Beyond IRR once more

Christoph Kaserer and Christian Diller of the Centre for Entrepreneurial and Financial Studies at Technische Universitöt in Munich have been taking a close look at how European private equity fund performance can be more closely assessed and compared with other asset classes. Here they describe the return distribution of European private equity funds – and in particular compare IRR with public market benchmarking

In this article we address two questions: firstly, how should a private equity fund's performance be measured? And secondly, what are the return characteristics of European private equity funds in comparison to the public markets? 1

It is well known that there are many different ways of measuring return characteristics of private equity funds. The industry itself mostly relies on Internal Rate of Return (IRR) or, even more basically, on a multiple-approach. As many readers will probably be aware, an important argument against using the IRR as a return measure is that with this approach it is assumed that the opportunity cost of capital invested in the fund is equal to the IRR. As the investment opportunities of a private equity fund may be rather singular, this is not an especially sound assumption. Moreover, in this way any comparison with other asset classes will be subject to distortion.

Due to these shortcomings, other performance measures have been proposed, the public market equivalent-approach (PME) being the most important among them. 2 Basically, under this approach the simplifying assumption is made that the opportunity cost of a private equity investment is equal to the rate of return of a public market benchmark. Starting from this assumption we derive a PME-measure defined as an investment volume multiple; i.e. a PME of x informs the investor that the cash flows generated by a private equity fund could be replicated by investing x Euros in the public benchmark for every Euro invested in the fund. Evidently, the PME can be used for benchmarking private equity returns. Moreover, the approach can be extended in order to give some indications about risk and correlation characteristics of the private equity asset class.

From an empirical perspective, the PME-approach (as well as the IRRapproach) often suffers from inaccurate cash flow recordings. Most importantly, in cases where the fund under analysis is not yet liquidated the last reported net asset value (NAV) normally is assumed to be a final fictive cash flow. Although this assumption makes sure that both approaches can be applied to almost every existing fund, it may lead to substantially distorted results as NAVs are subject to considerable valuation biases. 3

The idea behind the empirical part of our approach was to get rid of the NAV bias by inferring the performance of the private equity fund only on the basis of realised cash flows. In a very strict sense, this would allow us to analyse liquidated funds only. This might induce a bias as well though, as more recent vintage years would be underrepresented in our sample. As a result, we increased the dataset by adding mature funds, i.e. funds with a relatively small NAV. For those funds, valuation biases should have a small impact on performance recordings.

The empirical results of this article are based on a large dataset provided by EVCA and Thomson Venture Economics (TVE). It consists of 777 European private equity funds with vintage years from 1980 to 2003.

As mentioned above, we focused only on realised cash flows to calculate private equity returns. However, only 95 funds in the dataset had already been liquidated. Moreover, their average age was about 13 years. As we found that more recently founded funds have an above average return, looking at liquidated funds only would clearly cause a negative selection bias. 4

In order to solve this problem and to increase the size of the data set we added non-liquidated funds to our sample. This was done, however, under the restriction that the residual NAV of

such a fund was not higher than 10 per cent (sample I) or 20 per cent (sample II) of the undiscounted absolute sum of all previously accrued cash flows. 5 For these funds the residual NAV is treated as a fictive distribution accruing at the end of June 2003. Using these criteria we get two new samples with 200 funds (sample I) and 262 funds (sample II). Although this approach may suffer from a selection bias as well, it should be noted that we selected those funds that either already paid very high cash flows (positive selection) or those that had to reduce their NAV considerably (negative selection). The distribution of the vintage years of our funds is described in figure 1.

Using this European dataset we get the results presented in table 1. The pooled average IRR, i.e. the average of all funds in our data sample, is 10 per cent for liquidated funds, while the IRRs for the extended samples I and II are at a perceivably higher level of 13 and 14 per cent respectively. This result has to be compared with the result reported by Kaplan/Schoar (2003) for US-funds, where they found an average IRR of 17 per cent. 6 The distribution is heavily skewed as can be seen from the relatively low medians as well as from the very high first quartile levels. In fact, 25 per cent of the funds in sample I generated an IRR that was not lower than 17 per cent. Moreover, table 1 corroborates the view that in terms of IRR European buyout (BO) funds performed considerably better than European VC-funds. Finally, it should be noted that the variability of the IRR increase when the data set is enlarged. This is in accordance with our presumption that our method picks out well performing as well as bad performing funds.

In order to benchmark IRRs an excess-IRR is often proposed (defined as the IRR of a single fund minus the return on a benchmark index over the fund's lifetime). In table 2 we show the excess-IRRs for the European funds in our data set by using the MSCI Europe share index as well as the JPM European Government Bond Index. 7 The average excess-IRR is positive for all fund groups except for liquidated VC funds. Again, the benchmarked return is higher for buyout funds than for VC funds.


Liquidated Funds
Average 7.32% 12.64% 10.01%
Median 4.77% 9.79% 7.28%
75th Percentile 12.98% 18.67% 14.24%
25th Percentile -4.00% 8.23% 0.00%
Stdev 17.82% 17.67% 17.85%
Sample I
Average 12.00% 13.39% 12.69%
Median 8.05% 10.80% 9.14%
75th Percentile 15.65% 18.76% 17.13%
25th Percentile 1.90% 9.00% 4.45%
Stdev 22.06% 16.18% 19.34%
Sample II
Average 12.50% 15.63% 14.07%
Median 7.40% 11.00% 9.56%
75th Percentile 16.31% 19.95% 18.17%
25th Percentile 0.00% 1.69% 0.05%
Stdev 24.95% 20.59% 22.89%


Excess-IRR(CF) TO MSCI Europe Excess-IRR(CF) TO J.P. Morgan Govt. Bond Index
Liquidated Funds 47 48 95 47 48 95
Average -2.27% 3.37% 0.93% 6.55% 3.77%&pipe;
Median -4.17% -0.77% -2.70% -2.92% 3.33% 0.95%
75th Percentile 1.76% 9.47% 5.21% 6.67% 13.34% 7.51%
25th Percentile -10.84% -7.08% -9.21% -7.46% -5.08% -6.18%
Stdev 17.41% 19.14% 18.42% 17.95% 18.05% 18.13%
Sample I 101 99 200 101 99 200
Average 3.62% 5.29% 4.45% 4.69% 6.23% 5.45%
Median -1.37% 1.57% 0.61% 0.70% 3.26% 1.24%
75th Percentile 5.94% 12.56% 10.24% 7.89% 12.87% 10.94%
25th Percentile -8.02% -6.17% -7.32% -6.31% -5.81% -5.89%
Stdev 24.27% 17.16% 21.01% 22.12% 16.30% 19.42%
Sample II 131 131 262 131 131 262
Average 5.10% 8.25% 6.68% 5.15% 8.25% 6.70%
Median 0.64% 3.58% 1.71% 0.59% 3.48% 1.64%
75th Percentile 8.22% 12.87% 11.23% 10.49% 13.42% 12.51%
25th Percentile -6.99% -5.04% -5.92% -7.65% -4.73% -6.76%
Stdev 25.07% 20.63% 22.96% 22.07% 21.69% 24.53%


PME (MSCI Europe) BME (JPM European Govt. Bond)
Liquidated Funds
Average 0.82% 0.90% 0.86% 1.11% 1.07% 1.09%
Median 0.68% 0.89% 0.80% 0.81% 1.09% 0.99%
75th Percentile 0.97% 1.24% 1.10% 1.38% 1.37% 1.38%
25th Percentile 0.33% -0.51% 0.42% 0.54% 0.64% 0.58%
Stdev 1.01% 0.53% 0.81% 1.51% 0.60% 1.14%
value-weighed PME 0.94% 1.21%
Sample I
Average 0.96% 1.14% 1.24% 1.20%
Median 0.75% 0.86% 0.82% 1.06% 1.02% 1.03%
75th Percentile 1.17% 1.24% 1.23% 1.44% 1.43% 1.43%
25th Percentile 0.40% 0.59% 0.51% 0.66% 0.63% 0.66%
Stdev 1.15% 0.51% 0.89% 1.02% 0.59% 1.11%
value-weighed PME 1.04% 1.27%
Sample II
Average 1.01% 1.06% 1.03% 1.25% 1.06% 1.23%
Median 0.76% 0.92% 0.88% 0.99% 1.13% 1.07%
75th Percentile 1.22% 1.35% 1.27% 1.27% 1.42% 1.45%
25th Percentile 0.44% 0.61% 0.55% 0.60% 0.77% 0.66%
Stdev 1.15% 0.70% 0.95% 1.38% 0.74% 1.10%
value-weighed PME 1.16% 1.30%


PME (MSCI Europe) BME (JPM European Govt. Bond)
Liquidated Funds
Average 1.23% 1.25%
Median 0.63% 1.02% 0.82% 0.80% 1.23% 1.03%
Stdev 0.72% 0.40% 0.66% 1.02% 0.38% 0.87%
Sample I
Average 1.20% 0.95% 1.14% 1.36%
Median 0.82% 0.92% 0.87% 1.12% 1.21% 1.20%
Stdev 1.09% 0.25% 0.98% 0.43% 0.54% 0.32%
Sample II
Average 1.14% 1.08% 1.32% 1.20% 1.26%
Median 0.81% 0.96% 0.88% 1.15% 1.13% 1.17%
Stdev 0.90% 0.35% 0.63% 0.68% 0.39% 0.46%


MSCI Europe (Strategy 1)
Historical Returns 14.12%
Standard deviation 18.85%
Sharpe Ratio 58.00%
Private Equity Portfolio (Strategy 2)
Expected Return 14.68%
Standard deviation 19.21%
Sharpe Ratio 60.77%
Coefficient of Correlation 0.841
Number of Observations: 200
Time period: January 1980 – June 2003

1. The authors acknowledge support by the EVCA as well as by Thomson Venture Economics. A more detailed performance and asset allocation analysis for European Private Equity Funds can be found in EVCA Research Paper (2004): Performance Measurement and Asset Allocation for European Private Equity Funds. March 2004.

2. An approach very similar to the one used in this article is the PME+ propsed by Rouvinez (2004): Beating the Public Market. Private Equity International. In the industry a similar method, labelled as the index method, is already known; cf. footnote 2 and 3 in Rouvinez (2004). Another method was proposed by Rouvinez (2003): How Volatile is Private Equity? Private Equity International, June 2003, 22-24, for the sake of making an inference on the volatility of a private equity investment. For that purpose he used the assumption that cash flows are reinvested at a constant interest rate. In this way he was able to derive a specific risk and return assessment for a set of hundred private equity funds. His results indicate an average yearly return of 14.3% with a standard deviation of 34.4%.

3. Emery (2003): Private Equity Risk and Reward: Assessing the Stale Pricing Problem. Journal of Private Equity, Spring 2003: 43-50, documents evidence of stale pricing of private equity IRRs based on NAVs. A detailed summary with respect to the solutions proposed in the literature can be found in Kaserer/ Wagner/ Achleitner (2004): Managing Investment Risk of Institutional Investors – The Callange of Illiquidity. Forthcoming: Frenkel/ Hommel/ Rudolf (ed.): Risk Management, Berlin.

4. We document a significant positive correlation between the vintage year and the PME or the IRR, respectively. Cf. Kaserer/ Diller (2004): European Private Equity Funds – A Cash Flow Based Performance Analysis, CEFS Working Paper 2004-01.

5. Formally, we integrated a non liquidated fund in sample I resp. II, if it met the following condition: This ratio could be interpreted as the cash flow determined age of the fund. A similar idea can be found in Meyer/ Weidig (2003): Modelling Venture Capital Funds. Risk Magazine, October 2003.

6. Cf. Kaplan/ Schoar (2003): Private Equity Performance: Returns, Persistence and Capital Flows, MIT Sloan School of Management Working Paper 4446-03. They report an IRR of 17% for VC funds and 18% for BO funds.

7. This index is only available back to 1993. As we need a longer index history we use the German REXP index for periods from 1993 backwards. The REXP is a performance index of German treasury bonds over the whole maturity range.

8. It turns out, however, that the natural logarithm of the PME can be well approximated by a normal distribution. This is important for modeling returns on the basis of the PME.

9. It should be noted, nevertheless, that although the correlation between size of the fund and PME is positive, it is statistically not significant in this sample. Cf. Kaserer/ Diller (2004).

10. Cf. Kaplan/ Schoar (2003).

11. We assumed that the transaction costs for the index investment is 50bp a year. This is meaningful as otherwise the results would be biased against the private equity industry, given that the recorded funds' cash flows are net of management fees.