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Use and contrast the various ways of measuring private equity performance, outlining the strengths and weaknesses of each.

FRM® Part II · Risk Management and Investment Management · Private Markets Investing (up to section 3.3.10) · FRM2.IM.11.c

The idea

Private equity performance is measured with several tools, none complete. The internal rate of return (IRR) is the discount rate that sets the net present value of contributions and distributions to zero. It respects timing. Reading it as a compound return implies interim cash is reinvested at the IRR itself, which is an interpretation and a comparability limit, not a realised reinvestment return. It can be inflated by delaying capital calls with a credit line, and is unreliable for young funds. Multiples ignore timing. The realised multiple, which counts only cash already returned, is DPI = distributions ÷ paid-in capital. The unrealised multiple, RVPI, is residual net asset value ÷ paid-in capital, and it rests on the manager's valuation. Adding the realised and unrealised parts gives the total multiple, which is TVPI = DPI + RVPI. Public market equivalents such as Kaplan-Schoar compare the fund with an index by investing the same cash flows in the index. A ratio above 1 means outperformance. Direct alpha converts this into an annualised excess return. Never rank funds on one measure. Use IRR and TVPI together and benchmark with a PME.

Formulas

Total value to paid-in (TVPI)

TVPI = DPI + RVPI

DPI
cumulative distributions ÷ paid-in capital
RVPI
NAV ÷ paid-in capital

The denominator is paid-in capital, not the commitment. The multiple ignores timing, so read it with the IRR and benchmark it with a PME.

Kaplan-Schoar public market equivalent

KS-PME = Σ(Dₜ ÷ Iₜ) ÷ Σ(Cₜ ÷ Iₜ)

Dₜ
the distribution to the investor at date t
Iₜ
the public index level at date t
Cₜ
the contribution paid in at date t

Scaling each cash flow by the index is the same as investing it in the index. Above 1 the fund beat the index; it says nothing about the annualised margin, which direct alpha gives.

A practice question

From the question bank, with the reason each wrong option is wrong.

In private equity performance reporting, DPI (distributions to paid-in capital) is best described as:

  1. Residual net asset value divided by paid-in capital, a measure of unrealised valueWhy not: This is RVPI (NAV over paid-in capital), not DPI.
  2. Cumulative distributions to limited partners divided by cumulative paid-in capital, a measure of realised value - correct
  3. Distributions plus residual net asset value divided by paid-in capitalWhy not: This is TVPI (realised plus unrealised), not DPI.
  4. The annualised rate that sets the present value of contributions equal to distributionsWhy not: This is the internal rate of return, a time-weighted measure rather than a ratio of totals.

DPI = cumulative distributions / paid-in capital. It counts only cash already returned, so it does not rely on manager valuations. RVPI covers the unrealised residual value and TVPI = DPI + RVPI.

A harder one

An investor contributes USD 100 million to a fund at time 0, when a public equity index stands at 100. The fund makes a single distribution of USD 160 million at the end of year 4, when the index stands at 150, and has no remaining value. The Kaplan-Schoar public market equivalent (PME) of the fund is closest to:

  1. 1.60Why not: This is the TVPI (160 / 100), which ignores what the index did over the same four years.
  2. 1.07 - correct
  3. 0.94Why not: Inverts the ratio (150 / 160 pattern), so the fund looks like an underperformer when it is not.
  4. 0.63Why not: Divides the contribution by the distribution without any index adjustment (100 / 160).

KS-PME = (160 / 150) / (100 / 100) = 1.067. Contributions and distributions are scaled by the index, which is equivalent to investing the cash flows in the index. A value above 1 means the fund beat the index.

The hardest tier

A fund draws USD 100 million from an investor at time 0 and returns USD 200 million at the end of year 4, an IRR of 18.9 percent and a multiple of 2.0x. Suppose instead the manager finances the investment for one year on a subscription credit line at 5 percent, so that the investor is called USD 105 million at the end of year 1 and the distribution is unchanged. Which outcome is most likely?

  1. The reported IRR rises to about 24.0 percent and the multiple stays at 2.00xWhy not: Ignores the interest on the credit line, which increases the capital the investor pays in.
  2. The reported IRR stays at 18.9 percent and the multiple falls to about 1.90xWhy not: Assumes that delaying the call does not change the IRR; IRR is measured from the date of the investor's cash flows.
  3. The reported IRR falls to about 17.5 percent and the multiple falls to about 1.90xWhy not: Keeps four years of compounding on 105 instead of three, because the call is now delayed to year 1.
  4. The reported IRR rises to about 24.0 percent while the multiple falls to about 1.90x - correct

Without the line IRR = 2^(1/4) - 1 = 18.9 percent. With the line IRR = (200 / 105)^(1/3) - 1 = 24.0 percent over three years, and the multiple = 200 / 105 = 1.90x. Credit lines flatter IRR and depress multiples, so both must be read together.

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