Measuring private markets: J-curve, cash flows, smoothing and public proxies

Advanced12 min read · updated 22 October 2026 · 24 sources

Private markets (private equity, private debt, infrastructure and real estate in closed-end funds) cannot be measured with daily prices the way an ETF can. Instead there are capital calls, distributions and a fund value that the manager usually estimates only once a quarter. This article explains the J-curve, works through IRR, TVPI, DPI and the public market equivalent for a fund over ten years, and shows why smoothed valuations make risk look too small and how desmoothing (unsmoothing) and levered listed proxies correct for it.

How a closed-end fund works

Most private markets funds are closed-end: a manager (the general partner, GP) collects commitments from investors (limited partners, LPs) and calls the money only when it is needed. According to Kaplan and Strömberg (2009), a buyout fund usually runs for ten years, with extensions of up to three years; the fund invests in the first few years and then sells the holdings. The building blocks:

• Capital commitment: the amount you legally commit. It stays with you at first but must be available whenever it is called.
• Capital calls (contributions): drawdowns of part of the commitment to pay for acquisitions, costs and fees. Their total is called paid-in capital.
• Distributions: cash flowing back from sales, dividends and interest. Most of it arrives when holdings are sold; according to Kaplan and Strömberg (2009), the median holding period for buyouts is about six years.
• Net asset value (NAV): the manager's estimate of the value of the holdings still in the fund, usually reported quarterly.
• Dry powder: committed capital that has not yet been called, for a single fund or the whole market.

In other words, the full commitment is never invested at once, and the manager decides when the cash flows happen. That is why such funds are measured on a money-weighted basis rather than with the time-weighted return.

The J-curve: first negative, then positive

If you plot the cumulative net cash flows or the running IRR over the years, you usually get a J: the J-curve. Management fees are charged on the commitment from day one, transaction costs are added when deals are made, and new holdings are initially carried at cost or valued conservatively. Gains show up only when values rise and holdings are sold; how deep the dip goes depends on the pace of calls and distributions.

The curve can be engineered. With a subscription line, the fund first buys on credit and calls the money later. This is a short-term loan secured by the investors' outstanding commitments. According to ILPA (2017), the effect on the IRR is strongest early in the fund's life: an analysis of 498 funds cited there found a median of 2.06 percentage points more IRR after three years and still 0.35 to 0.45 percentage points at the end of the fund's life. In the guide's worked example, a two-year credit line lifts the IRR from 6.62% to 7.98%, while the multiple drops from 1.45 to 1.35 because of the interest. The fund does not get any better, only the metric does.

Worked example: a fund over ten years

A hypothetical fund with a commitment of 100, fees included in the calls, plus a stock index for comparison. All values at year-end:

Metrics: IRR, multiples and PME

The DPI shows what has already come back and does not depend on estimates. The TVPI, by contrast, includes the estimated NAV. The internal rate of return (IRR) accounts for timing but has weaknesses: it assumes that distributions are reinvested at the IRR; an early success on a small amount can keep the IRR of the whole fund high for good; when the signs of the cash flows change more than once, there can be several solutions; and the manager controls the timing of cash flows through calls, credit lines and early distributions. According to ILPA (2024), early distributions funded by NAV financing also have a considerable effect on IRR and DPI.

The public market equivalent (PME) compares the cash flows with an index. The oldest version, by Long and Nickels (1996), invests each call in a shadow portfolio of the index, withdraws each distribution from it and compares the IRRs; when distributions are high, this portfolio turns negative (in the example from year 8 on, ending at −33.82). Kaplan and Schoar (2005) instead divide all cash flows by the index level on the respective date (KS-PME): above 1, the fund has beaten the index. Sorensen and Jagannathan (2015) show that the KS-PME is equivalent to a valuation with a dynamic CAPM, needs no betas and, unlike the IRR, cannot be gamed through the timing of cash flows. The index should match the rest of the investor's portfolio. Direct alpha, following Gredil et al. (2023), turns this into an annual excess return: all cash flows are compounded with the index to a reference date, and the IRR is calculated from the result.

Planning cash flows: the Yale model

If you want to hold private markets for the long term, you need to forecast when money will be called and when it will come back. Takahashi and Alexander (2002) of the Yale endowment presented a model for this that became known as the Yale model; it needs only a few assumptions and allows scenarios for commitments, call and distribution rates and returns. In the usual notation:

How the model calculates year by year, how to estimate its parameters from fund data and how much you need to commit across many vintages to maintain a target allocation is shown in the article on the Takahashi-Alexander model.

Valuation and smoothing: why volatility looks too low

The NAV is an estimate, often derived from multiples of comparable public companies or from discounted cash flow models, and it is updated infrequently and with a lag. Reported quarterly returns therefore track the market in a muted and delayed way: they are autocorrelated, the measured volatility, correlation and beta are too low, and the Sharpe ratio is too high. The private credit article has a worked example. Ilmanen et al. (2020) note that the smoothed returns of private equity understate its economic risk, and suspect that many investors value precisely this smoothing. Driessen et al. (2012) also find that the reported NAVs of mature and inactive funds substantially overstate their value.

Desmoothing step by step

In the simplest method, following Geltner (1993), the reported return is an average of the true return and the last reported one. The degree of smoothing θ is estimated as the first-order autocorrelation of a long series; the true return can then be backed out:

Extensions allow for more lags: Getmansky et al. (2004) model the reported return as a weighted average of the true returns of several periods, and Loudon et al. (2006) describe a method that removes autocorrelation of any order (following Okunev and White). Couts et al. (2024) show that funds with similar assets share a common smoothing component that such single-fund methods do not fully remove. Systematic risk then remains understated.

Public proxies: levered listed substitutes

Instead of repairing smoothed series, you can stand in for private markets with exchange-traded assets of similar risk: a public proxy. Phalippou (2014) shows that buyout funds invest mainly in small value companies; against levered small-cap and value indexes, they lagged by 3.1% a year on average. L’Her et al. (2016) find no significant excess return left against a levered index matched on size and industry. Stafford (2022) replicates the selection and the extra leverage with stocks and margin borrowing and on average earns more than direct fund investments. Chingono and Rasmussen (2015) pick small, cheap, indebted US stocks that are paying down debt: an average return of 25.1% a year from 1965 to 2013, but with a standard deviation of 39.4%. According to Jegadeesh et al. (2015), listed private equity firms have a beta close to one and more systematic risk than an index built from reported NAVs.

You can estimate the leverage via beta. A company's beta is the weighted average of the beta of its equity and the beta of its debt; with a debt beta of zero and no taxes, it follows that:

Consequences for optimization and rebalancing

If you feed smoothed returns into an optimization, private markets look like an asset with high returns, low volatility and low correlation, and they get too much weight. With desmoothed series or a levered proxy, the advantage shrinks a lot. In rebalancing, the denominator effect comes on top: when stock markets fall, the denominator of the allocation shrinks, but private valuations barely fall or fall later, so the private markets allocation rises above its target. According to Saccone (2024), the valuations of private funds decoupled from stocks and bonds in 2022; investors who sold on the secondary market received on average only 81% of NAV.

Advanced: estimating risk from cash flows

• Time series from cash flows: Ang et al. (2018) derive a return series for private equity from the cash flows to investors and decompose it into exchange-traded factors and a time-varying private equity premium.
• Beta from cash flows: Driessen et al. (2012) estimate risk and excess return directly from the cash flows of 958 funds: venture capital with a high market beta and underperformance, buyouts with a rather low beta and no excess return.
• Annualizing: with autocorrelated quarterly returns, scaling up by √4 is biased (Lo 2002); positive autocorrelation makes annual volatility look too small.
• Liquidity risk: according to Franzoni et al. (2012), private equity carries the same liquidity risk as public equities; the premium for it is about 3% a year and explains the measured alpha.

What the research shows

• Kaplan and Schoar (2005): fund returns after fees roughly in line with the S&P 500, with wide dispersion between funds.
• Harris et al. (2014): buyout funds outperformed the S&P 500 by 20 to 27% over their life, more than 3% a year; venture capital outperformed only in the 1990s.
• Phalippou and Gottschalg (2009): reported returns are overstated; after fees, 3% a year below the S&P 500, and 6% on a risk-adjusted basis.
• Phalippou (2014), L’Her et al. (2016) and Ilmanen et al. (2020): with a levered small-cap or small-value benchmark, the outperformance shrinks or disappears.

Limitations and common mistakes

• Comparing IRR with an index return: money-weighted against time-weighted is not a fair comparison; that is what PME and direct alpha are for.
• Overrating TVPI before the end: a high TVPI with a small DPI rests on estimates.
• Overrating desmoothing: θ is itself estimated, the correction amplifies measurement errors, and short series vary widely.
• Choosing the wrong proxy: a large-cap index understates the risk of buyouts; venture capital, infrastructure or private debt need their own proxies.

How Portfolio Lab calculates

For the cash flows of a single fund, there is the Private markets tool in the Plan section. From the date, call, distribution and NAV, it calculates the IRR the way Excel's XIRR function does, PIC, DPI, RVPI, TVPI and the J-curve; against an index of your choice, the KS-PME, direct alpha and the Long and Nickels PME-IRR; and from the NAV returns, Geltner desmoothing, optionally also following Getmansky, Lo and Makarov. On top of that come the forecast with the Takahashi-Alexander model and commitment planning across several vintages. The details are in the private markets methodology.

In its other tools, Portfolio Lab works with price series. There, it represents private markets through listed proxies in Asset classes, such as Listed private equity (listed investment companies, via an ETF from 2007 and a US ETF before that), Listed infrastructure from 2006 or Listed private credit (BDCs). These market prices are not smoothed. Volatility and correlation in the Backtest, in Optimization and in the Monte Carlo simulation therefore tend to be higher than what fund reports show. You can rebuild a levered proxy like the one above: choose Equities US small cap value and set leverage per security in the backtest, financed at the money market rate plus a spread (1% a year by default). More in the asset class methodology.

This article explains a method; it is not investment or tax advice. Worked examples are simplified and rounded. All terms in the glossary.