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1 Performance Measurement and Asset Allocation for European Private Equity Funds Research Research Paper March 2004 Contributors CDC IXIS Capital Markets Center for Entrepreneurial and Financial Studies (CEFS-TUM), Technische Universität München

2 About EVCA The European Private Equity and Venture Capital Association (EVCA) exists to represent the European private equity sector. With over 950 members throughout Europe, EVCA s many roles include working to promote the asset class both within Europe and throughout the world, representing the industry in public affairs and developing professional standards. EVCA s services and information products range includes research and information papers, renowned large-scale conferences and networking opportunities, small-scale but industryspecific workshops and private equity management training courses through the EVCA Institute. EVCA s activities cover the whole range of private equity, from seed and start-up to development capital, buyouts and buyins, and the flotation of private equity-backed companies. Please note This publication does not purport to contain a complete explanation of the private equity asset class and any related securities. No statement in this publication is to be construed as a recommendation to purchase or sell a security or to provide investment advice. Private equity involves risk and is not suitable for all investors. Prospective private equity investors considering purchase of securities should reach an investment decision only after carefully considering the suitability of these securities in light of their own personal financial condition and objectives.

3 Contents Executive summary page 2 1. Introduction page 5 2. Asset allocation and European private equity: A first approach using aggregated data by Patrick Artus & Jérôme Teïletche, CDC Ixis Capital Markets page General remarks on private equity returns page Asset allocation among venture capital, equities and bonds in the European case page A naïve approach of asset allocation page The smoothing of venture capital returns page The correction of venture capital variance and of the correlation between venture capital and equities page A corrected asset allocation page Introducing buyout funds into the portfolio page Concluding remarks page European private equity funds A cash flow based performance analysis by Christoph Kaserer and Christian Diller Center for Entrepreneurial and Financial Studies (CEFS-TUM), Technische Universität München page Cash flow characteristics of European private equity funds page Return/risk characteristics of European private equity funds page The cash flow based IRR as a return measure page The cash flow based PME as a return measure page Risk characteristics of cash flow based returns page Correlation characteristics of different reinvestment hypotheses page Increasing the data universe page Results with respect to IRR page Relative Performance Characteristics page Private equity, asset allocation and limited liquidity page Cash flow patterns, liquidity risk, and performance assessment page Concluding remarks page Conclusion page Bibliography page 72 Appendix I page 73 Index of figures page 77 Index of tables page 78 Contributors page 80 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

4 Summary Executive Summary What should be the share of private equity in the portfolio of European institutional investors? This paper argues that the answer is between 5%-10% when the portfolio consists of private equity (i.e. venture capital and buyout funds), quoted equity and bonds. The research was conducted on behalf of EVCA and carried out by Patrick Artus and Jérôme Teïletche, CDC Ixis Capital Markets Research Department, and by Christoph Kaserer and Christian Diller, Center for Entrepreneurial and Financial Studies (CEFS-TUM) Technische Universität München. The authors of this paper make a case for the introduction of private equity into the framework of modern portfolio theory. Moreover, due to the characteristics of private equity itself, they were required to consider the following aspects within their analysis: The absence of a market providing pricing guidance for the assets in the portfolios of funds on a continuous basis. As a consequence the value of assets in portfolios is the result of an appraisal, leading to potentially stale pricing or a smoothing process. This causes issues with modern portfolio theory as the true volatility and correlation between asset classes can be understated. Determining the right performance metrics in order to compare the returns of private equity with more liquid asset classes. Two sets of data were used in order to conduct this analysis. The first one consists of periodical aggregate returns built on the sum of all the funds for a specific period of time (i.e. the sum of the cash flows and net asset values between the starting and the ending dates of the chosen period). The second set of data consists of cash flow patterns (amount and exact timing) based on data of individual funds. In a first stage, Patrick Artus and Jérôme Teïletche concentrated on correcting aggregate quarterly returns generated by the smoothing process. Figure 1 presents the outcome of this calculation for venture capital. It appears that the portfolio with the highest Sharpe ratio (i.e. the portfolio that gives the highest return per unit of risk) consists of 3% venture capital, 2% quoted equities and 95% of bonds. Moreover, the authors also looked at correcting returns generated by a smoothing process for the buyout segment of private equity. They were confronted with two key issues: The absence of a significant autocorrelation of aggregated returns on buyouts (i.e. a correlation function between a single, not random variable at different times), which questions the principle of smoothing processes; and The difficulty of finding an aggregate return that gives a correct representation of the dispersion of returns within the buyout segment. Because the study of aggregate returns and their potential correction did not lead to a fully satisfactory solution, an analysis of the individual cash flows generated by European private equity funds was needed to create a more thorough understanding of the role of private equity in the portfolio of institutional investors. 2 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

5 Executive Summary Figure 1: Efficient frontier for portfolios of venture capital, public equities and bonds (European data; 1994 Q Q2) Expected return (% per year) B A C Frontier with raw statistics D Portfolio A' (minimum variance): 1% VC, 3% Equities, 96% Bonds Frontier with corrected statistics Portfolio C' (Two assets portfolio): 16% VC, 0% Equities, 84% Bonds Portfolio B' (maximum of the Sharpe ratio): 3% VC, 2% Equities, 95% Bonds Portfolio D' (maximum return portfolio): 100% VC, 0% Equities, 0% Bonds Risk (% per year) Source: EVCA/CDC Ixis Capital Markets, based on data provided by Thomson Venture Economics In the second stage, Christoph Kaserer and Christian Diller conducted an analysis of the cash flows of a total of 780 European private equity funds. As mentioned, the smoothing process does not determine the results of the cash flow analysis. Initially, the authors described the time patterns of takedowns (also called draw downs) and disbursements. According to the study the average European private equity fund draws down 25% of the total committment when starting its business. Within the first three years 63% of the total committed capital will be invested in the fund. On the other hand, the calculations show that 53% of total disbursements are paid out to the limited partners within the first six years. By taking the ratio of these two measures, the authors argue that limited partners on average retracted the invested money after 7 and half years. Next, Christoph Kaserer and Christian Diller calculated various performance measures. They found that the internal rate of return (IRR) based on cash flows for 201 funds, which were either liquidated or had a small residual net asset value, is around 12%. The results also indicate an average IRR of buyout funds of 13.4% and of venture capital funds of 10.6%. A calculated Excess-IRR of the MSCI Europe stands at 4.4% for an average European private equity fund. Because of the shortcomings of the IRR calculation method, the authors developed a benchmark for returns based on the assumption that the limited partners, i.e. institutional investors, reinvested the distributions from the funds either in quoted equity or in bonds. This allows comparing returns of private equity with returns of public securities for the full life cycle of funds. Hereby the authors found an average public market equivalent of 0.93 and a value-weighted PME of A PME larger than one indicates that the investments into the observed private equity funds generate a higher terminal value than an equivalent investment into the MSCI Europe. Additionally the authors estimated the return, risk and the correlation structure of private equity based on the PME measure. Again the authors claim that the share of private equity in portfolios of institutional investors should be around 5%. Performance Measurement and Asset Allocation An EVCA Research Paper March

6 Executive Summary One of the most striking findings of this research relates to the determination of the relative contribution of venture capital and buyout investments to institutional portfolios (see figure 2). In this case, the returns produced by European private equity funds and their hypothetical reinvestment in the JP Morgan European Government Bond Index by the limited partners suggests a maximum Sharpe ratio for institutional portfolios comprising 5% of venture capital and 3% of buyout investments. Figure 2: Efficient frontier for portfolios of public equities, bonds, venture capital and buyout funds (Bond reinvestment strategy) ( ) 2 16% 14% EP_9% (26% VC, 26% BO, 28% Eq., 20% Bds.) Expected return (% per year) 12% 10% 8% 6% MSRP (5% VC, 3% BO, 7% Eq., 85% Bds.) BO VC Equities Bonds = MVP (0% VC, 0% BO, 0% Eq., 100% Bds.) 4% 0% 5% 10% 15% 20% 25% Standard Deviation (σ) Before concluding, it should be pointed out that those results are based on historical returns. Nevertheless, the authors reason that investors should build their portfolios on the ability of the respective asset classes in order to outperform their track records. Therefore, following basics should be taken into account in a strategic asset allocation. Bonds will probably not reproduce past returns due to the current low level of interest rates. Though it is true that the performance of the venture capital segment has been seriously reduced following the collapse of the Internet related investment trend in 1999/2000, this context has also made European private equity management teams experienced in managing investee companies through difficult times. Moreover, the increasing competition between buyout houses in Europe is emphasising the importance of differentiation via implementation of truly value adding strategies. The quantitative evidence based on historical returns and forecasts on the development of European private equity calls for a significant role of this asset class in the portfolio of institutional investors. 1 The following portfolios are marked in the diagram: MVP = Minimum variance portfolio, MSRP = Maximum Sharpe ratio portfolio (for a risk free interest rate of 3%), EP_9% = Efficient portfolio with an expected return of 9%. Moreover, the portfolios where 100% is invested in one asset class are marked, too. 4 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

7 1. Introduction What should be the share of private equity in the portfolio of an institutional investor? Modern portfolio theory offers an answer determined by the return, the volatility (in other terms the risk) and the correlation of private equity with other asset classes (typically, but not limited to, quoted stocks and bonds). Although offering a widely accepted framework, modern portfolio theory constitutes a challenge when applied to a set of asset classes comprising private equity. This challenge comes from the characteristics of the private equity asset class itself. According to modern portfolio theory, an asset class will see its share in an institutional investor s portfolio increased when, for a determined level of correlation with other asset classes, its return increases and its risk (i.e. volatility) decreases. Conversely, for a determined level of return and risk, the share of an asset class will increase when its correlation with other asset classes diminishes. The impact of correlation relates to the intuitive notion of diversification. A small correlation means a higher degree of diversification. The limited liquidity of private equity makes the level of return, volatility and correlation not directly comparable with more liquid asset classes like quoted stocks and bonds. Intuitively, the lower level of liquidity should lead to a premium in the return produced by private equity. The question is then to know if the excess return in exchange of the limited liquidity justifies the inclusion of private equity in a portfolio. The answer is clearly depending on the investment horizon of the institutional investors. Moreover, the limited liquidity brings with it that there is no market providing pricing guidance for assets in the portfolio on a continuous basis. As a result, the value of the assets in the portfolio is estimated via an appraisal, leading to a potential stale pricing or smoothing process. As a consequence, the true volatility of private equity and its correlation with other asset classes could be underestimated, leading to a potential over-commitment to the asset class according to modern portfolio theory. Another impact of the limited liquidity, combined with the very nature of private equity, i.e. developing companies over a long period of time, leads to a J-curve effect. The J-curve effect is observed not only for cash flows but also internal rates of return (IRRs). Typically, due to the management fees, an investor will observe in the first years of a life of a fund negatives IRRs. It will take several years, usually more than six, before the investors can get a true picture of the performance of the funds in their portfolio. This can negatively impact the share of private equity in a portfolio depending on the age structure of the benchmark used in order to gauge the performance of the asset class. Another issue stems from the performance metric used by the asset class. Because private equity fund managers have a direct influence on the timing of the cash flows (which is not the case for mutual funds managers for example), the performance of the industry is gauged by the IRR. But IRRs are not directly comparable with the returns extracted from indexes used to measure the performance of quoted stocks or bonds, because IRRs are dependent on the timing of the cash flows, while returns gained from indexes are not. A very important issue is also related to the ability to invest in the best performing funds. The spread observed between good and bad performers is significantly higher in the private equity asset class than the one observed for quoted stocks or bonds. In other words, aggregate indexes might not give a true picture of the dispersion of performances. Performance Measurement and Asset Allocation An EVCA Research Paper March

8 Introduction All those issues have recently initiated new research (see bibliography for more information), but most of the work done so far was concentrating on US private equity funds. This paper is another step forward in understanding and gauging the role of private equity in the portfolio of institutional investors by focusing on European funds. Based on data collected by Thomson Venture Economics, this document follows two approaches in order to solve some of the issues presented above: The first part, Asset allocation and European private equity: a first approach using aggregated data written by Patrick Artus and Jérôme Teïletche, CDC Ixis Capital Markets Research Department, deals with the stale pricing or smoothing process. In order to do this, this section is based on aggregate periodic IRRs of venture capital and buyout funds available through the VentureXpert database. A first efficient frontier is drawn from this analysis. The second part, European Private Equity Funds, a Cash Flow Based Analysis, conducted by Christoph Kaserer and Christian Diller, Center for Entrepreneurial and Financial Studies University of Munich, is on a database comprising cash flows from 780 funds 2. By producing Public Market Equivalent returns, this section also leads to the production of a second efficient frontier. The conclusion confronts the results gained through the two approaches. Because all findings in the first and second part are based on historic returns, a discussion regarding future developments concludes the document. 2 It should be noted that Thomson Venture Economics provided the Center for Entrepreneurial and Financial Studies University of Munich with an anonym database, i.e. it was not possible to connect cash flows with a specific fund. 6 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

9 Aggregated data 2. Asset allocation and European private equity: A first approach using aggregated data Patrick Artus Jérôme Teïletche CDC IXIS Capital Markets Research Department An analysis of the profitability of investments in private equity is no easy task. By definition, the value of investments is not known publicly at all times and does not result from the interaction of supply and demand on a centralised market. In practice, the value of investments in private equity is known in only a few specific occasions: While it remains within private equity: if the company receives new investments or if it moves from a general partner s portfolio to the portfolio of another (i.e. on a private equity secondary market); When it exits from the private equity sector: if another firm buys the company or if it is introduced to the stock market. Between these different periods, we can draw only on estimated values provided by the general partner. Moreover, the conventional investment manner 3 results in the internal rate of return (IRR) being the standard measure used throughout the industry. This contrasts with standard assets where profitability indexes are built as if the entire investment occurred in the initial period. 2.1 General remarks on private equity returns All in all, the profitability measures of private equity show several unique features that must be taken into account, notably if one wishes to compare the profitability of private equity with that of other financial assets. More specifically, we will discuss in this section three characteristics of profitability in private equity: (i) Biases of short- and long-term measures; (ii) IRR versus time-series returns; (iii) Dispersion of performances of funds within a category or according to the age of investment and the type of companies in which the investment is carried out. Characteristic 1: Biases of short- and long-term measures. As pointed out previously, the returns posted by private equity fund managers are disclosed only in a few specific circumstances: (i) if the investee company is introduced on the stock market; (ii) if the investee company is acquired; (iii) if it receives additional financing; (iv) if it files for bankruptcy (i.e. its value implicitly sinks to zero). These characteristics entail several biases in measuring private equity returns. These biases are different in nature in the near and long term. 3 We understand conventional investment manner in this context to be the opposition between, on the one hand, an initial investment (a draw-down or take down from the investor the limited partner to the fund managed by the venture capitalist the General Partner) and consecutive disbursements carried out at irregular dates and, on the other hand, a final value at a period that is also random. Performance Measurement and Asset Allocation An EVCA Research Paper March

10 Aggregated data In the short term, posted returns are based on estimated values (appraisal returns), drawn up by the general partners. Because they are seeking to be cautious or responding to a simple human reflex, the general partners can be tempted to smooth these returns, i.e. wait for a positive or negative event to be confirmed before factoring it into the value of the investment. Lets assume a major shock, such as the stock market crash in October 1987, when the S&P 500 index plummeted 20% in just one day on 19 October. Back then it took one year before the market reached again its pre-crash level, but as early as the beginning of November 1987 the index was at just 10% off that level, its closing level on 16 October 4. Late October was consequently characterised by major volatility in stock market returns. Let us imagine a partner who must value its holdings in unlisted companies. The market of listed companies, or segments of this market, provides a reference for drawing up such valuations, because both markets, for listed and unlisted companies, are exposed to common macroeconomic or sector risks. Faced with large fluctuations in the stock market, the general partner could be tempted to wait for the market to cool down before drawing up a valuation. It is likely that this will result in returns on his investments that appear less volatile than those of the stock market. From a more general point of view, this process of smoothing returns, inherent to the fact that estimated values are used for private equity, induces at least two evident biases: (i) an under-estimation of volatility; (ii) an under-estimation of the correlation with other assets, including those that constitute the reference for private equity (notably, stock market assets). These biases are referred to alternatively under the generic terms of stale pricing bias or smoothing bias. The best indicator for such a process of smoothing returns is an autocorrelative 5 structure characterised by positive and very high values for the first lags. When asset allocation is analysed via standard tools, these biases have dramatic consequences. In particular, they lead to allocations that are excessively in favour of the asset of which the returns are smoothed since its risk is individually undervalued (via the standard deviation) or collectively with the other assets (via correlation). The purpose of this study precisely consists in analysing the results in terms of allocation of private equity into investors portfolios made up of various standard assets. In particular, we have worked on relatively high frequency data, which is therefore likely to be significantly affected by the smoothing bias. When applying modelling as detailed in Appendix 1, we will see, however, that there are various solutions to offset this problem. These techniques are used in our empirical section. Note that the impact on average returns is not treated within the theoretical framework discussed in this study. In particular, it supposes that the entire information of real returns is found in the track record of smoothed returns. In the longer term, the average of returns might also be moved upwards. One reason lies in the selection bias discussed hereafter. Another reason, closer to our concerns in this part, is that any additional performance of private equity is perhaps simply the compensation for the lower liquidity of this asset. 4 After just two days (21 October), the market had already pared back nearly 15%, before falling anew subsequently. 5 The autocorrelation to the order k of a process denotes the expectation of the correlation between realised value of the process at time t (e.g. a return) and its realised value k periods ago. 8 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

11 Aggregated data Access to this premium would be acquired only by investors accepting to block their funds for a very long time, while investors with a shorter horizon lose this premium by selling the illiquid asset on the secondary market at a discounted price, however such approach has been ignored in this study. Note that, ceteris paribus, one favours private equity over other more liquid assets. Another solution consists in drawing exclusively on very long-term returns. With aggregated data, this gives rise to the problem that only extremely small samples are available for observations. Moreover, drawing on very long-term data does not protect the analysis totally against the existence of biases. In particular, the returns achieved in the long-term for private equity are likely to be affected by a selection bias. For, in practice, these returns are realised only when the company is acquired or is introduced on a stock market. In each case, the likelihood of observing a return is highly related to the likelihood that the value of the company is significant. This generates a selection bias, in the meaning that observed returns concern exclusively firms whose value has increased over time. Firms that have not seen their value rise, on the contrary, will be more likely to remain within the private equity segment. Cochrane (2001) has sought to model this selection bias in the case of venture capital in the United States 6. All in all, according to his results, taking into account the selection bias would result in the (log-) average returns of venture capital dropping from 108% to 15% per year. Another solution consists in concentrating on fund level rather than individual direct investments. In particular, the returns thus achieved probably include both successful projects as well as failures (including bankruptcies). Baier et al. (2002) show that in this case the results obtained are consistent with those based on individual projects by taking into account the selection bias. Therefore, the data used in this study, at aggregate level as well as individual level, covers funds only, not individual direct investments. Characteristic 2: IRR versus time-series returns As we pointed out previously, the IRR is the most appropriate measure of performance for investments in private equity. By contrast, for standard assets, i.e. equities and bonds, profitability is measured via performance indices. These indices do not take into account a specific structure of investments. Instead, they suppose that there are only two dates of interest: the starting point, which corresponds to the investment, and the end date, which corresponds to the date when the performance is recorded. Box 1 shows that it is extremely difficult to reconcile the two performance measures (see also examples in Part II). In fact, they can be equal in only the specific circumstance where the investment in private equity does not imply intermediate flow between the initial investment and the date of realisation. To tackle this problem, two solutions for either individual funds or for aggregate level can be adopted. In the first case (treated in the second part of this study), one applies to standard assets the structure of private equity cash flows. The result is a measure called Public Market Equivalent (PME) where we suppose that every time the investor initiates a cash flow in private equity (either investment or distribution), he initiates an equivalent cash flow with respect to the standard asset. PME is the IRR of this second type of investment. 6 His model is based on a CAPM for the returns on venture capital (in log terms), a logistic specification for the likelihood of being listed (or receiving additional financing) at date t and a linear specification for the likelihood of bankruptcy at date t, with the two probabilities being conditional on the value of the company at date t (the likelihood of remaining in the venture capital industry is deduced from the two other probabilities). Performance Measurement and Asset Allocation An EVCA Research Paper March

12 Aggregated data In the second case (which we treat in this first part), we define regular time intervals (quarterly or annual) to assess the profitability of private equity. More exactly, we calculate an IRR for one period. Net asset value (NAV) at the beginning of the period is booked as a negative cash flow. NAV at the end of the period is booked as a positive cash flow. The IRR that equalises both flows is similar to the Time Weighted Return (TWR) and represents a short-term measure of the profitability of private equity. The empirical work carried out in this first part is based on the latter measure using data provided by Thomson Venture Economics (TVE). In this part we analysed private equity at an aggregate level (as the IRR remains the most appropriate measure for the analysis of individual funds) and compared it with other assets. However, several remarks must be made in advance with respect to this measure: In the definition given above, we have supposed that there was no intermediate cash flow between the start date and the end date. In the case where an intermediate flow occurs, it is introduced into the calculation of the TWR. We then face again the problem of the comparison with standard assets. Nevertheless, if one concentrates on very short periods of time (such as quarterly periods), the likelihood of such a cash flow is relatively small. We include in the calculation only funds that: (1) have a real NAV at the end of the period, in the sense that it is not estimated or automatically reported by Thomson Venture Economics; (2) has a real NAV reported at the beginning of the period when the fund is set up and has its first cash flow during the covered period. Note that these restrictions fail to curb the problem of stale pricing that we treat in our empirical part, in the sense that a NAV can be repeated and included in the calculation as long as the general partner carry it out. We work on aggregate TWRs. TVE gives importance to a measure called Pooled TWR where the aggregation between the various funds is based on the sum of all cash flows for each fund by supposing one is dealing with just one fund. TVE also calculates simple averages of the IRR of each fund and this can bias results in the case where small funds post returns that diverge markedly from the average or averages of IRR weighted by the capital allocated to each fund and this is meaningful only if all investments are carried out the beginning of the life of the fund only. Excursion: IRR vs time-series returns Returns of private equity investments are of a particular type. They are dependent on times when investments are made and generally take the form of several injections before value is realised in the end. This is why the concept of Internal Rate of Return (IRR) is usually employed to measure performance for private equity. This measure is different from the one usually employed for other assets, where it takes the form of a time-series return. How can we reconcile both measures of the performance of an investment? 10 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

13 Aggregated data Let be the sample period. For each period up to, the managers of the private equity project are allowed to get a new financing. Let be the amount raised in period t. At time T, the value of the project is realised with terminal value. The IRR gives us an indication of the average per-period return associated with the different investment amounts. Formally, the IRR is defined as the solution of:. (1) From (1), it is obvious that the IRR depends on the structure of payments. The more the investments are realised at the end of the period, the higher the IRR. Let be the one-period continuously compounded stock market return at t. Here, we assume that it is computed in log terms such that where denotes the level of the stock market at time t. We denote by the average return observed over the sample period,. In traditional asset allocation models these average returns are compared for different assets. The problem is that it is difficult to reconcile IRR and. Implicitly, is computed as if all the investment was made at the beginning of the period (ignoring the impact of compounding). So, except in the special case when for (i.e. all the investments are made in the first period of the private equity investment), it seems impossible to compare IRR and. To illustrate this point, let us imagine an investor who invests each period the same amount (say 1/T) at. At time T, the total return on its portfolio would be we say the average return of the S&P 500 index was, about half the return, which is expected when between 0 and T. The only solution seems to reproduce the structure of investments in private equity funds using realised returns by other asset, that is:. (2) By comparing and, we get an idea about the difference in returns of private equity and of other assets. Assuming that IRR is small enough so that, we deduce that (saying private equity is more profitable than the stock market, while the investment dates are being the same in both cases) if and only if:, (3) that is, the IRR should be larger than a (structure of payments-) weighted stock market return. In the simplest case where stock market returns are constant,, the inequality (3) resumes to. Performance Measurement and Asset Allocation An EVCA Research Paper March

14 Aggregated data Characteristic 3: Dispersion of returns versus aggregate measure. The empirical analysis carried out in this study is based on the evolution over time of TWRs aggregated in a pool. In the case of Europe, we can draw on such private equity data only since Nevertheless, apparently the data of the beginning of the sample are not very representative. In particular, figure 3 clearly shows a structural change in the number of funds reporting since Consequently, our study will bear on the period Figure 3: Sample size of European returns All private equity Venture capital Number of funds Year Source: EVCA/CDC Ixis Capital Markets, based on data provided by Thomson Venture Economics Beyond the choice of the sample period, our empirical analysis, based on aggregated measures, implies several approximations insofar as these aggregate measures portray only imperfectly the dispersion of returns. A first source of dispersion of private equity returns is accounted for by the age of the investment. During the initial years, the investor in private equity has to expect negative cash flows and returns because of the initial investment and management fees paid to the general partner. This phenomenon is known as the J-curve phenomenon, illustrated in figure 4. At the beginning the return is negative, but subsequently the gradual increase in the valuation of the project little by little leads to positive returns. Generally speaking, the break-even point (i.e. when the IRR reaches zero) occurs around the fifth year of the investment. 12 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

15 Aggregated data Figure 4: The J-curve phenomenon IRR (%) Year Source: EVCA/CDC Ixis Capital Market This phenomenon is found again indirectly when one analyses the profitability of the various segments of private equity. Figure 5 shows the return-to-risk ratio for these various segments. We can notably see that the returns for the general partner specialised in companies that have already developed (expansion and later-stage investments) present a higher average and a lower risk than that of funds specialised in start-up companies (seed and start-up investments). Implicitly, this result reflects the fact that the J-shaped curve phenomenon will be less pronounced for the former than for the latter because the underlying firms will be able to post results faster or will be faster to withdraw from the private equity field. Figure 5: Risk/return profile for European private equity components (annual pooled weighted returns) 35 Seed/Start-up Standard deviation (%) Buyout and Mezzanine Venture capital All private equity Balanced venture capital Expansion/Later stage Arithmetic mean (%) Source: EVCA/CDC Ixis Capital Markets, based on data provided by Thomson Venture Economics Performance Measurement and Asset Allocation An EVCA Research Paper March

16 Aggregated data Note: for exact definition of the different segments, please refer to chapter 3. Venture capital comprises seed/start-up and development/expansion/later-stage funds as well as balanced venture capital funds (i.e. investing in the two previous mentioned categories). The buyout segment consists of both buyout and mezzanine funds. A second measure of dispersion concerns the diversity of performances by funds for a given period of time. To illustrate this phenomenon, the two charts below represent year after year the aggregate performance (pooled) as well as the first quartile (top of the vertical bar) 7 and the last quartile (bottom of the vertical bar) of the distribution of performances of all the underlying funds. For the following exercise and the two graphs the terms venture capital has been defined broadly as all early and later-stage investments and while the buyout segment is solely buyout investments and excludes mezzanine. Two points can be noticed. Figure 6: Dispersion of venture capital returns ( ) Pooled average 60 Return (% per year) Year Source: EVCA/CDC Ixis Capital Markets, based on data provided by Thomson Venture Economics 7 By construction, 25% of funds have a higher or equal performance than the first quartile and 25% of funds have a less good or equal performance to the last quartile. Note then that the totality of the vertical bar covers the funds corresponding to 50% of the distribution closest to the median. 14 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

17 Aggregated data Figure 7: Dispersion of buyout returns ( ) Pooled average Return (% per year) Year Source: EVCA/CDC Ixis Capital Markets, based on data provided by Thomson Venture Economics On the one hand, the dispersion of performances of funds seems to have increased markedly over time, and this is partly a consequence of the fact that all the monitored funds have increasingly grown larger. On the other hand, in certain years, the pooled statistic favoured in our study provides no more than a rough or even misleading measure of the performance of most funds. In particular, in certain years, the pooled statistic is equivalent to the first quartile; this can pose problems when the first quartile is positive while at the same time most funds have reported a negative performance. Note, nonetheless, that this criticism applies above all to buyouts and to a lesser extent only to venture capital (see for example 2001 and 2002). This is hardly surprising insofar as the buyout category is far more heterogeneous. This is why in our study, we have given preference first to venture capital (2.2). The case of buyouts is treated later and we will see that the problem of heterogeneity is far more prevalent in this case (2.3). 2.2 Asset allocation among venture capital, equities and bonds in the European case In this part, we analyse the problem of allocation between three assets: venture capital, equities and sovereign bonds. For the reasons mentioned previously, the period of analysis is 1994Q1-2003Q2. Equities are represented by the MSCI Europe index 8 ; it covers total performances, i.e. they are made up of capital gains and dividends. 8 This index was chosen because it is available for a long time while the Stoxx index is only available since In the second part of this study, we need data back to the early eighties. Note that the correlation between the Stoxx and MSCI Europe quarterly returns is above 99% over the period for which both are available. Performance Measurement and Asset Allocation An EVCA Research Paper March

18 Aggregated data The bonds used here are those of all the countries of the European Community (weighted in market value terms; JP Morgan index). Once more, we are dealing with total performances, including capital gains and the payment of coupons. Note that for standard assets (equities & bonds), we have adjusted performances for management fees in order to be in line with venture capital returns that are adjusted for fixed and variable fees. We have assumed that management fees are 50 bps for equities and 20 bps for bonds, typical of the fees paid by institutional investors. In a first section, we deal with the problem of asset allocation in a standard manner. In a second section, we illustrate the presence of smoothing of the venture capital returns. The third section proposes a correction of the impact of smoothing on the variance of venture capital and its correlation with equities. The last section proposes reformulating the problem of allocation from corrected statistics. The details of the methodology are provided in the Appendix I A naïve approach of asset allocation The standard problem of asset allocation needs to estimate the average, the standard deviation and the correlation matrix of returns on various assets. These various statistics are detailed in table 1 below and table 2 on the next page. It can be seen that over the period , the various assets have presented an average return that ranges from 7.4% for bonds to 9.8% for venture capital via 8% for equities. The risks associated to these various assets are also very different, with a naturally lower risk for government bonds and a similar risk for venture capital and equities although it is slightly lower in the former case. All in all, the Sharpe ratio is far higher for bonds and equivalent in the case of venture capital and equities. Table 2 shows a 33% correlation between venture capital and equities and for both, venture capital and equities, a correlation with bonds close to zero, which is more favourable for venture capital. Table 1: Descriptive statistics for quarterly returns (as %; after management fees) Venture Capital Equities Bonds Risk/return profile Geometric average/quarterly figures Geometric average/annualized figures Arithmetic mean/quarterly figures Arithmetic mean/annualised figures Standard Deviation / quarterly figures Standard Deviation / annualised figures Sharpe ratio (risk-free rate = 3.6%) 31% 24% 84% Dispersion measures Minimum Lower quartile Upper quartile Maximum Source: EVCA/CDC Ixis Capital Markets, based on data provided by Thomson Venture Economics 16 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

19 Aggregated data Table 2: Correlation matrix Venture Capital Equities Bonds VC Equities Bonds Source: EVCA/CDC Ixis Capital Markets, based on data provided by Thomson Venture Economics On the basis of such data, we obtain the efficient frontier as shown in figure 8 (after management fees). Figure 8: Efficient frontier for portfolios of venture capital, public equities and bonds (European data; 1994 Q Q2) Return (% per year) Portfolio D (maximum return portfolio): 100% VC, 0% Equities, 0% Bonds Portfolio C (Two assets portfolio): 22% VC, 0% Equities, 78% Bonds 7.5 Portfolio B (maximum of the Sharpe ratio): 8% VC, 2% Equities, 90% Bonds Portfolio A (minimum variance): 5% VC, 2% Equities, 93% Bonds Risk (% per year) Source: EVCA/CDC Ixis Capital Markets, based on data provided by Thomson Venture Economics The chart details a few points drawn from this efficient frontier 9. The portfolio with a minimal variance (A) is made up of 5% of venture capital, 2% of equities and 93% of bonds. The portfolio that maximises the Sharpe ratio when the risk-free asset is introduced (B) is made up of 8% of venture capital, 2% of equities and 90% of bonds. Other efficient frontier portfolios allow a higher ratio with a higher risk. They allocate assets increasingly to venture capital at the expense of equities and bonds. The weight of equities rapidly decreases from a maximum of 2% attained at the minimum variance portfolio and is equal to zero on point C. Then, venture capital substitutes to bonds from this portfolio onwards until one reaches the portfolio (RH scale) made up only of venture capital. 9 Strictly speaking, the efficient frontier, which maximises return for a given level of risk, starts from the portfolio with minimal variance. All the dots located below the portfolio with minimal variance (denoted by A in the chart above) are dominated (other portfolios allow a higher expected return to be achieved for a same level of risk) and do not belong to the efficient frontier stricto sensu. Performance Measurement and Asset Allocation An EVCA Research Paper March

20 Aggregated data All in all, the portfolios thus constituted give venture capital a substantial weight, notably at the expense of equities. As we will now see, this result is partly linked to a probable process of smoothing of venture capital returns The smoothing of venture capital returns The smoothing process of returns (or, in other words, the stale pricing bias) has a major implication on the dynamics of observed returns: they tend to be very auto-correlated. Table 3 shows the autocorrelation coefficient for lags ranging from 1 to 4 for the various assets. While equities seem to be non-autocorrelated, bonds and especially venture capital are marked by a major autocorrelation of their returns. While the autocorrelation of bonds is difficult to interpret 10, a smoothing process can probably account for that of venture capital. Table 3: Autocorrelation structure Lag Venture Capital Equities Bonds * * * Note: an asterisk denotes an autocorrelation significantly different from zero at the 95% confidence level. Source: EVCA/CDC Ixis Capital Markets, based on data provided by Thomson Venture Economics One can seek to detect the smoothing process empirically, as is detailed in the Appendix I. It is supposed the real venture capital returns are determined by an underlying factor (general state of the economy), which the stock market reflects satisfactorily. It is further supposed that observed venture capital returns are a moving average function of the real venture capital returns, i.e. they are smoothed. Starting from this hypothesis and drawing on the fact that stock market returns are not autocorrelated, the coefficients associated with the smoothing process can be calculated via the estimate of an equation that regresses venture capital returns on constant and variable lags of Equity market returns (including contemporary returns), while the number of lags is assessed by a 90% significance test. Over the period and in the case of Europe, this leads to the following estimate: 4) By comparison, a regression of venture capital returns on just contemporary returns on equities leads to the following estimate: 5) 10 A potential explanation is the downward trend in interest rates in the 1990s, with the continued disinflation process until the introduction of the euro and the steady improvement in public finances from 1993 to Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

21 Aggregated data From (4), we can deduce the implicit smoothing process of venture capital (see Appendix I; equations A9 and A10). More specifically, if we denote by the real (i.e. not smoothed) venture capital returns in period t, we can deduce the following relationship with observed returns : 6), so that,, with the notations of the Appendix I. Simplified, observed venture capital returns of a given quarter are approximately an equal-weighted average of real venture capital returns over three quarters (including the current quarter). In an aggregated approach, the Herfindahl 11 index associated with this structure is equal to The correction of venture capital variance and of the correlation between venture capital and equities By drawing on the estimated structure of the smoothing process, we can correct the following statistics (the most affected by smoothing): The standard deviation of venture capital returns; The contemporary correlation of venture capital returns with those on equities. In the first case, the corrected standard deviation is given by (see Appendix): i.e. 34% in annualised terms. In the second case, the corrected correlation between venture capital and equities is given by (see Appendix):, In the Appendix, we suggest that another way to correct the biases linked to smoothing is to draw on data with a lower frequency. From the annual data over the period , we obtain a standard deviation of 27.5% per year and a correlation between venture capital and equities of Applied to the present context, the index varies between 0 if the smoothing takes an infinite form (i.e. the returns are extremely smooth) and 1 if they are not smooth at all. The lower the index, the more returns seem to be smoothed. For the reader s information, a similar calculation in the case of the US venture capital with the Nasdaq as the reference market leads to a value of Therefore, European returns seem to be less smooth. Performance Measurement and Asset Allocation An EVCA Research Paper March

22 Aggregated data Consequently, the two comparison methods do not give absolutely similar results 12. Nevertheless, it should be noted that the differences tend to cancel one another out (with the annual estimates, the smaller individual risk of venture capital given by the standard deviation is offset in the portfolio by its higher correlation with equities), and as a result, in practice, the allocations obtained with either correction are broadly equivalent. Furthermore, the two corrections point in the same direction: (i) venture capital risk is higher than suggested by the original returns data; (ii) it is more highly correlated to the stock market A corrected asset allocation Drawing on corrected statistics, we obtain the following new efficient frontier represented by the blue curve. For comparison purposes, we simultaneously show the efficient frontier obtained previously with the original data. Figure 9: Efficient frontier for portfolios of venture capital, public equities and bonds (European data; 1994 Q Q2) Expected return (% per year) B A C Frontier with raw statistics D Frontier with corrected statistics Portfolio B' (maximum of the Sharpe ratio): 3% VC, 2% Equities, 95% Bonds Portfolio A' (minimum variance): 1% VC, 3% Equities, 96% Bonds Portfolio D' (maximum return portfolio): 100% VC, 0% Equities, 0% Bonds Portfolio C' (Two assets portfolio): 16% VC, 0% Equities, 84% Bonds Risk (% per year) Source: EVCA/CDC Ixis Capital Markets, based on data provided by Thomson Venture Economics Two points can be noticed: On one hand, the correction of the standard deviation and of the correlation naturally leads to an efficient frontier that is located lower on the right of the risk/return plan. This means that for an equivalent average level of return, the risk associated with new portfolios is high (e.g. portfolio D versus portfolio D that posts the same average return but a higher risk; 34% vs. 20%). 12 One needs to be aware of the fact that the sampling period is not absolutely equivalent between the quarterly and annual data, because of the loss of the first half of 2003 with respect to annual data. 20 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

23 Aggregated data On the other hand, the weight of venture capital tends to decrease to the benefit of bonds and to a lesser extent to equities. For the lower part, we mention as an example the portfolio A with minimal variance (1% of venture capital against 5% for A) or the portfolio B with a minimum Sharpe ratio (3% of venture capital against 8% for portfolio B). For the upper part, we mention the portfolio C where there are no more equities in the portfolio (16% of venture capital against 22% for portfolio C). To summarise the impact of the correction on all portfolios, we see that the share of venture capital is reduced in portfolios. However, the weight given to venture capital remains substantial, notably in the portfolios that would be chosen by investors who are not very risk-averse (upper part of the frontier). 2.3 Introducing buyout funds into the portfolio In the previous section, we have considered the case of venture capital funds only. The other important category of private equity is buyout funds, which represent around 40% of the total number of funds. Due to a bigger size than venture capital funds, buyout funds represent more than 60% of the total private equity funds raised between 1998 and The following figures do represent the number of funds, which serve as the universe upon which Thomson Venture Economics calculates aggregated returns. The first figure shows raw numbers while the second one expresses for each year and for each category the number of funds as a proportion of the maximum number of funds for a given category in the whole sample (this peak was achieved in 2000 or 2001 depending on categories). In the previous section, we have chosen to begin our analysis in 1994 as it did appear a structural break in the number of venture capital funds covered by TVE at this time. The figures illustrate that in the case of buyouts, this break took place probably later, in So one should be cautious with returns of this segment before that date. Figure 10: Sample size for European returns 300 Number of funds All private equity Venture Capital Buyout Year Source: EVCA/CDC Ixis Capital Markets, based on data provided by Thomson Venture Economics Performance Measurement and Asset Allocation An EVCA Research Paper March

24 Aggregated data Figure 11: Sample size for European returns as proportion of maximum number of funds 100% 90% 80% All private equity Venture Capital Buyout Maximal number of funds in % 70% 60% 50% 40% 30% 20% 10% 0% Year Source: EVCA/CDC Ixis Capital Markets, based on data provided by Thomson Venture Economics The following figures investigate whether the pooled average TWR are sensible measures of the whole distribution of buyout funds returns, as they jointly represent the pooled average (the blue point) and the upper quartile (top of the vertical bar) and the lower quartile (bottom of the vertical bar). This is not the case, at least very less than in the case of venture capital (see above for the same representation for the venture capital case). For instance, one can see that in 1999, the pooled average was larger than the upper quartile (note that this is something which is possible in statistical terms the maximum return is equal to 1144% in a year). For 2001 and 2002, we see that the pooled return is near the upper quartile. This does induce a significant positive return for the pooled sample (+6.4% in 2001 and +1.3% in 2002) while the returns were negative for the large majority of funds. For comparison, we have the following statistics for the same two years: average return -5.5% and -6.2%; median return -1.4% and 9.5%; capital-weighted average return -6.4% and -6.9%. Due to this fact, we have decided to consider simple average as representative measures of buyout returns. 22 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

25 Aggregated data Figure 12: Dispersion of buyout returns ( ) Pooled Average 60 Return (% per year) Year Source: EVCA/CDC Ixis Capital Markets, based on data provided by Thomson Venture Economics An important point is whether the returns of buyout funds are affected by a stale pricing bias. We could not find any clear evidence on that point, at least much less than in the case of venture capital. First, there is no sign of positive autocorrelation in the returns of buyout funds. Second, the returns are only weakly related to lagged equities returns. One might note furthermore that: These results on the stale pricing problem are not dependent on the aggregation method for buyout funds. There is no clear evidence of autocorrelation whenever funds returns are aggregated as a pool, as a simple average or using committed capital weights; An analysis of US data shows that the limited evidence if any of stale pricing in the case of buyouts compared to the case of venture capital is again observed. Note, however, that the difference is marked stronger in the European case; Whereas, in the case of venture capital funds, the smoothing process is a satisfactory explanation of the difference between quarterly and annual returns characteristics, it is difficult to reconcile the apparent lack of smoothing process for buyout and the fact that the standard deviation of buyout returns and their correlation with equities returns both increase with annual data 13. This last point again underlines than one should be cautious with aggregated returns of buyouts, notably when one tries to compare them with other assets (including other private equity categories). 13 With the simple aggregation method, the standard deviation for annual returns is 18.8% versus 10.0% (annualized) for quarterly returns. The correlation between buyouts and equities annual returns is 76% versus 11% for quarterly returns. Performance Measurement and Asset Allocation An EVCA Research Paper March

26 Aggregated data Our analysis is based on the period (data were not made available to us for buyouts in 2003). The following table gives the whole set of statistics (including corrected figures for venture capital returns) used for the asset allocation problem 14. Table 4: Statistics used for the asset allocation problem Returns (%) Venture Capital Buyouts Bonds Equities Average Std deviation Correlation matrix Venture Capital Buyouts Bonds Equities VC BO Bonds Equities Source: EVCA/CDC Ixis Capital Markets, based on data provided by Thomson Venture Economics These statistics lead to the efficient frontier of portfolios represented in the following figure. By and large, the results are very favourable to buyouts. Its share goes from 17% in the minimum variance portfolio up to more than 95% in the portfolio where there are no more bonds (entitled the two assets portfolio in figure 13). From this point, its share decreases regularly being replaced by venture capital up to the maximum return portfolio (not represented here for readability of figure 13) where there are only venture capital funds. Note that the maximum proportion of equities is only 2.5% and that this is attained in the minimum variance portfolio. Note also that venture capital only appears in the final part of the curve (the riskier one). Figure 13: Efficient frontier with quarterly returns (portfolio composed of buyout, venture capital, public equities and bonds) Two assets portfolio 4.2% VC; 95.8% BO; 0% Equities; 0% Bonds Expected return (% per year) Minimum variance portfolio 0% VC; 17% BO; 2.5% Equities; 80.5% Bonds Max Sharpe ratio portfolio 0% VC; 26.5% BO; 2.0% Equities; 71.5% Bonds Risk (% per year) Source: EVCA/CDC Ixis Capital Markets, based on data provided by Thomson Venture Economics 14 Note that the average arithmetic return is largely higher for venture capital once we exclude the first two quarters of Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

27 Aggregated data 2.4 Concluding remarks In this chapter, we analysed the asset allocation problem of private equity compared with other assets from the perspective of aggregated data, which was reconstituted from individual funds. Among the various potential biases, which are discussed in the introduction of this study, we have insisted on a bias known as the stale pricing problem or the smoothing problem. It implies that for illiquid assets, measures of individual and joint (i.e. with other assets) risks are likely to be downward biased. This has potentially large consequences in an asset allocation framework. We have illustrated the extent to which venture capital returns are exposed to this bias and how to correct for this (either using lower frequency data or inferring the smoothing process from the whole structure of returns). For buyouts, results are less clear-cut. We suspect that there might some difficulties with the aggregation of individual buyout funds. We have notably illustrated that popular aggregated measures (such as pooled aggregates) are not totally convincing representative measures of the whole distribution of returns. Summarising, the results presented above show that even when accounting for the stale pricing problem, there is a large interest for the insertion of private equity funds in the portfolio of European institutional investors. In our opinion, two interpretations of this result can be advanced: Either it highlights the fact that interest in private equity is very high and investors should raise its weight relative to the present situation up to a bracket ranging from 5% to 10% of all assets. For, even after taking into account the corrections that are detrimental for private equity and keeping in mind that we are dealing with net returns whereas returns on other assets are gross, the quantitative results are very positive for private equity; Or it can be considered that the corrections made in this study, although they lead to notable differences from the original results, remain insufficient since they do not factor in a selection bias by not correcting the average of returns. Notably, this problem is posted to be important in the case of buyout funds as shown by the very high average return. The analysis on individual data proposed in the second part can help dealing with this indecision. Performance Measurement and Asset Allocation An EVCA Research Paper March

28 26 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

29 Cash flow based 3. European private equity funds A cash flow based performance analysis Christoph Kaserer Christian Diller Center for Entrepreneurial and Financial Studies (CEFS-TUM) Technische Universität München This part of the study is based on a data set on European private equity funds that has been provided by Thomson Venture Economics (TVE) 15. Before we look at the cash flow based performance analysis, we are going to describe shortly the data set used for this work. It should be noted that TVE uses the term private equity to describe the universe of all venture investing, buyout investing and mezzanine investing 16. Actually, we have been provided with various information related to the timing and size of cash flows, residual net asset values (NAV), fund size, vintage year, fund type, fund stage and liquidation status for a total of 794 funds. Some 14 of these funds have been funds of funds. We excluded these funds from our data set as they combine a number of single private equity funds and, hence, provide redundant information for the purpose of this study. Moreover, given the small sample size it will not be possible to draw general conclusions with respect to the performance of this particular fund type. As far as the different fund types and stages are concerned it should be noted that we use, in accordance with TVE, the following definitions: Type definitions: Venture capital funds (VC): TVE uses the term to describe the universe of venture investing. It does not include buyout investing, mezzanine investing, fund of fund investing or secondaries. Angel investors or business angels are also not be included in the definition. Buyout funds (BO): TVE uses the term to describe the universe of buyout investing and mezzanine investing. It does not include venture investing, fund of fund investing or secondaries. Angel investors or business angels are also not be included in the definition. Stage definitions: Early-stage (ES): A fund investment strategy involving investment in companies for product development and initial marketing, manufacturing and sales activities 17. Balanced/Diversified (B): A venture fund investment strategy that includes investment in portfolio companies at a variety of stages of development (seed, early-stage, later-stage). Development, later-stage and expansion: (DEV, LS & EX): Development funds provide for the major growth expansion of a company whose sales volume is increasing. Although the company has clearly made progress, it may not yet be showing a profit. The money invested is used to finance the initial development of the young company. Later stage fund investment involves financing the expansion of a company which is producing, shipping and increasing its sales volume Buyout (BO): TVE uses the term to describe the universe of buyout investing and mezzanine investing. It does not include venture investing, fund of fund investing or secondaries. Angel investors or business angels are also not be included in the definition. The definition involves e.g. leverage buyouts (LBOs), management buyouts (MBOs) and bridge financing. 15 TVE is recording private equity data for five different world regions. One of them is Europe. 16 Fund of fund investing and secondaries are also included in this broadest term. TVE is not using the term to include angel investors or business angels, real estate investments or other investing scenarios outside of the public market. 17 We have included seed and start-up funds in this definition. Performance Measurement and Asset Allocation An EVCA Research Paper March

30 Cash flow based As one can see from table 5, around 59% of the sample funds are venture capital funds, while the remaining 41% are categorised as buyout funds. The average fund size according to the TVE-data is m 17. Variation in fund size is considerably high, as the largest fund is 132 times as large as the median fund. Moreover, as one might expect, buyout funds are on average about 3.7 times as large as Venture capital funds. As far as the liquidation-status is concerned, it should be noted from table 6 that only 95 out of the total of 780 funds have been liquidated before the end of the sample period, ending 30 June The average size of the liquidated funds is considerably smaller than that of the non-liquidated funds. Evidently, the average fund size has become larger for more recent vintage years. This effect may be driven by the growth of the private equity industry over the 1990s. Table 5: Sample funds by size and type Type All funds VC funds BO funds No. of Funds in % 58.7% 41.3% Size in mio. Average Median Stdev Funds * Size 142, , , in % 27.9% 72.3% Table 6: Sample funds by liquidation status Type All funds liquidated funds non-liquidated funds No. of Funds in % 12.2% 87.8% Size in mio. Average Median Stdev Funds * Size 142, , , in % 3.5% 97.2% As far as the stage of the sample funds is concerned, it can be seen from Table 7 that one quarter are early stage funds. As one may expect, the size of the funds differs perceivably depending on their stage. 18 It should be noted that TVE is calculating the fund size on the basis of committed capital. 28 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

31 Cash flow based Finally, the vintage year distribution of the sample funds can be found in figure 14, the vintage year being the year of fund formation and its first draw down of capital. In accordance with the growth of the private equity industry during the 1990s an unprecedented vintage activity took place in the period 1997 to However, also during the period 1987 to 1996 a continuous fundraising activity at a fairly impressive level took place. With the exception of the year 1992 about 30 to 40 new funds entered the market every year during this period. Table 7: Sample funds by size and stage Venture Capital Funds Buyout Funds LS & DEV ES B & EX BO Late Stage/ Developed/ Buyout Stage All funds Early Stage Balanced Expansion Funds No. Of Observ in % 25.4% 14.9% 18.5% 41.3% Size in mio. Average Median Stdev Funds * Size 142, , , , , in % 9.8% 11.8% 6.2% 72.3% Figure 14: Number of funds by vintage year (number of funds: 780) VC BO Number of funds Year Performance Measurement and Asset Allocation An EVCA Research Paper March

32 Cash flow based 3.1 Cash flow characteristics of European private equity funds In this section we are describing the cash flow patterns of European private equity funds. The peak of aggregate takedowns (also called draw downs, i.e. the money committed by the investors or limited partners actually invested in the fund) as well as distributions or disbursements, i.e. the money returned by the fund managers (or General Partner) to the investors (or limited partners) is in the year 2000, as shown in figure 15. Takedowns of committed capital by all the sample funds aggregated to 18.4bn in this year; simultaneously, distributions aggregated to 13.5bn. It should be noted that according to EVCA reports the aggregated volume of funds raised in the European private equity industry in the year 2000 was almost 44bn. Hence, we can infer that for this particular year the sample of funds provided by TVE for the purpose of this study covers about 43% of the fund volume tracked by the EVCA. The growth in the private equity industry is strongly correlated with the performance of the public equity market. In fact, figure 15 impressively proofs that the growth of private equity investments during the 1990s was strongly correlated to the lasting positive stock market performance during this period. Figure 15: Time pattern of aggregated sample funds cash flows (number of funds: 780) Take down (TD) Distribution (D) Value in mio Year 30 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

33 Cash flow based Figure 16: Funds takedowns and public equity market performance (number of funds: 780) Take down (TD) MSCI-Europe Index Value in mio MSCI-Europe Index Year 0 As far as structural issues of cash flow patterns are concerned four questions appear in this context. First, how long does it typically take until the general partner has taken down the committed capital? Second, what is the typical time pattern of disbursement? Third, how long does it typically take for a limited partner to get back his invested capital? Fourth, are these patterns different depending on fund size? An answer to the first question is given by figure 17. The average fund draws down 25% of the total investment volume when starting its business. Within the first three years 63% of total committed capital is invested in the fund. It should be noted that according to Ljungqvist/Richardson (2002) the average US fund draws down 57% of the committed capital within the first three years. Moreover, it seems that capital drawdown is faster for venture capital funds than for buyout funds. However, the difference is not that large, as general partner of venture capital funds have drawn down 70% of capital within the first three years, while for buyout funds this ratio is about 60%. Finally, from figure 18 it can be seen that there is only a slight difference in the take down patterns between the various stages. Only early-stage and balanced funds take down their capital faster than the average funds. Performance Measurement and Asset Allocation An EVCA Research Paper March

34 Cash flow based Figure 17: Time pattern of take downs for different types of funds (number of funds: 780) 100% 90% Cumulative take down (%) 80% 70% 60% 50% 40% 30% 20% 10% 0% VC BO Total Lifetime of a fund in years Figure 18: Time pattern of take downs by funds stage (number of funds: 780) 100% 90% Cumulative take down (%) 80% 70% 60% 50% 40% 30% 20% 10% 0% ES B LS & DEV & EX BO Total Lifetime of a fund in years 32 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

35 Cash flow based Two questions have been raised in the context of disbursements. First, what can be said about typical time pattern of disbursements? Interestingly, from figure 19 it follows that average disbursements are distributed almost uniformly over a fund s lifetime. This is true; at least, if we ignore the relatively small distributions funds disburse in their first year and after the year 12 of their lifetime. In fact, our calculations show that 53% of total disbursements are paid out within the first six years. Figure 19: Time pattern of distributions for different types of funds (number of funds: 780) 100% Cumulative distribution (%) 90% 80% 70% 60% 50% 40% 30% VC BO Total 20% 10% 0% Lifetime of a fund in years Performance Measurement and Asset Allocation An EVCA Research Paper March

36 Cash flow based Figure 20: Time pattern of distributions by funds stage (number of funds: 780) Cumulative Distributions (%) 100% 90% 80% 70% 60% 50% 40% ES B LS & DEV & EX BO Total 30% 20% 10% 0% Lifetime of a fund in years However, this uniform distribution does not hold for the single fund stages as can be seen from figure 20. In fact, for later-stage funds it takes much longer to achieve a 50% distribution ratio compared with the average fund in our sample. The second question regarding disbursements is even more important for investors in private equity funds and relates to the payback issue. In fact, from a liquidity oriented perspective it may be very interesting to have an idea how long it takes on average to get back the money from a private equity investment. It is very interesting to see from figure 21 that for a European private equity fund investor, it takes 7.4 years to get the money back. Ljungqvist/Richardson (2002) report that for US private equity funds the payback period is slightly below seven years. It should be noted that this is the payback period an investor faces, if he allocates his money according to the size of single funds. Moreover, we can see that buyout funds have a lower payback period than venture capital funds. 34 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

37 Cash flow based Figure 21: Value weighted average payback period (number of funds: 780) Total VC BO Distribution takedowns in multiples Lifetime of a fund in years Finally, to answer the fourth question raised of cash flow patterns, we investigate whether the payback period is really different depending on a fund s size. As one can see from figure 22 it is not clear, at least at a first glance, whether the payback behaviour is significantly different for different fund size brackets. In fact, a statistical analysis reveals that the partial correlation coefficient between these two variables is negative, but statistically not significantly different from zero. Hence, we have to conclude that the payback pattern does not depend on fund size. Figure 22: Payback period and fund size (sample I, number of funds: 201) 19 Median of the payback period in month Fund size quantiles (1 = low; 10 = high) 19 It should be noted that TVE is calculating the fund size on the basis of committed capital. Performance Measurement and Asset Allocation An EVCA Research Paper March

38 Cash flow based Another question in this context is, whether payback pattern changed over time. Here it is presumed that funds with vintage years in the 1990s had shorter payback periods as they had better exit opportunities than funds founded during the eighties or even earlier. This is corroborated by figure 23, which indicates that the payback has become shorter the later the fund has been founded. In fact, the correlation coefficient between these two variables is -0.5 and statistically highly significant. Figure 23: Payback period and vintage year (sample I, number of funds: 201) 160 Median of the payback period in month Vintage year of the fund 3.2 Return/risk characteristics of European private equity funds It has already been mentioned that a private equity investment can be undertaken directly or indirectly via a private equity fund. Therefore, risk-/return characteristics of private equity investments can basically be defined from two different perspectives, either if we assess the return distribution of a company s specific investment or if we assess the return distribution of an investment in a private equity fund. As far as risk management issues are concerned the first perspective is especially relevant from the viewpoint of a general partner, as he is supposed to make congruent decisions with respect to the allocation of capital to portfolio firms. The second perspective is relevant for a private or institutional investor who considers acting as a limited partner, i.e. to invest money in a private equity fund. Hence, when talking about return distributions one should make clear as to what kind of return processes he is referring to: returns generated at the level of a single portfolio company or returns generated at the level of a private equity fund. 36 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

39 Cash flow based As already mentioned, in this study we are focussing on return distribution at the fund level. From an economic point of view, the most important characteristic of private equity investments are the missing or highly imperfect secondary markets. As a consequence, for any single fund investment there are only a few points in time for which transaction prices can be observed: when limited partners pay in their capital and when the investment is liquidated. Usually, such transactions do not happen very frequently. As a consequence, no intermediate series of historical returns is available and, hence, estimating the performance of a private equity fund becomes a difficult issue. It is well known that there are at least two solutions in this regard 20. The first is to estimate a private equity fund s return on the basis of net asset values (NAV). This is the approach followed in the first part of this study, where the reader can also find an exposition of the methodological problems arising in this context. To put it in a nutshell, the basic problem is that net asset values are subject to valuation biases and, hence, returns estimated on this basis will be biased as well. The idea of the approach followed in this chapter is to circumvent these problems by inferring the private equity fund s return only on the basis of its cash flow history. In this way one could presume that an unbiased return estimation will be possible. However, even under this approach serious methodological problems will arise. They are discussed in the following section The cash flow based IRR as a return measure It is often argued that the return on a private equity investment should be measured by using a value (or dollar) weighted return measure, i.e. the internal rate of return (IRR). The IRR gives the discount rate that makes the present value of all cash flows equal to zero. Mathematically, the IRR can be expressed in the following way: Here T is the lifetime of the fund and CF t is the cash flow accrued over period t. The rationale behind this is the following. A value weighted return is heavily influenced by the time pattern of cash flows on which its calculation is based, while a time weighted return is defined as being independent of this time pattern 21. If a fund manager is interested in assessing the performance of an open-end public market investment fund, he will not have control over time patterns of cash flows and his performance should be measured on the basis of a time weighted return. In fact, this is what is done in quoted mutual funds open to retail and institutional investors. Things can be different, if one looks at a private equity fund. It could be argued that the general partner of such a fund has, at least to a certain extent, control over the time pattern of cash flows. If this is the case, it is asserted, his performance should be measured on the basis of a value-weighted return. 20 A detailed summary with respect to the solutions proposed in the literature can be found in Kaserer/Wagner/Achleitner (2004). 21 It should be noted that a time weighted return over a period of length T is simply the geometric mean of the single period return realizations; a value-weighted return can be regarded as a weighted average of these returns. Performance Measurement and Asset Allocation An EVCA Research Paper March

40 Cash flow based To understand the problems associated with this approach we use the following example: Table 8: Example for two funds with cash flows and NAVs T R t 10% 20% 5% (A) NAV t (A) CF t (B) NAV t (B) CF t Source: EVCA/CEFS-TUM Here, R t is assumed to be the true asset return of both funds A and B. This return normally is unobservable. The NAVs are unbiased and reflect the market value of residual assets. Of course, the time weighted return of both funds is the same, specifically it is equal to 11.5% in this example. Using this return measure, both fund managers would be attributed the same performance. However, due to the different time pattern of cash flows the IRR differs. Specifically, fund A has an IRR of 13.8%, while it is equal to 11.1% for fund B. The question is, does it make sense to say that the manager of fund A has performed better than the manager of fund B? As we know from standard textbooks, such a conclusion is not generally possible because of the reinvestment hypothesis used to calculate the IRR. In fact, what is assumed is that cash flows generated by the fund can be reinvested at an interest rate equal to the IRR. This, of course, makes no sense! First, it s not possible to invest the distribution in a private equity fund with an identical return and second it would lead to different reinvestment rates for cash flows accruing at the same time. If instead a correct reinvestment hypothesis is used, for instance that all cash flows are reinvested in an equal and constant interest rate, than it could happen that the ranking of two investment alternatives in terms of present value of cash flows is different for different interest rates. It is said, in this case, that the present value functions of the two investment alternatives intersect. The example above has been constructed in a way that such an intersection does not occur. Therefore, for every constant non-negative interest rate the present or terminal value of cash flows of fund A will be higher compared to fund B. In this specific case, the IRR can be used for ranking the funds, if the mentioned reinvestment hypothesis is accepted as purposeful. If, as an alternative, we assume that cash flows are reinvested on the public market then, due to varying public market returns, the ranking of both funds cannot be determined by their IRR, even if the specific assumptions used in this example hold. To sum up, the IRR in general cannot be regarded as a performance measure. However, under some very specific assumptions it could be said that the IRR could be regarded as an absolute performance measure. The IRR and the multiples are two established metrics to measure the performance of a fund in the private equity industry. Because of the above-described disadvantages of the IRR, we will develop a cash flow based relative performance measure in the following part. 38 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

41 Cash flow based The cash flow based PME as a return measure In order to see that under the alternative reinvestment hypothesis, where it is assumed that cash flows are reinvested in a public market instrument, the IRR cannot be regarded as a performance measure, we could have a look at the above presented example. Assume that R t is equal to the return of a public stock market index. If cash flows are reinvested in this index the terminal wealth of a given initial investment is the same for either fund and corresponds to a yearly return of 11.5%. Hence, under this reinvestment hypothesis both funds would perform identically. Therefore, a performance measure using this reinvestment hypothesis leads to the same result as using a time weighted return measure. We will see that the public market equivalent measure (PME) is a return measure with exactly this characteristic 22. This is important as calculating a time weighted return for a private equity fund normally requires the usage of NAVs. As we would like to avoid using NAVs due to their potential distortion, it is important to see that the PME-method is a way to estimate an admittedly very specific kind of a time weighted return without using NAVs. In order to see the mechanics of the PME-method the presented example is slightly modified in the following way: Table 9: Example for calculating the PME with different market returns Terminal T Wealth PME (A) R It 25% 20% 15% (A) CF t (B) R It 0% 0% 0% (B) CF t In this scenario we still have to deal with the same funds as before. However, the difference is that we assume that they are on the market at different calendar times. R It gives the return of a public market index over period t 23. In the example above, we assume that the two funds exist at different calendar times with different public market index returns. The index return R It for fund A is written down in row (A), row (B) represents fund B respectively. Using the hypothesis that cash flows are reinvested in this public market index, the terminal wealth achieved by an investor investing in either the index or one private equity fund can be calculated straightforwardly. The result is given above. What is interesting to see is that fund A, although it has a higher IRR than fund B, has a performance relative to the market index that is worse than the relative performance of fund B. This is because the cash flows related to both funds occur at different calendar times. Hence, from this perspective one could say that, in fact, the management of fund B performed better than the management of fund A. This result is opposite to the result obtained by using the IRR. Therefore, it should be emphasised that there is no predictable way in which IRRs are transformed into a PME based performance measure. 22 This is an important difference to similar methods proposed in the literature. For instance, Rouvinez (2003) puts forward the idea to assume that cash flows generated by a private equity fund are reinvested at a constant interest rate. In this case, of course, one obtains a ranking that will correspond to a time weighted return ranking only by chance. Moreover, this method has not the appealing characteristic of ranking the fund manager relative to a public market benchmark. We therefore do not follow the method proposed by Rouvinez. Another method is that proposed by Chen et al. (2002). They assume that cash flows are reinvested at the IRR. According to what has been said before it is obvious that we will not follow this idea. 23 It is not important here whether this is a stock or a bond or another asset class index. We only assume that this is a public market instrument where the investor could invest at any given point in time. Performance Measurement and Asset Allocation An EVCA Research Paper March

42 Cash flow based Moreover, the reader should be reminded that the method we are proposing is not completely new to the private equity industry. In fact, the so-called Index Method proposed by Bannock is, basically, equivalent to the PME based approach. There it is assumed, too, that cash flows generated by a private equity fund are reinvested in a public market index. Maybe, the reader not familiar with this approach might wonder in this context whether our example would still be meaningful, if we allow for more than a single draw down. To show that this is, in fact, the case, we assume that the first draw down in period t=0 is only 50 for both funds. As a consequence, there is an additional draw down in period t=1. We suppose this to be equal to 62.5 for fund A and 50 for fund B. The terminal wealth of total draw downs, in this case, would still be for fund A and 100 for fund B 24. Hence, the PME is unaffected, which is, of course, a result of the particular way draw downs have been chosen. What is more important, the PME still can be interpreted as the amount of money that an investor would have to invest in a public market index in order to end up with the same terminal wealth as if he would have invested one Euro, in terms of present value of all draw downs, in the private equity fund 25. By generalising these considerations we can derive the PME approach. The question simply is the following: Given that the investor invests in terms of present value 1 in a private equity fund, how many Euros would he have to invest in a given public market index in order to end up with the same terminal wealth? The PME is exactly the answer to this question. It is nothing else than the ratio of the terminal wealth obtained under the mentioned reinvestment hypothesis when investing in a private equity fund compared to the terminal wealth obtained when investing the same amount of money in the given public market index. The fund with the better performance relative to such an index has the higher PME. Hence, the PME is a relative performance measure. Mathematically, it is defined as follows: Here, R It is the net return of a public market index in period t, while cft is the normalized positive cash flow (distribution) of the private equity fund in period t 26. As we can only observe the returns on a market index that are gross of management fees, we will make the following correction in this study: For an equity index we assume management fees to be equal to 50bp per year, while for a bond index these fees are assumed to be equal to 20 bp. Hence, the net yearly return is equal the gross yearly return, as indicated by the index performance, times and times respectively. 24 This must hold because figures have been chosen in a way that the present value of draw downs is still 100 in both cases. 25 In fact, the terminal wealth calculation for a one Euro investment in the private equity fund is as follows: The present value of drawdowns for fund A is /1.25=100. Hence, for a 1 investment the terminal wealth is 1* *1= The terminal value of a 0.86 investment in the public market index is 0.86*1.25*1.2*1.15= The present value of drawdowns for fund B is 50+50/1=100. Hence, for a 1 investment the terminal wealth is 0.6* *1=1.23. Again, the terminal value of a 1.23 investment in the public market index is 1.23*13= In this context, positive cash flows are normalized by dividing every single positive cash flow accruing in period 1 or later with the present value of all investments, i.e. the present value of all negative cash flows. In this way the cash flows are normalized to an initial investment with a present value of Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

43 Cash flow based One last methodological remark with respect to this example should be made. From an investor s viewpoint the most important question is, of course, whether a private equity investment has a higher expected return than a public market investment. It should be noted that this question can be answered in two different ways. First, one can compare the public and the private investment on the basis of the PME. If there is more than one fund in the data universe the cross-sectional PME can be calculated as an average. In fact, assuming that funds A and B are our data universe we can say that for this sample the average PME is 1.045, indicating that on average the terminal wealth of a private equity investment is times as high as the average terminal wealth of a public market investment. Second, the out-performance of private equity can be calculated as the average of a return difference. In this case one calculates first the cross-sectional average performance of all the funds on the basis of their terminal wealth. This average return is then compared with the average of all public market investment returns that could have been realised as an alternative to the private equity investment. In our example the average three-year performance of the private equity funds is 35.8%, while the average three-year performance of the public market index is 36.2%. This may be quite surprising as we can see now that the ranking between the private equity funds and the public market can depend on the way returns are averaged. In our example the difference simply was that the PME is an average return ratio while the second method corresponds to an average return difference. In general, an investor would be more interested in estimating the return difference of two different investment alternatives, as this difference indicates the gain or loss in wealth per Euro invested when realising one strategy instead of the other. For this reason we do not stop with calculating the PME. Instead we use it for deriving a result with respect to the return difference between a private equity fund investment and a specific public market investment. This is done as follows. In order to transform the PME into an expected return we introduce the following definitions: Here, I t is the period t value of the public market performance index used for reinvesting private equity cash flows. Note, that a tilde indicates that we have to deal with a random variable. If the period is set equal to one year, y is the continuously compounded rate of return on a public market index investment. According to our definitions the return of a private equity fund over its whole lifetime can be written as: Here, it should be noted that the left hand side of the preceding equation gives the terminal wealth of a 1 private equity investment. The first expression on the right hand side gives the terminal wealth of a 1 investment in the public market index. According to our definition of the PME, we need a public market investment of PME* 1 in order to end up with the same terminal value as with the private equity fund. Performance Measurement and Asset Allocation An EVCA Research Paper March

44 Cash flow based Therefore, the right hand side has to be multiplied with PME. Now, by defining and using the definition of the total private equity return in the equation before we get: Assuming y and x to be identically and independently distributed (iid) the expected continuously compounded yearly returns can be derived as follows: Taking into account that σ y and σ x defines the standard deviation of the random variables x and y, the expectation of the yearly compounded rate of return is defined as follows: Risk characteristics of cash flow based returns As far as the IRR-measure is concerned, risk characteristics can simply be derived from calculating distribution parameters. For this purpose we will present the most common parameters used in the literature. These are the average, the median, the standard deviation, as well as the highest and lowest realised IRRs. For the PME the same distribution parameters can be calculated. However, we will be more interested in inferring the risk characteristics of private equity returns calculated on the basis of the PME approach. Under the already introduced assumption that x and y are identically and independently distributed (iid) it follows: From this it follows that the variance of the periodic yearly returns is calculated as follows: 42 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

45 Cash flow based Finally, it should be noted that under this approach it follows that the correlation coefficient of the continuously compounded yearly returns of a private equity investment and a public market index investment is defined as follows: Correlation characteristics of different reinvestment hypotheses In the preceding sections we did not make any specific assumptions with respect to the public market instrument, which is used for reinvesting a private equity fund s cash flows. For our empirical analysis we have, of course, to make specific assumptions with respect to the instruments used. For this purpose we will allow for two different strategies: 1) Cash flows are reinvested in the MSCI Europe Equity Index, 2) Cash flows are reinvested in the J.P. Morgan European Government Bond Index. Given this, the following two additional questions arise with respect to the correlation structure of the private equity investment: First, assuming that alternative 1) is realised, what is the correlation structure of the private equity investment return with the bond market? Second, assuming that alternative 2) is realised, what is the correlation structure of the private equity investment return with the equity market? The answers can be given in the context of the PME-approach presented here. In order to make things precise, let us assume that the formula introduced in the two preceding sections refer to alternative 1), i.e. a reinvestment in a public equity market index. If, instead, we would like to refer to alternative 2), i.e. a reinvestment in a public bond market index, we introduce the following formula: Here, R Bt is the return on the bond index in period t. The return of a private equity fund over its whole lifetime is then written as: with BME defined as the public bond market equivalent: Now, the total private equity return realised under alternative 2) can be written as: Performance Measurement and Asset Allocation An EVCA Research Paper March

46 Cash flow based Assuming x B and z to be identically and independently distributed (iid) expected continuously compounded yearly returns can be derived as follows: Taking into account that σ z and σ xb defines the standard deviation of the random variables z and x B, the expectation of the yearly compounded rate of return is defined as follows: Under the already introduced assumption that x B and z are iid it follows: From this it derives that the variance of the periodic yearly returns is calculated as follows: The correlation coefficient of the continuously compounded yearly returns of a private equity investment and a public bond market investment is defined as follows: Finally, for the correlation structures of private equity returns under alternative 1) with the public equity market returns and of private equity returns under alternative 2) with the public bond market returns it follows: 44 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

47 Cash flow based Increasing the data universe Before presenting the results in the next section we have to deal with a problem caused by the limited scope of our data set. It has been reported at the beginning of this chapter that out of a total of 780 funds we have 95 funds that have already been liquidated. Of course, inferring the performance of a fund on the basis of its cash flows requires knowing its whole cash flow history. In principle, this is only possible after a fund s liquidation. However, given that the age of the liquidated funds in our sample is about 13 years, one can easily see that restricting the analysis to liquidated funds could cause a bias as more recently founded funds would be systematically left out. From figure 26 and figure 30 it can easily be taken that by doing so we would exclude funds that had a very good performance. Restricting the analysis to liquidated funds only would, therefore, introduce a negative selection bias into the analysis. In order to mitigate this problem different approaches have been developed in the literature. Basically, their starting point is the question whether it may be possible to assume future cash flows of a fund sufficiently well on basis of its cash flow history. If this is the case, it would be possible to include not yet liquidated funds in the cash flow analysis without incurring a systematic bias in the analysis. Unfortunately, a closer look reveals that the problem is more difficult than it may seem at first. For instance, Kaplan/Schoar (2002) pursued the idea that if the correlation of the IRR (NAV) with the IRR (CF) 27 is high, performance figures based on one of the return measures should lead to similar results. As they found this correlation coefficient to be about 0.9 for funds with an age of at least five years, they concluded that including on top of the liquidated funds all funds with an age of at least five years could enlarge the data universe in their study. For this group of not liquidated funds they used the IRR (NAV) instead of the IRR (CF). This method, however, has some severe drawbacks. The fact that the IRR (NAV) and the IRR (CF) are highly correlated implies only that their changes are correlated over the funds lifetime. However, this does not imply that they are almost on the same level. This can easily be seen in figure 24. Even one or two years before liquidation both IRR-measures differ substantially. Hence, any approach stating that funds with a given minimum age would be included in the sample, like the one used by Kaplan/Schoar (2002), is not suitable for enlarging the data universe. 27 For an explanation of the meaning of these two different IRR definitions cf. section Basically, the first is an IRR treating the NAV as a last cash flow while the first is an IRR based on accrued cash flows only. Performance Measurement and Asset Allocation An EVCA Research Paper March

48 Cash flow based Figure 24: Average IRR (NAV) and IRR (CF) over a funds lifetime for liquidated funds (number of funds: 95) 20% 0% IRR (NAV)/(CF) in % -20% -40% -60% -80% -100% IRR (NAV) IRR (CF) Liquidation period in years We, therefore, propose another way for enlarging the data set. First of all, from figure 24 it follows that for doing this we have to make sure that there is no significant difference between the IRR (NAV) and IRR (CF). Basically, our idea is the following. When calculating the IRR (NAV) the residual NAV is considered as a last cash flow paid by the fund. Of course, the valuation bias caused by this approach is the least important the smaller the impact of this last hypothetical cash flow is. The first and most obvious way to make sure that this impact is small is to integrate only those funds in the sample whose residual NAV is small relative to the sum of absolute cash flows already paid in or out 28. Therefore, we will integrate a non-liquidated fund into our sample only if it meets the following condition: Here, RNAV N stands for the residual net asset value of a fund at end of period N 29. Of course, q is a parameter that has to be chosen in an arbitrary way. In this study we will work with a q equal to 0.1 for one sample and 0.2 for another respectively. Hence, we add non-liquidated funds to our sample if their residual value is not higher than 10% for one sample and 20% for another sample, respectively, of the undiscounted sum of the absolute value of all previously accrued cash flows. For these funds the IRR (CF) is calculated under the assumption that the residual net asset value represents a hypothetical distribution accrued by the end of our observation period. 28 A similar idea can be found in Meyer/Weidig (2003). 29 In principle, it would be better to use discounted cash flows in the denominator rather than undiscounted. However, we believe that this difference is not so important, given that it can be taken into account by adjusting the parameter q. Therefore, we stick to the approach presented here, as in this case the condition can be easily transformed into another very simple condition. 46 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

49 Cash flow based The condition stated above can be simplified by taking into account that the sum of cash flows can be rewritten in the following way: Here TD t is the capital paid into the fund at time t, while D t is the distribution paid by the fund at time t. Hence, in this way we disentangle draw downs from distributions. Now, taking into account that the following definitions hold the initial condition stating which funds should be added to the data set can be rewritten as follows: All funds that are not liquidated by 30 June 2003, and satisfying this condition for q=0.1 together with the liquidated funds are put in sample I, while all funds satisfying this condition for q=0.2 together with all liquidated funds are put into sample II. As we will see, sample I has 201 funds, while sample II has 263 funds. This is a perceivable increase given that we have only 95 liquidated funds Results with respect to IRR In this section we present the results that have been obtained with respect to IRRs. Initially we present in figure 25 the result obtained with respect to NAV based IRRs (IRR (NAV)). This figure is directly taken from TVE, without further examination towards accuracy from our side. As one can see, funds with vintage years after 1997 have performed unsatisfactory on the basis of the IRR (NAV). Evidently, this is due to a decline in market prices since 2000 and the induced pressure to decrease the book values of portfolio companies. Additionally, the J-curve phenomenon is responsible for the negative IRR (NAV) of the funds founded in the years 2000 till 2003, because the initial years of a fund are characteristic for negative cash flows (take downs) and fees which are paid to the general partner. Performance Measurement and Asset Allocation An EVCA Research Paper March

50 Cash flow based Figure 25: Average IRR (NAV) by vintage year (number of funds: 780) IRR (NAV) in % Year Source: Thomson Venture Economics Moreover, there is a second effect that can be seen from figure 25. Funds with vintage years 1992 to 1997 performed rather well on the basis of the IRR (NAV). By restricting our sample to liquidated funds only we create a downward bias, as one can assume that several funds with vintage years belonging to this period are not yet liquidated. This is an important motivation for increasing the data universe according to the method described in the preceding chapter. In this way we would include more funds with vintage years in the nineties in our sample. Simultaneously we can control for the selection bias by integrating only funds with small relative residual asset values. The private equity fund performance on the basis of IRR (CF) becomes visible in table 10. First of all, this table gives an overview of the sample used. As already described in the preceding section, we extended the data universe by generating samples I and II on top of the sample consisting of liquidated funds only. It should be noted that venture capital as well as buyout funds have almost identical weights by number of funds in our samples. 48 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

51 Cash flow based According to what has been said previously, the IRRs (CF) of samples I and II are perceivably higher than the IRR (CF) of the sample consisting of liquidated funds. In fact, starting with an IRR (CF) of 10% for the liquidated sample we reach an IRR (CF) of 12% for sample I and 14% for sample II. These figures are slightly lower than the results of Kaplan/Schoar (2003) for the US-market, as they report an average IRR of 17%. For buyout funds they report an IRR of 18%, for venture capital funds of 17%. Also these results are slightly higher than ours, as one can see in table 11. Simultaneously, the standard deviation of the IRRs increases significantly when expanding the data universe. Our method to include well performing as well as bad performing funds in the sample, has a positive the net effect and drives the IRR upward. Table 10: Size, IRR (CF) and payback of our samples Liquidated Funds Sample I Sample II Number of Ob Type VC BO Size in mio Average Stdev IRR(CF) Average 10.00% 11.98% 14.00% Min % % % Max % % % Stdev 17.80% 16.53% 22.80% Payback in month Average Stdev It also should be noted that the average payback in all the three different sub-samples is about 90 months or 7.5 to 7.8 years. This is nearly the same than the value-weighted average payback period of the total sample. Performance Measurement and Asset Allocation An EVCA Research Paper March

52 Cash flow based Table 11: Size, IRR (CF) and payback period of our samples by different fund types Size Sample: Liquidated funds Sample I Sample II VC BO VC BO VC BO Average Median Stdev IRR (CF) Average 7.32% 12.63% 10.57% 13.39% 12.50% 15.61% Median 4.77% 9.79% 7.72% 10.87% 7.40% 11.06% Min % % % % % % Max % 88.05% % 88.05% % % Stdev 17.82% 17.66% 16.92% 16.09% 24.95% 20.51% Payback in month Average Median Stdev Number of Observations Table 12: IRR (CF) minus contemporary MSCI Europe return Excess-IRR(CF) to MSCI Europe VC BO Total Liquidated Funds Average -2.27% 3.37% 0.58% Median -4.17% -0.77% -2.70% Min % % % Max 90.99% 84.13% 90.99% Stdev 17.41% 19.14% 18.42% Number of Observations Sample I Average 3.62% 5.26% 4.44% Median -1.37% 1.61% 0.63% Min % % % Max % 84.13% % Stdev 24.27% 17.08% 20.96% Number of Observations Sample II Average 5.15% 8.21% 6.69% Median 0.59% 3.46% 1.65% Min % % % Max % % % Stdev 27.07% 21.62% 24.49% Number of Observations Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

53 Cash flow based Table 12 reports the excess IRR (CF) of different sub-samples. This excess return is defined as the IRR (CF) of a single fund minus the IRR of the MSCI Europe index realised over the lifetime of the fund. For the cross-sectional statistics that are reported here, one can see, that in most of the cases the excess IRRs are positive. Table 13: IRR (CF) minus contemporary J.P. Morgan Government Bond return Excess-IRR(CF) to J.P. Morgan Govt. Bond Index VC BO Total Liquidated Funds Average 0.93% 6.55% 3.77% Median -2.92% 3.33% 0.95% Min % % % Max 98.13% 85.04% 98.13% Stdev 17.95% 18.05% 18.13% Number of Observations Sample I Average 4.69% 6.22% 5.45% Median 0.70% 3.33% 1.28% Min % % % Max % 85.04% % Stdev 22.12% 16.22% 19.38% Number of Observations Sample II Average 5.10% 8.23% 6.67% Median 0.64% 3.53% 1.71% Min % % % Max % % % Stdev 25.07% 20.55% 22.92% Number of Observations Moreover, buyout funds seem to have consistently higher IRRs than venture capital funds. A similar picture is presented in table 13 where the excess returns are given with respect to the J.P. Morgan Government Bond index. The IRRs of different vintage years can be inferred from figure 26. One can presume, funds that have been founded later have, on average, a higher IRR. The correlation coefficient of both variables is 0.4 and statistically highly significant. Performance Measurement and Asset Allocation An EVCA Research Paper March

54 Cash flow based Figure 26: IRR (CF) by vintage year 50% Median of the IRR (CF) 40% 30% 20% 10% 0% Vintage year of the fund A further aspect to look at is whether the IRR (CF) is different depending on the size of the fund. Based on the data presented in figure 27 no clear-cut answer to this question is possible. However, by calculating the coefficient of correlation one can see that this is positive and statistically highly significant. Hence, as far as the IRR (CF) is concerned we have to conclude that fund size has a positive impact on performance. Figure 27: IRR (CF) by fund size 18% 16% 14% Median of the IRR (CF) 12% 10% 8% 6% 4% 2% 0% Fund size quantiles (1 = low; 10 = high) 52 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

55 Cash flow based Additionally, it seems intriguing to find out if the structure of cash flows is related to performance measured in terms of IRR (CF). One would presume that well performing funds should be able to return the money earlier to investors and, hence, that there should be a negative association between the IRR (CF) and the length of the payback period, as it is indicated in figure 28. Moreover, the correlation coefficient between the two variables is negative and highly significant. Figure 28: IRR (CF) and payback period 40% 30% Median of the IRR (CF) 20% 10% 0% Payback period quantiles (1 = low; 10 = high) Relative Performance Characteristics The relative performance measures have already been introduced under In this section we will present the empirical results with respect to the PME and BME as well as with respect to the index and private equity funds returns R l, R B and R PE. We have chosen two different alternative indexes for calculating the public market equivalent. First, we used a public equity index, specifically the MSCI Europe index 30. Alternatively we used a public bond index. As we are performing a European study we decided to use a European government bond index, specifically we opted for the J.P. Morgan European Government Bond Performance Index. However, this index is only available back to As we need a longer index history we used the REXP index for periods from 1993 backwards We did not opt for one of the STOXX indexes, as they are available only back to The MSCI Europe has a much longer history. However, one can imagine that both indexes are highly correlated. 31 The REXP is a performance index of German treasury bonds over the whole maturity range. Performance Measurement and Asset Allocation An EVCA Research Paper March

56 Cash flow based Finally, we would like to emphasize again that we assumed the index investment not to be free of cost. This is necessary as otherwise a comparison between private equity returns, which are net of management fees, and public market index returns, which basically assume cost free investing, would be biased against the private equity industry. Of course, it is difficult to make a precise assessment of transaction costs, including management fees, associated with an investment in a public equity or bond market. These costs may differ from country to country as well as from investor to investor. Therefore, we finally agreed to assume transaction costs of 50bp per year for a public equity investment and 20bp for a public bond investment. Having said this we can now present our results. First of all, table 14 gives the distribution of PME for our three different sample definitions as well as different fund types. The average PME is only larger than the one for sample II, while the value-weighted average is larger than the one for sample I and II. Moreover, we can see that there are obviously some good performing funds with very high PMEs, but also some poor performers with PMEs close to zero. Also the standard deviation is rather high. Table 14: PME of private equity funds by sample definition PME VC BO Total Liquidated Funds Average Median Min Max Stdev value-weighted PME 0.94 Sample I Average Median Min Max Stdev value-weighted PME 1.04 Sample II Average Median Min Max Stdev value-weighted PME 1.16 Again we have to question whether the performance of the sample funds is different among different size brackets. Figure 29 gives the impression that there is no relationship between size and performance measured in terms of the PME. In fact, this is also true from a statistical point of view, as no significant correlation can be detected between these two variables. 54 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

57 Cash flow based Figure 29: PME and fund size Median of the PME Fund size quantiles (1 = low; 10 = high) As far as the relationship of the PME with the vintage year is concerned figure 30 gives a seemingly clear picture: the later the vintage year, the higher the PME on average. This is also true from a statistical point of view as there is a significant positive correlation between these two variables. This corroborates the view that private equity funds with vintage years during the nineties performed especially well. Figure 30: PME and vintage year Median of the PME Vintage year of the fund Performance Measurement and Asset Allocation An EVCA Research Paper March

58 Cash flow based Finally, we investigated if the structure of cash flows is related to performance measured in terms of PME. One would presume that well performing funds should be able to return the money earlier to investors and, hence, there should be a negative association between the PME and the length of the payback period. This is, in fact, true and is visualised in figure 31. Moreover, the correlation coefficient between the two variables is negative and highly significant. Figure 31: PME and payback Median of the PME Payback period quantiles (1 = low; 10 = high) As a second step we calculated the private equity returns RPE based on the PME approach. As shown in table 15 to table 19 the average yearly return of an investment in the MSCI Europe was 11.46% over the period with a standard deviation of 18.06%. Assuming a risk free interest rate of 3% the Sharpe ratio reaches 46.83%. The expected PME-based return of a private equity investment during this period was 8.77% for the sample of liquidated funds, 9.79% for the extended sample I and 10.35% for the extended sample II. The standard deviation is in a close range of 19% to 20%. For this reason, and taking into account that the return difference of private equity is always negative with respect to public equity, the Sharpe ratios for the private equity funds are distinctly lower than for the diversified public equity market investment. Finally, the PMEbased correlation coefficient between the private equity and the public equity returns are, depending on the sample definition, between 0.93 and Given the definition of the investment strategy, this is not surprising as distributions are reinvested in the public market index. An alternative to this is that cash flows generated by private equity funds are reinvested in a public bond market index. For that purpose we used the J. P. Morgan European Government Bond Performance Index chained up with the REXP Index in order to cover periods backward from The results are presented in the tables below. The average government bond index return over the period 1972 to 2003 was 7.84% with a standard deviation of 4.57%. This leads to a Sharpe ratio of 105%. 56 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

59 Cash flow based Compared the BME based private equity return under this reinvestment hypothesis is 6.95% for the sample of liquidated funds with a standard deviation of 8.23%. For sample extension I and II the rates of return are 8.13% and 8.15% with standard deviations of 8.98% and 10.97% respectively. Sharpe ratios are between 47% and 57% and therefore higher than for the public equity investment. Correlation coefficients with the bond market investment are between 43% and 53%. Table 15: PME and BME-based private equity and public market returns (liquidated funds, Returns based on a reinvestment of private equity distributions in public market indexes) Sample: Liquidated Funds J.P.M. European Govt. Index Historic Return 7.84% Standard deviation 4.57% Sharpe Ratio % Private Equity Estimated Return 6.95% Standard deviation 8.23% Sharpe Ratio 48.00% Coefficient of Correlation (1) corr[x,z] (2) corr[xb,y] corr[msci,jpm] Number of Observations 95 MSCI Europe Historic Return 11.46% Standard deviation 18.06% Sharpe Ratio 46.83% Private Equity Estimated Return 8.77% Standard deviation 18.88% Sharpe Ratio 30.58% Coefficient of Correlation Table 16: PME and-bme based private equity and public market returns (sample I, Returns based on a reinvestment of private equity distributions in public market indexes) Sample I J.P.M. European Govt. Index Historic Return 7.84% Standard deviation 4.57% Sharpe Ratio % Private Equity Estimated Return 8.13% Standard deviation 8.98% Sharpe Ratio 57.13% Coefficient of Correlation (1) corr[x,z] (2) corr[xb,y] corr[msci,jpm] Number of Oberservations 201 MSCI Europe Historic Return 11.46% Standard deviation 18.06% Sharpe Ratio 46.83% Private Equity Estimated Return 9.79% Standard deviation 18.99% Sharpe Ratio 35.78% Coefficient of Correlation Performance Measurement and Asset Allocation An EVCA Research Paper March

60 Cash flow based Table 17: PME and BME-based private equity and public market returns (sample II, Returns based on a reinvestment of private equity distributions in public market indexes) Sample II J.P.M. European Govt. Index Historic Return 7.84% Standard deviation 4.57% Sharpe Ratio % Private Equity Estimated Return 8.15% Standard deviation 10.97% Sharpe Ratio 46.97% Coefficient of Correlation (1) corr[x,z] (2) corr[xb,y] corr[msci,jpm] Number of Observations 263 MSCI Europe Historic Return 11.46% Standard deviation 18.06% Sharpe Ratio 46.83% Private Equity Estimated Return 10.35% Standard deviation 19.95% Sharpe Ratio 36.83% Coefficient of Correlation Table 18: PME and BME-based private equity and public market returns (sample I, buyout funds, Returns based on a reinvestment of private equity distributions in public market indexes) Sample I: Buy-out funds only J.P.M. European Govt. Index Historic Return 7.84% Standard deviation 4.57% Sharpe Ratio % Private Equity Estimated Return 7.93% Standard deviation 7.58% Sharpe Ratio 65.09% Coefficient of Correlation (1) corr[x,z] (2) corr[xb,y] corr[msci,jpm] Number of Observations 101 MSCI Europe Historic Return 11.46% Standard deviation 18.06% Sharpe Ratio 46.83% Private Equity Estimated Return 9.71% Standard deviation 18.70% Sharpe Ratio 35.88% Coefficient of Correlation From the tables 18 and 19 one can see that the return difference between buyout and venture capital funds is rather small under the PME approach. 58 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

61 Cash flow based Table 19: PME and BME-based private equity and public market returns (sample I, venture capital funds, Returns based on a reinvestment of private equity distributions in public market indexes) Sample I: Venture Capital Funds only J.P.M. European Govt. Index Historic Return 7.84% Standard deviation 4.57% Sharpe Ratio % Private Equity Estimated Return 8.33% Standard deviation 10.24% Sharpe Ratio 52.06% Coefficient of Correlation (1) corr[x,z] (2) corr[xb,y] corr[msci,jpm] Number of Observations 100 MSCI Europe Historic Return 11.46% Standard deviation 18.06% Sharpe Ratio 46.83% Private Equity Estimated Return 9.88% Standard deviation 19.30% Sharpe Ratio 35.67% Coefficient of Correlation Finally, we once more presume that the private equity returns are higher for funds with later vintage years. For this purpose we recalculated the returns for the funds in sample I, assuming that only funds with vintage years starting from 1989 are considered. The results are presented in table 20. As one can see, our presumption is correct. This sub-sample of private equity funds now generates an out-performance also with respect to the public market index. Table 20: PME and BME-based private equity and public market returns (sample I, Returns based on a reinvestment of private equity distributions in public market indexes) Sample I: Funds with a Vintage year later than 1989 J.P.M. European Govt. Index Historic Return 7.84% Standard deviation 4.57% Sharpe Ratio % Private Equity Estimated Return 10.39% Standard deviation 10.62% Sharpe Ratio 69.59% Coefficient of Correlation (1) corr[x,z] (2) corr[xb,y] corr[msci,jpm] Number of Observations 99 MSCI Europe Historic Return 10.26% Standard deviation 18.62% Sharpe Ratio 38.98% Private Equity Estimated Return 10.56% Standard deviation 20.44% Sharpe Ratio 36.99% Coefficient of Correlation Performance Measurement and Asset Allocation An EVCA Research Paper March

62 Cash flow based 3.3 Private equity, asset allocation and limited liquidity In this section it will be discussed what the implications of our findings are on asset allocation decisions. Two aspects seem important to us. First, the findings can be used to determine the specific asset allocation decision of an investor. This analysis has already been done in the first part of the study on the basis of risk/return-characteristics derived from the distribution of aggregated NAV. Here, this analysis is done on the basis of distributional parameters derived from cash flow streams, i.e. on the basis of effectively generated money. Second, we will cautiously approach the question whether the liquidity risk to be borne by the investor in private equity can be analysed on the basis of cash flow patterns reported in this study. Moreover, the question is to what extent future cash flow based performance of a fund can be deduced from past cash flow patterns. In the following part we are discussing asset allocation decisions with cash flow based returns. For this part of the analysis we use the results presented in table 16, i.e. we develop an asset allocation decision for two different alternatives: First, we use the return distributions derived under the equity reinvestment strategy, i.e. the assumption that cash flows generated by the private equity fund are reinvested in the MSCI Europe Index. Second, we use the return distributions derived under the bond reinvestment strategy, i.e. the assumption that cash flows generated by the private equity fund are reinvested in the J.P. Morgan European Government Bond Index. As we had different sample definitions we have to make a decision with respect to the question which results are most representative. We think that this is the case for results with respect to the intermediate sample I. Because, only those non-liquidated funds with a relatively small NAV, i.e. not higher than 10% of the absolute sum of total cash flows, are included on top of all liquidated funds. In this way, the influence of a biased NAV should remain small; simultaneously, the enlargement of the sample size is high enough in order to avoid a valuation bias due to the exclusion of recent vintage years. Hence, the parameters used are the following: Table 21: Distributional parameters of different asset classes ( ) Asset Class Returns p.a. Standard deviation p.a. MSCI Europe 11.46% 18.06% J.P. Morgan Europ. Gov. Bond 7.84% 4.57% PE (Equity Reinvestment) 9.79% 18.99% PE (Bond Reinvestment) 8.13% 8.98% Table 22: Correlation structure of different asset classes ( ) MSCI JPMEGB PE (EQ) PE (Bond) MSCI JPMEGB PE (EQ) n.a. PE (Bond) n.a Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

63 Cash flow based On the basis of this data we created the efficient frontier presented in figure 32. The private equity investment improves the diversification effect in a portfolio. For instance, the portfolio with the highest possible Sharpe ratio, at an interest rate of 3%, has a 3% private equity ratio, a 6% public equity ratio, and 91% bond ratio. This portfolio has an expected return of 8.1% and a standard deviation of yearly returns of 4.6%. If an investor would like to move forward along the efficient frontier the ratio of private equity increases. In fact, if the investor would seek a risk efficient portfolio with an expected return of 10% he would aim to invest 33% of its money in private equity, 57% in public stocks, and 10% in bonds. Figure 32: Efficient frontier for portfolios of public equities, bonds and private equity (bond reinvestment strategy) ( ) 32 16% Expected return (% per year) 14% 12% 10% 8% 6% MVP (0% PE, 1% Eq., 99% Bds.) MSRP (3% PE, 6% Eq., 91% Bds.) EP_10% (33% PE, 57% Eq., 10% Bds.) PE Equities Bonds 4% 0% 5% 10% 15% 20% 25% Standard Deviation (σ) However, one should be careful in interpreting these results. They have been derived under the assumption that cash flows generated by the private equity fund are reinvested in a European government bond portfolio. Skipping from this assumption to the second alternative, namely to invest cash flows in a public equity portfolio, could lead to a substantially different asset allocation. This is not surprising; this second reinvestment alternative correlates more with the public equity market and, hence, reduces the potential diversification effect. Moreover, as shown in table 21 and table 22 the risk premium generated by the private equity funds relative to the stock market was negative over the period Taking the almost identical standard deviation as well as the not surprisingly rather high correlation coefficient into account, one may expect that under this strategy the diversification effect of private equity is rather limited. In fact, in this case the minimum variance portfolio has only a 1.2% private equity ratio, while the maximum Sharpe ratio portfolio does not contain any private equity at all. 32 The following portfolios are marked in the diagram: MVP = Minimum variance portfolio, MSRP = Maximum Sharpe ratio portfolio (for a risk free interest rate of 3%), EP_10% = Efficient portfolio with an expected return of 10%. Moreover, the portfolios where 100% is invested in one asset class are marked, too. Performance Measurement and Asset Allocation An EVCA Research Paper March

64 Cash flow based A second issue that should be emphasized is the fact that our parameter estimation refers to the total cash flow history available. Of course, estimations may change, if another cash flow history would be taken into account. The impact of shortening the estimation period was presented in table 20. The interesting question here is whether this has a perceivable impact on the optimal asset allocation presented in figure 32. For this purpose we repeat the calculation of the risk efficient frontier using the following parameters. Table 23: Distributional parameters of different asset classes ( ) Standard deviation Asset Class Returns per year per year MSCI Europe 10.26% 18.62% J.P. Morgan Europ. Gov. Bond 7.84% 4.57% PE (Equity Reinvestment) 10.56% 20.44% PE (Bond Reinvestment) 10.39% 10.62% Table 24: Correlation structure of different asset classes ( ) MSCI JPMEGB PE(EQ) PE(Bond) MSCI JPMEGB PE (EQ) N/a PE (Bond) N/a Recalculating the asset allocation using these parameters gives similar results to those obtained above, although the diversification impact of private equity becomes more important. This is caused by the fact that the risk premium of private equity is not only positive with respect to a bond investment, but also with respect to a public stock market investment. As risk parameters as well as the correlation structure do not change substantially, it obviously follows that private equity should have a more prominent role in portfolio allocation. More specifically, as far as the bond reinvestment strategy is concerned the weight of private equity in the maximum Sharpe ratio portfolio goes up to 14%, alongside with weights for equity of 6% and bonds of 80%. Moreover, even if we look at the equity reinvestment strategy the role of private equity will still be important. In fact, the minimum variance portfolio, shown in figure 33, will have a 3% private equity ratio, while the maximum Sharpe ratio portfolio has a 4% private equity ratio. Public equity will not be held at all in the first portfolio, while it has a 1%-ratio in the second. If the investor seeks a risk efficient portfolio with an expected return of 9% he should invest 25% of its money in private equity, 20% in public stocks, and 55% in bonds. From this analysis we can conclude that if reasonable assumptions regarding parameter estimation procedures are in place, private equity will have a substantial role in asset allocation. Therefore, private equity diversification effects should not be neglected. 62 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

65 Cash flow based Figure 33: Efficient frontier for portfolios of public equities, bonds and private equity (equity reinvestment strategy) ( ) 33 12% 11% EP_9% (25% PE, 20% Eq., 55% Bds.) Expected return (% per year) 10% 9% 8% 7% MVP (3% PE, 0% Eq., 97% Bds.) MSRP (4% PE, 1% Eq., 95% Bds.) PE Equities VC Bonds 6% 0% 5% 10% 15% 20% 25% Standard Deviation (σ) Finally, it is interesting to know whether venture capital and buyout funds have a different role in asset allocation. For this purpose we use the results reported table 18 and table 19 relating to the PME-based performance of venture capital and buyout funds. Under the assumption that cash flows are reinvested in the public bond market index the following distributional parameters have been assumed. We used the following approach to derive the correlation of the venture capital segment and the buyout segment. From sample I we matched every venture capital fund with a buyout fund representing the same vintage year and liquidation year. Then the correlation of the variable x B for the resulting 33 pairs of funds was calculated. The results are summarized in the following two tables, table 25 and table 26. Further below, figure 34 gives an overview of the asset allocation decision on the basis that venture capital and buyout funds can be regarded as different asset classes. Both types of private equity funds have their own role in asset allocation, at least under the assumptions used for deriving the return parameters. Moreover, their weight should not be too different. This is a consequence of the fact that they have only a slight difference in their Sharpe ratio and that their returns are almost uncorrelated. 33 The following portfolios are marked in the diagram: MVP = Minimum variance portfolio, MSRP = Maximum Sharpe ratio portfolio (for a risk free interest rate of 3%), EP_9% = Efficient portfolio with an expected return of 9%. Moreover, the portfolios where 100% is invested in one asset class are marked, too. Performance Measurement and Asset Allocation An EVCA Research Paper March

66 Cash flow based Table 25: Distributional parameters of different asset classes ( ) Standard Asset Class Returns per year deviation per year MSCI Europe 11.46% 18.06% J.P. Morgan Europ. Gov. Bond 7.84% 4.57% VC (Bond Reinvestment) 8.33% 10.24% BO (Bond Reinvestment) 7.93% 7.58% Table 26: Correlation structure of different asset classes ( ) MSCI JPMEGB VC(Bond) BO(Bond) MSCI JPMEGB VC (Bond) ,060 BO (Bond) Figure 34: Efficient frontier for portfolios of public equities, bonds, venture capital and buyout funds (bond reinvestment strategy) ( ) 34 14% Expected return (% per year) 12% 10% 8% 6% 4% EP_9% (26% VC, 26% BO, 28% Eq., 20% Bds.) MSRP (5% VC, 3% BO, 7% Eq., 85% Bds.) BO Bonds = MVP (0% PE, 0% BO, 100% Bds.) VC Equities 2% 0% 5% 10% 15% 20% 25% Standard Deviation (σ) 34 The following portfolios are marked in the diagram: MVP = Minimum variance portfolio, MSRP = Maximum Sharpe ratio portfolio (for a risk free interest rate of 3%), EP_9% = Efficient portfolio with an expected return of 9%. Moreover, the portfolios where 100% is invested in one asset class are marked, too. 64 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

67 Cash flow based 3.4 Cash flow patterns, liquidity risk, and performance assessment From the analysis in the preceding section it has become clear that cash flow patterns have an important impact on a private equity fund s performance. Especially, we have seen that the shorter the payback period the better the performance of the fund. In this section we would like to briefly extend the analysis in two directions. First, a limited partner could be interested in assessing the liquidity risk associated with a private equity investment. In this case, he basically would be interested in assessing future distributions of the private equity fund. From a purely ex-ante point of view this could be done, for instance, by estimating the distribution of the payback period. This is reflected in figure 35, where the empirical as well as an assumed theoretical distribution of the payback period is given. It could be presumed that the natural logarithm of the payback period (measured in months) follows a normal distribution, at least to some extent. In fact, we can see from figure 35 that the normal density function does not perfectly match the empirical density. However, as a first approach we may assume normality. If this is the case, then the investor could assess its liquidity risk. For instance, given that for the sample used for calculating the normal density function in figure 35 has an expected value for the payback period of 92.6 months with a standard deviation of 51.8 months, we assume that with a probability of about 68% the payback of a randomly chosen fund will be between 48 and 136 months. Therefore, it follows also that the probability for a payback in less then four years is about 17%. This approach gives the investor the possibility to make an inference with respect to the timing of the distributions of a fund and, hence, to make an assessment with respect to liquidity risks incurred by investing in a private equity fund. Figure 35: Empirical and theoretical density of the log-payback Numbers 5 0 3,00 4,00 5,00 Log-payback in month Performance Measurement and Asset Allocation An EVCA Research Paper March

68 Cash flow based Furthermore, an investor may be interested whether it will be possible to learn about liquidity risk of a particular fund given that this fund already has a cash flow history. For instance, three years after the vintage year the investor knows the distributions and also the takedowns that this fund generated up to that time. Are there any conclusions that can be drawn from this information? Specifically, is it possible to make a more accurate assessment of future liquidity risk as well as with respect to the overall performance of the fund? This is, of course, a very comprehensive issue that cannot be treated in the context of this study. However, we would like to emphasize that there may be, in fact, a way to infer future cash flow patterns from cash flow history. In Table we report what we call the DPI transition probabilities. For this purpose we calculated the ratio of all distributions up to year three to all takedowns up to that year. The same ratio was calculated with respect to year six after vintage. Table 27: DPI transition probabilities Sample II Distributions to Take downs after 3 years Distributions to Take downs after 6 years Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5 Total Quintile 1 Count % of Total 5,4% 6,2% 4,2% 3,1% 1,2% 20,0% Quintile 2 Count % of Total 7,7% 4,2% 4,2% 2,3% 1,5% 20,0% Quintile 3 Count % of Total 1,2% 8,1% 2,7% 4,6% 3,5% 20,0% Quintile 4 Count % of Total 1,5% 1,5% 8,1% 5,8% 3,1% 20,0% Quintile 5 Count Total % of Total 4,2% 0,0% 0,8% 4,2% 10,8% 20,0% Count % of Total 20,0% 20,0% 20,0% 20,0% 20,0% 100,0% The information in Table 27 can be interpreted as follows. The funds belonging to quintile 1 are those funds, which have a DPI among the worst 20%. Accordingly, funds in quintile 5 are those funds, which have a DPI among the best 20%. Now, assume that a fund in year three had a rather high DPI so as to belong to quintile 5. The probability that this fund is still among the best 20% after six years is 54% 35. The probability that this fund in year six belongs to quintile 1, i.e. the group of funds with a DPI among the lowest 20%, is only 21%. Alternatively, we can assume that a fund belongs to quintile 1 in year three. The probability that this fund belongs to quintile 5 in year six is only 0.6%. Instead, the probability that this fund belongs either to quintile 1 or 2 in year six is 58%. Hence, we can conclude from this rather simple analysis that historical cash flow records can be used for assessing future cash flow patterns of a fund. This is important as it allows investors assessing liquidity risks as well as overall performance more precisely. It should be emphasized that funds with higher distributions at the beginning have, on average, a higher overall performance. 35 This probability is given by 10.8%/20%. 66 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

69 Cash flow based 3.5 Concluding remarks The objective of this part of the study was to infer risk and return characteristics of a private equity fund investment from realised cash flows only. This would allow an unbiased assessment. However, as it has been pointed out, there is no straightforward way to calculate meaningful performance figures from cash flows only. The approach developed here was based on the so called public market equivalent (PME), where it is basically assumed that all the cash flows generated by the private equity fund are reinvested in a public market index. For robustness reasons we used two different indexes, an equity index (MSCI Europe) as well as a bond index (J.P. Morgan European Government Bond Index). On this basis we were able to show that private equity indeed plays a substantial role in asset allocation decisions. In fact, the trade-off between risk and return faced by an investor could be improved by extending the investment universe with the private equity asset class. In the outcome, we also investigated the cash flow patterns of European private equity funds. In this way we were able to analyse the question, whether cash flow patterns are related to the overall performance of a fund. One of the most important results is the fact that funds with shorter payback periods have a higher performance. In addition, there is no clear relationship between the size of the fund and its performance. Moreover, we found some indications that the cash flow history of a fund can be used for assessing future cash flows and, in this way, predicting overall performance. However, complementary research is necessary in this respect. Performance Measurement and Asset Allocation An EVCA Research Paper March

70 68 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

71 4. Conclusion Using modern portfolio theory in order to answer what the share of private equity in an institutional investor's portfolio should be does not lead to a straightforward answer. One of the first reasons for the difficulty to deal with the private equity asset class in the conceptual framework of modern portfolio theory is related to the stale pricing or smoothing process. Patrick Artus and Jérôme Teïletche based their research on aggregate returns available through the Thomson Venture Economics database, VentureXpert. They clearly identified auto-correlated quarterly returns for venture capital, indicating the existence of a stale pricing process impacting the net asset value of the companies still in the portfolio. The stale pricing process has two main impacts: The observed volatility (i.e. the risk) of venture capital underestimates the true risk of this asset category. The observed correlation of the venture capital with other asset classes like bonds and quoted equities also underestimates the true risk. As a consequence, not correcting the stale pricing process would lead to a minimum variance portfolio comprising 5% of venture capital combined with 2% of public equities and 90% of bonds (see table 28 below). The portfolio, which offers the institutional investors the maximum Sharpe ratio obtained 8% of venture capital combined with 2% of public equities and 90% of bonds. After having developed a methodology for correcting the smoothing process, Patrick Artus and Jérôme Teïletche deducted that the minimum variance portfolio, or the one with the smallest risk, should comprise 1% of venture capital, completed by 3% of public equities and 96% of bonds. Moreover, it appears that the maximum Sharpe ratio portfolio should contain 3% of venture capital, with 2% of public equities and 95% of bonds. It should be noted that the maximum Sharpe ratio portfolio offers the best balance between return and risk. When trying to extend their methodology to the buyout segment, the authors encountered two kinds of difficulties: The absence of an autocorrelation between quarterly returns, which questions the existence of a smoothing process for this case as well as its usual treatment. Pooled returns do not always represent adequately the distribution of returns among buyout funds. However, because current aggregate returns and their potential treatment do not lead to a fully satisfactory solution, a cash flow based analysis has been introduced to have a better understanding of the role of private equity in an institutional portfolio. At a second stage, Christoph Kaserer and Christian Diller conducted a cash flow based analysis using data also provided by Thomson Venture Economics. When looking at the real cash flows generated by 201 European private equity funds, either liquidated or with a small residual net asset value compared to the cash flows the funds generated, the allocation of private equity in institutional investors portfolios could be determined without having to rely on the net asset value. In this analysis the challenge was of a different nature, namely finding the right return metric in order to allow a comparison with other asset classes. Performance Measurement and Asset Allocation An EVCA Research Paper March

72 Conclusion Because the internal rate of return cannot be compared to the return calculated from indexes, the authors assumed that all distributions from the funds to the limited partners were reinvested either in quoted equities or in bonds. From the time of the investment until the distribution, the return is depending on the ability of the general partner to multiply the money invested. Only after distribution of returns the limited partners can reinvest these in the reference index. This methodology, although by construction showing unexpected level of correlation between private equity returns and quoted equity or bonds returns, allows for the inclusion of the private equity asset class in the modern portfolio theory framework. In their conclusion Christoph Kaserer and Christian Diller obtained the following portfolios, when observing returns from private equity between : The minimum variance portfolio, i.e. the least risky but also least performing, consists solely of bonds The maximum Sharpe ratio portfolio on the contrary contains 5% venture capital, 3% buyout, 7% quoted equities and 85% bonds. Table 28: Share in percentage of venture capital and buyout in an institutional investor s portfolio (consisting of bonds, quoted equities and private equity) according to the two approaches developed: aggregated returns or cash flow based Analysis based on aggregated figures conducted by Cash flow based analysis conducted by Patrick Artus and Jérôme Teïletche Christoph Kaserer and Christian Diller Smoothing process Smoothing process not corrected corrected Venture capital Venture capital Venture capital Buyouts Minimum variance portfolio 5% 1% 0% 0% Maximum Sharpe ratio portfolio 8% 3% 5% 3% Source: EVCA/CDC Ixis Capital Markets/CEFS-TUM based on data provided by Thomson Venture Economics Table 29: Comparison of the shares of public equities versus private equities Analysis based on aggregated figures conducted by Patrick Artus and Jérôme Teïletche Cash flow based analysis conducted by Christoph Kaserer and Christian Diller Public Venture capital Public equities Venture capital Buyouts equities Minimum variance portfolio 1% 3% 0% 0% 0% Maximum Sharpe ratio portfolio 3% 2% 5% 3% 7% Source: EVCA/CDC Ixis Capital Markets/CEFS-TUM based on data provided by Thomson Venture Economics 70 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

73 Conclusion Following the two approaches presented in this paper, institutional investors may consider investing between 5% and 10% of their total assets in private equity, i.e. in venture capital and buyout funds. Though the results are based on historical performance, investors can use them to build their portfolios on the ability of the different asset classes to outperform historical returns. In this respect, some elements should be taken into account. Bonds will probably not perform as well as they have done recently due to the current low level of interest rates. Venture capital investments are expected to benefit in the forthcoming years from the experience gained by European venture capital management teams throughout the difficulties connected to the economic downturn and the collapse of overrated Internet investment valuations since Moreover, venture capital will profit from current entry prices at a low level with exit opportunities opening up again. Buyout firms have historically shown outstanding returns in Europe. Although the market has recently experienced rising competition between players in some specific segments, this competition has also called for more differentiation in their strategies to add value. Therefore, not only the quantitative analysis of historical returns suggest a significant share of private equity for institutional investors portfolios, but market forecasts indicate the attractiveness of this asset class, too. Performance Measurement and Asset Allocation An EVCA Research Paper March

74 5. Bibliography Chen P, Baierl, GT, Kaplan PD (2002) Venture Capital and its Role in Strategic Asset Allocation. Journal of Portfolio Management, Winter 2002: Cochrane JH (2001) The Risk and Return of Venture Capital. NBER Working Paper No. w8066 Getmanski M., Lo A.W., MAkarov I. (2003), An econometric model of serial correlation and illiquidity in hedge fund returns, NBER Working Paper n Kaplan S, Schoar A (2002) Private Equity Performance: Returns, Persistence and Capital Flows. NBER Working Paper No. w9807 Kaserer C, Wagner N, Achleitner A (2004): Managing Investment Risk of Institutional Private Equity Investors The Challenge of Illiquidity. Forthcoming: Frenkel M, Hommel U, Rudolf M (ed.) Risk Management Challenge and Opportunity, Berlin Ljungqvist A, Richardson M (2003) The Cash Flow, Return, and Risk Characteristics of Private Equity. NBER Working Paper No. w9454 Lo A.W. (2002), The statistics of Sharpe ratios, Financial Analysts Journal, vol. 57, pp Meyer T, Weidig T (2003) Modelling Venture Capital Funds. Risk Magazine, October 2003 Rouvinez C (2003) How Volatile is Private Equity? Private Equity International, June 2003: Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

75 I Appendix I Appendix I The implications of stale pricing on estimation of variance-covariance matrix and asset allocation problems The implications of the stale pricing problem (the smoothing of returns) on estimations of variance-covariance matrices of returns and, the implications on the solutions found in asset allocation problems (à la Markovitz) are the subject of the following analysis. This appendix is based on Getmanski et al. (2003) 36 and Lo (2002) 37 and provides extensions of their research. In the first section of this appendix, we describe the way the stale pricing can be modelled, introducing the general framework. In the second step, we analyse the implications of the stale pricing on the average and standard deviation of the distribution of returns and thus on the Sharpe ratio and common methods to correct any implicit bias. We also discuss the implications of the stale pricing problem for autocorrelation. In the third section, we analyse the impact of stale pricing on correlation of returns from several assets, where a smoothing process characterizes one or more assets. In the fourth and last section, we discuss two possible ways of correcting the observed bias. A1. The general framework Denote by the (continuously compounded) true return of private equity, with, where is an underlying factor (for instance, the stock market return) and is an idiosyncratic disturbance with. The true (or effective) return is not observed. In practice, the observed return at time t is a weighted average of past and present returns:. (A1) The smoothing process comes from (or is allowed by) the fact that the asset (in this case private equity) is of limited liquidity. In particular, the asset is subject to the stale pricing problem and the infrequent revaluation of investments (appraisal returns). We further impose the restrictions and so that all the information about can be inferred from the time series of. The dynamics of factor are crucial. In the case where they are serially correlated, analysis is greatly complicated. This is because, in this case, the dynamics of depend not only on the smoothing process but also on the dynamics specific to, which are created by that of the factor. 36 Getmanski M., Lo A.W., MAkarov I. (2003), An econometric model of serial correlation and illiquidity in hedge fund returns, NBER Working Paper n Lo A.W. (2002), The statistics of Sharpe ratios, Financila Analysts Journal, vol. 57, pp Performance Measurement and Asset Allocation An EVCA Research Paper March

76 Appendix I It is possible to generalise the results presented below to fit this case. The associated expressions are nonetheless far more complex. Furthermore, in our opinion, it is reasonable to impose the hypothesis of an identically and independently distributed (iid) factor. From a theoretical point of view, we are supposing that is auto-correlated which is in strong contradiction with the market efficiency hypothesis. The reason for this is that there are no major theoretical reasons why the factor would itself be auto-correlated. This is, except a) if we suppose that the factor is associated with the return of an asset that is itself not liquid and b) if we include excessively high frequencies where the micro-structural frictions i.e. bid-ask bounce and non-synchronous trading matter. Nevertheless, from an empirical point of view, the hypothesis of a lack of autocorrelation seems realistic for the main stock market indices, which are the natural candidates for the role of an underlying factor for private equity. Table 30 illustrates this point, with the exception of emerging equities, deemed to be not very liquid; the coefficient of first-order autocorrelation for monthly returns is weak for the main indices, including those that are representative of small capitalisation assets. Table 30: First-order correlation for stock markets indices (monthly returns; ) S&P 500 Small Caps MSCI World MSCI Emerging Russel % 6.3% -3.3% 17.2% 0.7% Source: EVCA/CDC Ixis Capital Markets A2. Implications on the average, the standard deviation and the autocorrelation structure of returns In this framework, we can deduce (see Getmanski et al. (2003)): (A2) (A3) (A4) Equations (A.2) and (A.3) show, while no bias is present in the mean return, that the variance is downward-biased. As a result, the Sharpe ratio is overestimated due to the decrease in variance implied by the smoothing process (cf (A.4)). For the autocorrelation structure, we get the following result: (A.5) 74 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

77 Appendix I Equation (A.5) shows that the smoothing process introduces some significant autocorrelation coefficients for while they are null in theory. A3. Implications on the correlation between several assets returns Equations (A.5) analyse the impact of the smoothing process in terms of correlation structure: (A.6) In equation (A.6), we see that the smoothing process implies a false correlation for and leads to a lower correlation for the analysed period. This last point is important in an asset allocation context. We can go one step further and analyse the case where two private equity investments, indexed by (1) and (2), are available. Both are subject to a smoothing process with coefficients and respectively. Using the same set of assumptions as before, we infer that: (A.7) Equation (A.7) expresses the fact that the contemporaneous correlation between both investments is underestimated, except in the special case when the smoothing process of returns is the same for both projects,. In summary, the previous results show us that an asset allocation analysis based on observed returns for illiquid assets (such as private equity) might lead to significant biases. Indeed, the risk of the less liquid asset is underestimated, because its correlation with liquid assets is underestimated and the correlation between less liquid assets or asset segments for instance if we jointly introduce the buyouts and venture capital segments is also underestimated. Everything else assumed equal, this would lead to retain spuriously large proportions of private equity in efficient portfolios. Performance Measurement and Asset Allocation An EVCA Research Paper March

78 Appendix I A4. Two solutions Two solutions in our opinion are available to deal with these biases. The first one is to consider long horizon returns. For instance, let us assume that the time series of observed returns is transformed in a time series of time-aggregated returns of non-overlapping intervals that is for. We deduce that: (A.8) The first term corresponds to the true average return observed over the time interval. The second term corresponds to the bias implied by the smoothing process. As is iid by construction, it is highly probable that this second term is negligible in face of the first one, since the former is composed of the sum of returns while the latter is composed of returns. In probabilistic terms, this bias is leaning towards 0 as. In other words, the more the data is time-aggregated, the less the moments of observed returns will be biased. The second way to deal with the limited liquidity bias is to use the theoretical results shown above. In particular, the smoothing process can be recovered from the empirical autocorrelation structure of or its relationship with the factor. The main difficulty in this last case is to correctly identify what the factor might be. In the case of private equity, the most likely factor is the stock market. Another difficulty is to estimate the lag order k. However, this last point can be easily dealt with via standard econometric tools. In practice, Getmanski et al (2003) propose to estimate the following regression: (A.9) and then to use the identification scheme: (A.10) Since the residuals from (A.9) are likely to be autocorrelated, the estimates will not be efficient despite their consistency. To check the quality of the representation, we can investigate whether the implied correlation structure is significantly different from the observed one or not. 76 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

79 Index of figures Figure 1: Efficient frontier for portfolios of venture capital, equities and bonds (European data; 1994 Q Q2) page 3 Figure 2: Efficient frontier for portfolios of equities, bonds, venture capital and buyout funds (Bond reinvestment strategy) ( ) page 4 Figure 3: Sample size of European returns page 12 Figure 4: The J-curve phenomenon page 13 Figure 5: Risk/return profile for European private equity components (annual pooled weighted returns) page 13 Figure 6: Dispersion of venture capital returns ( ) page 14 Figure 7: Dispersion of buyout returns ( ) page 15 Figure 8: Efficient frontier for portfolios of venture capital, equities and bonds (European data; 1994 Q Q2) page 17 Figure 9: Efficient frontier for portfolios of venture capital, equities and bonds (European data; 1994 Q Q2) page 20 Figure 10: Sample size for European returns page 21 Figure 11: Sample size for European returns as proportion of maximum number of funds page 22 Figure 12: Dispersion of buyout returns ( ) page 23 Figure 13: Efficient frontier with quarterly returns (portfolio composed of buyout, venture capital, equities and bonds) page 24 Figure 14: Number of funds by vintage year (number of funds: 780) page 29 Figure 15: Time pattern of aggregated sample funds cash flows (number of funds: 780) page 30 Figure 16: Funds takedowns and public equity market performance (number of funds: 780) page 31 Figure 17: Time pattern of take downs for different types of funds (number of funds: 780) page 32 Figure 18: Time pattern of take downs by funds stage (number of funds: 780) page 32 Figure 19: Time pattern of distributions for different types of funds (number of funds: 780) page 33 Figure 20: Time pattern of distributions by funds stage (number of funds: 780) page 34 Figure 21: Value weighted average payback period (number of funds: 780) page 35 Figure 22: Payback period and fund size (sample I, number of funds: 201) page 35 Figure 23: Payback period and vintage year (sample I, number of funds: 201) page 36 Performance Measurement and Asset Allocation An EVCA Research Paper March

80 Index Figure 24: Average IRR (NAV) and IRR (CF) over a funds lifetime for liquidated funds (number of funds: 95) page 46 Figure 25: Average IRR (NAV) by vintage year (number of funds: 780) page 48 Figure 26: IRR (CF) by vintage year page 52 Figure 27: IRR (CF) by fund size page 52 Figure 28: IRR (CF) and payback period page 53 Figure 29: PME and fund size page 55 Figure 30: PME and vintage year page 55 Figure 31: PME and payback page 56 Figure 32: Efficient frontier for portfolios of equities, bonds and private equity (bond reinvestment strategy) ( ) page 61 Figure 33: Efficient frontier for portfolios of equities, bonds and private equity (equity reinvestment strategy) ( ) page 63 Figure 34: Efficient frontier for portfolios of equities, bonds, venture capital and buyout funds (bond reinvestment strategy) ( ) page 64 Figure 35: Empirical and theoretical density of the log-payback page 65 Index of Tables Table 1: Descriptive statistics for quarterly returns (as %; after management fees) page 16 Table 2: Correlation matrix page 17 Table 3: Autocorrelation structure page 18 Table 4: Statistics used for the asset allocation problem page 24 Table 5: Sample funds by size and type page 28 Table 6: Sample funds by liquidation status page 28 Table 7: Sample funds by size and stage page 29 Table 8: Example for two funds with cash flows and NAVs page 38 Table 9: Example for calculating the PME with different market returns page 39 Table 10: Size, IRR (CF) and payback of our samples page 49 Table 11: Size, IRR (CF) and payback period of our samples by different fund types page 50 Table 12: IRR (CF) minus contemporary MSCI Europe return page 50 Table 13: IRR (CF) minus contemporary J.P. Morgan Government Bond return page 51 Table 14: PME of private equity funds by sample definition page Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

81 Index Table 15: PME and BME-based private equity and public market returns (Liquidated funds, Returns based on a reinvestment of private equity distributions in public market indexes) page 57 Table 16: PME and-bme based private equity and public market returns (sample I, Returns based on a reinvestment of private equity distributions in public market indexes) page 57 Table 17: PME and BME-based private equity and public market returns (sample II, Returns based on a reinvestment of private equity distributions in public market indexes) page 58 Table 18: PME and BME-based private equity and public market returns (sample I, buyout funds, Returns based on a reinvestment of private equity distributions in public market indexes) page 58 Table 19: PME and BME-based private equity and public market returns (sample I, venture capital funds, Returns based on a reinvestment of private equity distributions in public market indexes) page 59 Table 20: PME and BME-based private equity and public market returns (sample I, Returns based on a reinvestment of private equity distributions in public market indexes) page 59 Table 21: Distributional parameters of different asset classes ( ) page 60 Table 22: Correlation structure of different asset classes ( ) page 60 Table 23: Distributional parameters of different asset classes ( ) page 62 Table 24: Correlation structure of different asset classes ( ) page 62 Table 25: Distributional parameters of different asset classes ( ) page 64 Table 26: Correlation structure of different asset classes ( ) page 64 Table 27: DPI transition probabilities page 66 Table 28: Share in percentage of venture capital and buyout in an institutional investor s portfolio (consisting of bonds, quoted equities and private equity) according to the two approaches developed: aggregated returns or cash flow based page 70 Table 29: Comparison of the shares of public equities versus private equities page 70 Table 30: First-order correlation for stock markets indices (monthly returns; ) page 74 Performance Measurement and Asset Allocation An EVCA Research Paper March

82 Contributors Patrick Artus Head of the Research Department at CDC IXIS Capital Markets Jérôme Teïletche Quantitative analyst in charge of Asset allocation at CDC IXIS Capital Markets CDC IXIS Capital Markets Research Department CDC IXIS Capital Markets Research Department has in-depth knowledge of the financial markets and economic analysis techniques. The Research Department publishes market comments and economic and financial analysis. The EVCA project is managed by Patrick Artus, Head of the Research Department, and Jérôme Teïletche, quantitative analyst in charge of Asset allocation, and follows previous similar work for the French Association of Venture Capital (AFIC). Univ. Prof. Dr. Christoph Kaserer Scientific Director of the Center for Entrepreneurial and Financial Studies (CEFS) and holder of the chair of the Department of Financial Management and Capital Markets Dipl. Kfm. Christian Diller Research Assistant at the Center for Entrepreneurial and Financial Studies (CEFS) and the Department of Financial Management and Capital Markets The Centre for Entrepreneurial and Financial Studies (CEFS) is focused on research and teaching in the field of entrepreneurship and finance. The Center aims at delivering theoretically well-founded research dealing with real world problems in the context of entrepreneurial finance. As a part of Technische Universität München (TUM), the Center sees itself as an institution, which integrates technological know-how driven by cutting-edge research with financial management solutions for the industry. EVCA contributors Olivier Dupont EVCA Investor Relations Committee member FPCR Gestion Didier Guennoc EVCA Chief Economist 80 Performance Measurement and Asset Allocation An EVCA Research Paper March 2004

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