Why isn’t Markowitz portfolio optimization used more in practice?
This puzzle was considered by Richard O. Michaud thirty years ago and he termed it an enigma.
Richard MICHAUD | President and CEO | PhD in Mathematics from Boston University | Research profile (researchgate.net)
Michaud’s view was that:
“indifference of investment practitioners to mean-variance optimization technology, despite its theoretical appeal, is understandable in many cases” – in part due to a tendency towards “error maximization” already studied by Jobson and Korkie a decade prior.
A substantial literature devoted to robust versions of Markowitz has evolved but has not yet won the day in terms of popularity. The complexity also adds to what Michaud termed the “conceptual demands placed on managers” by optimization. Analogous shyness arises in forecasting, mixtures of experts and model ensembles where (usually) off-diagonals and sometimes the entire covariance matrix is ignored.
Yet, in the spirit of honoring Harry Markowitz’ seminal achievement by defense, I offer a link to sports markets and lessons learned therein. We need just a couple of mathematical observations:
1. Portfolio construction is thinly veiled betting on a “race” with a vast number of “horses” (mutually exclusive outcomes). As elsewhere, log-optimal betting is “price blind” and proportional to probabilistic belief … a beautiful mathematical accident.
2. The index portfolio is consistent with an equivalence class of beliefs about covariance (an orbit passing through a diagonal covariance matrix that is determined based on market capitalizations).
It follows that, morally speaking and sometimes exactly:
3. Fraction Kelly = Markowitz with covariance shrinkage
That’s really a statement about linearity from belief to investment, so long as you interpret gamblers ruin as relative to the index. It allows us to transfer practical experience in all sorts of domains back to portfolio allocation. And the most important practical observation is this:
4. Log-optimal betting is ruinous in practice, but fractional varieties outperform heuristics.
Usually, private estimates of probability (“R” say) are further from the truth “P” than the market “Q” is from “P”.
See the paper: [2107.08827] Optimal sports betting strategies in practice: an experimental review (arxiv.org)! For a wonderful survey using real data from realistic attacks on gambling markets. The authors do not throw the baby out with the bathwater, and in a pleasant departure from the norm they consider all three probability types, not two.
Based on 3 + 4 above, we might take a view on the popularity of optimization-based allocation that is kinder to Markowitz. Furthermore, just as there are plenty of people who tried Kelly betting and went bankrupt. Fractional Kelly might have saved them. However, there are probably many who tried naive versions of Modern Portfolio Theory, Markowitz’ legacy, and decided it was not to their taste.
Admittedly the second problem may be statistically tricker due to time scales, but that doesn’t mean Markowitz was wrong.
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Why isn’t Markowitz portfolio optimization used more in practice?
Why isn’t Markowitz portfolio optimization used more in practice?
