median values of the PME by decade, for direct and fund investments, along with the standard errors of the averages. Decade refers to the vintage year, so even though an investment is classified under the decade in which it originated, its return may be based on an exit in a different decade or the current net asset value.

One way to assess the relative risk and reward of each decade is to compare mass to the right of the center under each distribution. By this measure, the greatest mass of high return projects (measured by PME) is found in 1961-1969, followed by 2000-2009, followed by 1990-1999. The variance of the distribution appears smallest (not accounting for outliers) for the most recent decade, 2010-2019. This is expected given the large share of unrealized investments valued at close to their cost. Investments that originated in 1980-1989 exhibit the worst performance (measured by PME); the density function for that decade compared to investments made in 2010-2019 is skewed further to the left.

**Alternative Performance Measures** Though most of our analysis focuses on the PME vs. the S&P 500, we report for comparison portfolio performance measured in three other ways. First, we report the total value to paid-in capital (TVPI), or the sum of all distributions divided by the sum of all contributions, which is known as the multiple on invested capital (MOIC) or multiple of money when considering a realized investment.<sup>12</sup> Unlike the PME, this measure does not account for the time value of money.

Second, we report the internal rate of return (IRR).<sup>13</sup> Given the common use of IRR by private equity professionals to evaluate investment performance, for robustness we present key regression results using the investment-level IRR as a dependent variable. There are issues with this approach. The IRR is much more right-skewed compared to the PME, making the OLS regressions, though not the quantile regressions, less reliable. Additionally, the IRR is undefined for 138 investments that were written off and have zero or trivial positive cash flows. To retain these observations in the analysis and avoid selection bias, for these investments we code the IRR as -100%. Table A4 reports summary statistics for the IRR by decade, for direct and fund investments.

Third, we report the generalized public market equivalent (GPME) proposed by Korteweg and Nagel (2016), who observe that the PME can be affected by the performance of the market during the sample period. For instance, using the vocabulary of the CAPM framework, the PME will be greater than one if alpha is zero, but the portfolio has a beta greater than one and the PME is observed at a time when the market is performing well. Because it adjusts for the risk-free rates and returns of public equity markets during the sample period, the GPME will indicate less outperformance than the PME for high beta investments if the public market is doing well during the sample period. For the risk-free return we use the one-month U.S. treasury rate reported by CRSP. Similarly, the GPME will report more outperformance than the PME for low beta investments if

> 12Recall that if an investment has not been realized, its fair value on the final date in the data is treated as a distribution. It is on this basis that the sum of distributions is called “total value.”

> 13We use the XIRR function in MATLAB.

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