Choosing Shrinkage Targets for Risk-Based Portfolios
Summary
The document considers portfolio shrinkage targets that do not require expected-return estimates, including minimum-variance, risk-parity, equal-risk, equal-weight, and maximum-diversification approaches. Such targets can temper noisy return estimates used by mean-variance optimizers. It emphasizes that risk-based allocations still encode assumptions about expected returns, so judging them solely by conventional risk-return measures may conflict with the objective behind those allocations.
The cited discussion favors maximum diversification among three compared risk-based approaches and reports that it is robust to adding redundant assets, unlike the alternatives in that comparison. The document also points to research on shrinking the covariance matrix before optimization, which is a different procedure from shrinking final portfolio weights. It does not provide the underlying empirical tables or enough detail to assess the cited comparisons independently. Its practical lesson is to choose a shrinkage target that matches the investor’s objective and to distinguish weight shrinkage from covariance shrinkage.
Key ideas
- Risk-based portfolio weights can imply assumptions about expected returns even when they do not use explicit return forecasts.
- A shrinkage target should be chosen to match the portfolio objective.
- Maximum diversification is presented as robust to redundant assets in the cited comparison.
- Shrinking a covariance matrix before optimization differs from shrinking the resulting portfolio weights.
- Evaluating risk-based allocations only with conventional mean-variance criteria may be inconsistent with their goals.
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# Choice of prior as a shrinkage target in portfolio construction? # 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 by Tal Fishman (score 6, accepted) https://quant.stackexchange.com/a/2105 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. ## Answer by Karol J. Piczak (score 1) https://quant.stackexchange.com/a/2179 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?
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