The S-Curve: Bending the J-Curve in Private Equity

The J-curve narrative in private equity (PE) investments has accompanied the growth of private markets thus far. That narrative deserves a quiet obsolescence.

Here’s why.

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The J curve

Private market funds are not usually invested upfront. Rather, investors are contractually obligated to provide the investment manager with the necessary capital, over time and upon request, to finance the acquisitions that make up the investment portfolio. Portfolio investments are also not sold all at once, but are divested over time, with the corresponding cash proceeds returned to investors.

The J-curve describes the progressive performance of a PE fund, as measured by the internal rate of return (IRR), or the investor’s related net cash position. While it is indeed a function of how a PE fund uses cash over time, the J-curve is most often associated with the IRR narrative. By pointing to better future results, the history of the J-curve helps mitigate the generally unpleasant effect of the initial downward slide in the IRR, related to the high relative weight, in the calculation of the IRR, of expenses and fees incurred earlier in the life cycle of a PE fund.

The S curve

But the J-curve narrative has always simplified an underlying sigmoid pattern: an S-curve.

How does the S curve evolve the concept of the J curve? Modeling the impact of diminishing marginal returns in relation to the self-liquidating nature of private market transactions. In their various iterations, J-curves do not adequately describe the influence of time on cash flows. Time has a financial cost that makes more distant distributions progressively less relevant and leads to diminishing marginal returns.

Without a sigmoid correction, the J-curve may suggest that “patience” will lead to more money or higher returns and that the IRR reinvestment hypothesis will be true.

Understanding and managing the S-curve requires a duration-based, time-weighted performance calculation strategy. Duration marks where the J turns into an S and provides the interpretive and predictive shift that sharpens the pricing perspective and risk management.

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S curve, so what?

Investors want to better understand the risk and return prospects of their private market allocations. They want to know how it compares to other asset classes. They must also measure and manage their private market pace and overcommitment strategy.

Ex post closet indexing comparisons have limited practical application. Evaluating S-curves, however, provides actionable and quantifiable insights in terms of both benchmarking and performance.

The portfolio management possibilities of private market investments are more complex than those of more liquid asset classes. Equity portfolios, for example, can be built efficiently and are easier to rebalance. They remove the funding and reinvestment risk of private markets, as well as their target allocation challenges.

The J-curve narrative assumes annualized and chained IRRs, as do most current PE indices and metrics. Also, time-weighted rate of return (TWR) calculated using modified Dietz methods are really just indicators of IRR. They offer misleading performance information. Neglecting the risk-reducing effect of distributions is like assigning a value of Beta=1 to non-reinvested S&P 500 dividends: it biases portfolio risk information.

To visualize the difference, the steepest line in the chart below shows the return outlook for the money-weighted metrics currently in use. The most conservative line reflects the true average dollar creation over time based on S-curve information and time-weighted duration-adjusted return on capital (DARC) information.

Competing curves: the S curve vs. the J curve in private capital

Graph showing the S-curve of PE versus the J-curve

The J-curve line represents capital growth if IRR returns were applicable to the entire commitment and reinvestment was instantaneous. This requires a liquid market and reasonable securities trading at par. The S-curve, on the other hand, models the true dollar creation of the private fund portfolio: it puts the IRR in the context of time in a realistic framework of investment pace and overcommitment.

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The underlying thesis is supported by data. The average long-term IRR is 13.3%, according to McKinsey & Company, for example, but US pension funds reported long-term PE returns of 9.3%: a realistic overcommitment strategy in state stationary of 1.4x would be widely confirmed by the 1.5. x net multiple since inception obtained by a large global PE investor.1

Of course, performance numbers aren’t the whole story. Private market investing is about more than superior performance. The risk-adjusted contribution is equally essential. This can only be estimated with S-curves and DARC-weighted returns.

This is why incorporating the de-risking effect of durations, where S-curves twist, is critical to both accurate benchmark analysis and effective portfolio management.

1. A multiple of 1.5x and a related IRR of 13.3% imply a net duration of more than 3.2 years, approximated by the formula that joins TVPI and IRR: DUR=ln (Multiple)/ln (1+IRR) . Because the net duration is advanced (that is, it does not start at time zero), a reasonably standard three-year ramp-up phase increases the total duration to 6.2 years. In a simplified calculation, the 1.5x multiple is equivalent to the annualized DARC return of 6.6% since inception (ie 1.5^(1/6.2)-1= 6.6 %) and, in turn, to a time-weighted return of 9.3% on the constant. state invested capital, which requires 1.4x over-commitment (i.e. only 71% of the commitment is invested, so the fund’s DARC return is “leveraged” to calculate return on invested capital, 6.6 %/0.71=9.3% ).

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All posts are the opinion of the author. Therefore, they should not be construed as investment advice, nor do the views expressed necessarily reflect the views of the CFA Institute or the author’s employer.

Image credit: ©Getty Images / Photos by RA Kearton

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Massimiliano Saccone, CFA

Massimiliano Saccone, CFA, is the founder and CEO of XTAL Strategies, a fintech SME developing an innovative private market index platform and risk transfer solutions. He developed and patented a private equity performance valuation methodology, former member of the GIPS Alternative Strategies Working Group of the CFA Institute and author of a Guide on Alternative Investments for CFA Society Italy. Saccone has pioneering experience in the field of retail alternatives at AIG Investments (now Pinebridge), a global alternative investment manager, where he was managing director and global head of multi-alternative strategies and previously regional head from southern Europe. Before that, he was Head of Institutional Portfolio Management at Deutsche Asset Management Italy (now DWS). He is a CFA holder and qualified accountant and auditor in Italy, has a master’s degree in international finance from Collegio Borromeo and the University of Pavia and a cum laude degree in economics from La Sapienza University in Rome. He is also a lieutenant in the Guardia di Finanza Reserve, Italy’s financial law enforcement agency.

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