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Paul Brassey's avatar

In layman’s terms, does this mean that the model my financial advisor uses to construct my portfolio according to my risk preferences is based on nothing more than the model author’s assumptions?

Samir Varma's avatar

Yes — and it's even worse than you're framing it.

Your advisor's software isn't running the Koijen-Yogo demand system. What it is running — Modern Portfolio Theory, mean-variance optimization, "given your risk tolerance, here's your efficient frontier" — takes three inputs: expected returns on each asset, the covariance matrix among them, and a number that supposedly captures how much risk you can stomach. Every one of these is a modeling choice pretending to be a measurement.

Expected returns: nobody has ever measured next decade's return on equities. Your advisor's number is the historical average over some window (chosen by someone), adjusted by some model (chosen by someone), possibly shrunk toward a prior (chosen by someone). Change any of those and the "optimal" allocation moves. The first Emperor post — https://samirvarma.substack.com/p/the-emperor-has-no-alpha — was about this: peer-reviewed academic predictors of returns don't beat mindless data mining. The expected-return inputs are barely worth the paper they're printed on.

Covariance matrix: not observed. Estimated from a chosen historical window under the assumption that past correlations predict future correlations. This assumption fails spectacularly in exactly the moments when correlations matter most — the 2008s and 2020s of the world, when everything falls together and diversification evaporates. The number your advisor uses to tell you "these assets zig when those zag" was true on average in the past. It is not true when you need it.

Risk tolerance: your advisor gave you a five-question quiz. The quiz assigned you a number. That number was mapped, via a function chosen by the software vendor, to a point on the efficient frontier the software constructed from the two sets of estimates above. Neither the quiz nor the mapping is a measurement of anything about you. It is a paperwork exercise dressed up as personalization.

Now the Emperor 2 twist. Given all that, you might reasonably think: fine, the practitioner tools are rough, but at least the underlying academic theory is solid, and someday better estimates will filter down. This paper is why that hope is misplaced. The most-rigorous, most-cited, most-prestigious wing of academic asset pricing — the one that claims to measure the deep structural parameters of markets — turns out to be measuring nothing at all. It is model output all the way down. If the discipline your advisor's software inherits from cannot itself identify the objects it claims to measure, the software cannot inherit anything better than what it already has, which is nothing.

So: your portfolio is a stack of assumptions running on top of another stack of assumptions. The stack works well enough most of the time because markets go up most of the time and the tax you pay for false precision is small when nothing goes wrong. When something does go wrong — and it will — the assumption stack will not save you. It was never structural. It was always a story.

You could say (and defenders would) that the honest response is not to abandon the tools; they would argue that nobody has better ones. I would say that the honest response is to know what you are holding. You are holding a plan that is a stack of someone’s assumptions. And the output comes from those assumptions.

Richard Jordan's avatar

That was a great read. And it was exceptionally clear. Thank you.