This is why Markowitz isn't used much in the industry, at least not in a plug-and-play fashion. Empirical volatility, and the variance -covariance matrix more generally speaking, is a useful descriptive statistic, but the matrix has high sampling variance, which means Markowitz is garbage in garbage out. Unlike in other fields, you can't just make/collect more data to reduce the sampling variance of the inputs. So you want to regularize the inputs or have some kind of hybrid approach that has a discretionary overlay.

I have some familiarity with the Markowitz model, but certainly not as much as you do about the practical use — could you share notes/articles/talks on the practical use? I’m super interested to learn more.

Read "Advanced portfolio management" by Paleologo (ironically it's actually the introductory one of his two books), or "Active portfolio management" for a more thorough, older, longer book on the topic.

Markowitz isn't really used at all, but Markowitz-like reasoning is used extremely heavily in finance, by which I basically mean factor modelling of various kinds - effectively the result of taking mean-variance as a concept and using some fairly aggressive dimensionality reduction to cope with the problems of financial data, and the fact that one has proprietary views about things ("alpha" and so on)

Thanks, just bought the book! Some nice reading for the holidays!

Black-Litterman model is an example of how to address the shortcoming of unreliable empirical inputs.

You'll also see more ad hoc approaches, such as simulating hypothetical scenarios to determine worst case scenarios.

It's not math heavy. Math heavy is a smell. Expect to see fairly simple monte carlo simulations, but with significant thought put into the assumptions.

Oooooh this is cool, thanks!

> This is why Markowitz isn't used much in the industry

This may be one reason but the return part is much more problematic than the risk part.

Very true, although the off-diagonal terms in the variance-covariance matrix are also hard to estimate, which is a problem, especially when simulating worst case scenarios, which is often when correlations tend to break down.

That's the first thing I thought of. I read the opening of this article and thought "oh this could be applied to a load balancing problem" but it immediately becomes obvious that you can't assume the variance is going to be uniform over time

Upvoting b/c this comment is true, obviously I disapprove of insider trading.

Doesn't it make more sense to measure and minimize the variance of the underlying cash flows of the companies one is investing in, rather than the prices?

Price variance is a noisy statistic not based on any underlying data about a company, especially if we believe that stock prices are truly random.

Volatility is fairly predictable. Or at least much more predictable than returns