CHAPTER 15Constraints


Investors who deploy optimization to form portfolios often intervene in the optimization process by constraining the allocation to certain asset classes. Constraints, however, reduce a portfolio's efficiency. We show how to produce more efficient portfolios without imposing constraints. And at the same time, we address the concerns that induce investors to impose constraints in the first place.


Why do investors constrain their portfolios knowing that these constraints will produce a suboptimal result given their views about expected return and risk? The argument typically put forth is that investors lack sufficient conviction in their views. We disagree. Consider the following thought experiment. Imagine you know for certain the long-term future means, standard deviations, and correlations of the asset classes that you use to form your portfolio. Your conviction is, therefore, absolute. Nevertheless, it is likely that you will still be reluctant to allocate your portfolio in a way that is notably different from the norm, because within short subperiods the asset class returns most likely will diverge substantially from their long-term means, both positively and negatively, merely as a function of their standard deviations. You may well be able to tolerate subperiods of poor performance if most other investors experience similar poor performance, but you would likely be much less comfortable if you were the only investor ...

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