A relative weight constraint keeps two or more portfolio weights within a chosen ratio or difference. It preserves approximate allocation relationships while allowing optimization to adjust exposures. section 10.2.2
Global equity allocation
For US, foreign developed, and emerging equities weighted approximately 60%, 30%, and 10%, the US-to-emerging ratio is 6. A portfolio constraint might permit ratios from 3 to 12, or half to twice the reference ratio. section 10.2.2
Use either of these formulations:
- Ratio bounds: lᵢⱼ ≤ wᵢ/wⱼ ≤ uᵢⱼ, implemented under nonnegative weights as lᵢⱼwⱼ ≤ wᵢ ≤ uᵢⱼwⱼ. section 10.2.2
- Difference bounds: constrain wᵢ − wⱼ between lower and upper limits when an absolute gap matters more than a ratio. section 10.2.2
- For several assets, bound one weight or difference relative to their combined allocation, using a scalar such as α. section 10.2.2
constraints.append(l[i, j] * w[j] <= w[i]) constraints.append(w[i] <= u[i, j] * w[j])
CVXPY listing for imposing lower and upper ratio bounds between two portfolio weights. section 10.2.2
