> For the complete documentation index, see [llms.txt](https://laurence-wilse-samson.gitbook.io/textbooks/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://laurence-wilse-samson.gitbook.io/textbooks/financial-economics-claims-prices-holders/part-iv-the-investor-ecology/chapter_18_private_funds.md).

# Chapter 18: Private Funds — Private Equity, Venture Capital, and Hedge Funds

*Part IV: The Investor Ecology — Financial Economics: Claims, Prices, and Holders*

***

## Opening Episode: What Yale Did

David Swensen took over the Yale endowment in 1985, at thirty-one, with a portfolio that looked like every other university endowment's: overwhelmingly domestic stocks and bonds, held in marketable form, valued every day by a market anyone could observe. Yale's own accounts put roughly three-quarters of the fund in domestic marketable securities at the start. Within two decades that had inverted. The endowment's largest exposures were to leveraged buyout partnerships, venture funds, absolute-return managers, timber, and real estate — claims with no quoted price, no daily mark, and no way to get the money back before the manager returned it.

The reasoning, set out later in *Pioneering Portfolio Management*, was not that private assets are magic. It was an argument about who Yale was. A university endowment has a perpetual horizon, a modest spending requirement, no liability that can be accelerated, and no regulator forcing it to hold anything. Almost nobody else has that combination, and if illiquidity is a cost most investors must be paid to bear, the investor who bears it most cheaply should collect the payment. Add a second claim — that private markets are less efficiently priced, so manager selection matters more — and the allocation follows. Yale went looking for those managers and, being early and being Yale, got into their funds.

The returns that followed became one of the most consequential numbers in modern finance. Yale's own reports describe the endowment compounding at roughly 13 percent a year over the three decades after the mid-1980s, several points ahead of a conventional stock-bond portfolio, on a fund that grew from under $2 billion to tens of billions. The number was published annually, cited constantly, and imitated relentlessly. By the 2010s the "endowment model" was the default posture of large institutional capital: not only endowments but public pension plans, sovereign funds, family offices, and eventually insurers built allocations that would have been unrecognizable in 1985. Chapter 16's Table 16.1 shows where that ended up — alternatives at roughly a tenth of defined-benefit pension assets, and higher at the large public plans.

That imitation is the reason this chapter exists. A change in who holds private claims, on that scale, is a change in the market. But it rests on a comparison of private returns against public returns, and the comparison is much harder than the annual reports make it look. The underlying assets did not trade. Their prices were opinions, produced by the managers being evaluated, on a quarterly schedule, using models the investor cannot audit. The cash flows are real, but they arrive when the manager chooses. And the funds that stopped reporting are missing from every database.

So: when the assets don't trade, how do you know what the returns were? That question — not the description of fund structures, which is well covered elsewhere — is what this chapter is about.

***

## 18.1 The Form: Funds, GPs, and LPs

A private fund is a closed-end partnership with a finite life. The manager is the **general partner (GP)**; the investors are **limited partners (LPs)**. The structure is old, simple, and almost universal across buyout, venture, real assets, and much of private credit, and it differs from Chapter 17's mutual fund in every dimension that matters for pricing.

The form is worth a moment of history, because a structure this uniform is easy to mistake for a natural one. Private investment in unquoted companies is old; the limited partnership as its standard vehicle is not. It spread because it solved a particular information problem: an investor with money and no capacity to value or govern a private company must delegate to someone who has both, and needs an arrangement in which the agent's pay, tenure, and reputation are tied to realized cash rather than to reported value. Fenn, Liang and Prowse (1995), whose Federal Reserve staff study is the first full description of the market, draw the consequential inference — what turned private equity from a cottage business into an institutional asset class was the adoption of that contract, together with the regulatory changes that let pension funds sign it, rather than any improvement in the underlying investment opportunities. The form came first, and the money followed the form.

**Committed, not invested, capital.** LPs do not hand over money at the start. They sign a **commitment** — a contractual obligation to fund up to a stated amount when called. The GP issues **capital calls** as it finds deals, usually with ten days' notice, and returns cash through **distributions** as investments are exited. An LP therefore holds a liability of uncertain timing alongside an asset of uncertain value, which is why liquidity management, not portfolio construction, is the binding operational problem for a large allocator.

**A finite, closed life.** A typical fund has a five-year **investment period** for new deals and a ten-year term, extendable. There is no redemption right; an LP who wants out must sell in the secondary market (§18.6). The fund's capital is patient by contract rather than by disposition — the entire economic point, and the source of everything that follows about measurement.

**Fees in two layers.** The shorthand is "2 and 20": a **management fee** near 2 percent a year and **carried interest** ("carry") near 20 percent of profits. Both numbers hide the details that determine what the LP pays. The fee's *base* matters more than its rate: during the investment period it is normally charged on **committed** capital, including capital not yet called and sitting in the LP's own account, and afterward it steps down to a lower rate or to invested capital at cost net of realizations. A fee on committed capital is a fee on money the fund is not yet managing.

Carry is a share of profits, but "profits" is defined by a **distribution waterfall**: return of contributed capital, then a **preferred return** or **hurdle** (commonly 8 percent, compounded) paid entirely to LPs, then a **GP catch-up** in which the GP takes most or all of the next dollars until it holds its target share of profits, then a split at the carry rate. A **clawback** requires the GP to return carry if later losses mean it was overpaid on a whole-fund basis. Whether the waterfall runs on the whole fund (European) or deal by deal (American) determines when the GP is paid and how much clawback risk the LP carries.

### A worked fee example

Round assumed numbers throughout; nothing here is an estimate of any actual fund.

A buyout fund closes on **$1,000 million** of commitments. To keep the arithmetic in a single period, compress the fund's life: the entire $1,000 million is called at date 0, the investments are all made then, every portfolio company is sold at the end of year five, and the fund winds up. Its management fee is 2 percent of committed capital a year over those five years, drawn from the called capital as fees normally are, and the fee reserve is assumed to earn nothing.

* Fees, years 1-5: 0.02 x 1,000 x 5 = **$100 million**
* Capital deployed into companies: 1,000 - 100 = **$900 million**

A real fund runs a ten-year term and steps the fee down after the investment period to a lower rate or to invested capital at cost net of realizations. Those extra years would raise total fees and shrink the deployed base further, which sharpens the arithmetic below rather than changing its direction; they are left out because staggered calls and exits would make the waterfall a schedule rather than a table.

Suppose the portfolio companies are sold for **$2,000 million** in total at year five. Gross multiple on deployed capital: 2,000/900 = 2.22x.

Now run the waterfall, whole-fund, with an 8 percent compounded preferred return and a 100 percent GP catch-up to 20 percent carry. Because the whole commitment was contributed at date 0 and nothing was distributed before year five, the preferred return threshold is 1,000 x 1.08^5 = $1,469 million.

**Table 18.1: The distribution waterfall on a $1,000 million fund ($ millions)**

| Tier                                   | Paid to LP | Paid to GP | Cumulative distributed |
| -------------------------------------- | ---------- | ---------- | ---------------------- |
| 1. Return of capital                   | $1,000     | —          | $1,000                 |
| 2. Preferred return (to 8% compounded) | $469       | —          | $1,469                 |
| 3. GP catch-up (to 20% of profits)     | —          | $117       | $1,586                 |
| 4. Residual split 80/20                | $331       | $83        | $2,000                 |
| **Total**                              | **$1,800** | **$200**   | **$2,000**             |

*Source: Author's construction; assumed round figures, verified numerically.*

![Figure 18.2: The distribution waterfall](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-107a96b98c8f3202f12c2e1b6469043d46cc77b1%2Ffig_18_02_distribution_waterfall.png?alt=media)

**Figure 18.2: The distribution waterfall.** Table 18.1 drawn: the $2,000 million of exit proceeds on §18.1's $1,000 million fund, distributed tier by tier, with each tier's height showing what it pays and its colour showing who it pays. Return of capital and the preferred return are entirely the LP's; the catch-up tier is entirely the GP's; only the residual is split. The GP ends with $200 million — exactly a fifth of the $1,000 million of profit above contributed capital, which is what a flat twenty per cent carry with no hurdle at all would have paid. A full catch-up moves the timing of the GP's carry and not its amount. Replace it with a hard hurdle, charging carry only on profit above the preferred return, and the same waterfall pays the GP $106 million: the clause that reads as boilerplate is worth more than the hurdle it follows. The LP's net multiple is 1.80x, a net IRR of 12.5 percent, against a gross multiple of 2.22x on the $900 million actually deployed and a gross IRR of 17.3 percent — a fee drag of about 484 basis points a year. Counting the $100 million of management fee alongside the carry, the GP takes 27 percent of the $1,100 million of value the fund created, and more in a fund whose fee runs the full ten years. That fraction, not "2 and 20", is the number to carry. *Source: Author's construction from the worked fund of §18.1; assumed round figures, recomputed rather than transcribed.*

Three things to read off Table 18.1, which Figure 18.2 draws. First, with a **full catch-up the hurdle changes only the timing of the GP's carry, not its amount**: the GP ends with exactly $200 million, which is 20 percent of the $1,000 million of profit above contributed capital. An 8 percent preferred return with a 100 percent catch-up is a subordination provision, not a fee reduction. Replace it with a **hard hurdle** — carry charged only on profits *above* the preferred return, no catch-up — and carry falls to 0.20 x (1,000 - 469) = $106 million, roughly halving the GP's take. The catch-up clause, which reads as boilerplate, is worth more than the hurdle it follows.

Second, the LP's net multiple is 1,800/1,000 = 1.80x, a net IRR of 12.5 percent over five years, against a deal-level gross IRR of 17.3 percent: a fee drag of about 480 basis points a year.

Third, and most usefully: total GP compensation is $100 million of fees plus $200 million of carry, against gross value creation of 2,000 - 900 = $1,100 million. **The GP captures a little over 27 percent of the value the fund created** — and more than that in a fund whose fee runs the full ten years. That fraction, not the headline "2 and 20," is the number an LP should carry around.

Figure 18.3 varies the one thing Table 18.1 holds fixed — how well the fund did — and shows what each clause is worth across the range.

![Figure 18.3: The catch-up is worth more than the hurdle](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-3815723cba1d232a592a1f51cfff3222f38bb7d1%2Ffig_18_03_catch_up_and_hurdle.png?alt=media)

**Figure 18.3: The catch-up is worth more than the hurdle.** Panel (a) is carry to the general partner against the fund's gross multiple, under §18.1's full catch-up and under the hard hurdle the section contrasts it with. Both are zero until the preferred return is met. The catch-up tier then pays the GP at a hundred percent — the near-vertical segment — until it has caught up to a fifth of all profit, after which the two schedules run parallel, separated by a constant 94 million. At the chapter's own 2.22x the gap is the difference between 200 and 106. Panel (b) restates the same two schedules as a share of the profit, and it is the panel that settles the question. With a full catch-up the GP takes exactly twenty percent of the profit above contributed capital at every multiple above the catch-up point: the preferred return has changed the order in which the money is paid and not the amount. With a hard hurdle the share rises toward twenty percent from below and never reaches it, because the first 469 million of profit is permanently exempt. A preferred return is therefore a subordination provision rather than a fee reduction, and the catch-up clause — a sentence most term sheets treat as boilerplate — is worth more than the hurdle it follows.

### Who bears what

The GP-LP relation is the delegation problem of Chapter 16 §16.3 with two features specific to this form.

Carry is a **call option on the fund's assets**, struck at contributed capital plus the preferred return. Options are worth more when volatility is higher, so a GP whose fund is under water has an interest in risk the LP does not share — the standard convexity problem, sharpened because the LP cannot redeem. Management fees, by contrast, are a fixed claim that scales with **assets gathered**, so the GP's most reliable path to income is a larger next fund — and that path runs through *reported* interim performance during fundraising, a number the GP produces. Which is where §18.2 begins.

The LP, meanwhile, bears the timing risk on both sides: it cannot force a call, cannot refuse one without defaulting, and cannot force a distribution. Ang's *Asset Management* works through the resulting liquidity problem in the detail it deserves; this chapter asks what the structure does to measured returns.

Figure 18.1 is what that timing risk looks like from the LP's bank account.

![Figure 18.1: The J-curve](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-dfa75b9b024e8dcc1202c4d6927be42ab86f013f%2Ffig_18_01_the_j_curve.png?alt=media)

**Figure 18.1: The J-curve.** Cumulative net cash flow to a limited partner over a ten-year fund, with the annual calls and distributions drawn as bars beneath it. The shape is the reason for the name and it is a structural feature, not a bad outcome: capital goes out early and comes back late, so the LP is deeply negative for years before a single dollar of profit is realized. In this construction the position bottoms at 786 million of the thousand committed, in year four, and does not return to zero until year seven. Two consequences the table of §18.1 cannot show. The management fee runs on committed capital from year one, so it is charged against the deepest part of the trough — the LP is paying most while it has received least, which is why the fee drag looks so different measured against commitments than against realizations. And the LP that wants a steady allocation to the asset class must therefore commit across vintages continuously, since a single fund delivers exposure that ramps up and then runs off; that commitment pacing, not fund selection, is the operational problem an endowment actually has. The schedule of calls and distributions here is constructed, because §18.1 deliberately compresses the fund into one period; both totals are the chapter's, so the curve ends at that section's 1.80x net multiple.

***

## 18.2 The Measurement Problem

Everything in §18.1 was descriptive. This section is the chapter's argument.

A public fund's return is a fact about prices other people paid. A private fund's return is a construction, assembled from cash flows whose timing the GP controls and valuations the GP produces. The industry has three answers to "how did the fund do" — the multiple, the IRR, and the interim NAV — and each has a defect the fund's own structure makes exploitable. The simplest, the **multiple of invested capital (MOIC or TVPI)**, is distributions plus residual value over contributions: 1.80x in the worked example. It is honest about dollars and silent about time, and a 1.80x over five years is not the investment a 1.80x over twelve is. The other two need sections.

### IRR and what it does not do

The headline number is the **internal rate of return**: the discount rate setting the net present value of the fund's cash flows to zero. Write contributions as $$C\_t$$ and distributions as $$D\_t$$, the final NAV treated as a terminal distribution. The IRR solves

$$
\sum\_t \frac{D\_t - C\_t}{(1+\mathrm{IRR})^t} = 0
$$

It is a real number about real cash flows, and it has three properties that make it a poor summary of a private fund.

**It assumes reinvestment at itself.** An IRR is the rate at which the *fund's* capital compounds while it is in the fund. It says nothing about the LP's capital when it is *not* in the fund, which is most of the time. A fund returning 30 percent on money held for eighteen months has not given its LP 30 percent a year on anything.

**It neither aggregates nor compounds.** Take two funds held five years each: Fund A returns $10 million of commitments at a 25 percent IRR, Fund B returns $100 million at 5 percent. The commitment-weighted average of the IRRs is 6.8 percent; the IRR of the pooled cash flows is 7.5 percent. Neither is a portfolio return, which would require knowing what the uncalled and returned capital earned elsewhere. Chaining IRRs across vintages is meaningless in a way that chaining time-weighted returns is not, because each is defined over a different capital base and interval. "Our private equity program returned 14 percent" is a statement about a set of cash flows, not about a portfolio.

**It is manipulable by timing, and the industry has a tool for it.** The IRR rewards getting money back early and putting it in late, and both are available to a GP. Early partial exits — a dividend recapitalization in year two, a sale of a stake to a co-investor — raise the IRR with no change in the multiple. And since the 2010s most funds have used a **subscription credit line**: the GP borrows against LPs' unfunded commitments to close deals, then calls capital months or quarters later to repay the facility with interest.

Run it through the example. The base case is $1,000 million called at date 0 and $1,800 million distributed at year 5: a 1.80x multiple and a 12.5 percent IRR. Now let the GP borrow at 5 percent to defer the call by a year, so the LP contributes $1,050 million at year 1 and receives the same $1,800 million at year 5:

**Table 18.2: What a subscription credit line does to the headline number**

|                             | Multiple | Net IRR |
| --------------------------- | -------- | ------- |
| No credit line              | 1.80×    | 12.5%   |
| Line, call deferred 1 year  | 1.71×    | 14.4%   |
| Line, call deferred 2 years | 1.63×    | 17.8%   |

*Source: Author's construction; assumed round figures, verified numerically.*

The multiple falls, because the interest is a real cost the LP pays. The IRR rises by nearly 200 basis points at one year and more than 500 at two. Nothing about the investments changed. If the GP is measured on IRR — and during fundraising it is — the facility pays for itself in the metric even while destroying value in dollars.

### PME: measuring against what the money could have done instead

The fix is to stop asking what rate the fund earned and start asking what the LP would have had by putting the same cash flows into a public index. This is the **public market equivalent**, in the version that became standard, Kaplan and Schoar's (2005).

Let $$I\_t$$ be the level of a public total-return index at date $$t$$. Discount every fund cash flow at the *realized index return* over the matching interval and take the ratio:

$$
\mathrm{PME} = \frac{\sum\_t D\_t / I\_t}{\sum\_t C\_t / I\_t}
$$

A PME of 1.0 means the fund left the LP exactly where the index would have; 1.20 means the LP ended the fund's life with 20 percent more wealth than the same contributions and withdrawals would have produced in the index.

**Worked example.** Round assumed figures again. A fund calls $100 million at date 0 and another $100 million at year 2, then distributes $120 million at year 4 and $250 million at year 6. The index compounds at 8 percent a year throughout.

**Table 18.3: A public market equivalent, computed ($ millions)**

| Year $$t$$ | Contribution $$C\_t$$ | Distribution $$D\_t$$ | Index factor $$I\_t/I\_0$$ | $$C\_t/(I\_t/I\_0)$$ | $$D\_t/(I\_t/I\_0)$$ |
| ---------- | --------------------- | --------------------- | -------------------------- | -------------------- | -------------------- |
| 0          | 100                   | —                     | 1.0000                     | 100.00               | —                    |
| 2          | 100                   | —                     | 1.1664                     | 85.73                | —                    |
| 4          | —                     | 120                   | 1.3605                     | —                    | 88.20                |
| 6          | —                     | 250                   | 1.5869                     | —                    | 157.54               |
| **Total**  | **200**               | **370**               |                            | **185.73**           | **245.75**           |

*Source: Author's construction; assumed round figures, verified numerically.*

The PME is 245.75/185.73 = 1.32. The fund's own IRR is 15.2 percent and its multiple 1.85x; against an 8 percent index it delivered about 32 percent more terminal wealth than indexing the same flows. The calculation does what the IRR cannot: it charges the fund for calling capital when the market was cheap and credits the LP for capital that stayed in the index while uncalled.

PME also disciplines the credit-line trick. Rerun the deferred-call case with a line rate equal to the index return: the IRR still rises from 12.5 to 13.6 percent, and the PME is *unchanged* at 1.23. Deferring a call moves capital between the fund and the index, and PME prices that movement at the index return — so it registers a gain only when the fund borrows more cheaply than the LP's alternative, which at a 5 percent line rate against an 8 percent index it does, lifting PME from 1.23 to 1.26. The metric credits the real benefit and ignores the optical one.

Figure 18.4 puts the three metrics side by side on the same three funds, which are the same fund.

![Figure 18.4: Three numbers, three answers](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-2588a11bab56f3008ddd097487ddbf47e30b33ab%2Ffig_18_04_three_numbers.png?alt=media)

**Figure 18.4: Three numbers, three answers.** One set of investments, three ways of deferring the capital call, and three metrics that disagree about what happened. The multiple falls as the call is deferred, from 1.80x to 1.63x, because the interest on the credit line is a real cost the LP pays. The IRR rises over the same three cases, from 12.5 percent to 17.8, because the metric rewards holding capital for a shorter time and is indifferent to what the capital did while uncalled. Those two panels are the same fund getting worse and better at once, and a general partner measured on the second during fundraising has an instrument that produces the improvement on demand. The third panel is the discipline. The public market equivalent rises only modestly, from 1.23 to 1.30, and the dashed line says why: rerun the same deferrals with the line priced at the index return rather than at 5 percent, and the PME does not move at all. What the credit line actually delivers is the spread between the borrowing rate and what the LP's money would otherwise have earned, and PME prices exactly that and nothing else.

The costs of PME are worth stating plainly. It has no beta adjustment: comparing a levered buyout fund to the S\&P 500 implicitly assumes a beta of one, almost certainly too low, so a PME above one is a weaker claim than it looks. It is sensitive to the index chosen. And two funds with identical IRRs can have very different PMEs, because PME depends on what the market did while the money was out.

### Smoothed marks, understated betas, and "volatility laundering"

The third number is the interim **net asset value**, and it has the least claim to being a price. Between exits, holdings are carried at fair value estimated by the GP, reviewed by an auditor, updated quarterly — anchored on the last transaction, moved cautiously, and produced by a party with an interest in the number.

The statistical consequence is that reported returns are a smoothed version of true returns. The standard model is Getmansky, Lo and Makarov's (2004): if $$r\_t$$ is the true economic return and $$\tilde r\_t$$ the reported one, then with smoothing weight $$\omega \in (0,1]$$,

$$
\tilde r\_t = \omega r\_t + (1-\omega) \tilde r\_{t-1}
$$

Two results follow immediately, and they are the reason private assets look so attractive in an optimizer.

If true returns have market beta $$\beta$$, the beta estimated from reported returns against the *contemporaneous* market is $$\omega\beta$$. With $$\omega = 0.4$$ — a plausible degree of smoothing for quarterly private marks — a true beta of 1.2 is measured as 0.48. Dimson's (1979) fix, summing the coefficients on the contemporaneous market return and several lags, recovers the true beta; running the naive regression does not.

And if true returns are serially uncorrelated with volatility $$\sigma$$, the reported series has volatility

$$
\tilde\sigma = \sigma\sqrt{\frac{\omega}{2-\omega}}
$$

At $$\omega = 0.4$$ this is exactly half of $$\sigma$$. Reported volatility is halved, reported beta is cut by 60 percent, correlations with public equity fall, drawdowns disappear, and Sharpe ratios roughly double — all from the reporting convention alone, with no change in the economics of the assets.

The practitioner phrase for this is **volatility laundering**, coined by Cliff Asness, and the argument it names is the interesting one. It need not be a deception, because sophisticated LPs know the marks are smoothed; it may be a service they are willing to pay for. An asset that never reports a drawdown does not trigger a board conversation, does not breach a risk limit, and does not tempt trustees into selling at the bottom. On that reading, smoothing is a commitment device purchased at the cost of a lower true return — the Ulysses contract of institutional investing. On the other reading it is an accounting artifact that lets an agent report a risk profile his principal would not accept if it were measured properly. Both are live, and the discussion questions ask you to choose.

![Figure 18.5: Smoothed marks](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-ede19bf7854556aab44620fa79961c0143a7685b%2Ffig_18_05_smoothed_marks.png?alt=media)

**Figure 18.5: Smoothed marks.** Panel (a) is one simulated asset reported two ways: the true quarterly return, and the same series run through the smoothing filter at the section's weight of 0.4. Nothing about the asset differs between the two lines. What differs is that every drawdown is shallower, every recovery slower, and no quarter is ever as bad as it actually was — the reported series does not merely understate the variance, it removes the moments that would have prompted a conversation. Panel (b) is the algebra rather than a draw from it, because both of the section's results are exact. Reported beta is the true beta times the smoothing weight, and reported volatility is the true volatility times the square root of the weight over two minus the weight; at 0.4 the first is 48 percent of the truth and the second is exactly 50. Note that the two curves are close but not equal, and that the volatility bias is the milder of the two at every weight — which matters, because a Sharpe ratio is helped by the volatility bias while a beta-adjusted benchmark is defeated by the other one. The correction for the beta exists and is old: Dimson's, summing the coefficients on the contemporaneous market and several lags. Running the naive regression instead is a choice, and it is made every time a private asset enters an optimizer.

### What the credible evidence says

With the metrics established, the empirical record can be stated — qualitatively, because the fund-level data are proprietary and the honest summary is a direction rather than a number.

Kaplan and Schoar (2005) built the first careful fund-level study, using the cash flows of mature US buyout and venture funds. Their central finding was that **average fund returns net of fees were roughly comparable to the S\&P 500** — value-weighted somewhat above, equal-weighted somewhat below — with enormous dispersion and, notably, strong **persistence**: a GP whose current fund performed well tended to have a next fund that did too, a pattern absent in mutual funds (Chapter 17 §17.3) and suggestive of genuine, scarce, non-scalable skill.

Harris, Jenkinson and Kaplan (2014) revisited the question with broader data and reached a more favorable verdict for buyouts: **US buyout funds outperformed public equity net of fees in most vintages in their sample**, by a margin that is meaningful but not spectacular, with PMEs above one across most of the period. Venture was different — strong outperformance in 1990s vintages, roughly at or below public markets for 2000s vintages. Critical readings, of which Phalippou's is the most prominent, argue the buyout premium shrinks toward nothing once one accounts for embedded leverage, benchmarks against small-cap rather than large-cap indices, and treats fees on committed capital properly. The disagreement is about measurement, which is this section's point.

The finding that has clearly changed is **persistence**. Follow-on work by Kaplan and co-authors reports that the strong buyout persistence of the 1980s and 1990s largely disappears after about 2000, while it survives better in venture, where access to the best partnerships is rationed and a good early record buys deal flow. The natural reading is a Berk-Green story (Chapter 17 §17.3) arriving in private markets with a lag: when performance is observable and capital competitively supplied, successful GPs raise bigger funds, charge more, and compete for the same deals until net-of-fee alpha is bid down toward the market. Ilmanen, Chandra and McQuinn (2020) argue exactly that, tying the compression to the capital that arrived and the entry multiples it paid.

Two qualifications. Access was never free: Lerner, Schoar and Wongsunwai (2007) find endowments earned substantially better private-equity returns than other institution types — evidence that *who you are* determined which funds you got into, a rationing story rather than a selection-skill story, and one that weakens as everyone piles in. And the selection biases run the wrong way for optimism, since databases are built from LP disclosures and voluntary GP reporting.

> **Box 18.1 — What a limited partnership agreement contains**
>
> Section 18.1 gives the economics of the two-and-twenty contract. The document that implements it is a limited partnership agreement, and six of its clauses do most of the work.
>
> **The fee base.** Management fees are charged on committed capital during the investment period and typically on invested or net invested capital after it. Which base applies, and when the switch happens, changes the lifetime fee on a fund by a large multiple of any negotiated haircut to the headline rate.
>
> **The preferred return and the catch-up.** LPs receive their capital back plus a preferred return, often eight percent, before the GP takes carried interest. The catch-up then pays the GP a high share — sometimes all — of the next dollars until the split reaches the stated carry. A preferred return without a catch-up is a materially different contract from one with a full catch-up, and both are called eight and twenty.
>
> **Whole-fund against deal-by-deal.** Carry computed across the fund pays the GP only after the whole portfolio has cleared the hurdle. Carry computed deal by deal pays on each realisation, which advances the GP's cash by years. The **clawback** is the promise to repay excess carry at the end, and it is a promise from an entity whose principals may by then have distributed the money.
>
> **Key person and no-fault divorce.** The first suspends the investment period if named individuals stop devoting substantially all their time to the fund. The second lets a supermajority of LPs end the investment period without cause. They are the only real governance rights in a structure whose defining feature is that the LP cannot withdraw.
>
> **Confidentiality.** The LPA restricts disclosure of fund-level performance, which is why §18.2's measurement problem is structural rather than incidental. The data required to evaluate the asset class is contractually private, and what the public sees comes from the small subset of LPs that are themselves subject to public-records law.

***

## 18.3 Venture Capital

Venture capital shares the fund form of §18.1 and almost nothing else with buyouts. A buyout fund buys control of a cash-generating business, changes its capital structure and often its management, and sells it. A venture fund buys a minority stake in a firm with no cash flow, no collateral, and a high probability of being worth zero.

### The power law

Venture returns are not distributed around a mean in any useful sense. Within a fund, most investments return less than the capital put in, and essentially the whole fund return comes from a handful of positions — often one. Practitioners state this as a rule ("the best investment returns more than all the others combined"), and the distributions in the data are consistent with it: extreme right skew, a mode near zero, and a tail heavy enough that the sample mean is unstable and rises with sample size.

That shape changes the job. A public equity manager's problem is to be right more often than wrong. A venture manager's problem is to hold, and keep holding, the position that goes up a hundredfold, and to be indifferent to being wrong about the rest. Diversification within the fund becomes a necessity rather than a preference, because the probability of catching a tail event scales with the number of draws. Loss ratios stop being a measure of failure: a fund with no write-offs is a fund that never took the risks the asset class is paid for. And evaluation over a short window is close to uninformative, because the whole distribution lives in a tail that has not yet realized.

![Figure 18.6: What the limited partner actually sees](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-dde4d39e3ab65f2548ccc15761f52de121790257%2Ffig_18_06_what_the_lp_sees.png?alt=media)

**Figure 18.6: What the limited partner actually sees.** Net investment multiples, fund by fund, for every CalPERS private equity partnership of the 2000-2009 and 2010-2019 vintages, as reported under California's AB 2833 as of December 31, 2025. The striking thing is what is *not* here. The distribution above is right-skewed and nothing more: 63 mature funds with a median of 1.60x, a largest of 4.20x, and 8 percent that failed to return capital; 95 funds of the following decade with a median of 1.70x and a largest of 4.80x. There is no power law in it. That is not a contradiction of the paragraph above but a demonstration of it — the extreme distribution is a fact about *positions*, and a fund is a diversified portfolio of thirty or more of them, so the hundredfold outcome that carries a venture fund is averaged with its stablemates and arrives at the limited partner as two or three turns of capital. Diversification within the fund is not just a necessity for the general partner; it is the reason the investor's own return series looks so ordinary. Three cautions. This is one investor's book, and CalPERS is a large, sophisticated, access-advantaged buyer whose funds are a selected sample in both directions. The right panel's advantage over the left is partly an artifact of age, since much of its value is still the general partners' own marks rather than realized cash — §18.3's objection, visible. And no public plan discloses positions, so the distribution the section is actually about cannot be drawn from any free source at all; what can be drawn is its residue. *Source: CalPERS Private Equity Program fund performance review, published under California AB 2833. Author's calculations.*

Kerr, Nanda and Rhodes-Kropf (2014) give the economic reading: venture capital is a technology for running **experiments**. Each financing round buys an option to learn something — whether the technology works, whether customers will pay — at a cost small relative to the value of the information. The industry's structure follows from the payoffs to experimentation, not from any special ability to pick winners in advance.

### Staging and control as the financing technology

The contractual apparatus follows the same logic. Venture financing is **staged**: capital arrives in rounds conditioned on progress, so the investor holds an option to abandon and the entrepreneur faces a recurring test. The securities are **convertible preferred stock** carrying liquidation preferences, anti-dilution protection, and control rights — board seats, protective provisions, founder vesting — that shift with performance, so control migrates toward the investor in bad states and the founder in good ones. This is a nearly literal implementation of state-contingent control allocation, and Kaplan and Strömberg's work is the standard demonstration. *The contracting theory belongs to Chapter 21 §21.4, where state-contingent control is derived and Table 21.3's last row records exactly these terms; this section takes the instruments as given.*

### VC and innovation

Does any of this matter for the real economy? More than the industry's size would suggest. Kortum and Lerner (2000) find venture funding associated with substantially more patenting per dollar than corporate R\&D, addressing the endogeneity concern with a policy change that expanded pension funds' ability to invest in VC. Later work documents that venture-backed firms account for a strikingly disproportionate share of US IPOs, of public-market capitalization among firms founded in recent decades, and of corporate R\&D — shares far out of proportion to the fraction of firms that ever receive venture money. Whether venture capital *causes* this or selects firms that would have succeeded anyway is contested at the margin, but the association is not, and it is the strongest claim the asset class has on public attention.

### Cycles and dry powder

Venture is violently cyclical, and the cycle is a capital-supply cycle. Strong exits raise reported returns, reported returns attract commitments, commitments become **dry powder** — capital committed but not yet called — and dry powder chasing a roughly fixed supply of good companies raises entry valuations, lowering the returns of the vintage being deployed. Gompers and Lerner's work on the venture cycle documents the pattern; the 2021 vintage is the most recent illustration, its late-stage marks still being written down years later, which is §18.2's smoothing in slow motion.

***

## 18.4 Hedge Funds

"Hedge fund" is a legal category masquerading as a strategy. The defining feature is exemption from the Investment Company Act constraints listed in Chapter 16 §16.3 — the fund may lever, concentrate, short, and hold illiquid positions — in exchange for a restricted investor base. The exemption relied on is normally §3(c)(1), which limits the fund to 100 beneficial owners and in practice to accredited investors, or §3(c)(7), which admits an unlimited number of investors provided every one of them is a qualified purchaser, a considerably higher wealth threshold. Which exemption a fund elects is what determines who is eligible to invest in it. Everything else varies.

The economic form differs from private equity's in one respect that matters here: hedge fund capital is **redeemable**. Lockups, notice periods, and gates slow redemptions without eliminating them, and the fund is levered against prime brokers whose margin terms can change overnight. The capital is patient at the pleasure of two parties who can both withdraw at once, and typically do so in the same states of the world.

### The strategy set, briefly

Four families organize most of the industry. **Long-short equity** takes offsetting long and short positions to isolate stock selection from market direction, with net exposure a deliberate choice; it is the largest category by fund count and the closest to conventional active management. The **arbitrage** family — merger, convertible, fixed-income relative value, statistical — holds pairs of related claims whose prices should converge, earning a spread for supplying capital to a mispricing and bearing the risk that it widens first. **Global macro** takes directional positions in rates, currencies, and commodities from a view about policy and the cycle. **Managed futures** (CTAs) run systematic trend-following across liquid futures, a payoff resembling a long straddle that does well in the extended moves where everything else does badly. Pedersen's *Efficiently Inefficient* is the standard treatment of what each involves; this book does not duplicate it.

### The arbitrage-capital view

What hedge funds *are*, in this book's framework, is the marginal price-correcting capital. When a claim trades away from the value implied by related claims, someone must take the other side, and that someone must be able to lever, short, and hold an unconventional position. The institutions of Chapter 16 mostly cannot; hedge funds are the residual. That makes their capital structure a pricing variable rather than an administrative detail. Chapter 15 §15.5 supplies half the mechanism: under **performance-based arbitrage**, a manager whose position moves against him faces redemptions precisely when the opportunity has improved, so the supply of arbitrage capital contracts as the demand for it rises. Chapter 16 §16.5 supplies the other half, and is this book's canonical statement of it: leverage constraints, haircuts, and margin spirals force sales that fundamentals do not warrant. Neither is re-derived here, but the second one also runs the other way and pays: because forced sales are predictable — the constraint is observable and the timing follows from a redemption queue — a fund that can identify a distressed holder is compensated both for anticipating the sale and for eventually absorbing it, which is what the mutual-fund distress evidence in Chapter 16 §16.5 measures, read from the hedge fund's end. The point specific to this chapter is that the fund *form* — quarterly redemption with notice, gates that damage the franchise when used, prime-broker leverage repriced at the broker's discretion, and a high-water mark that makes the manager's own option worthless after a large loss — determines how patient this capital actually is. Fee and lockup terms are, in that sense, an input to asset prices.

### Fees, alpha, and where it goes

Hedge fund fees are the private-fund waterfall applied to a liquid portfolio: a management fee, an incentive fee of typically 20 percent, and a **high-water mark** so the manager earns incentive fees only on new highs. Realized loads are below the headline and have fallen, but remain multiples of an active mutual fund's.

Chapter 17 §17.3 supplies the framework for what happens next. In the Berk-Green equilibrium, skill is scarce, capital competitively supplied, and returns to scale decreasing; the fund grows until net alpha to the marginal investor is zero, and the skill rent is captured by the manager through size. Nothing in that logic is specific to mutual funds, and applied here it predicts what the industry's history shows: strong early net returns while strategy capacity was scarce, heavy institutional inflows after 2000, and a compression of net-of-fee returns toward benchmark-like performance even as gross alpha remained real. The summary is not that hedge funds have no skill, but that the aggregate net return to LPs has converged toward what Chapter 17's arithmetic says it must, while the dollars extracted have grown.

### The measurement problem, again

Hedge fund databases are worse than private equity's, in the same direction, because reporting is voluntary. **Survivorship bias** arises when funds that fail stop reporting and are dropped, so an index of surviving funds is an index of the ones that made it. **Backfill bias** arises because a fund joining a database may supply its prior track record, and funds join after a good run — so backfilled history is systematically better than live history. The studies that have tried to measure the combined effect (Fung and Hsieh; Malkiel and Saha, among others) put it at several percentage points a year, on the order of the entire reported excess return. The Getmansky-Lo-Makarov smoothing of §18.2 applies too, hardest to funds holding credit and other assets with infrequent quotes.

None of this makes hedge fund returns fictitious. It means an index return describes a self-selected, survivor-weighted, partly back-filled, partly smoothed sample — and that the honest corrections take a substantial bite out of it every time.

***

## 18.5 A Boundary: Private Credit

The fastest-growing private fund category since 2015 has been neither buyout nor venture but **private credit**: funds lending directly to mid-market companies that would once have been served by a syndicated bank loan or a high-yield bond. The structure is §18.1's closed-end partnership, sometimes wrapped in a business development company or an evergreen vehicle; the fee anatomy is similar at a lower carry rate; and §18.2's measurement problems apply in full, because a loan that never trades is marked by the lender that owns it. What is genuinely different is that this is an **intermediation** channel — credit and maturity transformation outside the banking system, funded by insurers and pension plans — so the interesting questions concern bank disintermediation, regulatory arbitrage, and resilience in a downturn. Those are developed in the companion volume: see *International Finance*, Chapter 9. This chapter's contribution is the fund economics and the measurement apparatus any assessment of the channel's returns has to use.

> **Box 18.2 — A gate, late 2022**
>
> The chapter's fund forms trade a redemption right against an illiquid portfolio, and the trade is invisible until the right is exercised at scale. Late 2022 supplied the demonstration.
>
> The vehicle in question is the non-traded, perpetually offered real estate fund sold to individual investors — a structure that grew rapidly through the low-rate decade by offering something the closed-end partnership of §18.1 does not: monthly subscriptions and periodic redemptions. The redemption right was never unlimited. The offering documents cap repurchases at a stated fraction of net asset value per month and per quarter, and provide that requests above the cap are honoured pro rata.
>
> Through the second half of 2022 rates rose sharply and listed real estate fell hard, while the fund's own net asset value — computed from appraisals rather than from trades — did not. Investors could redeem at a value that had not yet moved, and enough of them did that the caps bound. Redemptions were prorated for months.
>
> There is a version of this story in which somebody behaved badly, and it is the wrong version. The caps were disclosed, the appraisal methodology was disclosed, and the fund did what the documents said. The interesting fact is structural, and it is §18.2's smoothing problem seen from the liability side. An appraisal-based value is stale by construction; a stale value that has not fallen when observable prices have is an option to redeem at above fair value; and a redemption right subject to a cap is not a redemption right but a queue.
>
> Chapter 16 §16.5 gives the general form. A liquidity promise written against an illiquid asset is a promise that holds until enough holders want it kept, and the cap is what the manager has instead of a fire sale.

***

## 18.6 Who Holds the Illiquid Claim?

The chapter opened with Yale and must close with the holders who followed it, because the interesting economics of private funds is on the LP side.

**The endowment model, generalized.** Chapter 16 §16.2 describes the largest of these holders — defined-benefit plans with long-dated liabilities, and insurers whose capital charges determine what they may hold — and Chapter 16's Table 16.4 sizes the sovereign funds alongside them; add the endowments of the opening episode, with perpetual horizons and no liability at all. Each has a plausible claim to be the natural bearer of illiquidity risk, and each responded to a decade of low policy rates by raising its alternatives allocation — because a plan discounting liabilities at an assumed 7 percent cannot reach 7 percent from investment-grade bonds. The allocation is thus partly a horizon argument and partly a return-target argument: Chapter 16's reach for yield, arriving in a different asset class.

**The denominator effect.** The clearest evidence that the horizon argument is incomplete shows up in drawdowns. A plan with a 10 percent target allocation to private equity holds public assets that mark down 25 percent in a crash and private assets that mark down 5 percent, on a lag. The private *share* rises mechanically — the denominator shrank — and can breach a policy limit written in percentage terms. The plan then becomes a forced seller of private interests, or a forced non-committer to new funds, at exactly the moment when new vintages are cheapest. This happened in 2008-09 and again in 2022, and it is the structure of every other mechanism in Part IV: a constraint written on the holder, binding in the state where it does the most damage.

**Illiquidity as a feature.** Which raises the uncomfortable reading. Smoothed marks flatter a funded ratio, suppress reported volatility, and keep a plan out of the headlines in a bad year. For a public plan whose contribution rate is set from an actuarial funded ratio, that is not cosmetic — it is a real reduction in budgetary and political pressure. An asset reporting less risk than it bears is therefore genuinely valuable to the agent making the allocation, whether or not it is valuable to the beneficiary. That is the agency reading of illiquidity, and it stands alongside §18.2's commitment-device reading rather than replacing it. Both are true for different plans, and nothing in the reported returns distinguishes them.

**Secondaries.** The market's own answer to the LP's liquidity problem is the **secondary market**, in which an LP sells its fund interest, unfunded commitment included, to another investor. It has grown from a distressed-seller corner into a large intermediated market with dedicated funds, and now includes **GP-led** transactions — continuation vehicles in which a manager sells an asset from an old fund to a new one it also manages, at a price set by a process it runs. LP-led secondaries have historically priced at discounts to reported NAV, widening sharply under stress, and that discount is direct market evidence that reported NAV and realizable price differ. It is not an estimate of the smoothing on its own: the same discount prices the interest's illiquidity, the unfunded commitment and remaining fees the buyer takes on, whatever led this particular seller to sell, and the buyer's own required return. It is also Chapter 16's thesis in miniature: the price of a fund interest is set by how much capital is available to buy it, not by the value of what it holds.

**Retail access.** The current frontier is selling private assets to households. Interval and tender-offer funds offer periodic, capped redemptions; non-traded REITs and BDCs do something similar for real estate and private credit; European ELTIF rules have been rewritten to permit retail distribution; and managers have launched semi-liquid and ETF-wrapped vehicles pairing private assets with a liquid sleeve. The problem is always the liquidity transformation of Chapter 17 §17.5 in a harder setting: a vehicle offering monthly liquidity against quarterly-marked, non-trading assets must either hold a large liquid buffer, diluting the exposure it is selling, or ration redemptions, converting the promise into an option the manager writes. In late 2022 a large non-traded real estate vehicle hit its redemption cap and rationed withdrawals — what the structure is designed to do, and what its investors did not expect. Chapter 14's evidence on household investing suggests why regulators are nervous: the holder least equipped to evaluate a smoothed mark is being offered one.

**The grading.** A chapter whose argument is a measurement problem owes the reader an explicit line between what the measurement supports and what it does not, on the schema Chapter 6 §6.4 uses for the cross-section and Chapter 20 §20.5 for the demand system.

**Table 18.4: The state of the evidence**

| Claim                                                                                     | Status                                                                                                                                                                                                    |
| ----------------------------------------------------------------------------------------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| Reported private fund returns are constructions rather than prices                        | **Established.** IRRs turn on timing the GP controls and interim NAVs on valuations the GP produces; PME is the disciplined alternative and is what the credible literature uses                          |
| Buyout funds have outperformed public equity net of fees                                  | **Contested.** Broad data show outperformance in most vintages; the critical readings shrink it toward nothing once leverage, small-cap benchmarks, and fees on committed capital are handled differently |
| Performance persistence in buyout has largely disappeared since about 2000                | **Widely accepted**, and read as a Berk-Green outcome arriving with a lag; persistence survives better in venture, where access to the best partnerships is rationed                                      |
| Smoothed marks understate volatility and contemporaneous beta                             | **Established.** The smoothing model is arithmetic: at a plausible weight, reported volatility is half of true volatility and reported beta 40 percent of true beta                                       |
| Whether volatility laundering is an accounting artifact or a service the holder is buying | **Contested.** Both readings are live, both are true for different plans, and nothing in the reported returns distinguishes them                                                                          |
| That long-horizon holders are illiquidity's natural bearers                               | **Contested.** The horizon argument is incomplete: the denominator effect turns the longest-horizon holders into forced sellers in exactly the states where the premium should be paid                    |

*Source: Author's assessment of the literature discussed in §§18.2-18.6.*

**Where this goes.** The financing that makes all of it work — the leveraged loans and high-yield bonds behind buyouts, the prime brokerage that levers hedge funds, the repo funding the dealers on the other side — sits on intermediary balance sheets, and Chapter 19 asks what those balance sheets do to prices. The question this part has been building toward is what happens to an asset market when a growing share of its owners hold concentrated, illiquid positions they cannot rebalance. That is Chapter 20's demand system, and private funds are among its more awkward inputs, because a holder whose position has no observable price does not have an estimable demand curve.

***

## Elsewhere in the Series

* **Private credit as a lending and intermediation channel** — *International Finance*, Chapter 9. Section 18.5 keeps the fund economics and defers the channel.
* **The contracting theory behind staging, convertible preferred, and state-contingent control** — this book, Chapter 21 §21.4. Section 18.3 uses the instruments; Chapter 21 §21.4 derives why they take that form, and Chapter 25 §25.2 places them on the firm's financing arc.
* **The canonical statement that constrained capital moves prices** — this book, Chapter 16 §16.5. **Performance-based arbitrage and the redemption channel** — Chapter 15 §15.5. Section 18.4 cites both rather than re-deriving either.
* **Berk-Green, performance measurement, and the noise in alpha** — this book, Chapter 17 §17.3, applied to hedge fund fees in §18.4.
* **Pension and endowment balance sheets, delegation, and the agency problems of benchmarking** — this book, Chapter 16 §§16.2-16.3.
* **LBO debt, leveraged loans, and the CLO market in the crisis** — the 2008 crisis volume.
* **Demand-system asset pricing and what illiquid concentrated holdings do to estimated demand curves** — this book, Chapter 20.

***

## Summary

1. **The private fund is a closed-end partnership with no redemption right.** LPs commit capital that the GP calls and returns on its own schedule. The absence of a redemption right is the source of both the illiquidity premium the form is supposed to earn and the measurement problems the chapter is about.
2. **The fee anatomy matters more than the headline.** In the worked example of §18.1, a 2-and-20 fund with an 8 percent hurdle and a full catch-up delivers the GP exactly 20 percent of profits — the hurdle changes timing, not amount — and total GP compensation absorbs a little over 27 percent of the gross value the fund created. Replacing the catch-up with a hard hurdle nearly halves the carry.
3. **IRR is manipulable and does not aggregate.** It assumes reinvestment at itself, cannot be averaged or chained across funds, and rises mechanically when a subscription credit line defers capital calls — by more than 500 basis points for a two-year deferral in the worked case, while the multiple falls.
4. **PME is the disciplined alternative.** Discounting fund cash flows at the realized public index return asks what the same money would have done in the market. It neutralizes the credit-line effect, charges the fund for the timing of its calls, and is what the credible literature uses. Its weaknesses are the absence of a beta adjustment and sensitivity to the benchmark chosen.
5. **Smoothed marks understate risk by construction.** Under the standard smoothing model with weight $$\omega = 0.4$$, reported volatility is half of true volatility and reported contemporaneous beta is 40 percent of true beta. Whether this "volatility laundering" is an artifact or a service the holder is buying is a genuine question, not a rhetorical one.
6. **The performance evidence is a direction, not a number.** Kaplan and Schoar found average net returns roughly comparable to public equity with strong persistence; Harris, Jenkinson and Kaplan found buyout outperformance net of fees in most vintages, with venture strong in the 1990s and weaker after. Critics argue the buyout premium shrinks under leverage-adjusted, small-cap benchmarking. Persistence in buyout largely disappears after 2000 — a Berk-Green outcome arriving with a lag.
7. **Venture returns follow a power law.** Almost the whole fund return comes from a handful of positions, which makes loss ratios uninformative, diversification necessary, and short-horizon evaluation nearly meaningless. Staging and state-contingent control rights are the financing technology that makes experimentation fundable, and the evidence on VC-backed firms' share of patenting, IPOs, and R\&D is the asset class's strongest claim.
8. **Hedge funds are the book's marginal arbitrage capital, and their terms are a pricing variable.** Redeemable LP capital and prime-broker leverage make that capital withdraw exactly when mispricings widen — Chapter 15 §15.5 and Chapter 16 §16.5. Survivorship and backfill biases in hedge fund databases are large enough to account for much of the reported excess return.

***

## Key Terms

* **General partner (GP) / limited partner (LP)**: The manager of a private fund and its investors; the GP controls calls, distributions, valuations, and exits, and the LP has no redemption right
* **Committed capital**: The amount an LP is contractually obliged to fund on demand, and the usual base for the management fee during the investment period — distinct from the capital actually invested
* **Carried interest (carry)**: The GP's share of fund profits, typically 20 percent, paid through the distribution waterfall and subject to clawback
* **Hurdle (preferred return)**: A return, commonly 8 percent compounded, paid to LPs before the GP receives carry. With a full catch-up it changes the timing of carry, not its amount; as a hard hurdle it reduces carry substantially
* **Internal rate of return (IRR)**: The discount rate setting the net present value of a fund's cash flows to zero; sensitive to timing, not aggregable across funds, and inflatable by subscription credit lines
* **Public market equivalent (PME)**: The ratio of fund distributions to contributions, each discounted at the realized return on a public index; a value above one means the LP ended with more wealth than indexing the same flows
* **NAV smoothing**: The partial adjustment of reported fund values toward true values, which halves reported volatility and cuts reported contemporaneous beta at plausible smoothing weights; the practitioner term for the effect is *volatility laundering*
* **Power law**: The extreme right-skewed distribution of venture investment outcomes, in which essentially all of a fund's return comes from a very small number of positions
* **Dry powder**: Capital committed to funds but not yet called; its accumulation raises entry valuations and depresses the returns of the vintage being deployed
* **Denominator effect**: The mechanical rise in a portfolio's private-asset percentage when public marks fall and private marks do not, which can force sales or halt new commitments at exactly the wrong time
* **Secondaries**: The market in which LPs sell fund interests, including unfunded commitments, to other investors; LP-led transactions have typically priced at discounts to reported NAV, and GP-led continuation vehicles move assets between funds run by the same manager

***

## Readings

### Required

* Kaplan, S. and A. Schoar (2005). "Private Equity Performance: Returns, Persistence, and Capital Flows." *Journal of Finance* 60(4): 1791-1823. *The paper that introduced the PME used throughout §18.2 and established both the modest average net return and the strong early persistence.*
* Harris, R., T. Jenkinson and S. Kaplan (2014). "Private Equity Performance: What Do We Know?" *Journal of Finance* 69(5): 1851-1882. *The broader-data revisit; read it against the measurement critiques, since the disagreement is about benchmarks and leverage rather than about the cash flows.*

### Recommended

* Ang, A. (2014). *Asset Management: A Systematic Approach to Factor Investing*. Oxford University Press. Chapters on illiquid assets. *The standard treatment of illiquidity premia, liquidity management, and the allocator's problem — this chapter deliberately does not duplicate it.*
* Fenn, G. W., N. Liang and S. Prowse (1995). *The Economics of the Private Equity Market*. Board of Governors of the Federal Reserve System, Staff Study 168. *The market described from fieldwork before it had a performance literature: who the issuers, intermediaries, investors, and agents were, and how the limited partnership came to dominate. It is the source for §18.1's claim that the fund form is an institutional innovation rather than a given, and its 1980-1994 growth accounting shows that committed-but-uncalled capital is a decades-old feature and not a recent anomaly. Free from the Federal Reserve.*
* Pedersen, L. H. (2015). *Efficiently Inefficient: How Smart Money Invests and Market Prices Are Determined*. Princeton University Press. *Owns the hedge fund strategy detail compressed into §18.4.*
* Kerr, W., R. Nanda and M. Rhodes-Kropf (2014). "Entrepreneurship as Experimentation." *Journal of Economic Perspectives* 28(3): 25-48. *Why the power law and the staging technology are the same fact.*
* Lerner, J. (1997). "Venture Capital and Private Equity: A Course Overview." Harvard Business School working paper. *The canonical teaching sequence — raising the fund, sourcing, structuring and staging the investment, exiting — from which §18.3's treatment of staging and control as the financing technology descends. The institutional companion to Kerr, Nanda and Rhodes-Kropf above.*
* Getmansky, M., A. Lo and I. Makarov (2004). "An Econometric Model of Serial Correlation and Illiquidity in Hedge Fund Returns." *Journal of Financial Economics* 74(3): 529-609. *The smoothing model of §18.2, with the estimated smoothing weights by strategy.*
* Ilmanen, A., S. Chandra and N. McQuinn (2019). "Demystifying Illiquid Assets: Expected Returns for Private Equity." *Journal of Alternative Investments* 22(3): 8-22. *The case that the private equity return advantage has compressed as capital arrived.*
* Chen, J., S. Hanson, H. Hong and J. Stein (2008). "Do Hedge Funds Profit from Mutual-Fund Distress?" NBER Working Paper 13786. *The cleanest evidence for §18.4's arbitrage-capital view: part of hedge fund return is payment for standing opposite a holder who must sell. Read with Chapter 16 §16.5, which states the same fact from the constrained seller's side.*
* Standard and Poor's (2008). *A Guide to the Loan Market*. *The leveraged loan market as it stood before private credit displaced part of it — covenants, syndication, ratings, and who the buyers were. The reference point §18.5 needs to say what private credit actually replaced.*
* Swensen, D. (2009). *Pioneering Portfolio Management: An Unconventional Approach to Institutional Investment*. Free Press. *The opening episode's argument in its author's own words; read it as a claim about who the investor is, not about which assets are good.*
* Brunnermeier, M. K. *Institutional Finance* (ECO467) course materials, Princeton University. *A graduate course on the constrained-holder half of this chapter, with modules on hedge fund performance evaluation, merger arbitrage worked end to end, and arbitrage under a capital constraint. Useful where §18.4 compresses: one strategy carried through its whole mechanics is the anchor a short section cannot supply.*

***

## Discussion Questions

1. **IRR against PME, with a trap.** Two funds each call $100 million at date 0 and distribute $200 million at year 5. Their IRRs are identical at 14.9 percent. Fund X operated in a window in which the public index compounded at 20 percent a year; Fund Y's window saw the index compound at 3 percent. Compute each fund's PME. (You should get roughly 0.80 and 1.73.) Which manager should be given the next mandate, and what would you need to know to answer that instead of the question the arithmetic answers? Now change the setup so Fund X's IRR is *higher* than Fund Y's while its PME is still lower, and explain in one sentence what the IRR is measuring that the PME is not.
2. **Are smoothed NAVs a bug or a service?** A public pension board sets its contribution rate from an actuarial funded ratio and reports portfolio volatility to a legislature. Its private equity allocation reports half the volatility and 40 percent of the beta that the underlying assets bear. Argue first that this is a genuine service the board is buying — a commitment device that prevents selling at the bottom, worth paying for in expected return. Then argue that it is an agency problem — the agent reporting a risk profile the principal would refuse. What observable would separate the two? Does your answer change if the board's own consultants estimate the true beta and present it alongside the reported one?
3. **The catch-up clause.** Rework the §18.1 waterfall with (i) no hurdle at all, (ii) an 8 percent hurdle with a full catch-up, (iii) an 8 percent hard hurdle with no catch-up, holding gross proceeds fixed at $2,000 million. Rank them by GP compensation. Which of these three does an LP negotiating a term sheet care most about, and why is the clause it should fight over the one that gets least attention?
4. **Subscription lines and the incentive to use them.** Suppose an LP evaluates GPs on IRR and a competing LP evaluates them on PME. A GP can borrow at 5 percent against unfunded commitments; the LP's alternative use of uncalled capital earns 8 percent. Who gains and who loses from a one-year deferral, in dollars? Now suppose the line rate is 10 percent. What does each metric report, and what does the divergence tell you about designing a manager-evaluation contract?
5. **The denominator effect and who should hold illiquidity.** A plan with a 10 percent private-equity policy limit sees public markets fall 30 percent while private marks fall 5 percent on a two-quarter lag. Trace what happens to the plan's measured allocation, its commitment pacing, and its realized returns over the following three years. Given your answer, is a policy limit expressed as a percentage of portfolio value the right instrument? Propose an alternative, and say what new problem it creates.

***

## Problems

**Problem 1 — The waterfall at a different outcome.** Take the fund of §18.1: 1,000 of commitments, all called at date 0, a management fee of 2 percent of committed capital a year for five years drawn from called capital, every company sold at the end of year five, an 8 percent compounded preferred return, a 100 percent GP catch-up, and 20 percent carry, on a whole-fund basis. All figures are in millions of dollars.

(a) Confirm the fee total and the capital deployed, and compute the preferred-return threshold. (b) The companies are sold for 1,600 rather than 2,000. Rebuild Table 18.1 tier by tier and report what the LP and the GP each receive. (c) Compute the LP's net multiple and net IRR, the gross multiple and gross IRR on deployed capital, and the fee drag in basis points a year. Compare the drag with the figure §18.1 reports for the 2,000 case. (d) Now let the companies sell for exactly the preferred-return threshold. Compute the GP's carry. Then compute the GP's marginal share of the proceeds between that threshold and 1,600. Explain what the number says about §18.1's claim that carry is a call option struck at contributed capital plus the preferred return. (e) Replace the full catch-up with a hard hurdle, so that carry is charged only on profits above the preferred return. Recompute the GP's carry at proceeds of 1,600 and at 2,000, compare each with the catch-up figure, and state at which outcomes the catch-up clause is worth most to the GP.

**Problem 2 — IRR, multiple, and the credit line.** A fund calls 100 at date 0 and distributes 200 at the end of year five. A public total-return index compounds at 9 percent a year throughout. All figures are in millions of dollars.

(a) Compute the fund's multiple, its IRR, and its Kaplan-Schoar PME. (b) The GP instead arranges an early partial exit, distributing 40 at the end of year one and 160 at the end of year five. Recompute the multiple and the IRR. Which of the two moved, and which did not? (c) Return to the base case and add a subscription credit line at 6 percent that defers the call by a year, so the LP contributes 106 at the end of year one and still receives 200 at the end of year five. Compute the multiple, the IRR and the PME. Then repeat the whole calculation with a line rate of 12 percent. (d) Set the three metrics side by side for the base case and the two line rates. Which metric improves in both cases, which deteriorates in both, and which one changes direction? State what that change of direction is measuring, and why it is the property that makes PME a usable evaluation contract. (e) Verify §18.2's two-fund example: Fund A returns 10 of commitments at a 25 percent IRR over five years and Fund B returns 100 at 5 percent over five years. Compute the commitment-weighted average of the two IRRs and the IRR of the pooled cash flows, and say in one sentence why neither is the LP's portfolio return.

**Problem 3 — Fee drag over a full term.** A buyout fund closes on 500 of commitments and runs a ten-year term. It charges 2 percent of committed capital a year in years one to five and, after the step-down, 1.5 percent of committed capital a year in years six to ten, all drawn from called capital at date 0, and deploys the remainder into companies at date 0. The preferred return is 8 percent compounded, with a 100 percent catch-up to 20 percent carry, whole-fund. Everything is sold at the end of year ten. All figures are in millions of dollars.

(a) Compute total fees over the fund's life, the capital deployed, and fees as a percentage of commitments. Compare the last figure with §18.1's compressed five-year example. (b) The companies sell for 1,100. Compute the gross multiple and gross IRR on deployed capital, run the waterfall, and report the LP's net multiple and net IRR. Note what happens to the catch-up tier and why. (c) Compute the fee drag in basis points a year, and the GP's total compensation as a share of the gross value the fund created. (d) Repeat (b) and (c) with an exit at 1,600. (e) Compare the GP's share of value created in (c) and (d) with §18.1's figure of a little over 27 percent. Explain the direction of each difference, and name the two contract terms an LP should negotiate before it negotiates the headline rate.

**Problem 4 — What smoothing does to the numbers.** Reported returns follow §18.2's model, $$\tilde r\_t = \omega r\_t + (1-\omega)\tilde r\_{t-1}$$. True quarterly returns are serially uncorrelated, with a standard deviation of 12 percent, a market beta of 1.3, and a mean excess return of 2 percent a quarter. The smoothing weight is $$\omega = 0.35$$.

(a) Compute the reported contemporaneous beta and the reported volatility. (b) Compute the true and reported quarterly Sharpe ratios and their ratio. Show that the ratio is $$\sqrt{(2-\omega)/\omega}$$, and check the result against the chapter's statement that Sharpe ratios roughly double at $$\omega = 0.4$$. (c) The reported series loads on the $$k$$-th lag of the market with coefficient $$\omega(1-\omega)^k\beta$$. Compute the first four coefficients and their running sum, show that the infinite sum is $$\beta$$, and find how many lags a Dimson regression needs in order to recover 90 percent of the true beta. Say what that horizon amounts to at the frequency private marks are produced. (d) A mean-variance investor allocates $$w^{\ast} = \mu/(\gamma\sigma^2)$$ to the asset. Compute the ratio of the allocation chosen on reported moments to the allocation true moments would justify, and express it in terms of $$\omega$$ alone. (e) Section 18.2 gives two readings of the smoothing, and §18.6 gives a reason a plan sponsor might value it. State both readings. Then name the one market price §18.6 identifies as direct evidence that reported NAV and realizable value differ, and say precisely why the chapter warns that it is not, on its own, an estimate of $$\omega$$.

**Problem 5 ★ — Selecting a fund.** A plan is choosing general partners. Treat a fund's realized PME as the sum of its GP's true skill and independent noise. Across a vintage, fund PMEs have a cross-sectional standard deviation of 0.45, and the noise in a single fund's PME around its GP's true skill has a standard deviation of 0.40. The benchmark PME is 1.00.

(a) Decompose the cross-sectional variance and compute the standard deviation of true skill. Then compute the shrinkage weight — the fraction of an observed deviation from 1.00 that should be carried into a forecast of the GP's next fund. (b) A GP's last fund returned a PME of 1.35. Compute the forecast for its next fund. (c) Section 18.2 reports that buyout persistence largely disappears after about 2000 while venture persistence survives better. Represent that with a shrinkage weight of 0.05 for a post-2000 buyout GP and 0.30 for a venture GP, and recompute the forecast in each case from the same observed 1.35. (d) The plan pays a placement fee of 1 percent of commitments and carries 25 basis points a year of its own costs over the fund's ten-year life. Express the total as a hurdle in PME terms, and say which of the two forecasts in (c) clears it. (e) Two threats to the exercise. First, §18.2 notes that the databases are built from LP disclosures and voluntary GP reporting. If the observed vintage mean PME is 1.10 while 15 percent of funds are missing with a true mean of 0.70, compute the true vintage mean and say what it does to the benchmark used above. Second, state what Lerner, Schoar and Wongsunwai's finding implies about whether a plan can actually buy the venture persistence it has just estimated.

***

## Selected Solutions

*Solutions to Problems 1 and 2 follow. Solutions to the remainder are in the instructor materials.*

**Problem 1.**

(a) Fees are $$0.02 \times 1{,}000 \times 5 = \mathbf{100}$$, so capital deployed is $$1{,}000 - 100 = \mathbf{900}$$. The preferred-return threshold is $$1{,}000 \times 1.08^5 = \mathbf{1{,}469.33}$$, of which 469.33 is the preferred return itself.

(b) At proceeds of 1,600 the waterfall runs three and a half tiers rather than four:

| Tier                 | Paid to LP   | Paid to GP | Cumulative   |
| -------------------- | ------------ | ---------- | ------------ |
| 1. Return of capital | 1,000.00     | —          | 1,000.00     |
| 2. Preferred return  | 469.33       | —          | 1,469.33     |
| 3. GP catch-up       | —            | 117.33     | 1,586.67     |
| 4. Residual 80/20    | 10.67        | 2.67       | 1,600.00     |
| **Total**            | **1,480.00** | **120.00** | **1,600.00** |

The LP receives **1,480** and the GP **120**. Note where the money went: proceeds fell by 400 against Table 18.1, and the LP absorbed 320 of it while the GP absorbed 80 — exactly the 80/20 split, because the fall happened entirely inside the residual tier.

(c) The LP's net multiple is $$1{,}480/1{,}000 = \mathbf{1.48\times}$$, a net IRR of $$1.48^{1/5} - 1 = \mathbf{8.16}$$ **percent**. Against the 900 actually deployed the gross multiple is $$1{,}600/900 = \mathbf{1.78\times}$$ and the gross IRR $$\mathbf{12.20}$$ **percent**, so the fee drag is $$\mathbf{404}$$ **basis points a year** against the 484 of §18.1's 2,000 case. **The drag is smaller in the worse outcome**, because carry is the part of the drag that scales with success and the management fee is the part that does not.

(d) At proceeds of exactly 1,469.33 the GP's carry is $$\mathbf{0}$$: the first two tiers absorb everything. Between that threshold and 1,600 the GP receives $$120 - 0 = 120$$ out of $$1{,}600 - 1{,}469.33 = 130.67$$ of additional proceeds, a marginal share of $$\mathbf{91.8}$$ **percent**. That is the option statement made concrete. Carry is a call struck at contributed capital plus the preferred return: it pays nothing at or below the strike, and just above the strike the GP's delta is not twenty percent but nearly one, because the catch-up tier pays the GP at a hundred percent until it has caught up. *An option with a delta near one just above its strike is a very steep claim, and it is held by the party that chooses the fund's risk.*

(e) Under a hard hurdle the GP receives $$0.20 \times (\text{proceeds} - 1{,}469.33)$$:

| Proceeds | Carry with catch-up | Carry with hard hurdle | Difference |
| -------- | ------------------- | ---------------------- | ---------- |
| 1,600    | 120.00              | 26.13                  | **93.87**  |
| 2,000    | 200.00              | 106.13                 | **93.87**  |

The catch-up is worth 93.87 at both outcomes, because once it has completed — at cumulative distributions of 1,586.67 — the two schemes pay the GP at the same marginal rate of twenty percent, and the whole of the difference has already been banked. So the catch-up clause is worth **most, in proportional terms, at outcomes just above the point where it completes**: at proceeds of 1,600 it multiplies the GP's carry by 4.6, and at 2,000 by only 1.9. *A clause that is worth the same absolute amount at every good outcome is worth relatively most at the mediocre ones — which are the outcomes most funds actually deliver.*

**Problem 2.**

(a) Multiple $$200/100 = \mathbf{2.00\times}$$; IRR $$2^{1/5} - 1 = \mathbf{14.87}$$ **percent**; Kaplan-Schoar PME $$= 200/(100 \times 1.09^5) = \mathbf{1.30}$$. The fund beat the index by thirty percent of the contributed capital, discounted.

(b) The multiple is unchanged at $$\mathbf{2.00\times}$$ — it is a sum of dollars and does not know what a date is. The IRR rises to $$\mathbf{19.21}$$ **percent**. **Only the IRR moved**, and it moved by more than four percentage points on a rearrangement that changed no cash flow's size and created no value.

(c) With a subscription line the LP contributes $$100(1+i)$$ at the end of year one and still receives 200 at the end of year five:

|              | Base case         | Line at 6%        | Line at 12%       |
| ------------ | ----------------- | ----------------- | ----------------- |
| Contribution | 100.00 at $$t=0$$ | 106.00 at $$t=1$$ | 112.00 at $$t=1$$ |
| Multiple     | 2.00x             | **1.887x**        | **1.786x**        |
| IRR          | 14.87%            | **17.20%**        | **15.60%**        |
| PME          | 1.300             | **1.337**         | **1.265**         |

(d) The **IRR improves in both cases**, because deferring the contribution shortens the measured holding period whatever the line costs. The **multiple deteriorates in both**, because the LP pays the interest and the multiple counts every dollar it pays. The **PME changes direction**: it rises at a line rate of 6 percent and falls at 12 percent. What that change of direction measures is whether the borrowing beat the alternative — the LP's money, left in the index, would have compounded at 9 percent, so borrowing at 6 percent to defer the call creates value and borrowing at 12 percent destroys it. **PME is the only one of the three that asks the LP's actual question**, which is not "how fast did this money grow?" but "was I better off here than in the index?" That is the property that makes it a usable evaluation contract: it cannot be improved by a timing choice that does not beat the benchmark, and neither the IRR nor the multiple has that property.

(e) The commitment-weighted average of the two IRRs is $$(10 \times 0.25 + 100 \times 0.05)/110 = \mathbf{6.82}$$ **percent**. Pooling the cash flows gives a contribution of 110 at date 0 and a terminal value of $$10 \times 1.25^5 + 100 \times 1.05^5 = 158.15$$, an IRR of $$\mathbf{7.53}$$ **percent**. Neither is the LP's portfolio return, because both assume the 110 was committed and at work from the first day: in fact the LP holds committed-but-uncalled capital somewhere else, at some other return, and its portfolio return depends on that third number — which no fund reports and which is the LP's own problem rather than the GP's.

***

## Data Exercise: Building a PME Without Buying the Data

The point of this exercise is partly the exercise and partly the obstacle. Fund-level private markets data — Preqin, Burgiss/MSCI, PitchBook, Cambridge Associates — are expensive, licensed, and mostly unavailable to students, which is itself the chapter's argument about measurement. What is free is the disclosure that large public plans are required to publish.

**Part A — A public plan's private equity program (free data).** CalPERS publishes its Annual Comprehensive Financial Report (ACFR) and a separate, legally mandated private equity program review as free PDFs, and several other large public plans (CalSTRS, the State of Wisconsin, the Washington State Investment Board, the Oregon Investment Council) publish comparable material, sometimes down to individual fund-level IRRs and multiples.

1. Retrieve the most recent ACFR. Record the plan's target and actual allocation to private equity, the reported one-, five-, and ten-year returns for the private equity program, and the benchmark the plan uses for it. Write down, in one sentence each, what kind of return the plan is reporting (time-weighted? pooled IRR?) and what the benchmark is (a public index? a public index plus a fixed spread? a peer universe?).
2. Retrieve the same figures from the ACFR of ten years earlier. Has the target allocation changed? Has the benchmark changed? A changed benchmark is a finding, not a nuisance — note what the change did to reported relative performance.
3. Locate the plan's fund-level disclosure (CalPERS publishes cash contributed, cash distributed, remaining value, and net IRR by fund). Pick five funds of the same vintage. Confirm for yourself that their reported IRRs cannot be averaged into a program IRR, and compute the pooled multiple that *can* be aggregated.

**Part B — A toy PME (free data).** Ken French's data library provides monthly market returns and the risk-free rate at no cost.

1. Build a monthly total-return index level $$I\_t$$ from the market factor plus the risk-free rate, starting at 1.00 in the earliest month you need.
2. Take one fund's cash flows from Part A.3 — or, if the disclosure gives only annual aggregates, construct a plausible schedule and label it as assumed — and compute the Kaplan-Schoar PME by discounting each contribution and distribution at $$I\_t$$. Treat remaining NAV as a terminal distribution and say why that is a strong assumption.
3. Recompute the PME using (i) a small-cap benchmark and (ii) the market index levered 1.5 times, financed at the risk-free rate. Report all three PMEs side by side. How much of the fund's apparent outperformance survives a benchmark that resembles what a buyout fund actually holds?
4. Recompute the fund's IRR after shifting every contribution date forward by four quarters and charging 5 percent annual interest on the deferred amount. Report the change in IRR, in multiple, and in PME.

**Part C ★ (if you have institutional access).** With Preqin or Burgiss/MSCI through a university subscription, replicate the Harris-Jenkinson-Kaplan exercise on one asset class and a decade of vintages: compute vintage-year median PMEs against the S\&P 500, then against a small-cap index. Before running anything, write one paragraph on how funds enter the database, what happens to a fund whose GP stops raising capital, and which direction each of those facts biases your estimate.