measuring private equity returns that are commonly used in the industry and
constructs aggregate ... from the BVCA's Performance Measurement Survey (
PMS). ..... 400. 600. 800. 1000. 1200. 1400. 1987 1989 1991 1993 1995 1997
1999 ...
Measuring private equity returns and benchmarking against public markets Colin Ellis, University of Birmingham,
[email protected] Sonal Pattni, BVCA,
[email protected] Devash Tailor, BVCA,
[email protected]
Executive summary Private equity is still a relatively young asset class, with some unique characteristics. One feature is the very irregular timing of cashflows, and a consequence of this is that private equity relies on measures of returns that are not standard in other asset classes. As such, new investors can be unclear or unaware of the differences between the common methods for measuring private equity performance and comparing it with returns from other asset classes. This paper sets out different methods for measuring private equity returns that are commonly used in the industry and constructs aggregate indices for the UK asset class. It also considers methods for comparing private and public equity returns and demonstrates the importance of considering cross-sectional variation between public and private equities. Keywords: private equity; performance measurement; aggregation; public market comparison
Acknowledgements We are very grateful to Mark Drugan of Capital Dynamics, members of the BVCA’s Research Advisory Committee, and BVCA colleagues for their comments and advice. All remaining errors are our own. The views expressed in this paper are those of the authors and do not necessarily reflect those of the BVCA. 1
Contents Page no.
1.
Introduction
3
2.
Methodological discussion
4
2.1
Key PE multiples
4
2.2
Advantages and drawbacks of multiples
6
2.3
The internal rate of return (IRR)
6
2.4
Advantages and drawbacks of IRRs
7
2.5
Modified IRR (MIRR) and isolated MIRR
10
2.6
Aggregation issues
12
2.7
Constructing PE indices
14
Making comparisons with public markets
18
3.1
The Public Market Equivalent (PME) method
18
3.2
Short positions and PME+
19
3.3
Choosing the appropriate public index
20
3.4
Correlation analysis: time series vs. cross section
21
3.
4.
Summary & conclusions
25
References
26
2
1. Introduction
A key concern for financial investors is deciding how to allocate their assets, or where to put their money. Central to this is the risk-reward trade-off that is offered by different asset classes. For mainstream financial assets, such as bonds or equities, measures of returns are relatively simple to construct and well-understood. The current or historical yield (and sometimes the expected yield) is fairly easy to calculate, although the ex-ante risk of default can be less clear. Where possible, riskadjusted measures of returns are often used. But gauging the financial performance of private equity (PE)1 funds is more difficult. Unlike bonds and equities, which have defined markets and good liquidity to enable investors to buy and sell assets, commitments to PE funds are typically held for long periods of time. Furthermore, the time profiles of the investments are very different. For bonds and equities, investors invest money at the point of purchase, receive regular dividends or coupons, and receive final proceeds at the point of sale. Depending on whether market prices have risen or fallen over time, the sale price could be higher or lower than the initial purchase price. Cashflows for private equity are rather more irregular. For instance, once an investor has made a commitment to a fund it may not be called upon for many months or years, but then will be called upon many times over the life of the fund at unpredictable intervals. This irregular timing of cashflows between PE funds and their investors is one of the defining characteristics of the asset class. In light of these distinctions, measuring PE returns requires a different approach to measuring the performance of more traditional asset classes. There are two widespread measures in the industry, namely money or cash multiples and the so-called ‘internal rate of return’. Both measures have advantages and disadvantages, and have sometimes been criticised as unrepresentative of ‘real’ returns. In addition, the comparison of PE returns with public markets can be fraught with difficulty. This paper contributes to this debate, first by describing and explaining the different measures of PE returns, and then examining the different weighting and aggregation approaches that are used to produce industry-wide estimates of returns. We also construct indices of UK PE returns using data from the BVCA’s Performance Measurement Survey (PMS). Finally, we examine the nature of crosscorrelations between PE funds and public equity markets, highlighting some potential concerns with an aggregated time-series approach.
1 Throughout this paper, we use ‘private equity’ to refer to the whole universe of private equity investments, notably including both venture capital and buyout investments.
3
2. Methodological discussion
When measuring PE returns, investors must consider a number of issues that also affect other asset classes. These include whether to look at gross or net performance (i.e. once fees, and in the case of PE carried interest, are subtracted), and comparisons with the alternatives that are on offer. However, in the case of PE, due to the irregularity of cashflows the standard time-bound return measures are inappropriate. In its simplest form, the buy-and-hold return on a zero-coupon bond would be given by:
In the case of coupon-yielding securities, or dividend paying equities, the calculation becomes a little more complex. Coupons and dividends are typically assumed to be re-invested into the fixed-income security or equity at the prevailing market price when they are paid. However, the basic structure of the return calculation – final cash returned as the numerator and initial investment as the denominator – broadly remains the same. Private equity, however, is somewhat different. Due to the irregularity of PE cashflows, and the lack of a genuine re-investment option, this sort of return calculation is not appropriate for the asset class. Instead there are currently two widely accepted approaches for calculating PE returns. The first is to present so-called ‘multiples’, and the second is the internal rate of return (IRR). We will consider each in turn.2
2.1
Key PE multiples
Simply put, multiples are typically calculated as the ratio of cash paid out (also known as distributions) to total funds that the investors supplied to the PE fund manager (also known as draw downs or capital calls). The main disadvantage of this approach is that it does not consider the timing of those cashflows. Depending on the precise multiple used, unrealised returns may also be included in the calculation. There are three key measures of multiples.3
•
Distributions to Paid In (DPI) capital
Talmor and Vasvari (2011) offers a good guide to performance measurement, and indeed private equity more generally. Another ratio, of Paid In to Committee Capital (PICC), measures the proportion of money that has been drawn down from all the funds that investors have committed. However, it does not measure returns. 2 3
4
The DPI simply tells us what proportion of money that has been drawn down by GPs has so far been paid back. If this figure were one, then investors would have so far received back exactly the same amount that they had initially paid. Typically, over the life of a PE fund, the DPI will start at zero, and gradually rise as the fund matures. As such, the DPI is not a good measure of returns in two situations. The first is where the fund is not yet at the end of its life as, by definition, this measure of returns excludes all unrealised returns (i.e. the value of equity stakes and other instruments in unsold companies). The second is where a fund has yet to invest all of its capital, which can result in an interim DPI that may be unusually volatile as early investments potentially exit and/or new money is drawn down. Real returns will even be negative in the short term, as fees are drawn before investments are made.
•
Residual Value to Paid In (RVPI) capital
The RVPI measures how much of a fund’s return is unrealised, relative to the money that investors have paid in. This unrealised or residual value – often referred to as a ‘net asset valuation’ – is subjective and may be calculated using a variety of methods. However, previous research suggests that there is little sign of systematic bias in valuations, at least for relatively mature funds (Ellis and Steer, 2011). The RVPI measure excludes any previous distributions the PE fund may have made, so again represents an incomplete picture of returns.
•
Total Value to Paid In (TVPI) capital
The TVPI gives the overall (but potentially unrealised) performance of a PE fund. It tells us what multiple of the investment would be returned to investors if the unrealised assets were sold at current valuations and added to distributions that had already been received. The TVPI is the best overall multiple measure of returns, although there will obviously be uncertainty about the final outcome for as-yet unrealised investments. Simple algebra shows the relationship between these three measures:
5
2.2
Advantages and drawbacks of multiples
The key advantage of multiples as a measure of PE returns is that they are very simple to understand. Multiples are frequently used by PE funds to give investors an indication of how individual investments have performed – for instance, a 1.5x result tells investors that they have received a 50% return on their investment. However, multiples also suffer from clear drawbacks. The most obvious of these is that they do not consider the timing of draw downs or distributions within the investment process, and hence implicitly do not consider the time value of money. A multiple of 1.5x delivered over a ten year period is not an especially strong performance, in terms of the implied geometric annual return. This suggests that, when multiples are used as a measure of PE performance, investors should also be told the duration of the investment. Concerns have also been raised that multiples do not provide investors with information about the underlying risk of the investments, or the potential reinvestment performance of distributions. However, this critique also applies to measures of returns in some other (more traditional) asset classes. When a listed company pays out dividends it provides little information about the covariance of its share price with other equities, or advice on the return shareholders can expect from investing that dividend elsewhere. For the purposes of this paper, we focus on the elements of return measurement that are unique to private equity.
2.3
The internal rate of return (IRR)
The second common measure of PE returns is the IRR. Technically this is the discount rate that ensures that the net present value (NPV) of a series of (positive and negative) cashflows is equal to zero. In economic terms it is best represented as the denominator-based element of the nonlinear calculation:
where NPV denotes net present value, Ci denotes cashflow in period i, and r is the calculated internal rate of return. In practice PE funds are typically long-lived, and interim estimates of returns must be based on implicit assessments of expected future cashflows. This is measured by the ‘net asset value’ (or NAV) of the fund. In these instances the IRR calculation at period i becomes:4
4 Technically, the discount rate applies to the final NAV as well. For simplicity, this has been subsumed in both this and the subsequent equation.
6
Ellis and Steer (2011) describe NAVs and their role in interim measures of IRR in more detail, and investigate their accuracy. Once funds are sufficiently mature – typically, around four to six years after the first draw down – they find no evidence of systematic over- or under-valuation across a sample of closed UK funds. The equation set out above can be applied both in a forward-looking and backward-looking context. The best IRR estimate of returns is the so-called ‘since inception’ measure, where all cashflows in the fund (or deal) and the latest valuation are used in the calculation.5 However, backward-looking measures of returns can also be prevalent. These are often referred to as ‘ten year’ or ‘three year’ returns, depending on the length of time over which the return is calculated. Backward-looking return measures are calculated by ‘liquidating’ the residual fund value at the start of the time period (and treating it as a negative cashflow), and then considering cashflows and the final NAV over the remaining life of the fund. Technically, for a five year backward-looking IRR, this implies that the IRR is calculated as:
2.4
Advantages and drawbacks of IRRs
The main advantage of an IRR is that it provides a percentage-based metric for returns that explicitly takes the irregular timings of PE cashflows into account. An IRR is normally measured as a per annum percentage (% p.a.). However, the main disadvantage of an IRR is that it is more complex than it can first appear, with a number of resulting issues that investors may not always be aware of. The IRR is a non-linear denominator-based measure of returns. It is not a standard time-bound numerator-based return, unlike most buy-and-hold estimates of returns. Nor is it directly comparable with these standard measures of returns. When we compare PE with other asset classes, the IRR cannot simply be lined up next t0 the buy-and-hold return from a fixed income fund, for example. The non-linear nature of the IRR is the source of much misunderstanding. Figure 1 illustrates this non-linearity, plotting the implied discount rate that would ensue from the sorts of standard models of consumption behaviour, where the discount rate is normally expressed as a numerator-based measure:
5
Technically, this implies that the summation of discounted cashflows starts in period 0 (i=0). 7
Figure 1: Relationship between numerator and denominator-based discount rates 0.45
1.14
0.40
1.12
0.35
1.10 Implied IRR (LHS)
0.30
1.08
0.25 1.06 0.20 1.04
0.15 0.10
1.02
Sum of β and IRR (RHS)
1.00
0.05 0.00
0.98 0.7
0.75
0.8
0.85
0.9
0.95
1
Numerator-based discount rate (β)
The non-linear nature of the IRR means that IRR algorithms can sometimes fail to solve – it is more computationally complex than a multiple.6 The non-linearity can also cause potential confusion – for example, if a fund closes after five years but is assumed to have lived for an extra five years without doing anything, the five and ten-year IRRs will be identical. This is because there are no extra cashflows to discount between years six and ten (although any fees drawn during that time would lower the IRR). This also applies when returns from funds with different durations are considered. Table 1 presents an example using illustrative data. Fund A in the table is only active for four years – so its IRR really corresponds to the return over that four year period. Fund B, by contrast, is active for seven years, and its IRR corresponds to that duration. However, the raw IRR data themselves do not indicate this timing difference. Furthermore, if the IRR calculation for Fund A was calculated up to Year 7, then the addition of three extra years would have no impact on the calculated IRR as the numerator for all three years would be zero.
6 However, this algorithm is present or can easily be constructed in most major software packages. The appropriate function in Excel is XIRR.
8
Table 1: Hypothetical PE fund cashflows Fund A
Fund B
Year 1
-1000
-1000
Year 2
1300
0
Year 3
500
0
Year 4
0
0
Year 5
0
800
Year 6
0
0
Year 7
0
500
61%
6%
IRR
This example demonstrates a related issue with IRRs: early distribution of cashflows and early termination of a fund can boost measured returns, as IRRs can implicitly put very high weight on short-term returns. This follows from the geometric discount rate that the IRR formula implies and is illustrated in Figure 2. Under high IRRs, future cashflows are discounted very quickly and hence have relatively little implicit ‘weight’ in the underlying calculation.
Figure 2: Impact of IRRs on discounted cashflows (a) 120
Present value of £100 5% IRR 10% IRR 20% IRR 30% IRR
100 80 60 40 20 0 0
1
2
3
4
5 6 7 8 9 Number of years in the future
10
11
12
13
(a) This chart shows the present discounted cashflow of £100 at a future date, under the IRRs that are assumed for illustrative purposes. For instance, with an IRR of 20%, £100 in four years’ time is only worth £48 today.
This means that PE fund managers face incentives to deliver cash more quickly to shareholders. Some commentators have suggested that fund managers may choose to manipulate the timing of returns to their advantage, for instance by distributing cashflows near the end of a fund’s life when it may have little impact on the measured IRR. For instance, if Fund A in Table 1 distributes another £100mn in 9
Year 8, the measured IRR will still be 61%. However, any change in the timing of distributions can potentially also have a knock-on impact to the performance-related proceeds that fund managers can enjoy.7 As these timing issues already hint, a full and accurate picture of returns is only presented by the since-inception IRR. While backward-looking measures of returns can provide some guide to the recent performance of funds, by definition they will not cover some areas of a fund’s life. And given the irregular nature of PE cashflows, and the non-linear return algorithm, this means that backwardlooking IRRs can also be very volatile and potentially misleading. Figure 3 plots three, five and tenyear returns for a genuine fund in the BVCA’s Performance Measurement Survey (PMS), along with the since-inception return as it evolved over time. Anyone expecting substantial returns on the basis of the 66% five-year estimate would clearly have been disappointed. In contrast, since-inception IRRs paint a more accurate picture of true returns.
Figure 3: An example of since-inception and backward-looking returns 80% 70% 60%
Five-year return
50% 40% 30% 20%
Ten-year return
Three-year return
10% 0% -10%
Since-inception return
-20% -30% 0
2.5
1
2
3
4
5
6 7 Year
8
9
10
11
12
13
Modified IRR (MIRR) and IMIRR
In response to these concerns about IRRs, alternative measures of returns have been proposed. The most noteworthy of these is the Modified Internal Rate of Return, or MIRR. In truth, the so-called MIRR is fundamentally different from the IRR (and is not really an internal rate of return at all, in economic terms). The IRR is named for its use in discounting internal cashflows, and is a denominator-based measure of returns. In contrast the MIRR is a numerator-based measure
7 Ellis (2011) describes the typical form of incentive structure for these performance-related proceeds, often referred to as ‘carried interest’. As carried interest is only payable once the preferred return (or hurdle rate) has been reached, which is annually compounded, fund managers are incentivised to exit swiftly.
10
of returns that is more akin to a standard buy-and-hold measure of returns.8 Broadly speaking, the MIRR is calculated as:
Importantly, the MIRR assumes that investors earn money on their capital (at an interest rate known as the ‘saving rate’) before it is drawn down by PE fund managers, and that after distributions are returned to investors they are able to earn further money on those funds (the ‘investment rate’). As such, the MIRR is essentially akin to a conventional numerator-based measure of returns such as the FTSE All-Share Total Return index, which takes account of dividends paid by its constituent members. As an example, consider Table 2, which is taken from Phalippou (2008). The investor commits £100 in Year 0, and then receives £150 in Year 1, and £50 in Year 3. The assumed reinvestment rate for the investor is 12% per annum.9 In order to calculate the MIRR, it is necessary to accumulate the post-PE investment returns each year. Column A shows the post-PE investment return earned each year and column B shows the cumulative fund value.
Table 2: Calculating a MIRR (a) Investment
Cumulative
return (A)
return (B)
0
0
Timing
PE cashflow
Year 0
-100
Year 1
150
0
150
Year 2
0
18
168
Year 3
50
20.2
238.2
Year 4
0
28.6
266.7
Year 5
0
32.0
298.7
Year 6
0
35.8
334.6
Year 7
0
40.2
374.7
Year 8
0
45.0
419.7
Year 9
0
50.4
470.1
Year 10
0
56.4
526.5
Year 11
0
63.2
589.7
Year 12
0
70.8
660.4
(a) Numbers have been rounded to one decimal place.
Confusion about this distinction often surfaces with claims about the so-called reinvestment rate, which flip between numerator and denominator-based measures of returns. Simply put, the IRR and MIRR are not comparable because they are fundamentally two different measures of returns. 9 Arguably, this seems high. But our focus here is on replicating the results in Phalippou (2008), where this assumption is made. In practice, it would be possible to construct a MIRR, using total return indices for either public equities or gilts (these are discussed in Section 3.3). One issue here would be the possibility of investors going short when large draw downs were made, in the event that market prices had moved against them. 8
11
In order to calculate the reported MIRR of 17% in Phalippou (2008), the final cumulative return of £660.4 is compared with the original £100 investment and geometrically discounted: /
Given that non-linear algorithms already exist for the calculation of IRRs, the MIRR is at least as computationally intensive. There are, however, more fundamental concerns about the MIRR. First and foremost, it is arguably not genuine a measure of PE returns, most obviously because the saving and investment rates that investors earn are beyond the control of PE fund managers. Investors in private equity generally accept this point. The MIRR formula is essentially similar to that of a multiple, albeit with a time superscript added, and the added complication of the saving and reinvestment rates. One other obvious drawback of this MIRR, as reported in Phalippou (2008), is that it assumes the PE fund ‘continues’ long after the final distribution (i.e. after Year 3 in Table 2). This means that the final return estimate is biased towards the investment rate which is assumed in the calculation (in this case 12%). The author addresses this by proposing a modified form of the MIRR known as the ‘isolated MIRR’ or IMIRR. This measure of returns is only calculated over the active life of the fund (in this case, up to Year 3): /
Phalippou (2008) recommends using the IMIRR for individual funds but the MIRR for aggregated estimates of returns across several funds. Aggregation is an important issue for PE returns more generally; the next section examines this in more detail, and highlights some issues with this aggregate MIRRs.
2.6
Aggregation issues
Thus far, the discussion has implicitly assumed that returns are being calculated for individual investments or funds. However, in practice, industry-wide measures of returns are also of interest, not least for benchmarking purposes.10 In order to do this, there needs to be some method of combining returns data across different funds. In other fields, the simplest approach would be to weight different fund returns together in a standard fashion:
10
For a good discussion of benchmarking and concerns with commercial datasets, see Harris et al (2011). 12
where α denotes the weight attached to each fund. However, deciding upon appropriate weights is non-trivial. In principle, options include fund commitments, total draw downs, or plausibly the maximum of these two measures (as some funds ask for extra funds beyond initial commitments). But the different timing and duration of different funds should ideally also be taken into account – a fund delivering returns over five years should be treated differently to an identically sized fund delivering returns over ten years. In light of these sorts of weighting issues, a common approach when calculating aggregate measures of returns is to pool the data across funds. This approach assumes that the different cashflows and valuations come from a single entity rather than multiple PE managers. This means that cashflows from all funds are treated as if they were part of one large fund, and valuations are summed to get aggregate NAV figures. This simple approach is frequently used, but implicitly ignores growth and inflation effects,11 meaning that in truth aggregate return estimates will be biased towards later funds. While pooling is a simple way of aggregating across different sized funds, care is required when interpreting the results. Table 3 presents three hypothetical funds with different cashflows but the same starting draw down period.
Table 3: Pooling hypothetical fund returns Fund A Dates
Fund B Cashflows
Dates
Fund C Cashflows
Dates
Cashflows
31/12/2005
-1000
31/12/2005
-1000
31/12/2005
-1000
31/12/2006
1300
31/12/2006
0
31/12/2006
0
31/12/2007
500
31/12/2007
0
31/12/2007
0
31/12/2008
0
31/12/2008
0
31/12/2008
0
31/12/2009
0
31/12/2009
500
31/12/2009
800
31/12/2010
0
31/12/2010
0
31/12/2010
600
31/12/2011
0
31/12/2011
600
31/12/2011
0
IRR
61%
2%
8%
On an individual fund basis, the IRR of fund A is 61%, Fund B is 2%, and Fund C is 8%. If the cashflows from these three funds are pooled together the aggregate IRR is 12%, compared with the average individual fund IRR of 24%. The lower pooled IRR reflects the fact that the distributions for Funds B and C are delayed relative to Fund A. However, the effect would have been reversed with two early-paying (and high IRR) funds and one later fund. Notwithstanding the aggregation issues that are present with a weighting approach, care must therefore be taken with pooled IRRs.12
11 As national income and wealth typically grow over time, it may not be appropriate to weight different funds together solely on the basis of nominal fund sizes. In economic terms, a £100mn fund established in 1980 is not equivalent to a £100mn fund from 2005. One way to adjust these nominal weights would be to take account of inflation, using either a consumer-based or whole-economy measure. But that will fail to take account of economic growth: this means that, even if private equity’s proportional allocation within overall investments were constant, fund sizes would still increase over time. As such it could arguably be appropriate to adjust fund sizes by nominal GDP, rather than just inflation. 12 Concerns also arise when constructing pooled MIRRs; typically, given the growth in the PE industry over time, these will by construction be biased towards the assumed saving rate.
13
2.7
Constructing PE indices
The rationale for constructing an aggregate measure of PE returns is to summarise how a large group of PE funds perform. An obvious extension of this approach is to construct a PE index – a measure of how the industry as a whole has delivered returns over a long period of time. The BVCA is well placed to lead this effort given the long pedigree of its Performance Measurement Survey (PMS). Every year the BVCA collects raw cashflow and valuation data from its members, in order to provide investors with good benchmarks of PE returns. Data are only collected from noncaptive members and is reported on a net-of-fees basis, in order to reflect the type of return that investors can genuinely expect. The 2010 report compiled data from over 450 UK-managed funds and as such is the most comprehensive source of UK PE returns.13 Constructing a PE index is complex using IRR methodology; by its very nature indexation tends to lend itself more naturally to a multiples-based approach. The Thomson Reuters/EVCA PE index pools cashflows across funds and calculates the resulting changes in value on a cashflow-neutral basis. The change in the PE index (PEI) between period i and period j is calculated as:
These changes are usually calculated over fixed periods of duration, and then chained together to form an index. In the case of the PMS the net valuations are provided once a year, so the appropriate duration is one year. Using BVCA data, this yields the PE index shown in Figure 4 below: over the sample shown, the average annual growth rate is 11.4%.
13
The PMS is described more fully in BVCA (2011). 14
Figure 4: A representative UK PE index (a) Per cent 35
Index, 1994=100 1400 1200
30
Annual change (RHS)
25 1000
20 15
800
10 600
5 0
400
-5 200
PMS index (LHS)
0 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009
-10 -15
(a) Calculated using all BVCA fund data.
Some investors may require higher frequency data than this annual series provides. There are several possible options in response, including constructing quasi-NAVs using observed cashflows to generate higher-frequency valuation measures. These can then be used to calculate index changes over subperiods. In practice, however, this approach is not very different from a simple interpolation process, especially when aggregating across a large number of funds.14 One alternative would be to interpolate between the annual observations using some other indicator variable, following the procedure set out by Chow and Lin (1971). Figure 5 presents results for this approach, using the LPX5015 as the indicator variable. This series is highly volatile, and so the resulting return estimates are more variable than simple quadratic interpolation alone would suggest. Even restricting changes to an annual frequency, the LPX50 appears to be far more volatile than standard measures of PE returns: the variance of annual growth rates is almost 12 times that of the PE index we constructed (Figure 4).
14 Discussions with fund managers have indicated that, aside from large draw downs or distributions, NAVs typically do not change much over a three-month period. 15 The LPX50 is an index of the 50 largest listed private equity companies, which meet certain liquidity constraints. For more detail see: www.lpx-group.com.
15
Figure 5: Interpolated PE returns 200
Percentage changes on a year earlier
LPX50
150
PE index, quadratic interpolation PE index, LPX50-based interpolation 100
50
0
-50
-100 1995
1997
1999
2001
2003
2005
2007
2009
A final option for constructing a PE index would be to properly take account of the growing market over the past 20 years, and construct a genuinely chain-linked measure of returns.16 In the presence of changing market or fund sizes, simple aggregation methods can result in misleading growth rates over time, which chain-linking can resolve. In technical terms, this approach requires annual updating of the individual fund weights; the return on each fund within each year is calculated, and these growth rates are then weighted together using the sizes of ‘live’ funds as the weights.17 In this way we can accurately capture the returns that are on offer from active funds. However, in practice this approach is also unrealistic: it implicitly assumes that investors liquidate their PE holdings at the end of each year and then re-invest in all live funds one day later at prevailing NAVs. As such, there is a trade-off between the beneficial statistical properties of a genuinely chain-weighted index and investors’ ability to mimic it in practice.
See Whelan (2000) for a discussion of chain-linking and its implications. As discussed in section 2.6, the precise weighting system matters. For simplicity, individual year-weights were calculated using residual fund values. The underlying data are the same as in Figure 4. As with Bunn and Ellis (2012), who construct hazard functions for price changes, each first fund-level observation is the change between the first and second fund positions that are observed. 16 17
16
Figure 6: Chain-weighted PE index 40 35
Percentage changes on a year earlier
30 25 20 15 10 5 0 -5
Simple pooled PE index
-10 -15 1987
Chain-weighted PE index 1989
1991
1993
1995
1997
1999
2001 2003 2005 2007 2009
Figure 6 suggests that, overall, the impact of different aggregation methods on benchmarks of PE returns may not be particularly large.18 The average annual growth in the chain-weighted index is 13.4%, compared with 11.4% for the simple PE index. However, although this suggests that pooled estimates of returns can offer a reasonable representation of aggregate performance, investors will still want to compare these measures of PE returns to other asset classes, and in particular public equity markets. The next section discusses this in more detail.
18
Barring the very start of the sample, where the data comprised of a relatively small number of funds. 17
3. Making comparisons with public markets
The previous section discussed methods for measuring PE returns as well as aggregation and indexation issues. Another key concern for investors is the need to compare returns across asset classes. Given the nature of IRRs, it is not appropriate to match them against the sort of standard measures of returns used in other fields; IRRs are not comparable with time-based measures of returns such as yields on bonds or measures of total returns either from individual equities or public indices as a whole. In light of this difficulty, this section describes methods for comparing public markets with IRRs in a meaningful fashion.
3.1
The Public Market Equivalent (PME) method
Given the lack of comparability between IRRs and time-based returns, previous work has examined how public market data can best be compared with PE returns. One of the most common means of doing so was devised by Long and Nickels (1996), who proposed the Public Market Equivalent (PME) method.19 The PME allows investors to compare IRRs with the returns that public markets would have yielded over the same timing of cashflows.
Table 4: Illustrative PME return Date
Unit
PE
PME
fund
Public index
PME
value (IV)
NAV
data
PMV calculation
(PMV)
Year 0 (Y0)
Draw down (C0)
-80
-80
100
80
Year 1 (Y1)
Distribution (C1)
40
40
112
49.6
= PMVY0*(IVY1/IVY0) – CY1
Year 2 (Y2)
Draw down (C2)
-50
-50
110
98.7
= PMVY1*(IVY2/IVY1) – CY2
Year 3 (Y3)
NAV
120
107.7
120
107.7
= PMVY2*(IVY3/IVY2)
12.7
7.8
IRR (%)
= - CY0
Table 4 presents an illustrative PME calculation. The PME method creates a hypothetical investment vehicle that exactly mimics private equity cashflows. Because the cashflows are identical, and the estimation methodology is the same, the difference between the PE IRR and the PME is determined by the resulting NAV for the hypothetical investment vehicle. This hypothetical NAV is sequentially calculated by taking draw downs as further investments into the relevant public index, and distributions as investors selling their ‘shares’ in it. If the simulated NAV for the hypothetical investment vehicle is larger than the PE fund’s NAV then the PE fund has underperformed public markets, and vice versa.
19
This was originally known as the Index Comparison Method (ICM). 18
3.2
Short positions and PME+
The PME method is relatively simple to use, and allows investors to properly benchmark PE fund managers against other markets. However, the method also has some limitations. The most obvious of these is that, depending on the evolution of the public market index, the hypothetical PME vehicle may end up in a ‘short position’, i.e. holding a negative NAV. This could occur when distributions exceed draw downs in flat underlying markets, or where the cashflows broadly match but market prices are falling. It will also happen when PE funds outperform public markets and subsequently close: as the residual valuation of closed PE funds is zero, a negative NAV for the PME vehicle would result. Comparing a ‘long’ PE fund with a hypothetical ‘short’ position in public markets does not make sense. Furthermore, such short positions may even result in nonsensical or incalculable IRRs. As such, various modifications have been proposed. In particular, Rouvinez (2003) has proposed the PME+ method. This essentially applies the logic of the PME in a different way. In the PME approach, the cashflows are assumed to be identical between the PE fund and the hypothetical investment vehicle, with only the NAVs differing. As the IRR calculation is the same, this means that this difference in the NAVs drives the difference in between the estimates of returns. With PME+, a different hypothetical vehicle is constructed. This time the NAV of the PE fund and the PME+ vehicle are the same, and instead the distributions of the PE funds are adjusted by a scaling factor that ensures that the NAVs are identical. As these distributions represent investors ‘selling securities’ in the PME+ model, this makes sure that the PME+ vehicle does not end up having to ‘sell’ more securities than it actually owns.20 Technically, the scaling factor λ is calculated as:
where
and CC denotes capital calls (draw downs), D denotes distributions, and I denotes the public index used for the comparison, and N is the final time period considered. The PME+ is therefore more computationally intensive than the PME. But if PE funds have outperformed public markets in the
20
One alternative adjustment is to restrict the distribution from the hypothetical vehicle to be no greater than its current NAV. 19
past, this extra complexity is necessary to avoid the problem of ‘short’ positions in the hypothetical vehicle.21
3.3
Choosing the appropriate public index
In principle both the PME and PME+ methods can be used to compare the performance of PE funds to any other asset class. In practice, there are two mainstays in most investment managers’ portfolios: fixed income securities and public equities. For both of these asset classes it is most appropriate to consider the ‘total return’ indices, which take account of coupon payments and dividends. Total return indices for the FTSE All Share and UK gilts are shown in Figure 7 below.
Figure 7: Total return indices for UK public markets Indices, 1 Jan 1999 = 100 230 210 190 FTSE All Share
170
Gilts
150 130 110 90 70 50 1998
2000
2002
2004
2006
2008
2010
2012
Source: Bloomberg
The simplest way of constructing a PME/PME+ estimate is to use these aggregate indices in constructing the hypothetical investment vehicle. However, in practice previous research has suggested that sector-selection can play a part in driving PE fund returns (Gottschalg et al, 2010). As such, when benchmarking against public markets, investors may wish to use the PME/PME+ method not on the basis of a published equity index as a whole, but construct specific and representative industry mixes from public markets. For simplicity, however, we use the broad FTSE All Share total return index. Using both the PME and PME+ approach, the PMS data indicate that PE funds have significantly outperformed public equity benchmarks since 1986 (Figure 8). This chimes with recent research from Harris et al (2011), which revised and updated the seminal paper by Kaplan and Schoar (2005). 21 One potential issue with PME+ is that distributions are scaled (partly) based on the final ratio of NAV to the public index. Depending on how this ratio evolved over time, this could potentially depress PME+ IRRs.
20
Figure 8: Comparing UK PE funds with PME and PME+ (a) 16
Percentage return per annum
14 12 10 8 6 4 2 0 IRR
PME
PME+
(a) 1987 vintage funds onwards.
However, while these return estimates are now comparable, they still have different characteristics. In particular, the PME/PME+ method makes no adjustment for the illiquid nature of PE investments. Furthermore, the absolute performance of the different assets does not address an important consideration for portfolio managers: how to allocate capital among different asset classes. The next section touches on this, in the context of cross-sectional return variation.
3.4
Correlation analysis: time series vs. cross section
Using commonly applied techniques, we have demonstrated that UK PE funds have, overall, outperformed public equity markets over the past 25 years. However, headline performance is not the only relevant factor when investors are considering different asset classes. The degree of covariance between asset classes also matters. 22
22
For more detail on the capital asset pricing model (CAPM) with representative agents, see Cochrane and Hansen (1992). 21
Figure 9: Evolving IRRs 20
Per cent per annum
15 10 5 0 -5
Since-inception PMS FTSE All-Share (PME+)
-10 -15 -20 1988
1990
1992
1994
1996
1998
2000 2002
2004
2006
2008
2010
A common means of estimating the co-movement between PE funds and public markets is to track the returns over time. Figure 9 shows since-inception IRRs based on the BVCA PMS and the equivalent PME (based on the FTSE All Share) from 1988.23 Over the sample as a whole the correlation between the two series is 0.18. Since 1996, when the UK PE market is generally considered to be more ‘mature’, the correlation is 0.23. This positive correlation between PE returns and the FTSE PME is unsurprising. One of the valuation methods for unrealised PE investments is to use public market ratios, such as earnings (or EBITDA) to revenues. If public markets rise, then so will NAVs calculated on this basis, leading to positive correlation. However, by construction the series in Figure 9 will suffer from a degree of serial correlation that could affect estimates of covariance between the two series.24 In addition, previous work in other economic fields by Imbs et al (2005) and Mumtaz et al (2009) has demonstrated that aggregation bias can result in sector-wide series exhibiting different time-series properties than the underlying individual data series. In light of this, it is also appropriate to consider the cross-sectional correlation between PE funds and public markets. Rather than aggregating across PE funds and constructing metrics of public returns, an alternative is to construct PME equivalents for each PE fund individually. We can then examine the cross-sectional return between the individual PE fund IRRs and their hypothetical PME vehicles. The results from this approach, using PMS data, are shown in Figure 10 for closed funds and Figure 11 for open funds, respectively.25 Because a significant number of funds in the PMS are closed, and
The returns are calculated on a pooled basis, showing the total return across all funds at the date shown. This may be less visible in the FTSE All-Share return if equity markets are volatile. 25 For this exercise, we define funds as ‘closed’ if they have zero residual valuations for two or more years. Where PME+/IRR calculations did not solve, these funds were excluded. 23
24
22
performed relatively well, we used the PME+ approach to calculate public market performance, to avoid concerns about ‘short’ positions.
Figure 10: Cross-sectional correlations between closed PE funds and public markets 40
FTSE All-Share (PME+, %)
30 20 10 0 -60
-40
-20
0
20
-10
40
60
80
Fund IRR (%)
-20 -30
Figures 10 and 11 illustrate the extent to which unrealised valuations influence the correlation between PE returns and public markets. For closed funds the correlation between PE returns and the FTSE All-Share is 0.29, although that falls to 0.11 when the four outliers are excluded; this is both statistically insignificant and lower than the time-series result. For open funds, however, the correlation is much higher (and statistically significant) at 0.42. A comparison of the two charts also illustrates the uncertainty around PE valuations, which can be substantial (Ellis & Steer, 2011). Overall, these results suggest that the observed correlation between PE funds and public markets may largely reflect interim PE valuations, which by construction partly reflect public equity prices. At the same time, it is not suggestive of a simple ‘buy and hold’ approach with leverage, where the PE fund has little impact on the investee company’s performance.26 If that were the case, we would expect a higher correlation between the returns of closed funds and public markets.
26
This is consistent with recent evidence from Kaserer (2011). 23
Figure 11: Cross-sectional correlations between open PE funds and public markets FTSE All-Share (PME+, %)
100 80 60 40 20 0 -100
-50
0
50
-20
100
150 Fund IRR (%)
-40 -60 -80
24
4.
Summary & conclusions
The illiquid nature of private equity investments, and the irregular timing of cashflows both from investors to fund managers and vice versa, mean that private equity returns are typically measured in a different manner to other asset classes. In particular, the main measure of performance is typically the internal rate of return (IRR). As a non-linear denominator-based measure of returns, IRRs are not comparable with typical denominator-based measures of returns. Care must also be taken when looking at PE performance over a short-term or backward-looking basis. The best way to use IRRs is to look at fund performance on a ‘since inception’ basis. This paper has also discussed other issues that investors must consider when looking at IRRs as measures of returns, and described simple methods for benchmarking PE funds against other asset classes (in particular public equity markets). We have also described how indices can be constructed from PE cashflow data and demonstrated the importance of considering cross-sectional covariance as well as time series behaviour. For the former, it is crucial to differentiate between open and closed funds. Provided investors have some awareness of the nature of IRRs and their characteristics, used properly they can offer a good guide to PE returns. The BVCA is committed to providing this guidance to investors through its annual Performance Measurement Survey, and will continue to break new ground in this field.
25
References
Bunn, P, and Ellis, C (2012), ‘How do individual UK producer prices behave?’, The Economic Journal, Vol. 122, No. 558, pages F16-F34. BVCA (2011), Performance Measurement Survey, available at: http://admin.bvca.co.uk/library/documents/Performance_Measurement_Survey_2010.pdf Chow, G, and Lin, A (1971), ‘Best linear unbiased interpolation, distribution, and extrapolation of time series by related series’, Review of Economics and Statistics, Col. 53, No. 4, pages 372-75. Cochrane, J, and Hansen, L (1992), ‘Asset Pricing Explorations for Macroeconomics’, in NBER Macroeconomics Annual, edited by Olivier J. Blanchard and Stanley Fisher, Mass.: M.I.T. Press. Ellis, C (2011), ‘The microeconomic structures of private equity’, BVCA Research Article, November. Ellis, C, and Steer, J (2011), ‘Are UK venture capital and private equity valuations over-optimistic?’, BVCA Research Report, April. Gottschalg, O, Talmor, E, and Vasvari, F (2010), ‘Private equity fund level return attribution: evidence from UK based buyout funds’, BVCA Research Report, June. Harris, R, Jenkinson, T, and Kaplan, S (2011), ‘Private equity performance: what do we know?’, Chicago Booth Research Paper No. 11-44. Imbs, J, Mumtaz, H, Ravn, M, and Rey, H (2005), ‘PPP strikes back: aggregation and the real exchange rate’, Quarterly Journal of Economics, Vol. 120, No. 1, pages 1-43. Kaplan, S, and Schoar, A (2005), ‘Private equity performance: returns, persistence, and capital flows’, Journal of Finance, Vol. 60, No. 4, pages 1,791-823. Long, A, and Nickels, C (1996), ‘A private investment benchmark’, mimeo; paper presented to AIMR Conference on Venture Capital Investing, February. Mumtaz, H, Zabczyk, P, and Ellis, C (2009), ‘What lies beneath: what can disaggregated data tell us about the behavior of prices?’, Bank of England Working Paper No. 364. Phalippou, L (2008), ‘The hazards of using IRR to measure performance: the case of private equity’, mimeo. Rouvinez, C (2003), ‘Private equity benchmarking with PME+’, Venture Capital Journal, August, pages 34-38. Talmor, E, and Vasvari, F (2011), International private equity, Wiley, Chichester. Whelan, K (2000), ‘A guide to the use of chain aggregated NIPA data’, Division of Research and Statistics, Federal Reserve Board, mimeo.
26
