Portfolio Optimization Constraints

Question

Wondering which are some standard constraints in portfolio optimization in practice?

For example, assuming we want to maximize expected returns subject to a risk constraint, typically we may have

-constraints on gross exposure -constraints on net exposure -constraints on individual asset gross exposure etc.

Is there a good document/ book that has standard constraints that are used in practice?

Answer 1

Constraints obviously also depend on the problem formulation (for example: weights sum to 1 will translate to active weights sum to 0 if we optimize relative positions)

Apart from the most important ones the unit investment constraints (weights sum to 1 or money invested sums to NAV), sometimes short-selling constraints, very often you see constraints on the number of securities held or traded.

Depending on the problem, also constraints on portfolio characteristics, such as FX exposure, Non-rated or asset class exposures.

Unfortunately there is no standard literature on this. The reason for this being: Every optimization problem is different and the constraints come from the practical application itself.

Disclosure/Addendum: One thing is considering constraints, the other one is translating them into a format the optimizer understands. More often than not, this is harder than you think.

Answer 2

I have worked with:

Portfolio stability constraints

• Long-only constraints (to avoid unrealistic short positions)
• Maximum and minimum allocation to asset classes

Liquidity and illiquidity constraints

• Minimum posititon in liquid instruments (money market, govies, etc.)
• Maximum hair-cut due to forced selling

Concentration constraints

• Asset within asset class concentration constraint (eaxh asset should not be 100% of the exposure in the particular asset class)

Portfolio factor beta exposure

• Minimum and maximum limits to the relative beta exposure of the portfolio aganst a given factor (e.g. market factor)

There will certaintly be more possible constraints (see e.g. the implementation here).