Endowment Performance

Jun 27, 2020 by Richard M. Ennis
Ennis (2020) examined the diversification and performance of large educational endowment funds and public pension funds in the U.S. over the decade ended June 30, 2018. Alternative investments were shown to have ceased being the putative diversifiers they were prior to the Great Financial Crisis of 2008 and to have become a serious drag on the performance of institutional funds. A composite of large endowment funds underperformed a passive benchmark by an average of 1.6% per year, and a composite of public pension funds underperformed by 1.0%. Investment costs, which were estimated independently of performance measurement, approximate the respective margins of underperformance of the institutional composites.

 

This paper provides further insight into the performance of educational endowment funds. It updates returns through June 30, 2019. Additionally, using a novel dataset of returns for individual educational endowment funds, it analyzes those returns in cross section. The paper attempts to disentangle the performance effects of (1) equity exposure, (2) portfolio size, (3) degree of reliance on alternative investments, and (4) style tilts. Like the prior work, this paper underscores the fact that diversification with high cost is a recipe for failure.

 

THE ENDOWMENT STYLE

 

We have become accustomed to hearing and reading of “the endowment model.” There is, in fact, no canonical model for managing endowment funds. There are, however, certain recurring investment themes often associated with their management. We refer to these themes a bit more modestly as elements of endowment style. They include:

  • Active Management. The ability of endowed institutions to identify and exploit investment skill is an overarching theme among endowments, which make little use of passive investments (14% of assets in 2018, according to Greenwich Associates[1]). Their willingness to pay for perceived skill is exemplified by their large commitments to hedge funds and private equity.

  • Equity Orientation. The belief that equity investments, broadly speaking, should predominate portfolio holdings is widespread among endowment managers. That said, equity exposure varies among institutions, largely based on the size of their portfolios. Large funds maintain an average effective equity exposure of 72%, with figures of 80% or more being not uncommon. Small funds average 63% (particulars follow).

  • Private Markets. Private markets are a central focus of many endowment managers and their advisors. They are viewed as riper for exploitation by skillful investors as well as being a source of diversification. Along with hedge funds, private investments form the core of what are commonly known as alternative investments, or “alts.” Larger endowments avail themselves of private market opportunities and other alts to a greater extent than do the smaller ones.

  • Value Over Growth. Some observers believe there is, or at least has been in the not-so-distant past, a bias in favor of value stocks over growth on the part of many endowments. Any such bias may have lessened as a result of the underperformance of value relative to growth during the last decade or so.

The endowment style of investing produced superior results in the 1990s and early years of this century, so much so that it has become a subject of enduring interest among investors around the world.

 

LONG-TERM PERFORMANCE

 

Hammond (2020) reviews the long-term performance of educational endowments. Over the last 50 years the average endowment earned 8.5% per year, compared with 9.3% for a 60/40 passive benchmark, for a shortfall of 0.8% per year.[2] The full story, though, is richer, as conveyed by Exhibit 1. The 60/40 portfolio beat the average in four of the five decades, with the decade ended 2009 being the sole exception. The decade ended in 2009 coincides with the glory days of the endowment style of investing. The cohort of large endowments, in particular, enjoyed an advantage of 460 bps in that decade. Two additional observations may help to provide context for the results summarized in Exhibit 1. First, the modern endowment investing style was not a factor in the first two decades (70s and 80s) reported on there; in that era stocks and bonds sufficed for all. Second, equity exposure, broadly defined, is not a constant across cohorts or over time. From what we can glean from Nacubo archival data, “60/40” was probably a pretty good benchmark across the board in the earliest decade.[3] Equity exposure began to rise, however, in the decades that followed, especially among the large endowments. We believe that this fact largely accounts for the return spread among cohorts in the decade ended 1989, when equities outperformed bonds by a wide margin and before alternative investments had made real headway with the large endowments. These results leave us with insight into how investment practice has evolved over half a century. What remains unexplained is what transpired at about the time of the Global Financial Crisis of 2008 to cause endowments to lose their steam.

 

Exhibit 1

Long-Term Performance of Educational Endowments
 

Decade

Ending 6/30

Large

Cohort

 

Average

Small

Cohort

60/40

Passive

2019

9.0%

8.4%

7.7%

10.5%

2009

6.1

4.0

3.9

1.5

1999

14.0

12.9

12.3

14.6

1989

15.0

13.7

12.7

14.8

1979

4.6

4.5

4.5

5.6

Source: Hammond (2020)

 

PERFORMANCE SINCE 2009

Performance by Size Cohort
We begin our analysis with a comparison of six endowment fund cohorts (774 funds in total) defined by dollar value of investment portfolio.[4] Exhibit 2 provides key statistics for the cohorts. Note the wide range of practice in terms of the use of alternative investments (as defined by Nacubo), from 7% of assets for the smallest cohort to 51% for the largest. Exhibit 3 summarizes the performance benchmarks used and performance results. The start date for the analysis is July 1, 2008. As in our 2020 article, we use returns-based style analysis to establish portfolio benchmarks, using the quadratic programming technique originated by Sharpe (1988). The technique enables the analyst to determine which index returns statistically explain the risk-return characteristics of a portfolio, or a composite of them as in the present case.[5] Then we regressed cohort returns on their respective benchmarks to derive risk-adjusted returns, as reported in Exhibit 3. The benchmarks fit the returns well, with R2’s that round to .99 and (small) standard error terms of 0.8% to 1.5%. The (derived) effective total equity allocations are reasonable on their face, ranging from 63% to 72%. Risk-adjusted returns (alphas) for the various cohorts fall within a range of -1.1% to -1.8%, with t-statistics of -2.7 to -4.9. These results are consistent with the findings of our previous paper. A key takeaway from Exhibit 3 is that risk-adjusted performance of endowments is consistent across cohorts of fund size, i.e., there is no evidence of larger funds doing better than smaller ones after adjusting for risk.[6]

 

 

Exhibit 2

Nacubo Size Cohorts
 

 

Nacubo

Cohort

 

Number

of Funds

Median Asset Value

(Millions)

Average

Allocation to Alternatives[7]

 

11-Year Return

1.  <$25 M

60

$17

7%

5.58%

2.  $25-50 M

93

37

15

5.32

3.  $51-100M

152

74

21

5.21

4.  $101-500M

280

350

29

5.25

5.  $501M to $1B

82

730

38

5.47

6.   >$1 B

107

1,987

51

5.94

 

 

Exhibit 3

Benchmark Weights and Performance Statistics of

Endowments by Size Cohort for the Eleven Years Ended June 30, 2019
 

 

 

 

Cohort

Derived Exposure (%)

Regression Statistics

 

 

Bonds

 

U.S. Equity

Non-U.S. Equity

 

Total Equity

 

 

R2

Standard Error (%)

 

Alpha (%)

 

Alpha

t-Stat

1

37

44

19

63

.988

1.1

-1.14

-2.7

2

33

46

21

67

.994

0.8

-1.52

-4.9

3

33

45

22

67

.993

0.9

-1.49

-4.3

4

30

49

21

70

.991

1.1

-1.69

-4.2

5

30

54

16

70

.985

1.4

-1.81

-3.5

6

28

56

16

72

.985

1.5

-1.46

-2.7

 

A Limited Value Effect

We test for the presence and possible effect of a value-stock bias, or value tilt. To do so, we introduced an additional independent variable in the returns-based style analysis to represent the value factor.[8] Exhibit 4 presents results of the analysis. There is indeed an identifiable value effect evident in the data, and it is most pronounced in the smaller fund-size cohorts. In Cohort 1, for example, 47 bps of 126 bps of negative excess return is associated with introduction of the value factor. The effect diminishes as fund size increases and disappears entirely for the cohort comprising the largest funds (#6). The intuition for this may be that funds in Cohort 1 have 46% of their assets in domestic common stocks, whereas Cohort 6 funds average just 11%. In other words, there simply may have been greater opportunity for a value-stock bias to manifest itself among the smaller funds (which also lack the resources and asset size for all-out investing in alternative assets).

 

Exhibit 4

Breakdown of Excess Return Between Value Tilt and Other Sources

for the Eleven Years Ended June 30, 2019
 

 

 

 

Excess Return

 

 

 

 

Cohort

 

 

 

Composite

Return

 

 

 

Benchmark

Return

 

 

 

 

Total

 

 

 

Due to

Value Bet

 

Due to Other Bets &

Costs

1. Smallest

5.58%

6.85%

-1.26%

-0.47%

-0.79%

2.

5.32

6.90

-1.58

-0.17

-1.41

3.

5.21

6.79

-1.58

-0.23

-1.35

4.

5.25

7.03

-1.78

-0.15

-1.63

5.

5.47

7.42

-1.94

-0.13

-1.82

6. Largest

5.94

7.52

-1.58

0.00

-1.58


Cross-Sectional Analysis of Individual Funds

For the present study, we created a dataset of fiscal-year annual returns and percentage allocations to alternative investments for 43 endowment funds with assets greater than $1 billion.[9] We created a benchmark for each individual fund using the same returns-based methodology used for the cohort benchmarks. We then regressed individual fund returns on their unique benchmark. Exhibit 5 summarizes key results. The schools there are ranked in descending order of alpha. 

The funds’ alphas range from a high of +2.07% to a low of -3.56%. None of the positive alphas are statistically significant. Eleven of the negative alphas are statistically significant. Note the wide range of effective equity exposure — from 60% (Vanderbilt) to 86% (Carnegie Mellon). The degree of diversification (R2) also varies widely — from .835 (MIT) to .995 (Missouri). Pronounced underperformance is evident across the range of both equity exposure and diversification.

 

Exhibit 5

Diversification and Performance of Large Endowment Funds

 for the Eleven Years Ended June 30, 2019
 

 

Rank

 

School

Effective Equity Exposure

 

R2

 

Alpha

 

t-stat

1

Massachusetts Institute of Technology

64%

0.835

2.07%

1.25

2

Bowdoin College

71%

0.870

2.03%

1.26

3

Michigan State University

69%

0.969

1.39%

1.94

4

Williams College

71%

0.931

0.99%

0.86

5

University of Pennsylvania

67%

0.941

0.73%

0.73

6

Columbia University

68%

0.953

0.56%

0.60

7

University of California

69%

0.957

0.32%

0.36

8

University of Richmond

63%

0.937

0.29%

0.30

9

Dartmouth College

70%

0.917

0.25%

0.20

10

Princeton University

77%

0.910

0.23%

0.16

11

Rice University

71%

0.978

0.18%

0.29

12

University of Missouri

68%

0.995

0.01%

0.05

13

University of Virginia

76%

0.966

-0.01%

-0.02

14

University of Notre Dame

73%

0.955

-0.12%

-0.13

15

Rutgers University

62%

0.975

-0.18%

-0.31

16

Yale University

77%

0.902

-0.21%

-0.14

17

Wellesley College

69%

0.967

-0.22%

-0.29

18

Northwestern University

62%

0.940

-0.42%

-0.44

19

Brown University

74%

0.919

-0.87%

-0.66

20

Pennsylvania State University

72%

0.987

-0.92%

-1.75

21

University of Rochester

70%

0.956

-0.97%

-1.05

22

Amherst College

74%

0.952

-1.06%

-1.07

23

North Carolina State University

71%

0.888

-1.18%

-0.79

24

Stanford University

78%

0.969

-1.19%

-1.40

25

Vanderbilt University

60%

0.875

-1.24%

-0.93

26

Purdue University

74%

0.990

-1.25%

-2.75

27

University of Chicago

64%

0.872

-1.38%

-0.85

28

Duke University

84%

0.985

-1.42%

-2.23

29

Washington University in St. Louis

71%

0.969

-1.47%

-1.87

30

UCLA Foundation

74%

0.919

-1.56%

-1.22

31

University of Michigan

80%

0.989

-1.59%

-3.16

32

University of Pittsburgh

76%

0.987

-1.76%

-3.25

33

University of Washington

74%

0.936

-1.82%

-1.58

34

Carnegie Mellon University

86%

0.964

-1.84%

-1.80

35

Case Western University

69%

0.964

-1.88%

-2.35

36

University of North Carolina

75%

0.870

-2.00%

-1.18

37

University of Southern California

78%

0.990

-2.11%

-4.34

38

Tulane University

78%

0.936

-2.16%

-1.79

39

University of Georgia

80%

0.992

-2.67%

-6.25

40

Ohio State University

74%

0.934

-2.82%

-2.34

41

Cornell University

80%

0.972

-2.93%

-3.57

42

Harvard University

80%

0.956

-3.13%

-2.99

43

Southern Methodist University

72%

0.900

-3.56%

-2.54

 

Median

72%

0.955

-1.06%

n/a

 

Conclusion

The overarching conclusion of this section is that endowment funds have underperformed passive investment by a significant margin during the study period, no matter how one slices the data.

 

 THE VANISHING ALTERNATIVE ADVANTAGE


We have established the following:

  • Effective equity exposure is the overwhelming determinant of risk and return, with 99% of return variance explained by stock and bond indexes alone across size-cohorts of funds.
  • Fund size is not a determinant of risk-adjusted performance, which is consistent across cohorts of asset size.
  • A value bias is evident. It has had a negative effect on risk-adjusted performance during the period of this study, mainly among smaller endowments. Even there, it accounts for a minor part of observed underperformance.

Advocates of alternative investments claim that they are a source of diversification and incremental risk-adjusted return. The sections that follow examine these propositions.

 

Empirical Analysis of Alts’ Diversification Effectiveness

We use returns-based diversification analysis to determine which asset classes are the prime contributors to the diversification of large endowment funds. (Recall that the large-fund cohort has a 51% allocation to alts.) Our approach is to introduce explanatory variables (asset classes) one at a time to determine their diversification effect, employing two measures: R2 and the standard error of the regression (tracking error). Exhibit 6 shows the diversification measures for each iteration. The first row of the table illustrates the powerful influence of investing beyond global stocks and bonds in the decade from July 1999 through June 2008. The R2 rose from 0.75 to 0.97, and tracking error decreased from nearly 6% to 2% with the inclusion of alternative investments. In the 11 years that followed, alternatives had a negligible impact on endowment diversification, with the R2 already at 0.99 with global stocks and bonds alone (Column 2).

 

Exhibit 6

Diversification Patterns of Large Endowment Funds Pre- and Post-GFC:

R2 and Tracking Error

 

 

 

 

1.

U.S. Stocks

and Bonds Only

 

2.

Admit Non-U.S. Stocks

 

3.

Admit

Real Estate

 

4.

Admit

Private Equity

 

5.

Admit

Hedge Funds

 

 

1999-2008

0.66

(6.7%)

0.75

(5.7%)

0.75

(5.7%)

0.91

(3.4%)

0.97

(2.0%)

 

2009-2019

0.98

(1.6%)

0.99

(1.4%)

0.99

(1.4%)

0.99+

(0.8%)

0.99+

(0.5%)

 

Exhibit 7 graphically illustrates that the benchmark comprising U.S. stocks and bonds plus non-U.S. stocks is the near-exclusive driver of return for the large fund composite. It shows the regression of the large fund composite on its benchmark consisting solely of stocks and bonds in the proportions shown for Cohort 6 in Exhibit 3. The slope (beta) is 0.99. R2 is .993 and the standard error of the regression is a minimal 1.4%. The intercept, or alpha, is -1.46% (t-statistic of -2.4). We note in passing that the annual standard deviation of return for composite and benchmark are nearly identical, at 11.10% and 11.16%, which is to say there is no evidence of “volatility dampening” in the return series of the alts-heavy composite. Moreover, in this analysis we make no attempt to adjust for the return-smoothing characteristic of alternative investments, which account for 51% of the assets of the composite.

 

Exhibit 7

Regression of Large Endowment Fund Composite on Benchmark Returns

Eleven Years Ended June 30, 2019   

 
 


 

These are remarkable results: Stock and bond indexes capture the return-variability characteristics of alternative investments in the composite of large endowment funds for all intents and purposes. Alternative investments do not have a meaningful impact. The finding that the correlation between a composite of funds averaging 51% alts exposure and a marketable securities benchmark is near-perfect runs counter to the popular notion that the return properties of alts differ materially from those of stocks and bonds. That, after all, is an oft-cited reason for incorporating alternative investments in institutional portfolios. But  as we see here, alt returns simply blend in with broad market returns in the context of standard portfolio analysis. Furthermore, evidence of volatility-dampening is absent.

 

Performance Impact of Alternative Investments

Our previous paper indicated that the alts-heavy style of implementation has been a serious drag on the performance of public pension funds during the decade following the Great Financial Crisis of 2008. Exhibit 8 (from the earlier paper) illustrates that the risk-adjusted return of public pension funds decreases sharply as alt exposure increases. (The slope coefficient of -0.049 has a t-statistic of -2.9.)

 

Exhibit 8

Public Pension Fund Alpha vs. Exposure to Alternative Investments

Ten Years ended June 30, 2018

Exhibit 9 is similar to Exhibit 8. It shows total fund alpha versus alts allocation for the six endowment fund size-cohorts (described in Exhibit 2) through June 30, 2019. The regression line pertains only to Cohorts 1-5. The R2 is .89. The slope coefficient is statistically significant (t-stat of -4.9), and the standard error of regression is a mere 0.10%. A very strong relationship exists, in other words. For funds with alts allocations of up to about 40% of total assets, the story is the same as for the public funds, namely: (1) alts detract from performance and (2) the more you have, the worse you do. For Cohorts 1-5, a reduction in total fund alpha of ~20 bps is associated with every 10% of assets allocated to alts. A 40% alts allocation results in a penalty of 79 bps.

 

Exhibit 9

Relationship of Total Fund Alpha to Alts Allocation Percentage

For Nacubo Endowment Fund Cohorts

(Eleven Years Ended June 30, 2019)

In terms perhaps better suited to trustees of endowment funds with less than a billion in assets and others who may not be conversant with statistical jargon, the message here is this: Liquidate your alternative investments and put the proceeds into index funds. Do it now.

 

Cohort 6 (funds with assets greater than $1 billion) stands apart from Cohorts 1-5 in Exhibit 9, statistically as well visually. Total fund alpha of Cohort 6, although still negative by nearly 1.5%, is 64 bps better than the regression equation would indicate for an average allocation to alts of 51% (a 6.5-sigma outlier relative to the regression line). It is reasonable to conjecture that the more skilled practitioners of alternative investing are to be found among those with the heaviest allocations there. Which is to say, there is arguably an indication of skill among at least some of the practitioners of alternative investing. Anecdotally, three (and only three) stand out with positive total fund alphas of greater than a percentage point. They are MIT, Bowdoin College and Michigan State University. All maintain alts allocations of 55% or more and, yet, achieved alphas at the total fund level of +2.07%, +2.03% and +1.39%%, respectively. Alas, even these fetching figures do not rise to the level of statistical significance.[10]

 

Exhibit 10 provides support for the results reported above. It shows the simple average of annual excess returns for private real estate, buyout funds and hedge funds before and after the GFC.[11] Positive added value in the early period turned negative in the one that followed.

 

Exhibit 10

Average Annual Excess Return of Alternative Investments

Before and After the GFC
 

Sources: Cambridge Associates, FTSE NAREIT, L’Her er al. (2016), Sullivan (2020)

 

Exhibit 11 illustrates the excess return of the large endowment composite over 21 years. It is the picture of a paradigm shift that dates to fiscal year 2009.

 

Exhibit 11

Annual Excess Return of Endowment Composite Relative to Benchmark

(Fiscal Years Ended June 30)

 

COST AND DIVERSIFICATION

 

We posit that portfolios of marketable securities cost the investor 0.5% to 0.7% of asset value, the percentage varying with the mix of stocks and bonds, the use of passive versus active management and turnover rates. The cost of alternative investments begins at about 1% of asset value for open-end diversified core equity (ODCE) real estate funds. Estimates of the cost of private equity investing approximate 6.0% of invested capital.[12] The cost of hedge funds, non-core real estate and private debt fall between those extremes. We put the cost of a typical portfolio of diverse alternative investments in the range of 2 to 4% of asset value annually. We estimate that across the spectrum of endowment funds, their cost of investing ranges from 1 to 2% of assets.[13] Assuming a cost of 0.6% for marketable securities and 2.5% for a diverse portfolio alternative investments, a portfolio with an allocation of 50% to alts would incur an annual cost of 1.55% of assets. The median R2 of the individual funds reported on in Exhibit 5 is .96 with an associated standard error of return relative to benchmark of 2.7%. If an endowment fund with that degree of diversification incurs costs of 1.5% annually, the likelihood of it underperforming the benchmark over a decade is 96%.[14] Here lies the crux of the problem of running high-cost diversified portfolios: The math simply doesn’t work.

 

 

CONCLUSION

 

Notwithstanding the existence of a handful of arguably skillful endowment fund managers in the realm of alternative investments, the vast majority of endowment funds incur costs that overwhelm the limited opportunity to exploit mispricing. The alt-heavy approach to investing has failed to provide a diversification benefit and has significantly underperformed simpler approaches employing stocks and bonds alone. Absent a change in strategy, the great majority of endowment funds, large and small, are likely to underperform by a significant margin in the years ahead. Those confident of their ability to identify truly profitable alternative investments consistently should concentrate those investments to a greater extent, just as they should do with traditional active portfolios. Absent such confidence, they should shift assets to passive investments.

 

REFERENCES

 

Ennis, Richard M. 2020. “Institutional Investment Strategy and Manager Choice: A Critique.” Journal of Portfolio Management (Fund Manager Selection Issue): 104-117.

 

Hammond, Dennis. 2020. “A Better Approach to Systematic Outperformance? 58 Years of Endowment Performance.” The Journal of Investing August 2020.

 

McKinsey & Co. “Equity Investments in Unlisted Companies: Report for the Norwegian Ministry of Finance.” November 2017.

 

Phalippou, L., and O. Gottschalg. 2009. “The Performance of Private Equity Funds.” The Review of Financial Studies 22 (4): 1747–1776.

 

Sharpe, W. F. 1988. “Determining a Fund’s Effective Asset Mix.” Investment Management Review (September/October): 16–29.

 

 


[1] See “2018 U.S. Institutional Market Trends,” Greenwich Associates, January 2019.

[2] Nacubo archival records are the source of returns, which are represented as net of fees. “60/40” incorporates the S&P 500 for stocks and Bloomberg Barclays Aggregate, or its equivalent, for bonds in the early years.

[4] Source: Nacubo Endowment Study 2019. While the 2019 Nacubo study reports on seven cohorts, we combined the Over $100 million - $250 million and Over $250 million - $500 million cohorts into one (as shown in # 4 in Exhibit 2) for consistency with past Nacubo studies where only six cohorts are reported. All Nacubo returns are represented as net of fees.

[5] The indexes used are Russell 3000, MSCI ACWI ex-U.S. and Bloomberg Barclays Aggregate.

[6] We use the term “risk-adjusted return” to describe value added as the intercept resulting from regression of a composite’s or fund’s return on a benchmark index. The terms “risk-adjusted return,” “intercept” and “alpha” are used interchangeably throughout the paper. We use “excess return” to describe the simple difference between the returns of a composite and its benchmark.

[7] Equal-weighted average of underlying institutions’ allocations to alt assets within the cohort.

[8] The value factor is defined as the difference between the returns of Russell 3000 Value and Russell 3000 Growth indexes.

[9] The Nacubo Study reports on seven size cohorts, one of which comprises 107 institutions with endowments greater than $1 billion in value. However, Nacubo does not identify individual schools. To create the individual fund dataset, we began reviewing the annual reports of schools with the largest endowments, starting with Harvard University. We soon discovered that many either do not report endowment fund returns, do not report the 11 consecutive returns required for the present study or have fiscal-year-ends other than June 30. We wound up acquiring complete return series for 35 of the 50 largest endowments. From there, we added data for other schools with assets greater than $1 billion, as best as we could locate them. An indication that the final sample of 43 funds may not be representative of all 107 funds (with assets greater than $1 billion) is that the average 11-year annual return of the sample exceeds that of Nacubo’s $1-billion-plus fund cohort by approximately 40 bps. While the 43 individual fund returns we obtained are not suspect in our minds, they may not be truly representative of the large fund cohort. Accordingly, we use the individual fund returns only in cross-sectional analysis and not as indicative of the large fund cohort itself. We assume, without confirmation, that returns are net of fees.

[10] There is a parallel here with the experience of professional gamblers. We know that the majority of amateurs entering a casino will depart losers. Studies have shown that a tiny percentage (about 1%) of professional gamblers exit winners with some consistency. (These happen to be the whales.) Another group (about 5%) usually exit losers, albeit with smaller losses than the Average Joe. The three large endowments cited above are analogous to the group of about 1% of gamblers cited in a study of fantasy-sports betting by McKinsey & Co. In both cases, there are rare winners in a game marked by a preponderance of losers of varying degree.

[11] For real estate, we subtract the returns of the FTSE NAREIT All-Equity REIT Index from those of the Cambridge Associates Real Estate Index, using quarterly IRRs to estimate TWRs for the Cambridge series. For buyout funds these are the average excess returns reported by L’Her et al. (2016) in Tables 3 and 4 for size-, leverage- and sector-adjusted returns. The hedge fund excess returns are as reported by Sullivan (2020).

[12] See McKinsey & Co. (2017) and Phalippou and Gottschalg (2009).

[13] See our previous work for a detailed discussion of the cost-estimation procedure.

[14] The probability reflects the area under a normal distribution curve with a tracking error of 2.7% and incorporating a cost of 1.5% per year.