Optimization Isn't Broken, Your Inputs Are: Kritzman's Defense

By 2010 a consensus had formed, and it was a comfortable one. Optimizers are estimation-error maximizers. Optimized portfolios lose to naive equal weighting out of sample. DeMiguel, Garlappi and Uppal had run fourteen models against 1/N and none of them consistently won. The lesson everyone drew: do not bother optimizing, just split your money evenly.

Mark Kritzman, Sebastien Page and David Turkington wrote a paper saying, in effect: hold on. Look at what you were feeding it.

The problem: a rigged trial

Their argument turns on a single, deeply unglamorous methodological point, and it is worth stating carefully because it is the entire paper.

In the studies that concluded 1/N wins, how were the optimizers given their expected returns? Overwhelmingly, by taking a short rolling window of recent historical returns, typically five or ten years, and using the average as the forecast of what comes next.

Now think about what that produces. Over any given five-year stretch, some assets will have done wonderfully and some terribly. Feed those averages in as forecasts and you are telling the optimizer things like: "Japanese equities are expected to return minus 3 percent a year, and this emerging market fund is expected to return 22 percent a year, forever."

Nobody believes that. No sane investor would ever hold those views. They are not forecasts, they are recent history wearing a forecast costume. And an optimizer fed a forecast that an asset will lose 3 percent per year in perpetuity will, quite reasonably, short it aggressively.

So the horse race was not "optimization versus equal weighting." It was "optimization fed nonsense versus equal weighting." Optimization lost that race, and it deserved to. But that tells you about the nonsense, not about optimization.

The key idea via analogy: blaming the calculator

Suppose you had a calculator and someone tested it by typing in the wrong numbers. The answers come out wrong. You conclude: calculators do not work, better to guess.

That is the shape of the error Kritzman and coauthors are pointing at. An optimizer is a machine for converting your beliefs into a portfolio. It has no opinions. If you hand it a set of beliefs no human would endorse, it will construct the portfolio implied by those beliefs, and that portfolio will look insane, because the beliefs were insane. The optimizer is functioning correctly and telling you something true: this is what your stated views actually imply. If you do not like the answer, you did not really hold the views.

What they did

They ran thousands of tests across a range of datasets, comparing optimized portfolios against equal-weighted ones. The crucial variation was in how the expected returns were formed.

With short rolling windows, they reproduced the standard finding: 1/N looks good.

With longer-term samples, so that the return estimates are more stable and less driven by whatever happened to do well recently, optimized portfolios outperformed equal weighting.

With naively contrived but plausible assumptions, meaning simple, defensible views that a reasonable person might actually hold rather than an extrapolation of recent history, optimized portfolios again outperformed equal weighting.

Their conclusion is direct: the apparent superiority of 1/N does not come from a defect in optimization. It comes from the practice of using short rolling samples of past returns as forecasts of future returns, which produces implausible expectations that no investor would defend if stated out loud.

Why it mattered

• It rescued optimization from a caricature. The "optimizers are useless" conclusion had become a lazy talking point. This paper forced the field to distinguish between two very different claims: "optimization amplifies input errors," which is true and important, and "optimization is not worth doing," which does not follow.
• It relocated the problem to where it belongs: forecasting. The real difficulty in portfolio construction is that expected returns are hard. That difficulty does not go away if you stop optimizing. It is just hidden, because 1/N is itself a portfolio implying a set of views, and nobody asks what those views are.
• It exposed the hidden assumptions in 1/N. Equal weighting is not assumption-free. It implicitly asserts that every asset in your universe has an identical risk-adjusted appeal. It also depends entirely on which assets you chose to put in the universe, a decision that is itself a massive portfolio choice, and one the 1/N benchmark gets for free without scrutiny.
• It improved practice. The lesson that you should not use short historical averages as return forecasts is now much more widely internalized, and portfolio construction increasingly uses equilibrium returns, valuation-based estimates, or explicit judgment rather than raw trailing means.

The honest limitations

• The debate is not settled and this paper did not settle it. The 1/N camp has responses. In particular, the question of whether "plausible" long-run inputs give you an unfair advantage, since you may be using information about long-run averages that a real-time investor would not have had, is a genuine concern about look-ahead.
• "Plausible assumptions" is doing a lot of work. The paper's argument is that if you feed the optimizer sensible inputs, it beats 1/N. That is close to a tautology unless "sensible" is defined without hindsight, and defining it that way is exactly the hard problem. The critique of short rolling windows is unimpeachable; the constructive alternative is more contestable.
• It does not resolve the estimation error problem. Michaud, Best and Grauer, and Chopra and Ziemba are all still right. Optimizers really do amplify errors in expected returns. This paper argues that the answer is to have better inputs, not to abandon the tool, but better inputs are hard to come by.
• The results depend on the asset universe. Optimizing across a handful of broad, distinct asset classes with different risk characteristics is a much friendlier problem than optimizing across hundreds of highly correlated stocks. The case for optimization is strongest exactly where the case for 1/N is weakest, and vice versa.

The one-line takeaway

Kritzman, Page and Turkington argued that the famous defeat of optimization at the hands of naive equal weighting was an artifact of feeding optimizers short rolling averages of past returns as if they were forecasts, a practice no investor would endorse if the resulting views were stated plainly, and that with plausible inputs, optimization earns its keep.