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Replicating Private Equity with Value Investing, Homemade Leverage, and Hold-to-Maturity Accounting Erik Stafford* December 2015 ABSTRACT
traded equities with these characteristics have high risk-adjusted returns after controlling for common^ Private equity funds tend to select relatively small firms with low EBITDA multiples. Publicly factors typically associated with value stocks. Hold-to-maturity accounting of portfolio net asset valueeliminates the majority of measured risk. A passive portfolio of small, low EBITDA multiple stocks with modest amounts of leverage and hold-to-maturity accounting of net asset value produces an unconditionalreturn distribution that is highly consistent with that of the pre-fee aggregate private equity index. The passive replicating strategy represents an economically large improvement in risk- and liquidity-adjustedreturns over direct allocations to private equity funds, which charge average fees of 6% per year.
- (^) Stafford is at Harvard Business School (estafford@hbs.edu). I thank Malcolm Baker, Josh Coval, Victoria Ivashina, Kristin Mugford, André Perold, David Scharfstein, and Adi Sunderam for helpful comments anddiscussions. Harvard Business School’s Division of Research provided research support.
The professional and active management of private equity investments is widely believed to have many unique advantages over passive portfolios of publicly traded equities. Specialized knowledge (Leland and Pyle (1977)), monitoring (Diamond (1984)), and access to credit markets (Ivashina and Kovner (2011)) are a few ways in which intermediated investing may provide advantages over a non-intermediated strategy. To the extent that these are material advantages in equity investing, the pre-fee returns on an aggregate private equity index are expected to outperform a passively managed portfolio comprised of otherwise similar public investments. This paper investigates whether an outside investor can replicate the risks and returns of a diversified private equity allocation with passive investments in public equities using similar investment selection, leverage, and the calculation of portfolio net asset value under a hold-to- maturity accounting scheme. The Cambridge Associates Private Equity Index is used as a proxy for the returns earned by limited partners who have diversified allocations to private equity investments. Over the period 1986 to 2014, the mean excess return on the private equity index, before fees, is 18% per year with an annualized volatility of 17% and a market beta of only 0.7. The literature on the cross section of expected stock returns suggests that a portfolio of low beta value stocks represent a promising starting point for matching the attractive risk and return properties of private equity. There is strong empirical evidence that value firms earn high stock returns (Stattman (1980), Rosenberg, Reid, and Lanstein (1985), Fama and French (1992)). These papers empirically link realized excess equity returns to a firm’s ratio of book equity, BE , to market equity, ME. Interestingly, I find that the operating cash flow (EBITDA) multiple is a more powerful variable than BE / ME for sourcing a value premium in stocks, producing a larger spread in returns and driving out the statistical significance of BE / ME in Fama-MacBeth (1973)
selected for a going-private transaction. In fact, the average pre-transaction market beta for the public-to-private firms is 1. Return smoothing is an acute concern for the private investments being considered here, particularly when comparing to the accurately measured risks of replicating portfolios comprised of relatively liquid publicly traded investments. A growing literature challenges the accuracy of the return reporting process for hedge funds, documenting both conditional and unconditional return smoothing (Asness, Krail, and Liew (2001), Getmansky, Lo, and Makarov (2004), Bollen and Pool (2008)), as well as manager discretion in marking portfolio NAVs (Cassar and Gerakos (2011), Cao et al. (2013)). Jurek and Stafford (2015) demonstrate that over the period from 1996 to 2014, return smoothing in just two key months (August 1998 and October 2008) is sufficient to statistically obscure the exposure to downside market risks. An investor relying on the accuracy of reported returns infers that average pre-fee hedge fund alphas are 6% to 10% per year, while an investor who is skeptical of the accuracy of reported returns cannot statistically reject the presence of downside market risks and pre-fee alpha estimates of zero. In light of the evidence on the importance of return smoothing in altering the measured risk properties of hedge fund returns, special attention is focused on whether the strikingly attractive risk properties of the aggregate PE index could be due to the return reporting process. To investigate how the reporting process can alter inferences about risks, two different accounting schemes are used to report portfolio net asset values from which periodic returns are calculated. The first is the traditional market-value based rule where all holdings are reported at their closing price. Portfolios comprised of stocks with market betas averaging 1, with portfolio leverage of 2x, have measured portfolio betas near 2 under the market-value based accounting rule. The second accounting scheme is based on a hold-to-maturity rule, whereby securities that
are intended to be held for long periods of time are measured at cost until they are sold. Over periods where security valuations are increasing on average, this accounting scheme appears to provide a conservative estimate of portfolio value and therefore will perhaps understate leverage. However, an additional feature of this accounting scheme is that it significantly distorts portfolio risk measures by recognizing the profits and losses on the underlying holdings only at the time of sale. Consequently, portfolios with highly statistically significant measured betas near 2 under the market-value reporting rule have measured beta that are statistically indistinguishable from zero under the hold-to-maturity reporting rule. This suggests that the long holding periods of private equity portfolios, combined with conservativism in measuring asset values can effectively eliminate a majority of the measured risk. Overall, the results push against the view that private equity adds value relative to passive portfolios of similarly selected public equites. The mean returns can be matched in a variety of ways in passive portfolios with firms sharing the characteristics of those selected for private equity portfolios. The critical difference appears to be in the marking of the portfolios and the resulting estimates of portfolio risk. The remainder of the paper is organized as follows. Section I evaluates a value investing strategy based on operating cash flow multiples. Section II studies the asset selection tendencies of private equity investors. Section III develops a simple strategy for replicating the risks and returns of the aggregate private equity index with firms with similar characteristics to those selected by private equity investors, similar portfolio leverage, and hold-to-maturity accounting for portfolio net asset value. Finally, Section IV concludes the paper.
channel, namely non-systematic risk exposures, or market mispricing, which is expected to translate into positive risk-adjusted returns. Table I summarizes returns for five portfolios formed on MEBITDA. The portfolios are formed monthly based on information assumed to be known at the beginning of the month. Equity market values are assumed to be known with no delay. Debt market values are assumed to equal their book values and to be known with a reporting delay of three months. Similarly, all other accounting data are assumed to be known with a three month reporting delay. The EBITDA multiple is calculated as the value of the firm divided by EBITDA, so long as EBITDA exceeds $1 million. Firms that do not satisfy the minimum EBITDA requirement at the time of portfolio formation are excluded from the analysis. The value of the firm is the sum of the market value of equity from CRSP (price per share multiplied by shares outstanding) and the book value of long-term debt from Compustat. Annual EBITDA is the four-quarter sum of quarterly EBITDA from Compustat. Table 1 confirms the basic premise behind value investing. There is a strong monotonic relation in the realized excess returns across portfolios formed on MEBITDA over the period 1986 to 2015. Portfolios comprised of low multiple stocks (i.e. the bottom quintile of all CRSP stocks with annual EBITDA in excess of $1M) have high excess returns, averaging 20% per year for the equal-weight portfolio and 13.4% for the value-weight portfolio, while portfolios comprised of the high multiple stocks (top quintile) have average excess returns of 4.6% and 5.6% for equal- and value-weight portfolios, respectively. Over this same period, the excess return on the value-weight market portfolio is 7.8%. The annualized volatility is reasonably similar across portfolios, such that Sharpe ratios share the same pattern as the excess returns.
Finally, Table 1 shows that systematic risk exposure does not explain this pattern. The unexplained mean excess return (or alpha), as measured by the intercept from a time series regression of the portfolios excess return onto the zero-investment portfolios suggested by either the Sharpe (1964) and Lintner (1965) capital asset pricing model (CAPM), the Fama and French (1993) three-factor model (FF3), the Fama and French (2014) five-factor model (FF5), or the FF5 plus a momentum factor, UMD, shares the same strong monotonic relation across MEBITDA portfolios over this period. 1 A long-short portfolio that is constructed by being long low MEBITDA stocks and short high MEBITDA stocks earns an alpha in excess of 1% per month (t-statistic over 8) against either the CAPM or FF3 model when stocks are equally weighted in the portfolio. Value- weighting produces smaller alphas for the long-short portfolio, but they remain reliably positive, with a monthly alpha of 80 basis points (t-statistic = 4.1) against the CAPM and a monthly alpha of 50 basis points (t-statistic = 3) against the FF3. The Fama and French five-factor model includes a factor called RMW, which is long stocks with robust profitability and short stocks with weak profitability, and CMA, which is long low investment stocks and short high investment firms. Fama and French (2014) find that these factors weaken the statistical power of HML in explaining the cross section of returns. For the portfolios formed on MEBITDA , HML remains statistically significant after including these factors. Additionally, with regressions that include these additional factors result in economically large and highly reliable intercepts for the low MEBITDA portfolios and for the long-short portfolios. In light of the success of MEBITDA in producing a large spread in returns and abnormal returns, it is interesting to investigate the statistical power of this characteristic in
(^1) Factor returns are from Ken French’s website.
II. Asset Selection by Private Equity Funds There is little empirical evidence on the specific asset characteristics that private equity (PE) funds select for their portfolios. Based on aggregates of activity, it appears that private equity investments are not evenly distributed throughout the economy, or through time (Kaplan and Strömberg (2009)). Most detailed data related to private equity investments is at the fund level, where cash flows are used to calculate the internal rates of return (IRRs) of individual funds. The highly limited data availability on the financials and governance of private firms is a major obstacle to knowing which asset characteristics are associated with private equity asset selection. The approach in this paper follows Axelson, Jenkinson, Strömberg, and Weisbach (2013) whereby the subsample of public equities that have been taken private is studied, recognizing that the investments in private firms are not completely representative of the full sample. For example, the public targets in this sample are likely to be considerably larger than the private targets that are excluded. The sample of buyouts of public firms allows the pre- transaction financial characteristics to be collected from Compustat and CRSP. The data on public targets taken private by private equity firms come from the Thompson Reuters Merger and Acquisition database where the acquiring firm is identified as a financial buyer and the transaction results in at least 80% ownership of the target firm over the period 1983 to 2014. This results in 711 firms that can be linked to CRSP and Compustat. The sample size is in line with the U.S. sample of 694 deals identified by Axelson, Jenkinson, Strömberg, and Weisbach (2013) over the period 1980 to 2008. Table 3 reports results from regressions explaining which firm characteristics are associated with private equity buyouts from 1984 to 2014. Both ordinary least squares (OLS) and logistic regressions of a binary “PE-selected” variable on firm characteristics are reported (OLS
in Panel A and logistic in Panel B). All of the specifications include year fixed effects. The reported OLS coefficients are multiplied by 100. The firm characteristics are firm size, proxied by either equity market capitalization (ME) or total revenues (sales); EBITDA multiple ( MEBITDA ); market beta; profitability measured as the ratio of EBITDA to sales; market leverage ratio measured as long-term debt to the sum of long-term debt and ME; the three-year net equity issuance variable (ISS) described in Daniel and Titman (2006); and the book-to-market equity ratio (BE/ME). The firm characteristics are all assumed to be known at the time of the event. The event time is measured as the announcement date. Stock market variables (ME) are assumed to be known with no delay. Accounting variables are assumed to be known with a three-month delay. The regressions indicate that among the public firms taken private, PE funds tend to invest in relatively small firms as proxied by either ME or sales, with these variables being highly statistically significant in all specifications. The selected firms tend to have relatively low recent net equity issuance and relatively low profitability. Additionally, the selected firms tend to be value firms. BE/ME is positively associated with the event (firms with high BE/ME are considered value firms) and MEBITDA is negatively associated with the event. When both variables are included in the same specification, MEBITDA tends to eliminate the statistical reliability of BE/ME. Interestingly, market beta and leverage are not reliable predictors of the PE selection. The leverage result is consistent with Axelson, Jenkinson, Strömberg, and Weisbach (2013) who find that the leverage choice by the PE fund for the target firm is unrelated to the target firm’s leverage and the industry average leverage ratio at the time of the transaction, seemingly determined by aggregate credit market conditions.
Associates’ Private Investments database is collected from over 1,700 institutional fund managers, covering 5,700 funds, and includes the quarterly net return to investors. Quarterly returns are calculated from the unaudited quarterly financial statements and the audited annual financial statements prepared by the fund managers for their limited partners (i.e. outside investors). The quarterly return series begins in 1986Q2 and extends to 2015Q2. Harris, Jenkinson, and Kaplan (2014) compare the private equity return data across various commercial datasets and find that the Cambridge Associates returns are consistent with those from Burgiss and Prequin, while the returns from Venture Economics appear to be biased downwards. The basic premise being investigated is whether portfolios comprised of investments with similar characteristics earn similar returns, as opposed to how the returns are shared between the investor and the fund manager. Therefore, it is most natural to attempt to replicate the pre-fee return to private equity. To estimate pre-fee returns, I treat the observed net-of-fee time series as if it represented the return of a representative fund that was at its high watermark throughout the sample, charging a 2% fixed fee plus a 20% performance fee, both payable quarterly on positive returns.^3 The difference between the mean pre-fee and net-of-fee returns represents an approximation of the all-in fee paid by investors. Table 5 reports a summary of the annual and quarterly excess returns to private equity, both pre-fees and net-of-fees, along with the returns to the value-weight U.S. stock market index. The returns are measured in excess of the one-month U.S. Treasury bill return. There are several striking features of the private equity return properties. First, the implied all-in fee paid by investors exceeds 6% per year, which is economically large. As a point of reference, the realized
(^3) Jurek and Stafford (2015) apply a similar calculation to hedge fund return indices.
market risk premium over this period is 8%. Second, the reported private equity returns have relatively little risk. The net-of-fee quarterly returns (i.e. the raw data) have an annualized volatility of 9.6% over a period where the market return volatility is 17.1%. Similarly, the measured CAPM beta from the net-of-fee quarterly excess returns is 0.4. The low measured volatility and beta result in economically large Sharpe ratios and risk-adjusted returns. Taken at face value, private equity allocations have delivered roughly half the risk of the aggregate stock market index and roughly double the realized return. The high mean realized return seems to provide enough comfort to large institutional investors to make economically large allocations (Lerner, Schoar, and Wang, 2008). Further evidence that institutional investors find the risk/return profile of private equity highly attractive comes from the success of recent fund raising efforts with estimates of private equity buying power (including generous credit terms) exceeding $2 trillion at the end of the sample period (Bain & Co (2015)).^4 Given the nature of the investments, return smoothing is a concern. Private investments require considerable discretion in marking the portfolio net asset value and this process is likely to destroy the covariance structure in returns and lead to downward biased estimates of risk, particularly over economically benign periods. Evidence from hedge fund returns suggests that unconditional (Asness, Krail, and Liew (2001), Getmansky, Lo, and Makarov (2004)) and conditional (Bollen and Pool (2008, 2009)) return smoothing, due to asset illiquidity and discretion in marking portfolio NAVs (Cassar and Gerakos (2011), Cao et al. (2013)), creates a significant downward bias in the measured risks in these portfolios. The challenge is likely to be
(^4) Bain & Co. (2015) report that at the end of 2014, PE funds have over $1.2 trillion of dry powder (committed, but non-deployed capital) that is likely to be levered at least 2 times.
The private equity index is unlikely to represent a highly stable asset class as the industry composition is likely to change, leverage varies through time, and capital calls (investor flows) can significantly change the weights of new investments relative to older ones. In light of these issues, I proceed by first constructing a long-term buy-and-hold strategy that selects firms with low EBITDA multiples, combined with modest amounts of broker-supplied leverage through a portfolio margin account designed to mimic the underlying exposures of the private equity index. Second, I demonstrate how a conservative cash flow based net asset value rule, as opposed to a market value based rule, can effectively destroy all evidence of market beta and drawdowns, while preserving the mean return of the well-marked underlying portfolio over the sample period.
B.1. Constructing a Replicating Portfolio At the end of each month from 1980 to 2014, all publicly traded firms listed on CRSP are sorted based on their EBITDA multiple, as calculated earlier. Firms with M (^) EBITDA in the bottom three deciles of the monthly distribution are selected to be included in the replicating portfolio. This choice reflects the tendency for private equity firms to select firms with low EBITDA multiples in the public deals analyzed in Tables 3 and 4 and for these value firms to be associated with relatively high average realized returns as demonstrated in Table 1. A constant target portfolio leverage, L , of 2.0x is assumed based on the tendency for private equity transactions to increase the leverage of the underlying firms selected. Here, leverage is applied to the portfolio through a margin account. The typical publicly traded firm has a market debt-to-value ratio of roughly 30% (Assets/Equity = 1.43), while this ratio is increased to nearly 70% (Assets/Equity = 3.33) as the result of a private equity transaction (Axelson, Jenkinson, Strömberg, and Weisbach (2013)). An outside investor holding the pre-
LBO equity, but wanting the post-LBO levered return would need to apply portfolio leverage, measured as portfolio assets divided by portfolio equity capital, of 2.3x = 3.33 / 1.43. Borrowed funds are assumed to pay the one-month U.S. Treasury bill yield. As argued earlier, a crucial component of the portfolio strategy is a fairly long holding period, providing some scope for discretion in the calculation of the portfolio net asset value. Investments are held in the replicating portfolio for 4 years in the portfolio referred to as Strategy
- Over the course of a long holding period, many stocks initially selected for their value properties will no longer have these properties. Therefore, Strategy 2, which otherwise has identical portfolio management rules, exits individual positions that have realized annualized returns of 50% in addition to those that have been held for four years. This triggers nearly half of the positions to be liquidated prior to the four year default holding period. Due to the long-term holding periods and the buy-and-hold strategy, portfolio weights for newly added positions are determined each month by calculating a target number of holdings as the sum of current positions plus the number of additions less the number of firms exiting the portfolio. The current equity capital times target portfolio leverage divided by the target number of holdings determines the amount that is equally invested in each new addition. This results in the realized portfolio leverage varying slightly through time.
B. 2. A Portfolio Marking Rule based on Portfolio Cash Flows A portfolio consisting of long positions of liquidly traded securities like publicly traded equities is typically marked-to-market value based on the day’s closing prices of each underlying position. The equity capital is determined as the residual of the total portfolio asset value net of any borrowing. Under this market value based accounting system, the equity capital evolves over time by cumulating the daily profits and losses for the underlying securities based on daily
B. 3. Summarizing the Returns Table 6 reports summary statistics for the returns on the two replicating portfolios, under both the market value and hold-to-maturity accounting schemes. Panel A reports results for portfolios that are marked-to-market value based on month-end security prices as reported in CRSP. Panel B reports results under the portfolio hold-to-maturity accounting scheme described above, with portfolio values primarily being updated when positions are liquidated. Panel A shows that Strategy 1 earns an annualized excess return of 21% over the sample period, which is somewhat higher than the pre-fee private equity excess return of 16%. Similarly, Strategy 2, designed to more accurately represent a portfolio comprised of value stocks, earns an annualized excess return, averaging 19% over the period. The risks of both replicating portfolios are extreme. Both replicating Strategy 1 and Strategy 2 experience a massive drawdown during the financial crisis of 2008, with both portfolios losing more than 85% of their value relative to their historical peak valuation. Arguably, this is consistent with secondary market transaction prices of private equity investments at the time. For example, in February 2009, Forbes describes the gap between market transaction values and the asset values reported by some of the private equity firms in the Harvard University endowment, managed by Harvard Management Company (HMC).^6
Mendillo did move quickly to deal with the private equity portfolio. One of her first moves atHMC, which she initiated before the markets started to fall in earnest, was to sell between $ billion to $1.5 billion of Harvard’s private equity assets in one of the biggest such sales everattempted. The high bids on such assets have recently been 60 cents on the dollar, says Cogent Capital, an investment bank that advised Harvard on the sale. Cogent says the big discounts aredue to “unrealistic pricing levels at which funds continued to hold their investments” and “fantasy valuations.”
(^6) http://www.forbes.com/2009/02/20/harvard-endowment-failed-business_harvard.html.
… So what are Harvard’s private equity stakes worth? Most private equity investors like Harvardhave been waiting for their money managers to finish marking down their assets following a brutal 2008. It is a slow process that lags the public markets by as much as 180 days, saysWilliam Frieske, a performance consultant at Northern Trust, which administers endowment accounts. But one clue to what may be coming can be found in Harvard’s own portfolio. It owns units ofConversus Capital, a publicly traded vehicle that holds slices of 210 private equity funds. Conversus has cut its net asset value by 21% since last summer to make a “best estimate.” Yetstock investors think things are a lot worse. Conversus shares have fallen 67% since June 30 and are trading at a 62% discount to the net asset value.
The estimated market betas of the replicating portfolios are 1.9 and 1.5, which is in line with what is expected for portfolios targeting leverage of 2x. Interestingly, the CAPM alpha for the Strategy 1 replicating portfolio is not reliably different from zero, although the point estimate is economically large at 7% per year. The Strategy 2 replicating portfolio, which liquidates positions after high realized returns in an attempt to more accurately maintain a value portfolio, has a marginally statistically significant alpha of 7% per year ( t- statistic = 2.15). The massive drawdowns in 2008 for the replicating portfolios are striking. The drawdown based on reported returns for private equity is only -20%. If the replicating portfolios are properly reflecting the risks, how can discretion in marking-to-market reduce the appearance of the risks so dramatically? The results in Panel B suggest a possibility. Panel B repeats the analysis shown in Panel A for the same two replicating portfolios, but under the hold-to-maturity accounting scheme. In other words, all transactions and portfolio holdings are identical under each accounting scheme, only the calculation of the portfolio net asset value is different. Consequently, the mean excess returns continue to be large, averaging 15.8% and 15.0% per year
