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.

  • $\begingroup$ what is the difference between items i and ii? $\endgroup$ – Patrick Burns Oct 5 '11 at 14:30
  • $\begingroup$ That is a bit vague - I mean minimum risk portfolio for a specified level of target return (say the risk-free rate). $\endgroup$ – Ram Ahluwalia Oct 5 '11 at 15:04
  • $\begingroup$ and by minimum variance portfolio, it would mean a portfolio of risk free bonds? $\endgroup$ – icequations Oct 24 '11 at 16:42
  • $\begingroup$ "minimum variance" meaning the left most point on an efficient frontier consisting of some mix of stocks $\endgroup$ – Ram Ahluwalia Oct 24 '11 at 17:35
  • $\begingroup$ in continuing +Patrick Burns question, how would you use a 'minimum risk' portfolio as a shrinkage target? I see the global minimum variance as natural, but aren't you contradicting yourself by saying that the minimum risk portfolio is a candidate shrinkage target with the advantage of not needing return estimates. I see, three possibilities 1] global min. variance portfolio 2] equal weighted portfolio 3] market portfolio as shrinkage targets. I don't get how the portfolios along the 'frontiers' are each a shrinkage target. $\endgroup$ – Vishal Belsare Feb 3 '12 at 13:13

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.

* 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.

  • $\begingroup$ Hmm - I will def'y take a look, thank you! $\endgroup$ – Ram Ahluwalia Oct 6 '11 at 1:20
  • $\begingroup$ This is an excellent paper and actually answers my question since they provide citations to the empirical research of the various priors as well. They pose a formidable challenge to the use of priors other than the market-cap weighted portfolio. $\endgroup$ – Ram Ahluwalia Oct 6 '11 at 16:35

First of all, I'm not sure I got it right. You're directly shrinking the final result (vector of asset weights), right?

If that's the case, it may not be exactly what you're looking for, but you may still have a look at some papers by Ledoit and Wolf.

Specifically, in Honey, I Shrunk the Sample Covariance Matrix they propose that shrinkage always be applied to the covariance matrix before proceeding with any further work. They then compare out-of-sample performance of different shrinkage targets.

So I suppose it is shrinkage applied in another phase of MVO than what you've mentioned, but it may still be of interest to you. By the way, you mind sharing some references you mentioned in the first sentence?

  • 1
    $\begingroup$ Check out Clarke, de Silva, and Thorley (2011). $\endgroup$ – Tal Fishman Oct 17 '11 at 14:10
  • $\begingroup$ You can think of some weight vector as a shrinkage target, which also corresponds to some properties of the covariance matrix. Jagannathan & Wang's paper on the implication of no-short-sale constraint helps get it, i.e. a constraint of non-negative weights has an equivalence in shrinking to covariance matrix (toward some prior). $\endgroup$ – Vishal Belsare Jul 25 '12 at 13:17

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