An analysis of the risk-return relationship of private equity in comparison to public market equity

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An Analysis of the Risk-Return Relationship of Private Equity in

Comparison to Public Market Equity

University of Amsterdam

Faculty of Economics and Business BSc Economics & Business

Author: Farid Chemali Miranda

Student number: 10621113

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PREFACE AND ACKNOWLEDGEMENTS

I am grateful to numerous people who made this project possible. Firstly, I would like to thank my supervisor, Dr. Jan Lemmen, who helped me overcome all my difficulties throughout this research. I would like to thank my family who has supported me along my study career, particularly my grandparents Faridd and Cecilia, without whom none of this would have been possible. Lastly, I would like to thank my friends, who have been a family away from home.

Statement of originality

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ABSTRACT

Evaluating illiquidity risk in 64 Listed Private Equity funds from the United States, this paper examines whether or not the incurred liquidity risk is worth the expected stock return. To assess this, this study uses the structure of the Fama and French framework, augmented with a liquidity factor and a sentiment factor using a dataset drawn from the United States equities market. This study’s results do not find the added liquidity and investor sentiment risk to be significant. Further, results suggest the additional risk factors do not enhance the model’s explanatory power measured in terms of the Adjusted R2 . Given the sample, this paper cannot conclude that Private Equity returns are higher than those of the Public Market Equity.

JEL Classification: G12, G32, G41

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1 Introduction

Over the past few decades, there has been considerable adjustments to the risk and pricing of returns of Public Market Equity (PM hereafter) investments, as opposed to those of Private Equity (PE hereafter) investments. This is surprising in light of the rising appeal of PE investments for independent investors, given the seemingly over-performance of PE over PM. However, similarly to alternative investments, the performance of PE in contrast to the equity market returns cannot be assessed by means of a one-to-one relationship due to the nature of this alternative asset class. Portfolios belonging to institutional investors, including but not limited to: pension funds, high net-worth individuals, insurance agencies, as well as endowments, have increasing been impacted by private equity investments. Playing an important role in the investment industry, private equities are not short-term and liquid, thus the risk and pricing of return does not use a standard evaluation tool. In general terms, private equity is designed to embrace positive change within an organization, as it relates to: public company going private, acquisition financing, expanding into a new business, and conveying operational change.

Returns associated with private equity are based on operational and financial improvements and restructuring. Although ownership imposes a strategic attention to a long-term horizon, contrary to the public market’s focus to earnings, private equity has the opportunity to generate significant returns on investment. Taking private equity investments, as a whole, this asset class’ performance measures has looked favourably regarding risk and return despite the increasing attention, and thus cash stream inflow, are slightly diminishing subsequent returns.

PE Fund managers, or General Partners (GP hereafter), do not have the obligation to disclose performance measures or returns. When they do, it is typically the Internal Rate of

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of returns, and thus the commitment of capital for longer time frames, short-term performance is irrelevant in PE investments. Neither the company managers, GP, nor the underlying investors get compensated for this time frame which makes PE investments not comparable to those of the PM (European Private Equity & Venture Capital Association, 2015, p. 8). In addition, PE funds have minimum Net Worth, investing experience, and risk tolerance qualifications to qualify to invest in PE funds. Due to this and other requirements an investor must meet to qualify for Limited Partner (LP hereafter), the broad majority of private investors are excluded from the exposure PE grants. This considered, and particularly after the 2008 financial crisis, PE funds are seeking to attract smaller investors by the means of issuing publicly traded shares, labelled Listed Private Equity (LPE hereafter) funds, which have been trading on considerable discounts, even up to 60% since early 2009 (Williams, 2016).

Considering the increasing demand from smaller private investors for this asset class, an inert Initial Public Offerings (IPO) market may incentivise entrepreneurs who seek an increase in capital to shift to PE for investments that will compromise and tie down their investments for a longer time period, albeit getting higher returns (Bain & Company, 2015). Despite the fact that Private Equity is a relatively new industry, it can play a significant role in the future of investment markets (BVCA's Limited Partner Committee, 2015, p. 10). This, along with the importance for investors to benchmark their investments against the market, the following research question is addressed in this paper:

Does the exposure to higher risk incurred from investing on Private Equity over the Public Market yield higher returns?

To answer the research question, this paper analyses risk and returns in Listed Private Equity by making a time series regression on the Fama & French Three factor Model:

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This model scrutinises how a security’s expected return, Ri, is influenced by the sensitivity of the return of the market and two portfolios representing the size and value risk factors compared to the risk-free rate Rf , where the risk-free rate is measured as the one-month Treasury bill rate at the beginning of the observed month (Fama & French, 1997, p. 155). That is, (Rmrkt – Rrf) representing the market risk premium, SMB is the size risk premium based on market capitalisation, and HML is the value risk premium calculated as the difference in returns between high book-to-market ratio and low book-to-market ratio (Fama & French, 1997, p. 156). Where β𝑚𝑘𝑡, βsize , and βvalue represent the corresponding factor loading of each risk factor.

Additionally, a data sample of 64 LPE funds from the S&P 500 Listed Private Equity Index, is used to provide an empirical analysis. There is a wide range of scholarship analysing PE investments, but few that analyse the performance of Listed PE. The fact that historical market prices of LPE are available allows for a better assessment of the performance, which is benchmarked against the S&P 500 Exchange Traded Fund (SPY), which aims to replicate the returns of the S&P 500 Index. As Eugene Fama and Kenneth French extended the CAPM, creating the Fama-French model, Pastor and Stambaugh suggested there be an additional liquidity factor to be included in the application and, similarly, Baker and Wurgler suggest to include a sentiment factor to enhance the models explanatory power. Thus, this paper augments the CAPM with the Fama-French factors, a liquidity risk factor, and a sentiment risk factor. This would enable investors to mandate additional premium for holding illiquid assets within a portfolio as well as have exposure to the influence of investor sentiment on the expected returns (“Required Rate on Equity: CAPM, Fama-French & Build-up Model”). Subsequently, Jensen’s alpha, α, is calculated to benchmark LPE against the market to determine the degree to which PE outperforms PM equity. This would mean the model would change to the following:

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Ri - Rf = α + βmrkt *(Rmrkt – Rrf) + βsize *SMB + βvalue * HML + βΛ *Λ + βsentiment * SENT (2)

Where Λ, SENT, βΛ, and βsentimentrepresent the liquidity factor, sentiment factor, liquidity factor

loading, and sentiment factor loading respectively.

Private equity investments are illiquid; yielding investors returns relative to investing in public markets. Due to the illiquid nature pertaining to private equity investments, determining how much to commit to any specific private equity to obtain a specific target in a portfolio creates uncertainty. The commitment risk associated with private equities is based on the time horizon related to the realizations and capital calls. This varies from public market investing, as no separation between invested and committed capital is made; trading remains consistent. Illiquidity is best described as the cost of commitment. Hence, such cost can vary amongst investors when examining whether or not the higher risk incurred from investing in private equities rather than public market equities indeed yields higher returns. In a like manner, investor’s sentiment prior the period being analysed plays a part in asset pricing, influencing subsequent returns particularly for small, volatile, distressed, new, and similar stocks (Baker & Wurgler, 2006, p. 2).

The remainder of this paper is structured as follows. In section 2, relevant literature is discussed, followed by the Model analysed along with the hypotheses being tested in section 3. Next, the sample data is presented in section 4. The results of the statistical analysis alongside its analysis are presented in section 5. Lastly, section 6 concludes this paper, presents its limitations, and proposes further research.

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2 Relevant Literature

2.1 Theoretical Approach

The study conducted by Montana Capital Partners AG’s co-founder/partner, Dr. Christian Diller, and Vice President, Dr Christoph Jäckel, analyses the risk associated with a portfolio of PE funds. Unlike PM equity investments, private equity is not owned, traded, or exchanged publicly, i.e. it is not quoted on the stock market. Spanning across all stages of an organization’s life cycle from venture capital to restructuring capital, private equity investments provide stock market investors access directly into private companies’ information to reach decisions. Based on specific characteristics of PE investments, it is not applicable to use the standard performance evaluation tools used on other asset classes. By means of a Monte Carlo simulation the critical risks associated with private equity, such as market, funding, liquidity, and capital risks are assessed. An empirical analysis measures and examines whether or not the risk that the investor’s invested capital will not be returned may be reduced (Diller & Jackel, 2015, p.20). The analysis of three individual PE firms determines that the risk associated with funding and capital is drastically reduced through diversification. Based on the datasets, an additional analysis was conducted measuring realization risk as it pertains to the decrease in value from inception of observation through the end of the funds’ life cycle. This study marked the first of its kind in relation to private equity investments; the results exhibit that the risk of investors losing capital over the entire holding period is only 1.4%, in portfolios containing 20 funds, and 0.8%, in portfolios containing 50 funds (Diller & Jackel, 2015, p. 27). Results take into consideration adjustments pertaining distributions and capital calls. Based on the results from this study, these private equities demonstrated the associated risk of investing in PE is not as risky as alleged by market investors; the risk associated with this asset class should be theorized differently.

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Evaluating the performance of private equity of nearly 1,400 venture capital funds, as well as U.S. buyout funds, the Harris, Jenkinson, and Kaplan study provided evidence of performance not previously captured exceeding the public market. Using a dataset derived from Burgiss, a private company which develops and offers private capital investment tools and services, similar to that of the leading commercial datasets Cambridge Associates and Preqin, this study documented that there was a consistent outperformance of 20% to 27% over the life of the fund (Harris, Jenkinson & Kaplan, 2012). Compared to the S&P 500 ranges, the outperformance was greater than 3% on an annual basis for their sample period (Harris, Jenkinson & Kaplan, 2012). From the 1900s to the 2000s, venture capital funds went from outperforming to underperforming against public equities. However, the results from the study identified an enhanced performance subject to the various risk controls and indices that are indicative of outperformance. The statistical relationship among the public market equities, multiples and internal rate of return, based on the Burgiss data, lead to the approach of combining summary level data with patterns, in which there was complete cash flow facts. Tying together the cash flows on the fund-level of the Burgiss data, the study examined the connection associated with market-adjusted performance (public market equity) and the performance measures: internal rate of return and multiple of capital invested. The regression results indicated that multiples of the invested capital, as well as the internal rate of return, evidenced public market equities variation at minimum of 93%, with over 90% of the years noted as vintage (Harris, Jenkinson & Kaplan, 2012). The multiples of the invested capital enhanced explanatory power more than the internal rate of return; however, the study suggests such multiples are more adequate than IRRs when measuring private equity performance. The findings from the Harris, Jenkinson, and Kaplan study specify that buyout funds, in comparison to the public market equities, have outperformed over most periods within the sample.

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Cumming, Haß, and Schweizer study illustrated private equity benchmarks, with consideration of the three commonly used indices, the option of using the private equity proxy imposes a substantial impact on a portfolio’s performance measures, as well as the risk/return relationship. Using the created index, the study captures more accurate financial reporting than what is currently used. Due to the accuracy of reporting, the facilitation of the private equity markets, as well as institutional risk for partners is developed. The analysis of the empirical methods used in the study can be applied to private equity as it pertains to any illiquid alternative market investments, including but not limited to: real estate, art, infrastructure, among others. During the phase of distribution of assets as it pertains to PE proxies, the study measured conditional value-at-risk (CVaR), in which the annual return on the portfolio had 90% confidence level for a diversified benchmark (Cumming, Haß, & Schweizer, 2013, pp.3517- 3518). Using the appropriate benchmarks is crucial to the private equity market investments, as the study completed by Cumming, Haß, and Schweizer calculate risk exposures and requirements of risk capital. The use of inadequate benchmarks for PE might mislead investors to allocate capital inappropriately, affecting the entire PE industry as well as the investor’s portfolio management and risk-profile (Cumming, Haß, & Schweizer, 2013, pp. 3520-3521).

Comparing the Fama and French model for risk adjustment, Rahim and Mohd Nor analyse two liquidity-based three-factor models, by adjusting the standard HML factor for two liquidity factors and evaluating their model’s ability to forecast portfolio returns. Rahim and Mohd Nor’s research used common stocks of listed firms based on a sample of 27 portfolios sorted on size and book-to-market ratio, size and share turnover, staying in line with the Fama and French literature. The datasets used were from the periods of 1987 through 2000 for creating the estimation model and included 2001 to 2004 as it pertained to the forecasting sample. Re-writing the Fama and French model in a time-series regression form, the researchers test the following model:

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Ri,t – RF,t = αi + βi ( RM,t – RF,t ) + di(HMLLiq,t) + li(LMHj,t) + εi,t (3)

Using the rewritten time-series regression form, the Fama and French HML factor was replaced with “SiLiq”, LMH, which combines the market risk premium with Size and Liquidity premiums. Similarly, F&F’s SMB factor is substituted to form “DiLiq”, which represents the combination of market risk premium with ‘DI’stress (HML) and ‘LIQ’uidity premiums, LMH. The replacing of SiLiq and DiLiq represent the illiquidity premiums being tested within portfolio samples. The results from the Rahim and Mohd Nor study indicated the ability to forecast portfolio returns improved by incorporating illiquidity risk, using the proposed three-factor model (Rahim & Mohd Nor, 2006). Rahim and Mohd Nor’s findings evidence a greater performance of the liquidity-adjusted Capital Asset Pricing Model versions than the Fama-French Model, allowing for the argument that investors indeed require an additional premium to compensate for the illiquidity and distress risk inherent from PE investments (Rahim & Mohd Nor, 2006, p. 58).

Equivalently, Chai, Faff, and Gharghori examined the impact of liquidity on stock returns based on the context of the Fama and French model. Their research explores the concept of whether or not liquidity is the missing factor of asset pricing. Their study adds the liquidity factor to Carhart’s four-factor model and engages individual and system techniques of regression. Based on the work of Amihud and Mendelson from 1986, Chai, Faff, and Gharghori utilized the knowledge that there is a link between a stock liquidity and its stock return. Research was based on the equities market in Australia; however, the study indicated there is a significant premium for illiquidity. Evidence from the study indicates that liquidity explains why there is some variation of returns in stock even after there is control regarding the size and book-to-market ratio (Chai, Faff, & Gharghori, 2013). Based on their Australian market data

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power to contemporary asset pricing models. Delving into previous research such as Brown and Zhang’s 1997 study, Chai, Faff, and Gharghori found “markets that allow limit orders tend to have a lower execution-price risk and have a higher level of liquidity” (Chai, Faff, & Gharghori, 2013, p. 376). Based on the well documented relationship among returns and liquidity, this study further explored four caveats.

The four concepts at which Chai, Faff, and Gharghori’s study aims at include the following: 1) enhance the sample to include more powerful asset pricing research to stocks that were richer and increased the sample period of 1982 – 2006; 2) adopt the illiquidity factor and a creative way of how to measure illiquidity; 3) research performed regarding the asset pricing to be based on Fama-French model to involve structure of liquidity portfolio; 4) investigate the significance of liquidity with known factors or variables: market, size, book-to-market ratio, and momentum that affect stock returns (Chai, Faff, & Gharghori, 2013, pp. 376-377).

Exploring the importance of the liquidity factor between the proposed timeframe, using the Fama-French framework, Chai, Faff, and Gharghori’s study indicated the following findings: illiquidity is related to liquidity as well as to stock returns; cross-sectional regressions validate the ability of liquidity to explain stock returns even after controlling for size, book-to-value ratio, and momentum (2013, p. 393). Based on the regression results, Chai, Faff, and Gharghori find there is sufficient evidence to support the impact of liquidity in asset pricing; however, the added liquidity factor portrays only marginal improvements of the model’s explanatory power (2013, p. 394).

In a like manner, a study performed by Franzoni, Nowak, and Phalippou for the Network for Studies on Pensions, Ageing, and Retirement (Netspar) scrutinizes on the intrinsic diversification benefit of PE investments. They take a data set composed of the precise cash flows generated by numerous liquidated PE investments from the Center for Private Equity Research, CEPRES; who collects data directly from PE investment houses who are, by contract,

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bound to report accurate cash flows generated from every investment made since the inception of the fund (Franzoni, Nowak, & Phalippou, 2011, pp. 4-5). The researchers use Pástor and Stambaugh’s four-factor model, and find significant loadings in all but one of the factors, fund size (Franzoni, Nowak, & Phalippou, 2011, p. 5).

For the market factor, book-to-market factor, and liquidity factor, Franzoni, Nowak, and Phalippou find significant factor loadings of 1.3, 1.0, and 0.64 respectively which brings the constant, or alpha, of the model almost to zero and portraying a 3% annual liquidity risk premium (2011, pp. 2-3). The significant loading of the liquidity factor, suggest that PE is notably exposed to the same liquidity risk factor as PM equity and the like asset classes. The elevated leverage characteristic of PE investments, opposed to those in the PM, make it receptive to the availability of capital from debt providers, predominantly banks and Hedge Funds, who are unquestionably sensitive the variations in funding liquidity (Franzoni, Nowak, & Phalippou, 2011, p. 21). This means, that during times of low funding liquidity, PE investors may find themselves in a position to have to liquidate their assets or accept higher funding costs (Franzoni, Nowak, & Phalippou, 2011, p. 22). Thus, there is a clear interrelationship between market liquidity and PE returns, which arises from the reliance of PE performance on the availability of capital from debt providers and its correlation with market liquidity (Franzoni, Nowak, & Phalippou, 2011, p. 22).

An estimation of risk and market expectations of returns of PE is analysed by Jegadeesh, Krӓussl, and Pollet using the CAPM as a starting point to be further developed by the inclusion Fama and French factors. Their findings suggest market expectations of PE earning abnormal returns are of approximately 1% year over year (Jegadeesh, Krӓussl, & Pollet, 2009, p. 4). Nevertheless, Jegadeesh, Krӓussl, & Pollet’s results also imply that market expectations of Fund of Funds (FoF), or PE, earning extreme abnormal returns in the long-run is close to zero

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PE and LPE by means of the augmented Capital Asset Pricing Model. Their time series regressions results show the Fama and French factor SMB to be significantly greater than zero for both PE and LPE, meaning that both behave like small rather than large firms since the majority of PE investments are made in smaller firms than the average listed firms (Jegadeesh, Krӓussl, & Pollet, 2009, p. 23). In addition, the beta for the HML factor for both PE and LPE are not significantly different, and not significantly different from zero for PE but the contrary for LPEs. This essentially shows how LPE is more sensitive to value firms than for growth firms (Jegadeesh, Krӓussl, & Pollet, 2009, pp. 23-24). This is congruent with PE characteristics, since there are major investments in buyouts and venture capitals (VC) which are more likely to be value firms opposed to growth firms (Jegadeesh, Krӓussl, & Pollet, 2009, p. 24). Overall, Jegadeesh, Krӓussl, and Pollet conclude there is no particular difference in the risk profile of PE and LPE, despite showing differences in the geographic composition of each, making LPE risk-return analysis an appropriate representation of the risk-return relationship of PE (Jegadeesh, Krӓussl, & Pollet, 2009, pp. 24-25).

2.2 Empirical Approach

Following the Capital Asset Pricing Model (CAPM), the Fama and French model has been debated amongst researchers on whether the associated value and size premiums are due to the associated risk factors of the firm. Many of the categories are due to inaccuracy of the past earnings growth within the market and latter correction of errors of mispricing. The Fama French model has been well renowned for its ability to predict portfolio stock returns. Capturing the systematic risk, the Fama and French model is significant in explanatory power aligning the systematic risk that overcomes or succeeds the economy. The three-factor Fama and French model is a method designed to take into consideration the systematic risk of the market, the size

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and the value of firms. It was designed by Nobel Laureate Eugene Fama and Kenneth French. Used for evaluating the risk and return of stocks, is renowned due to its ability to reveal the key factors that drive stock performance returns. The Fama and French three factor model provides insight on the key factors within a portfolio allowing for better portfolio management and a possible higher expected long-term return. Fama and French prove that portfolios formed on a mixture of book-to-market ratio, size in terms of market capitalisation, and other variables such as earnings/price, cash flow/price, capture the majority of the spread in the cross-section of average returns (Fama & French, 1996, p.156). Extending the research, the two researchers examined the asset pricing with consideration of bond returns, as well as common stocks, using time-series regressions ( Fama & French, 1996). As concluded by Bhatt and Rajaram, the results from Fama and French research indicate the expected return on a portfolio in addition to the risk free rate is explained by how sensitive the return is to each of the three factors (Bhatt & Rajaram, 2014).

To analyse a stock, the three factor Fama-French model separates a stock’s returns within specific risk factors and their corresponding loading, including: beta (market), size, and value. In comparison to the market, the beta risk factor evaluates the volatility of investing in a particular stock, it mainly assesses the sensitivity of an investment to the market. If beta equals one, the security is following the flow of the market. However, if beta is greater than one, the stock is expected to have higher volatility. Size measures the extra risk within small companies’, also known as small caps stocks. Small cap stocks react differently than stocks within a large company, also noted as large cap stocks. Long-term, small company stock produces higher returns; the surplus return is priced due to the associated higher level of risk of investing. The distinct risk factor, value, is the ownership of attractive valuations of the less favoured stock. The value risk factor stocks are based on companies with lower earnings growth rates; however,

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long-term perspective, value stocks produce returns that are higher than growth stocks at higher stock prices as well as higher earnings. Value stocks are assessed based on higher risk. As the Fama-French three-factor model isolates stock returns based on beta, size, and value risk factors, a stock’s ability to perform, measured by Jensen’s alpha, α, is assessed for its potential over a long-term return. Adding the three risk factors to the regression, the Fama and French model explanatory power, measured by 𝑅2 and Adjusted 𝑅2, increases significantly. The final model is as follows:

Ri - Rf = α + βmrkt *( Rmrkt – Rrf) + βsize *SMB + βvalue * HML + εi (4)

Using the formula above, Fama and French Three Factor model takes into account portfolio’s rate of return, Ri , risk-free return, Rf, and return based on the entire stock market (Fama and

French Three Factor Model). Both SMB and HML within the formula represent small cap minus the big cap stocks and the high book-to-market minus the low book-to-market ratio stocks, which measures the surplus returns as it relates to the market as a whole. The coefficients, βsize and βvalue, values range between 0 and 1. If βsize reflects: 1, a portfolio of small

cap, and if 0, a portfolio of large cap. If βvalue reflects: 1, a portfolio of high book-to-market

ratio, and if 0, a portfolio of low book-to-market ratio. Via a time-series linear regression, the Fama and French model explains excess return of an investment portfolio given the corresponding statistical weight to each of the three factors.

Parting from the Fama and French model, Pastor and Stambaugh investigate the added explanatory power that a liquidity factor brings to the existing, and extensively used, Fama and French asset pricing model. To do so, they question the discrepancies in sectional expected returns and how they relate to the sensitivity of the returns to changes in aggregate liquidity of the market (Pastor & Stambaugh, 2001, p. 1). Logically, investors might require a premium for

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assets that are more sensitive to aggregate liquidity, since the liquidation of assets is costlier when the general market liquidity is lower, that is an investor prefers holding assets that are less like to need liquidation when aggregate liquidity is low (Pastor & Stambaugh, 2001, p. 2). In their study, Pastor and Stambaugh compare daily stock prices and their respective volume in every month through a 37 year time frame, 1962 - 1999, to construct a monthly market-wide liquidity measure using the equally weighted average of liquidity of individual stocks on the AMEX and NYSE (Pastor & Stambaugh, 2001, p. 3). Similar to previous studies, the liquidity betas in their regression prove to have a critical role in asset pricing, predicting abnormal returns of over 9% in contrast with regressions only on the three Fama and French factors (Pastor & Stambaugh, 2001, p. 2).

To reach their conclusion, an analysis of the relationship between a stock’s expected return and the sensitivity of the return to aggregate liquidity is performed, taking in consideration other factors considered significant in asset pricing. A portfolio-based approach is used to ensure liquidity betas are disperse, forming 10 portfolios sorting on the predicted value of the aggregate liquidity coefficient (Pastor & Stambaugh, 2001, p. 10). The following multiple regression of the stock’s excess return at a given point in time, ri,t, as the dependent

variable and the market, MKT, small-minus-big market capitalization stocks, SMB, and high-minus-low book-to-market ratio stocks, HML, as the independent variables is executed:

ri,t = α + βi,L * L + βi,M *(MKT) + βi,S *SMB + βi,H * HML + εi,t (5)

Subsequently, Pastor and Stambaugh control for all of the above factors by sorting portfolios by the predicted liquidity betas, historical liquidity betas, and by size. Their results reveal systematic discrepancies in expected returns on portfolios sorted by predicted liquidity betas,

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returns in stocks with more sensitivity to aggregate liquidity shocks (Pastor & Stambaugh, 2001, p. 13-15). Moreover, by sorting on historical betas the results show the outcome does not depend entirely on the incorporation of the additional Fama and French variables, also affirming the differences in alphas resulting from the larger set of variables (Pastor & Stambaugh, 2001, p. 17). Likewise, while sorting portfolios by market capitalisation, unsurprisingly, portfolios composed of the smaller firms prove to be more receptive to shocks in the market-wide liquidity (Pastor & Stambaugh, 2001, p. 18). Thus, this approach shows that in average the smallest decile, less liquid portfolios, exhibit large and significantly positive liquidity betas while the higher deciles don’t show a clear pattern and are not significantly different from zero (Pastor & Stambaugh, 2001, pp. 18-19). Altogether, corroborating that higher sensitivity of the stock to aggregate liquidity suggest higher expected returns.

Notwithstanding, Malcom Baker and Jeffrey Wurgler investigate how the cross section of stock’s expected returns does not only depend on the cross-section of systematic risks, but its significantly influenced by the investor’s sentiment. Similarly to Pastor and Stambaugh, Baker and Wurgler take the Market, small-minus-big market cap, and high-minus-low BE/ME factors in their analysis and maintain the time-honoured Fama and French asset pricing model’s accounting definitions. Theoretically, small, highly volatile, distressed, new, exceptional growth potential, no dividend and the like stocks are more susceptible to be affected by fluctuations in investor sentiment (Baker & Wurgler, 2006, p. 2). Consequently, when sorting stocks by book-to-market deciles, the middle deciles are shown to be less affected by changes in investor sentiment, that is, when sentiment is low at the beginning of the period then stocks at the top and bottom deciles display higher expected returns relative to their unconditional average (Baker & Wurgler, 2006, p. 3). Their research takes a sample of all traded common stocks for a 39 year time span, from 1962 until 2001, and groups them according to specific

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qualifications such as profitability, firm size, dividends, assets, age, and growth potential (Baker & Wurgler, 2006, p. 11).

On this ground, Baker and Wurgler take six proposed proxies for investor sentiment from other scholars to form a composite able to encompass the commonalities between them, mainly, factors directly influencing sentiment. The similarities observed across the abovementioned proxies are: closed-end discount, number and average returns in the first day of IPOs, share turnover as measured by trades in the NYSE, equity share in new issues, and dividend premium (Baker & Wurgler, 2006, p. 13). The close-end proxy is measured by calculating the mean difference between NAV of the close-end fund and their corresponding market price, showing an inverse relationship with investor sentiment (Baker & Wurgler, 2006, p. 13). High returns during the first day of an IPO have a direct relationship with positive investor sentiment (Baker & Wurgler, 2006, p. 14). Similarly, share turnover, or liquidity, make a valuable index for sentiment finding that high turnover is a projection of low returns (Baker & Wurgler, 2006, p. 14). Equity share, that is, gross equity issued divided by gross equity plus long term debt issued, is another factor influencing investor sentiment inversely (Baker & Wurgler, 2006, p. 14). Lastly, the dividend premium proxy for relative investor demand for stocks paying dividends in comparison to no-dividend stocks to observe the investors behaviour (Baker & Wurgler, 2006, pp. 14-15).

After combining all proxies to form the final composite proxy, the effect of the principal components of each proxy on investor sentiment is analysed in terms of magnitude and direction. Thereafter, the cross-section of each component is controlled for, accentuating their influence in investors sentiment and how its value prior to the beginning of the term affect the subsequent expected returns. This allowed the researchers to scrutinize the predictive power of the various components, and how these effects become apparent only after isolating them

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predictability can be known in advance. The study concludes that for stocks that are not simple to value and arbitrage are affected more by investor sentiment. This means that when sentiment level is below the sample average, small, highly volatile, distressed, new, exceptional growth potential, no dividend, and similar stocks earn, on average, higher consecutive returns (Baker & Wurgler, 2006, p. 26).

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3 Analysis of Model

To analyse whether the higher risk incurred from investing into private equity funds over public market equity yields higher returns, the performance, in terms of excess returns, is measured taking the CAPM model as a starting point. Subsequently, the two Fama and French Factors for size and value are incorporated in the model. Furthermore, this research incorporates a liquidity factor, in Pastor and Stambaugh fashion, as well as a sentiment factor, alike Baker and Wurgler, to run a time series regression on the following final model:

Ri - Rf = α + βmrkt *(Rmrkt – Rrf) + βsize *SMB + βvalue * HML + βΛ *Λ + βsentiment * SENT (6)

The dependent variable, Ri - Rf , represents the excess weekly returns of both, market-wide, LPE indexes PSP and IPRV independently. The explanatory variables represent a mix of existing literature on asset pricing models. First, the Fama and French factors: (Rmrkt – Rrf) which represents the exposure of excess returns to the market risk premium, SMB which represents the small minus big market capitalisation factor, and HML representing the high minus low value stocks. The additional factor added to the standard Fama and French Three Factor Model is liquidity, Λ, represents the aggregate liquidity of the market as presented and defined by Pastor and Stambaugh. Further, this paper’s model also includes an investor sentiment factor, SENT, from Baker and Wurgler research on asset pricing.

The β coefficients presented above measure their corresponding asset pricing factor’s loading, that is, the magnitude of the effect of the individual risk factors on the excess return of the index. Based on Pastor and Stambaugh the liquidity coefficient, βΛ , is expected to be positive as the investor should be rewarded for holding illiquid assets, which is one of the main characteristics of PE investments. Likewise, according to Baker and Wurgler the sentiment coefficient, βsentiment , should also be positively related to excess returns. This is formally presented in Hypothesis one and two.

Hypothesis 1:

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H1: A positive relation exists between Aggregate Liquidity of the market and expected

excess returns of PE.

Hypothesis 2:

H0: No relation exists between investor sentiment and the expected excess returns of

PE.

H1: A positive relation exists between investor sentiment and the expected excess

returns of PE..

Lastly, a third hypothesis is formed to analyse whether PE outperforms PM investments. Based on the review literature, it is expected for Jensen’s alpha, the constant of the regression, to be positive. Thus, the below hypothesis is tested:

Hypothesis 3: H0: α ≤ 0 H1: α > 0

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4 Sample Data

To statistically examine if the risk is worth the return a sample of two exchange traded funds is used, both of which are composed of the constituents of the S&P Listed Private Equity Index. That is, PowerShares Listed Private Equity ETF, PSP, and iShares S&P Listed Private Equity ETF, IPRV, are tested. The S&P LPE Index is comprised of all of the publicly traded companies in the United States of America with particular key words within their business description, among those, but not limited to: Acquisitions, Business Development Company, Buyout, Mezzanine, Recapitalization, Principal Investment, Private Equity, & Venture Capital (S&P 500 Listed Private Equity Index, 2014, p. 4). In addition, Fund of Funds, Special asset class acquisition companies, business development, investment trusts and Publicly-listed investment companies, are also included within the Index (S&P 500 Listed Private Equity Index, 2014, p. 4). It is important to note that companies with a high degree of idiosyncratic risk such as real estate income trust and property trusts (REITs), and companies whose primary activities include energy exploration and transportation and mining are excluded from the index (S&P 500 Listed Private Equity Index, 2014, p. 5). After reviewing the business description, the S&P Dow Jones Indices determines based on the existing documentation if the companies comprised in the Index are indeed directly involved in private Equity Investment (S&P 500 Listed Private Equity Index, 2014, p. 5). Lastly, companies have to meet certain criteria including a minimum Market Capitalization of $150 million, stocks have to have three-month average trading of half a million American Dollars at each rebalancing date, the stock necessarily has to trade on a developed and established market exchange and the volume of stocks traded much be at least, on average, 10,000 shares a day of the last 12 months (S&P 500 Listed Private Equity Index, 2014, pp. 5- 6).

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alpha, to assess the performance of LPE and the market. The sample data is comprised with data for a nine and a half year time span, from March, 2007 until November, 2016. The length of the data set is set by the shortest series, meaning that there is available data for all factors in the proposed model. Current and historical share price information has been obtained from the DataStream database. The data for the Fama and French factors is extracted from Kenneth R. French website from the Tuck School of Business. Similarly, the sentiment factor data is extracted from the Stern School of Business website where Baker and Wurgler data is available.

Lastly, the returns for each index are calculated as ln (Xt)-ln(Xt-1), and the excess returns (XCS_indexname) are those returns minus the risk free rate for the corresponding date, defined as the one-month Treasury Bill extracted from the Board of Governors of the Federal Reserve System of the United States of America.

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5 Results and Discussion of Statistical Analysis

This section presents the results obtained from the regressions performed to analyse the proposed five factor capital asset pricing model. In order to test the model and answer the hypotheses, a regression is performed using the excess returns of PSP (Table 1) and IPRV (Table 2) as the dependent variables. First, only the market risk premium is included as the independent variable as seen in column (1) of both tables, this being the base equation for the model. Next, a different risk factor is added to the regression, creating a two factor asset pricing model. If the added factor is significant, then that model is the new base equation for the analysis and subsequently another factor is added, otherwise the factor is dropped and another risk factor is added. This process is repeated until all the proposed risk factors are tested, which is presented from column (2) to (5) of both tables. Lastly, an F-test is performed after running each regression to F-test the fit of the regression, that being its overall significance. It is important to note that this being a time-series regression, observations being a week apart from each other, and the fact that the sample time-frame includes the 2008 financial crisis, both data autocorrelation and heteroskedasticity are present; thus, all regressions are performed using robust standard errors.

Table 1 shows the regressions results of the excess return of PowerShares LPE ETF index on the different risk factors. While adding all the individual risk factors as explained above, the market risk is consistently negative and statistically significant across all regressions. This shows an inverse effect of excess return of the market on the excess return of the index in question, in average of 0.9108. Consequently, all joint F-tests performed for PSP index reject the null hypothesis, since at least one of the factors included in the regression has an effect in the dependent variable, suggesting good fit of the model.

Furthermore, the coefficients of the Fama and French model, HML and SMB, show a positive and a negative relation respectively with the excess returns of PSP. However none of these two factors is statistically significant. The size factor not being significant is in-line with

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is not expected. This can be explained from the similarities in book-to-market ratio of the companies constituting the PSP index and the benchmark. Further, the coefficients for aggregate liquidity and investor sentiment are both positive. Given both coefficients are not significant, the null hypothesis of Hypothesis 1 and Hypothesis 2 cannot be rejected. Additionally, the inclusion of liquidity and sentiment does not show a significant increase in explanatory power as measured by the adjusted R-squared, contradicting the scholarship of Baker and Wurgler(2006) and Pastor and Stambaugh (2001). Out of all the regressions in Table 1, the model including the market risk factor and the size factor only, column (2), shows the highest explanatory power and thus this is the preferred model. This model explains 31.2% of the variation of the dependent variable and gives a positive and significant constant, rejecting the null hypothesis of Hypothesis 3, suggesting LPE outperforms the market.

TABLE 1: Time series regression results of the cross section of excess returns and the proposed risk factors for index PSP

Explanatory variables (1) (2) (3) (4) (5) (6) mktrf -0.886*** -1.013*** -0.876*** -0.886*** -0.893*** -1.019*** (0.148) (0.126) (0.162) (0.149) (0.150) (0.142) smb 0.0359 0.0261 (0.204) (0.214) hml -0.0362 -0.0159 (0.211) (0.219) aggliq 0.00254 0.00748 (0.0251) (0.0250) sent 0.00156 0.00245 (0.00730) (0.00755) Constant 0.00330* 0.00322* 0.00327 0.00334 0.00337* 0.00346* (0.00197) (0.00189) (0.00201) (0.00209) (0.00172) (0.00177) Observations 454 444 454 454 446 436 R-squared 0.264 0.312 0.264 0.264 0.266 0.315 Adjusted R2 0.309 0.261 0.261 0.263 0.307

Column (6) show the results for the complete 5 factor model presented, that is equation (6) of this paper.

Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1

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Table 2 shows the regressions performed to the second index used as a proxy to analyse the return of PE, that is the iShares S&P LPE ETF. The same approach depicted above is followed to assess which model better assesses the variation of the excess returns of the dependent variable. Similar to the regressions performed for PSP, the market risk factor is highly significant and negative in all regressions. This shows in average an inverse relation of 0.812 across all regressions. By the same light, all F-tests performed reject the null hypothesis, suggestive of an overall significance of all the regression models presented in the table.

The coefficient SMB added in column (2) shows significant negative results at a 5% level of significance. Similarly the results of Table 1, the size risk factor is negative, also implying a negative relation with the excess returns of LPE. This results are in line with Jegadeesh, Krӓussl, and Pollet (2009) research, meaning that LPE behaves more like small rather than large firms in this sample, which are more sensitive to investor sentiment as concluded by Baker and Wurgler (2006). The model presented in column (2) of Table 2 is the new base model to be analysed. Furthermore, the value factor, HML, also shows a negative, non-significant, coefficient. This is likely due to the fact that this research does not pool the constituents of the LPE index by size, which may lead to an overall similarity of average book to market ratio of the dependent variable and the benchmark. Congruent with the results of Table 1, the liquidity and sentiment factor are positive but not significant. This again fails to reject the null hypothesis of Hypothesis 1 and Hypothesis 2. Once again, the model with the highest explanatory power is that of column (2), in this case where all the coefficients included are significant. The preferred model shows how the market risk premium and the size risk factor explain 22.7% of the variation of excess returns of LPE. The preferred model fails to reject the null hypothesis of Hypothesis 3, so it cannot be concluded that LPE outperforms the market altogether.

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TABLE 2: Time series regression results of the cross section of excess returns and the proposed risk factors for index IPRV

Explanatory variables (1) (2) (3) (4) (5) (6) mktrf -0.832*** -0.814*** -0.779*** -0.817*** -0.818*** -0.783*** (0.0923) (0.0975) (0.0981) (0.0974) (0.0995) (0.0997) smb -0.469** -0.500*** -0.467** -0.476** -0.506*** (0.190) (0.186) (0.190) (0.199) (0.195) hml -0.114 -0.123 (0.155) (0.159) aggliq 0.0186 0.0235 (0.0214) (0.0213) sent 0.00330 0.00345 (0.00643) (0.00648) Constant 0.00153 0.00125 0.00114 0.00157 0.00142 0.00172 (0.00199) (0.00199) (0.00199) (0.00201) (0.00203) (0.00203) Observations 454 444 444 444 436 436 R-squared 0.224 0.231 0.232 0.231 0.232 0.234 Adjusted R2 0.222 0.227 0.226 0.226 0.226 0.225

Column (6) show the results for the complete 5 factor model presented, that is equation (6) of this paper.

Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

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6 Conclusion

Studies have examined the impact liquidity and investor sentiment have on the associated risk and expect return of PE. This research re-examines the role of liquidity and sentiment in asset pricing and whether the incurred risk of 64 Listed Private Equity Funds is worth the expected return using the CAPM as the basis and adding the Fama and French risk factors, an illiquidity factor, and an investor sentiment risk factor. Based on the nine and a half year period from 2007 to 2016, the key findings of this research indicate illiquidity and sentiment do not relate to the associated risk and stock return. Using the cross-sectional regressions as it pertains to liquidity and sentiment, the study provides evidence to explain LPE stock returns based on five risk factors.

Opposed to the reviewed academic literature, liquidity and investor sentiment does not have a significant role in predicting or forecasting the associated stock return as it pertains to asset pricing. Augmenting the Fama and French model with the risk factors proposed by Pastor and Stambaugh (2001) and Baker and Wurgler (2006) does not improve the model’s explanatory power measured by the Adjusted R-squared. Findings have indicated the impact of size, value, liquidity, and investor sentiment on stock returns do not explain the returns of the two LPE indexes used. The liquidity factor in the 12 regressions performed for this study does not show a significant effect on excess returns nor on explanatory power, opposed to the academic research done by Pastor and Stambaugh (2001), Franzoni, Nowak, and Phalippou (2011), Rahim and Mohd Nor (2006), and Chai, Faff, and Gharghori (2003). These authors suggest that liquidity has a significant positive effect on a security’s expected returns. Similarly, the results pertaining investor sentiment contradict the literature of Baker and Wurgler (2006), as results do not show significant coefficients in either of the indexes examined. This said, the three hypotheses proposed in this research are not statistically rejected, and as such this paper

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equity does indeed yield higher returns, opposed to Harris, Jenkinson, and Kaplan (2012) research.

In light of the contrary results this paper presents, it is important to highlight certain limitations it entails. Firstly, opposed to the literature reviewed, each index is not split in 10 portfolios and ranks them by size, value, liquidity of the market, and investor sentiment prior each period, which may lead to distorted results. Furthermore, this study doesn’t analyze credit conditions that can be measured by the yield spread that may have significant influence on the effect of liquidity on expected returns. Additionally, there is no distinction between a pre- and post- financial crisis in 2008 which is part of the sample, possibly skewing regression results.

To better asses the risk-return relationship of PE compared to PM equity and to determine if PE does indeed outperform PM, further research should be performed considering the following suggestions to obtain more significant results. The individual firms composing both indexes can be analyzed independently and not in an index as a whole, then splitting them into different portfolios as it is done in Fama and French research published in 1996. By further ranking the portfolios by market equity, and book to market ratio, the effect of the distinct risk factors can be measured across stocks with different characteristics and draw more significant conclusions. Moreover, including bond factors such as default risk, term structure of interest rates, and credit market conditions can also increase the quality of the results. Lastly, a bigger sample can be analyzed which enables analysis on distinct shocks to the market such as the 2008 financial crisis or the dot-com bubble.

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An analysis of the risk-return relationship of private equity in comparison to public market equity