Where to Apply Long-Only Constraints in Black–Litterman Portfolios

Summary

The note explains why a Black–Litterman model does not itself prevent negative portfolio weights. The model combines a prior return estimate with investor views to produce expected returns; weight constraints belong to the subsequent portfolio optimization step.

For a long-only portfolio, the answer recommends adding nonnegative-weight constraints to the optimizer alongside the fully invested constraint that weights sum to one. The discussion uses a Markowitz minimum-variance optimization as an example and says the same constraint can be applied regardless of the optimizer’s objective. It is a concise conceptual answer rather than a worked derivation: it does not compare constrained optimization methods or discuss transaction costs, leverage, or other portfolio limits.

Key ideas

• Black–Litterman estimates expected returns from a prior and investor views.
• Weight restrictions are applied during portfolio optimization, not in the return-estimation stage.
• A fully invested long-only portfolio can require weights to sum to one and each weight to be nonnegative.
• The note gives no numerical example or comparison of optimizer implementations.

Tags

# Black-Litterman model with only positive weights


# Black-Litterman model with only positive weights












I'm trying to realize Black-Litterman Model for my stocks portfolio, but under optimization, I get a subset of weights with negative values. I want to get only positive weights. IS it possible to add constraints to the Black-Litterman Model? Thank you.

## Answer by Luigi87 (score 3, accepted)

https://quant.stackexchange.com/a/63931

The problem is not Black-Litterman.

B-L aims at finding an estimation of expected return based on a prior objective and some views. The prior is based on market neutral portfolio composition (or your benchmark) and the views are for the returns, so no constraint on weights can be added in this phase.

The fact that you get negative weights is entirely due to the optimisation phase. If you simply run a Markowitz min variance optimisation, which means having only 2 constraints, thus sum of weights equals 1 AND each weight bigger than zero, then you will never end up with negatve weights. It is simply a matter of adding the second in your optimisation, whatever it is your cost function.

So the answer is no, you cannot impose positive weights during the Black-Litterman stage, you need to impose it during the optimisation.

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