitivity of the Mean–Variance Model to Inputs
  2. 4.2 Constant Investment Opportunities
  3. 4.3 Time-Varying Investment Opportunities
    1. Summary
    2. Problems
    3. Appendix: Mixed Estimation with Multiple Assets
    4. Endnotes


The previous chapter developed the machinery of the M-V model and illustrated its application through a series of examples and problems. In this chapter we address the issue of estimating the inputs—expected returns, variances, and covariances—required to make the model operational.

The M-V framework is the workhorse of practical asset allocation. Almost everyone uses it, yet virtually nobody is entirely happy doing so. Without doubt, the primary cause of dissatisfaction is the model's sensitivity to its inputs. Small changes in the inputs—especially the expected returns—can cause substantial changes in the “optimal” portfolio.1 Frequently a small change is sufficient to drive the optimal portfolio from one corner solution to another. That is, a small change causes some assets to drop out of the optimal portfolio altogether and other assets, which had been absent before, to suddenly emerge with substantial weight in the new portfolio. This problem becomes more acute as the number of asset classes increases. The same problem arises in a different form if we allow short positions—that is, if we do not impose a long-only constraint. In this case the optimal portfolio ...

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