Understanding the J-curve

In this extract from Private Equity Mathematics, Ivan Herger lays out the potential models for the J-curve.

Investors should expect a greater return from private equity than they can yield from public equity investments due to illiquidity and long-term commitment. In contrast to public equity, private equity investments initially produce negative returns and accumulate negative net cash flows for a relatively long time period. Investors have to bear this in mind when setting up a new program or approving new investments. Due to the characteristics of the return and cashflow profile, this pattern is called the J-curve. It illustrates the tendency of private equity funds to deliver negative returns and cashflows in the early years and then produce investment gains and positive cashflows later in the investment fund’s life as the portfolio companies mature and are gradually exited. Portfolios of funds have a similar J-curve pattern, but usually the J-curve effect is more pronounced for private equity in the sense that it takes longer to report a positive internal rate of return as capital calls of funds are drawn over a longer period of time.

The shape of the J-curve

The depth and length of a J-curve depends on several factors. First, the J-curve is influenced by the level of fees early on in the fund’s life. Management fees are typically based on the entire amount of committed capital. In addition to the negative cashflow due to the early years of investments, fees can deepen or prolong the J-curve. Second, a fund usually makes different types of transactions: some are very successful, those that meet expectations and those that underperform. The lattermost can usually be identified fairly quickly and hence written down or off early on in the fund’s life. For the companies that meet or exceed expectations, it takes time to implement the changes that create value and finally realize a positive outcome. Third, the J-curve effect is also more pronounced where private equity managers are more conservative, when they write down assets early on or carry the value of their investments close to cost until they are forced to write up the value of their assets close to or at the time of the realization. While these differences in valuation among managers are gradually disappearing with the acceptance of mark-to-market valuations, private equity managers still have some leeway in valuing their investments.

Fourth, the most important factor for determining the shape of the J-curve is the timing of the investments and divestments. The more quickly fund managers invest capital, the steeper the J-curve; the longer it takes to generate distributions, the longer (and usually deeper) the trough of the J-curve.

However, there are instruments that can mitigate the relatively late distributions in an investment program. First of all, investors can try to manage fees effectively. However, this might be challenging as terms in today’s private equity landscape are (at least to some extent) standardized and have similar patterns. Second, investors can acquire lower-yielding investments such as mezzanine loans that promise current income. Third, they can effectively structure their investment program to incorporate early returns by shifting some of the later gains to the earlier returns. Finally, secondaries are a powerful tool to reduce the J-curve effect, especially if acquired at a discount to net asset value.

All of these measures can be modeled in a cashflow model with the objective of predicting the cashflow pattern (and the length and depth of the J-curve) of a private equity investment program.

Modeling private equity cash flows and NAVs is challenging, mainly for two reasons: first, publicly available data is scarce and second, the asset class is illiquid. However, the illiquidity premium is also precisely the main reason why private equity as an asset class outperforms public asset classes.

The following points examine what a J-curve model should describe, and what factors influence the model:

  1. Timing of cashflows – how long is the investment period, when do distributions start and what does net cashflow look like?
  2. Timing of performance – how and to what extent do managers write up or write down NAVs?
  3. Market performance – how is the overall private equity market developing and what influence does this have on a portfolio of private equity funds?

Various models are used for predicting private equity cashflows and NAV development. This chapter briefly discusses the different modeling techniques and then goes into more detail about one specific method, the so-called conditional historical simulation.

Public benchmarks (any public index) and private benchmarks (for example, provided by Thomson Venture Economics or Cambridge Associates) describe overall market performance. They can be used to predict overall private equity market performance in the future. However, neither public benchmarks nor private benchmarks provide information about the timing of cash flows and performance.

 Shape functions can predict cashflows and the timing of a fund’s performance. Take downs, distributions and NAV are described by smooth functions (for example, Weibull distributions) that are usually derived as averages from historical data.

Shape functions provide a model that is simple to understand because it shows the future cash flows as single smooth lines. However, it has several limitations: a) because of the short historical sample of private equity data of about 25 years, predictions for the future are solely based on a limited historical sample, and b) the simple use of shape functions will not provide variations around the average patterns, nor will it account for private equity market performance.

Based on the historical cashflow and NAV data of individual funds, historical simulations can be performed. A Monte Carlo simulation based on historical data predicts cashflows of a given portfolio. For every run in the simulation, the historic fund data is combined in a random way that respects certain boundary conditions, such as fund geography and type. For example, for a portfolio consisting of five US buyout funds and two European venture funds, the stochastic model would randomly select five US buyout funds and two European venture funds from the underlying fund database, and then add the corresponding cash flows and NAV data points. As a result, every run of the simulation produces a cash flow curve and a forecast for the NAV. After adding several thousand of such runs, the results of the simulation can then be statistically evaluated. The advantage of such an approach is the detailed prediction of cash flows and of the timing of the performance. Apart from average cases, a stochastic model also predicts possible variations in the cash flows and the NAVs and their likelihood. However, the model implies that the historical data accurately describes future private equity market performance. This is a rather bold statement in light of the fact that private equity data is only available for the last 20 to 30 years.

Various aspects of the models described above can be combined in order to obtain a model, the conditional historical simulation, which unites most of the advantages of the individual models.

The basis of the conditional historical simulation is the historical simulation described above, which is expanded with a stochastic simulation of a public market index (for example, use a GARCH process for the S&P 500 index). For every run in the simulation, the stochastic path of the index is used to scale the distributions of the private equity portfolio,5 and to adjust the NAVs of the underlying funds. This additional factor eliminates the bias inherent in the underlying historical data (for example, much of the available private equity data is from a period of high equity returns which contrasts with the relatively low equity returns of the 2000s). The stochastic index needs additional input parameters that can be adapted to the current market situation and the economic outlook.

Ivan Herger was managing director, head of solutions for Capital Dynamics and is now a yoga instructor. 

This is an extract from Private Equity Mathematics, available from the PEI bookstore