Small changes
Dual sensitivity is first-order. It is most reliable for small perturbations.
Reference 0009
Dual Sensitivity Cheat Sheet
How to use a constraint dual as a local forecast for changing a portfolio limit.
Minimization Rule
constraint: x <= limit dual: lambda >= 0 change: limit increases by delta new optimal value - old optimal value ≈ -lambda * delta
Maximization Rule
constraint: x <= limit shadow price: lambda >= 0 change: limit increases by delta new utility - old utility ≈ lambda * delta
Portfolio Translation
asset cap dual -> value of allowing more asset weight sector cap dual -> value of allowing more sector exposure turnover dual -> value of allowing more trading risk limit dual -> value of allowing more risk budget
Trust Conditions
Same active set
If a different constraint starts binding, the old dual may stop being a good forecast.
Correct convention
Minimization and maximization use opposite-looking value-change signs.
Model, not truth
A dual measures value inside the current model, not guaranteed real-world alpha.
Lesson 0007 Numbers
cap_A = 0.70
upper dual_A = 0.09
increase cap_A by 0.01:
predicted minimization change = -0.09 * 0.01
= -0.0009
Use this page with Lesson 0009, Reference 0008, and Reference 0006.