Performance attribution for private investments

Key takeaways

• A value creation bridge splits the equity gain into revenue growth, margin change, multiple change and net debt reduction, and the four parts must sum to the total gain.
• The split depends on the ordering convention because revenue, margin and multiple interact; in the example the multiple effect is $54m if measured last and $30m if measured first, a $24m interaction term.
• Leverage turns the same operating result into a much larger equity multiple: the example deal returns 4.1x with debt and 2.4x on an illustrative unlevered basis.
• Part of any multiple expansion usually reflects the market rather than the manager; comparing with the movement in comparable company multiples separates the two in plain terms.
• Fund attribution by sector, entry year and deal shows concentration: in the example fund one deal produced 71.6% of the total gain, and the other five deals together returned 1.39x.
• The capital-weighted loss ratio and the spread of deal outcomes describe risk that a fund multiple hides, and past top performance should be treated as evidence to test, not a guarantee.

Why attribute returns

Two managers can present the same 2.0x gross fund multiple. One bought companies at average prices, grew them, improved their margins and sold them at similar multiples. The other bought at average prices, did little to the businesses, and sold into a market where valuations had risen across the board. The multiples are identical. What an LP can expect from each manager's next fund is not.

Attribution is the tool for telling them apart. It works at three levels. At the deal level, a value creation bridge decomposes the change in equity value into operating and financial drivers. At the fund level, gains are grouped by sector, geography, entry year, deal size or deal team to see which parts of the strategy worked. At the manager level, attribution across several funds asks whether the drivers that produced past returns are still present.

Attribution is analysis, not accounting. It rests on conventions (which driver is measured first, what counts as the market's contribution) and on data that GPs provide. Its value is in the questions it prompts, and those questions are sharper when the conventions are stated.

The value creation bridge

Start from the identity that links a company's equity value to its operations. Enterprise value (EV) is EBITDA times the valuation multiple, and EBITDA is revenue times the EBITDA margin. Equity value is EV minus net debt. So equity value = revenue x margin x multiple - net debt. The change in equity value between entry and exit can be split into four parts by changing one input at a time.

Revenue growth is the change in revenue valued at the entry margin and entry multiple. Margin change is the change in margin applied to exit revenue at the entry multiple. Multiple change is the change in multiple applied to exit EBITDA. Net debt reduction is entry net debt minus exit net debt, which reflects cash the business generated and used to repay borrowing (or, if negative, additional borrowing such as a dividend recapitalization). This ordering, revenue then margin then multiple, is one common convention, and the next section shows why it matters.

Worked example: Cedar Logistics

Cedar Logistics is a hypothetical company bought by a fund at a revenue of $200m, a 15 percent EBITDA margin and an 8.0x multiple, with $144m of net debt (4.8x EBITDA). The fund owns all of the equity. Five years later it is sold at $300m of revenue, an 18 percent margin and a 9.0x multiple, with net debt reduced to $90m (1.7x EBITDA). There were no interim dividends or further equity investments.

The equity grows from $96m to $396m, a gain of $300m and a 4.1x multiple, or an IRR of 32.8 percent over five years. The bridge attributes 40 percent of the gain to revenue growth, 24 percent to margin improvement, 18 percent to the higher multiple and 18 percent to debt paydown.

Ordering and the interaction term

Revenue, margin and multiple multiply each other, so when two of them change together there is a piece of the gain that belongs to both. Whichever driver is measured last collects that joint piece. In the sequential convention above, the multiple is measured last and applied to exit EBITDA, so it collects the interaction between EBITDA growth and multiple expansion: the extra $24m EBITDA was valued at the higher multiple.

Measure the multiple first instead, applied to entry EBITDA, and the multiple effect shrinks to $30m while the EBITDA effects grow. Neither is wrong. A GP that wants to emphasize operating value creation will naturally prefer to measure the multiple first, which is why the convention must be disclosed. A neutral alternative splits the interaction term evenly, which gives the midpoint of the two orderings.

Leverage and cash generation

The deleveraging bar in the bridge shows debt being repaid from the company's cash flow. That is genuine value to the equity, but it depends on two things at once: the business generating cash, and the capital structure directing that cash to lenders. Leverage has a second, larger effect that the bridge does not show directly. By funding most of the purchase with debt, the fund put in only $96m of equity for a $240m business, so every dollar of enterprise value gained is a much larger percentage of the equity.

An unlevered comparison makes the effect visible. It asks what the equity multiple would have been if the fund had bought the whole enterprise with equity. The comparison needs an assumption about the interest the company would not have paid; the example below uses a hypothetical $40m of cumulative after-tax interest over the five years. The operating result is the same. The multiple is very different.

Skill, beta and leverage in plain terms

Practitioners separate a private equity return into three broad sources. Beta is the part that came from the market: the general level of valuations, the economy and the sector's fortunes, which any owner of a similar business would have enjoyed. Leverage is the part that came from financing: debt magnifying whatever the market and the business delivered. Skill, sometimes called alpha, is what is left: better selection, better prices at entry, operational improvements and better timing of exits.

Leverage and beta are not bad; LPs knowingly pay for exposure to both. But they are available more cheaply elsewhere. A public equity index provides market exposure at almost no cost, and leverage can be added to it. The fees and carry of a private fund are justified by skill, so diligence focuses on evidence that returns exceeded what market movement and leverage alone would have produced. The PME methods covered earlier in this track answer this at the fund level. At the deal level, a simple approach compares multiple expansion with the change in multiples of comparable listed companies over the same period.

Fund-level attribution by sector and vintage

At the fund level the same principle applies: break the total gain into parts that sum to it. The natural cuts are by sector, by entry year (the year each deal was made, the deal-level counterpart of a fund's vintage), by deal size, by geography and by the deal partner responsible. Each cut shows the gain, the invested capital and the multiple for its group, and each group's contribution to the fund's multiple is its gain divided by the fund's total invested capital.

Fund P is a hypothetical fund with six deals, including Cedar Logistics. It invested $400m and holds or has realized $819m of value, a 2.05x gross multiple. The sector cut shows that industrials produced 80 percent of the gain. The entry-year cut shows that the deals made in 2018 produced all of it, with the 2019 and 2020 deals together slightly below cost. Those two findings point to very different questions for the manager.

Loss ratio, dispersion and persistence

A fund multiple averages good and bad outcomes, so two funds with the same multiple can carry very different risk. The capital-weighted loss ratio measures how much invested capital was lost on deals that returned less than cost: the sum of (cost minus value) over losing deals, divided by total invested capital. A companion figure is the count of losing deals. For Fund P the loss ratio is 20 percent and two of six deals lost money.

Dispersion describes how widely deal outcomes are spread, and concentration how much of the gain depends on a few deals. Fund P's deal multiples range from 0.00x to 4.13x, and Cedar Logistics alone produced 71.6 percent of the gain. Without it, the other five deals returned 1.39x. An LP underwriting the next fund has to ask whether a Cedar-like outcome is a repeatable result of the strategy or a single event.

That question is the core of the persistence debate: do managers whose past funds performed well tend to do well in their next funds? Academic and practitioner research on private equity has examined it at length, and the findings vary by strategy, by period and by how performance is measured. What can be said without citing figures is that the evidence is not strong enough to treat past top performance as a guarantee, that the next fund is often raised before the previous one's performance is known, and that changes in team, fund size and strategy can break any link. Attribution helps by showing whether the drivers of past returns are still present.