[kadyrbekovhamit-cyber]

With a market prior and views equal to that prior, bl_weights() should recover the market weights. For cov=diag(.04,.09,.16), caps [500,300,200], delta=2 and rf=.04, it returns [.541353,.282707,.175940] instead of [.5,.3,.2]: the inversion uses total rather than excess returns.

This retains the constructor's existing risk_free_rate kwarg and subtracts it only when computing implied weights. Explicit total-return priors can pass the same rate; zero remains the default for excess-return priors. Posterior returns, posterior-covariance convention and normalization are unchanged.

The same weight solver's singular fallback incorrectly uses the cached view-space matrix self._A. The patch uses its local asset-space matrix delta*cov instead. With duplicate A/C assets and one view it previously raises incompatible dimensions; with three views it silently returns equal thirds instead of [.3,.4,.3].

Validation: the original six regressions gave 4 failures / 2 passes. The complete Black–Litterman module plus seven new cases passes: 28 passed. Tests include zero/nonzero rf, explicit/market priors, both singular shapes and unchanged handling of duplicate exact views. Related #541 introduced the fallback; #762 concerns a different posterior-covariance convention; #763/#764 concern raw-weight normalization, which this PR does not alter.

Tested against main a6638d2, Python 3.12, numpy 2.2.6, pandas 3.0.6; sequential single-thread numerical execution. AI-assisted investigation and patch; reproducible tests included. No production-loss claim.

[arhancanli]

Re-derived the headline number outside the repo: with cov=diag(.04,.09,.16), caps [500,300,200], delta=2, rf=.04, the prior is rf + deltaSigmaw_m, and solving (delta*Sigma) w = prior then normalising gives [0.5414, 0.2827, 0.1759] (matches the PR), while subtracting rf first gives [0.5, 0.3, 0.2]. So the bug and the fix check out on the arithmetic (I did not run the repo's test suite).

Two things I noticed in the diff:

1. The new paragraph in docs/BlackLitterman.rst is appended after the numbered reference list [4], so it will render under References instead of next to the risk-free-rate discussion. It probably wants to sit in the section on priors.
2. test_neutral_views_recover_market_weights covers the constructor's risk_free_rate, but bl_weights(risk_aversion=...) can override delta. A case calling bl_weights with a different risk_aversion and rf != 0 would show whether the weights still sum to 1 and what the docs promise there, since prior and weights then use different deltas.