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Short answer: The Takahashi-Alexander model is a deterministic framework for projecting capital calls, distributions, and net asset value across the life of a private markets fund. It was developed at the Yale University Investments Office and published in the Journal of Portfolio Management in 2002. It requires five parameters: fund life, call rate, growth rate, yield, and bow factor. It is the standard approach institutional investors use for private markets pacing and liquidity planning, and it is the model MyFO applies to project fund cash flows.
Key takeaways
- The model projects three linked series: capital calls, distributions, and NAV, across a fund's full life.
- It is deterministic. One set of inputs produces one projection, not a probability distribution.
- Capital is called as a fixed percentage of remaining unfunded commitment, which produces front-loaded drawdowns that decay over time.
- Distributions are a percentage of opening NAV, governed by a rate that rises as the fund ages.
- The bow factor controls the shape of that distribution curve and is the parameter that most affects projected TVPI.
- Parameters differ materially by asset class. Private credit and private equity produce very different profiles from the same equations.
- Accuracy improves at the portfolio level. Applied to a single concentrated fund, smooth modelled curves will not match lumpy actual distributions.
What the Takahashi-Alexander model does
Dean Takahashi and Seth Alexander, then senior director and associate director of the Yale University Investments Office, published Illiquid Alternative Asset Fund Modeling in the Journal of Portfolio Management in Winter 2002. The paper describes a model that enables institutional investors to project future asset values and cash flows for funds in illiquid alternative asset classes including venture capital, leveraged buyouts, real estate, and natural resources.
It is widely referred to as the Yale model. Subsequent literature identifies it as among the earliest work formalising a deterministic predictive model of limited partner contributions, distributions, and NAV, and it remains the reference point from which later stochastic approaches were developed.
Deterministic means a single run produces a single projected path rather than a distribution of outcomes. Scenario analysis is performed by re-running the model with different parameter sets, not by sampling within one run.
The equations
The model is four recursive relationships evaluated period by period.
Capital calls are a constant percentage of what remains uncalled:
Because the base shrinks each period, this produces a drawdown curve that is heavy early and decays geometrically. This matches observed fund behaviour without requiring a separate schedule to be specified.
Distributions are a percentage of opening NAV, where the percentage rises with fund age:
NAV links the two and compounds at the assumed growth rate:
The J-curve is an output of these equations rather than an assumption fed into them. Early periods are dominated by calls with minimal distributions, so NAV builds. Later periods invert.
The five parameters
Two of these warrant specific comment.
Yield applies selectively. It sets a floor on the distribution rate and is relevant for strategies that generate income before exit, which in practice means private credit, real estate, and infrastructure. For buyout and venture strategies, where returns are realised through exits rather than current income, yield is generally set at or near zero.
Bow is the parameter that does the most work. Because TVPI is a derived output rather than an input, and because a higher bow defers distributions and leaves NAV compounding for longer, bow can be solved backwards from a target TVPI. Holding fund life, call rate, and growth rate constant, a higher bow produces a higher projected TVPI. Calibrating against TVPI is generally more reliable than calibrating against distribution curves directly, since TVPI is the more consistently reported figure.
A worked projection
Applying the model to a $10M commitment with fund life of 12 years, call rate of 35%, growth rate of 13%, yield of zero, and bow of 2.5:
Figures in $M. Terminal period assumes full liquidation.
Three observations from the output. Roughly 73% of the commitment is called in the first three years. NAV peaks in year 5, after which distributions exceed the combination of calls and growth. DPI crosses 1.0x in year 8, meaning the position does not return its called capital until two thirds of the way through the fund's life.
That third point is the operationally significant one. A commitment made today creates a liability that is largely funded within three years and is not repaid for eight.
How parameters differ by asset class
The same equations describe every strategy. The parameters do not.
Private equity draws steadily over four to five years with distributions concentrated from year five onward. Yield is typically zero and the bow is moderate.
Venture capital has a longer effective life, slower realisations, and a higher bow, reflecting distributions concentrated late and driven by a small number of exits. Zero yield.
Private credit deploys faster, returns capital earlier and more smoothly, and carries a meaningful yield floor because interest income is distributed throughout the life of the fund rather than at exit. Lower bow.
Real estate and infrastructure sit between the two, with a yield floor reflecting rental or contracted income and a fund life extended by longer hold periods.
Using a single parameter set across an entire private markets portfolio will misstate the timing of both calls and distributions. Calibrating per asset class is the difference between a projection that is useful for liquidity planning and one that is not.
Limitations
It is deterministic. The output is one path. It does not quantify the probability that calls arrive faster than projected, which is the scenario that actually creates a liquidity problem. Sensitivity analysis requires running multiple parameter sets and comparing them.
Smooth curves do not describe individual funds well. Actual distributions are lumpy. A concentrated fund holding six positions may distribute nothing for two years and then make a single large distribution. Practitioner analysis notes that the model's curves fit better as the number of funds in a portfolio increases, since aggregation smooths the underlying lumpiness. The model is more dependable across a portfolio of commitments than against any single fund.
Output quality is bounded by parameter quality. The equations are simple and stable. The judgement sits entirely in calibration, and a well-formed projection built on unexamined parameters will look credible while being wrong.
Subscription lines distort historical calibration. Where funds use credit facilities to defer capital calls, observed historical call timing reflects the facility rather than the underlying investment pace. Call rates calibrated from that data without adjustment will understate how quickly capital is genuinely required.
How MyFO applies the model
Investment data is tracked in MyFO, and the MyFO performance engine applies the Takahashi-Alexander model to project capital calls and distributions across private fund positions, consolidated with the other expected inflows and outflows on the balance sheet.
To see this across an existing portfolio, book a call.
The bottom line
The Takahashi-Alexander model remains the standard framework for private markets pacing because it captures the structure of LP cash flows with five parameters and no unnecessary complexity. Its value depends on calibration by asset class, on being applied across a portfolio rather than a single fund, and on being maintained as commitments and actual drawdowns change. Modelled once in a spreadsheet, it decays. Maintained against live positions, it is the basis of a defensible liquidity plan.
To see the model applied across an existing set of fund commitments, book a call.
FAQ
How does the model handle a fund that is already partway through its life?
The projection begins from current state rather than from inception. Existing NAV becomes the opening balance, cumulative calls to date determine remaining unfunded commitment, and the distribution rate is evaluated at the fund's current age rather than at year one. A fund in year six of a twelve-year life starts with a distribution rate already well up its curve.
Does the model account for recycling or recallable distributions?
Not in its base form. The standard formulation treats distributions as permanently returned. Where a fund can recall distributed capital, unfunded commitment is understated by the recallable amount, and liquidity planning based on the unadjusted projection will understate the obligation. This is a manual adjustment in most implementations.
Why forecast at all when GPs issue capital call notices with a notice period?
Because the notice period is measured in days and the liquidity decision is measured in quarters. A ten business day notice is sufficient time to wire funds only if the cash already exists in an appropriate form. The purpose of pacing is to identify periods where multiple commitments draw simultaneously, which is visible months ahead in a projection and not visible at all in a notice.
Is there a stochastic alternative?
Yes. Later work developed continuous-time stochastic versions and market-sensitive extensions that model NAV growth as variable rather than fixed. These produce distributions of outcomes rather than single paths. They also require more parameters and more data. For most family office pacing purposes the deterministic model with multiple scenario runs is the practical choice.
Educational content, not investment advice. Cash flow pacing models rely on historical patterns and assumptions. Actual contributions and distributions will differ from projected figures.
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