The fill ratio is one division. What it does to the investor's return depends on the NAV path during the wait, not on the delay itself.
When tenders exceed the repurchase offer, every request is filled in the same proportion: offer divided by tenders. A 5 per cent offer met by requests for 20 per cent of the shares fills 25 per cent of each request, so an investor tendering 4,000 shares sells 1,000 and must tender again. Re-tendering every quarter at that fill, 31.6 per cent of the position is still in the fund a year later, and it takes 10.4 quarters to get 95 per cent out.
Worked in full in The Credit Investor by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
An interval fund promises liquidity at intervals, not on demand. Each quarter it offers to buy back a fixed share of its own shares at NAV, between 5 and 25 per cent under the US rule, and may take up to a further 2 per cent if more is tendered. Above that, proration applies. The fund below is assumed not to use the extra 2 per cent; if it did, the 25 per cent fill would become 35 per cent. The arithmetic is simple; what it does to the investor's return is less obvious, and it is not what most people expect.
| Input | Value |
|---|---|
| Investment / shares / NAV at purchase | 100,000 / 4000 / 25.00 |
| Distribution per share a quarter | 0.5625 (9.00% a year on cost) |
| Quarterly repurchase offer, share of outstanding | 5% |
| Tenders received, share of outstanding | 20% |
| Full tender lodged at quarter | 12 |
| Quarters prorated, then paid in full | 4 |
| Recession path: SOFR cut from quarter 5, losses tripled in quarters 5 to 8 | 1.50 points / 5.25% of NAV |
Fill ratio = shares offered ÷ shares tendered = 5% ÷ 20% = 25%
Shares repurchased = shares tendered × fill ratio = 4000 × 25% = 1,000
Left after n prorated quarters = (1 − fill)n = 75%4 = 31.6%
Quarters to get 95% out = ln(5%) ÷ ln(1 − fill) = 10.4
In Excel: =MIN(1,Offer/Tendered) for the fill, and =LN(0.05)/LN(1-Fill) for the time to exit.
| Offer | Tenders | Fill | Shares sold |
|---|---|---|---|
| 5% | 5% | 100.0% | 4000 |
| 5% | 8% | 62.5% | 2500 |
| 5% | 10% | 50.0% | 2000 |
| 5% | 20% | 25.0% | 1000 |
| 10% | 20% | 50.0% | 2000 |
At a 50 per cent fill the exit takes 4.3 quarters; at 25 per cent it takes 10.4. Demand for liquidity is not spread evenly: tenders rise exactly when credit conditions worsen, so the fill falls when investors most want out.
In the book's recession path the fund's NAV per share has fallen to 21.92 by quarter 12. The investor tenders everything; the gate fills a quarter of each request for four quarters and pays the rest at quarter 16.
| Quarter | Shares sold | NAV | Cash received | Shares left |
|---|---|---|---|---|
| 12 | 1,000 | 21.92 | 24,173 | 3,000 |
| 13 | 750 | 21.68 | 17,950 | 2,250 |
| 14 | 562.5 | 21.44 | 13,325 | 1,687.5 |
| 15 | 421.875 | 21.19 | 9,889 | 1,265.625 |
| 16 | 1,265.625 | 20.94 | 27,214 | 0 |
Cash received includes the distributions on the shares still held. Paid in full at quarter 12, the same investor would have received 89,944 at once and earned an IRR of 5.28 per cent. Gated, the IRR is 5.37 per cent. The gate did not cost a return; it added 0.09 points.
The reason is in the yield. The shares left in the queue kept paying 0.5625 a quarter, 10.26 per cent a year on a NAV of 21.92, while NAV drifted down 4.49 per cent over the year. Waiting earned slightly more than the investment's own IRR. Discounted at a 2.50 per cent bill rate, the gated flows are worth 91,422 at quarter 12, 1,478 more than the cash paid in full. In the base case, with no recession, the IRR is 7.38 per cent gated or not.
The arithmetic flips quickly once the marks keep coming. Apply an extra markdown to NAV in each gated quarter:
| Extra markdown a quarter | Gated IRR | Cost against 5.28% paid in full, points |
|---|---|---|
| 0% | 5.37% | −0.09 |
| 1% | 4.88% | 0.40 |
| 2% | 4.39% | 0.89 |
| 5% | 2.95% | 2.34 |
The break-even is an extra markdown of only 0.18 per cent a quarter. A gate costs nothing when the fund is healthy and a great deal when its NAV is still being written down, which is when gates are imposed. The cost of proration is the NAV risk you are forced to keep, not the delay itself.
The fee stack that produces the 9.00 per cent distribution and the falling NAV is worked in what a private credit interval fund earns after fees.
Fill = offer ÷ tenders: 25 per cent here, leaving 31.6 per cent of a position in the fund after four quarters. Price the wait with the NAV path, not the calendar: in the book's recession the gate added 0.09 points, but 1 per cent of extra markdown a quarter turns that into a cost of 0.40. The repurchase proration table, the gate and every path are live formulas in the free workbooks for this case.
Under the US interval fund rule, between 5 and 25 per cent of outstanding shares per repurchase offer, with up to a further 2 per cent if tenders exceed the offer. Beyond the offer, requests are prorated: a 5 per cent offer against tenders for 20 per cent fills 25 per cent of each request, or 35 per cent if the fund also takes the extra 2 per cent.
Divide ln(5 per cent) by ln(1 minus the fill ratio) to get the quarters needed to sell 95 per cent of a position. At a 25 per cent fill that is 10.4 quarters; at 50 per cent, 4.3. After four quarters at 25 per cent, 31.6 per cent of the shares are still held.
Only if NAV falls faster than the distributions earned while waiting. In an illustrative recession with NAV at 21.92 and distributions worth 10.26 per cent a year, the gated investor earns 5.37 per cent against 5.28 paid in full. An extra NAV markdown of 1 per cent a quarter turns that into a 0.40 point cost.
This article is one calculation from The Credit Investor. 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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