A square-root rule sets the refresh interval for each manager from the review cost, the hazard of a deterioration and what finding it late costs.
Refresh operational due diligence at the interval that balances the cost of a review against the expected cost of a problem going unseen: T = √(C ÷ (λ × k × (1/d − ½))). With an illustrative 25,000 per review, 100,000 a year of cost while a deterioration is undetected and an 80 per cent chance a review catches it, the answer is about 35 months for a low-risk manager, 22 for a medium-risk one and 14 for a high-risk one. A tiered cycle of three, two and one years costs 977,917 a year across 40 managers, 154,167 less than reviewing everyone every three years.
Worked in full in Operational Due Diligence in Private Equity by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Allocators often set the refresh cycle by habit: every manager every two or three years, or "before each re-up". Both leave money on the table, because the risk that something changes at a manager is not the same across the book, and the cost of finding out late is not either. The trade-off can be written down and solved.
| Input | Value |
|---|---|
| Cost of a full refresh, C (analyst days, travel, specialist input) | 25,000 |
| Expected cost a year while a deterioration is undetected, k | 100,000 |
| Chance a review detects an issue that is present, d | 80% |
| Annual chance of a material operational deterioration, λ: low / medium / high risk | 4% / 10% / 25% |
| Managers held: low / medium / high risk | 20 / 15 / 5 |
The cost k is the hardest input and the most important to argue about. In a closed-end fund an investor cannot redeem, so early detection is worth what it lets you do: push for remediation through the LPAC or the side letter, size or decline the next commitment, tighten monitoring of the existing one. It is the expected loss avoided by doing those things a year earlier. The hazard λ comes from the manager's last rating: a firm with a key-person-heavy back office, a new administrator or rapid growth in assets sits in the high tier.
A deterioration that arises at a random moment between two reviews waits, on average, half the interval before the next one. If that review misses it, which happens with probability 1 − d, it waits a full interval more, and so on.
E[time hidden] = T/2 + T × (1 − d)/d = T × (1/d − ½)
With d = 80%: 1/0.80 − 0.5 = 1.25 − 0.5 = 0.75 × T
So a three-year cycle leaves the average problem hidden for 2.25 years, not 1.5. Weak reviews leave problems hidden for longer than the cycle suggests: a desk-based questionnaire that catches 60 per cent of issues has a multiplier of 1.167, so a three-year cycle hides the average problem for 3.5 years.
Annual cost(T) = C/T + λ × k × T × (1/d − ½)
The second term is the arrival rate of problems times how long each stays hidden times what each hidden year costs; it assumes deteriorations are rare enough not to overlap.
The first term falls as reviews get rarer; the second rises. Setting the derivative to zero:
T* = √(C ÷ (λ × k × (1/d − ½)))
Medium risk: λ × k × 0.75 = 0.10 × 100,000 × 0.75 = 7,500; 25,000 ÷ 7,500 = 3.333; √3.333 = 1.83 years, about 22 months.
Excel: =SQRT(C/(Lambda*k*(1/d-0.5)))
At the optimum the two halves of the cost are equal: for the medium-risk manager, 13,693 of review spend and 13,693 of expected undetected cost, 27,386 a year in all.
| Tier | λ | Optimal interval | Months | Annual cost at optimum |
|---|---|---|---|---|
| Low risk | 4% | 2.89 years | 35 | 17,321 |
| Medium risk | 10% | 1.83 years | 22 | 27,386 |
| High risk | 25% | 1.15 years | 14 | 43,301 |
The interval scales with the square root of the hazard: a high-risk manager is 6.25 times as likely to deteriorate as a low-risk one, and gets reviewed 2.50 times as often, not six times.
Nobody schedules a review every 1.83 years. The cost curve is flat near the optimum, so rounding to whole years costs little, as long as each tier is rounded to its own interval.
| Interval | Low risk | Medium risk | High risk |
|---|---|---|---|
| Every year | 28,000 (+61.7%) | 32,500 (+18.7%) | 43,750 (+1.0%) |
| Every 2 years | 18,500 (+6.8%) | 27,500 (+0.4%) | 50,000 (+15.5%) |
| Every 3 years | 17,333 (+0.1%) | 30,833 (+12.6%) | 64,583 (+49.1%) |
| Every 4 years | 18,250 (+5.4%) | 36,250 (+32.4%) | 81,250 (+87.6%) |
| Policy | Reviews a year | Review spend | Total annual cost |
|---|---|---|---|
| Everyone every year | 40.0 | 1,000,000 | 1,266,250 |
| Everyone every 2 years | 20.0 | 500,000 | 1,032,500 |
| Everyone every 3 years | 13.3 | 333,333 | 1,132,083 |
| Tiered: 3 / 2 / 1 years | 19.2 | 479,167 | 977,917 |
The tiered cycle does about the same number of reviews as a uniform two-year cycle and costs 54,583 a year less, because it moves effort from managers where little changes to the five where most of the risk sits. Against a three-year cycle, the saving is 154,167. The review count also tells you the staffing: 19.2 full refreshes a year is the input to how many managers one ODD analyst can cover.
Treating the re-up as the review trigger. It ties the cycle to the fundraising calendar, often four or five years, rather than to risk; on a high-risk manager a four-year cycle costs 81,250 a year against 43,301 at the optimum, 87.6 per cent more. The second mistake is assuming a review that happened found everything: with d at 80 per cent, one problem in five survives it.
Interval = √(review cost ÷ (hazard × cost of being late × (1/d − ½))). Here about three years for low-risk managers, two for medium and one for high, which beats any uniform cycle. Whether the programme pays at all is the subject of whether operational due diligence is worth what it costs, and the rating model that sets each manager's tier is in the free workbook for this case.
It should depend on the manager's risk. On illustrative inputs, a 25,000 review and 100,000 a year of cost while a problem is undetected, the optimal interval is about 35 months for a low-risk manager, 22 months for a medium-risk one and 14 months for a high-risk one. Rounded to three, two and one years, the cost is within 1 per cent of the optimum for each.
Because a problem a review misses waits for the next cycle. Expected time hidden is T times (1/d minus a half), where d is the detection rate. At 80 per cent detection that is 0.75 times the interval, so a three-year cycle leaves the average problem hidden for 2.25 years rather than 1.5.
Usually not. It ties the cycle to fundraising, often four or five years, rather than to risk. For a high-risk manager a four-year cycle costs 81,250 a year in review spend and expected undetected cost, against 43,301 at the optimal interval of 1.15 years, 87.6 per cent more.
This article is one calculation from Operational Due Diligence in Private Equity. 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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