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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