The desire to compare private equity performance with public equity performance leads to challenges resulting from cash flow timing issues. Two metrics for comparing private equity fund performance with that of a public market equivalent are demonstrated to be mathematically connected. Consequently, the results of both methods become comparable.
How Is This Research Useful to Practitioners?
Because private equity managers control cash flows, private equity performance is generally measured using the internal rate of return (IRR, a money-weighted measure). Public equity performance is generally measured using a time-weighted return (TWR) in order to neutralize the timing of cash flows. Unlike private equity fund managers, public equity fund managers have no control over cash flows, which makes a TWR measure more appropriate than an IRR measure.
Despite the differences in return measurement, a number of metrics exist to compare private equity fund performance with that of a public market equivalent. Each metric is still restricted by cash flow timing issues, making it difficult to compare findings among the different metrics.
The author demonstrates how two particular metrics, the Global Endowment Management Implied Private Premium (GEM IPP) and the direct alpha (DA) method, are mathematically connected. The former calculates an arithmetic difference in performance, and the latter calculates a geometric difference in performance. When mathematically linked with each other, the two metrics become comparable.
The “new twist” on alpha is a geometric version of its calculation.
How Did the Author Conduct This Research?
The author demonstrates the calculation of GEM IPP and DA using data in a spreadsheet from Gredil, Griffiths, and Stucke (working paper 2014). After applying the DA metric process, the author finds the private equity fund internal rate of return (PEF-IRR), the DA metric, and the internal rate of return of the public market equivalent (PME-IRR, which equals PEF-IRR less DA—an arithmetic difference). He then uses the DA metric to find the PME-IRR as a geometric difference rather than as an arithmetic difference—that is, PME-IRR* = [1 + PEF-IRR]/[1 + DA] – 1. The asterisk denotes the geometric difference calculation of PME-IRR.
Next, the author applies the GEM IPP metric process and demonstrates that the GEM IPP metric equals PEF-IRR less PME-IRR*. By doing so, the author connects the two metrics mathematically.
The numerical demonstration of the two metrics having a mathematical connection is convincing, and I think the development of a mathematical proof/structure for the different metrics might allow researchers to connect additional metrics in the future. Unfortunately, I think this may be easier said than done, given the complex nature of internal rate of return calculations.