Did U.S. Long-Short Equity hedge funds outperform the U.S. market index (S&P500) during the period 1995 - 2013?

(1)

Did U.S. Long-Short Equity hedge funds

outperform the U.S. market index (S&P500)

during the period 1995 - 2013?

Marliah Schoute (10211276)

Supervisor: Liang Zou

Faculty Economics & Business

Bachelor’s Thesis Finance and Organization (6013B0326)

- January 2015 -

(2)

1. Introduction

Hedge funds have increased their presence in the financial markets and business press since their creation approximately 60 years ago (Ackermann, McEnally, Ravenscraft, 1999). Especially over the past 20 years, hedge funds as an asset class have become more and more popular (Malkiel & Saha, 2005). According to Aggarwal and Jorion (p. 238, 2010), “assets under management have increased from an estimated $39 billion in 1990 to more than $1.8 trillion in 2007. Correspondingly, the number of funds has increased from 610 to more than 10,000.” Furthermore, in 1997, there existed more than 1200 hedge funds that managed a total of over $200 billion.

Hedge funds are smaller in number and size compared to mutual funds, but their developed popularity reflects the importance of this alternative investment vehicle for institutional investors and wealthy individuals (Ackermann et al., 1999). Hence, one question that arises with the increasing number of hedge funds, is whether and how these funds are able to generate superior performance compared to other investment options, like the market index. Therefore, the research question of this thesis is: Did U.S. Long-Short Equity hedge funds outperform the U.S. market index (S&P500) during the period 1995 up to and including 2013?

The topic of hedge fund performance is already widely discussed within the existing literature. Among others, Ackermann et al. (1999), Amin and Kat (2003), Kosowski et al. (2007), and Fung, Hsieh, Naik, and Ramadorai (2008) have already published studies within the field of hedge fund performance. This study, however, differs from this literature in various ways. First and most importantly, it uses data from 1995 up to very recently in 2013, which has not been included in any study thus far. Second, apart from studying the period 1995 to 2013 as a whole, this research also studies some shorter time periods within this 19-year period. Thirdly, this study focuses purely on U.S. Long-Short Equity hedge fund sub-strategies. This could be an advantage for investors who are especially interested in investing in equity-related funds. Finally, this study focuses on applying various performance measuring methods, which can give a wider perspective on the performance of hedge funds.

This thesis is organized as follows. The first part covers the theoretical framework, including, among others, the historical background and various characteristics of hedge funds. The second part describes the data, the third part presents the methodology and part four shows the results. Finally, part five concludes.

(4)

2. Theoretical Framework

2.1 Hedge Fund Theory

Hedge funds exist for over more than 5 decades. Most of the literature, for example Stulz (2007), Kosowski et al. (2007), and Edwards (1999) state that Alfred W. Jones started the first hedge fund in 1949. Jones raised $60,000 and invested $40,000 of his own money to pursue a strategy of investing in common stocks and hedging the positions with short sales. Ever since this simple beginning, the number of hedge funds has increased rapidly. In addition, the interest in different hedge fund strategies has changed between 1990 and 2004 (Agarwal & Naik, 2005). Around 1990, the macro strategy was the leading strategy, with 71% of total assets under management (AUM). Later, in 2004, this share had fallen down to 11% and the equity hedge strategy became the most popular, with 31% of total AUM in 2005 (p. 182 Stulz, 2007). In the same period, there has also been a change in the type of investor in hedge funds from individual investors to big institutional investors. It started with the typical high net-worth individual investors who invested in macro funds. Nowadays, there are mainly institutional investors, like pension funds, who invest in hedge funds for diversification reasons, pursuing investment instruments with low correlation with other popular asset classes like equities and bonds.

Hedge funds have many different characteristics. They can be described as active investment vehicles that are not heavily regulated and have great trading flexibility (Fung et al. 2008). They follow very advanced investment strategies and promise to deliver returns to their investors that are not affected by fluctuations in financial markets. Furthermore, according to Stulz (p. 175, 2007), hedge funds can only issue securities privately. Their investors have to be individuals or institutions that satisfy requirements set out by the Securities and Exchange Commission (SEC). This is to assure that the investors are well informed and can endure a significant loss. Domestic (U.S.) hedge funds usually are limited partnerships with less than 100 investors. For that reason they are exempt from the SEC’s Investment Company Act of 1940 (p. 834, Ackermann et al., 1999). Because they have such limited regulation, hedge funds can be very flexible in their investment choices. They can use short selling, leverage, derivatives, and highly concentrated investment positions to boost returns or lower systematic risk. They can also try to time the market by moving rapidly across various asset classes. In addition, hedge funds attract mainly institutions and wealthy individual investors, with minimum investments typically ranging from $250,000 to $1 million.

(5)

The lack of regulation of hedge funds can be unfavorable for future investors who seek the most profitable investment opportunity. Specifically, Fung and Hsieh (2004) state that the lack of transparency of hedge fund operations and a lack of performance-reporting standards make it difficult to forecast hedge fund performance that reflect the current economic outlook. Furthermore, the rather short history of hedge fund returns makes evaluating their long-term performance difficult. All the previously discussed hedge funds characteristics together greatly limit the information content of hedge fund indexes that are constructed by using common methods.

An additional, and important, feature of hedge funds is that they have a different fee structure than traditional long-only managers – who purely invest in undervalued assets. Besides having a management fee, hedge funds also have an incentive fee (Agarwal & Naik, 2005). The incentive fees are usually conditional to a hurdle rate and high-water mark provisions. A hurdle rate provision means that the manager only earns the incentive fee if the funds’ return is above a chosen hurdle rate, such as the risk-free rate like LIBOR. The high-water mark provision determines that the manager can earn the incentive fee only if the fund’s net asset value (NAV) exceeds its previous highest. As a result, hedge fund managers have strong incentives to generate positive returns because their pay depends primarily on performance. Brav, Jian, Partnoy, and Thomas (p. 1735, 2008) state that “a typical hedge fund charges its investors a fixed annual fee of 2% of its assets plus a 20% performance fee based on the fund’s annual return.” According to Edwards (1999), the intentions of a fee structure are to attract superior fund managers and to align the interests of these managers and investors. Whether an incentive fee actually succeeds in aligning these interests is not clear. Although large incentive fees give fund managers a large and immediate share of profits, they may also result in managers taking up an irresponsible and risky strategy in the hopes of receiving a large incentive fee if things go well.

2.2 Equity hedge fund sub-strategies

Hedge fund investment strategies are categorized into style categories (Stulz, 2007), which indicate that there are various hedge fund strategies that can be researched. According to Stulz (2007), the Long-Short Equity style, which includes the Equity Hedge strategies analysed in this study, is with 31% of the industry total the most popular. For this reason, this research focuses on hedge funds that have assets in the Long-Short Equity hedge strategy. Specifically, it will look at the performance of US Equity hedge fund sub-strategies versus the S&P500 (market) index based on monthly returns.

(6)

According to the Hedge Fund Research report (2014), the US Equity hedge hund strategy can be defined as a strategy that uses long and short positions in equity and equity-related instruments to minimize market risk. This strategy can subsequently be subdivided into nine sub-strategies. The sub-strategies that are applied in this study are the following:

Equity Market Neutral, Quantitative Directional, Energy/Basic Materials,

Technology/Healthcare, Short Bias, Fundamental Growth, Fundamental Value, Multi-Strategy Investment, and Equity Hedge Total. The characteristics of each sub-strategy can be found in Appendix A.

2.3 Hedge fund performance in existing literature

There is an extensive amount of literature published on the performance of hedge funds. As expected, each has its own research method leading to different results. The following are some of the results of three of the leading literature that are frequently referred to in this thesis.

Kosowski et al. (2007) investigate hedge fund performance from 1990 to 2002 by using the bootstrap and Bayesian method. Using 4 different databases and the seven-factor model of Fung and Hsieh (2004) as performance benchmark, they conclude that the abnormal performance of top hedge funds cannot be associated to luck and that hedge fund abnormal performance is stable at annual horizons. The persistence in performance over the long term is especially stronger with, among others, the Long-Short Equity strategy. In their research, Kosowski et al. (p. 241, 2007) find an alpha of 4.1% per month for the Long-Short Equity strategy. In comparison, the top fund-of-funds had an alpha of 1.6% per month.

In another research, performed by Ackerman et al. (1999), they find that hedge funds consistently beat mutual funds, but not standard market indices. Especially in 1994-1995 hedge funds tend to underperform the S&P500 market index. Ackermann et al. (1999) infer that the hedge funds’ ability to outperform the market depends on the time period, the market index, and the hedge fund category. On a pure risk-adjusted basis, by looking at the Sharpe Ratio of hedge funds compared to those of the market indices, hedge funds again did not significantly outperform all market indices. This is especially the case in the period 1994-1995, where the hedge funds only outperformed one market index; the MSCI EAFE. However, when looking at a longer time period for the Sharpe Ratio, they find results indicating that hedge funds did outperform a majority of market indices.

The research of Amin and Kat (2003) investigates whether hedge funds offer a superior risk-return tradeoff. They look at monthly returns of 77 hedge funds and 13 hedge

(7)

fund indices during the period 1990-2000. For their analysis, they use a continuous-time version payoff distribution-pricing model that does not require any assumptions about the return distribution of the funds that are evaluated. The results show that, as an independent investment vehicle, hedge funds do not yield superior risk-return tradeoffs. 12 of the 13 indices and 72 of the 77 hedge funds are concluded to be inefficient. However, when they looked at hedge funds in the context of a portfolio, the results were better. When mixed with the S&P500 index in a portfolio, seven of the 12 indices and 58 of the 72 inefficient hedge funds were able to yield efficient payoff profiles.

Finally, Fung et al. (2008) investigate hedge fund performance by using funds-of-funds from 3 different databases for the time period 1995 up to and including 2004. Funds-of-funds are hedge Funds-of-funds that invest in portfolios of other hedge Funds-of-funds. In short, one of the results is that the average funds-of-funds did not generate abnormal alpha, except in the period between October 1998 and March 2000. However, a subset of funds-of-funds consistently delivered alpha. On average, 22% of the funds delivered statistically significant and positive alphas.

Based on these results, it can be concluded that different research methods and other important research characteristics combined can lead to potentially different outcomes.

2.4 Bias in hedge fund data

This thesis and its results are based upon the monthly returns of hedge fund data. However, it is important to acknowledge that hedge fund data are subject to many biases (Fung and Hsieh, 2000). Therefore, it is essential to discuss these important characteristics and their conclusions in the following paragraphs.

Stulz (2007) and Kosowski et al. (2007) argue that biases are partly due to the fact that hedge funds are not regulated; they don’t need to disclose their performance. According to Stulz (p. 184, 2007), “databases exclusively report the performance of hedge funds that voluntarily send their returns to the sponsoring organizations.” Moreover, a hedge fund might not release its performance data for several reasons. First, it might not be open for investors to invest in, in which case the fund will not benefit from advertising its performance. Also, they could have forgot to send in the data form, or the hedge fund’s performance might even have been poor.

In general, there are several biases that appear when working with hedge fund data. The first one is selection bias (Fund and Hsieh, 2000). Selection bias occurs if the hedge funds in a certain portfolio are not representative of all the hedge funds in the world. A hedge

(8)

fund manager needs to give the hedge fund consultant an approval before information about the hedge fund can be issued to third parties. This creates the chance of selection bias, because only hedge funds with acceptable performance want to be included in the database. This in turn results in higher returns of funds in the database than the returns of all existing funds. Thus, the database may not provide a real picture of the performance of all funds. Kosowski et al. support this theory (p. 235, 2007). Many funds are subject to an incubation period during which they develop a record of performance by using money from managers or sponsors before they request investment from external investors. Usually funds that exhibit good performance continue to approach external investors. Furthermore, since it is forbidden for hedge funds to advertise themselves, a possibility is to publish information about their performance by reporting their return history to different databases.

A second type of bias mentioned by Fung and Hsieh (2002) is survivorship bias. This type of bias arises when a database of hedge funds only includes funds that still operate in a certain period, and excludes those funds that have stopped operating during that period. Reasonably, funds cease to operate when performance is poor. As a result, the historical return performance in the database is biased upward and the historical risk is biased downward compared to the universe of all funds. Similar to selection bias, survivorship bias is also a natural bias that arises during the whole process of hedge fund existence (p. 293, Fung and Hsieh, 2000). Because the universe of hedge funds is not observable, survivorship bias cannot be entirely solved when analysing hedge fund data.

A third type of bias, as mentioned by Agarwal, Fos, & Jiang (2013) and Baquero, ter Horst, & Verbeek (2005), is the multi-period sampling bias or look-ahead bias. It is closely related to survivorship bias and also known as an “ex post conditioning bias”, as stated by Baquero et al. (p. 494, 2005). This bias appears because researchers set condition on funds’ survival to perform an econometric analysis of performance persistence and other issues. The applied methodology implicitly or explicitly conditions upon survival over a number of consecutive periods. For example, when inspecting performance persistence, the fact that funds disappear in a regular way during the ranking or evaluation period may cause a bias (Baquero et. al., 2005).

A fourth type of bias, appointed by Capocci and Hübner (2004), Agarwal et al. (2013) and Titman and Tiu (2011), is called instant history bias or backfilled bias. This type of bias arises when the historic performance of a fund is filled in after its inclusion in the database. This can result in an upward bias because funds with a poor track record probably won’t

(9)

request to be included in the database, in contrast to funds with a good performance history, which are more likely to include their performance.

A fifth type, which is closely related to backfill bias, is the incubation bias (Agarwal et al., 2013). Incubation bias appears when hedge funds use private capital to construct their track records and when they report better performance over the incubation period.

Finally, the last bias that Agarwal et al. (2013) mention is stale price or return smoothing bias. This bias results from hedge funds that invest in illiquid securities or deliberately smooth their returns to reduce their volatility.

2.5 Solutions for bias

According to Fung and Hsieh (2002), the Hedge Fund Research database has attempted to correct for some of the biases. This is indeed supported by the Hedge Fund Research report (2014). The report states that any bias concerning the larger funds that is created by various weightings is greatly reduced, especially for strategies that contain a small number of funds. In addition, a fund will be removed from the database when it liquidates, when the fund managers requests removal, or when it fails to accomplish the requirements of a voting. By eliminating a fund’s past performance on the day of liquidation, HFR performs the most effort to limit survivorship bias. Similarly, when a new fund is added to the index, the historical performance of the new fund will not affect the index’ historical performance up to the date of inclusion. Finally, if a non-liquidated fund does not report to the HFR database for three straight months, the fund will be removed from the database. Despite these efforts, Fung and Hsieh (2002) argue, measurement bias in research is unavoidable.

Mitigating all bias in hedge fund research data often requires rather complex methods using difficult to obtain information, which makes it very complicated to implement in this thesis. Therefore, this part will suggest and describe some examples and solutions of methods that solve for bias conducted by several profound authors. These solutions could then be expanded on this thesis in further research, in order to mitigate the biases that are present.

One alternative to mitigate the biases in hedge fund data is suggested by Fung and Hsieh (2000). They propose using data on funds-of-hedge funds (hedge funds that invest in portfolios of other hedge funds) to measure the combined hedge fund performance, rather than data on individual hedge funds. This is based on the idea that the investment experience of hedge fund investors can be used to estimate the performance of hedge funds. They argue that funds-of-hedge funds returns are a more accurate representation of the returns earned by hedge fund investors. Fung et al. (2008) support this theory and elaborate on it. As an

(10)

example, they consider the case of a hedge fund that is near liquidation. This fund has a reason to stop reporting private data a few months before the withdrawal. Therefore, the hedge fund’s return history in the database will not show the entire amount of losses incurred by its investors. On the other hand, a fund-of-funds investing in the same hedge fund is more likely to overcome the downfall of one of the investments in its relatively more diversified portfolio. Hence, the fund-of-funds’ return gives a better picture of the losses that investors experience in the underlying hedge fund. Moreover, fund-of-funds returns reflect the cost of limitations that are involved when investing in hedge funds, and they also reflect the costs of managing a portfolio of underlying hedge funds, as they are reported net of additional fees.

Regarding selection bias, Fung and Hsieh (p. 299, 2000) state that while some hedge fund managers are ambitious to provide data about their good performance to vendors' databases, other managers intentionally don’t hand in their good performance data. This limits the size of the selection bias. Fung and Hsieh (2000) express that it would be very interesting to study the selection bias in hedge fund and commodity fund databases. However, to do this accurately, input from the investors of funds is needed. Nonetheless, these investors do not normally make their performance data public to database vendors, which makes is difficult to precisely study the selection bias. Even more, Fung and Hsieh (2002) argue that the extent of selection bias in a database is difficult to measure empirically, because it is impossible to compare the observed portfolio of hedge funds with the unobservable hedge funds in the population.

Kosowski et al. (2007) mitigate, among others, for survivorship bias in their research. Because most database vendors started issuing their data from 1994, these data sets do not include information on funds that stopped operating before December 1993 (Kosowski et al., p. 235, 2007). This causes survivorship bias. Kosowski et al. (2007) mitigate this bias by concentrating on post-January 1994 data, as also is done in this thesis. In addition, Kosowski et al. mitigate the incubation and backfill bias in their bootstrap analysis (2007). They do this by excluding the first 12 months of each fund’s history in the database, regardless of whether that history is backfilled or not (since incubation bias may occur in a fund’s history even though it is not backfilled). Then, they bootstrap the residuals of the funds from the incubation and backfill bias-adjusted sample. Although it is common for survivorship bias to arise, Amin and Kat (2003), Fung and Hsieh (2000), and Liang (2001) estimate the survivorship bias in hedge fund data to be between 1.5% and 3% per year, which will not necessarily affect the results in a significant way.

(11)

Titman and Tiu (2011) study hedge fund performance from six different databases and are especially concerned about backfilling bias. They reduce their sample significantly to mitigate its effect. Titman and Tiu (p. 130, 2011) assume that the problem is more frequent among smaller funds and therefore they eliminate all funds with less than $30 million of AUM. Specifically, if a fund starts with less than $30 million but later has $30 million in assets, it is included in the sample from the time at which the AUM reach $30 million and is kept in the sample as long as the fund exists (regardless of the AUM). In addition, Titman and Tiu (2011) remove the first 27 months from the history of each fund. They came to 27 months by analysing different hedge fund indexes, which are not subject to backfilling biases, to indexes that were made by using funds whose n initial monthly returns were excluded. By analysing the number of initial returns that are removed from the history of each fund, Titman and Tiu (2011) build an index that resembles the index reported by the database, and hence, mitigating the backfilling bias.

An alternative method to reduce the backfilling bias is proposed by Ackermann et al., (1999). Ackermann et al. (p. 868, 1999) argue that: “an indirect approach to addressing backfilling, commonly employed in equity market papers using COMPUSTAT data, is to eliminate the first two years of reported data. These years should contain the most backfilled data. Given that hedge fund time-series data are limited, eliminating two years a priori is too costly.” Alternatively, Ackermann et al. (1999) suggest comparing the results for every time period with and without the removal of the first two years of each fund’s returns. If removing the two years does not influence the results, backfilling is possible to be of no concern.

3. Data

3.1 Databases

The quantitative data used in this study is obtained from various databases.

The data for the monthly hedge funds returns is collected from the Hedge Fund Research, Inc. (HFR) database. HFR is a research firm specializing in the collection and analysis of alternative investment information. It is one of the industry's most widely used commercial databases of hedge fund performance (Hedge Fund Research, 2014). Part of the HFR Hedge Fund database is the Hedge Fund Research Monthly Indices (HFRI) database. This specific database provides the data for this study. The HFRI is an equally weighted index for all hedge funds in the HFR database (Fung & Hsieh, 2004). It ranges from the industry-level of the HFRI Fund Weighted Composite Index, which contains over 2200 funds, to the

(12)

more specific-level of the sub-strategy classifications. The HFRI database provides the strategy returns net of all fees performance and AUM (p. 3, Hedge Fund Research, 2014). Furthermore, the HFR database is also used in the leading literature from Ackermann et al. (1999), Kosowski et al. (2007) and Fung et al. (2008), which indicates the degree of reliability of this database. In addition, it is important to mention that for three out of the nine equity hedge sub-strategies the data from the HFRI is only available from January 2008. Excluding these three strategies would not be desirable since it would make the final conclusion incomplete. On the other hand, ruling out the data of the other 6 strategies from 1995 up to 2008 would make the magnitude of the data set very small. Therefore, there will be a distinction between the periods 1995 to 2013 and 2008 to 2013, in which the first period contains only 6 sub-strategies and the last period contains all 9 sub-strategies. For the remainder of this research, the period 1995 to 2013 will mostly be referred to as Period I and the period 2008 tot 2013 as Period II. All periods in between will just be referred to by their years.

The benchmark in this research will be the S&P500 index. The S&P500 index replicates the performance of the U.S. Equity market and is widely used as a benchmark in research on hedge fund performance, e.g. by Ackermann et al. (1999) and Kosowski et al. (2007). Therefore it is also used as the benchmark in this research. The data for the monthly returns of the S&P500 are obtained from the Kenneth R. French Library (2014). From here we also retrieved the risk-free rate, which is the One-month U.S. Treasury Bill rate.

3.2 Using monthly returns; pros and cons

Ackermann et al. (1999) argue that using data of monthly returns has some powerful advantages in contrast to using annual returns, but also some drawbacks.

One advantage of using monthly returns is that they substantially increase the accuracy when using a standard deviation measure of risk. Furthermore, data of monthly returns are essential for some aspects of survival bias analyses. On the other hand, there are also disadvantages of using monthly data. The first drawback is the appearance of backfilling bias when using a database that contains only annual data. However, since the HFR database uses monthly returns, this issue is mitigated. A second problem with arises from evaluating returns net of incentive fees. Incentive fees are usually based on the performance of the hedge fund manager over a quarter or year. The net monthly return (excluding fees) can only be evaluated after the incentive period is finished and even then, when assigning it to the months within the incentive fee period, it can be rather arbitrary. Nonetheless, the calculation of the net monthly

(13)

return is something that hedge funds and investors take very seriously and try to do as accurate as possible. Ackermann et al. (1999) advise that when doing hedge fund research with monthly data, it is important to wait until midyear to obtain data for the prior year so that the corrected data regarding net monthly returns is entered. Luckily, this holds for this thesis.

4. Methodology

4.1 Cumulative return

The main reason of this research is to find out whether investors are better off investing in Long-Short Equity hedge funds or the market index. Therefore we start by showing the cumulative return of all equity sub-strategies for various years. This reveals a quick but partial overview of the performance of the different strategies and can possibly provide a picture of what could be expected from the results of this thesis.

The cumulative return is calculated by indexing the monthly returns. For Period I, January 1995 is indexed at 100 and for Period II; January 2008 is indexed at 100. The first month of each strategy is calculated with the following formula:

𝐶𝑅_!,! = 100×(1 + 𝑅_!,!) (1)

In this formula, 𝐶𝑅!,! is the cumulative return for strategy i in month j, (where j=1,2,...,12),

and 𝑅!,! is the normal monthly return of strategy i in the jth month. Next, the cumulative return

of all following months for each strategy is calculated by:

𝑁𝑀𝐶𝑅!,! = 𝐶𝑅!,!!!×(1 + 𝐵!,!) (2)

Here, 𝑁𝑀𝐶𝑅_!,! is the next month’s cumulative return for strategy i in month j, 𝐶𝑅_!,!!! is the cumulative return of strategy i in the previous month, and 𝐵_!,! is the normal monthly return of strategy i in month j.

Since researching only the cumulative returns is by all means not sufficient enough to form a conclusion for the research question, this thesis also includes 2 other research methods. These are the statistical sign test and the non-parametric bootstrap. In addition, we will also compute the Sharpe ratio to look at the level of risk, which is an important component when investigating investment returns.

4.2 Statistical sign test

According to Dixon and Mood (p. 557-558, 1946) the sign test is most useful under de following three conditions:

(14)

2. Each of the two observations of a given pair arose under similar conditions; 3. The different pairs were observed under different conditions.

Furthermore, the sign test does not require the data to be normally distributed; they only need to be independent of one another. Since these conditions are all applicable to the data used in this study, the sign test turns out to be an alternative performance measure.

The sign test is based on the signs of the difference between two observations. In this study these observations are the monthly returns of each independent hedge fund sub-strategy versus the S&P500. The signs for each month can be positive (+), negative (-), or zero. For example, if the Quantitative Directional Index return is higher than the S&P500 index’ return in a certain month, this will result in a plus sign. If some of the differences are zero, half of them will be given a plus sign and half a minus sign (Dixon & Mood, 1946).

According to Dixon and Mood (1946), if there is no difference in the monthly returns of the two strategies, the positive and negative signs should be distributed by the binomial distribution with 𝑝 =!_!. The null hypothesis is that there are no differences between the monthly returns, which means that each difference has a probability distribution with median equal to zero. The null hypothesis will be rejected in case the amount of positive and negative signs differ significantly from equality, and thus meaning 𝑝 >!_!. These hypotheses can also be written as the following one-sided test:

H0: The median of hedge fund i – S&P500 = 0 vs.

H1: The median of hedge fund i – S&P500 > 0

with i being any of the 9 hedge fund strategies.

We performed a data analysis for the sign test as described above by using the statistical software program Stata. The number of months included in the test is at least 72 and at most 228. These are considered to be large enough number of observation and therefore it will yield more reliable results (Dixon & Mood, 1946).

According to Whitley and Ball (2002), the good features of the sign test are that it is intuitive and very simple to perform. However, an obvious disadvantage is that it simply assigns a sign to each observation, corresponding to whether it lies above or below the hypothesized value, and does not take the size of the observation into account. The following paragraph therefore examines the performance on basis of the abnormal performance, which is represented by alpha.

(15)

4.3 Non-parametric bootstrap

Hedge fund performance is difficult to evaluate because of the non-normal distribution of their returns, which is caused by their dynamic trading strategies and their holdings of derivatives securities (Kosowski et al., p. 237, 2007). This problem can be resolved by using the bootstrap approach.

The bootstrap is a nonparametric statistical method to derive the characteristics of the sampling distribution of estimators (Schmidheiny, 2012). It resamples the empirical distribution of complex measures of the observed data. The great advantage of this method is that, since it is a non-parametric test, it does not make assumptions about the distributions and true values of the parameters, indicating that the data does not have to be normally distributed. The bootstrap allows the user to work with non-normal data, like hedge fund returns in this case, and to draw valid statistical conclusions from the data. Kosowski et al. (p. 237, 2007), support this logic, including three other advantages of the bootstrap when analysing hedge fund performance. First, the statistical significance of alpha can be better evaluated by using a nonparametric approach such as the bootstrap. Second, by using this method, there is no need to estimate the entire covariance matrix that describes the joint distribution of individual funds. And third, the processing of the bootstrap provides a common way to deal with unknown time-series dependencies that are due to, for example, heteroskedasticity or serial correlation in the residuals from performance regressions.

According to Schmidheiny (2012), the bootstrap method takes the sample (the values of the dependent and independent variables) as the population and the estimates of the sample as true values. Rather than drawing from a specified normal distribution by a random number generator, the bootstrap draws with replacement from the sample. Therefore, the sampling distributions of the original data should be close to sampling distributions under the bootstrapping process.

In addition, Kosowski et al. (2007) state that the basic idea behind the bootstrap approach is to compare the observed performance to the performance in artificially generated data samples in which variation in performance is completely caused by sample variability or luck. The performance in this case is measured by alpha (𝛼). To test alpha for significance, the null-hypothesis is as follows:

H0: 𝛼! = 0, meaning there is no abnormal performance vs.

H1: 𝛼! ≠ 0, meaning there is abnormal performance.

(16)

In order to evaluate the performance of the nine different Equity hedge fund sub-strategies, we regress the monthly returns of each sub-strategy on the monthly returns of the market index (S&P500). Equation (3) resembles the regression to evaluate the performance of the sub-strategies. It is partly derived from the one used by Kosowski et al. (2007).

𝑟_!! _{= 𝛼}

!+ 𝑀!+ 𝜀!! (3)

where 𝑟_!!_{is the monthly rate of return of sub-strategy i in month t in excess of the risk-free}

rate, 𝛼! is the abnormal performance of sub-strategy i over the regression time period, 𝑀!! is

the monthly return of the S&P500 index in period t in excess of the risk-free rate, and 𝜀_!!_{is the}

error term or residual. The following paragraph illustrates the algebraic approach of the bootstrap analysis, which is derived from Kosowski et al. (2007).

Considering the residual-only resampling bootstrap, a sample is drawn with replacement from each sub-strategy. The i residuals are saved in the first step, which creates a time series of resampled residuals 𝜀_!,!!_{, 𝑡 = 𝑠}

!!, 𝑠!!, … , 𝑠!"! , where b=1 for bootstrap resample

number one. The sample is drawn so that it has the same number of residuals as the original sample for each sub-strategy i. This resampling method is then implemented for the remaining bootstrap repetitions b = 2,…,B. In this thesis b = 1000 replications, which is recommended in the research of Andrews and Buchinsky (2001). Using more replications yields statistical quantities with a higher degree of accuracy. Next, for each bootstrap repetition b, a time series of bootstrapped monthly returns of each fund is constructed. This sets the null hypothesis of no abnormal performance, i.e. 𝛼_! = 0, resulting in the following regression:

𝑟_!,!! _{= 𝑀}

!+ 𝜀!,!!, 𝑡 = 𝑠!!, 𝑠!!, … , 𝑠!"!, (4)

where 𝑡 = 𝑠_!!_{, 𝑠}

!!, … , 𝑠!"! is the time reordering created by resampling the residuals in

bootstrap repetition b. From Equation (4) it can be seen that alpha is zero. Kosowski et al. (2007) argue that this is due to the fact that the residuals are drawn from a sample that has a mean of zero by construction. Nevertheless, regressing the returns for the bootstrap samples on the returns of the market index may result in a positive or negative alpha. A positive alpha is generated when the bootstrap draws an abnormally higher number of positive residuals and a negative alpha exists in the case of an abnormally high number of negative residuals.

According to Schmidheiny (2012), Stata has included the bootstrap method for cross-section data. The bootstrap sampling and summarizing results are automatically done in Stata. Therefore, we use Stata to perform the above bootstrap method for all nine sub-strategies. The regression in Stata reports bootstrap standard errors including the confidence intervals and p-values, from which we will look for significance in alpha.

(17)

4.4 Sharpe ratio

The analyses made thus far do not take into account the differences in risk between hedge funds and the market index. According to Ackermann et al. (1999), hedge funds are able to boost their returns by taking on extra risk. On the other hand, some are created to reduce risk. Since these characteristics can have influence on their returns, it is also important to compute the risk-adjusted returns. Therefore, the risk-adjusted performance measure applied here is the Sharpe ratio.

The Sharpe ratio is also known as the reward-to-variability ratio and is defined as:

!_!!!_!

!_! (5)

where R_iis hedge fund i’s average return for a given period, R_fis the average riskless rate of return (One-month-Treasury Bill Rate) in that period, and 𝜎_!is the standard deviation of the individual hedge fund return over the period considered (p. 851, Ackermann et al., 1999).

According to Edwards (1999), the Sharpe ratio is widely used by financial economists and practitioners to compare different investment on the basis of risk-adjusted return. It is known as the trade-off between the risk premium, measured as the return minus the risk-free rate, and the risk, measured by the standard deviation of the returns (p. 161, Bodie, Kane and Marcus, 2011). If a hedge fund has a higher Sharpe Ratio compared to other strategies, this indicates that it has a higher risk-adjusted return.

To test for statistical significance between the difference in the Sharpe ratios from the S&P500 and the Equity hedge sub-strategies, we apply a statistical test designed by Jobson and Korkie (1981). The formula that is used in this thesis to get the test statistic is derived from the original one by Blitz and van Vliet (2007) and is defined as:

𝑧 = −

!"!!!"! ! !! !!!!,! ! ! !(!"!!!!"!!!!"!!"!!!!!,!! ) (6) where SRi and SRM refer to the Sharpe ratios of respectively the Equity hedge sub-strategy

portfolio (the mean of all sub-strategies in one period) and the market index, 𝜌_!,! refers to the correlation between the two portfolios i and M, and T refers to the number of periods observed (in this case months). The null hypothesis of the test is:

𝐻_!: 𝑆𝑅_! − 𝑆𝑅_! = 0 𝑣𝑠. 𝐻!: 𝑆𝑅!− 𝑆𝑅! ≠ 0

(18)

5. Results

5.1 Cumulative return

Applying the formulas to the strategies in Period I yields the results in Table 1. The results for Period II can be found in Appendix B. In addition to the tables, we made accompanying graphs that show the fluctuations in cumulative returns (Figure 1 below, Figure 2 in Appendix B). Table 1 and Figure 1 show that from approximately 2002, three out of five sub-strategies had higher cumulative returns than the market index. Especially the Energy/Basic Material (EBMI) strategy shows outlying high performance. However, the financial crisis of 2007-2009 (Ben-David, Franzoni, & Moussawi, 2012) had substantial influence on the cumulative return of all strategies. Especially the drop of 38.4% for the EBMI strategy between 2007 and 2008 is highly remarkable. The Short Bias Index (SBI) is the only strategy that had an increase in cumulative return from 2007 to 2008 of 28.4%, as opposed to the others that experienced a decrease. This is due to the fact that this strategy invests in equity markets that are declining, which is beneficial during a financial crisis.

Ben-David et al. (2012) state in their research that hedge funds still outperformed the U.S. stock market during the financial crisis. This could be due to the fact that hedge funds can actively manage their portfolios and therefore could react quickly when they saw the first signs of declining performance. However, at the end of 2009, from all five Equity hedge fund sub-strategies, the SBI strategy had a lower cumulative return than in 2008, which contradicts with the conclusion of Ben-David et al.

Table 1. Cumulative returns of eight different years for the period 1995 – 2013, 100=1995 Yearf Strategy 2000 2005 2007 2008 2009 2010 2011 2013 S&P500 287.47 271.80 319.72 196.67 242.80 273.83 273.83 402.46 HFRI EMNa _200.53 _244.89 _276.74 _260.36 _264.08 _271.61 _265.83 _291.44 HFRI QDb 281.78 447.69 583.19 449.38 513.72 558.75 518.69 617.14 HFRI SEBMc _569.80 _{1208.30 1633.41 1007.63} _1429.08 _1677.85 _1398.29 _1331.61 HFRI STHd 514.02 521.52 681.64 567.59 713.82 780.61 790.41 1019.85 HFRI SBIe _83.63 _95.01 _96.85 _124.37 _94.48 _77.46 _77.73 _52.37 a_{= Hedge Fund Research Index Equity Hedge (HFRI EH): Equity Market Neutral Index,}b_{= HFRI EH:} Quantitative Directional Index, c_{= HFRI EH: Sector – Energy/Basic Materials Index,}d_{= HFRI EH: Sector –} Technology/Healthcare Index, e = HFRI EH: Short Bias Index, f = Indicating end of years cumulative return, i.e. the month December.

(19)

For Period II it can also be seen that the financial crisis had a rather large impact on cumulative results. Similar to Period I, the only strategy that had an increased cumulative return during the financial crisis was the SBI. This outperformance is very obvious, as can be seen in Figure 2 in Appendix B. The peak was in February 2009 and represents an increase of 28.6% since February 2008. At the other end is the S&P500, which had a decrease of 44.8% during that same period. Clearly, investors who invested in the Short Bias Index before the start of the financial crisis, and withdrew their money at the peak in 2009 had a significant profit, as opposed to those who invested in the market index. These results can be interesting for investors who seek even higher risks with higher profits and who are able to quickly switch between these different strategies.

The strategy that had the highest cumulative return at the end of 2013 was the Technology/Healthcare Index (THI), which is in accordance with the results from Period I. Thus, investors that had invested in this sub-strategy at the end of the financial crisis would have earned a higher return than when they would have invested in the market index during the same period.

5.2 Statistical Sign test

Table 2 shows the results of the sign test performed in Stata. With a significance level of 5%, none of the outcomes are significant, so in neither case the null hypothesis is rejected. Thus, from the period 1995 up to and including 2013, based on a one-sided binomial test, there is not enough evidence to conclude that the Equity hedge sub-strategies outperformed the S&P500. To get more refined results, Period I is split up into three periods: 1995-2000, 2001-2006, and 2007-2013. This yields somewhat the same statistical results. Only for the period 2001-2006, there is enough statistical evidence that the Quantitative Directional Index (QDI) and the EBMI outperformed the S&P500. In period II, only the Fundamental Growth Index

(20)

(FGI) and Fundamental Value Index (FVI) have significant results at the 5% level. All these results are tabulated in Appendix B.2.

Table 2. Statistical one-sided Sign test, period 1995 - 2013

n all n observed n expected p-value*

Sign Sign

One-sided

Two-sided Strategies Positive Negative Zero Positive Negative Zero

EMNa_–S&P500 ₂₂₈ ₉₄ ₁₃₄ ₀ ₁₁₄ ₁₁₄ ₀ _0.9968 _0.0096 QDIb_{– S&P500} ₂₂₈ ₁₁₃ ₁₁₅ ₀ ₁₁₄ ₁₁₄ ₀ _0.5787 _0.9472 SEBMc_{– S&P50} ₂₂₈ ₁₁₃ ₁₁₅ ₀ ₁₁₄ ₁₁₄ ₀ _0.5787 _0.9472 STHd_{– S&P500} ₂₂₈ ₁₁₉ ₁₀₉ ₀ ₁₁₄ ₁₁₄ ₀ _0.2756 _0.5512 SBIe – S&P500 228 93 135 0 114 114 0 0.9978 0.0065 EHTIf – S&P500 228 112 116 0 114 114 0 0.6297 0.8426

a = Hedge Fund Research Index Equity Hedge (HFRI EH): Equity Market Neutral Index, b = HFRI EH: Quantitative Directional Index, c = HFRI EH: Sector – Energy/Basic Materials Index, d = HFRI EH: Sector – Technology/Healthcare Index, e = HFRI EH: Short Bias Index, f = HFRI EH: Equity Hedge Total Index.

*= 0.05 significance level.

5.3 Non-parametric bootstrap

The results for the non-parametric bootstrap can be found in Appendix B.3. Table B.3. shows that in each of the periods 1995-2000 and 2001-2006 four out of six strategies had a significant alpha. In both consecutive periods, the Equity Market Neutral Index (EMN), EBMI and Equity Hedge Total Index (EHTI) had a significant alpha. These were respectively 0.45 and 0.17, 1.66 and 1.03, and 0.76 and 0.33. From 2007 to 2013 only the THI and the SBI strategies had significant alpha, but only at the 5% level. In Period I, four out of six strategies had a significant alpha at 5%, from which the EMN and EHTI were also significant at the 1% level. These alphas are respectively 0.20 and 0.34. Lastly, for Period II, which includes all nine sub-strategies, only the THI and SBI had significant alpha (0.29 and -0.37 respectively).

Overall, these bootstrap results do not show a consistent outperformance of the sub-strategies. The outperformance that did have significant results can be explained by the managerial skills that hedge funds are able to use. However, their performance varies between periods and also depends on each individual sub-strategy. A reason of these inconsequent results could be the economic events of the past 20 years. According to Fung and Hsieh (2004), there have been a number of market events between 1994 and 2002 that had negative consequences for hedge fund performance. One of them was the collapse of Long-Term Capital Management (LTCM), which caused substantial volatility in hedge fund returns

(21)

followed by another market turmoil with the events of September 11th 2001 also had a great impact. Later, in 2002, the market had to cope with the consequences of the scandals of Enron Corporation and WorldCom. Lastly, the financial crisis of 2008 also had a great impact on hedge fund performance (Ben-David et al., 2012). With such a broad range of market events that affected hedge funds negatively over the past years, it is evident that the results for the different sub-strategies vary between the different periods. Certainly, the market index will also have felt the consequences of these economic downfalls. However, since hedge funds tend to take on more risk and have higher volatility it is more likely that these funds tend to undergo a greater negative impact.

5.4 Sharpe ratio

After calculating the Sharpe ratio for each sub-strategy and the S&P500, we also looked at the significance between the differences in Sharpe ratios. The results in Table 4 show that although many of the Sharpe ratios are higher than the S&P500, not all are significantly higher. For the period 2001-2006 all hedge fund strategies had higher Sharpe ratios, but only three out of six are significant. Between 2007-2013, two sub-strategies had a higher Sharpe Ratio, whereas only one is significant. Three sub-strategies had a higher Sharpe ratio in Period II, but only the THI strategy had a significant higher Sharpe ratio than the S&P500. The period 2007-2013 could be seen as the worst example period for the hedge fund sub-strategies. During this period only the EHTI had a higher Sharpe ratio, although this is only a slight difference. Of course, this period is influenced by the financial crisis, but you can see that all sub-strategies’ Sharpe ratio have declined compared to the previous period. This is in contrast with the S&P500, which had an increase in Sharpe ratio. In conclusion, the hedge fund sub-strategies did not consistently outperformed the U.S. market index on basis of their risk-adjusted performance during the period 1995 to 2013.

Edwards (1999) writes that between 1989 and 1998 equally weighted and value-weighted portfolios of all hedge fund had significantly higher Sharpe ratios than the S&P500 stock index. The ratios were 1.58 and 1.47 respectively for the hedge fund portfolios versus 0.86 for the market index. Therefore, it could be interesting for further research to investigate these kind of portfolios with the data in this thesis. However, it is important to take in mind that the results could also be due to the favourable economic conditions for hedge funds during that specific period. The period studied in this thesis includes several periods with financial turmoil. Furthermore, Edwards (1999) argues that when predicting a financial assets future return, a 10-year period is relatively short to make definite conclusions. In addition, a study

(22)

by Lo (2002) warns for the results of the Sharpe ratio when researching more volatile investment strategies like hedge funds. That is, performance of highly volatile strategies is more difficult to measure than that of less volatile strategies. This could result in less accurate estimates of the Sharpe ratio for hedge funds.

6. Conclusion

The goal of this research was to investigate whether Long-Short Equity hedge fund sub-strategies performed better than the U.S. market index during the period 1995 up to and including 2013. Hedge funds have become more popular as investment vehicles over the past few decades and the fact that they promise higher returns than the market makes it interesting to look at the actual performance they achieve. This thesis has applied several methods for evaluating hedge fund performance. In addition, the Sharpe ratio is computed to get insight about the risk exposure of these hedge funds.

Our results show that over the course of the whole period and looking at all research methods, not all hedge funds significantly outperformed the U.S. market index. Considering cumulative return, some sub-strategies had higher returns, but others underperformed the market. The statistical sign test and non-parametric bootstrap analysis show same results. During the earlier periods, hedge funds showed more outperformance, but in the second half of the period their relative performance declined. It is important to note the effect of certain economic events that may have affected hedge fund performance more than the market. Of course, this greater impact is also due to the fact that hedge funds tend to take on higher risks

Table x. Sharpe ratios and significance for different periods between 1995 and 2013 Sharpe ratio (z-statistic)j

1995-2000 2001-2006 2007-2013 1995-2013 2008-2013 S&P500 0.27 -0.003 0.07 0.11 0.08 EMNa 0.58 (-2.10*) 0.30 (-1.63) 0.05 (0.2) 0.26 (-1.97*) 0.05 (0.29) QDIb 0.25 (-0.20) 0.20 (-3.37*) 0.06 (0.25) 0.18 (-1.53) 0.03 (1.07) EBMc 0.34 (2.29*) 0.34 (-2.64*) -0.01 (1.01) 0.20 (-1.37) -0.04 (1.43) STHId 0.30 (-0.27) 0.02 (-0.36) 0.25 (-2.67*) 0.19 (-1.38) 0.24 (-2.43*) SBIe -0.05 (1.52) 0.01 (-0.05) -0.19 (1.25) -0.07 (1.48) -0.22 (1.32) FGIf - - - - 0.02 (0.31) FVIg - - - - 0.11 (0.91) MSIh - - - 0.09 (-0.52) EHTIi 0.47 (-1.88) 0.23 (-3.02*) 0.08 (-0.16) 0.24 (-2.89*) 0.06 (-0.08) a = Hedge Fund Research Index Equity Hedge (HFRI EH): Equity Market Neutral Index, b = HFRI EH: Quantitative Directional Index, c = HFRI EH: Sector – Energy/Basic Materials Index, d = HFRI EH: Sector – Technology/Healthcare Index, e = HFRI EH: Short Bias Index, f = HFRI EH: Fundamental Growth Index, g = HFRI EH: Fundamental Value Index, h = HFRI EH: Multi Strategy Index, i = HFRI EH: Equity Hedge Total Index, j = round up to two decimal places, statistical significance at the 5% level denoted by *.

(23)

shows that although hedge fund sub-strategies had higher Sharpe ratios, not all are

significantly higher. With the results of the Sharpe ratio, it is important to take in mind the economic events that have taken place.

Our findings are in line with Ackermann et al. (1999), who find that hedge funds do not consistently beat standard market indices. Also on a pure risk-adjusted basis, by looking at the Sharpe Ratio of hedge funds compared to those of the market indices, hedge funds again did not significantly outperform all market indices in their research. However, our result contradict with that of Kowowski et al. (2007) who conclude that hedge fund abnormal

performance is stable at annual horizons. The persistence in performance over the long term is especially stronger with, among others, the Long-Short Equity strategy, which we also

investigated.

The limitations of this study could be the relatively small database used. Given the fact that hedge fund data is hard to obtain, this thesis does not contain the widest and most detailed information about hedge funds data. Also the factors that could influence hedge fund

performance are not directly addressed in this study. Furthermore, although the effects of bias in our data are discussed, some biases are not accounted for in this study. This could have had an influence on our results.

Suggestions for future research could therefore be to use a greater data set with more factors influencing hedge fund performance. In that way, the results could get more defined. In addition, having access to more detailed data information could also help in addressing the bias issues exist in hedge fund data. Furthermore, since this study focuses purely on U.S. Long-Short Equity hedge fund sub-strategies, it is interesting to also investigate the other strategies that are part of the hedge fund universe.

(24)

7. Appendices

Appendix A: Equity hedge sub-strategies

The following equity hedge sub-strategies are analysed in this thesis.

Equity Market Neutral Uses complex quantitative techniques of analysing price data to determine information about future price movements and relationships between securities.

Quantitative Directional Uses advanced quantitative analysis of price and other technical and important data to set relationships between securities and to select securities for purchase and sale.

Sector – Energy/Basic Materials

Uses investment methods that are designed to identify

opportunities in securities in specific niche areas of the market, in this case the industrial sector. The manager of the fund has a degree of expertise in this area that exceeds that of a market generalist. This strategy is implicitly sensitive to price

fluctuations that are influenced by shifts in supply and demand factors, and to broader economic trends concerning the industry sector.

Sector-

Technology/Healthcare

Uses certain investment methods constructed to recognize opportunities in securities in specific niche areas of the market, in this case technology and healthcare. With this strategy, the expert manager focuses on companies that operate in the development, production and application of the technology and biotechnology sector, and that are connected to production in the pharmaceutical and healthcare industry.

Short-Bias Aims to analyse the valuation characteristics of the underlying companies with the goal of identifying overvalued companies to invest in. Short biased strategies can vary the investment level or the level of short exposure throughout market cycles.

However, the dominant characteristic is that the manager keeps a consistent short exposure and expects to outperform

traditional equity managers in equity markets that are declining. Fundamental Growth This strategy is based on analytical techniques in which funds

invest in companies that are expected to have more earnings in growth (e.g. in earnings, profitability, sales or market share) and more capital appreciation than those of the overall stock market, or the broader equity market.

Fundamental Value Funds using this strategy invest in undervalued companies in comparison to relevant benchmarks. The funds are focused on characteristics of the firm’s financial statements in absolute sense and relative to other similar securities and market indicators.

Multi-Strategy Investment In this strategy, managers take both long and short positions in mainly equity and equity derivative securities. Managers can use a wide variety of investment methods, including both quantitative and fundamental techniques. Strategies can be largely diversified or narrowly focused on specific sectors and can range broadly in terms of levels of net exposure, leverage employed, holding period, concentrations of market

(25)

Appendix B: Results

The following tables show the results of the cumulative return, the statistical sign test and the bootstrap performed for different periods.

B.1 Cumulative return

Table B.1 Cumulative returns for the period 2008 – 2013, 100=2008 Yeari Strategy 2008 2009 2010 2011 2012 2013 S&P500 61.51 75.94 85.65 85.65 97.13 125.88 HFRI EMNa _94.08 _95.43 _98.15 _96.06 _98.92 _105.31 HFRI QDb 77.06 88.09 95.81 88.94 95.30 105.82 HFRI SEBMc _61.69 _87.49 _102.72 _85.61 _80.79 _81.52 HFRI STHd _83.27 _104.72 _114.52 _115.96 _122.47 _149.62 HFRI SBIe 128.41 97.55 79.98 80.26 66.42 54.07 HFRI FGIf _62.86 _86.92 _98.76 _85.74 _92.93 _103.34 HFRI FVIg 73.17 91.48 101.45 94.23 104.89 125.54 HFRI MSIh _80.03 _93.65 _99.51 _94.37 _100.81 _117.07 a = Hedge Fund Research Index Equity Hedge (HFRI EH): Equity Market Neutral Index, b = HFRI EH: Quantitative Directional Index, c = HFRI EH: Sector – Energy/Basic Materials Index, d = HFRI EH: Sector – Technology/Healthcare Index, e = HFRI EH: Short Bias Index, f = HFRI EH: Fundamental Growth Index, g = HFRI EH: Fundamental Value Index, h = HFRI EH: Multi Strategy Index, i = Indicating end of years cumulative return, i.e. the month December.

(26)

B.2 Statistical Sign test

Statistical significance at the 1% and 5% level denoted by ** and * respectively.

Table B.2.1. Statistical Sign test, period 1995 - 2000

n all n observed n expected p-value

Sign Sign

One-sided

EMNa –S&P500 72 27 45 0 36 36 0 0.9878 0.0444 QDIb_{– S&P500} ₇₂ ₂₉ ₄₃ ₀ ₃₆ ₃₆ ₀ _0.9618 _0.1249 SEBMc_{– S&P50} ₇₂ ₃₇ ₃₅ ₀ ₃₆ ₃₆ ₀ _0.4531 _0.9063 STHd_{– S&P500} ₇₂ ₄₀ ₃₆ ₀ ₃₆ ₃₆ ₀ _0.2048 _0.4096 SBIe_{– S&P500} ₇₂ ₂₉ ₄₃ ₀ ₃₆ ₃₆ ₀ _0.9618 _0.1249 EHTIf – S&P500 72 36 36 0 36 36 0 0.5469 1.000

a = Hedge Fund Research Index Equity Hedge (HFRI EH): Equity Market Neutral Index, b = HFRI EH: Quantitative Directional Index, c = HFRI EH: Sector – Energy/Basic Materials Index, d = HFRI EH: Sector – Technology/Healthcare Index, e = HFRI EH: Short Bias Index, f_{= HFRI EH: Equity Hedge Total Index.}

Table B.2.2. Statistical Sign test, period 2001 – 2006

Sign Sign One-

sided

EMNa –S&P500 72 33 39 0 36 36 0 0.7952 0.5560 QDIb – S&P500 72 46 26 0 36 36 0 0.0122* 0.0245 SEBMc– S&P50 72 44 28 0 36 36 0 0.0382* 0.0764 STHd_{– S&P500} ₇₂ ₃₈ ₃₄ ₀ ₃₆ ₃₆ ₀ _0.3620 _0.7239 SBIe_{– S&P500} ₇₂ ₃₂ ₄₀ ₀ ₃₆ ₃₆ ₀ _0.8556 _0.4096 EHTIf_{– S&P500} ₇₂ ₄₁ ₃₁ ₀ ₃₆ ₃₆ ₀ _0.1444 _0.2888

a = Hedge Fund Research Index Equity Hedge (HFRI EH): Equity Market Neutral Index, b = HFRI EH: Quantitative Directional Index, c = HFRI EH: Sector – Energy/Basic Materials Index, d = HFRI EH: Sector – Technology/Healthcare Index, e = HFRI EH: Short Bias Index, f_{= HFRI EH: Equity Hedge Total Index.} Table B.2.3. Statistical Sign test, period 2007 – 2013

Sign Sign

One-sided

EMNa_–S&P500 ₈₄ ₃₄ ₅₀ ₀ ₈₄ ₈₄ ₀ _0.9685 _0.1011 QDIb – S&P500 84 38 46 0 84 84 0 0.8369 0.4452 SEBMc_{– S&P50} ₈₄ ₃₂ ₅₂ ₀ ₈₄ ₈₄ ₀ _0.9893 _0.0188 STHd_{– S&P500} ₈₄ ₄₁ ₄₃ ₀ ₈₄ ₈₄ ₀ _0.6282 _0.9132 SBIe_{– S&P500} ₈₄ ₃₂ ₅₂ ₀ ₈₄ ₈₄ ₀ _0.9893 _0.0375 EHTIf_{– S&P500} ₈₄ ₃₅ ₃₉ ₀ ₈₄ ₈₄ ₀ _0.9494 _0.1557

a = Hedge Fund Research Index Equity Hedge (HFRI EH): Equity Market Neutral Index, b = HFRI EH: Quantitative Directional Index, c = HFRI EH: Sector – Energy/Basic Materials Index, d = HFRI EH: Sector –

(27)

Technology/Healthcare Index, e = HFRI EH: Short Bias Index, f_{= HFRI EH: Equity Hedge Total Index.} Table B.2.4. Statistical Sign test, period 2008 – 2013

Sign Sign

One-sided

EMNa_–S&P500 ₇₂ ₂₉ ₄₃ ₀ ₃₆ ₃₆ ₀ _0.9618 _0.1249 QDIb_{– S&P500} ₇₂ ₂₉ ₄₃ ₀ ₃₆ ₃₆ ₀ _0.9618 _0.1249 SEBMc_{– S&P50} ₇₂ ₂₄ ₄₈ ₀ ₃₆ ₃₆ ₀ _0.9985 _0.0063 STHd – S&P500 72 34 38 0 36 36 0 0.7220 0.7239 SBIe – S&P500 72 26 46 0 36 36 0 0.9936 0.0245 FGIf_{– S&P500} ₇₂ ₄₃ ₂₈ ₀ ₃₆ ₃₆ ₀ _0.0480* _0.0959 FVIg_{– S&P500} ₇₂ ₄₅ ₂₇ ₀ ₃₆ ₃₆ ₀ _0.0222* _0.0444 MSIh_{– S&P500} ₇₂ ₄₂ ₃₀ ₀ ₃₆ ₃₆ ₀ _0.0973 _0.1945 EHTIi_{– S&P500} ₇₂ ₂₈ ₄₄ ₀ ₃₆ ₃₆ ₀ _0.9778 _0.0764

a = Hedge Fund Research Index Equity Hedge (HFRI EH): Equity Market Neutral Index, b = HFRI EH: Quantitative Directional Index, c = HFRI EH: Sector – Energy/Basic Materials Index, d = HFRI EH: Sector – Technology/Healthcare Index, e = HFRI EH: Short Bias Index, f = HFRI EH: Fundamental Growth Index, g = HFRI EH: Fundamental Value Index, h = HFRI EH: Multi Strategy Index, i = HFRI EH: Equity Hedge Total Index.

B.3 Bootstrap

The following table shows the results of the bootstrap performed in Stata for the five different periods. Statistical significance at the 1% and 5% level is denoted by ** and * respectively.

Table B.3. 1995-2000 n=72 Strategies Observed Coeff. (t-score) Standard Error

Bias p-value 95% C.I.

S&P500 𝛼 (EMNa₎ 0.08 (2.54) 0.45 (3.81) 0.03 0.119 -0.001 -0.000 0.011 <0.001** 0.018;0.138 0.221;0.689 S&P500 𝛼 (QDIb₎ 0.86 (16.71) 0.08 (0.30) 0.052 0.269 -0.001 0.002 <0.001 0.767 0.763;0.966 -0.447;0.606 S&P500 𝛼 (EBMIc₎ 0.48 (3.44) 1.66 (2.19) 0.138 0.759 0.000 0.061 0.001 0.029* 0.205;0.747 0.175;3.15 S&P500 𝛼 (THId₎ 1.16 (10.28) 0.72 (1.31) 0.113 0.550 0.004 0.006 <0.001 0.192 0.936;1.378 -0.359;1.797 S&P500 𝛼 (SBIe₎ -1.29 (-11.11) 1.15 (2.01) 0.116 0.572 -0.002 -0.008 <0.001 0.045* -1.512;-1.058 0.028;2.270 S&P500 𝛼 (EHTIf₎ 0.54 (12.04) 0.76 (3.88) 0.045 0.196 -0.001 0.01 <0.001 <0.001** 0.451;0.627 0.376;1.14 2001-2006 n=72 S&P500 𝛼 (EMNa₎ -0.03 (-1.30) 0.17 (2.40) 0.023 0.072 0.000 -0.002 0.193 0.016* -0.074;0.015 0.032;0.314 S&P500 𝛼 (QDIb₎ 0.79 (15.95) 0.55 (3.08) 0.05 0.178 0.001 0.012 <0.001 0.002** 0.694;0.889 0.199;0.896 S&P500 0.37 (3.53) 0.105 0.002 <0.001 0.165;0.578

Did U.S. Long-Short Equity hedge funds outperform the U.S. market index (S&P500) during the period 1995 - 2013?