The closed-form optimisers of mean-variance optimisation are never run raw: institutional portfolios carry sector limits, factor exposure limits and — most consequentially — long-only mandates. Constraints exist for good reasons (implementability, mandate compliance, diversification), but each one prevents active weights from fully expressing the forecasts, and that information loss is measurable. This note quantifies it: the sector-selection vs stock-selection decomposition that justifies sector neutrality, the asymmetric damage done by the long-only constraint, and the transfer coefficient that patches the Fundamental Law for constrained reality. The headline number to retain: a typical long-only mandate throws away roughly a third of the paper IR.
Learning objectives. By the end of this note you should be able to:
- explain why constrained optimisation is the norm and what "information transfer" means;
- derive the sector/stock-selection alpha decomposition and argue for sector-neutralising value factors;
- explain why long-only wastes the short side of the signal, and how the loss scales with tracking error;
- define the transfer coefficient and use , with its caveat;
- describe 130/30-style relaxations.
In this lesson
- 7.1 Why constraints exist
- 7.2 Sector-neutral constraint
- 7.3 Long-only constraint
- 7.4 Long-only vs long-short IR; the transfer coefficient
- 7.5 Constraints in the bigger picture
The full lesson, with worked examples and exercise solutions, is for members.
Read the full lessonNew to SelfMadeQuant.com? See membership options or browse the Portfolio Theory and Quantitative Investment syllabus.