[kadyrbekovhamit-cyber]

efficient_risk(..., market_neutral=True) currently applies the sum(weights)=1 global-minimum-volatility lower bound before solving the sum(weights)=0 problem. That rejects feasible low-risk neutral portfolios.

For returns [.1,0], covariance .04*I, bounds (-1,1) and target volatility .05, weights [.05/sqrt(.08),-.05/sqrt(.08)] are feasible and analytically optimal. The current precheck rejects them because the fully-invested lower bound is sqrt(.02).

Apply that precheck only when market_neutral=False; the solver still evaluates all user constraints. Tests cover three low-risk targets, updating the target parameter, preservation of the fully-invested rejection and a genuinely infeasible neutral constraint.

Validation: original regressions 5 failed / 1 passed; patched efficient-frontier module plus regressions 77 passed / 4 skipped. Main a6638d2; Python 3.12, cvxpy 1.9.3. Related #569 discusses minimum-volatility rejections but does not supply this market-neutral counterexample; #362 concerns sector constraints, which this patch does not change.

AI-assisted investigation and patch; numerical work was sequential and single-threaded. This is a feasibility-check correction, not a claim about production portfolios.

[arhancanli]

I checked out this branch (Python 3.12, cvxpy 1.9.3) and ran the two-asset case from the description with efficient_risk(0.05, market_neutral=True). With bounds (-1, 1) it returns [0.17678, -0.17678], which equals 0.05/sqrt(0.08), so the precheck removal does what the PR says.

Two things I'd add tests for, since the precheck was the only thing that stopped some bad inputs early:

1. Bounds that cap the weights below the analytic solution, e.g. (-0.02, 0.02) with target 0.05. I get [0.02, -0.02] (feasible, volatility below the target, because the constraint is <=). That is fine, but it is not in the test file and the other tests all use wide bounds where the answer is exactly [a, -a], so a future change that tightens the constraint to equality would not be caught.
2. Bounds that exclude negatives, e.g. (0.1, 1). The existing code warns "Market neutrality requires shorting - bounds have been amended" and solves anyway (I get [0.1768, -0.1768]). Unrelated to this PR, but the test for the infeasible case only covers an added constraint, so a note on whether the amended-bounds path is intended here would help reviewers.

The if not market_neutral placement looks right to me: the 1/sum(pinv(cov)) value is the minimum for sum(w)=1 only, and sum(w)=0 has zero as feasible risk.