We have often discussed the Black-Litterman approach/model in the forum. What I was wondering is: is it possible to formulate relative views in the model. Relative in the sense $$ \mu_1 > \mu_2 $$ where $\mu_i$ is the expected return (as a view) of asset $i$.

It is clear how to formulate relative views of the form $$ \mu_1 - \mu_2 = v, $$ where the view is that I expect asset 1 to have a return $v$ percent greater as the return of asset 2. However I don't want to fix $v$.


1 Answer 1


Indeed I think you can, but it comes at a price. To be clear: Neither have I done this myself nor have I attempted it.

The main idea is typical Bayesian: In computing the posterior return parameters for the random variable $\mu$, you can calculate the conditional expectation subject to your inequality constraints, say $A\mu \leq b$).

There are three, fundamentally different, problems I see with this approach:

  • Computational Complexity: How do we solve the integral $\mathbb{E}[\mu|A\mu \leq b]$? This should be a standard Bayes problem with plenty of literature (stochastic integration?)

  • View Formulation: What does it mean to have uncertainty attached to the views in the view matrix while constraining the return distribution to fulfill the inequalities all the time?

  • Following Optimization: What I'm not completely sure about: Considering the fact that the distribution of the posterior is not normal anymore, is it still appropriate to proceed with standard mean-variance optimization? (I would guess the answer is yes - at least if we assume a normal market)

There is a paper that claims to solve the first point by providing an algorithm and also presents a method to add uncertainty to inequality parameters. From what I saw so far I think its definitely worth a look and should fill in all the gaps there are still in the answer.

  • $\begingroup$ Thanks for this answer. I will have a look at the paper provided ... it conforms my feeling that my case is not easily covered. $\endgroup$
    – Richi W
    Jul 12, 2016 at 6:31
  • $\begingroup$ @Richard its definitely not possible in the standard model $\endgroup$
    – vanguard2k
    Jul 12, 2016 at 6:59

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.