CFA Level III · Level III Core

Asset Allocation with Real-World Constraints: formula sheet

Full chapter guide

Key formulas

IPS constraint checklist: Liquidity + Time horizon + Taxes + Legal/regulatory + Unique circumstances; Use this as the framework for every constraint question. There is no calculation behind it. Risk tolerance is not on this list, because it belongs to the risk objective.
Risk tolerance rule (part of the risk objective): Overall risk tolerance = lower of (ability to take risk, willingness to take risk); This is part of the risk objective, not a constraint. Keep it separate from the constraint checklist. Constraints such as horizon and liquidity influence ability to take risk. If ability and willingness conflict, the lower governs.
After-tax return (simple, annual): After-tax return = pre-tax return × (1 − tax rate); Applies when the whole return is taxed each year at one rate. For deferred or mixed gains and income, state the assumption you use.
Liquidity need as share of portfolio: Share to keep liquid ≈ expected cash outflows over the period ÷ portfolio value; A simple check of the share of the portfolio to keep liquid. The amount of liquid assets needed is roughly the expected cash outflows. It is a sizing aid, not a prescribed CFA formula.
Weight drift: Current weight = Asset value ÷ Total portfolio value; Compare with target weight and the band. Recompute the total after each asset's change in value.
Percentage-range rule: Rebalance if weight < target − band or weight > target + band; Bands can be set per asset class. Illiquid or costly assets usually get wider bands. Decide whether to return to target or only to the band edge.
Calendar rule: Rebalance at fixed intervals (for example every quarter or year); Trade only at review dates, whatever the drift.
Liquidity premium (concept): Required return on illiquid asset ≈ comparable liquid return + liquidity premium; A rough guide only, not a precise estimate.
Band width and costs: Higher transaction costs, higher volatility tolerance or low correlation → wider bands; Higher risk aversion, high correlation between assets or highly volatile assets → tighter bands. Rule of thumb from the rebalancing framework, not an exact law.
After-tax return, taxed annually on income: r(after-tax) = r × (1 − t); Use when the whole return is taxed each year at rate t, such as interest in a taxable account.
Taxable account with deferred capital gains: After-tax FV = V_n − t_cg × (V_n − B), where V_n = V0 × (1 + r)^n; V_n is the pre-sale value and B is the cost basis. Tax is paid once at sale on the gain only.
Tax-deferred account after-tax value: After-tax value = V0 × (1 + r)^n × (1 − t_w); Contribution is pre-tax and growth is untaxed. Tax rate t_w applies to the full withdrawal.
Tax-exempt account after-tax value: After-tax value = V0 × (1 + r)^n; Contribution is made from after-tax money. Growth and withdrawal are untaxed.
Effective annual after-tax growth, taxed each year: FV = V0 × [1 + r × (1 − t)]^n; Taxes paid each year from the account. Income is reinvested after tax.
After-tax risk (full loss offset): σ(after-tax) = σ × (1 − t); Holds only if losses give a tax benefit at the same rate. State this assumption.
IPS constraint categories: Liquidity, time horizon, tax, legal and regulatory, unique circumstances; ESG and ethical preferences usually fall under unique circumstances. Legally mandated exclusions fall under legal and regulatory.
Negative screening: Exclude sectors, companies or practices by rule; Simple and clear, but it can create sector bias and higher tracking error.
Best-in-class screening: Select the highest ESG-rated issuers within each sector; Keeps sector exposure near the benchmark. Relies on rating quality, which varies between providers.
Thematic investing: Allocate to themes such as clean energy or water; Concentrated exposure to a theme. Not the same as broad ESG integration.
Active tracking error: Tracking error = standard deviation of (portfolio return − benchmark return); Use it to describe how much an ESG-constrained portfolio can deviate from the unconstrained benchmark.
Institutional policy framework: Return objective + Risk tolerance → Constraints (liquidity, horizon, legal/regulatory, taxes, unique) → Allocation; Use this order for every institution. Constraints come before asset classes.
Endowment return objective: Required return ≈ (1 + spending rate) × (1 + inflation) − 1, plus any cost of managing the fund; Use the spending rate the question gives. Simple addition is acceptable only as an approximation. Show the method you choose.
Funded ratio: Funded ratio = Plan assets ÷ PV of plan liabilities; Below 1 means underfunded. A lower ratio generally reduces the sponsor's ability to take risk.
Surplus: Surplus = Plan assets − PV of liabilities; Surplus risk is the risk that matters in liability-relative thinking.

Quick revision

Constraints change the practical allocation, not the client's objectives.
Name the binding constraint first, then explain its effect on the portfolio.
Illiquid assets raise liquidity risk, so a liquidity reserve and a lower allowed allocation may be needed.
Rebalancing means trading back toward target weights, and transaction costs and illiquidity limit how often you do it.
Wider rebalancing ranges reduce trading costs but allow more drift from the target.
Compare returns after tax, not before tax, when taxes apply to the client.
Asset location places tax-inefficient assets in tax-advantaged accounts where the rules allow.
ESG can be applied by exclusion, integration, tilting or engagement, and each has different effects on the portfolio.
An ESG or other mandate may limit the opportunity set, so state any expected cost to return or diversification.
Institutional approaches must reflect the liabilities, funding status, time horizon and governance of the institution.
Check that the recommendation still meets the return objective and risk tolerance after adjustments.
Show calculations in full and give a number that is clearly labelled.

Common mistakes

Treating risk tolerance or return goals as constraints. Fix: Keep objectives (return, risk) apart from constraints (liquidity, horizon, taxes, legal, unique). Risk tolerance is part of the risk objective, although constraints such as horizon and liquidity influence ability to take risk.
Saying a long time horizon means any amount of risk is acceptable. Fix: Check willingness too, and remember that liquidity needs also limit ability. Overall risk tolerance is the lower of ability and willingness.
Treating the liquidity premium as a guaranteed extra return. Fix: Describe it as compensation for illiquidity risk, and weigh it against cash needs and the cost of selling in stress.
Using reported private asset volatility and correlations directly in optimization. Fix: Say that returns are smoothed, risk is understated and the optimizer overweights the asset. Unsmooth, adjust inputs or cap the weight.
Applying one tax rate to all returns Fix: Split the return into interest, dividends and gains. Use the rate stated for each.
Taxing capital gains every year Fix: Unrealised gains grow untaxed. Tax the gain once at sale, on value minus cost basis.
Treating exclusionary screening and best-in-class as the same thing. Fix: Exclusionary removes whole sectors or activities. Best-in-class keeps the top-rated issuers in every sector.
Assuming ESG constraints always lower returns. Fix: Say the effect depends on the approach and the data. Restrictions reduce the opportunity set, but ESG factors may also affect risk and cash flows.
Treating the endowment model and the Norway model as fixed recipes. Fix: Describe the features the question gives: illiquid alternatives and equity tilt for one, broad liquid, low-cost and rules-based for the other. Then link to the investor's liquidity, governance and resources.
Saying the DC plan sponsor sets the plan's risk tolerance and allocation. Fix: In a DC plan the participant bears investment risk. The sponsor builds the menu, default option and education.

Exam tips

In essay sets, name the constraint first, then give its effect. One clear sentence per point earns marks more reliably than long prose.
Read command words. Identify needs only a name. Justify needs a reason tied to the vignette.
When a vignette gives dates and amounts, convert them to a liquidity need and a horizon stage.
If ability and willingness conflict, say overall risk tolerance is the lower of the two.
For institutions, look for regulation and liabilities first. For individuals, look for horizon, liquidity and unique wishes.
When a question gives smoothed or appraisal-based returns, say they understate risk and lead to an overweight in optimization.
For a command word like 'justify', give the recommendation and one reason tied to the client, then stop.
Show the weight calculation (value ÷ total) even if the answer is a single number.