Master Thesis
Performance Characteristics of Publicly Traded Private
Equity Investment: Applying Market Price Approach
Name: Fan Zhang
Supervisor: Dr. R.Almeida Da Matta
MSc Business Economics, Finance track
University of Amsterdam, Amsterdam Business School
Statement of Originality
This document is written by Student Fan Zhang, who declares to take full responsibility for
the contents of this document.
I declare that the text and the work presented in this document is original and that no sources
other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of
completion of the work, not for the contents.
Abstract
As one important asset class to diversify the investment risk, private equity is always
attractive. But the opaque data makes it difficult to precisely evaluate the performance. To
overcome the shortcoming, the paper will focus on the common shares that issued by the
private equity companies, and analyze their performance by constructing three representative
indexes. I identify 92 qualified companies from 2005 to 2014 and document their risk-return
characteristics by applying market price model. In addition, I estimate the systematic risk of
stocks in different regions, and find the risk-return characteristics are not identical.
Furthermore, I also investigate the risk exposures of the indexes constructed by different
strategies and find significant differences among them.
Table of Contents
Section 1. Introduction ... 1
Section 2. Background ... 4
2.1. A snapshot on publicly traded private equity instruments ... 4
2.2. Development of private equity common shares investment ... 6
2.3. Advantage of investing publicly traded private equity company stock ... 8
Section 3. Literature review ... 9
Section 4. Dataset and methodology ... 13
4.1. Data source ... 13
4.2. Sample selection ... 14
4.3. Sample characteristics ... 15
4.4. Methodology ... 18
Section 5. Empirical results ... 22
5.1. Basic risk-return characteristics description... 22
5.2. Performance evaluation applying CAPM model ... 23
5.2.1. Risk-return estimation of three indexes ... 24
5.2.2. Correlation and diversification effect ... 27
5.2.3. One-year rolling risk-return structure of three indexes ... 28
5.2.4. Systematic risk in different regions ... 29
5.3. Performance evaluation applying risk premium approach ... 32
5.4. Performance overview ... 36
Section 6. Conclusion ... 38
Reference ... 43
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Section 1. Introduction
Private equity has always been popular for institutional investors because of its low volatility and potential high return. After the financial crisis, more investors realized the importance of asset allocation and began to increase the proportion of private equity in their portfolios for its low correlation with traditional asset classes. Though private equity has been one favored alternative investment, its performance estimation is ambiguous due to its data opaqueness. Furthermore, the limited partnership is only available for most institutional and high-wealth individual investors who have capacity to take the illiquidity risk and tolerate the potential loss. Despite the abundant researches on private equity, there still lacks a consistent conclusion to evaluate the performance of private equity, not even mention its risk and return characteristics. Even though, private equity is still attractive in ordinary individuals’ eyes for its diversification benefit.
In general, investors could access to the private equity investment through some publicly traded private equity instruments such as listed private equity fund. With the financial market quickly developed, many investment vehicles are created to meet the demands. Now there are many publicly traded private equity instruments for choice. Different from traditional private equity investment which has a high barrier to entry, the publicly traded private equity instruments are easy to invest on the exchange and the potential risk exposure of the investments are almost the same as investing directly in private equity. According to the research report from Prequin, the return of listed private equity funds have 94 percent correlation with that of the unlisted ones in the last decade, meaning that their returns are
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highly similar. So investors could reasonably using publicly traded private equity instruments as a substitute for private equity without encountering the complicated contracts.
So far, there is four kinds of private equity investment vehicles listed on the exchange can be found: listed private equity fund, FoF, ETF and company common shares. For the first three types, the return depends on the management skill to some degree which is hard to quantify in the analysis. But the performance evaluation for the listed private equity company stocks is objective since it is totally based on the market price. The stock price could reflect the company performance directly and avoid the subjective adjustment influence existed in fund return.
Today, many private equity companies have shares issued on the exchange and the asset class comprised by those stocks is quickly expanded and favored among investors. In fact, a few ETFs and indexes have already built to trace the asset class performance, but they provided different results. One reason is the rebalance strategy applied behind each index could matter the final performance, another reason may be caused by the differentiation in management ability. So to objectively evaluate the performance of this asset class, I would construct three indexes to fully reflect the characteristics in the asset class in the paper.
According to the report from Reuter, there’re around two hundred companies listed on the exchange whose business mainly dealt with private equity investments, but this number is less than fifty ten years ago. Because the number of private company that has stocks issued on the exchange has limited for many years, most of the research use the data that includes all instruments belongs to the publicly traded private equity vehicles so the observations in their
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sample are heterogeneous which may lead a biased conclusion. To overcome the problem, the paper would set a sample comprised by private equity company stocks only and ensure the analysis is built on a homogeneous basis.
According to the empirical evidence so far, the listed private equity investment instruments have shown a high correlation with the performance of unlisted private equity, and many institute investors begin to increase the proportion in this sector for liquidity reason. As one type of publicly traded private equity instruments, weather investing in the private equity company stocks has the same diversification effect as investing in traditional private equity is a meaningful topic. Inspired by the idea, I would estimate the risk-return characteristic of the sample that only includes private equity company stocks and document detailed analysis.
The paper would try to answer the following questions: 1, if the risk of the asset class comprised by private equity company stocks especially higher than other industries; 2, if excess return exists in the asset class as that found in private equity investment; 3, if the risk-return characteristics of the asset class are discrepant in different currency regions; 4, if the risk exposures of the asset class are consistent with the market index; 5, how the asset class performance linked with traditional private equity investment and the possibility to use it as a substitute for alternative investment in asset allocation.
This would be the first paper focus on the study of a sample comprised with private equity company stocks. One reason is the number of observations is limited many years ago, so it is not possible to study such an asset class that time. Another reason is this asset class is developing, there lacks a specialized database to collect the information. The observations in
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the paper are handle-collected from many resources. With the observation numbers quickly increasing and more attention to the asset class, it is meaningful to make a detailed study and document the risk-return characteristics as a reference.
The paper is structured as follows. The second section provides background of the publicly traded private equity instruments investment. The third section reviews the related literature. The fourth section describes the dataset and methodology in detail. The fifth section presents the empirical results. The sixth section concludes the paper.
Section 2. Background
2.1. A snapshot on publicly traded private equity instruments
Private equity has experienced a rapid growth and been categorized as one of the most important alternative asset classes. An engagement in private equity can either be done by a direct investment for the limited partnership or by an investment through a listed instrument such as a fund. Until the 1990s, the former type was the main channel to participate in private equity. It made private equity much more like an asset class for institutions and rich individuals. Financial crisis taught a lesson that never put all eggs in one basket, so more investors shift attention to private equity investments as a way to diversify the whole risk. To meet the growing demands for private equity investments and help avoid the complicated contract design in traditional private equity, many publicly traded private equity investment instruments are created. Today, investors could invest in these instruments easily as trading common shares at a little cost without facing the management fee.
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Though the publicly traded private equity instruments are created to simulate private equity investments which could diversify the systematic risk in a portfolio, low entry barrier makes them correlated more closely with the market activity than traditional private equity does. After the financial crisis, risk management has been emphasized and diversifying the asset allocation is being strengthened even for individual investors. As instruments listed on the exchange, frequent trading activity brings liquidity to these investments and this sector is expanding quickly after 2000. Many investors use publicly traded private equity investments to replicate private equity exposure, and evidences show that the strategy works well.
Investing in publicly traded private equity instruments has many advantages over investing in traditional private equity. To simply sum up, the dual characteristics designed in these instruments make them especially attractive for investors.
First, the risk-return characteristics correlated with the public market. Because the instruments are easily accessed on the exchange, the performance is obviously influenced by the market expectations linked with market volatility to some degree. Due to the potential short-term volatile fluctuations, investing at a discount and gaining without exposure to complicated management fee structure becomes possible in publicly traded private equity instruments. Furthermore, volatility from active trading eliminate the liquidity risk which is a main problem faced by traditional private equity investors.
Second, the risk-return characteristics correlated with traditional private equity business. Obviously, the publicly traded instruments are invented as representatives for private equity investment, so their performance should be highly correlated. Though the performance of
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publicly traded private equity instruments are interfered by the market volatility to some degree, the long-term performance still determined by the underlying private equity business. There’re different kinds of publicly traded instruments for investors to choose, so it is not hard to replicate the same exposures as private equity investment. Furthermore, the data of listed private equity instruments are fully disclosed and investors could make adjustments quickly which seems impossible in traditional private equity investments.
As we can see, investing in publicly traded private equity instruments is more flexible and the trading mechanism could meet most investors’ requirements. With more frequent trading activity in the sector recent years, the distinct characteristics presented in the instruments are attracting more investors to participate in. Today, even institute investors also begin to raise the portion allocated to publicly traded instruments for liquidity needs.
2.2. Development of private equity common shares investment
Among kinds of publicly traded private equity instruments, one type is private equity company common shares. It sounds paradoxically, but there are around a hundred private equity companies issued shares on the exchange worldwide so far and the number keeps increasing in the past ten years. Different from other publicly traded companies which supply real products, the business of private equity company is invisible so the stock price directly reflects the expectation from public investors. For investors whose conditions are restricted from private equity investment, stock issued by the private company is an alternative choice and could be used as a substitute because of the similarities showed in their performances.
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In fact, the rudiment of the publicly traded private equity company stock could trace back to the early 1980s in U.S. To support the country’s small and mid-sized businesses, U.S established “business development company” (BDC) which in fact is a form of publicly registered investment company. BDCs are listed on the exchange and traded similar to REITs. The return of BDCs is coming from revenues invested in small companies and looks like IRR in private equity investment. In addition, BDCs allow investors to purchase a share in the open market. Interestingly, most companies issued BDCs are these private equity companies who later have their stocks traded on the exchange and the number of BDCs keeps decreasing since more private equity companies listed on the exchange.
According to one financial report, BDC index has delivered a 213% total return and its historical performance also surpassed the S&P 500 on both a current yield and total return basis. The marvelous return fully reflected the private company’s excellent asset management skill and attracted more investors participate in business involved with private equity company. So once a private equity company begins to issue common shares, it always welcomed by the market investors and make the asset class comprised by publicly traded private equity company stocks noticeable than others.
Today there’re a few funds traced the performance of the publicly traded private equity company stocks. The differences in the funds’ performance highlight the sector's complexity. Unlike the funds which are managed and adjusted by professionals, the paper would evaluate the performance of the asset class applying a general accepted method to allocate the weights without interfering from subjective rebalance. As mentioned before, more private equity
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companies are listing on the exchange and this asset class is in a developing stage. Having a clear understanding of the characteristics before blindly investing is important for investors who have interest in private equity company stocks. In fact, with the number of stocks increased in the asset class, there is more subjective space left for investors, which means more potential opportunities to make excess return by wisely allocation.
2.3. Advantage of investing publicly traded private equity company stock
As one kind of publicly traded private equity instruments, the frequent trading activity in the market makes liquidity not a major problem in private equity company stock investment. Furthermore, no minimum investment requirements and simple trading structure provide the asset class another advantage over traditional private equity investment. Due to being quoted on the exchange, investors can freely choose stocks in the asset class and make adjustment anytime without exposing to management fee and other contract arrangements which exist in traditional private equity investment.
Despite the easy access in trading mechanism design, the asset class also provides a research advantage over traditional private equity investment study. Clearly, the availability of stock market data makes objective performance evaluation possible for this asset class. In contrast to infrequent disclosure of private equity investment, the transparent information and continuous quoting of private equity stocks overcome the survivorship and selection biases which are commonly existed in private equity research. The market data provide a strong convenience to estimate the risk-return characteristics for the asset class. Furthermore, evaluating asset class comprised by private equity stocks listed on the exchange also excludes
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the influence from management skill which is generally reflected in fund’s performance. Applying market price model to investigate characteristics is reliable for this asset class and the conclusion is more objective than that of traditional private equity. Meanwhile, comparing the performance of the asset class with traditional private equity investment performance could provide investors another view to understand the risk-return characteristic of private equity investment.
Section 3. Literature review
As one attractive alternative asset class, there is a lot of literature studying on the performance of private equity funds. Because of the opaque data and complicated return distribution structure, no final conclusion made to evaluate the private equity performance so far. In general, private equity investment is thought to outperform the public market, but many studies have rejected this hypothesis. In addition, survivorship bias and selection bias in private equity database also impede a consensus for estimation. Meanwhile, as more private equity vehicles listed on the exchange, some scholars have turned their attention to the developing sector in financial market and documented their performance. Though the selection bias is unavoidable, the estimation based on fully disclosed market data is less disputed. Considering different analytical method and database applied in each paper, the empirical results seem various in the private equity performance evaluation. The following part would provide a brief review of the related researches in the field so far.
Moskowitz and Jorgensen (2002) used a broadly defined private equity dataset and found that the average annual return to all privately held companies was about two to three percentage
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lower than the publicly traded equity over period 1989 to 1998, and the private equity return also presented more volatility despite its high correlation with public return. Though people named the finding “Private equity premium puzzle” and a lot of scholars began to testify it later, the dataset used in the paper made the finding not that convincible because it excluded most public investments from private equity funds.
Ljungqvist and Richardson (2003) used a cash flow based approach to analyze the private equity funds, and reported an average of five to eight percent over the publicly indexes outperformance over period 1981 to 2001. Different from others, their dataset are based on an exclusive access to cash flow data so the paper could provide performance evaluation considering accurate timing of investment and be avoid of management subjective valuations. In the paper, they also checked the risk-return profile of the private equity funds and estimated the beta of private equity funds is greater than one. Furthermore, they pointed out that the outperformance might relate to the type of funds other than compensation for systematic risk.
Kaserer and Diller (2005) studied the determinants of the private equity funds’ performance in Europe. They applied a cash flow method in analysis to testify their hypothesis. They pointed out that the average excess return over the public market have directly related with the cash flow timing and especially so for venture funds who are more sensitive than other types of private equity. The illiquidity character also accounted for the variation of private equity funds’ return. They documented that the GPs’ skills mattered the funds’ performance significantly which could be seen as an unsystematic risk. Furthermore, they stated that the
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whole performance of private equity funds was not closely related to public market.
Martin and Petty (1983) published the first paper focused on listed private funds performance. They obtained 17 venture capital firms price data from 1973 to 1979 and excluded 6 inactive trading ones. Though the sample only includes 11 observations, the small sample showed a superior return compared with the public market from 1973 to 1979. They further documented that the average volatility of these firms return were higher than the market but the systematic risk was lower than 1 measured by β.
Brophy and Guthner (1988) computed the beta of 12 publicly traded venture capital funds and investigated the performance using weekly data from 1981 to 1985. They concluded that the funds achieved a higher return than S&P500 and other growth-oriented mutual funds. In addition, they pointed out that the risk of each fund was high, but the whole risk of the portfolio that constructed by those funds was low.
Huss (2005) has studied the performance difference between listed private equity funds and unlisted private equity funds. The author used performance of LPX 50 TR index as a substitute for listed private equity funds. His analysis showed little difference between the net performance of listed funds and that of unlisted funds applied a cash flow method. He concluded that one could reasonably assume listed and unlisted private equity investments performed in an almost equal way based on the empirical evidence. The high correlation between return of listed private equity funds and unlisted private equity funds supported the idea that publicly traded private equity funds would be an appropriate alternative for unlisted private equity investment. But using LPX50 TR index to represent the whole listed private
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funds’ performance was disputed, and the evaluation was biased because the index return was directly influenced by the management skill.
Zimmermann, Bilo, Christophers, and Degosciu (2005) used a dataset included 287 publicly traded private equity instruments from 1986 to 2003 worldwide to document the asset class’ characteristics. They studied the risk–return profiles using a subsample included 114 liquid instruments and found that the performance of publicly traded private equity instruments outperformed the public market indices in the period from 1986 to 2000. Furthermore, the adjustment strategy (in terms of weighting and rebalancing) in the investment portfolio would influence the final performance dramatically. After adjusting risk estimates for liquidity bias, the Sharpe ratio of the fully rebalanced strategy portfolio was above the world stock market. They pointed out that there was a small positive bias existed essentially during all periods, which was different from the standard performance literature view. Though they did a lot of detailed job, the sample was constructed with heterogeneous publicly traded private equity instruments, and the estimation based on such a sample was biased even they have addressed the liquidity issue.
Jegadeesh, Kräussl and Pollet (2009) estimated the risk and expected returns of publicly traded private equity funds based on the market price from 1994 to 2008. They used data set included 129 publicly traded private equity funds and also analyzed the characteristics of 24 FoFs which focused on investment in private equity field. Their results indicated that the market expected publicly traded private equity to earn a zero to marginally negative abnormal returns net of fees. They also found both publicly traded and unlisted private equity funds
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exhibited a positive correlation with GDP and had a beta close to one. In addition, they noticed that any abnormal returns in excess of two percent (no matter negative or positive) were inconsistent with market prices over time.
Until now, the study papers on publicly traded private equity instruments are limited. Because the number of publicly traded private equity investment instruments keeps increasing and the sector develops quickly, the sample in the former papers has changed a lot and the conclusion may not be applicable for today. Furthermore, the heterogeneous observation used in the study sample makes it hard to be a convincible estimation.
With more private equity companies listed on the exchange, the performance of the specified asset class is noticeable. Constructing the sample of homogeneous observations and applying a market price model, the paper would overcome the heterogeneity bias in the former study and provides an objective analysis. Using data in the last decade that includes financial crisis period, the analysis would help investors understand on how much degree the asset class could be used as alternative investments to diversify the whole risk. The paper could be seen as a supplementary in the field of publicly traded private equity investments research.
Section 4. Dataset and methodology
4.1. Data source
There are four types of publicly traded instruments to link with traditional private equity investment: ETF, listed private equity funds, funds of funds, common stocks. To avoid the subjective factors in performance analyze and evaluate the risk-return characteristics
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objectively, the paper would use the company stock data specifically. The data related to publicly traded private equity company is obtained from different resources include Thomson One, LPX Group index, S&P listed private equity index and PowerShares listed private equity index, Bloomberg and Thomson Reuters.
4.2. Sample selection
Rough potential observations are more than thousands through the public resources mentioned above. So I apply some more serious selection criteria to distinguish the qualified observations, the criteria include:
-Companies use their own capital to invest the private equity business and the investment return is their main profit source and
-Companies whose core business is private equity funds management.
The two criteria could exclude most of asset management companies who have minor capital involved in private equity business and effectively distinguish the companies whose major business field concentrated in private equity investment. Use the criteria to select the data from different resources and match them one by one, 102 qualified publicly traded private equity companies are screened out preliminarily.
Then, the paper wants to learn the performance of this asset class applying market price approach, so I use Datastream to obtain the market trading information. The time period used in the paper is from 2005 to 2014, so ten companies that has been acquired or delisted during the past ten years are excluded. Finally, the data sample is restricted to 92 companies and the
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following sections provide research based on the market data of the 92 companies’ stocks.
4.3. Sample characteristics
The sample includes 92 publicly traded private equity companies from 2005 to 2014. To better describe the constitution of the sample and reflect the features of the 92 companies, I categorized them into five group based on their market capitalization. The group classification is listed below:
“Nana” company: the market value smaller than $50 million
“Micro” company: the market value is between $50 million and $300 million
“Small” company: the market value is between $300 million and $2 billion
“Mid” company: the market value is between $2 billion and $10 billion
“Big” company: the market value is larger than $10 billion
Table 1 shows the descriptive statistics of the sample used in the paper. As shown in Panel A, 92 publicly traded private equity companies are finally identified in the year 2014 and the number is 52 in the beginning of 2005. So we can see that the number of publicly traded private equity companies is increasing and this asset class is developing quickly in the last ten years. But one noticeable thing is that the growing speed is slowdown after 2008. So being publicly traded is a trend for private equity company, but the decreasing listing speed after financial crisis may reflect that the private equity business is sensitive to economy environment and most companies show a prudent attitude for listing on the exchange after
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crisis.
Panel B summarizes market capitalization of different group size and Panel C describes the distribution of the observation in detail. The market capitalization of each company is calculated based on the data in the end of 2014. The sample only includes one private equity company belongs to the “big” company by market value; almost half of the sample is in the “Small” company group. The mean market value of the sample is $1339.45 million and the median is $421.39 million. The distribution of the location in the sample is also imbalanced. 49 are from Europe region and 26 of them locate in the UK, 37 companies are from United States and the other 6 are from other continents. The reason of the discrete distribution may because the financial market of Europe and America is highly developed and more integrated than other regions’, so the private equity companies are more optimistic to list in the Europe and America market. Because the location is relatively concentrated, so the paper would also document the risk-return characteristics of the company listed in UK, US and Euro markets separately.
As mentioned before, most of the private equity companies belong to small market capitalization scope, so it’s normal that their stocks are not that liquid compared to large market capitalization stocks. To objectively address the liquidity issue of the asset class, I use spread and turnover rate together to reflect the situation. In this paper, spread is defined as
Askrt−Bidrt
Adj−Pricert, where Askrt is the daily ask price of company r at closing time t, Bidrt is the daily
bid price of company r at closing time t and Adj − Pricert is the adjusted closing price of company r at time t. I use 𝑉𝐴𝑟𝑡
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turnover by value in US dollar at time t and 𝑀𝑉𝑟𝑡 is the market capitalization in US dollar at time t. Typically, a narrower spread and higher turnover rate mean active trading behavior of a stock, which compose a liquid signal for one stock, and imply that using market price approach to measure risk-return characteristics is accurate.
Table 2 provides the descriptive statistics data of the spread and turnover rate for observations in the sample. The mean and median of spread are 3.3% and 0.57% respectively; the volatility is 234%, which imply the spreads of publicly traded private equity stocks are highly divided. But the spread also shows different level among the five market capitalization groups. The higher the market value, the narrower the spread is. In fact, the average spread of a “Big” company is only 0.14%, but the average spread of a “Nano” company is 12.73%, which may lead a liquidity bias when face block trading and investors have to take the bias into consideration if they enjoy frequently trading.
The mean and median of turnover rate in the sample are 4.35% and 0.066% respectively, and the volatility is 59.33%, which is less volatile than it in the spread. There’re also differences among different market value groups, but the distribution of turnover rate implies another liquidity situation. In fact, the highest turnover rate is found in “Micro” group, which is 8.99%, and the lowest turnover rate is in the “Big” group company, which is 0.38%, even lower than the “Nano” group whose turnover rate is around 0.71%. Generally, a higher the turnover rate suggests frequent trading activity of one stock, which means more liquidity. Since the spread and turnover rate of the sample give two different implications, combine them together, I think the liquidity level is acceptable and all stocks are tradable for most
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investors interested in the asset class.
Illiquidity is one important characteristic in the traditional private equity investment, and the spread and turnover rate in publicly traded private equity company stocks also reflect this characteristic in some degree. For investors who utilize the publicly traded private equity asset class to substitute traditional private equity position, buy and hold strategy is appropriate and the potential illiquidity issue of the stocks could be eliminate in the long run. So I construct the indexes without regular rebalance and use ten year as a research period to evaluate the performance, and liquidity issue shown in the sample would not lead obvious estimation bias applying a market price approach.
4.4. Methodology
To learn the risk-return characteristics of this developing asset class comprised of publicly traded private equity company stocks, three indexes are built for analyzing. Several issues involved in constructing indexes are addressed here:
First, the number of publicly traded private equity companies is increasing during the last decade, so the weight of indexes would be recalculated once the new company listing taken place.
Second, the currency of the market price data has been translated into U.S dollars based on the exchange rate that day, so the U.S data is adopted once involved with the risk free rate and spread selection.
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the trading may not that active as observed in other industry stocks. I would make comparisons to address the illiquidity issue among indexes built by different methods, but no company would be excluded because of illiquidity. Reason to do so is illiquidity is one important character of private equity business, it’s normal to be reflected in the price spread and investors should accept it instead of avoiding.
Fourth, the average performance is calculated based on data in the last ten years’ period, which means a buy and hold strategy applied without new company listing. Reason to do so is because private equity investment itself is quite illiquid and has a long lockup period, so using ten years’ market data as one analyze cycle and compare the stock average performance with traditional private equity performance is stable and objective than using data in short run. Furthermore, the potential liquidity bias would be eliminated in the long run applying a buy and hold strategy.
To fully reflect the risk-return characteristic of the private equity company stocks, I design three indexes applying different allocation methods to catch their features:
A. A market value weighted index: MV-Index
The weights are determined by the relative market capitalization of the company stock. The dividends are adjusted daily and the weights are adjusted based on the market capitalization proportion in the previous trading day. The reason to do so is for an investor, if you rebalance every day, then the weight must be calculated based on the market price data in the previous trading day.
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One feature of the market value weighted index is that it could capture the risk-return characteristics of the underlying asset class from the market aspect, but a potential problem is a heavy weight may concentrated in a few large market capitalization companies and their performance could influence the index directly. However, the performance of the market value weighted index is the most straightforward method to compare with other publicly market indexes.
The method to construct the MV-Index is below:
(1) MIt= MIt−1∗ ∑ MVrt−1
MVt−1
n
r=1 ∗PrtP∗Adjrt−1rt
Where MIt is the value of the index at time t, MVrt−1 is the market value of stock r at time
time t-1, MVt−1 is the sum of the market values of all stocks at time t-1. Prt is the price of stock r at time t. Adjrt is an adjustment factor of price to reflect stock dividend or capital change in case.
B. An equally weighted index: EW-Index
An equal proportion of wealth is allocated among the underlying assets regardless of each stock’s market capitalization or economic size. The equally weighted index could overcome shortcoming of market value weighted index by giving each stock an equal weight, but the potential problem is the liquidity issue that exists in the private equity company stocks may lead a bias in performance analyze. To eliminate the illiquidity influence, I will only rebalance the index when a new company stock listed and apply a buy and hold strategy otherwise. The reason not to rebalance the index frequently is to reflect some practical matters
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using equally weighted method. First, the potential bid-ask spread bias in trading may absorb the potential return if rebalance too frequently. Second, equally weighted allocation is supposed to replicate the illiquidity exposure in private equity investment, which means investors who use equally weighted method are expected to have a long hold period.
The method to construct the EW-Index is below:
(2) EIt= EIt−1∗1n∗ ∑ Prt∗Adjrt
Prt−1
n r=1
Where EIt is the value of the index at time t, n is the number of stocks listed at time t, Prt is
the price of stock r at time t. Adjrt is an adjustment factor of price to reflect stock dividend or capital change in case.
C. A price weighted index: PW-Index
The index value is generated by adding price of each stock and the weight is determined by stock price per share. So a high price stock performance would influence more than a low price one in the index. The reason to construct a price weighted portfolio index is because the price is a quite sensitive indicator to imply the company performance, especially so for private equity company because their profit is totally depends on the asset management skill and capital operation ability. In an efficient market, any good information from a private equity company would attract abundant investors quickly, and stock is the priority choice for investors who don’t have access to limited partnership. So the price is a sensitive indicator for private equity company performance since it could reflect the investors’ expectation rapidly in an efficient market.
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The method to construct the PW-Index is below:
(3) PIt= PIt−1∗ ∑ Prt
Pt
n
r=1 ∗PrtP∗Adjrt
rt−1
Where 𝑃It is the value of the index at time t, Prt is the price of stock r at time t, Pt is the sum of the price of all stocks at time t. n is the number of stocks listed at time t. Adjrt is an
adjustment factor of price to reflect stock dividend or capital change in case.
Section 5. Empirical results
5.1. Basic risk-return characteristics description
Table 3 presents the basic risk-return characteristics of the three indexes. To compare with the market indexes straightforward, I also list the return, volatility and Sharpe ratio of MSCIWORLD index here. The return and volatility have been annualized based on data during 2005 to 2014 and the average one-year T-bill rate is used as risk free rate in Sharpe ratio calculation. In addition, five lag autocorrelations of each index provided here as a part of these indexes’ characteristics.
As presumption, the EW-Index and PW-Index outperformed among the five indexes but the MV-Index underperformed. The mean annualized return of PW-Index and EW-Index is 15.21% and 12.77% separately without taking more volatility than general market indexes. The Sharpe ratio of the two indexes is 0.807 and 0.653 which are much higher than the world indexes. However, the MV-Index return is not that good, it only attains a 2.63% annualized return and the annualized volatility is 19.66%, which is much higher than the average. The Sharpe ratio of the MV-Index is the lowest among the four indexes. One possible reason for
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the underperformance of the MV-Index is because the weight is heavily concentrated in a few companies whose performance may not properly represent the whole asset class. In fact, 15 companies accounts for 69.18% weight in the MV-Index which means the index is not diversified. Another explanation is some big companies suffered more loss in the financial crisis and this effect has been augmented by the biased weight distribution, so their performance directly dragged the whole index performance.
Two ratios to describe the liquidity issue are displayed in Table 4. There are dramatically differences among the three indexes. The mean spread of MV-Index is 0.56%, and the volatility is 2.92%, both suggest a lower trading cost. But the turnover rate of MV-Index is 1.12%, which is the lowest in the three indexes. The situation of EW-Index is totally opposite; the turnover rate is 1.77% which suggests more frequent trading activity. But high volatility exists in EW-Index spread and turnover rate may result in an unstable liquidity expectation. For block trading in EW-Index, investors have to take liquidity as a risk to consider. The liquidity issue in EW-Index doesn’t exist in the other two indexes, there’s no obvious difference in MV-Index and PW-Index liquidity indicator. In fact, the spread and turnover rate in PW-Index could be viewed as a good trade-off among the three indexes.
5.2. Performance evaluation applying CAPM model
To further analyze the performance, the classical CAPM model is adopted. Though there are a lot of discussions related to CAPM which question its accuracy, the empirical evidence still supports the model in the long run analysis especially when the evaluated sample is consisted with large number of stocks. In the paper, all indexes are constructed by the 92 observations,
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and the analysis period is 10 years, both could meet the requirements to apply the model and ensure performance evaluation based on the CAPM model is convincing.
The indexes are purely constructed by publicly traded private equity stocks and the currency has transformed to US dollars, so the composites are homogeneous and the approach used for analyzing is generally applicable without bias. In this part, I will provide the regression result applying the CAPM model and also calculate the Jensen’s α (listed in Table 3) so that the performance of different indexes could be clearly presented and compared.
5.2.1. Risk-return estimation of three indexes
The sample is constructed by observations in period from 2005 to 2014, and one characteristic of the private equity investment is the long locking period. To reflect this point, I use the 10-year Treasury bond yield at the beginning of 2005 as the risk free rate in analysis, which is 4.23% specifically. Due to the three indexes are comprised by stocks listed worldwide, so the MSCIWORLD index performance is used as the proxy for the market return in this part. In addition, as mentioned before, the stocks are concentrated in three currency regions, so the risk-return characteristics of the company stocks would be analyzed using CAPM based on currency region in the latter part, and investors could see clearly if there’s significant difference of systematic risk in different region.
The systematic risk and expected abnormal return α from the market in CAPM model is: E(rI− rf) = αI+ βI[E(rM) − rf]
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used to check expected abnormal return from the market. Typically, in an efficient financial market, the “αI" does not exist in the long run and the “βI" is close to 1.
Table 5 presents the regression result applying the CAPM model for three indexes. The expected abnormal return doesn’t exist for both MV-Index and EW-Index at a 99% significance level, but a daily expected abnormal return from the market 0.0399% is found in the PW-Index. Also, the adjusted R square is more than 70% for MV-Index and PW-Index, which means the estimation are pretty accurate, but this number is a little bit lower for EW-Index, which is only 51%.
In Panel A, we could assume that the MV-Index performance perfectly coincides with the CAPM model expectation: with no abnormal return in the long run and a systematic risk close to 1. Panel B lists the F-test result for βI, and we could not reject the assumption. However, the MV-Index underperformed the world market index, and the annual Jensen’s α is -1.24%. One reason is because MV-Index composite are concentrated in a few large market capitalization companies and the index is not totally diversified from asset allocation view. Another reason has mentioned before, I adopted a 10 year T-bond yield issued in the beginning of 2005 as risk free rate, which doesn’t reflect the influence of financial crisis in 2008. The risk free rate 4.23% looks higher today, but for private equity investors, preparing for financial crisis in the long lock period is always good, so applying a long-time treasury rate as risk free rate for private equity investment estimation is prudent and a good thing. Using ten years data as one performance analysis cycle and lock the risk free rate at the beginning is meaningful. The performance evaluation would be more reliable than applying a
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short-term treasury rate as risk free rate, especially for long time horizon performance study.
Though the MV-Index fit the CAPM expectation well, the underperformance in the last ten years implies that the big market capitalization private equity company may be more sensitive to the bad economic situation than others. In 2002, Moskowitz and Jorgensen have pointed out that the average annual return to all privately equity held companies are lower than publicly traded equity from 1989 to 1998 and the MV-Index of private equity company stocks result is consistent with the conclusion. So if investors want to replicate the risk exposures like traditional private equity business, then using market value weighted allocation strategy to invest private company stocks is not a good idea.
Different from MV-Index, the annually Jensen’s α of the EW-Index is 8.79%. The systematic risk explained by the market is 0.697 and the adjusted R square is 51%, both are lowest among the three indexes. Considering the financial crisis in 2008, the mean annual return 12.77% in the long run without more volatility than market index is quite attractive. The low βI meet the requirement to diversify the investment risk like traditional private equity
investment does. So the result implies that EW-Index could be the best one to replicate the risk-return characteristics of traditional private equity among the three indexes, and EW-Index also reflects some illiquidity characteristics as those presented in private equity investment. So for long-term investors who prefer private equity investment, allocate asset by equally weighted strategy within the publicly traded private equity stocks is a good way.
PW-Index is the winner among the three indexes: With the highest mean annually return 15.21% and the lowest volatility 16.82% among the three indexes. The risk-return
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characteristic in PW-Index also has its own feature. Different from the former two, there exists an expected abnormal annual return 10.929% applying the CAPM model and the annual Jensen’s α is only 0.35%. The systematic risk is 0.826 and the R square with the market is 73.8%. So we can say that most of the excess return in PW-Index is expected from the market and the high R square in regression strengthens the explanation reliability. With a lower systematic risk and an abnormal expected return significantly exists, PW-Index is appropriate for investors who want to replicate the private equity return without more uncertain risk exposures. The expected abnormal α from the market may because the stock price is a sensitive indicator of the private equity company performance and reflects the investors expectation efficiently, so the outperformed company price would increase and has more weight in the PW-Index which finally formed an expected abnormal return.
The result implies different risk-return characteristics of the indexes even though they are constructed by the same observations. But one common feature is no high systematic risks implied in the CAPM model. Typically, investors think private equity are more risky and should have a higher βI, but the result contradicts the intuition. On the contrary, the average lower systematic risk observed in the sample suggests that the asset class have potential to eliminate the whole investment risk to some degree. All three indexes reflect the private equity business risk –return characteristics from different aspects.
5.2.2. Correlation and diversification effect
Private equity is typically used as an asset class to diversify the risk, so a lower correlation with other publicly market index will have a good effect. In this part, I calculate the
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correlation of the private equity company stocks with other influential public stock indexes in the world and results displayed in Table 6.
Before calculating the correlation among each indexes, I run the Jarque-Bera test to check the normal distribution assumption first. Panel A presents the test result. The test result implies that the return of the publicly traded private equity company stocks is highly non-normal distributed, so the correlation coefficients are calculated as Spearman correlation coefficients.
Panel B presents the Spearman correlation coefficient between indexes. Obviously, all the correlations between the public indexes are positive and the EW-Index shows average lower coefficients with other markets than MV-Index and PW-Index, and the lower correlation of EW-Index is coincided with the result in CAPM model. Look at the table as a whole, the diversification effect implied by correlation from the three indexes in the paper is not obvious, but the average low correlation between UK and US market suggests that if an investor wants to diversify the risk of the whole asset, investing in different regions maybe a better choice.
5.2.3. One-year rolling risk-return structure of three indexes
To better catch the risk-return characteristics of the publicly traded private equity company stocks over time, I open a one year rolling window to reflect the dynamic change of the risk-return profiles and Figure 1 shows the structure. Because the period includes 2008, the year that financial crisis happened, so the figure shows an abrupt down shape in the crisis year which implies that the private equity business is quite sensitive to the macro finance environment. I use the annual MSCI world index return as a benchmark in the figure, and we
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can see the return pattern of the three indexes are almost the same before 2010, all exhibit a sharp down trend in the 2008 and recover quickly in the following two years, and the trend between volatility and return are reverse most of time which is coincide with the assumption. But after 2010, the trends show different pattern. Both MV-Index and PW-Index show a mean-reverting trend after 2010, but the volatility of MV-Index falls down more quickly after 2012 and keeps a low flat trend then as the return lingers around the market mean. The figure of EW-Index shows a high annual return and keeps it at a high level in the whole 2013, and the volatility increases and keeps at a high level in that year as well. At least we can see clearly that the EW-Index outperformed in 2013 though the trend didn’t last any longer. From the figures, we can tell that the private equity company stocks performance are acute to the investment environment and this asset class also shows strong recovery ability as well. The performance of the asset class becomes less volatile compared with it before 2010, which may be caused by the weak global economy and less investment opportunity.
5.2.4. Systematic risk in different regions
In this part, I investigate the publicly traded private equity company stock performance in three currency regions: Euro region; UK; US. The methodology to study their performance and risk-return characteristics are the same in the previous part. Three indexes: market valued weighted index, equally weighted index and price-weighted index are constructed respectively based on the regional sample which composed with private equity company stocks. CAPM model is used to evaluate the performance from the market view and the difference of risk-return characteristics in these regions could be easily and objectively
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compared.
Table 7 summaries the performance of indexes constructed in different currency regions and presents their basic risk-return characteristics. Table 8 displays the detailed result applying the CAPM model. In Euro region, all three indexes outperformed the local market index Eurostoxx50, and the systematic risk implied by the euro market is generally lower than systematic risk of the indexes constructed worldwide. The equally weighted index has an annual Jensen’s α of 10.61% and its volatility is 16.44%, which makes it become the outperformed one among the three indexes. There is an abnormal return 13.41% significantly exists (at 99% level) in the price-weighted index and it sounds quite attractive for investors who don’t want to face more uncertain risks. But one noticeable thing is that the expected abnormal return is only found in the price-weighted index of market in the Euro region, which may be explained as the investors in Euro market treat stock as an efficient way to invest in private equity and the stock price could be used as an accurate indicator to reflect the company performance.
The result in UK region is underperformed compared with other regions and the average performance of the publicly traded private equity company stocks doesn’t meet the expectation. Both market value weighted index and equally weighted index underperformed the local market index FTSE 100 of 0.7% and 1.3% respectively. But the annual volatility of equally weighted index in UK is only 11.5%, which is much lower than the FTSE index whose is 19.3%, and the systematic risk of equally weighted index implied from CAPM is only 0.331. In spite of its bad performance in the long run, the low volatility and low βI make
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the equally weighted index attractive from the risk management view. Equally weighted index could be considered as a substitute for the traditional private equity investment because its low correlation with local market. As the only index outperformed the local market index, price weighted index in UK region also presents a relative low systematic risk than the systematic risk of indexes in other regions, but the abnormal return could not be explained by the market effectively.
Because the financial market in US is quite developed, and there are many indexes could be used as a proxy for local market, so I adopt Nasdaq, Russell2000 and SP500 as market indexes and run regression separately in US region. The risk-return characteristics of three indexes in US show own features which are not identical with the other two regions. One noticeable difference is the systematic risk implied from CAPM model is much higher than it shows in other regions. One possible reason is that the US financial market is quite developed so the asset class shows more market characteristics. Another reason may be the trading activity is more frequent and the active trading connects the asset class closely to the market, so the systematic risk βI is higher than observed in other regions. The performance of three indexes is different within US, and the market value weighted index of publicly traded private equity company is underperformed compared to the local market, and the equally weighted index exhibits the highest volatility among all indexes investigated.
Comparing the risk-return characteristics in the three currency regions, the systematic risk is dramatically different. The asset class in UK shows more potential to be used as an alternative investment because its low systematic risk correlation with market and low volatility on
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average, the asset class in US is highly correlated to the market and more volatile, so it shows more market risk-return characteristics than other regions’. The performance of the asset class in Euro part is stable and consistent with performance of the asset class worldwide. In addition, the price weighted indexes constructed based on local private equity company stocks have outperformed the other two indexes in the last decade, and this result is fit the result worldwide, so we could say that stock price is a good indicator to reflect the private company performance. For investors who are interested in this asset class, allocate the asset in different regions utilized the different risk characteristics mentioned above could receive a good effect.
5.3. Performance evaluation applying risk premium approach
To further learn the characteristics of the developing asset class comprised with publicly traded private equity company stocks, I would expect there’s a strong relationship with the economic environment. That means, the performance is exposed to global risk indicators which are used to measure the macro financial investment environment. Generally, scholars like to use business cycle and credit cycle to describe the macroeconomic situation, so I try to choose indicators to reflect the two cycles at the most degree. There are several indicators could be considered, and financial market performance sometimes been used to measure credit cycle, considering the CAPM model has provided the systematic risk analysis from the market view in the last sector, to avoid repeating and also for limiting the endogenous problem among explainable variables, the market index performance is excluded here.
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excess return of publicly traded private equity company stocks, and the basic model to learn the relation between publicly traded private equity company stock performance and global risk exposures is below:
(𝑅𝐼− 𝑟𝑓) = 𝛼0+ 𝛽1∆𝐺𝐷𝑃𝑡+ 𝛽2𝐶𝑟𝑒𝑑𝑖𝑡𝑡+ 𝛽3𝑉𝑜𝑙𝑖𝑡𝑖𝑙𝑖𝑡𝑦𝑡+ 𝛽4𝐿𝑠𝑝𝑟𝑒𝑎𝑑𝑡+ 𝛽5𝑇𝑠𝑝𝑟𝑒𝑎𝑑𝑡+ 𝛽6∆𝐼𝑃𝑂𝑡+ 𝜀𝑡
The explainable variables listed above are:
-∆𝐺𝐷𝑃𝑡: short for GDP growth rate in OECD region. This is an indicator to reflect the
business cycle, which directly reflects the real economic situation. The rate is collected only for countries in OECD region, because companies in the sample is concentrated in those countries, so using GDP of OECD is appropriate and limit the evaluation bias.
-𝐶𝑟𝑒𝑑𝑖𝑡𝑡: short for credit spread. This is an indicator to measure the spread between Baa and AAA corporate bond. It is used to reflect the funding environment. The tighter spread generally means more liquidity in the financial market. But after the financial crisis, to support the real economy, the credit spread has hit the lowest level in history. So this indicator may be better explained when applied in a long observation period.
-𝑉𝑜𝑙𝑖𝑡𝑖𝑙𝑖𝑡𝑦𝑡: short for stock market volatility. This is an indicator to measure the financial volatility and also used to compensate for the exclusion of market performance in explainable variables. As we know, the financial market index has a strong negative correlation with volatility index VIX, so adding this variable in the regression, is a substitute for the market index performance to some degree, it also to eliminate the omitted variable problems in the
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regression so the evaluation is more accurate. The volatility data is adopted CBOE VIX index which has developed for a long time and been a mature index to reflex the market volatility expectation.
- 𝐿𝑠𝑝𝑟𝑒𝑎𝑑: short for long-short term spread. The is an indicator to measure the spread between three month US treasury bill and 10 years US treasury bond. Typically, the long locking investment period in private equity investment require the investors have a long term expectation, so the increasing spread in the long run would imply a higher return expectation.
-𝑇𝑠𝑝𝑟𝑒𝑎𝑑𝑡: short for Treasury-Eurodollar spread. This is an indicator to measure the
difference between three-month US Treasury bill and three-month Eurodollar deposits. As the correlation indicated before, the financial market in US and UK are lowly correlated which may provide a good diversification effect for investors. To decrease the investment risk, investors may allocate their asset in different regions and the spread between US treasury and Eurodollar deposits could also reflect the balance situation in the global financial system.
-∆𝐼𝑃𝑂: short for IPO volume change. This is an indicator to measure the IPO volume change in the OECD countries. Most traditional private company are involved in IPO business. As one of the most import profit resource, the IPO volume change supposed to have a positive correlation with the private equity company performance. Furthermore, IPO volume change is an important indictor to reflect the financial activities, which implies the credit situation.
The dependable variable (𝑅𝐼− 𝑟𝑓) is defined as excess return. Different from the CAPM model, the 𝑟𝑓 rate uses one-year Treasury bill yield. The reason is to reflect the relationship
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between performance and economic situation, using short-term rate as risk-free rate could capture the dynamic adjustment accurately than locking it to a long term T-bond rate here.
In the previous part, the CAPM model has presented a high correlation between global stock market and MV-Index of publicly traded private equity company stock and the market itself could explain the return of MV-Index well. So in this part, I only investigate the risk exposures of EW-Index and PW-Index, together with the MSCIWORLD Index. By comparing the risk exposures of the three indexes, investors would have a better understanding about why the index comprised by the traditional private equity company may different from the public market and been used as one alternative asset class to replicate the performance of traditional private equity investment.
Table 9 presents the regression result between performance from different indexes and global risk exposures. All indexes present a strong negative relationship with volatility; on the other hand, it implies a positive relation with market return. Positive relationships with credit spread and GDP are also found to explain the performance to different degree, and another common characteristic of indexes performance is they are not sensitive to the long-short term spread. But there are also some differences exist among them. As shown in the table, the private equity company stock indexes show a stronger positive relation with GDP than the market, and also show a positive relationship with short term treasury-Eurodollar spread which doesn’t found in market. Interestingly, the direct relationship with IPO is found in PW-Index, not EW-Index whose characteristics are more closely to traditional private equity business. Considering the CAPM model result in the former part, maybe IPO activity is a
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positive signal to performance of a private equity company. So once a private equity company is involved in IPO business, then the market would directly reflect the good information in its stock price, and that is why there’s an abnormal return expected from market exist in PW-Index.
From the table, we can see that the private equity company stocks indexes face more risk exposures than public market index, which indicate that the private equity business is more sensitive to macroeconomic environment than other industries. And the negative constant showed in both EW-Index and PW-Index also indicates there is more other global risk exposures could be considered to explain the excess return in the publicly traded private equity asset class.
5.4. Performance overview
In this section, I compared the performance of publicly traded private equity stock indexes constructed in the paper, traditional private equity investment and the S&P listed private equity index. S&P listed private equity index is known as one important index that provide tradable exposure to the publicly traded private company stocks. Also, the S&P listed private equity index was managed by professionals and would adjust irregular based on the market situation, so it is supposed to be a good benchmark to evaluate the performance of the indexes constructed in the paper and help investors understand if there’s significant difference in the asset class if let professionals manage the capital.
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equity index is only -1%, and its volatility is 26.46% which is much higher than other indexes. So the average performance of S&P listed private equity index is not ideal in the last decade though it could obtain two digit returns in several years as well. The annual return of traditional private equity investment is 10.92% and the volatility is around 12% according to the report from Thomson One. However, the survivorship bias and selection bias in the traditional private equity performance evaluation make the two numbers underestimated the potential risk for investors.
Figure 2 lined the annual performance of EW-Index, S&P listed private equity index and traditional private equity funds in the last ten years. We can see that the trend of the indexes are highly correlated, but the traditional private equity has been less volatile after the crisis, on the other hand, the return from traditional private equity is not that attractive compared with the public traded indexes that composed with the private equity company stocks. Traditional private equity investment is deemed as one important alternative asset class to eliminate the whole market risk in asset allocation, but the consistent trend performance showed in the figure doesn’t support this view. Also, the performance and volatility observed in last ten years doesn’t show a potential high return in private equity investments. In fact, the publicly traded private equity asset class shows more investment potential compared with others. One reason for the outperformance is because the capital management ability of companies issued stocks are better than the peers who can’t list on the exchange. It also explains why the performance of indexes constructed in the paper without subjective selection is better than the S&P listed private equity index which is managed by professionals. The
