What is most surprising about the aggregate calculations of private market performance?
The widespread “tolerance” of mathematical errors, gross inaccuracy and representativeness among private market investors, advisors, enthusiasts, detractors and even academics.
In traditional asset classes, investment professionals are laser-focused on every “micron” of performance difference in their attribution analyses. With private market assets, however, over-reaching is the order of the day.
The turbulent waters of private equity performance attribution
The variability of cash flows makes the attribution of return on private market assets much more difficult: returns are not generated by a stable underlying asset base, so there is no possibility of reinvestment or capitalization .
As I’ve written before, today’s performance attribution toolset is made up of metrics: internal rates of return (IRR), total payables (TVPI), public market equivalents (PMEs), and various alphas, that work in a unique way. at best, but cannot be generalized.
So what does generalization actually mean?
In non-mathematical terms, generalization allows for meaningful comparisons. We should be able to tell whether a given IRR or TVPI is objectively “better” than another, representing more return or less risk.
Given two comparable investments, is an IRR of 15% better than 10%? Although the optical illusion implies that it does, we can’t actually give a precise answer without more data. We need information on time and capital invested. This means time-weighted metrics rather than the money-weighted approaches currently in use.
That 10% IRR may be preferable if earned over a longer period of time, say four years instead of two years for the 15%. This leads to a multiple of invested capital (MOIC) of 1.4x for the 10%, which is higher than the 1.3x MOIC of the 15%. But we still need a duration component to reach a reasonable conclusion.
According to the IRR narrative, money recouped earlier could be reinvested at the same rate of return. But that’s just a guess. In fixed income, a prepayment is usually treated as reinvestment risk. Past performance is no guarantee of future results.
But we disturb the waters even more and throw another stone.
Is a 1.4x MOIC better than a 1.3x? Of course, right? In fact, it all depends on the actual capital deployed versus the capital that was committed to deploy. If the 1.4x MOIC occurs with mined capital that is only 50% of a benchmark commitment and the 1.3x is made with an identical commitment that is 100% mined, the latter beats the former.
Based on this logic, all derived PME and alpha calculations suffer from the same conceptual limitations. As a result, all money-weighted quartile information and rankings of and about private market investments can create significant data distortion.
In mathematical terms, generalization implies that additivity is a precondition for any robust statistical analysis. The above example shows that without accurate additivity, we cannot determine a representative average.
The rules of financial mathematics dictate that averaging rates is possible only through compounding. But IRR cannot be properly compounded over time. When IRRs are presented as annualized or horizon measures, or even worse in terms of accuracy from the beginning returns, can seriously misrepresent actual returns.
But even if the IRR could be increased as in our MOIC example, without further information on capital utilization, the nature of MOICs prevents us from adequately averaging their performance.
The average IRR of our two hypothetical investments is not 12.5%, nor is the average MOIC of 1.35 times the average real return. Again, we need a duration component and capital weighting data before we can make meaningful estimates.
The grouping trap
The gross approximation is even more striking in aggregate private equity return calculations. Studies often pool cash flows, treating those from different funds as if they were from a single fund. This distorts the data even more than our previous examples.
Annualized differences worth many basis points are treated without regard to precision or mathematical representativeness.
Grouping of cash flows
The table above shows the cash flows of three funds of different sizes and vintages individually, pooled and pooled and weighted. That is, cash flows are calculated pro forma, weighting individual cash flows with the relative weight of individual funds.
The pooled IRR of 9.14% differs from both the individual funds’ (mathematically incorrect) weighted average IRR of 6.95% and the pooled weighted IRR of 8.13%. However, the performance number should unequivocally represent the value created by the funds.
What’s worse from an accuracy perspective is this the pooled figures are presented as returns over the 10-year horizon, or from its inception to the last reporting date. So even with the most conservative pooled weighted return, the assumption from the start suggests that the pooled 800 units of invested capital would become (1+8.13%) ^10=2.18x, or 1,748 units .
From the start, the bundled returns create an obvious disconnect. The 800 units of equity invested in the three funds produced “only” 1,160 units of equity, well below the “impression” implied by the pooled returns since inception.
Unwarranted confidence is often the result of the return of the initial horizon. As the example shows, they generate the illusion of increased wealth, by a factor of 1.5x in this case. This helps explain why marketing documents show too many 10x private market benchmarks.
The DaRC life preserver
Some of the best advice I’ve ever received is to never rely on flows coming from a pool or the sea, or just aggregate calculations. Always take care of yourself.
To prevent accurate information from drowning in the PE pool, the duration-adjusted return on capital (DaRC) methodology provides the necessary duration framework. It first corrects multiples by considering the timing of cash flows and then takes advantage of the additivity attributes of duration.
As a result, the pooled multiple remains in line with actual cash flow balances: 1.45x. Then, with the appropriate net duration of 4.68 years, we calculate a credible time-weighted average net DaRC return of 8.39%.
To optimize risk allocation and management for a diversified portfolio, we need accurate performance numbers. But today’s private market metrics too often fall short of that benchmark. We can do better.
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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.
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