portfolio_balancing: trace the risk-return frontier with solver shadow prices#83
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portfolio_balancing: trace the risk-return frontier with solver shadow prices#83chriscoey wants to merge 2 commits into
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…w prices Extend the prescriptive stage to use solver sensitivity information (constraint duals) to trace the bi-objective risk vs return efficient frontier efficiently. - Read the return-floor constraint's dual via solve(sensitivity=True) on HiGHS. By the envelope theorem that dual is the frontier's local slope d(variance)/d(return), so each solve yields a Pareto point and its slope with no finite differencing. - Add three frontier drivers compared at equal solve budget: grid (blind even spacing), adaptive (step sized by the current shadow price), and dichotomic (split the interval with the largest chord-vs-tangent gap, sampling at the tangent crossover). The dual-guided drivers approximate the frontier far more tightly than blind spacing. - Materialize the chosen frontier as a FrontierPoint Concept with integrity constraints requiring that neither return nor risk decreases along it, a relational statement of Pareto-efficiency (non-decreasing with a small relative tolerance so near-equal crisis-scenario points do not spuriously trip it). - Switch the QP from Ipopt to HiGHS (HiGHS returns the sensitivity duals the frontier search relies on); bump relationalai to 1.9.0. - Rewrite the README for the new flow: shadow-price sign convention, the three-driver comparison, the max chord-gap quality metric, and refreshed expected output. Co-Authored-By: Claude Opus 4.8 <[email protected]>
… docs A solve can report OPTIMAL yet return no primal rows (e.g. an unstable or timed-out reasoner handing back a hollow result). Treat that as a non-result in solve_epsilon so the frontier drivers fall back through the same path as infeasible, instead of KeyError-ing on the missing "scenario" column in _extract_allocations. Expand the solve_at SystemExit message to name this case. Also clarify surrounding comments and docs: the module-scope rules-in-loop suppression, POSITION_LIMIT feasibility note, the LOCALLY_SOLVED back-end note, the pair_gap tangent-crossover docstring, the frontier_adaptive anchors-only guard, and the README's Anchor 2 per-scenario output and infeasibility note. Co-Authored-By: Claude Opus 4.8 <[email protected]>
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Why
The
portfolio_balancingtemplate walks the risk/return efficient frontier. It previously sampled the frontier blindly — evenly spaced return targets, each an independent solve, with no signal about where the curve actually bends. Now that the prescriptive solver returns sensitivity information, the dual of each return-floor constraint is the local slope of the frontier (envelope theorem:shadow_price = d(min variance) / d(return target)). That turns frontier tracing from guesswork into a guided search, and gives the template a concrete, teachable use of solver duals.What changed
Stage 3 now solves with
sensitivity=Trueand uses the per-scenario shadow prices to trace the frontier three ways, compared at the same solve budget:The run prints an approximation-quality table (max chord-gap per driver — dichotomic is tightest at equal budget), a shadow-price-vs-secant table showing each dual matches the finite-difference slope, and the existing base-vs-crisis stress test (per-scenario frontier with exact dual marginals and the knee point).
Supporting changes:
1.9.0(sensitivity support), matching the other sensitivity templates.How to validate
Run
python portfolio_balancing.pyagainst a prescriptive-capable engine (sensitivity support required). The README's expected-output block matches a fresh run end-to-end:557.93> adaptive415.17> dichotomic202.30I ran this end-to-end on a current engine; output is numerically stable across runs.