Using Black–Litterman Priors for Portfolio Rebalancing
Summary
The note considers applying Black–Litterman in an ongoing portfolio rebalancing process. It asks whether previous portfolio weights can serve as the prior when new expected return forecasts arrive. The response says the framework can incorporate market views and also views about transaction costs, including estimates based on market impact, average volume, and position size.
Using exact previous weights as a prior creates a point-mass issue. One proposed modeling choice is to represent those weights, or market-capitalization weights, with a normal distribution centered on them and a small variance, which keeps the model analytically tractable. For a simplified diagonal model that ignores covariance, shrinking current weights toward the prior period's weights is also suggested as potentially effective. The discussion is conceptual and reports one contributor's experience; it does not provide a full implementation or comparative performance evidence.
Key ideas
- Black–Litterman can be used to update portfolio views during rebalancing.
- Previous portfolio weights can inform the prior, but exact weights create a point-mass issue.
- A normal prior centered on previous or market-capitalization weights can make the model tractable.
- Transaction-cost views can be incorporated using estimates such as market impact, volume, and position size.
- In a diagonal model, shrinking weights toward their previous values may be useful.
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# black litterman for rebalancing # black litterman for rebalancing I've noticed in my backtests that "shrinking" the expected returns vector towards zero tends to improve the performance. This has led me to investigate shrinkage methods for the forecasts/expected return vector vs the traditional "shrinkage" as applied to the risk/covariance matrix estimation. One structured way to do this is the Bayesian approach - which seems to lead to Black Litterman. There is some advice on shrinking the expected returns vector here What methods do you use to improve expected return estimates when constructing a portfolio in a mean-variance framework? but I'm wondering if people tend to perform Black Litterman in an online sense as in portfolio rebalancing. E.g. this would mean using your previous weights/portfolio positions as your prior and updating your prior with your new expected return forecasts at the next time step. Is this a common approach/use case of Black Litterman? ## Answer by Forgottenscience (score 4, accepted) https://quant.stackexchange.com/a/35960 There are some technical problems with using your previous weights as priors (that is, they are point measures), but yes, the Black-Litterman framework is suitable for this. You can essentially include any view point you have on the market within the model and let it affect your position size. This also includes views on transaction costs (based on such measures as market impact, average volume, position size etc.). If you work with a simple diagonal model (ignoring covariance), I have found it effective to shrink the weight toward the previous periods value. Regarding the point measure issue, it is a reasonable modelling assumption to assume a normal distribution with mean equal your previous weight (or the market capitalized weight) and a sufficiently small variance. This makes the model analytically tractable.
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