What you will learn
- Return versus utility
- Risk constraints
- Turnover costs
- Multiple objectives
Return versus utility
An optimization objective defines what is being maximized or minimized. Return, drawdown, variance and utility are different quantities. A solution can be optimal for a poorly chosen objective and still be unsuitable for the actual decision.
Risk constraints
Constraints define permitted exposure, turnover, concentration or other limits. They should reflect the problem rather than be adjusted retrospectively to make a favorite result feasible. Check whether a proposed solution satisfies every constraint.
Turnover costs
Turnover and transaction costs can change the optimum. A gross-return objective may prefer frequent reallocations whose gains disappear after costs. Include the implementation model in the objective or evaluation consistently.
Multiple objectives
Multiple objectives require explicit trade-offs. A frontier describes alternatives under assumptions, not one universally best point. Explain the preference or constraint that selects a candidate from the alternatives.
Worked example
An optimizer chooses a portfolio with the highest estimated return but twice the allowed concentration. Its objective value does not make it a valid solution to the constrained problem.
Try it yourself
Define an objective and two constraints for a hypothetical research allocation, then state how infeasible solutions should be reported.
Show the worked solution
For example, compare net expected benefit under stated assumptions subject to exposure and turnover limits. An infeasible candidate should be flagged or rejected, not presented as the winner without its violations.
Apply this to your course project
Compare a simple rule with an optimized alternative under perturbation and held-out scenarios.
Keep the calculation inputs, assumptions and decisions with your work. Practical exercises are self-reviewed; the scored knowledge checks assess the questions shown, not an independent certification of practical competence.