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?


1 Answer 1


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.

  • $\begingroup$ Thanks for your response! Are you familiar with any standard ways to choose priors? For example in a long short/ pure alpha strategy (I'm assuming I wouldn't want to use the market portfolio as a prior) would you use equal weights or risk parity or minimum variance etc for the prior? $\endgroup$
    – Michael
    Sep 9, 2017 at 16:55
  • $\begingroup$ Not sure there is a standard way. I would probably initialize with equal weights as it is parsimonious and repeatable across all strategies - I prefer to avoid minimum variance, and in my mind risk parity is more suited to multi-asset portfolios, but I have no strong opinion on it. If your goal is risk parity why build a model that would move away from it? For subsequent periods I would initialize with the previous period's weight, and possibly estimate the sample variance from the entire set of weights as an uncertainty proxy. $\endgroup$ Sep 10, 2017 at 12:16

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