The Private Equity J-Curve, Modeled for One Household

The J-curve that hurts a household is the cash curve, not the IRR curve. In the Kauffman Foundation's venture portfolio, reported IRR followed an "n" shape more often than the textbook J-curve, which appeared in only 29 percent of the funds assessed for that shape¹. The cash hole is not a reporting artefact. It is always there, and it is arithmetic: calls come first, distributions come later.

I'm not an LP adviser, and nothing here is advice on any fund. I build software for lower-market deals, and I treat a cash calendar the way I treat any other system: model it, then stress it. The model below is a household-scale version of the one Yale's investments office published in 2001, run from a script used for this post.

Your commitment is not your investment

For example, you sign for $100K. You wire a fraction of it at close. The rest can be called over the next several years, on the fund's schedule and its notice period, not yours.

Takeaway: the full commitment and the first wire are different amounts.

Two J-curves, and only one of them is guaranteed

The IRR J-curve is the one most explainers draw: negative early returns turning positive as the fund matures. Kauffman looked for it in its own portfolio and mostly didn't find it. Reported IRR peaked around month 16 and the shape was closer to an "n" than a "J"; 25 funds, or 29 percent of those assessed for that curve, showed the textbook shape¹, while a separate return analysis covered 94 funds².

The cash curve doesn't need a textbook shape to be real. Contributions arrive on a schedule the manager sets. Distributions arrive later, on a schedule nobody sets in advance. Net those two and you get a curve that goes down first no matter what the IRR is doing.

Takeaway: reported IRR in years 1 to 4 can move differently from net cash because the former reflects valuations while the latter reflects calls and distributions.

The model, in four lines

Takahashi and Alexander's model, published by Yale's investments office in 2001, describes a fund in four rules: calls are a rate on the commitment still uncalled, distributions are a rising share of net asset value, NAV grows at a rate G, and the fund has a fixed life L³. I ran three scenarios through it.

Base is the paper's own worked example: 13 percent NAV growth, a 12-year life. Slow is my own calibration, chosen so its distribution path sits close to Cambridge Associates' actual pooled DPI (distributions to paid-in) path for 2011-to-2013 vintage US private equity, as reported at Jun 30, 2020⁴. Flat is a fund that only ever returns the capital it was given, growth rate zero.

This is a deterministic model. It gives one path per set of inputs, which is exactly the limitation its own critics point out: no range, no probability, just a shape⁵. Every number below is [illustrative model], not a return forecast for any real fund.

Takeaway: a model like this gives you a shape and a calendar. It does not give you a forecast.

One fund: how deep, how long

In this illustrative model, for a single $100K commitment, all three scenarios go roughly 80 percent underwater before they recover, and the depth barely changes across them. What changes is the length.

Base: deepest point negative $79K in year 4, back to zero in year 8, final multiple 1.88x [illustrative model, E791]. Slow: deepest negative $86K in year 5, back to zero in year 10, final multiple 1.60x [illustrative model]. Flat, the fund that only returns capital: deepest negative $81K in year 4, and cash doesn't return to zero until year 12 or 13 [illustrative model].

One fund, one $100K commitment: how deep, how long

For a $100,000 commitment, cumulative net cash by year under three scenarios. Base: deepest -79,000 in year 4, back to zero in year 8, final multiple 1.88x. Slow: deepest -86,000 in year 5, back to zero in year 10, final multiple 1.60x. Flat, a fund that only returns capital: deepest -81,000 in year 4, back to zero only in year 12 to 13. Cambridge Associates' own pooled DPI path for US private equity sits close to the slow scenario.

Year 8, slow (calibrated to cambridge's pace): cumulative net cash −$38K per $100K committed.

Calls (below zero)Distributions (above zero)Cumulative net cash

Base (paper's worked example)Slow (calibrated to Cambridge's pace)Flat (returns capital only)

Year:

8

Cambridge's own pooled US PE DPI path [E795]: 0.03x at 3.5y, 0.13x at 4.5y, 0.39x at 6.5y, 0.49x at 7.5y, 0.69x at 8.5y, 1.01x at 9.5y, 1.52x at 11.5y. It sits close to the slow scenario.

Source: Takahashi and Alexander model, Yale Investments Office (2001), paper's worked example (base) and our slower calibration (slow)³⁶. Cambridge Associates pooled US PE DPI by vintage age, Jun 30, 2020⁴. Model outputs are [illustrative model], run from j-curve-pacing-model.py.

Figure data

One fund, one $100K commitment: how deep, how long

Year	Base (paper's worked example): cumulative net cash	Slow (calibrated to Cambridge's pace): cumulative net cash	Flat (returns capital only): cumulative net cash
Year 1	−$25K	−$25K	−$25K
Year 2	−$49.7K	−$49.9K	−$49.7K
Year 3	−$72.8K	−$74.5K	−$73.2K
Year 4	−$79.3K	−$85.1K	−$81K
Year 5	−$72.9K	−$86.5K	−$78.1K
Year 6	−$54.6K	−$79.4K	−$67.5K
Year 7	−$26.1K	−$63.2K	−$51.5K
Year 8	$8.9K	−$37.6K	−$33.6K
Year 9	$43.5K	−$5.1K	−$17.6K
Year 10	$70K	$27.5K	−$6.6K
Year 11	$84.1K	$50.9K	−$1.4K
Year 12	$88K	$60K	$0K
Year 13	$88.1K	$60K	$0K
Deepest point	−$79.3K in year 4	−$86.5K in year 5	−$81K in year 4
Break-even year	Year 8	Year 10	Year 13
Final multiple of the commitment	1.88x	1.60x	1.00x

Per $100K commitment; model outputs, not a forecast for any fund.

Cambridge's own pooled DPI data for actual PE funds sits close to my slow scenario: 0.69x at about 8.5 years, 1.01x at about 9.5 years⁴. That isn't a coincidence. I calibrated the slow scenario to match it, but that historical DPI path does not establish how any fund will distribute cash. The flat illustration returns to zero in year 12 or 13, rather than never [illustrative model].

Takeaway: the depth of the hole barely changes across scenarios. The number of years you're in it changes a lot.

Three ways to commit $500K

Because a fund may call less than the full amount you sign for, a commitment and a target exposure are not the same number³. Yale's own early rule of thumb for its venture program was to commit roughly 50 cents for every dollar of exposure it actually wanted outstanding, built up as a series of funds rather than one⁶. The illustrative calendars below compare a $500K commitment made at once with $500K committed over five years; the $250K figure instead follows Yale's separate rule of thumb for $500K of target exposure [illustrative model, E792].

For example, a household might compare two ways to commit $500K over time with a separate ongoing plan. Plan A puts it all into one vintage year. Plan B spreads $100K a year across five vintages. Plan C keeps committing $100K a year indefinitely.

Same $500K, three calendars

Three household plans committing $500,000 to private equity, slow scenario. Plan A, one vintage: deepest cash hole $432,000 in year 5, peak uncalled commitment $375,000. Plan B, $100,000 a year for five years: deepest cash hole $389,000 in year 7, peak uncalled commitment $169,000. Plan C, $100,000 a year ongoing: deepest cash hole $506,000 in year 9, peak uncalled commitment $175,000.

A. $500K into one vintage

deepest −$432K (yr 5) · peak unfunded $375K

B. $100K a year for 5 years

deepest −$389K (yr 7) · peak unfunded $169K

C. $100K a year, ongoing

deepest −$506K (yr 9) · peak unfunded $175K

Calls (below zero)Distributions (above zero)Cumulative net cash

Slow scenario throughout, years 1 to 14. Same $500K committed three ways.

Source: Takahashi-Alexander model, slow scenario calibrated to Cambridge Associates' pooled US PE DPI path, run from j-curve-pacing-model.py³⁶⁴. Model outputs are [illustrative model], not a forecast for any fund or household.

Figure data

Same $500K, three calendars

Year	A. $500K into one vintage: cumulative net cash	B. $100K a year for 5 years: cumulative net cash	C. $100K a year, ongoing: cumulative net cash
Year 1	−$125K	−$25K	−$25K
Year 2	−$249.7K	−$74.9K	−$74.9K
Year 3	−$372.6K	−$149.5K	−$149.5K
Year 4	−$425.7K	−$234.6K	−$234.6K
Year 5	−$432.3K	−$321.1K	−$321.1K
Year 6	−$396.9K	−$375.5K	−$400.5K
Year 7	−$316K	−$388.7K	−$463.7K
Year 8	−$188.2K	−$351.8K	−$501.3K
Year 9	−$25.7K	−$271.8K	−$506.4K
Year 10	$137.4K	−$157.9K	−$479K
Year 11	$254.4K	−$27.6K	−$428.1K
Year 12	$299.9K	$95.6K	−$368.1K
Year 13	$300.2K	$193.3K	−$308.1K
Year 14	$300.2K	$258.4K	−$248K
Deepest point	−$432.3K in year 5	−$388.7K in year 7	−$506.4K in year 9
Peak uncalled commitment	$375K	$169K	$175K

$500K committed in total, slow pacing scenario; model outputs.

Under the slow scenario: Plan A's deepest cash hole is $432K in year 5, and its modeled year-end uncalled balance after the first $125K call is $375K, down from the initial $500K commitment [illustrative model]. Plan B's deepest hole is $389K in year 7, with a peak uncalled commitment of $169K [illustrative model]. Plan C, which never stops committing, goes deeper still: $506K in year 9, with a peak uncalled commitment of $175K [illustrative model].

Takeaway: pacing across vintages roughly halves the modeled peak year-end uncalled balance and trims the deepest hole by about a tenth, but it doesn't make the years shorter [illustrative model].

The year calls stop being your problem

In Plan B under the slow scenario, you're funding calls from cash outside the fund for seven straight years, with about $94K in gross calls and about $87K in net outflow in year 5 [illustrative model]. That's not a worst case. Market data backs the assumption up: in 2022 and 2023 combined, US private equity managers called nearly $64B more than they distributed, and US venture managers called more than they returned in 9 of the 10 quarters from January 2022 to mid-2024⁷.

Bain's 2026 report on the broader market: distributions fell to 14 percent of net asset value in 2025, the fourth straight year below 15 percent, and 53 percent of surveyed LPs say undrawn commitments are limiting their ability to make new ones⁸. Average holding periods at exit are running around seven years, up from five to six years in 2010 to 2021⁹.

Takeaway: the fast and slow scenarios illustrate different cash calendars, not outcomes to expect from a particular fund.

Newer venture data agrees with the slow read. Carta's Q1 2026 sample of 2,775 venture funds shows median DPI for 2019 and 2020 vintages just above zero, with fewer than half of those funds having returned any capital yet¹⁰. This is a vendor data source, not an independent benchmark, and the cited third-party report attributes the figures to Carta.

Pacing across vintages also paces your tax paperwork, and not in a good way. Every additional vintage year is another fund sending its own K-1. Long Angle's survey of its own members reports a median $3,000 annual CPA cost and 10 to 20 K-1s a year across a typical private-markets portfolio, arriving between February and September, with most funds extending to September 15¹¹. A calendar that spreads calls across five vintages is also a calendar that spreads K-1 season across five separate documents, every year, for as long as any of those funds stay open.

Takeaway: pacing is a liquidity decision first. Its tax-paperwork cost is real but secondary, and it's worth knowing before your first extension deadline surprises you.

How this breaks

• Committing money you need for the first calls, then selling something else at a bad moment to cover one.
• Assuming distributions from an earlier fund will pay the calls on a newer one. The model above shows they can arrive years later than that assumption needs them to.
• Over-committing to reach a target exposure, then watching a slow exit market delay the time before you're self-funding⁷⁸.
• Missing a call. Limited partnership agreements carry real remedies for a missed call, and the notice period is short. The applicable LPA, rather than a summary of another agreement, determines the remedies and notice period.
• Forgetting that the NAV a fund reports is a mark, not cash you can spend, and that marks stay unsettled for years¹².

Takeaway: the model's deepest cash hole is one illustrative path, not a worst-case outcome.

Our private investment liquidity budget is the blank calendar this post fills in with numbers. And our guide to private market return dispersion covers the other half of the same decision: which strategy and manager you're funding these calls into.

What I'd check

1. I'd build a one-sheet ledger for every commitment: amount called, amount still uncalled, and a call calendar built from the model above.
2. I'd compare the script's slow scenario with the paper's own example and note that both are illustrative model paths.
3. How much of the near-term uncalled commitment could be met from available liquidity? For Plan B, the modeled year-end uncalled balance peaks in year 5 [illustrative model].
4. I would not count on a future distribution to pay a future call until it has actually landed in the account. In 2022 and 2023, US private equity managers called nearly $64B more than they distributed⁷.
5. In the illustrative calendars, pacing commitments across vintages reduces the deepest cash hole but pushes self-funding later than a single-year commitment [illustrative model].
6. I'd read the default clause in every limited partnership agreement I sign, before I sign it.

Direct small-business deals can have a different cash shape from a fund's multi-year drawdown. That changes the liquidity question. It does not remove the underlying risk, and this post isn't a claim that it does.

Source notes

The pacing model is our own work, built on the published Takahashi-Alexander framework, and every model output is labeled [illustrative model]. This post makes no recommendation of any fund, manager, allocation size or commitment pace.