Jürgen Borchers and Lars Körner of Cologne-based funds of funds manager CAM Private Equity explain the benefits of a private equity-focussed risk management model

The recent credit crisis in the financial industry has emphasised the importance of risk management to institutional investors. Current and future regulatory requirements, combined with increasing volatility in the international capital markets, reflect the need for improved risk transparency. Alternative assets such as private equity have not been adequately addressed in the field of risk management. Classic quantitative risk management methods used for public equities are not easily applied to private equity due to the unique characteristics of the asset class. As institutional investors increase their private equity allocations, the demand for an effective risk management of private equity portfolios will continue to rise. CAM Private Equity has developed a Value-at-Risk (VaR) simulation model designed specifically to measure the market risk of a private equity fund portfolio.

Extensive knowledge of an asset class and its specific risks is a prerequisite for proper risk management. Private equity investment risks are varied and differentiated. General market price risk is the primary risk factor in connection with short- and mediumterm value fluctuations. Other risk factors like operational risk, default risk and liquidity risk play a comparatively minor role, particularly in a well diversified fund portfolio with a long-term investment perspective. General market price risk is comprised of valuation risks, currency risk, concentration risk, and business cycle risk. In order to integrate private equity investment risks into an internal risk management system, institutional investors must characterise their own liquidity profile, regulatory requirements and asset/liability duration.

Risk measurement, which involves calculation of risk-adjusted parameters, has been seldom utilised in private equity. Limited access to relevant historical data has been a significant obstacle to risk measurement. Private equity funds are, by their nature, private and closed, which means that performance and cash flow data are available only to limited partners. Any robust and credible financial simulation model that is based on historical data must also cover an adequate time series. Several reputable financial data vendors provide a wide range of data on private equity funds, but this data is of limited value for risk measurement because of deficiencies in data density, aggregation, and composition.

CAM Private Equity has successfully developed a simulation model for quantifying the VaR of a private equity fund portfolio. This VaR model generates a single key measure that can be consistently applied in risk management procedures and reporting. Complemented by scenario analyses, stress tests and performance indicators, the investor gets a proper understanding of the risk and reward profile embedded in his or her portfolio.

Risk management is an integral part of the overall investment process at CAM Private Equity. Risk management is applied not only in portfolio construction and asset allocation but also in pre-commitment due diligence of fund managers. Risk management has an impact on diversification across fund managers, investment strategies, investment stages, regions, and business cycles. It is also important in post-commitment monitoring activities in an actively managed portfolio. Not only qualitative but also quantitative factors must be considered for proper risk management. Quantitative risk measurement places new requirements on private equity investors to ensure increased risk transparency and comparability.

Most existing risk management models used by institutional investors have been based on simplified assumptions. Traditional risk measurement techniques applied to capital investments – such as the VaR model – were originally developed for highly liquid, publicly traded assets like securities and bonds. To incorporate factors relevant to private equity such as quarterly valuations, limited fungibility, availability of data, and long duration, CAM has designed with the support of Deloitte & Touche GmbH (especially Dr. Thomas Siwik and Dirk Stemmer) a Value-at-Risk model specifically for measuring the VaR of a portfolio of private equity fund investments (see graph above).

Risk is defined in this model as deviation from market expectation (the market return curve) and, therefore, is related to the specific return development of a typical private equity investment (as derived from historical data). The market return curve is based on published data by Venture Economics and used for calibration of systematic risk. A parametric distribution function must be used in order to simulate a fund's returns. The skewed t-distribution is the best fitting distribution function for explaining the empirically observed skewness and excess kurtosis of the market return curve (particularly evident in the left tail). Based on observed returns in time t, the model simulates the distribution function in time t +1.

Risk measurement, which involves calculation of risk-adjusted parameters, has been seldom utilised in private equity

A private equity fund portfolio is typically diversified over various fund classes, regions and vintage years. Because of its significant impact on total risk, economic diversification is addressed through separate modeling of different diversification criteria. For a comprehensive view of all diversification factors, correlations are reflected at two levels in the model: between four investment segments (US buyout, US venture capital, European buyout, and European venture capital) and between the funds within these segments. In addition, the model considers explicitly the impact that the fund lifetime has on the risk of the portfolio by reflecting the vintage year of the fund holdings, i.e. through the separate parameterisation of the distributions function for the various stages of the fund cycle.

The historical development has shown that the volatility of fund returns varies significantly in the course of the fund lifetime: while the volatility of periodic returns is high during the first years, it is decreasing over time. Due to the recognition of these characteristics, the model displays the economic diversification of a typical private equity fund portfolio.

Since returns cannot be represented by a normal distribution, it is not possible to use a multi-dimensional distribution function that considers parameter interdependencies such as correlations. CAM, therefore, uses a common approach from the credit risk modelling called the copula function. The copula function combines any marginal distribution to obtain a total distribution. The VaR is then the empirical quantile of this simulated distribution after several simulation aggregation steps (e.g., 10,000 steps).

Our VaR model generates the VaR for a portfolio of private equity fund investments using modern statistical methods. Characteristics unique to the private equity asset class are incorporated in a manner that enables quantification of the VaR of an investor's own private equity portfolio.

A diversified portfolio of private equity fund investment s ( for example, a portfolio of 20 fund investments across more than four private equity segments) provides a risk-return profile that is comparable to a well-diversified stock portfolio. The model demonstrates the importance of diversification across several vintage years and investment segments. The VaR increases dramatically as the number of funds or vintage years is reduced. The model incorporates several adjustable parameters such as different confidence levels, time periods, correlation parameters, and distribution functions.

Quantitative measures are combined with qualitative risk factors, scenario analysis and score-cards as part of risk monitoring and reporting. Adequate tools and resources are essential for summarising and analysing all available information on a portfolio and target funds. Our model maintains the advantages of professional portfolio construction already established at an early stage through appropriate diversification. In addition to diversification, selection and access to the best fund managers are crucial for optimising the risk-return profile of a fund portfolio.