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Portfolio Optimization Developments Beyond Markowitz

Article Quant Q&A · Author: shudup
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Summary

The discussion surveys approaches developed to address practical weaknesses in mean-variance optimization. It highlights Black-Litterman, equal risk contribution or risk parity, minimum-volatility portfolios, and resampled efficient frontiers as ways to reduce dependence on estimated expected returns. It also describes conditional value-at-risk optimization, which uses a different measure of portfolio risk, and mentions goal-based investing as another framework for individual investors.

The replies emphasize that portfolio results depend on the quality of the inputs and on trading costs. Suggested covariance-related research includes multi-factor risk models, covariance shrinkage, and random matrix methods for cleaning eigenvalues. One answer cautions that CVaR optimization can produce concentrated, riskier portfolios. The exchange offers pointers rather than a comparative study: it supplies no performance data or evidence that one method is universally superior, and it notes that trading costs matter especially in multi-period portfolios.

Key ideas

  • Mean-variance optimization is sensitive to errors in expected return estimates.
  • Risk parity and minimum-volatility approaches can construct portfolios without expected-return forecasts.
  • Black-Litterman and resampled frontiers are presented as responses to estimation challenges.
  • Conditional value-at-risk replaces variance as the risk criterion in one alternative optimization framework.
  • Covariance modeling and trading costs remain important practical issues.

Tags

Portfolio constructionRisk managementStatistics
Full text
# State-of-the-art MVO methods?


# State-of-the-art MVO methods?












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

## Answer by nbbo2 (score 4)

https://quant.stackexchange.com/a/61132

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".

## Answer by Michael Isichenko (score 1)

https://quant.stackexchange.com/a/67900

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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