AN ALM ANALYSIS OF PRIVATE EQUITY. Henk Hoek

Transcription

1 AN ALM ANALYSIS OF PRIVATE EQUITY Henk Hoek Applied Paper No January 2007

2 OFRC WORKING PAPER SERIES AN ALM ANALYSIS OF PRIVATE EQUITY 1 Henk Hoek 2, 3 Applied Paper No January 2007 Ortec Finance Research Center P.O. Box 4074, 3006 AB Rotterdam Max Euwelaan 78, The Netherlands, ABSTRACT This paper focuses on the role of private equity in strategic asset allocation decisions. Rather than following the hurdle approach, we model private equity by a stochastically extended version of the model presented in Takahashi and Alexander (2001). We estimate this model using data from Venture Economics. The new model was evaluated by using expert opinion of a group of private equity investors. These specialists in particular critically evaluated whether the dynamics generated by the model are sufficiently in accordance with the behavior of private equity in real life. Given the new model for private equity we analyze the added value of private equity in strategic asset allocation, in particular from the perspective of institutional investors like pension funds. Keywords: private equity, scenario analysis, asset and liability management JEL Classification: C15, C32, C61, G11, G23, G24 1 This is a working paper version of an earlier internal research report from We have benefited from the help of NIB Private Equity (AlpInves in providing the data and given useful comments on an earlier draft. 2 Ortec Finance Research Center. Please comments and questions to alex.boer@ortec-finance.com. 3 Copyright 2007 Ortec Finance bv. All rights reserved. No part of this paper may be reproduced, in any form or by any means, without permission from the authors. Shorts sections may be quoted without explicit permission provided that full credit is given to the source. The views expressed are those of the individual author(s) and do not necessarily reflect the views of Ortec Finance bv.

3 1 Introduction In strategic asset allocation we observe an increasing interest in so-called alternative investments such as hedge funds, commodities and private equity. Until a few years ago the focus was mainly on generating additional excess returns, or alpha. Nowadays the interest of investors fortunately extends to the diversification aspects of alternatives as well. However, the added value of alternative investments frequently is based on models which only moderately describe the real life behavior of these investment categories. For example, frequently the added value of these investments is quantified by a so-called hurdle approach, which only takes into account an estimated Sharpe ratio of these investments, and an estimated correlation with a worldwide equity benchmark. As a result the quantitative substantiation of the role of these investment classes in strategic asset allocation is not accurate enough. This paper focuses on the role of private equity in strategic asset allocation decisions. Rather than following the hurdle approach, we model private equity by a stochastically extended version of the model presented in Takahashi and Alexander (2001). We estimate this model using data from Venture Economics. The new model was evaluated by using expert opinion of a group of private equity investors. These specialists in particular critically evaluated whether the dynamics generated by the model are sufficiently in accordance with the behavior of private equity in real life. Given the new model for private equity we analyze the added value of private equity in strategic asset allocation, in particular from the perspective of institutional investors such as pension funds. The paper is organized as follows. In section 2 we give a short overview of the literature on modeling private equity and describe the model proposed by Takahashi and Alexander, as well as our stochastic extension of this model. After presenting the data in section 3 we present and discuss our estimation results in section 4. The estimated model is used for the purpose of ALM analyses in section 5 and the relevant conclusions are drawn in section 6. 1

4 2 Modeling Private Equity Recent years have seen a still moderate but growing number of papers on the risk and return of private equity. Some authors focus on modeling and/or estimating the return characteristics of individual private equity investments, like Cochrane (2003), other authors focus on describing private equity funds, e.g. Kaplan and Schoar (2003) and Ljungqvist and Richardson (2003), while others try to construct an index/benchmark for private equity as in Peng (2001) and Quigley and Woodward (2002). All these authors face the same problems: data on private equity investments are relatively scarce, usually from databases with a bias due to self-reporting issues, and difficult to interpret, due to the nature of a private equity investment. Like real estate, a substantial part of the annual return on private equity is unrealized, being the result from (often rather subjective) valuation of the investment. For this reason some authors, like Ljungqvist and Richardson (2003), only consider rate of returns based on actual cash flows. As a result, the final realized rate of return of a private equity investment can only be obtained at the end of the lifetime of the investment. Their research shows that, just using cash flows, up to year ten the net cash outflow (capital distributions minus capital contributions) is negative. However, the financial position of an institutional investor, like a pension fund, needs to be evaluated yearly. As a result, our interest is not only in modeling realized returns on Private Equity investment, but in modeling realized as well as unrealized returns. The unrealized return is captured by the development of the Net Asset Value of the Private Equity investment, which is reported by the fund manager. Of course biases may occur due to the valuation issues involved, making unrealized returns subjective compared to returns which are calculated using actual cash flows. However, for the purpose of ALM, we need both realized and unrealized returns. For this purpose we consider the model presented in Takahashi and Alexander (2002). Their model resembles the actual investment process, distinguishing cash inflows (contributions), cash outflows (distributions) and the valuation of committed capital (Net Asset Value). As a result also the illiquidity of Private Equity is modeled. In their model the timing of all cash flows, as well as the return on committed capital, is deterministic. First, in order to describe the model, we introduce the following definitions: CC: PIC(: CR(: C(: D(: DR(: NAV(: committed capital paid in capital in year t contribution rate in year t capital contribution in year t distribution in year t distribution rate in year t Net Asset Value ultimo year t Investment in a Private Equity Fund starts with committing capital CC to the fund. This capital is not invested immediately, but gradually. In year t the institutional investor obtains a capital call and has to 2

5 contribute part of the remaining capital commitment: C( = CR( (CC PIC(). Note that in practice the sum of all yearly contributions only rarely equals the committed capital: usually funds under invest, although also overinvestment may take place. Once the investment has started, its value, measured by the Net Asset Value, will change over time, due to new contributions, unrealized returns (due to valuation) and realized returns (distributions): NAV ( [ NAV ( t 1) (1 + G( ] + C( D( = (2.1) where G( measures the rate of return on invested capital in year t. Assuming C( = 0 we get NAV ( D( = NAV ( t 1) (1 + G( ) + (2.2) clearly demonstrating that G( combines both unrealized and realized returns. To complete the (deterministic) model, we define the distribution rate in year t as DR( D( NAV ( + D( = (2.3) Note that also the contribution rate could be modeled. However in our analysis we assume that the contribution rates equal their historical averages. In their paper Takahashi and Alexander consider simple deterministic functions to model the contribution and distribution rate, and assume a fixed yearly growth rate G(. Although this is a useful approach to analyze the dynamics of a private equity investment, it is of little use for the purpose of strategic asset allocation as the asset class is not analyzed in a portfolio context, where dynamics and correlations between asset classes play an important role. Our main extension of the model of Takahashi and Alexander is that we assume that both the rate of return G( and the distribution rate DR( are stochastic and depend on underlying factors. First, for the rate of return G( we assume that the return on Private Equity depends on the return on Public Equity. However, contrary to Public Equity, valuation ( marking-to-market ) takes place with some delay, such that unrealized returns lag returns on the stock market. Defining returns on the stock market by R(, the average stock return by AR and the cumulative contribution rate at t as CUM(, this gives the following model: Ln(1 + G( ) = a(0) + a(1) CUM ( + b(0)( R( AR) + b(1)( R( t 1) AR) + + b( p)( R( t p) AR) + ε ( (2.4) 3

6 where we assume that ε(, t=1 T is Normally distributed with mean 0 and variance σ 2. We expect returns on Private Equity to be skewed and choose to use a logarithmic transformation. Also we include CUM(, the cumulative contribution rate at time t, indicating that more and higher capital calls reflect increasing profit opportunities. The distribution rate can only take values between 0 and 1 and is therefore modeled by DR( Ln = c(0) + c(1) A + c(2) G( t 1) + c(3) CUM ( 1 DR( + d(0)( R( AR) + d(1)( R( t 1) AR) + + d( q)( R( t q) AR) +υ( (2.5) Here A stands for age and denotes the number of years that have passed since the vintage year. We assume that as this age of the project increases, also the distribution rate will increase. We include the lagged rate of return G(t-1) as regressor to capture the effect that empirically a (large) increase in valuation often precedes the actual distribution. Finally, again we also include the cumulative contribution rate CUM( as a regressor, expecting a higher distribution rate following higher contributions. 4

7 3 The data In order to estimate the model described in section 2 we use data from Venture Economics. These data consist of quarterly numbers on contributions, total distributions and net asset values per vintage year, ranging from 1990 up to For our ALM model yearly data are needed: we aggregate the cash flows per year, and only consider the Net Asset Value in the final quarter of each year. Also, we assume that on average cash flows take place in the middle of the year, such the development of the Net Asset Value becomes: NAV ( C( D( C( D( NAV ( t 1) + (1 + G( ) = (3.1) Given data on C(, D( and NAV( the return series G( and distribution rate DR( can easily be computed 4. We obtain these series for each vintage year, for both Venture Capital and Buy Out investments, for US as well as Europe. For the current analysis we only consider US data. All data are at the aggregate level, and give, per vintage year, the sum of all contributions, distributions and Net Asset values of all Private Equity Funds which are included in the database. In appendix A we present graphs of the computed G( and DR( series. Some characteristics of the data are given in Table 3.1 and Table 3.2. The IRR is computed from T T C( 0 = + D( t t t= 0 (1 + IRR) t= 0 (1 + IRR) (1 + + NAV ( T ) T IRR) (3.2) where NAV(T) is the Net Asset Value ultimo 2002: Ljungqvist and Richardson (2003) set this value to zero in their computation of the realized rate of return. Note that the computation of G( is not value-weighted, in contrast to the computation of the Internal Rate of Return (IIR). In most cases the average growth rate underestimates the IRR of the investment: negative returns on a small amount of capital is equally weighted as positive returns on large amounts of capital. Table 3.1 and Table 3.2 show that on average the return, as well as the volatility, on venture capital has been substantially higher than on buyouts. This corresponds with the characteristics found by Jones and Rhodes-Kropf (2003). The graphs in appendix A give part of the explanation for the large difference: returns on venture capital show a large peak in the boom year 1999, whereas the peak in the buyouts returns is only moderate. 4 The data include the effect of management fees, but not of carried interest : typically a fee of 10%-20% of positive returns has to be paid. In the ALM analysis we assume that the cost of carried interest is 15%. 5

8 Table 3.1: Characteristics US VC Vintage Average G( Stdev G( IRR Table 3.2: Characteristics US BO Vintage Average G( Stdev G( IRR

9 4 Estimation results Using the data from Venture Economics we have estimated the model presented in section 2. Table 4.1 and Table 4.2 present the estimation results for US Venture Capital. We have used dummy variables to take account of the 1999 peak. Table 4.1: Estimation results, G( US VC Table 4.2: Estimation results: DR( US VC Both the excess return on the stock market (contemporarily and with a lag of one years) and the cumulative contribution rate have a positive effect on the rate of return of the venture capital investment. The same applies to the distribution rate, which also depends positively on the lagged rate of return, indicating that valuation precedes exits. 7

10 The results for Buyouts are given in Table 4.3 and Table 4.4. Table 4.3: Estimation results, G( US BO Table 4.4: Estimation results: DR(, US BO Results are similar to the results for venture capital: returns on the stock market and the cumulative contribution have a positive effect on the return on buyouts. However, the magnitude of the estimated coefficients is significantly smaller, reflecting the lower average return and volatility of buyouts compared to venture capital over the sample period. As mentioned before, our definition of rate of return is not value-weighted, so a good fit of the model for the growth and distribution rate does not necessarily imply that the estimated development of the Net Asset Value and distributions (assuming the actual contributions) coincides with the actual development. To investigate this, Figure 4.1 shows the estimated and actual values of the NAV and distributions (in dollars) for US venture capital and buyouts from vintage year

11 Figure 4.1: Actual and estimated NAV and Distributions Although the lines do not exactly match, in particular in years with high returns/distributions, the patterns are very similar. The same conclusion holds for the other vintage years, although the mismatch increases for the later vintage years (also because only few data points are available for these years). We therefore conclude that our model gives, at least historically, a satisfactory description of the development of the Net Asset Value and Distributions of Private Equity investments. 9

12 5 ALM analysis Finally, we apply the estimated model to analyze the added value of private equity in the strategic asset allocation of an institutional investor. Using a Vector Autoregressive model, we have simulated scenarios for inflation, interest rates and stock returns. Scenarios for the development of private equity (Net Asset Value and distributions) are obtained by combining the scenarios of the stock returns with the estimated models. Also, residual variation is taking into account by simulating innovations from the distribution of the estimation residuals. We assume that these innovations consists of two components: the first error component is common for all buyouts or venture capital investments in a certain year (so independent of the vintage year), while the second error component is idiosyncratic 5. We assume that the correlation between the total error between the annual returns of two private equity investments equals 0.5. Within our ALM model we consider yearly rebalancing of the asset portfolio, with the exception of the private equity investment. Due to the illiquidity of private equity we do not allow selling of private equity, so the percentage invested in private equity can only decline due to exits or a lower valuation of invested capital. We also assume that the committed capital that is not yet contributed is invested according to the asset mix of the pension fund. Finally, we have to make an assumption about the maximum lifetime of the private equity investment. We assume that distributions (and contributions) take place up to year twelve of the investment, and that the pension fund obtains 25% of the Net Asset Value ultimo year twelve (this 25% can be interpreted as a kind of recovery rate used in credit risk models). In the database we noticed that sometimes the Net Asset Value did not change in the last couple of years, such that no amortization took place. We admit that this assumption is rather ad hoc, but lack of data (only the vintage years 1990 and 1991 have lifetimes over twelve years) makes detailed analysis of the closing of funds currently impossible. First, we consider the added value in an asset only context. In Figure 5.1 we see that the meanvariance frontier shifts slightly to the top-right corner, indicating that adding private equity to a portfolio with equity and bonds is more efficient. However, the effect is only moderate. Next we consider the added value in an ALM context. We look at two criteria: the average annual net contribution rate, and the probability of underfunding. The effect of adding private equity to the strategic asset allocation as shown in Figure 5.2 is very clear: assuming an average net contribution of 8% the probability of underfunding can be reduced from 12% (with an asset allocation of 50% equity and 50% bonds) to 4% (with an asset allocation of 20% equity, 10% private equity and 70% bonds). 5 In general, idiosyncratic means related to the unique circumstances of a specific security, as opposed to the overall market. Idiosyncratic risk is also referred to as unsystematic risk which can be virtually eliminated from a portfolio through diversification. 10

13 Figure 5.1: Asset-only analysis of Private Equity (6% BuyOuts, 4% Venture Capital) 10% equity 10% private equity 50% equity 10% equity no private equity 50% equity Figure 5.2: ALM analysis of private equity (6% BuyOuts, 4% Venture Capital) 50% equity 50% equity no private equity 10% private equity 10% equity 10% equity 11

14 6 Conclusion In this paper we have presented a model to describe the risk and return of private equity, taking important practical aspects of private equity, such as illiquidity and valuation, into account. Our model is a stochastic extension of the model presented by Takahashi and Alexander. The model is estimated using aggregate data from Venture Economics for US venture capital and buyouts. Application of the model to the strategic asset allocation of a pension fund reveals a positive role for private equity as an asset class. One direction for future research is to extend the sample of Private Equity Funds. Also, we intend to extend our model with a stochastic model for the contribution rate and investigate how this might affect the results. 12

15 Appendix A: Data: growth rates G(: actual - - fitted 13

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17 Appendix B: Distribution rates DR(: : actual, - - : fitted 15

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19 References Cochrane, J The risk and return of venture capital, Working Paper, Graduate School of Business, University of Chicago. Jones, C.M., and M. Rhodes-Kropf The price of diversifiable risk in venture capital and private equity, Working Paper, Graduate School of Business, Columbia University. Kaplan, S., and A. Schoar Private equity performance: returns, persistence and capital flows, Working Paper, Graduate School of Business, University of Chicago. Ljungqvist, A., and M. Richardson The cash flow, return and risk characteristics of private equity, Working Paper 9454, National Bureau of Economic Research. Peng, L Building a venture capital index, Working Paper, Economics Department, Yale University. Quigley, J.M., and S.E. Woodward Private equity before the crash: estimation of an index, Working Paper, University of California. Takahashi, D., and S. Alexander Illiquid alternative asset fund modeling, Working Paper, Yale International Center for Finance, Yale University. 17

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