The Problem With Robo-Advisors’ Use of Mean Variance Optimization

Why Optimizers Can Be "Error Maximizers"

Sophisticated traders (such as hedge funds and large asset managers) use MVO, but they always take great care to constrain the optimizer, because without constraints the optimizer would produce crazy portfolios. In fact, it's often said that optimizers are error maximizers. Here's why: The optimizer works with parameters that are not certain. We don't know 'true' variance of any security; we don't know its 'true' correlation with other securities; and we certainly don't know the future return on those securities. So we work with estimates of those parameters.

Despite its computational power, an optimizer is essentially a dumb machine. For example, it thinks that a return of 7 is preferable to a return of 6.5.  The reality is that we don't know true returns; we are just forecasting them and there is significant uncertainty in our forecast. The difference between a return of 7 and 6.5 may be almost non-existent because we are essentially guessing about the future, whereas the optimizer assumes that 7 is better and loads up on that security[1].

Similarly, we estimate correlation between assets A and B to be .4 and correlation between A and C to be .45. If you already hold A in a portfolio and all else is equal, the optimizer will tend to add B and not C, because it sees a lower correlation. But correlations are notoriously unstable. When a crisis hits, your .4 and .45 go closer to 1, even though the difference between 4. and .45 was contrived. So the optimizer was really maximizing the error in your initial estimate.

Optimizers can be precisely wrong as opposed to broadly right. The ones used by large institutions today correct for many of these error maximization problems with sophisticated techniques such as resampling, robust optimization and, cone algorithms. And even with all the safeguards, the sophisticated institutional optimizers still run only under close supervision of experienced analysts.

The first generation of robo advisors is not using these sophisticated technologies, but rather the techniques that were used before the 2008 crisis. Letting machines that are essentially error maximizers automatically build investment portfolios is not a great idea – in fact it's a terrible idea for your clients. Just because it can be done, doesn't mean it should be.

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