In recent months public discussion of the financial markets has been dominated by the credit crisis and high volatility on the stock markets. While publicly listed companies and hedge funds were significantly impacted by the crisis, the majority of private equity funds have been affected only to a limited extent. After all, private equity is an asset class with a long-term horizon and short-term fluctuations only make a small difference to overall performance.

In view of the current crisis we take a close look here at the risk in private equity to find answers to the following questions: What is the risk of an investment in private equity? How can that risk be measured? How far can it be reduced with diversification?

**INVESTED CAPITAL AT RISK**

Due to the long-term investment horizon of private equity and the absence of market prices during the holding period, traditional risk measures which are used for public market investments are not easily applied to private equity. We therefore introduce a new risk measure for private equity investments which is similar to the long-term historical Value at Risk (VaR) approach of public markets and which takes into account the peculiarities of private equity investments ^{1}.

Similar to the Value at Risk approach, we calculate the amount of money such that there is a 99 percent probability (confidence level) of the portfolio losing less than that amount over a given period of time. Since private equity is an illiquid asset class in which market valuations are not regularly available, we use the entire lifetime of the private equity fund portfolio as the time period and calculate the probability density function on a cross-section of different fund returns. The risk measure is based on the amount of money that an investor has invested into private equity funds (paid in capital) and assesses their “invested capital at risk” (iCaR).

In the following analysis, we calculate the “invested capital at risk” based on a historical simulation, assuming that the return patterns in the future will have a probability distribution similar to the historic values ^{2}.

This analysis uses performance data provided by Thomson Venture Economics. A total of 2,699 funds (1,015 buyout funds and 1,684 venture capital funds) were included in the analysis. The funds have their investment focus either in Europe or the US and have different strategies and vintage years between 1983 and 2003; due to J-curve effects we excluded immature funds. Cash flows and reported NAV numbers are taken into account up to 30 June 2007.

Figure 1 (see previous page) shows the probability density of the multiples of an investment in one randomly chosen private equity fund in a randomly chosen vintage year. The multiple used is “Total Value to Paid In” (TVPI) which measures the ratio of net asset value and the sum of all distributions to the total of invested capital. The highest probability (the mode of the distribution) is located at a multiple of 1, i.e. the most probable outcome of a random investment into a single private equity fund is that the investor will get back the invested capital. However, there is a relatively strong probability both of loss for the investor and also of achieving substantial gains.

The 1st percentile of the historical distribution is located at a multiple of 0.16 which corresponds to an “invested capital at risk” (iCaR) of 84 percent. This implies that the private equity investor has a confidence level of 99 percent of losing less than 84 percent of their investments by the end of the fund's lifetime.

**DIVERSIFICATION REDUCES RISK**

The example presented shows that investing in a single private equity partnership can be risky and that the amount of money lost can be relatively high. However, it is well known that diversification reduces risk and tends to increase the return of a portfolio ^{3}. The right skewed distribution of private equity multiples is responsible for this effect ^{4}.

Diversification can be implemented in different ways. In the following, we concentrate our analysis on two dimensions of diversification: the number of fund commitments per

vintage year and the number of vintage years. Spreading the commitments over a number of vintage years and over a number of funds per vintage year has a positive effect on the risk exposure of a private equity portfolio. However, the effect differs for both dimensions, i.e. spreading commitments across one fund per year over 15 vintage years has a different effect than committing to all 15 funds in the same vintage year.

For further analysis, we conducted Monte Carlo simulations that construct portfolios randomly out of the funds in the database and calculate their multiples. All portfolios invest globally and they are broadly diversified in terms of fund focus.

Figure 2 (above) shows the empirical distributions of portfolio multiples of 10,000 randomly constructed portfolios using different selection criteria. The grey distribution corresponds to an investment in a random fund as described above. The black distribution reflects an investment strategy in which an investor allocates money to 15 randomly chosen private equity funds in a single randomly selected vintage year. This strategy sharply reduces the risk. The left tail of the distribution has moved towards the right and the probability of losing money is consequently reduced. This is also reflected in a lower iCaR of only 22 percent, i.e. an investor loses less than 22 percent of the invested capital in 99 percent of all cases.

Alternatively, the investor may choose to diversify across a number of consecutive vintage years. In order to run the simulation as realistically as possible, a vintage year is first chosen at random and then investments are made in a defined number of funds in that and following years. The simulation gives rise to the green distribution. Diversification over a number of vintage years therefore not only reduces the risk (iCaR of zero percent) but also increases the average performance of the portfolio. It can also be seen that diversification by number of vintage years has a stronger effect on risk reduction than diversification over the number of funds. Two effects are responsible for this: first, the risk of loss is not constant over different vintage years and, second, the typical private equity diversification effect kicks in because of the right skewed distribution of multiples per individual vintage year.

Finally, the red distribution shows the combination of both dimensions of diversification, namely an investment timeframe of 15 years and investments in 15 private equity funds per year. In addition to the substantial reduction of risk on the left-hand side of the distribution, one can see a further shift of the entire distribution into the positive area. The investor has no risk of losing capital (iCaR of zero percent) with a probability of 99 percent because the entire distribution lies in the positive multiple range. Because the 1st percentile case is located at a multiple of 1.56 the investor has historically received more than one and a half times the invested money with a 99 percent confidence level. This implies that the investor can even in bad cases generate a significant positive return to cover the cost of capital.

At the same time, the tails of the distribution are smoothed to a large degree and the highest probability is now located at a multiple of 1.84. The price for this enormous risk reduction is a decrease in the possibility of achieving an extraordinarily large multiple, i.e. the fat tail of the distribution on the right side has disappeared as shown in the red distribution of figure 2.

**MAPPING THE RISK OF PRIVATE EQUITY**

After having presented some specific examples of diversified investment strategies, we will now look at the risk of a variety of portfolios. Again with the aid of Monte Carlo simulations, we calculate risk combinations for an investment timeframe of between 1 and 15 years as well as for investments in 1 to 15 funds per vintage year. In order to demonstrate the changes in the portfolio risk, the “invested capital at risk” (iCaR) measure is used.

Figure 3 (above) presents the results of the risk analysis of diversified portfolios. The x-axis shows the diversification over vintage years while the y-axis shows the number of fund investments per vintage year. The colours represent the values of the risk measure. It is evident that the risk of an investment in a broadly diversified portfolio of private equity funds was historically very low and can be reduced to almost zero in the 1 percent case (red area in figure 3).

The graph shows that even a relatively small degree of diversification considerably reduces the risk of a private equity investment. Assume that an investor begins with the development of a private equity programme and invests in five private equity funds in the first year. As the graph shows, he bears a risk (iCaR) that in 99 percent of cases he will incur a loss of less than 20 percent to 30 percent (the turquoise coloured area) of his capital invested at the end of the fund's lifetime. If he keeps to his investment pace of five funds per year, he can reduce his risk after three years to less than 10 percent of capital invested (the orange coloured area). Note again that this loss has occurred historically with a probability of only 1 percent. After diversifying over only five vintage years, the investor, in 99 percent of all historic portfolio simulations, does not lose any capital at all which is reflected in an iCaR of zero (the red-coloured combination of number of funds and vintage years).

These risk analyses are based on random selections of private equity funds across the global market for private equity; investments are therefore made in European and US funds and in venture capital as well as buyout funds. Funds operating in different geographies and investing in different types of companies have different risk characteristics, which can also be mapped.

As an example, Fig. 4 (following page) shows the universes of venture capital and buyout funds and presents their invested capital at risk measure separately.

It can be seen that an investor has to diversify over more venture funds than buyout funds in order to reach a similar risk exposure. With a diversification over three funds per vintage year and three years the “invested capital at risk” of the buyout sector is zero, while it is still between 20 percent and 30 percent for venture capital funds. To reach a similar risk position the investor has to invest in at least five funds per year during seven vintage years. In a more detailed analysis it is also possible to calculate the risk of various stages, e.g. mega, large, mid and small cap or various venture capital stages.

**CONCLUSION**

The risk measure “invested capital at risk” can be used to assess the risk of private equity investments. We have calculated the “invested capital at risk” for a number of different portfolios using historic performance data. We have shown that diversification over a number of funds committed in one vintage year reduces risk. A broader spread over a number of vintage years, however, reduces the risk even more and also increases the expected return of the portfolio. A combination of both diversification strategies and a globally diversified private equity portfolio results in zero “invested capital at risk” at the 99 percent confidence level.

All results presented above are based on random fund selection. Given the fact that there is a very wide span between good and poor private equity funds, risk in private equity can be significantly reduced further by positive fund selection skills. This implies that a portfolio of a given diversification of a skilled investment manager has a lower “invested capital at risk” (iCaR), or that he can reach a given iCaR with a lower degree of diversification.

A similar risk analysis can also be undertaken for any kind of portfolio allocation. The methodology can be used to assess the current risk position of the portfolio and to adjust the future commitment programme in order to reach a risk-optimised portfolio.

Christian Diller and Ivan Herger are vice presidents in portfolio & risk management at Capital Dynamics, one of the world's largest private equity asset managers, with an exclusive focus on private equity. Capital Dynamics has offices in Zug (Switzerland), London, Birmingham (UK), New York, San Francisco and Hong Kong.