### PME Benchmarking Methods

### Samuel Henly

∗### August 12, 2013

Executive Summary

PME metrics benchmark the performance of a fund (or group of funds) against an indexed alternative investment. For example, one could use a PME to compare the performance of a PE fund to the performance of publicly-traded stocks indexed by the Russell 3000 Index. When PMEs are generated for many funds, the PME values can be used to rank fund performance controlling for broader market behavior.

This brief accompanies the PitchBook 3Q 2013 Global PE & VC Benchmarking and Fund Performance Report, where the company is debuting aggregate PE and VC performance indices utilizing PME methods.

### Introduction

Motivation. The two most common measures of PE performance, IRR and cash multiples, are adequate
measurements of fund performance when used judiciously.1_{However, IRR and cash multiples can’t be directly}

compared to indices that are used to evaluated performance in mainstream asset classes. The purpose of public-market equivalent benchmarks (PMEs) is to make fund performance directly comparable to the performance of indexed asset classes.

Outline. In this brief, I introduce three measures that can be used to compare the performance of private equity to public markets.

PME benchmarks compare the performance of a fund, or a group of funds, with an indexed alternative investment. That is, PMEs compare the performance of funds with an entirely separate class of assets, rather than directly with a group of peer funds. Industry participants might find PME benchmarks useful in comparing a private equity fund’s performance to similar publicly-traded equities; for example, a PME could be used to compare a healthcare-oriented PE fund to publicly-traded healthcare stocks. Going further, PMEs would allow individuals with sufficient data to compare the market-adjusted returns attained by individual funds, generating fund performance quantiles.

The first two PME variants I will discuss rely on the creation of a fictional PME vehicle using the cash flows of a real PE fund. Once this vehicle, representing an index, is created, its IRR can be computed for apples-to-apples comparisons with the PE fund. Unfortunately, PE funds that significantly outperform the PME vehicle will produce nonsensical output under the first method. The second method avoids this problem, at some cost of comparability.

The last PME variant avoids the creation of an intermediate vehicle, and instead generates a cash multiple that discounts PE fund cash flows by indexed market returns.2

### Long-Nickels PME: A Public Market Equivalent

Definition and Interpretation. First proposed in 1996,3 _{the Long-Nickels PME (hence, simply ’PME’)}

benchmark answers the question: if an investor had made contributions to an indexed fund instead of a PE fund, and if these contributions (and the resulting distributions) were the same size and made at the same time as they were for the PE fund, what would the return be? In this sense it is arelative measure of performance.

When using PME benchmarks, a PE fund is compared to a hypothetical alternative investment, the PME vehicle. The idea is to take cash flows of a PE fund, redirect them to (or from) the PME vehicle, and obtain the vehicle’s NAV for use in an IRR calculation.

1_{For a thorough discussion see Ellis et al (2012),}_{Measuring private equity returns and benchmarking against public markets.}

BVCA Research Report.

2_{In their 2013 working paper Private Equity Performance: What Do We Know?, Robert Harris, Tim Jenkinson, and Steven}

Kaplan use this PME measure to evaluate US private equity performance.

3_{Long, Austin M. and Craig J. Nickels (1996),} _{A Private Investment Benchmark}_{. Presented at AIMR Conference on}

An Example.4 _{Consider the following set of net contributions and index values, and the resulting}_{N AV}

P M E

values calculated in each period.5

Period Period Net Contribution Index PME Vehicle NAV PME Vehicle NAV calculation

1 80 100 80 80·100 100 2 -30 120 66 80·120 100−30· 120 120 3 50 90 99.5 80· 90 100−30· 90 120+ 50· 90 90 4 0 100 110.6 80·100 100−30· 100 120+ 50· 100 90

In each period when net contributions are positive–that is, when an investor pays into a fund–the NAV of the fictional PME vehicle is updated with a purchase of equal value of the indexed asset. For example, in the first period, a contribution of $80 to the fund is mirrored by an $80 purchase into the indexed asset. When net contributions are negative–when an investor receives distributions in excess of his or her contributions–an equal quantity of the indexed asset is sold. In the second period, for example, $30 of the indexed asset is sold when the investor receives a $30 distribution.

Note, finally, that the value of each net purchase (or sale) of the indexed asset is tracked. Consider the initial $80 purchase. In the second period, its value has increased to$80·120

100 = $96as the index increases

to120 from100; but, in the following period, its value drops to$80· 90

100 = 72 as the value of the index

plummets. Of course, the denominator of this asset purchase will always be100, the value of the index at the time of the purchase. Similarly, the $30 sale in the second period will always have a denominator of

120, the value of the index in the period of its sale.

For an explicit formula for PME NAV computation, please refer to Appendix A.

### PME+

Shortcomings of PME. Consider a twist on the example in the previous section:
4_{Adapted from Ellis et al (2012),}_{supra}_{note 1.}

t cnet,t It N AVP M E,t N AVP M E,t calculation 1 20 100 20 20· 100 100 2 30 100 50 20· 100 100+ 30· 100 100 3 -40 50 -15 20· 50 100+ 30· 50 100−40 50 50 4 0 50 -15 20· 50 100+ 30· 50 100−40 50 50

What’s this? In period 2, it seems that the PME vehicle has a negative NAV. Not a negative return–a negativevalue! It’s difficult to assign meaning to a result like this; one interpretation is that PE-matching cash flows result in a short position in the indexed asset. Even if one accepts this curious interpretation, it doesn’t help the fact benchmarking with a PME is impossible in this case: one can’t compute an IRR for an investment with a negative NPV. (Try it in Excel, if you like–you’ll get an error.)

The PME+ uses a computational fudge to work around this issue.

PME+ Defined. To avoid negative NPVs, Rouvinez6 _{proposed keeping final-period NAV–rather than}

cash flows–constant between the PE fund and the PME vehicle.

In the PME+ method, the NAV for the PME+ vehicle is computed identically to the NAV for the PME
case, with the exception that distributions are scaled by a constant7_{. This constant is chosen to ensure that}

final period NAV is equal for the PME+ vehicle and the PE fund. The PME+ method does not ensure a positive PME vehicle NAV forevery period, but this is the usual result.

The downside to PME+ is that it does notperfectly match the cash flows of the PME vehicle to the cash flows of the PE fund. However, it does match themreasonably well, andconsistently.

For an explicit formula for PME+ computation, and for an example, please refer to Appendices B and C, respectively.

### KS-PME

KS-PME is a Market-Adjusted Cash Multiple. In a 2005 paper8_{, Kaplan and Schoar proposed an}

alternative PME method that this brief will refer to as KS-PME.9Rather than creating a separate (fictional) investment vehicle, as the previous methods do, the KS-PME discounts cash flows in a cash multiple computation by the returns to a public index since the fund’s inception. The KS-PME may take the form of either a TVPI-like metric or a DPI-like metric; an explicit formula for each is presented in Appendix D.

6_{Rouvinez (2003),}_{Private Equity Benchmarking with PME+}_{. Venture Capital Journal, August: 34-38.}
7_{A constant is just a fixed number: some examples are}_{1}_{,} 1

4,π, and 0.3. So, if a $1000 distribution is made by the PE, and the scaling constant is1

2 the PME+ vehicle distribution is $500.

8_{Steven Kaplan and Antoinette Schoar, Private Equity Performance: Returns, Persistence, and Capital Flows. Journal of}

Finance 60(4): 1791-1823.

9_{The authors have subsequently referred to their method as the Market-Adjusted Multiple to distinguish it from the}

Ongoing funds should be compared with public market indices using the TVPI-like metric, while fully-realized funds should use the DPI-like measure.10

A Simple Example. Consider the following simple example where a fund’s DPI is computed side-by-side with a DPI-like KS-PME:

t contributiont distributiont It DP It KS−P M EDP I,t

0 20 0 100 0 0

1 10 10 100 0.33 0.33

2 0 40 50 1.67 3

First consider the last-period DPI:DP I2= 1.67, indicating that the total amount paid out by the fund

(50) is 67% more than was paid into the fund (30).

Now, compare the DPI figure with the KS-PME value in the last period: KS−P M EDP I,2= 3. The

KS-PME returns a number nearly twice the value of DPI. Why the difference? The distribution in the final period was made at a time when the public market was collapsing. The KS-PME is so much larger than the DPI because the fund managed to produce a huge distribution in a period when the alternative asset had fallen in value. Put another way: compared to the alternative asset class, the fund was doing even better than it appeared to have done in a vacuum.

### Using Public Market Equivalent Metrics

Long-Nickels PME and PME+. Using a PME or PME+ vehicle’s contributions, distributions, and NAV, one can compute the IRR for the reference security. The IRR so computed will be directly comparable to the original fund. For example, had the PME vehicle been liquidated in period 4, its IRR would have been 4.43%; if the PE fund had produced an IRR of anything greater than 4.43%, its manager could claim that it had outperformed the public index.

There are several considerations to be aware of when using PME benchmarks.

First, one must be careful when choosing an index. Indices used for comparison ought to provide some insight into a fund’s performance. Comparing the performance of a VC fund to, say, the Russell 3000 Index is not as useful as a comparison to a PME benchmark based on a small-cap index; PitchBook currently uses the Russell 2000 Growth Index for VC benchmarking. Worse, if the index ignores dividend payments or coupons produced by alternative investments, the PE fund will seem to outperform to a greater extent than it really did.

Second, the PME is better-used to judge the performance of mature funds where remaining NAV is small relative to contribution size; the PME has an implicit assumption that an investor is able to liquidate his or her holdings in the last period, and this assumption is less important if the final NAV is small.

Third, while cash multiples can be computed for PME vehicles, I strongly advise against it. Because of the methods used to construct a fund vehicle, its cash multiples (especially those relying on distributions) will be uselessat best. If cash multiples are necessary for analysis, the KS-PME should be used.

Finally, when a fund significantly outperforms the market, the PME benchmark will produce nonsense. In these instances, a PME+ benchmark will usually salvage the situation, at the cost of fudging.

Kaplan-Schoar PME. The Kaplan-Schoar PME may be easier to interpret than the Long-Nickels PME and the PME+. If its value is greater than1, then a fund produced a positive return, accounting for the opportunity cost of investing in the indexed market. Greater KS-PME values imply proportionately greater performance, and so funds can be compared directly by their KS-PME value with no further computations. An additional relative advantage of the KS-PME is its resilience: it will remain a valid measure in the face of exceptional PE performance without computational prestidigitation.

Unlike the Long-Nickels PME and the PME+, the KS-PME does not attend to differences in the timing of payments. If contributions to two funds are identical and timing and size, for example, and each fund makes an identically-sized distribution when the index has the same value (but in different periods), the funds will nevertheless produce the same PME. This result is analogous to the treatment of cash flow timing in IRR and cash multiple metrics. However, it is less significant in the KS-PME, because the opportunity cost of an alternative asset is explicitly accounted for.

As with the Long-Nickels PME and the PME+, care should be taken in the selection of an index, and
the index should account for dividend payments. Additionally, DPI- and TVPI-like variants of the KS-PME
exist; the DPI-like variant should be used with fully-realized funds, and the TVPI-variant for ongoing funds.
Finally, the KS-PME has some useful properties for asset pricing models;11_{the specifics are beyond the}

scope of this brief but may be interesting to the quantitatively-inclined reader.

11_{See Morten Sorensen and Ravi Jagannathan’s 2013 working paper The Public Market Equivalent and Private Equity}

## Technical Appendix

### A

### PME Computation

To compute the PME, one needs two data series: net fund contributions for each period, and public index values for each period. For simplicity, denote net contributions in periodtas

cnet,t=contributiont−distributiont

and denote the public index value at timet asIt. Then the PME NAV can be computed as

N AVP M E,t=
t
X
s=0
cnet,s
_{I}
t
Is

The index can alternatively be computed recursively, using the value from the last period:

N AVP M E,t=cnet,t+N AVP M E,t−1· It It−1 Note that It It−1

is the gross return from investing in an indexed security from t−1 tot. Similarly,

It

It−n

is the gross return for holding an indexed security fromt−ntot.

### B

### PME+ Computation

In order to compute PME+ returns overT periods, wheret= 0, . . . , T, one uses

N AVP M E+,t=
t
X
s=0
(contributions−λT ·distributions)·
_{I}
t
Is
where
λT =
(Sc−N AVP E,T)
Sd
and
Sc =
T
X
s=0
contributionss·
_{I}
T
Is
Sd =
T
X
s=0
distributionss·
IT
Is

Note in particular that λT is computed using the final period’sN AV for the PE fund. The intuition

N AVP E,T = Sc−λTSd
=
T
X
s=0
contributions·
_{I}
T
Is
−λT ·
T
X
s=0
distributions·
_{I}
T
Is
=
T
X
s=0
(contributions−λT ·distributions)·
_{I}
T
Is
= N AVP M E+,T

That is,λT is chosen to ensure that NAV for the PE fund and the PME+ vehicle are equal in the final

periodT.

### C

### PME+ Example

Let’s go back to the example from the main body in the beginning of the PME+ section. I’ve replaced the

cnet,tcolumn with adistributiontcolumn and acontributiontcolumn.

t contributiont distribtiont It N AVP M E,t N AVP M E,t calculation

0 20 0 100 20 20·100 100 1 30 0 100 50 20·100 100+ 30· 100 100 2 0 40 50 -15 20· 50 100+ 30· 50 100−40 50 50

Let’s say that in the original PE fund,N AVP E,2= 20.

Once we have these data, the first step to computing a PME+ index is to computeλT. The steps to

do so follow. Start withSc andSd; note thatT = 2.

Sc =
T
X
s=0
contributions·
_{I}
T
Is
= 20· 50
100 + 30·
50
100 + 0·
50
50
= 25
Sd =
T
X
s=0
distributions·
_{I}
T
Is
= 0· 50
100+ 0·
50
100 + 40·
50
50
= 40

Now, to get the value ofλT: λT = (Sc−N AVP E,T) Sd = (25−20) 40 = 1 8

Finally, rewrite the original table usingλT to find N AVP M E+,t for each period.

t contributiont distribtiont It N AVP M E+,t N AVP M E+,t calculation

0 20 0 100 20 20· 100
100
1 30 0 100 50 20· 100
100+ 30·
100
100
2 0 40 50 20 20· 50
100+ 30·
50
100−
1
8
4050_{50}

Note thatN AVP M E+,T =N AVP E,T!

### D

### KS-PME Computations

DPI-like KS-PME. First, consider the slightly-adapted formula from Sorensen and Jagannathan’s working
paper12_{:}
KS−P M EDP I,T =
PT
t=0
distributiont
1+RM,t
PT
t=0
contributiont
1+RM,t
Here, we have

distributiont = distribution from a fund in periodt

contributiont = contribution from a fund in periodt

1 +RM,t =

It

I0

, whereIt=index value in periodt

Some omitted algebra leaves us with a more palatable formula:
12_{Morten Sorensen and Ravi Jagannathan (2013),}_{supra}_{note 11.}

KS−P M EDP I,T =
PT
t=0
_{distribution}
t
It
PT
t=0
contributiont
It

TVPI-like KS-PME. The KS-PME can be adapted for use in evaluating an active fund by adding discounted, last-period remaining value to the numerator:

KS−P M EKS−T V P I,T =
N AVT
IT +
PT
t=0
_{distribution}
t
It
PT
t=0
_{contribution}
t
It