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Exposed to the J-Curve: Understanding and Managing Private Equity Fund Investments

Understanding the correlation of private equity to other asset classes and, indeed, within its own sub-segments is a fundamental part of developing a fund investment strategy. In an extract from a newly published book, Ulrich Grabenwarter and Dr Tom Weidig discusses the correlation and how it should be related to portfolio construction.

Sample chapter - Chapter 6

Asset allocation to and within private equity

Correlation between private equity and other asset classes

Why is correlation important?

The strength of the relationship, that is the correlation, of private equity to other asset classes is important to asset allocation because the diversification effect of adding private equity to a portfolio consisting of other asset classes increases the lower the correlation. In general, the less correlated assets are within a portfolio, the lower the risk of the portfolio because low and high performances happen independently of each other and cancel out each other. Thus, if private equity were less correlated with other assets within a bigger portfolio, a greater capital allocation to private equity would make sense. The discussion of correlation is conducted on two different levels: based on conceptual arguments, for example, the exit price level of portfolio companies is influenced by the stock market and the correlation between private equity and public markets therefore must be strong; and on empirical numerical evidence, for example, looking at the historical correlation between a private equity index and a public stock market index such as the Dow Jones and concluding that the correlation between the two is low. For investors, this discussion is important, as they want to know whether the diversification effect from adding private equity to a portfolio of publicly traded stocks is high, or, if this is not the case, whether the risk-adjusted return on their overall portfolio improves. If the case for neither of the two is convincing, investing in private equity is not useful.

What are the problems when determining correlation?

What is the correlation between private equity and a public index? The question appears to be clear, but its meaning is less easily understood: is it the correlation between direct investments and the index, or between a private equity index and the public index? For example, a private equity investor cannot hold an index of private equity, but can only invest in several private equity funds, whereas public equity investors can hold the index. Thus, a correlation study between a constructed private equity index and a public index is not directly relevant to the investor as the investor can only invest in a small part of the available private equity funds.

But there are additional issues with correlation. First, returns on private equity funds are measured using internal rate of return (IRR) or multiple; public market products use time-weighted return (TWR). Thus, they use two different return measures, which makes it meaningless to compute a correlation between the two time series. In theory, a volatility of private equity could be computed using the TWR where the inputs are the quarterly reported net asset values (NAVs) plus the cash flows in between. As explained above, changes in NAV are artificially low due to infrequent updates and the conservative valuation methods. Any correlation computation will therefore reveal a low relationship to public indices. Second, even in public markets, the study of correlation is viewed with suspicion. Correlation typically fluctuates substantially and changes dramatically with the period of sampling. Hence the saying: 'Lies, volatilities, and correlations'. Moreover, during a severe downturn or market crash all asset classes become much more correlated. Third, there are two ways to approach the question of correlation, namely whether it is correlation of the cash flows or the overall return. However, the overall return, that is the fund's IRR or public market equivalent (PME), might be less correlated. A fund manager typically invests over the first five years and divests over the last years, and the returns between two direct investments is less correlated when the first happens in year one and the second in year five than for the same year. This effect might become important and reduce the correlation with the stock market.

How strongly correlated is private equity to public indices?

Many early studies claim a low or moderate correlation, but their methods are flawed. These studies mainly use the two well-known private equity indices from Cambridge Associates and from Thomson Venture Economics, which create time series based on the drawdowns, distributions and the NAV of the unrealised investments. And, as shown before, the volatility is artificially low, which leads to an artificially low correlation. This view is supported by Singer, Staub and Terhaar (2003), but also by Gompers and Lerner (1999) who authoritatively state that: 'Many institutions ...have increased their allocation to venture capital and private equity in the belief that the returns of these funds are largely uncorrelated with the public market ...But there appears to be many linkages between the public and private equity market values. Thus, the stated returns of private equity funds may not accurately reflect the true evolution of value and the correlations reported by Venture Economics and other industry observers may be deceptively low. To ignore the true correlation is fraught with potential dangers.'

Even without looking at empirical evidence, amount and timing of distributions should be correlated to the stock markets. A boom in the stock market means better opportunities for successful IPOs, more cash in the pocket of trade buyers and higher valuations for companies. Several academic studies(1) have looked at the relationship between exits and the stock market, and find a significant correlation. The market conditions affect the decision to go public, and the exit opportunity.

To summarise, the distributions of a fund are clearly affected by the markets. Thus, investors should expect that when the stock market goes down, distributions will also dry up, though possibly with a time lag of a few months(2). Still, even if distributions dry up during a downturn, the value of the portfolio company might not have been lost but postponed with an exit a few years later. This realisation leads to the question of whether the fund performance is less correlated because it is the aggregated performance of 10 to 20 portfolio company investments spread over 10 years. The bad and good periods might cancel out each other to some extent.

Finally, several researchers have tried to overcome the problem with correlation due to infrequent valuation, and devised several methods. They all find non-zero moderate to high correlation between a corrected private equity index and a public index.(3)

Asset allocation to private equity

Standard asset allocation and its problems

The standard procedure for asset allocation was first proposed by Markowitz, and is based on maximisation of the risk-adjusted portfolio return. The general idea is twofold: first to estimate for each asset class its future return and risk and the correlation between the asset classes using historical data, and then to find the appropriate weighting for each asset class that makes the risk-adjusted portfolio return maximal. In essence, the bigger a weight the asset class has in the optimal portfolio the higher must be its risk-adjusted return and/or the lower its correlation with other asset classes. The approach is conceptually very instructive to understand the dynamics of asset allocation; that is in the world of mathematical finance, until reality kicks in during implementation. There are many problems with the approach:(4) returns are often not distributed (which goes against Markowitz's assumption), extreme events are not included, correlation between asset classes is not stable, especially in a market crisis, lack of liquidity and marketability is completely ignored, and estimation of historical data is problematic. These issues already apply to publicly traded assets!

How much capital to allocate to private equity funds?

To be absolutely clear, there is no and never will be a definite answer to this question. The Markowitz approach is very useful in the sense that the investor understands the main dynamics on constructing an efficient portfolio. However, its implementation for liquid products is difficult to get right, and very difficult for illiquid products. Rather than being obsessed by numbers, the investor should take a step back and look at the big picture.(5) To start with, the question is not about digits behind the comma, but rather: should there be no allocation, between 5 per cent and 10 per cent, or more? Investors with no long-term investment horizon should not allocate capital to private equity. Most institutional investors with the appropriate long-term investment horizon who have concluded that private equity exposure improves their risk-adjusted portfolio return should be able to invest from 5 to 15 per cent of their assets in private equity. This recommendation is in line with the current allocations by institutional investors.(6) A quantitative analysis in the style of Markowitz might tilt the balance between a smaller share of between 5 per cent and 10 per cent, or a share of between 10 per cent and 15 per cent.

Correlation between private equity funds of different investment foci

An investor not only needs to look at the correlation to the public markets, but also at the correlation between different segments of private equity. Again, such a study is difficult to undertake, because there are no real indices for each segment such as public indices. Private equity indices do exist that considers all drawdowns, distributions and NAVs, but no investor can invest in this way. Therefore, investors should look at the correlation between returns of private equity funds and different investment foci. The question is: how correlated are the performances of funds that start in the same year with funds of the same market segment and funds of other markets?

The following study(7) provides an example. The analysed market segments are both from the United States and Europe, and comprise early-stage venture capital funds copyright material and mid-market funds composed of late-stage venture capital and small to medium-sized buyout investments. There are 10 correlations of markets possible (four within the same markets or market segments and six between different markets). Exhibit 6.1 shows the results of this correlation study. The correlation within the markets is greatest and around 40 percent, and is small between markets. This result shows that there are indeed different market segments that move relatively independently of each other. A further interpretation of the findings is tricky, because the strength of the correlation varies with the sampling period, but does not change the qualitative statement made. Further, investors should be aware that even though there seem to be significant diversification benefits for a mixed portfolio regarding the overall returns and risks, the distributions from the different market segments are very likely more strongly correlated, that is if the stock market goes down, all distributions dry up.

Asset allocation within private equity

Investing in a broad range of funds across several vintage years

Once investors have fixed the asset allocation to private equity, often within the allocation to alternative investments, they need to decide how to implement this part of their global long-term investment programme. The first implementation issue arising is the allocation of capital to various private equity sub-segments and vintage years to ensure a well-diversified portfolio. But like the asset allocation to private equity, it is no easy task to convincingly construct the portfolio with an optimal combination of different subtypes such as: venture capital and buyout, US, Europe and emerging markets, technology and traditional sectors, and across several vintage years. The investor also faces a new issue, namely investment constraints. For example, a portfolio might be diversified across vintage years but not across stages and sectors, because a balancing for stage and sector might make it impossible to have an equal amount of high-quality funds per vintage year.

There are no fixed rules on how much to allocate to different sub-segments. Generally, the private equity fund investor should invest in funds across a broad range of regions, vintage years, sectors, managers and stages. Of course, some investors might decide to exclude some market segments due to meager historical risk-adjusted returns, foreign private equity due to unwanted currency risks, or technology funds due to high NASDAQ index exposure.

Implementing the asset allocation goal

Thus, implementation of a chosen asset allocation is not straightforward and far more tricky than for a portfolio of liquid assets. Essentially, the private equity fund investor needs to master two important tasks:

• select high-quality investments and make sure that the fund investments are well-structured and monitored, as shown in Part II; and
• ensure the efficient implementation of the private equity investment programme by balancing and monitoring the portfolio while ensuring sufficient liquidity and diversity, as shown in Part III.

Some institutional and high net worth investors do not want to take on these tasks and choose to invest in funds indirectly. They should consult Part IV for a discussion of alternative investment vehicles.

1 See, for example, Gompers and Lerner (1999).

2 See Weidig, Kemmerer and Born (2004).

3 See EVCA (2004b), Peng (2001)and Quigley and Woodward (2003),and Gottschalg, Phalippou and Zollo (2004).

4 See, for example, Swensen (2000).

5 Nevertheless, EVCA (2004b) and Schmidt (2004)have taken on these challenges, and came up with asset allocation weights: 5 per cent for venture capital and 8 per cent for buyout funds.

6 See, for example, Blaydon, Wainwright and Hatch (2003), Singer, Staub and Terhaar (2003),and EVCA (2004b).

7 Study undertaken by Weidig for this book.

This was an extract from 'Exposed to the J-Curve: Understanding and Managing Private Equity Fund Investments by Ulrich Grabenwarter and Tom Weidig', published by Euromoney Books.

Further information can be found on the Euromoney website: http://www.euromoneybooks.com/default.asp?page=4&productID=3648