Description of the General Approach

In general, venture capital returns can vary significantly among different investments. Therefore, a merely deterministic forecast of the returns of an individual venture capital investment or fund will only provide an incomplete picture of the “true” return dynamics. In a more appropriate modelling setup, the return of an individual venture capital investment or of a venture capital fund must be a stochastic variable. In the following, let IRR denote the random return of an individual venture capital investment, where returns are measured by the Internal Rate of Return (IRR) of the investment. To model the dynamics of this random variable, we draw upon the existing empirical research on the determinants of venture capital investment performance. As already stated in the literature review above, the returns of venture capital investments are, in general, influenced by various factors such as the fund manager’s experience or the overall macroeconomic conditions.

Let X₁,...,XK denote a collection of k=1,…,K variables that influence the return of a specific venture capital investment. Thereby, any of these K variables can either be stochastic or deterministic, depending only on the nature of the specific factor. Under these assumptions, a model that relates these variables to the Internal Rate of Return IRR of a venture capital investment can be written as

),

where L(⋅) is a function that relates the distribution of the K independent variables to the distribution of IRR. If this function and the deterministic values or probability distributions of the K independent variables are explicitly known, then this model specifies the probability distribution of the Internal Rate of Return. However, it would be very difficult to work out this relationship analytically. Therefore, we propose a simple multi-factor model of the form

IRR=α +β₁X₁+β₂X₂+...+β_KX_K +U, (1) where ^U is an error term for which U~N(0,σ²) is assumed. The constant coefficients

βK

β

α, ₁,..., of this model can be estimated by a simple OLS Regression analysis. In a second step, the results from this regression analysis can be used as a data-generating process for our subsequent simulation procedure of the performance of a venture capital fund portfolio.

Therefore, our performance projection and risk management methodology involves two consecutive steps: first, an Econometric Analysis and Modelling of the individual venture capital investment returns; second, a Monte Carlo Simulation of the returns of a venture capital fund, where the regression results from our econometric analysis are interpreted as data-generating processes for the individual investment return IRRs.

The basic intuition behind our approach is to model the relationship between individual portfolio returns and investment-specific as well as macroeconomic factors by the simple multi-factor model given in equation (1) that can be estimated by an OLS Regression. For our regression analysis, we build upon the prior literature by investigating the determinants of venture capital investment performance based on a comprehensive venture capital data sample provided by CEPRES. The data provides precise information about each cash injection from the investor to the portfolio company and each cash distribution from the company back to the investor.

Therefore, we can precisely calculate the actual investment IRRs for each portfolio company based on monthly cash flows. Furthermore, the dataset enables us to analyse the influence of

accounts for the influence of the investment managers, the fund and the portfolio company characteristics, as well as differences in transaction structures. Furthermore, we include several macroeconomic factors in our regression analysis. As venture capital investments are typically investments in young innovative companies, characterized by substantial informational asymmetries and uncertainty, the outcome of an investment is to a high degree ”opportunity-driven”. The high risk and return potential of venture capital investments is depicted by a high number of write-offs on the one hand, and extraordinary returns of the top performing companies on the other. These positive and negative outliers are often more the result of mere chance, i.e, they are usually less affected by factors such as the overall macroeconomic conditions. Therefore, leaving these outliers in our regression analysis of the investment performance determinants could substantially bias the regression coefficients. For this reason, we at exclude total losses with an IRR of -100% and out-performers, defined as investments with an IRR above +99%, and perform the analysis only with the remaining deals, the so-called “normal-performer-sample”. This also has the advantage that historical returns for the “normal-performer-sample” are in good approximation normally distributed, as shown in the following section.

In the second step, we draw on the results from the previous econometric analysis to simulate the returns distribution of a venture capital fund. In specific, this is done by using the previous regression results as a data-generating process for a Monte Carlo simulation of the returns of the individual investments in the fund portfolio. Monte Carlo methods have been introduced into the finance literature by Boyle (1977) and are now widespread among many financial applications. For a comprehensive overview also see the classical textbook of Glasserman (2003). The basic idea behind this technique is that the behaviour of a random variable can be assessed by the process of actually drawing lots of samples from the underlying probability distribution and then observing the behaviour of the resulting artificial distribution.

This is especially useful in our case, as the “true” distribution of the IRR is analytically not

tractable. Using the estimated regression coefficients αˆ,βˆ₁,...,β^ˆK from our multi-factor model, the IRR of an individual venture capital investment can be simulated by using the equation

IRR_j =αˆ+βˆ₁X_1j +βˆ₂X_2j +...+βˆ_KX_Kj +U_j, (2) where IRRj denotes the Internal Rate of Return in the jth iteration of our simulation procedure, with ^j=1,...,^M. In each simulation trial j, we must specify the values of the factors X₁j,X₂j...XKj. This is done by either assigning a constant value to the factor in all simulation trials (if the factor is deterministic) or by drawing values from the corresponding specified probability distributions of that factor (if the factor is stochastic). The detailed procedure for this is explained in section 3.4. Furthermore, the values of Uj are drawn from a normal distribution with mean 0 and variance σ², where σ² is the variance of the residuals from the regression analysis. If the total number of simulation trials M is considerably large, then we get an empirical distribution of the investment IRRs that will converge towards the distribution of the IRR that is specified by the multi-factor model in equation (1). In order to form a venture capital fund portfolio, the simulation procedure of equation (2) can be repeated for different venture capital investments with different characteristics such as different industry backgrounds. However, for the purpose of our regression analysis, we only accounted for individual normal deal returns, while write-off and out-performer deal returns were systematically excluded from the analysis. For the fund portfolio simulation, write-off and out-performer deal returns must now be re-integrated. This can be achieved by the following approach. For the total losses, the projected IRR will always be set to -100%, for the normal performers, the projected IRR of each deal is determined by running the simulation according to equation (2), for the out-performers, a simulation process randomly assigns a return out of the empirical return distribution of the investments in this group. The weighting for each of these subsets in the fund portfolio is thereby based on the historical ratios of write-offs, normal and out-performer deals in a venture capital fund portfolio. This calculation

of this iterative approach is a frequency distribution of the portfolio IRR. Therefore, our model captures diversification effects or risk in the sense of having a variation of the expected values.

In order to illustrate the dynamics of our approach, simulation results for two fictitious venture capital funds are presented. At the core of this simulation study is a unique set of detailed cash flow data provided by CEPRES. Before the two consecutive steps of our performance projection and risk management model are illustrated in detail with real data, we start by giving a descriptive analysis of the data sample employed for the subsequent study.