Public Market Equivalent

Overview

The public market equivalent (PME) is a collection of performance measures developed to assess private equity funds and to overcome the limitations of the internal rate of return and multiple on invested capital measurements. While the calculations differ, they all attempt to measure the return from deploying a private equity fund's cash flows into a stock market index.

Long-Nickels PME

The first PME measure was proposed by Austin M. Long and Craig J. Nickels in 1996. The analysis is referred in the industry as Long Nickels PME, LN-PME, PME, or ICM. Long and Nickels stated that they preferred the acronym ICM (Index Comparison Method): The ICM is also known as the Public Market Equivalent (PME). We prefer the term ICM, because it better describes the methodology, which is not limited to the use of a public market index to calculate its results The PME analysis is covered under US patent 7058583

Methodology

Long and Nickels compared the performance of a private equity fund with the S&P500 Index by creating a theoretical investment into the S&P using the Private Equity fund cashflows :

When paying a capital call, we assume that the same amount is used to 'buy the index' When receiving a distribution, we assume that the same amount of the index is sold. As the index price evolves, the value of the theoretical amount invested in the index changes. When receiving a valuation for the fund, we can then compare the value of the fund investment to the theoretical value of the index investment.

Negative cashflows are treated as contributions. On the first period, a $100 call in the fund is matched by a $100 investment into the index. On the second period, the $100 index investment is now worth $105, to which is added $50 of new investment. A positive cashflow is treated by decreasing the index investment by the same value. On the valuation period, we compare the valuation received from the fund to the value of the theoretical investment. The PME IRR is obtained by computing an IRR with the index valuation as the final cashflow. The Long Nickels PME tells how an equivalent investment in the public market would have performed. This then needs to be compared to the actual IRR of the fund. In the above example, the IRR is 1.13 percentage points above the PME, which means that the private fund outperformed the public index. The difference between the IRR and the PME is called the IRR spread.

Formula

The PME is an IRR on the cashflows of the investment, using as final cashflow an adjusted PME NAV.

N A

V

P M E

=

∑

s

T

C

s

×

I

T

I

s

{\displaystyle NAV_{PME}=\sum _{s}^{T}C_{s}\times {\cfrac {I_{T}}{I_{s}}}}

Where :

C

s

{\displaystyle C_{s}}

Limitation

As stated in Long and Nickels paper: If a private investment greatly outperforms the index because it makes frequent, large distributions, it is possible for the final value determined by the index comparison to be negative. In effect, the frequent large withdrawals from the index result in a net short position in the index comparison This can be simulated in the previous example by having a period where the fund distributes a large amount and the index dives :

When the final valuation of the theoretical investment is negative, the IRR formula for the PME may not return any results. Even if a PME can be calculated, while the investment stays negative, every increase in the index will be interpreted as a hit in the performance of the theoretical investment : on the above example, the value of the index went back up to 120, which had a negative impact on the value of the theoretical investment. Even if the investment eventually goes back into positive values and a PME can be computed, the time spent under 0 will be improperly taken into account. The next methods by Rouvinez, and Kaplan and Schoar are partly designed to address this issue.

PME+

The PME+ was initially described in 2003 by Christophe Rouvinez in a paper Private Equity Benchmarking with PME+. It is written to resolve a common issue of the Long Nickels PME : an investment outperforming the index will yield a negative value in the index theoretical investment.

PME+ Methodology

Instead of modifying the NAV of the investment, the PME+ discount every distribution by a factor computed so that the NAV of the index investment matches the NAV of the fund.

Like the Long Nickels PME, the PME+ needs to be compared to the IRR. An IRR outperforming the PME means that the fund outperformed the public index.

PME+ Formula

Using Henly Notation in PME Benchmarking Method:

N A

V

P M E + , T

=

∑

s = 0

t

( c o n t r i b u t i o

n

s

−

λ

T

. d i s t r i b u t i o

n

s

) .

I

t

Modified PME

The modified PME (or mPME) method was released by Cambridge Associates in October 2013. It provides an alternate way to tackle the negative NAV limitation of the LN-PME. Like the LN-PME and the PME+, the mPME consider an hypothetical public investment whose performance follows the public benchmark. Each contribution in the private investment is matched by an equal contribution in the public investment. However, rather than subtracting the distributed amounts from the public investment, we compute the weight of the distribution in the private investment, and remove the same weight from the public one.

Formula

For each distribution, a distribution weight is calculated

D

w e i g h t , t

=

D

t

D

t

+ N A

V

t

{\displaystyle D_{weight,t}={\cfrac {D_{t}}{D_{t}+NAV_{t}}}}

The NAV of the theoretical investment is then calculated as :

N A

V

m P M E , t

= ( 1 −

D

w e i g h t , t

) × ( N A

Kaplan Schoar PME

Kaplan Schoar PME was first described in 2005 by Steve Kaplan and Antoinette Schoar. While the Long Nickels PME returns an IRR, the Kaplan Schoar PME (or KS-PME) returns a market multiple. A simple explanation of its computation is described into Sorensen & Jagannathan paper: Let X(t) denote the cash flow from the fund to the LP at time t. This total cash-flow stream is divided into its positive and negative parts, called distributions (dist(t)) and capital calls (call(t)). Distributions are the cash flows returned to the LP from the PE fund (net of fees) when the fund successfully sells a company. Capital calls are the LP’s investments into the fund, including the payment of ongoing management fees. The distributions and capital calls are then valued by discounting them using the realized market returns over the same time period, and the [KS-]PME is the ratio of the two resulting values:

Formula

When considering an investment at time T. The KS-PME first considers the current valuation of the investment as a distribution at date T. KS-PME is then defined as

K S − P M E =

F V ( D i s t )

F V ( C a l l )

{\displaystyle KS-PME={\cfrac {FV(Dist)}{FV(Call)}}}

with

F V ( D i s t ) =

∑

t

( d i s t ( t ) ×

I

T

I

t

)

{\displaystyle FV(Dist)=\sum _{t}(dist(t)\times {\cfrac {I_{T}}{I_{t}}})}

F V ( C a l l ) =

∑

t

( c a l l ( t ) ×