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

Key formulas

Required (nominal) return, geometric form

Required return = (1 + spending rate) × (1 + inflation) × (1 + cost rate) − 1

Spending rate is the payout ÷ assets. Cost rate covers management and administrative expenses. This form compounds the three components. It is one convention, not a universal rule. Many cases accept the simple sum below. Follow the definition the case gives, and state which form you used.

Required return, approximate form

Required return ≈ spending rate + inflation + cost rate

Quick sum. It is often accepted, and you should use it when the question allows an approximation or the numbers are small. State which form you used.

Real return objective

Real return objective = (1 + required nominal return) ÷ (1 + inflation) − 1

This is the return needed to preserve purchasing power while funding spending and costs. It follows the geometric convention, so if the case defines the objective as spending plus costs, use that definition. Use the inflation that applies to the institution, such as a higher education cost index, if given.

Simple spending rule

Spending = spending rate × beginning market value

Easy to apply and linked to the market, but spending is volatile when markets move.

Smoothed spending (rolling average) rule

Spending = spending rate × average market value of the last N years

Smooths spending and budget shocks, but lags the market. Spending can stay high after a fall.

Hybrid (Yale-type) spending rule, one common version

Spending = weight × prior-year spending × (1 + inflation) + (1 − weight) × spending rate × prior-year market value

This is one common version. Cases may define the rule differently, for example with a different inflation measure or market value date, so use the definition given in the case. The weight on prior spending sets how smooth the payout is: a higher weight gives steadier spending, a lower weight ties spending more closely to the market.

Real required return

Real required return = spending rate + investment costs

Use when the objective is stated in real terms. Costs are management and administration fees as a percent of assets.

Nominal required return (simple approximation)

Nominal ≈ spending rate + costs + inflation

Additive approximation. It slightly understates the exact answer, so use it only if the question clearly allows an approximation.

Nominal required return (exact)

Nominal = (1 + real required return) × (1 + inflation) − 1, where real required return = spending rate + costs

Compounds the real return with inflation. Use this form for a precise answer.

Simple spending rule

Spending(t) = spending rate × Market value(t − 1)

Fully market-linked. Spending is volatile because it follows the latest value.

Rolling-average (smoothing) rule

Spending(t) = spending rate × average of the market value over the prior n years (often 3 to 5)

Averaging dampens swings. Spending lags the market.

Geometric spending rule

Spending(t) = smoothing rate × [Spending(t − 1) × (1 + inflation(t − 1))] + (1 − smoothing rate) × [spending rate × Market value(t − 1)]

A weighted average of inflation-adjusted prior spending and the market-based amount. A higher smoothing rate gives more stable spending.

Overall risk tolerance rule

Overall risk tolerance = lower of (ability, willingness)

If the two conflict, the more conservative one governs. State this explicitly in your answer.

Ability factors (above-average signals)

Long or perpetual horizon + low spending dependence + large reserves + stable funding → higher ability

Reverse each factor for below-average ability: short horizon, heavy reliance on endowment, thin reserves, volatile donations.

Willingness factors

Board and committee attitudes, stated comfort with losses, reputational concerns → willingness

Use only what the vignette states or clearly implies. Willingness is not computed from numbers.

Annual liquidity need

Annual cash need = spending rate × beginning asset value + expected capital calls + other known outflows

Use it to show liquidity is moderate or low as a share of assets. Compare the result with liquid assets held.

Spending amount

Spending = spending rate × asset value (or average of past values)

Rate and base come from the spending policy. Spending is a liquidity need and also feeds the return objective.

Required return link

Required return ≈ spending rate + inflation (+ costs) for real value preservation

A perpetual horizon means spending and inflation must be covered to keep purchasing power. Use the figures given in the vignette.

Constraint checklist

Liquidity, Time horizon, Tax, Legal and regulatory, Unique circumstances

Cover all five in a constructed response. Say none applies only if the vignette shows none.

Required nominal return

Required return = (1 + spending rate + cost of investing) × (1 + inflation) − 1, which is approximately spending rate + costs + inflation

Use the exact form if the question gives all inputs and asks for precision. Costs include management and fund fees if the question states them.

Real return needed to preserve capital

Real return needed ≈ spending rate + investment costs

Inflation is then added to get the nominal figure. Spending of 4% and costs of 1% means a 5% real return.

Exact real return

Real return = (1 + nominal return) ÷ (1 + inflation) − 1

Use this when the question asks for an exact real return rather than an approximation.

Unfunded commitment exposure

Total private exposure = NAV of private assets + unfunded commitments

Use this when you test whether the true illiquid exposure is above a policy limit.

Required return

Required return ≈ spending rate + inflation + investment costs

Use the geometric form (1 + spending)(1 + inflation)(1 + costs) − 1 if the question asks for precision. Compare with the portfolio's expected return.

Liquid asset coverage

Coverage = liquid assets ÷ (spending + unfunded commitments expected to be called + other cash needs)

A ratio below 1 over the stress period signals a liquidity problem. Use stressed values for liquid assets.

Unfunded commitments exposure

Effective alternatives exposure = invested alternatives + unfunded commitments

Commitments are future exposure. Include them when judging the true allocation limit.

Illiquidity premium test

Net expected alternative return − comparable liquid asset return = premium; compare premium with the cost of illiquidity

Use returns after fees. The premium must be adequate for the lock-up, valuation uncertainty and extra risk.

Stress-adjusted allocation after a fall

New weight = (weight × (1 + asset return)) ÷ (1 + portfolio return)

Shows the denominator effect: illiquid assets look bigger when liquid assets fall.

Quick revision

• The IPS lists objectives (return, risk) and constraints (liquidity, horizon, legal and regulatory, tax, unique needs), plus governance and review.
• An endowment usually has a perpetual horizon, so it can hold more long-term and illiquid assets.
• Basic return objective: spending rate plus inflation plus costs, to preserve real value.
• Check whether the question wants a nominal or real required return, and whether to add or compound.
• Spending rules smooth payouts: a rule based on a moving average of past values reduces the effect of market swings.
• Risk ability and willingness are assessed separately; if they conflict, the lower one generally governs.
• High dependence on endowment payouts in the operating budget lowers risk ability.
• Liquidity needs include spending, capital calls on private investments and rebalancing needs.
• Legal constraints can include donor restrictions and rules on prudent investing and spending.
• The endowment model favours diversification into alternatives; its costs include illiquidity, high fees and valuation lag.
• When evaluating a portfolio, test it against each IPS item in turn and state which ones it fails.
• Answer the command word asked, give only the number of points requested, and keep each point tied to the case facts.

Common mistakes

• Adding spending and inflation but leaving out investment costs. Fix: Always scan the case for management or administrative costs and include them in the required return.
• Stating an overall risk tolerance without separating ability and willingness. Fix: Give both parts with a reason each, then state the overall tolerance. If they conflict, the lower one governs.
• Leaving out investment costs from the required return. Fix: Always scan the case for management or administration fees and add them.
• Adding inflation twice, or using inflation when the objective is real. Fix: Underline whether the target is real or nominal before calculating.
• Merging ability and willingness into one vague rating. Fix: Give two separate ratings with separate reasons, then combine them.
• Rating ability high because the endowment needs a high return. Fix: Rate ability only on horizon, spending dependence, reserves and funding stability. A high needed return does not raise capacity.
• Saying liquidity need is high because the endowment pays out every year. Fix: Compute spending plus other outflows as a share of assets. A few percent is usually a moderate need. Judge it from the numbers.
• Writing a perpetual horizon and stopping there. Fix: Say the horizon is perpetual and then note the annual spending and any known cash needs. This supports long-term risk assets with enough liquid reserves.
• Recommending the endowment model for every endowment. Fix: Fit the allocation to the client. A small endowment with little governance capacity and high spending needs may be better served by a more liquid approach.
• Ignoring unfunded commitments when measuring illiquid exposure. Fix: Add unfunded commitments to the NAV to get true exposure, and check that liquid assets can fund the calls.

Exam tips

• Show the required return calculation line by line, and type the final number clearly. A correct number on its own earns full credit, so avoid rounding too early.
• Read the command word. 'Determine' needs the answer, 'justify' needs a reason from the case, and 'state' needs only the statement. Do not write more than asked.
• Give only the number of responses requested, in the order asked. Extra responses may not be evaluated.
• Split risk tolerance into ability and willingness every time, and name the overall result.
• Quote a case fact in each justification. A fact-linked reason earns more than a general statement.
• Check if the item asks for real or nominal before touching a calculator, and compound the real return with inflation for the exact nominal answer.
• In essays, type the number on its own as the answer and show working above it if space allows.
• When asked to compare rules, name the trade-off: spending stability versus tracking the fund's value.