risk - Choice of prior as a shrinkage target in portfolio construction?

There's various research showing how priors such as the minimum variance portfolio turn out to be a surprisingly effective shrinkage target in portfolio construction.

The sell point of these priors is they do not require a return estimate. Therefore these shrinkage targets add ballast to otherwise noisy return estimates fed into "error-maximizing" optimizers.

There are several candidate priors for shrinkage targets that do not require an expected returns term: i) minimum variance portfolio, ii) minimum risk, iii) equal risk , and iv) equal weight portfolio.

Is there out-of-sample research on the return-risk performance of these portfolios for S&P 500 or other indices? Perhaps there is another prior that I have not considered.

Answer

I know you're really looking for some empirical work on this topic, but I think the following theoretical paper puts your question into proper perspective.*

Risk-Based Asset Allocation: A New Answer to an Old Question by Wai Lee, JPM 2011.

Overall, he finds that supposedly risk-based approaches to portfolio construction are really making implicit assumptions on expected returns, and if their performance is evaluated on a traditional mean-variance basis, then we must closely examine those implicit assumptions. In other words, to evaluate a risk-based approach using risk-return metrics is fundamentally inconsistent with the use of such approaches to begin with.

NEW: A recent (10/13/2011 publication date) research piece from Deutsche Bank does an in-depth study of three major risk-based approaches to asset allocation:

• Minimum variance



• Risk parity


• Maximum diversification

They find in favor of maximum diversification (see Choueifaty and Coignard (2008), your list left this one out), which is also the only one of the three robust to the inclusion of redundant assets. If you are a client, it is called "Risk Parity and Risk-Based Allocation," but I could not find it on the public internet.

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^{* Your question may be an instance of the Pounding A Nail: Old Shoe or Glass Bottle? problem. The correct answer is that your shrinkage target should be determined by your objective function, and if your objective is mean-variance efficiency, then you shouldn't be shrinking towards a purely risk-based target to begin with.}