I learned Markowit'z mean-variance optimzation in school.

Now I've been googling a bit, and to my surprise, Markowit'z is STILL being used by most people, AFAIK.

Are there really not some state-of-the-art algorithms/models developed recently (say, between 2005-2020) that are well-proven and known to be better than basic Markowitz?

Basically my question seeks modern models (or literature speaking of those models, i.e. a survey paper).

Thank you


2 Answers 2


Since Markowitz there has not been any big breakthrough in a new direction in portfolio theory. Rather, people are trying to cope with the well known shortcomings of Markowitz Optimization (of which the biggest is the difficulty of estimating expected returns). Interesting developments include: Black-Litterman model, as well as Equal Risk Contribution (aka Risk Parity), Min Vol, and other methods that don't use expected returns. The Resampled Frontier by Michaud illustrates the problem caused by misestimation of expected returns and perhaps is the best you can do to cope with it.

Another interesting development in another direction is Conditional Value-at-Risk Portfolio Optimization developed by Uryasev, where CVaR replaces Variance as the portfolio risk criterion.

Then there is Goal Based Investing https://en.wikipedia.org/wiki/Goal-based_investing which I personally find a rather weak contribution, but is much praised by some https://investmentsandwealth.org/getattachment/d772a88e-903f-43f6-bf90-f938079e2812/IWM15NovDec-GoalsBasedBetterOutcomes.pdf as a step beyond Markowitz for individual investors.

These are the topics I would cover if I was asked to present "what is new since Markowitz".


Markowitz (quadratic programming) is fine as far as you believe in your covariance of returns and don't incur trading costs, neither of which is true in real portfolios. CVAR (linear programming) based optimization was explored by MIT group, but I think the LP approach tends to result in more concentrated and riskier portfolios.

There are two needed developments which have been addressed since Markowitz. Re: covariance, there is a large literature. Keywords to look for: (1) multi-factor risk model, (2) covariance shrinkage, (3) random matrix theory and eigenvalue cleaning.

Re: trading costs, especially in a multi-period setting, there are some published results including groups from Stanford, Berkeley, CFM, Imperial College, and myself.


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