5
Returns, Risk Premiums and Risk Factor Allocation
Investors who invest in illiquid asset classes expect to achieve higher returns, compensating them for the lack of liquidity they have to accept. From a portfolio standpoint, the illiquid nature of investments in limited partnership funds makes it difficult, if not impossible, to continuously rebalance an investor's portfolio – a key assumption in standard asset allocation models (Ang and Sorensen, 2011; Ang et al., 2011). Shares in limited partnership funds cannot easily be liquidated, despite the development of a secondary market in recent years, as we discuss in Chapter 6. In addition to market liquidity risk, investors face funding risk, or commitment risk, as they have to be able to respond to capital calls at any given point in time. Since capital calls and distributions are stochastic, investors may suddenly become overcommitted or undercommitted, moving investors away from their optimal portfolio and reducing diversification benefits (Phalippou and Westerfield, 2012). Measuring and managing funding and market liquidity risk is essential for investors in illiquid asset classes, an issue we return to in the second part of this book.
Quantifying the risk premium in illiquid asset classes is subject to considerable conceptual and statistical challenges. While the literature on investment returns of illiquid assets has expanded significantly in recent years as more data have become available, most studies have focused on comparing such returns with returns of liquid assets. However, as we discuss in this chapter, studies focusing on risk-adjusted returns, and especially on returns adjusted for liquidity risk, have remained rare and their results should still be viewed with considerable caution as this literature continues to evolve. Despite the significant difficulties in measuring risk in private equity and real assets as illiquid asset classes, a growing number of institutional investors are adopting an asset allocation approach that aims explicitly at harvesting asset-specific risk premiums. More specifically, as we outline in the second part of this chapter, the risk factor allocation strategy seeks to exploit diversification gains from uncorrelated investment risks – as opposed to uncorrelated returns as emphasized in traditional mean–variance approaches.
5.1 RETURNS AND RISK IN PRIVATE EQUITY
Many asset allocators construct their portfolios according to a two-step process. In the first step, investors generally determine the desired share of each asset class in the overall portfolio. In the second step, investors then design particular investment strategies within each asset class (Sharpe, 2007). In this chapter, we are primarily concerned with the first step. As we have seen in Chapter 2, illiquid asset classes are essentially limited to long-term investors with appropriate liability profiles. Their long-term liabilities allow them to invest in illiquid asset classes that promise higher returns in compensation for a higher degree of illiquidity. But do illiquid asset classes actually generate comparatively higher (risk-adjusted) returns? In addressing this question, the natural starting point is to compare private equity returns with public equity returns; two asset classes that are identical in terms of their position in the capital structure of companies, but subject to fundamentally different degrees of liquidity.
5.1.1 Comparing private equity with public equity returns
As far as leveraged buyouts are concerned, GPs usually employ a combination of three measures to create value and achieve superior returns for their LPs:
- Strategic measures include buy-and-build initiatives, divestments of non-core businesses and development of new products and markets, aimed at enhancing EBITDA growth and usually leading to multiple expansions.
- Operational measures are focused on improving product quality and sales effectiveness, reducing overhead costs and optimizing the company's value chain.
- Financial measures aim at maximizing capital efficiency and optimizing the company's capital structure.
In implementing strategic, operational and financial measures, GPs pay particular attention to effective governance structures, ensuring that the company's management's interests are fully aligned with the owners' interests. Management teams of portfolio companies are therefore incentivized by giving them a large equity upside through stocks and options. At the same time, the management team is usually also exposed to the downside by requiring executives to make a meaningful investment in the company.
There is ample evidence from the 1980s that buyouts have led to considerable gains in operational performance and increases in firm values or both (for a review of the literature, see Kaplan and Strömberg, 2009). Unfortunately, there is still much less evidence from the 1990s and the most recent buyout boom. An exception is Guo et al. (2011), who study 192 buyout transactions completed between 1990 and 2006. Surprisingly, they find that gains in operational performance were substantially smaller than documented for deals of the 1980s, which appears to contradict the growing emphasis on operational measures relative to financial leverage. Overall, however, Guo et al. find that returns to either pre- or post-buyout capital invested are positive and significant, a result which is consistent with earlier studies of buyout transactions in the 1980s. Importantly, the value creation appears to be long-lasting: Cao and Lerner (2009) who study reverse leveraged buyouts (initial public offerings (IPOs) of firms that had previously been bought out by private equity investors) find that such transactions outperformed non-private equity IPOs even after five years.
As far as European buyouts are concerned, Kaserer (2011) analyses 332 mid-market buyout transactions from 1990 to 2011. Employing a novel approach to decompose the returns into different value drivers – earnings growth, multiple expansion and financial leverage – he finds that around two-thirds of gross returns in European buyout transactions are attributable to strategic and operational measures aimed at increasing earnings. By contrast, multiple expansion was found to be negligible. While the leverage effect was estimated to contribute another third, it was statistically insignificant, leading Kaserer (2011) to conclude “…that if there is any benefit to leverage, it may be reaped by the seller instead of the buyer in a buy-out transaction”.
Somewhat different results are reported by Achleitner et al. (2011), who studied performance drivers of European and North American buyout transactions completed between 1986 and 2010. Specifically, the authors provide evidence that returns have been more broadly based, with multiple expansion playing a meaningful role in addition to operational improvements and leverage. Finally, Acharya et al. (2013) examine 395 buyout transactions in Western Europe between 1991 and 2007. Correcting for leverage, they find abnormal performance to be significantly positive on average, driven by greater growth in sales and greater improvement in EBITDA to sales ratio (margin) relative to those of quoted peers.
Notwithstanding the role of individual value drivers, there is general agreement that buyout transactions have generated profits for private equity funds. But this does not necessarily mean that investments in private equity partnerships represent attractive investments for LPs. To begin with, sellers may capture a significant amount of the value a private equity firm creates as the latter generally pays a significant premium in buyout transactions. Furthermore, as we discussed in the previous chapter, GPs receive significant compensation from their LPs in the form of management fees and carried interest. What matters for LPs are the partnership's distributions net of fees and carried interest, as opposed to the gross returns the GP achieves.
There are a growing number of studies which aim to measure the net-of-fees returns of private equity funds and compare them with the returns a LP would have received if he had invested the same amount of capital in a public market index (for an overview, see Diller and Wulff, 2011). Using a dataset from Thomson Venture Economics (TVE) consisting of 169 (largely liquidated) US buyout funds that were raised before 1995, Kaplan and Schoar (2005) compared how much a LP earned net of fees with what the investor would have earned in an equivalent investment in the S&P 500. In order to make the performance comparable, the authors employ a measure known as the public market equivalent. This measure is calculated by investing (or discounting) all cash outflows of a fund at the total return to a public market index (in this study the S&P 500) and comparing the resulting value with the value of the cash inflows (all net of fees) to the fund invested (discounted) using the total return to the public market index. Thus, the PME circumvents a well-known problem with IRRs, which lies in the reinvestment hypothesis of the underlying cash flows.1 The PME has a value of 1 if an investment in a limited partnership achieves exactly the same returns as an investment in the public stock market. The PME is larger (smaller) than 1 if an investment in a limited partnership outperforms (underperforms) an investment in the public stock market.2
For the buyout funds in their sample, Kaplan and Schoar (2005) report a PME of 0.97, indicating that, net of fees, such partnerships have slightly underperformed the public market. The underperformance was somewhat higher (PME = 0.93) when average returns were measured on a size-weighted basis. Thus, Kaplan and Schoar (2005) did not find the outperformance often given as justification for investing in private equity as an illiquid asset class.3 Using a slightly updated version of the Kaplan and Schoar dataset, Phalippou and Gottschalg (2009) obtained qualitatively similar results. In fact, assuming that the market value of non-liquidated mature funds equals zero (complete write-offs), their findings suggest an even greater degree of underperformance of buyout funds on a net-of-fees basis. The sobering conclusion one might draw from these studies is that even on a risk-unadjusted basis, investments in private equity are rather unattractive. This conclusion gains even more weight if one factors in that private equity investors accept a high degree of illiquidity. Thus, it seems that from a return perspective commitments to buyout funds make sense only if investors are able to commit capital to upper-quartile funds for which significant outperformance is found.
Turning to VC investments, which are typically unleveraged, the picture appears comparatively brighter, at least for the period before the tech bubble. Based on a TVE sample of 577 VC funds, Kaplan and Schoar (2005) calculate a size-weighted PME of 1.21, indicating that LPs in such funds received significantly higher returns than a similar investment in public stocks would have generated. For all private equity funds in their sample, Kaplan and Schoar (2005) thus report a size-weighted average PME of 1.05, implying a slight outperformance of private equity as an asset class compared with a public market investment.4
More recent research suggests that private equity has probably outperformed by a wider margin than earlier studies (Kaplan and Schoar, 2005; Phalippou and Gottschalg, 2009) found. As mentioned above, these studies used a dataset from TVE, which, however, shows on average considerably lower private equity returns than other data providers – such as Burgiss, Cambridge Associates, Preqin and State Street (Harris et al., 2010, 2012; Cornelius, 2011). As Figure 5.1 shows for US buyout funds, IRRs reported by different data providers follow a similar pattern over time, but differ by several hundred basis points in individual vintage years. These variations are due to the very nature of the data – namely that information about fund returns is private. While some data providers rely on voluntary and Freedom of Information Act (FOIA) disclosures by GPs and LPs (Preqin, Thomson), others obtain data from LPs who use them for back-office services and fund investment monitoring (Burgiss, Cambridge Associates). While no database contains all funds ever raised, arguably the former are particularly prone to selection bias and problems with data updating.
Figure 5.1 Comparing four different benchmarks for US buyout fund returns (IRR, net of fees).
Source: Harris et al. (2012).
The suspicion that TVE may have understated the true returns of private equity funds finds support in recent research by Stucke (2011), who analyses in detail the return data reported by the vendor. More specifically, he finds that the NAV for a significant number of funds in the TVE dataset were not updated, presumably because Thomson stopped receiving data from GPs/LPs and simply repeated the last known NAV in subsequent quarters. This was the case in a significant number of funds, with fund-level IRRs falling with the passage of time in the absence of recorded cash flows. Correcting for this inertia, Stucke (2011) finds significantly higher fund returns than were reported in earlier research.
Harris et al. (2012) use a dataset provided by Burgiss, a back-office service provider. This dataset is not only particularly comprehensive in terms of the number of funds constituting the benchmark, but is also arguably less prone to selection bias and problems with data updating. Their results suggest that earlier studies are likely to have understated the performance of private equity funds, particularly for buyouts. In fact, the degree to which the performance of buyout funds is likely to have been understated is far from trivial: Harris et al. (2012) estimate an average outperformance versus the S&P 500 of between 20% and 27% over the life of the average US buyout fund, or more than 3% per year. On an unweighted basis, the authors find an average PME of 1.22 for the vintage year period from 1984 to 2008; on a capital-weighted basis, the estimated average PME is 1.27. In fact, of the 25 vintage years in the sample, only five had average PMEs of less than 1 (see Figure 5.2) As far as VC funds are concerned, the authors find that this asset class has outperformed public markets substantially in the 1990s, but underperformed in the 2000s.
Figure 5.2 US buyout returns – vintage year public market equivalents.
Source: Harris et al. (2012).
The results obtained by Harris et al. (2012) are materially similar to those reported by Robinson and Sensoy (2011), whose analysis is based on data provided by a large LP. Their database includes not only US buyout funds but also international partnerships. Although PMEs from Burgiss and Robinson and Sensoy differ for individual vintage years, both studies agree that buyout PMEs exceed on average 1.0, indicating that private equity funds have generated superior returns compared with public equity investments.
Similar conclusions are also drawn by Higson and Stucke (2012), who use cash flow data provided by Cambridge Associates. Their sample includes US buyout funds raised between 1980 and 2008. As far as liquidated funds from 1980 to 2000 are concerned, the authors report excess returns of about 450 bps per year; excess returns increase to over 800 bps if the sample is extended to partially liquidated funds up to 2005. Importantly, however, the cross-sectional variation is found to be considerable, with just over 60% of all funds doing better than the S&P 500 and excess returns being driven by top-decile rather than top-quartile funds. Furthermore, the authors find a significant downward trend in absolute returns over all 29 vintage years in their sample.
While the Harris et al. (2012) and Higson and Stucke (2012) papers find significant outperformance, the question arises as to whether the S&P 500 represents an appropriate benchmark for private equity returns. Based on data by Capital IQ, a leading data vendor, Phalippou (2012) stresses that 95% of the enterprise values reported for leveraged buyout transactions are below USD 1, 175 million, which is close to the largest stock in the Fama–French small cap index. According to Harris et al. (2012), however, the relative performance of US buyout funds is surprisingly insensitive to the benchmark. In fact, the authors obtain essentially identical results when they calculate PMEs on the basis of the Russell 2000, which measures the performance of US small-cap stocks.5
An even thornier issue pertains to risk. While the recent literature suggests that US buyout funds have outperformed public equity investments, in and of itself this tells us little as to whether LPs are adequately compensated for the greater risk they take when committing capital to private equity partnerships.
5.1.2 Market risk and the CAPM
Investment risk is generally perceived as the variance of returns over time. The greater the variance, the riskier the asset class. Other things being equal, asset classes whose returns are more stable will receive a larger portion of an investor's portfolio (and vice versa). Put differently, investors are willing to allocate capital to asset classes with a higher variance of returns only if they get compensated through higher expected returns. The relationship between the returns and their variance is expressed by the Sharpe ratio, which, in its original form (Sharpe, 1966), 6 is calculated by dividing (i) the historical excess return, E[R], over the riskless rate of interest, Rf (typically the 3-month treasury bill rate) by (ii) the standard deviation of its excess return, σ:
It is one of the greatest achievements in finance theory, however, to show that at least part of the risk is diversifiable, or idiosyncratic. What matters in the portfolio context is the extent to which asset returns are correlated, an insight that has its roots in the groundbreaking contributions by Markowitz (1952), Treynor (1962), Sharpe (1964), Lintner (1965) and Mossin (1966). Based on this insight, MPT attempts to maximize expected portfolio returns for a given amount of portfolio risk (or, equivalently, to minimize portfolio risk for a given level of expected returns), by carefully allocating capital to diverse asset classes. In efficient and complete markets with no restrictions, the optimal allocation is determined in such a way that the expected rate of return of an asset reflects the systematic, or non-diversifiable, risk of the asset in a broader investment portfolio. This risk is usually called market risk or beta risk. This is the essence of the CAPM, which stipulates that the price paid for an asset is determined by the degree to which the market portfolio's risk/return characteristics improve when the asset is added to it.
Public market equivalents, as calculated by Kaplan and Schoar (2005) and Harris et al. (2012), implicitly assume that market risk in private equity is 1. This might or might not be correct. Buyout deals are leveraged, with an average debt-to-equity ratio in US and European transactions of roughly 60:40 over the past 10 years. Leverage amplifies returns as well as losses, which, other things being equal, would suggest a beta of greater than 1. In other words, a beta of 1 would require other factors (e.g., structural and operational improvements in portfolio companies) just offsetting the impact of leverage on returns.
Some studies have attempted to estimate market risk and excess returns in buyouts and VC explicitly. However, the nature of private equity investing, the reporting of returns and the limited availability of performance data make this a difficult task.7 First of all, standard asset-pricing models have been developed for marketable assets that are traded in transparent, liquid and essentially frictionless markets. These assumptions hardly apply to private equity investing (or similar investments in real assets). Second, private equity returns are observed infrequently, with the standard databases potentially subject to sample bias due to the over-representation of well-performing funds. Thus, the estimated alphas and betas may need to be adjusted to provide meaningful measures of returns and risk for private equity investments.
While some studies have used fund-level data to measure alpha and beta, others have employed deal-level data. As far as the former are concerned, Ljungqvist and Richardson (2003) examine cash flow data from a large LP investing in funds raised between 1981 and 1993, with the sample consisting of 19 VC funds and 54 buyout funds. They find an average fund IRR (net of fees) of 19.81%, compared with the average S&P 500 return of 14.1% during this period, implying a considerable outperformance of the former. In order to estimate beta risk, Ljungqvist and Richardson then assign each portfolio company to one of 48 broad industry groups and use the corresponding average beta for publicly traded companies in the same industry. For buyouts the authors obtain a beta of 1.08, for VC investments they estimate a beta of 1.12. Given the estimated returns and the market risk in private equity, Ljungvqist and Richardson (2003) interpret the 5–6% excess returns as an illiquidity premium. Note, however, that these results are not adjusted for higher (lower) leverage used for buyouts (VC) compared with the S&P 500.
Driessen et al. (2011) present a new empirical method to estimate alphas and betas from fund-level cash flows. Using data from 272 mature buyout funds raised between 1980 and 2003, the authors find betas of 1.3 to 1.7 depending on the specification of the underlying model. While buyout funds in their sample have a slightly negative alpha of 0.4–1%, the estimates are statistically insignificant. As far as VC funds are concerned, the Driessen et al. sample contains 686 partnerships. The authors find betas of 2.4 to 2.7, with negative alphas of 0.7–1%.
Other academic studies use company-level data. Such data may be advantageous in the sense that they contain more disaggregated information, which may lead to more precise estimates of risk and allows for an analysis of risk and return as a function of individual company characteristics. However, researchers using company-level data face their own set of challenges. To begin with, company-level cash flow data exclude management fees and carried interest paid by the LPs. As a result, estimated risks and returns reflect the gross-of-fees risks and returns of the investments, not those earned by the LPs. Second, company-level data require continuous-time specifications, whereas the standard CAPM is designed on a discrete-time basis, implying that it does not compound over time. However, while this is a standard problem in empirical finance, Ang and Sorensen (2011) point out that the continuous-time specification can no longer be interpreted as the abnormal arithmetic return, as in the standard discrete-time version of the CAPM. Instead, as they suggest, the abnormal return (i.e., the “alpha”) can be obtained by adding 0.5 times the square of the estimated volatility: α = δ + 0.5σ2.
As far as VC investments are concerned, there are two major studies that use company-level data: Cochrane (2005) and Korteweg and Sorensen (2011). Using VC company data, both studies find high volatility, which leads to high arithmetic alphas. In fact, Cochrane reports an estimated alpha of 32% annually, which appears very high, given return estimates using fund-level data. At the same time, he finds a slope of 0.6–1.9 for the systematic risk, which appears low. By contrast, Korteweg and Sorensen obtain substantially higher betas, in the range of 2.6 to 2.8. Consistent with this, the authors find alphas that are positive but modest. While the alphas in the late 1990s are found to have been very high, they were negative in the 2000s, a result which is broadly in line with return estimates using fund-level data (e.g., Harris et al., 2012).
Studies on buyouts using deal-level data have remained even rarer. An exception is Franzoni et al. (2012), who use data from CEPRES, an independent advisory firm originally set up as a joint venture between Deutsche Bank and the University of Frankfurt. Their sample includes around 7200 buyout investments between 1975 and 2006. Depending on the specification of the model, the authors find betas of 0.9 to 1.4 and alphas of 0.4% to 9.3%.
Our brief review of recent academic research suggests that there remains considerable uncertainty as to the (excess) returns and market risk in private equity. Systematic risk estimates vary considerably, and to the extent that the true beta is over- or underestimated, the true PME is under- or overestimated. So how sensitive are the PME estimates we reported above to variations in the beta values? One way to look at this is suggested by Harris et al. (2012), who estimate PMEs under the assumption that an alternative investment earned, respectively, 1.5 times and 2 times the return on the S&P 500. This assumption is made to estimate the possible impact of levering up investments in public stocks to levels that are found in financial sponsor buy-side transactions. Interestingly, the PMEs turn out to be remarkably insensitive to the multiple of the S&P 500 return, which leads the authors to conclude “…that systematic risk does not explain our PME results for buyout funds”.
Similar results are obtained by Robinson and Sensoy (2011), who use a proprietary database from a large LP. Specifically, by varying beta they lever the S&P benchmark return used in the PME calculation for buyouts to trace out the “levered PME” beta relation for each fund. While at low levels an increase in beta has a significant impact on the PME, the authors find strongly diminishing effects as beta is raised further. For example, raising the beta from 1 to 1.5 (the high end of buyout beta estimates in the literature) lowers the average levered PME from 1.18 to 1.12 – still a significant outperformance relative to public equity.
5.1.3 Stale pricing and the optimal allocation to private equity
To the extent that academic studies employ cash flow data from largely or fully liquidated funds to estimate risk and returns in private equity, they do not have to worry about stale pricing, a well-known phenomenon in illiquid asset classes. Stale pricing refers to the fact that reported fund returns are generally based on a combination of actual cash flows and NAV calculations of the residual value of the fund for partnerships that are not yet fully liquidated. Despite important industry-led efforts and more stringent accounting rules, 8 NAV calculations remain to a certain degree subjective. Furthermore, valuations are infrequent and usually available only with a delay. However, as market value changes that are not directly observable usually feed only gradually through the reported data, GPs' estimates of remaining values generally represent “smoothed” series.
The disadvantage of using fully liquidated funds is, of course, that the data which can be used is by definition relatively old, given the typical lifespan of a limited partnership. Given that markets may be subject to structural shifts, practitioners typically prefer using more recent data. One example is VC investing, where fund returns in the 2000s appear to have fallen substantially short of their spectacular performance in the late 1990s. However, to the extent that investment portfolios are determined on the basis of fund-level data that include a significant number of relatively young partnerships, it is important for asset allocators to adjust reported returns for stale pricing. Unless corrected for, stale pricing leads to artificially low correlations with the rest of the investment portfolio. Given the uncertainty surrounding true asset pricing and beta measures for private equity and other illiquid assets, LPs may therefore hold portfolios whose risk/return profile is sub-optimal. To the extent that the true beta is underestimated, investors will be overexposed to private equity (and vice versa).
To see how, Conroy and Harris (2007) employ fund-level data obtained from TVE to calculate efficient portfolios consisting of private equity (buyout funds), public equity (S&P 500 for large firms and NASDAQ for smaller firms) and bonds.9 In a standard CAPM framework, they estimate that the optimal allocation to private equity would be 20%, if the representative investor targets annual returns of 10%. With this allocation, the investor's overall portfolio would have an estimated standard deviation of 5.8%. With an expected portfolio return of 12% the optimal allocation to private equity would need to be raised to 50%, implying an increase in the standard deviation to 6.6%.
In a second step, Conroy and Harris (2007) “de-smooth” reported private equity returns in order to deal with the well-known stale price problem in illiquid asset classes. Instead of using raw data reported by GPs, the authors propose “de-smoothing” returns by using a standard Dimson (1979) approach, which takes the current observed reported return as a weighted average of current and past true returns.10 However, while this method focuses on the risk (variance), it accepts the reported returns as the true reflection of the performance of individual funds and the asset class overall. Recalculating the variance–covariance of private equity, Conroy and Harris (2007) find the true risk of private equity to be significantly higher. In fact, the estimated beta jumps from 0.53 using raw data to 1.17 using adjusted data. With private equity being considerably riskier than unadjusted estimates imply, the portfolio weight attached to private equity is considerably smaller at any given expected portfolio return. For instance, with an expected portfolio return of 10%, private equity would be allocated 14%, six percentage points less than implied by the unadjusted raw data.11
Conroy and Harris's (2007) findings support early research by Gompers and Lerner (1997), who examine the investments of one single private equity firm (Warburg Pincus) between the first quarter of 1972 and the third quarter of 1997. Using raw data, they find an arithmetic average annual return (gross of fees) of 30.5%, with a beta of 1.08. However, when they mark-to-market the portfolio and regress the “refreshed” returns on market returns, the beta in the CAPM regression increases to 1.44.12 Although the intercept in the regression is still positive, the authors caution that “the stated returns of private equity funds may not accurately reflect the true evolution of value, and the correlations reported by Thomson Economics and other industry observers may be deceptively low. To ignore the true correlation is fraught with potential dangers.”
5.1.4 Informed judgments and ad hoc adjustments to the mean–variance framework
Instead of using econometric techniques to correct for stale pricing and other anomalies in illiquid assets, some investors, such as the Yale Investment Office (Swensen, 2009), use informed judgments in making adjustments to the observed historical return and volatility characteristics and correlations with other asset classes. For example, whereas the historical correlation coefficient of private equity and US public equity returns is estimated at 41% using raw data, in their asset allocation the Yale Investment Office assumes a coefficient of 70%. As Swensen (2009) puts it: “Assuming that private equity investments generate 12 percent returns with a risk level of 30 percent represents an appropriately conservative modification of the historical record of 12.8 percent with a 23.1 percent risk level.” Similarly, the correlation coefficient between returns on real assets and public US stocks is adjusted upwards to 20% from 1% using raw data. At the same time, the Yale Investment Office uses lower expected returns compared to the reported historical performance of the asset class.
However, in modifying the risk and return assumptions about non-marketable assets and adjusting the correlation matrix between them and other assets, investors should be aware that even relatively small changes can lead to rather dramatic changes in portfolio weights. Especially in illiquid assets, it may be difficult to implement such weights, given their long-term nature and the potentially limited availability of investment opportunities in individual market segments. In addressing this problem in practical applications, it has been suggested by Black and Litterman (1992) to implement an approach that is sometimes described as the “CAPM in reverse”. Specifically, their model takes into account that investment managers tend to think in terms of weights in a portfolio rather than balancing expected returns against the contribution to portfolio risk. The starting point in the Black–Litterman approach is the market equilibrium returns, which provide a neutral reference point in the sense that they clear the market if all investors have identical views. However, the model allows investors to deviate from the neutral market equilibrium by explicitly formulating their own return expectations and specifying the degree of confidence they have in the stated views. The optimal portfolio is then simply a set of deviations from neutral market capitalization weights in the directions of portfolios about which views are expressed.
Furthermore, in adjusting their mean–variance framework, investors should take into account dynamic risk – a key lesson learned from the recent global financial crisis. While the CAPM is static in the sense that correlations are assumed to remain unchanged, in reality risk in the system as a whole may rise, shifting otherwise “normal” correlations of returns among asset classes rapidly upwards. Such shifts may lead to a serious underestimation of risk in portfolio construction. As Spence (2009) explains, an important part of portfolio risk is not stationary. This risk is systemic, and when risk in the system as a whole rises, “normal” correlations of returns among asset classes shift rapidly upwards. If this happens, diversification and hedging models and risk mitigation strategies are bound to malfunction. At the same time, as we discussed above, dynamic risk caused havoc with investors' cash flow models, and when the parameters of these models suddenly shifted due to reduced distributions, the suspension of redemptions, increased margin calls from hedge funds and collateral, some investors were faced with an acute lack of liquidity. Given this experience, a growing number of investors factor in a dynamic risk component and add a complementary part of liquid investments to their illiquid allocations.
5.1.5 Extensions of the CAPM and liquidity risk
While the CAPM has remained the workhorse of asset pricing and is still widely used as a framework for thinking about investments, its various limitations have motivated researchers to develop new approaches. One important limitation in empirical applications arises from the fact that the CAPM uses only one variable (beta) to describe the relationship between returns of a portfolio and returns of the market as a whole. A major extension of the CAPM is the Fama–French (1993) model, which uses three variables. Specifically, the model adds two factors to the CAPM to reflect a portfolio's exposure to small caps and value stocks, two assets that are found to have done better than the market as a whole. In empirical applications, the Fama–French three-factor model has a significantly higher explanatory power than the CAPM, with small caps and value stocks having higher expected returns than large caps and growth stocks.
Another important extension of the CAPM has been suggested by Pastor and Stambaugh (2003), who add a fourth factor to take into account liquidity risk in a portfolio. Specifically, the Pastor–Stambaugh model predicts that market-wide liquidity is an important factor for pricing stocks. Acharya and Pedersen (2005) develop a theoretical model for the liquidity premium in asset pricing, concluding that negative liquidity shocks are associated with both lower contemporaneous and higher predicted future returns.
The Fama–French and Pastor–Stambaugh extensions have been developed for marketable assets, just like the original CAPM. However, recently some researchers have applied these models to private equity as an illiquid asset class. Franzoni et al. (2012) find a significant beta on the liquidity risk factor, implying a risk premium of about 3% annually.13 In interpreting their results, the authors note that due to their high leverage buyouts are sensitive to the capital constraints faced by the providers of debt to private equity, who are primarily banks, hedge funds and collateralized debt obligations (CDOs). In times of high risk aversion and low market liquidity, private equity fund managers tend to find it more difficult to refinance their investments, potentially undermining the performance of their funds.
The liquidity risk premium estimated by Franzoni et al. (2012) for VC and buyout funds is broadly in line with what practitioners generally view as an adequate compensation for the illiquidity of their investments in private equity partnerships. Factoring in this liquidity premium, the findings by Harris et al. (2012) and Higson and Stucke (2012), combined with Robinson and Sensoy's (2011) sensitivity analysis, suggest that private equity represents an attractive asset class for investors. However, this conclusion is not undisputed. As an alternative approach to estimating the liquidity risk premium, Sorensen et al. (2012) calibrate a model of the LP's portfolio choice problem, including the illiquid private equity investment. For a representative LP, they find a substantial illiquidity premium. The cost of illiquidity is similar in magnitude to the combined costs of management fees and carried interest. Moreover, they argue that the public market equivalent measure typically used to evaluate the performance of private equity does not appropriately capture the costs of the risk and illiquidity of these investments. However, more work is needed on risk and liquidity to put this conclusion on a more robust basis.
5.1.6 Liability-driven investing and risk factor allocation
As we have discussed in Chapter 2, accessing the illiquidity risk premium requires an appropriate liability structure as well as an appropriate risk management. Importantly, however, the CAPM – and its various extensions – essentially ignore the liability side of the investor. Strictly speaking, therefore, it is appropriate as an allocation tool only for investors who have virtually no liabilities that lead to predetermined payouts. In practice, family offices and foundations come closest to this type. All others, however, have to take into account their liabilities when allocating capital to different asset classes. An increasing number of pension plans and life insurers are therefore adopting some form of liability-driven investing (LDI) in a consistent framework of asset liability management (ALM), 14 moving away from assets-only frameworks.
Basically speaking, LDI approaches focus on managing the size and composition of the asset pool and the related liability with respect to their sensitivities to changes in interest rates, inflation and other factors determining the capital market environment (Cambridge Associates, 2011). Thus, LDI frameworks take into account risks that affect both sides of investors' balance sheets. The importance of this approach became particularly obvious in the recent financial crisis, which turned out to be the perfect storm for DB pension plans. The combination of sharp declines in equity prices and market-based liability discount rates led to a serious deterioration in the funding status of many pension plans. This situation is often exacerbated in periods of economic stress when sponsors experience declining cash flows and more expensive access to capital markets to fulfil their legal or contractual obligations of making plan contributions.
In allocating capital in an LDI framework, investors have to define their risk-free or risk-neutral position. To be sure, this position is different from assets-only investment approaches where the risk-free asset is generally considered high-quality government bonds (e.g., US Treasuries). Instead, in an LDI framework the risk-neutral asset pool is defined in such a way that it perfectly hedges the investor's liability. This pool serves as a benchmark for evaluating the trade-off between expected returns and risk, given the risk appetite of the investor. The risk appetite itself depends on the individual circumstances of the investor. As far as pension funds are concerned, for example, key variables include: the size of the plan liability relative to the size of the sponsor's balance sheet; the potential size of future contributions relative to the sponsor's projected free cash flow; and the correlation between the sponsor's operations and the return of risky assets and changes in interest rates (Cambridge Associates, 2011).
Consistent with this approach, some institutional investors have decided to create two portfolios – a hedging portfolio and a growth portfolio. The hedging portfolio aims to minimize the volatility between the size of the asset pool and the related liability, which is known as “surplus risk”. For DB pension plans, this risk is generally a function of changes in interest rates and inflation, both of which affect the liability value for the sponsor. In hedging surplus risk, investors typically buy fixed-income instruments with interest rates that in the ideal case have exactly the same derivation as the discount rate. In cases where benefits are indexed to inflation, hedging portfolios usually rely on inflation-linked bonds and inflation swaps. The exact structure of the hedging portfolio is determined by whether the investor's approach focuses on simply matching durations or cash flows, or a hybrid approach between the two.
The growth portfolio aims to generate excess returns in order to reduce contributions. In pursuing this objective, a growing number of investors have shifted to a risk-focused asset allocation approach that may be better suited to capture potential diversification benefits. Importantly, investors who have already adopted this approach typically employ simplified asset allocation frameworks that emphasize risk factors as key drivers of return. Institutions that are moving into this direction include some of the world's largest asset allocators, such as CalPERS, the Canadian Pension Plan Investment Board, 15 the Danish pension fund ATP, the Norwegian Sovereign Pension Fund and the sovereign wealth funds of New Zealand and Alaska. In fact, some investors have allocations to as few as four or five broad categories, as opposed to highly granular asset class buckets that were common in the pre-crisis era. In a risk factor allocation, illiquidity risk is explicitly taken into account, alongside other risk factors such as equity risk, term risk and credit risk. Each risk factor offers a particular reward for investors (see Figure 5.3). Accessing these premia requires investments in specific asset classes, whose allocations are determined in an ALM framework. As far as private equity is concerned, returns are generated from both an equity risk premium and an illiquidity risk premium.
As the WEF (2011) emphasizes, the increasing switch to a risk factor allocation approach within an LDI framework has been motivated not least by the disillusionment about traditional investment strategies. In the pre-crisis era, investors' attention had focused on choosing increasingly granular asset class buckets, which however limited their insight into the underlying drivers of risk and return in their portfolios. Instead of delivering the stable returns the well-diversified strategies had promised, many investors found themselves short of liquid assets they could call upon during the crisis. Unlike traditional CAPM-based strategies, the risk factor allocation approach treats asset classes as ways of accessing the key underlying risk and return factors. The attractiveness of this approach lies in its intuitive simplicity.
It is too early to tell whether the risk factor allocation approach will actually help investors generate superior returns on a risk-adjusted basis. The international investor community is therefore following closely CalPERS' experience. Introduced in mid-2011, its “new alternative asset classification” follows a risk-based asset allocation strategy with two hedging portfolios to protect against extreme market risks and rising inflation. The rest of the portfolio is a combination of growth-oriented assets that include public and private equity and real assets. The new and old asset allocation targets are shown in Table 5.1. For each asset class a strategic plan is developed, an issue we return to in Part III of this book.
Table 5.1 CalPERS alternative asset classification
5.2 CONCLUSIONS
Long-term investors in illiquid asset classes accept higher risk as they are unable to rebalance their investment portfolios on a continuous basis, a key assumption in standard asset allocation models. Thus, investors generally demand a higher premium in compensation for this risk. In this chapter, therefore, we have reviewed the literature on risk-adjusted returns in private equity, an asset class that is essentially identical to public equity in terms of its role in a company's capital structure, except for its substantially high degree of illiquidity. Our results can be summarized as follows:
- On a risk-unadjusted basis, private equity investing through limited partnerships is found to outperform public equity by a significant margin.
- While return comparisons between private equity and public equity are generally based on public market equivalents that implicitly assume beta to be 1, the majority of studies that focus on market risk explicitly find betas of greater than 1.
- However, sensitivity analyses suggest that under reasonable assumptions for beta, PMEs for private equity are still greater than 1, implying outperformance on a risk-adjusted basis.
- Studies that focus specifically on liquidity risk find premiums in the range of 2–4%.
Despite important efforts to estimate returns to private equity and the risk associated with investments in this asset class, our review of the literature suggests that it is too early to say with sufficient confidence whether the apparent outperformance of private equity is sufficient to compensate investors for the risks they take and whether the investments outperform on a risk-adjusted basis. This uncertainty has important implications for investors' asset allocation strategies. Whereas in the pre-crisis era most investors followed a traditional CAPM-based approach that sought to diversify risk in an increasingly granular way, more recently a rising number of asset allocators have begun to adopt a risk factor allocation approach that embraces risk explicitly. Critically, as we discuss in the second part of this book, such an approach is particularly predicated on the development of well-functioning internal risk management systems.
1 In reporting their returns in terms of IRRs, private equity funds implicitly assume that cash proceeds have been reinvested at the IRR over the entire investment period. For example, if a fund reports a 40% IRR and has returned cash early in its life, it is assumed that the cash proceeds were invested again at that rate. In practice, however, such investment opportunities are rare.
2 Rouvinez (2007) proposes a PME approach that is based on the IRR methodology. In this approach, he uses the original contributions to a fund and scales the distributions in such a way that the final NAVs of the two cash flow streams – from the private and public markets – are identical. Based on these two new cash flow streams, the IRRs can be calculated and compared. Rouvinez's results suggest an outperformance of 300 bps for funds raised between 1980 and 2003. Day and Diller (2010) estimate an outperformance of private equity compared with the S&P 500 of more than 600 bps.
3 However, under plausible assumptions about management fees and carried interest, Kaplan and Schoar (2005) explain that gross PMEs would be at least 13% higher than the estimated net PMEs. As a result, gross PMEs would be well above 1, both on an equal and size-weighted basis.
4 Diller and Kaserer (2009) show a PME of 1.05 for European private equity funds (buyouts and VC) covering vintages from 1980 to 2003.
5 Significantly different results are reported by Phalippou (2012), who uses cash flows provided by Preqin for 392 US funds raised between 1993 and 2010. He finds PMEs of close to 1 if returns are benchmarked against a small-cap mutual fund managed by Dimensional Fund Advisor, which offers passive low-cost exposure to small-cap stocks. The largest market capitalization considered by the fund was USD 1, 130 million, as of December 2011, corresponding to an enterprise value that is higher than that of the 95th largest leveraged buyout reported by Capital IQ.
6 Recognizing that the risk-free rate changes with time, Sharpe himself later revised the ratio as follows: S = (E[R − Rf])/σ, with E[R − Rf] representing the expected value of the excess of the asset return over the benchmark return and σ being the standard deviation of the excess of the asset return, 
7 Specifically, the CAPM assumes that all investors have access to the same information and agree about the risk and expected return of all assets. Further, it is assumed that there are no taxes or transaction costs and the market portfolio consists of all assets in all markets, where each asset is weighted by its market capitalization. There are no preferences between markets and assets for individual investors, who choose assets solely as a function of their risk/return profile. Finally, all assets are infinitely divisible as to the amount which may be held or transacted.
8 For instance, the International Private Equity Valuation (IPEV) Guidelines, which have recently been revised to take into account the evolution of fair value accounting requirements and practices around the globe, especially as promulgated by the Financial Accounting Standards Board (FASB) in the United States and the International Accounting Standards Board (IASB).
9 Return and risk estimates for buyout funds are based on quarterly TVE data from 1989 to 2005.
10 Getmansky et al. (2004) suggest an alternative approach of “de-smoothing” the volatility of private equity returns. Applying this methodology to a dataset of European private equity funds increases the volatility of returns to 35% per year as described in Diller (2007). Alternative methods are discussed in Kaserer et al. (2003).
11 Diller and Jäckel (2010) calculate returns and volatility using a dataset of 1717 US buyout and VC funds raised between 1983 and 2005. The study assumes that private equity distributions are fully reinvested, employing an approach proposed by de Zwart et al. (2007). Diller and Jäckel (2010) find a standard deviation of 23% compared with 16% for public stocks, whereas private equity outperformed by 2.5% per year, achieving average returns, net of fees, of 14.13%. The correlation between private equity and the public market index was estimated at 63%.
12 In quarters where there is neither an investment nor a write-down, Gompers and Lerner (1997) adjusted the portfolio value by the change in the matched industry public market index.
13 Metrick (2007) provides some estimates for venture capital. In a simple textbook example of the Pastor–Stambaugh model, he estimates the average return to the liquidity factor at 3% per year for the sample period from 1966 to 2004. However, splitting the sample period into different sub-periods, Metrick (2007) obtains a return of nearly 6% since 1980.
14 There is a rapidly expanding literature on ALM. Readers with a particular interest in the technical details of ALM are referred to Hoevenaars (2008), whose work has influenced the strategic asset allocation approach of ABP Investments, one of the world's largest pension asset managers in the pension industry. For a discussion of private equity in an insurance company's asset allocation within an ALM framework, see Achleitner and Albrecht (2011).
15 For details, see the Harvard Business School case study on the Canadian Pension Plan Investment Board (Hardymon et al., 2009).