Three spending rules run through the same crash on an illustrative endowment with 30 per cent in private equity, and what smoothing the payout does to the liquid assets that have to fund it.
The hybrid spending rule associated with Yale sets this year's spending at 80 per cent of last year's spending grown by inflation, plus 20 per cent of a target rate times the endowment's value. On an illustrative endowment of 1,000 with 30 per cent in private equity, a year in which liquid assets fall 28 per cent cuts spending by 2.5 per cent under the hybrid rule against 25.3 per cent under a flat 5 per cent. The price is paid elsewhere: spending rises to 10.3 per cent of the liquid assets that fund it, and six years on the endowment is 798.9 instead of 831.3.
Worked in full in Alternative Investments by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
An endowment or foundation funds a budget, salaries, grants and scholarships, that cannot be cut by a quarter in a bad year without real damage. It also has to preserve the purchasing power of the capital for later beneficiaries. A rule that spends a fixed share of current value honours the second aim and fails the first. Smoothing rules trade some of one for the other, and the trade gets sharper when a large part of the portfolio is in illiquid funds whose reported values lag the market.
| Input | Value |
|---|---|
| Value at the start of year 1 | 1,000 |
| Values at the start of the two prior years | 940 and 970 |
| Last year's spending | 48.5 |
| Target spending rate | 5% |
| Hybrid weights, prior spending / target rate | 80% / 20% |
| Inflation | 2.5% |
| Liquid assets / private equity at the start | 70% / 30% |
| Liquid returns, years 1 to 6 | 12%, −28%, 10%, 15%, 9%, −5% |
| Private equity reported returns, years 1 to 6 | 12%, −8%, −2%, 10%, 12%, 2% |
Spending is set and paid at the start of each year, out of liquid assets. There is no rebalancing and capital calls are assumed to net against distributions, so the private equity sleeve drifts with its own marks.
Fixed: St = 5% × Vt
Moving average: St = 5% × average(Vt−2, Vt−1, Vt)
Hybrid: St = 80% × St−1 × (1 + inflation) + 20% × 5% × Vt
Excel, hybrid: =w*S_prev*(1+infl)+(1-w)*rate*V
Vt is the value at the start of the year. Yale's own weights and target rate have changed over time; the 80/20 and 5 per cent here are illustrative. Yale also applies the target rate to a lagged market value rather than the current one, which smooths the payout further.
Year 2 is the crash. At the start of year 3 the hybrid endowment is worth 796.4, of which 487.3 is liquid.
Fixed: 5% × 795.0 = 39.7
Moving average: 5% × average(1,000.0, 1,065.7, 798.1) = 47.7
Hybrid: 0.80 × 51.5 × 1.025 = 42.2, plus 0.20 × 5% × 796.4 = 8.0, total 50.2
The hybrid rule spends 10.4 more than the fixed rule in the year after the crash, an effective 6.30 per cent of the endowment's value.
| Year | 5% of value | 5% of 3-year average | Hybrid 80/20 |
|---|---|---|---|
| 1 | 50.0 | 48.5 | 49.8 |
| 2 | 53.2 | 50.6 | 51.5 |
| 3 | 39.7 | 47.7 | 50.2 |
| 4 | 39.7 | 44.2 | 49.0 |
| 5 | 42.6 | 40.4 | 48.5 |
| 6 | 44.6 | 41.8 | 48.3 |
| Total | 269.8 | 273.3 | 297.1 |
| Worst one-year cut | −25.3% | −8.5% | −2.5% |
| Peak spending / liquid assets | 8.6% | 9.8% | 10.3% |
| Value at the end of year 6 | 831.3 | 824.4 | 798.9 |
The hybrid rule delivers what it promises: no cut deeper than 2.5 per cent through a 28 per cent fall in the liquid book. The moving average only delays the damage, cutting in years 3, 4 and 5 in turn. And the hybrid's stability is financed out of capital: 27.3 more spent over six years, and an endowment 32.4 smaller, 3.9 per cent, at the end.
The private equity sleeve makes the crash look milder than it is. Its reported marks fall 8 per cent while listed assets fall 28, so its share of the endowment drifts from 30.0 to 38.8 per cent, the denominator effect described in how to calculate the denominator effect. Spending computed on total value is then paid out of a liquid book that has shrunk much more: 10.3 per cent of liquid assets under the hybrid rule in year 3, against 7.1 before the crash.
| Weight | Worst cut | Year 3 spending | Six-year total | End value | Peak spend / liquid |
|---|---|---|---|---|---|
| 0% (fixed rule) | −25.3% | 39.7 | 269.8 | 831.3 | 8.6% |
| 50% | −10.6% | 46.6 | 279.7 | 818.5 | 9.6% |
| 70% | −5.1% | 49.0 | 289.8 | 806.9 | 10.1% |
| 80% | −2.5% | 50.2 | 297.1 | 798.9 | 10.3% |
| 90% | −0.1% | 51.2 | 306.3 | 789.0 | 10.7% |
Every step up in smoothing buys a gentler budget with capital and liquidity. Near 90 per cent the rule barely responds to markets at all, which works only if the long-run return really covers the target rate plus inflation and costs, the test in whether a private foundation can pay out 5 per cent forever.
Choosing the smoothing weight for the budget and the private equity allocation for the return, in two different meetings. The rule fixes how much cash leaves each year; the allocation fixes how much of the portfolio can supply it. A heavily smoothed rule on a portfolio with a large illiquid sleeve concentrates the stress on the liquid assets in exactly the years they have fallen most, and that is when capital calls tend to continue.
The book follows a foundation's commitments, calls and distributions to the return that actually reaches it, and the free workbook for this case runs the cash-flow engine, including the denominator effect, on its own schedule.
Spending this year = w times last year's spending times (1 + inflation) + (1 minus w) times the target rate times the endowment's value. With w at 80 per cent, a 5 per cent target and 2.5 per cent inflation, last year's 51.5 and a value of 796.4 give 42.2 + 8.0 = 50.2. Yale's own weights and rate have changed over time; these are illustrative.
To protect the budget they fund from market swings. In the illustrative case a flat 5 per cent of value cuts spending from 53.2 to 39.7 after a crash, 25.3 per cent in one year; a three-year average cuts it by 8.5 per cent at worst, the 80/20 hybrid by 2.5. The cost is that spending stays high when the endowment is low.
Spending is paid from liquid assets, and private equity marks fall less and later than listed markets. After a 28 per cent fall in liquid assets the illustrative endowment's private equity share drifts from 30.0 to 38.8 per cent, and hybrid spending rises from 7.1 to 10.3 per cent of what can actually be sold.
This article is one calculation from Alternative Investments. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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