Case Study in Portfolio Management: Institutional (SWF): formula sheet

Key formulas

Stabilization fund profile

Purpose: smooth budget/economy → liquidity high, risk tolerance low, horizon short to medium

Expect liquid, lower-risk assets and limited illiquid exposure.

Savings fund profile

Purpose: intergenerational wealth → liquidity low need, risk tolerance high, horizon long

Can hold equities, private markets and real assets; liquidity needs are low.

Development fund profile

Purpose: fund projects or industrial policy → investment tied to domestic/economic goals

Returns may be balanced against policy aims; check the mandate.

Reserve investment fund profile

Purpose: higher return on excess reserves → liquidity moderate to high, risk moderate

May need to support the currency, so some liquidity must be kept.

Pension reserve fund profile

Purpose: fund future pension liabilities → return must meet liability growth, horizon long but defined

Link allocation to the liability timing and size.

Nominal return objective

(1 + real return) × (1 + inflation) − 1

Exact form. The approximation is real return + inflation. Use the exact form when the case gives it or asks for precision.

Real return needed from spending

Spending rate + cost of running the fund (if asked) + any real growth target

Fund-level real return for a fund that preserves real capital. Add inflation to get the nominal figure.

Overall risk tolerance rule

Overall risk tolerance = lower of ability and willingness

If ability is below average and willingness is above average, overall is below average.

Real return from nominal

(1 + nominal) ÷ (1 + inflation) − 1

Use when the case gives a nominal target and you need a real one.

Constraint to implication link

Fund purpose → liquidity need and time horizon → feasible illiquid share and return target

Use this chain to justify each constraint in an IPS answer.

Liquidity versus return trade-off

Higher liquidity need → lower illiquid allocation → lower expected illiquidity premium

A qualitative rule, not a calculation. Always state the direction.

Santiago Principles

Voluntary principles on legal framework, governance, accountability and investment practices

Know them as voluntary and as covering governance, transparency and sound investment practice.

Unsmoothing appraisal returns (single lag)

r*(t) = [r(t) − φ × r(t−1)] ÷ (1 − φ)

r(t) is the observed (smoothed) return and r*(t) is the unsmoothed return. φ is the smoothing parameter, between 0 and 1. The unsmoothed series has a higher standard deviation than the observed series. Use it only if the question gives φ.

Portfolio expected return

E(Rp) = Σ wi × E(Ri)

Weights must sum to 100%. Compare the result with the IPS required return.

Portfolio variance (two assets)

σp² = w1²σ1² + w2²σ2² + 2 w1 w2 ρ σ1 σ2

Raising ρ or σ for illiquid assets raises portfolio risk.

Rebalancing band check

Rebalance if |actual weight − target weight| > allowed range

Use the range given in the IPS. Wider ranges mean lower trading cost but more drift.

Active return

Active return = portfolio return − benchmark return

Active management is justified only if expected active return net of fees is positive after adjusting for risk.

Quick revision

• The fund's type and purpose come first; objectives and constraints flow from them.
• A savings fund for future generations usually has a long horizon and can take more risk.
• A stabilisation fund must be ready to fund budget gaps, so liquidity and capital preservation matter more.
• Return objective: state the target and what it must cover, such as inflation and spending needs.
• Risk objective: separate ability to take risk from willingness, and the lower of the two usually limits risk.
• Liquidity: match the need for cash to the share held in liquid assets, and be cautious with illiquid holdings.
• Time horizon: a long horizon supports illiquid and growth assets, but check for multiple stages or spending needs.
• Legal and regulatory: follow the fund's mandate and any rules on what it may hold.
• Governance: clear roles, accountability and decision processes affect how complex a strategy can be.
• Link every recommendation to a specific objective or constraint in the vignette.
• In essays, follow the command word and give only the number of responses asked for, in order.

Common mistakes

• Giving every SWF a long horizon and high risk tolerance. Fix: Tie horizon to withdrawal rules. A stabilization fund may need cash soon, so it is more liquid and less risky.
• Mixing up stabilization and savings funds. Fix: Stabilization smooths the budget now. Savings shares wealth across generations.
• Stating overall risk tolerance as the higher of ability and willingness. Fix: Use the lower of the two. A constraint that limits risk always wins.
• Mixing real and nominal figures when building the return objective. Fix: Label every number real or nominal. Add inflation only once and say which form the answer is in.
• Treating every SWF as having a long horizon and low liquidity need. Fix: Start from the fund's purpose. A stabilization fund needs high liquidity and a shorter horizon.
• Listing constraints without saying what they do to the portfolio. Fix: Add the effect on allocation after every constraint, such as a larger liquid share or fewer sectors.
• Accepting reported volatility of private assets at face value. Fix: State that smoothing understates risk and correlation. Unsmooth the data and raise the risk inputs before comparing allocations.
• Giving every SWF a high equity and alternatives weight. Fix: Check the fund type. A stabilization fund needs liquidity and capital protection, so its illiquid weight must be low.

Exam tips

• Read the first sentences of a case for the purpose; it usually reveals the type.
• Always follow the type label with a consequence for liquidity, horizon and risk.
• Watch for mixed-purpose funds and say which objective dominates.
• If asked to 'justify', give the case fact plus its implication in one or two sentences.
• Read the command word in bold. If it says 'determine' or 'calculate', give the number or conclusion first. If it says 'justify', give the reason.
• Show the arithmetic for return objectives, but remember a correct number alone earns full credit for a calculation.
• Quote a cue from the vignette for each of ability and willingness, so each point is clearly earned.
• Keep real and nominal labelled in every line. Use the form the question asks for.