Beating the public market

The public benchmark problem
Every private equity investor has been confronted with the issue of benchmarking the return of a private equity portfolio against the return of a public index in order to answer the simple question: “Did it perform better than the public market?” The question may seem trivial, but the answer is not.

The problem is as follows: whereas the performance of most asset classes can be depicted by indexes or time-weighted returns, private equity is usually described by cash flows (see Figure 1). Although private equity time-weighted returns can be computed using the Dietz formulas (1), these returns are not suited for direct comparison as they rely on the evolution of net asset value (NAV) over time. The trouble with private equity NAV is that it suffers from valuation bias (the value of the assets are open to interpretation) whereas a quoted market price is not.

In addition, the low frequency of performance reporting in private equity creates a certain lag in valuations, which makes comparison of short-term performance more challenging. For these reasons, it seems legitimate to say that one cannot compare private equity time-weighted returns to the ones of other liquid asset classes. This is one reason why private equity performance is also usually described more accurately by the internal rate of return. IRR is a cash on cash return measure, which takes into account both the timing and size of the underlying cash flows, and which does not rely on NAV history.

To date, the standard approach to the benchmarking problem has been the public market equivalent method (PME, also know as the index method) developed in the early 1990s. (2) (3) With this approach, one compares the cash on cash returns obtained by investing in private equity with a benchmark based on the hypothetical cash returns obtained by buying and selling an index-tracking fund at the same rate of investment.

However, although the PME approach appears attractive, the method is not reliable (4). It often leads to situations where the benchmark return does not make sense, or simply does not exist. In general, for all cases where the private equity portfolio outperforms the benchmark, the benchmark portfolio will eventually end up with negative values. In other words, it must be shorted to match the performance of the outperforming private equity portfolio. Comparing your long private equity portfolio with a short position in the public market obviously does not make sense.

This effect is best illustrated by way of an example. Figure 2 shows the running NAV of a private equity portfolio comprising all funds with vintage year 1990 from the Venture Economics database, as well as the PME which in this case is the NAV of an investment in a S&P500 total return index-tracking fund matching the private equity cash flows over time. The NAV of the index-tracking fund position is negative from 1998 onwards, pointing to the short exposure in the index. Despite the large negative final cash flow corresponding to the final NAV, the IRR of the benchmark can be computed and yields 19.3 per cent, which on first sight compares well with the 21.5 per cent achieved with the private equity portfolio. This indicates a two per cent premium for private equity, but this actually understates the real out-performance, as will be shown below.

Resolving the issues using PME+
A refined adaptation of PME, called PME+ (5) avoids the “going short” problem by selling a fixed proportion of the cash flows, as opposed to the exact same amount. By doing so one can prevent having to sell more than the size of the index position, and hence avoiding the short position. The right proportion of cash flows – the so-called distribution scaling factor – is set by matching private equity NAV and index-tracking fund NAV at the end of the benchmarking period, so as to maintain the same level of exposure to the respective asset classes going forward. The distribution scaling factor is fully determined by the private equity cash flows, final NAV and the time series of the index. (See the boxed item Benchmarking with PME+ below for the analytical computation of the scaling factor and for technical details on the approach.)

Applying the PME+ technique to the vintage 1990 private equity cash flows from the Venture Economics database, produces a distribution scaling factor of 85.2 per cent. This means that with disbursements equal to 85.2 per cent of the private equity distributions, the index-tracking fund will end up with the same NAV as private equity by the end of 2002. Keep in mind that the scaling factor is dependent on the benchmarking index (here the S&P500 Total Return) and that it is not necessarily smaller than one. A scaling factor smaller than one indicates out-performance of private equity, whereas a scaling factor larger than one points at private equity under-performance.

Figure 2 shows that PME NAV becomes negative as early as mid 1998 until the end of the period, thus distorting the benchmarking process, whereas PME+ NAV follows a similar profile to the private equity NAV, ensuring a comparable level of exposure over the entire period. The IRR of PME+ cash flow pattern amounts to 16.5 per cent as opposed to the 19.3 per cent obtained with the standard PME method, indicating a five per cent premium for investing in vintage 1990. The question now therefore is, where does the three per cent difference come from?

Figure 3 represents the historical evolution of private equity IRR, PME IRR and PME+ IRR over time. The behaviour of private equity IRR, starting in the negative range and then sharply increasing over time, is the typical ‘J-curve’ effect. This initial low performance derives mainly from the impact of management fees and the time required to generate additional value. The value creation period stretches from 1990 to 1995, whereas the period 1996 and onwards is focused on exiting investment companies. As the index-tracking funds considered with this approach don't bear any costs, the early years of PME and PME+ IRR are simply reflecting S&P500 total return levels. The benchmark measures begin to diverge in 1997, where the low level of exposure resulting from the PME analysis (see the evolution of PME NAV in Figure 2) fails to pick up the large gains that the index registered over the 1997-1998 period. Furthermore, the short position over the period 2000-2002 results in a performance increase for PME: clearly not a sensible result given the decreasing index benchmark.

It is worth noting that the error resulting from the short position may work out for, or against, the benchmark, depending on the performance of the index over the period in question. As a consequence, the standard PME method does not even consistently understate or overstate returns, but rather randomly impacts the analysis. PME+ on the other hand shows a more stable four to five per cent out-performance of private equity versus the S&P 500 total return for the past six years, reflecting the influence of declining public valuations on private realisations. PME+ yields more sensible benchmarking results that can also be used to interpret the observed effects. Consequently, PME+ appears to have the characteristics of a sensible, repeatable and therefore useful benchmarking tool for the private equity industry.

Further uses of PME+
PME+ can also be used as a way of turning a given index performance into real cash flows. In a sense, it acts as the converse of the Dietz formulas: whereas these deliver the time-weighted returns associated with some cash flows, PME+ returns a set of adjusted cash inflows and outflows which reflect the overall performance of a given index. Such a method can be used for many different purposes.

The obvious application is benchmarking, where the IRR of two sets of cash flows are compared after the disbursements or one of them have been adjusted to match final NAV. Another important field is simulation. There are many ways to generate index returns with the characteristics of a given market, but it is much more difficult to create sensible cash flow patterns compatible with these characteristics. The distribution scaling approach used for PME+ does this easily. By adjusting the distributions so as to match the performance of a given index, one obtains a method for simulating private equity cash flows corresponding to different market conditions.

The beauty of the methodology is that it is very general. Firstly, there are many ways to adjust cash flows. The linear scaling of the distributions described above is the simplest modification, which does not alter the characteristics of the pattern, and in particular, does not affect the timing of the cash flows. The major advantage of this approach is that once the index is known, the scaling parameter is unique and can be computed analytically. In fact, any other simple operations, such as a forward shift of the capital calls, a backward shifts of the distributions, or a scaled combination of both types of shifts can be implemented to simulate the effects of various changes in economic conditions.

Secondly, different types of simulations can be obtained depending on how an index is sampled. Historical values of a given index over different time windows can be used for historical simulations. Rating analysis based on Monte Carlo simulations may rely on stochastic simulations of a benchmark index (6). Global scenario analysis across several asset classes may be achieved with the help of indices driven by exogenous factors. These examples demonstrate the flexibility of the methodology, which will find many applications for risk measurement and management.

Christophe Rouvinez is a partner in Capital Dynamics, an independent provider of investment banking and asset management services for private equity investors. Capital Dynamics has offices in Zug, Switzerland and New York.