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Memorandum

TO: Private Investments Subcommittee of the Asset Management Advisory Committee

FROM: Division of Economic and Risk Analysis (“DERA”),1 U.S. Securities and Exchange 

Commission

DATE: September 1, 2020

RE: Academic Literature on Potential Benefits for Portfolio Efficiency of Private Equity 

Investments

This memorandum is intended to facilitate consideration by the Subcommittee of certain issues 

relating to private equity investments, namely whether private equity, as an asset class, provides 

incremental portfolio efficiency benefits vis-à-vis other assets classes, such as public equity and 

debt.

2 The memorandum proceeds in two steps. First, it surveys the literature on the risk-adjusted 

returns of private equity investments relative to various public market benchmarks. Second, it 

collects the main findings in the literature as to whether expanding an investor's opportunity set 

to include private equity as an asset class may provide portfolio efficiency benefits by improving

the risk-return tradeoff of an investor’s portfolio. This memorandum is based on a review of 

academic literature and DERA has not undertaken an independent analysis of the risk-adjusted 

returns or potential portfolio efficiency benefits of private equity investments. 

The private equity literature is still evolving and has not reached a consensus on the appropriate 

method for measuring risk-adjusted returns in this market nor on whether private equity returns 

provide portfolio efficiency benefits above and beyond the investment opportunities available in 

public markets. This lack of consensus is attributable to various factors, including the 

inapplicability of traditional public market measures of risk and return to the private equity 

market.

This memorandum draws on several recent literature surveys of private equity performance. 

First, (Kaplan & Sensoy, 2015) review the academic literature on the performance of private 

equity investments that focuses on their performance relative to the public equity market, 

including a limited discussion of risk-adjusting private equity returns. Second, (Korteweg A. , 

2019) surveys the evolution of the literature on risk-adjusting private equity returns and 

summarizes the results of most studies to date. Finally, (Døskeland & Strömberg, 2018) provide 

a survey oriented towards determining whether a pension fund should expand its investment 

 1 This is a memorandum by the staff of the Division of Economic and Risk Analysis of the U.S. Securities and 

Exchange Commission. The Commission has expressed no view regarding the analysis, statements, findings, or 

conclusions contained herein. 2 The surveyed literature generally categorizes private equity funds into two main types: leveraged buyout and 

venture capital. (See, for example, Korteweg A., 2019.) As this memorandum describes the surveyed literature, it 

follows this general convention.
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mandate to include private equity investments. All three surveys also include additional

background on the private equity industry beyond what this memorandum covers.

Background

This memorandum focuses on private equity funds, which are usually organized as limited 

partnerships in which investors (the limited partners, or “LPs”) commit capital to a fund that 

makes investments in portfolio companies.3 Typically, the fund's general partner (or “GP”) hires 

an affiliated investment adviser who uses the committed capital to invest in portfolio companies 

and plays an active role in how those portfolio companies are managed and operated.4

A private equity fund's LPs typically pay a management fee to the investment adviser, typically 

assessed on the committed capital in the early years of a fund and invested capital in the later 

years, and a carried interest allocation to the GP, for portfolio company returns above a prespecified hurdle rate.5 In addition, GPs sometimes, and depending on various factors, charge

other fees, such as monitoring fees, to the fund’s portfolio companies in exchange for services 

provided to those portfolio companies, which can affect the after-fee return to LPs.

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 According

to (Døskeland & Strömberg, 2018), the majority of empirical studies support the notion that 

investments by private equity funds improve the performance of portfolio companies, adding 

economic value before accounting for fees. The literature on risk-adjusted private equity returns 

generally focuses on the investment returns to fund LPs after subtracting the cost of the 

investment, including the management fee, the carried interest allocation, monitoring fees and 

any other costs (“after-fee returns”).

Measuring Returns 

Studies state that a major impediment to assessing the risk and return characteristics of private 

equity is that, unlike public securities, neither the interests in private equity funds nor their 

portfolio companies trade on public markets at regular frequencies.7 Therefore, typical risk 

measures that might inform portfolio choices, such as volatility and covariance, are difficult to 

compute. To measure after-fee returns, which are most relevant to investors in private equity 

funds, researchers typically use LPs’ after-fee cash flows, including their invested capital and 

any distributions the fund pays.8 While earlier studies used the internal rate of return (IRR) for 

these cash flows to measure performance, possible issues with the IRR have led researchers to 

employ other measures in the literature.9

The public market equivalent (“PME”) of (Kaplan & Schoar, 2005) is, thus far, the dominant 

performance measure in the literature. The PME is a multiple that measures the cumulative 

 3 See, for example, (Kaplan & Sensoy, 2015). 4 See (Kaplan & Sensoy, 2015) and (Metrick & Yasuda, 2010) for a more detailed discussion of the structure of 

private equity funds.

5 See, for example, (Lemke, Rube, & Lins, 2019). 6 See (Phalippou, Rauch, & Umber, 2018) for a discussion of these fees in the context of buyout funds. 7 See, for example, (Kaplan & Sensoy, 2015). 8 Some studies, e.g. (Cochrane, 2005), analyze the gross returns to individual investments in portfolio companies. 9 See (Ang & Sorensen, 2012), (Kaplan & Sensoy, 2015), and (Korteweg A. , 2019) discuss the strengths and 

weaknesses of IRR and alternative measures in more detail.
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return to an investment over a benchmark, typically a public equity index such as the S&P 500.10 

(Sorensen & Jagannathan, 2015) provide theoretical support for this measure by showing that 

using the PME is equivalent to using a stochastic discount factor (SDF) for an investor with log 

utility. Studies incorporating the latest datasets find that both the venture capital and leveraged 

buyout segments of the private equity market consistently outperform the public equity market 

when measured using PME.11

The generalized PME (“GPME”) is a relatively new extension of the PME that uses modern 

empirical asset pricing techniques to value private equity cash flows. For example, (Korteweg & 

Nagel, 2016) use a more general SDF than (Sorensen & Jagannathan, 2015), calibrating its 

parameters to match the return distribution of other publicly traded assets and applying them to 

private equity cash flows. The study posits that this approach has the benefit of more accurately 

controlling for market performance in a given sample period as well as the leverage employed by 

some private equity funds. Using data on venture capital (“VC”) funds and VC portfolio 

companies, (Korteweg & Nagel, 2016) find that the PME can incorrectly indicate overperformance relative to a benchmark. Recent applications of this technique expand the set of 

factors used to calibrate the SDF on publicly traded securities before pricing private equity 

investments.

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(Ang, Chen, Goetzmann, & Phalippou, 2014) use a statistical approach to infer a latent quarterly 

series of returns to private equity investments. They explain that more traditional factor 

estimation techniques can then be used to assess the extent to which private equity returns are 

driven by typical public equity market factors versus being driven by potentially novel risk 

factors that are not available in public markets (measured by the “alpha” of private equity returns 

relative to a given benchmark factor model). They find that while private equity returns 

substantially capture known public market factors, there is some statistically significant evidence 

that they believe suggests that private equity returns do not fully span public market exposures.

Other frequently-referenced approaches to measuring private equity returns include (Jegadeesh, 

Kräussl, & Pollet, 2015), who analyze the returns of European fund-of-funds that invest in 

private equity as well as publicly-listed private equity firms, and (Boyer, Nadauld, Vorkink, & 

Weisbach, 2018), who use proprietary data from over-the-counter transactions in the secondary 

market for LP interests in private equity funds to measure returns.

Portfolio Efficiency

There is no clear consensus in the surveyed literature as to whether a typical public market 

investor could achieve a more efficient risk-return tradeoff if given the ability to invest in private 

equity as an asset class. This is the result of data limitations and the lack of consensus in the 

literature with respect to how private equity returns should be measured and adjusted for risk, as 

well as how those risk-adjusted returns should be interpreted. Therefore, this section presents the 

main results from the surveyed literature in two categories: studies that find support for the

portfolio efficiency benefits to private equity, and studies that do not find such support. 

 10 See, for example, (Kaplan & Sensoy, 2015). 11 See (Harris, Jenkinson, & Kaplan, 2014), (Harris, Jenkinson, & Kaplan, 2015), and (Kaplan & Sensoy, 2015). 12 See (Gredil, Sørensen, & Waller, 2019) and (Gupta & Nieuwerburgh, 2019).
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Results unsupportive of portfolio efficiency benefits

Assuming PME is an accurate measure of fund performance, early studies such as (Kaplan & 

Schoar, 2005) and (Phalippou & Gottschalg, 2009) cautiously find that private equity 

outperforms public market equivalents. And, while recent results in the literature using more 

comprehensive data sets produce private equity PMEs that consistently outperform the public 

market, there is still no consensus on the extent to which these results accurately adjust for risk. 

More recent generalizations of PME, such as the GPME measure in (Korteweg & Nagel, 2016), 

suggest that PME can be misleading because once it is adjusted for risk, VC funds and VC 

portfolio companies no longer exhibit superior risk-adjusted returns relative to public markets.

Two studies suggest that the risk and return of private equity is captured by tradable public 

equity market factors, which could imply that investors can obtain an equivalent risk-return 

trade-off via public market investments. (Franzoni, Nowak, & Phalippou, 2012) find that the 

“alpha” of VC investments is not significantly different from zero once a systematic liquidity 

factor is included in the factor model, which they find suggests that any premium these 

investments offer over the market return is compensation for liquidity risk that is also obtainable 

in public markets. Similarly, (Stafford, 2017) finds that the returns to leveraged buyout funds can 

be replicated in public markets by a strategy that invests in small-cap low EBITDA firms, and 

that this strategy produces CAPM alphas that are consistent with other studies of buyout returns 

in the literature.

Heterogeneity in GPs’ skill and heterogeneity in investors’ ability to choose among managers 

have led to heterogeneity in investors’ experience of private equity performance. Specifically,

some studies suggest (a) that the skill of GPs and their affiliated investment advisers is persistent 

across the funds that they manage, (b) that there is substantial cross-sectional heterogeneity in 

the performance of GPs and their affiliated investment advisers, and (c) that different types of 

LPs vary in their ability to identify this skill.13 Surveys of private equity oriented towards its 

potential role in an institutional portfolio, such as (Ang, Goetzmann, & Schaefer, 2009) and 

(Døskeland & Strömberg, 2018), refer to those studies and emphasize the importance of building 

internal teams that can assess the skill of GPs and their affiliated investment advisers and 

leveraging an institution’s size to obtain access to highly-skilled GPs and affiliated investment 

advisers. In addition, these surveys recommend that these institutions explore ways to reduce the 

impact of the fees on private equity returns by, for example, internalizing some fund 

management functions and directly participating in co-investments alongside other LPs.

Results supportive of portfolio efficiency benefits

Given the current lack of consensus regarding how the returns to private equity should be 

adjusted for risk, some studies present PME as a simple, straightforward metric. Studies using 

the most comprehensive data sets state that both buyout and venture capital funds consistently 

outperform the public market.14 This finding is relatively robust to benchmarking against 

alternative market indices that may match the risk of private equity investments more closely, 

 13 See (Kaplan & Schoar, 2005) and (Korteweg & Sorensen, 2017) for analyses of skill persistence among private 

equity GPs. See, also, (Lerner, Schoar, & Wongsunwai, 2007) who show that some types of institutions, such as 

endowments, are better at identifying follow-on funds from GPs that are likely to outperform. 14 See, e.g. (Kaplan & Sensoy, 2015).
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including small-cap stocks, small value stocks, and small growth stocks, as well as levered 

positions in a market index such as the S&P 500.15

In addition, (Døskeland & Strömberg, 2018) and (Korteweg & Nagel, 2016) point out that any 

abnormal private equity returns relative to a given benchmark, factor model, or stochastic 

discount factor could reflect unique risks and associated risk premia in the private equity market 

that are not captured by public market factors. For example, (Ang, Chen, Goetzmann, & 

Phalippou, 2014) find statistical evidence suggesting that private equity returns are not 

completely spanned by typical public market factors, while (Sorensen, Wang, & Yang, 2014)

provide a theoretical model that they find shows investors may earn a premium for bearing 

liquidity risk that is unique to investments like private equity.

Finally, (Ang, Chen, Goetzmann, & Phalippou, 2014) acknowledge that even if private equity 

returns in the data can be replicated by exposure to public market factors, directly investing in 

private equity markets could be a more cost efficient way to obtain those exposures after taking 

transaction costs into account. (Døskeland & Strömberg, 2018) point out that the market 

capitalization of private equity funds is a substantial fraction of the market capitalization 

associated with some of these public market factors, and they state that obtaining this exposure in 

public markets may be cost prohibitive. In addition, the authors point out that, ex-ante, it is 

difficult to anticipate the extent to which a private equity replication strategy should load on each 

of these factors because estimates of these loadings change across sub-samples in the data and 

may change over time as the private equity industry varies investments in different industries, 

geographies, and sectors.

References

Ang, A., & Sorensen, M. (2012). Risks, Returns, and Optimal Holdings of Private Equity: A Survey of 

Existing Approaches. Quarterly Journal of Finance, 2(3), 1-27.

Ang, A., Chen, B., Goetzmann, W., & Phalippou, L. (2014). Estimating Private Equity Returns from Limited 

Partner Cash Flows. Journal of Finance, 73(4), 1751-1783.

Ang, A., Goetzmann, W. N., & Schaefer, S. (2009). Evaluation of active management of the Norwegian 

government pension fund–global. Report to the Norwegian Ministry of Finance.

Boyer, B., Nadauld, T., Vorkink, K., & Weisbach, M. (2018). Private Equity Indices Based on Secondary 

Market Transactions. National Bureau of Economic Research.

Cochrane, J. (2005). The Risk and Return of Venture Capital. Journal of Financial Economics, 75(1), 3-52.

Døskeland, T. M., & Strömberg, P. (2018). Evaluating investments in unlisted equity for the norwegian 

government pension fund global. Report for the Norwegian Ministry of Finance.

Franzoni, F., Nowak, E., & Phalippou, L. (2012). Private Equity Performance and Liquidity Risk. Journal of 

Finance, 67(6), 2341-2373.

 15 See (Harris, Jenkinson, & Kaplan, 2014) and (Harris, Jenkinson, & Kaplan, 2015).
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Gredil, O., Sørensen, M., & Waller, W. (2019). Evaluating Private Equity Performance Using Stochastic 

Discount Factors. Working Paper.

Gupta, A., & Nieuwerburgh, S. (2019). Valuing Private Equity Strip by Strip. National Bureau of Economic 

Research.

Harris, R., Jenkinson, T., & Kaplan, S. (2014). Private Equity Performance: What Do We Know? Journal of 

Finance, 69(5), 1851-1882.

Harris, R., Jenkinson, T., & Kaplan, S. (2015). How Do Private Equity Investments Perform Compared to 

Public Equity.

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Economics, 124(3), 535-562.

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Sorensen, M., Wang, N., & Yang, J. (2014). Valuing Private Equity. Review of Financial Studies, 27(7), 

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Stafford, E. (2017, May). Replicating private equity with value investing, homemade leverage, and holdto-maturity accounting. Working Paper. Retrieved from https://ssrn.com/abstract=2720479