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HEDGE FUNDS, BANKS AND SYSTEMIC RISK
DURING THE 2007-2009 FINANCIAL CRISIS
Rafael L. Santiago
University of Amsterdam, Amsterdam, Netherlands Thesis Supervisor: Dr. Ward Romp
University of Amsterdam, Faculty of Economics, Amsterdam, Netherlands
Abstract
Firstly, I provide a brief overview of the evolution of both the hedge fund and banking industries, leading to systemic risk exposures. Then, I discuss the channels through which hedge funds could generate systemic risk, emphasizing the most obvious and important one: through banks’ direct exposures. Additionally, I consider different measures for systemic risk, and decide to implement the one that directly relates banks and hedge funds for the 2007-2009 Financial Crisis. The period selected to represent the financial downturn goes from September 2007 to July 2009. The chosen measure was initially proposed by Chan et al. (2007). The authors claim that they were the first to consider the impact of hedge funds on systemic risk. In order to assess the exposures of banks to the hedge fund sector, first, I construct two bank indexes. Using monthly total returns data, I create equal- and value-weighted bank indexes to represent the banking sector. Additionally, I gather monthly returns for thirteen different hedge fund indexes and the S&P 500. Then, I perform multiple regressions of the bank indexes on the S&P 500 and the hedge fund indexes during the aforementioned period. Furthermore, I construct new hedge fund indexes by grouping the initial ones and giving them equal weights, and also, the study period is extended in order to avoid several shortcomings that were present in the initial period. The results show that banks were certainly exposed to some hedge fund indexes, with smaller banks proving to be more exposed than larger institutions. This result suggests that hedge funds might generate systemic risk exposures. However, both small and large banking institutions showed that they were more exposed to market risk, which was captured by the S&P 500 index.
2 Contents
1. Introduction………... 3
2. Review of the literature………. 7
3. Data and methodology……….. 13
4. Empirical results………... 21
5. Conclusions……….... 45
3 1. Introduction
The term “hedge fund” refers to the alternative investment vehicle first developed by Alfred Winslow Jones in 1949. While it lacks a formal definition, many have come to distinguish them as privately organized pooled investment vehicles that are not widely available to the public, are administered by professional investment managers and deploy a great amount of unconstrained investment strategies. Generally, they are highly leveraged and make excessive use of derivative instruments in aims to achieve greater absolute returns, also known as “alpha”. In addition to its primary investors, which are very wealthy individuals and institutional investors, hedge fund managers usually have stakes in the funds. At first glance, the previous description of “hedge fund” might appear puzzling. Nevertheless, when Winslow Jones created the first fund it was used to combine long positions in undervalued stocks and short positions in overvalued stocks, attempting to minimize the influence of the overall market movements (L’Habitant, 2002). Hence the name “hedge fund”.
The hedge fund industry has experienced monumental growth since it first was founded. By 1968 the Securities and Exchange Commission (SEC) estimated that there were a total of 140 funds operating (President’s Working Group on Financial Markets, 1999). Then, by the late 1990s there were around 2,500 to 3,500 active hedge funds; and by 2007 the Financial Stability Forum (2007) estimated that there were more than 9,000 funds operating. Despite the enormous growth that the industry has experienced, it still remains relatively small when compared to other financial sectors. Traditional financial institutions, such as commercial banks, mutual funds, pension funds and insurance companies manage a greater amount of aggregated assets. However, due to highly active trading strategies and great amount of leverage used, hedge funds have the potential to disrupt the financial markets (President’s Working Group on Financial Markets, 1999).
Along with the increase in the number of hedge funds, the industry has evolved tremendously throughout the years (Garbaravicius and Dierick, 2005; Financial
Stability Forum, 2007; Hildebrand, 2007). In its origins, hedge funds engaged in “hedged” trading or market neutral strategies with aims to eliminate the risk of market fluctuations. At the present time they also pursue directional strategies that entail speculating on the direction that the overall market is going to move. In addition, there
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are event-driven strategies, combinations of different strategies (multi-strategy funds) and Funds of Hedge Funds (FOHF). The latter refers to funds that invest in different hedge funds, providing investors greater diversification and less risk. The development of different strategies has been a consequence of the lack of restrictions on the type of instruments that hedge funds can use, given their unregulated nature. The absence of (or limited) regulation is a key difference when compared to other financial institutions.
The growth of the hedge fund industry has coincided with developments and innovations in the global financial system. The creation of new financial instruments and investment vehicles brought considerable changes in the broad financial sector. The accelerated evolution of the financial system started to take place in the 1970s with the innovation of financial products, intermediaries and processes in most advanced
economies (Mishkin, 2010). At the time, modern instruments and processes heightened the competition between banks and other financial institutions. Before this decade, traditional banking institutions used to earn monopoly rents, given the existence of barriers to entry and pricing restrictions. Well-established regulations were in place, resulting from the Great Depression. However, monopoly rents attracted numerous competitors, establishing pressure on traditional banking institutions (Beck, 2008; Mishkin, 2010).
The increase in competition persisted during the 1980s (Edwards, 1993). Traditional intermediaries had developed new roles, such as providing broker dealer services and managing pension funds. Instruments such as stock index futures and securitizations of mortgages were introduced. Technological advances also promoted the introduction of electronic trading, automatic teller machines and other new processes. The search for cost-effective funding channels and new sources of profits gave rise to countless innovations. Financial institutions grew in size and complexity, and traditional banking commenced to decay. The process became known as
disintermediation (Edwards, 1993; Edwards and Mishkin, 1995; Butler and Klee, 2002; Rajan, 2006; Mishkin, 2010). During the process of disintermediation banking
institutions experienced an increase in off-balance sheet activities. The traditional low return-on-equity banking business shifted to high return-on-equity strategies. Banks began to earn higher profits by taking more risks.
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The 1990s decade came to be acknowledged as a period of change. The heightened competition phase came to an end, and financial institutions shifted to a period of codependency (Borio, 2007; Knight, 2007; Mishkin, 2010). Institutions were no longer competing against each other; instead they started doing business together. For instance, firms ceased to grant loans with the intention to hold, and began selling them to other financial institutions and investors. Roles had shifted from originate-to-hold models to originate-to-distribute models (Borio, 2007; European Central Bank, 2008; Bord and Santos, 2012). Moreover, banks started to use repurchase agreements for short-term funding and derivatives trading to support risk transfers. There was also a rise in securitizations, in which different types of debt were pooled, consolidated and sold to investors. In turn, symbiosis among financial institutions was beginning to take form.
In 1999 the repeal of the Glass-Steagall Act by the US government liberated banking institutions from several constraints. The act prohibited commercial banks from participating in the investment banking business. Evidently, the repeal of the act gave way to an unstoppable growth of banking institutions and the expansion to a whole new set of activities (Barth, Brumbaugh Jr. and Wilcox, 2000). The newly broad-based institutions became able to undertake financial activities such as underwriting, retail and investment banking, brokerage services, asset management, proprietary trading and venture capital. In this way, financial institutions started benefiting from new sources of profits. Nevertheless, there were a number of concerns emerging in the financial sector. While banks began earning higher amounts of profit, their risk exposures became more complex and interdependent (Rajan, 2006; Borio, 2007; Knight, 2007).
At this time financial institutions had developed close ties among themselves, and hedge funds were not the exception (Chan et al., 2007; Financial Stability Forum, 2007; Gropp, 2014). Banking institutions and hedge funds became more interrelated by engaging in numerous activities. Firstly, hedge funds started to attract greater amounts of bank capital. Since hedge funds are characterized for using high amounts of leverage, banks started to perceive new investment opportunities by providing lines of credit to them. In addition to credit, banks also began providing prime brokerage and other banking services to hedge funds. Similarly, hedge funds earned profits for providing investment management services to banking clients. They were also starting to engage in counterparty trading activities. In this way, revenue streams of banks were
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increasingly exposed to the hedge fund industry. Moreover, banking institutions expanded and established proprietary trading units. Proprietary trading occurs when a banking institution trades stocks, bonds, derivatives, commodities or other financial instruments with its own money, rather than depositors’ money. Trading units may follow different investment strategies, and operate very similar to hedge funds. Consequently, risk exposures of the hedge fund industry started generating concerns among the banking sectors. Furthermore, regulators and banking officials acknowledged that hedge funds could in fact have a significant impact on the financial system. In turn, this could lead to systemic risk (President’s Working Group on Financial Markets, 1999; Garbaravicius and Dierick, 2005; Bernanke, 2006; Chan et al., 2006; McCarthy, 2006; Chan et al., 2007; Financial Stability Forum, 2007; Kambhu et al., 2007; Lo, 2008a).
In this paper, I attempt to put in practice a risk measure for hedge funds with aims to quantify the potential impact of hedge funds on systemic risk, while applying it to aggregate hedge-fund returns data. Following Chan et al. (2007), I perform regression models relating the banking sector to hedge funds. In the previously mentioned article, the authors proposed regressing banking sector indexes on hedge fund indexes in an attempt to conclude whether or not the banking sector had significant exposure to certain hedge fund indexes. My task is to perform similar regressions in order to examine the results, and provide support or opposing views to Chan et al. (2007) findings. However, my period of interest is the time when the financial sector was experiencing a substantial downturn, the 2007-2009 Financial Crisis. Specifically, the period selected to represent the Crisis is from September 2007 to July 2009.
In the next section I review the literature on hedge funds and systemic risk while discussing the different channels through which the former might create the latter, and consider different measures for it. In Section 3 I analyze the data on hand and describe the methodology used. The empirical results are presented and analyzed in Section 4; and in Section 5 I provide several conclusions.
7 2. Review of the literature
“Systemic risk” is a difficult concept to define. For this reason, numerous authors have defined it in different ways. DeBandt and Hartmann (2002) define it as the risk of experiencing a systemic event. They state that a systemic event takes place when a shock affects a considerable number of financial institutions or markets, and severely impairs the general well-functioning of the financial system by affecting the efficiency and effectiveness with which savings are channeled into real investments. Kambhu et al. (2007) state that an essential feature of systemic risk is when financial shocks have the potential to affect substantially the real economy. In their view, this is the defining feature of a systemic crisis, and the distinction from a purely financial event. Billio et al. (2010) define it as the probability that a series of correlated defaults among financial institutions, occurring over a short period of time, will trigger a withdrawal of liquidity and widespread loss of confidence in the financial system as a whole. The European Central Bank (2010) defines it as a risk of financial stability that impairs the functioning of a financial system to the point where economic growth and welfare suffer materially. Other authors focus on more specific attributes (Mishkin, 2007; Caballero, 2010; Acharya et al., 2010; Rosengren, 2010; Moussa, 2011). For consistency purposes, in aims to deliver unambiguous conclusions, I will follow Chan et al. (2007) definition of “systemic risk”. It is defined as the possibility of a series of correlated defaults among financial institutions that occurs over a short period of time, often caused by a single major event. Typically, the common example of systemic risk is a banking panic, which historically was not uncommon in the US and led to the creation of the Glass Steagal Act of 1933 (Mishkin, 2010).
Acknowledging the fact that hedge funds can potentially create systemic risk through diverse channels, various economists have addressed this concern and
attempted to construct different measures for it. For example, Garbaravicius and Dierick (2005) distinguish three different channels through which hedge funds could affect financial stability. Firstly, the failure of a large individual or group of hedge funds could lead to a wide range of repercussions for exposed banks and financial markets.
Secondly, a mismanagement of exposures to hedge funds at an individual bank or banks could also lead to a systemic crisis through contagion effects. Lastly, hedge fund
activities impact on financial markets could initiate instability in the financial system. The authors affirm that the most obvious channel through which hedge funds could
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impact the financial system is through direct credit exposures of credit institutions and securities firms. These direct exposures are principally the result of their role as prime brokers, which include a number of different activities, such as provision of leverage, issuance of credit lines and trading exposures. However, credit institutions and
securities firms also face a series of indirect risks stemming from hedge fund activities. These indirect risks, in turn, are very difficult to measure (Garbaravicius and Dierick, 2005).
Similarly, Hildebrand (2007) asserts that “the primary potential transmission channel of systemic risk is through counterparty credit risk exposure”. The author highlights that the link between hedge funds and financial stability relates to the
possibility that large losses in hedge funds get transmitted to large internationally active banks, acknowledging the fact that financial intermediaries extend credit to hedge funds, which in turn is used for hedge funds’ investments in excess of their capital base. Fung and Hsieh (2006) also coincide, stating that “hedge funds can become the
transmission mechanism of systemic risk because they borrow from and trade with regulated financial institutions”. Additionally, Hildebrand (2007) argues that in a stressed market, banks that provided credit to hedge funds might demand additional collateral or force hedge funds to liquidate positions. Consequently, market volatility increases and prices drop even more. It could also lead to a reduction of market liquidity. In this manner, Geithner (2006) stresses, banks’ incentives to minimize their own exposure could lead to an amplification of the initial shock, and further lead to a broader disruption of market liquidity.
On their part, Kambhu et al. (2007) claim that “hedge funds create systemic risk to the extent that they can disrupt the ability of financial intermediaries or financial markets to efficiently provide credit”. Furthermore, they point out that this link to the real economy might occur through banks’ direct exposures to hedge funds, among other channels; and that hedge funds are capable of exacerbating financial shocks. The direct linkage between banks and hedge funds occurs through their counterparty exposures, for example, short-run financing for leveraged positions, prime brokerage activities and trading counterparty exposures. In the article, the authors also state that BIS has estimated that banks’ direct exposures to hedge funds have been growing proportionately with the hedge fund industry, although the magnitude remains unknown. McCarthy (2006) also discusses the transmission mechanism by which the
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collapse of one or more hedge funds might lead to a financial distress, stating that the direct effect would be on the hedge fund’s counterparties. Particularly, the direct effect would be on the prime broker dealers that maintain business activities with the hedge funds. He declares that, as chairman of the Financial Services Authority (FSA), they examine prime brokerage exposure to hedge funds of approximately 15 financial institutions, which covers more than 150 funds. From this examination, they concluded that hedge funds to which broker dealers are exposed were continuing to grow.
Furthermore, the Financial Stability Forum (2007) asserts that systemic risk might arise from hedge funds in two different ways: directly, arising from banking institutions direct credit exposures to hedge funds; or indirectly, arising from hedge fund actions that might cause deterioration in market liquidity and prices, causing further distress at one or more institutions. It is also stated that indirect exposures, e.g., via wide market liquidity erosion, are difficult to measure. Moreover, the Financial Stability Forum (2007) claims that given the significant source of revenue that hedge funds provide to large financial institutions, the linkages between them have become tighter and deeper than they ever were. This implies that the balance sheets and revenue streams of the banking institutions are increasingly exposed to problems in the hedge fund industry. It is pointed out in the article that direct exposures stem from a wide set of activities, such as prime brokerage services, direct lending and investments in hedge funds. Direct exposures estimates can be very uncertain due to the limitations in methodologies and assumptions of potential exposure models (Financial Stability Forum, 2007).
Similarly, the President’s Working Group on Financial Markets (1999) concludes that hedge funds’ use of excessive leverage increases the probability that financial problems could be transmitted to other institutions, increasing also the likelihood of a general breakdown in the functioning of the financial system. The transmission could be either direct, through losses inflicted on creditors and trading counterparties, or indirect, affecting other market participants through price movements that result from the lack of investors willing to accept more risks. Commonly, large complex banking institutions are the most likely to have meaningful exposures to hedge funds.
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In addition, the President’s Working Group on Financial Markets (1999) agrees on the fact that the disclosure of more information and transparency of hedge funds is required in order to develop direct and proper risk measures, and to conceivably enhance the judgment of potential investors and counterparties. At the Federal Reserve Bank of Atlanta’s 2006 Financial Markets Conference, Bernanke (2006) delivers a speech in which he discusses systemic risk implications of the rapid growth of the hedge fund industry. He remarks that, as a common observation, hedge funds are “opaque”, in the sense that information about their portfolios is usually limited and provided in an infrequent basis. Additionally, information provided by a hedge fund might vary significantly, depending on the recipient of such information. For this reason, in order to measure risks accurately, financial authorities would need more data from major market participants, especially from hedge funds.
In a written testimony addressed to the US House of Representatives Committee on Oversight and Government Reform, Lo (2008a) acknowledges that it is necessary to construct risk measures that are “sufficiently practical and encompassing to be used by policymakers and the public”. However, he recognizes that in order to develop such measures, hedge funds and other financial institutions that are considered part of the shadow banking system would be required to provide more transparency to regulators. Among the information that would need to be disclosed there are assets under
management, leverage, liquidity, counterparty relationships and portfolio holdings. Moreover, Lo (2008a) admits that inferences in his research regarding systemic risk and hedge funds are “indirect and circumstantial” as a consequence of the lack of
transparency in the hedge fund industry. Likewise, Garbaravicius and Dierick (2005) assert that “it is very difficult to provide any conclusive evidence on the impact of hedge funds on financial markets”; and that “it is challenging to make an unambiguous assessment of the impact of hedge funds on financial stability” due to the lack of information on their activities, financial structure and interaction with banks. They also acknowledge that “management of banks’ exposures to hedge funds is complex and requires continuous improvements and vigilance to keep up with developments”. For these reasons, Lo (2008a) promotes the use of other indirect measures designed for hedge funds (Chan et al., 2006; Chan et al., 2007; Lo, 2008b).
Given the lack of reliable and complete hedge fund data, most economists interested in hedge funds and systemic risk have taken the task to construct and develop
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“indirect” risk measures. For instance, Gropp (2014) discusses the development of a statistical model in Adams et al. (2013) that links and estimates the risk in commercial banks, investment banks, insurance companies and hedge funds. The model is used to measure spillover effects. Firstly, risk is estimated for each type of financial institution. Then, the authors eliminate common components that affect all the institutions
simultaneously. In this manner, the focus is on the stress that flows from one institution to another. The model is able to distinguish the direction of the spillover flows between pairs of institutions; and is estimated during tranquil and crisis periods. In their study, Adams et al. (2013) surprisingly find that hedge funds may be the most important transmitters of shocks to the rest of the financial market, even more important than commercial banks or investment banks. Moreover, they find that the effects increase in importance “during volatile market conditions, such as the 2007-2009 Financial Crisis”. The model of this research focuses on statistical relationships, given the lack of detailed information on how much risk different financial institutions are exposed to, their assets and liabilities. The unavailable information would be necessary in order to explain the mechanisms underlying estimated spillovers and trace the effects back to economic relationships. However, Gropp (2014) emphasizes that the kind of data needed is not available for the hedge fund industry. At the same time, he recognizes that hedge funds are systemically important and that “hedge funds may amplify systemic risk more than previously thought”.
Other indirect measures of systemic risk were proposed by Billio et al. (2010). The authors develop econometric measures in which they capture the
interconnectedness among monthly returns of hedge funds, banks, brokers and insurance companies based on Granger-causality tests and principal components analysis. The findings exhibit that all four sectors became highly interrelated over the previous decade, increasing systemic risk in the finance and insurance sectors. As well as the previously discussed literature, Billio et al. (2010) stress the fact that given the unavailability of direct information concerning leverage and linkages, statistical relationships are able to yield valuable indirect information about the build-up of systemic risk. Moreover, they state that “the dynamics of the hedge fund industry suggest that an econometric approach may still provide more immediate and actionable measures of systemic risk”. Similarly, Boyson et al. (2010) investigate contagion from lagged bank and broker returns to hedge fund returns. Furthermore, Bisias et al. (2012)
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perform a survey of various quantitative measures of systemic risk in the economics and finance literature.
The discussion about the impact of hedge funds on systemic risk has its origins in a seminal paper authored by Chan, Getmansky, Haas and Lo. In Chan et al. (2007), the authors attempt to quantify the potential impact of hedge funds on systemic risk by developing new risk measures for hedge funds. Among the measures developed, I only consider the regression models in which the banking sector is related to hedge funds. The motivation for focusing my study in such measure emerges from the fact that banks’ direct exposures to hedge funds are widely considered to be the most important and obvious channel through which hedge funds affect the financial system, as
mentioned in the previously discussed articles. In addition, Allen (2001) highlights the importance of mapping out relationships between financial institutions when studying financial stability and systemic risk.
Chan et al. (2007) argue that systemic risk involves distress in the banking sector. Then, they examine the relation between the returns of publicly traded banks and hedge fund index returns. Firstly, using monthly total returns of publicly traded banks, equal- and value-weighted portfolios are constructed. The returns of these portfolios are used as proxies for the banking sector. Afterwards, they regress each bank index return on the S&P 500 and various hedge fund index returns. Initially, they regress the equal-weighted bank index on the S&P 500 and its first two lags. Next, they add a hedge fund index and its corresponding first two lags as regressors. They perform equivalent regressions with 13 other hedge fund indexes, for a total of 15 regressions. Lastly, they add various hedge fund indexes in the same regression. The authors execute similar regressions using the value-weighted bank index as the independent variable. Before continuing, the authors acknowledge that “correlation between the return of bank stocks and hedge fund indexes do not necessarily imply any causal relations”. However, they claim, “if a bank engages in illiquid hedge fund strategies, for example, which is becoming more common as banks struggle to deal with increased competition and decreasing margins, then these regressions should pick up significant factor exposures to certain hedge fund indexes”. Finally, the authors concluded that the banking sector had significant exposure to certain hedge fund indexes, which implies that they share the presence of common factors. This could also imply that dislocations among hedge funds affect banks. Chan et al. (2007) assert that this is a channel by which the hedge
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fund industry generates systemic risk exposures. Nevertheless, the authors acknowledge that this measure of systemic risk is “indirect”, and that is “open to debate and
interpretation”. As mentioned before, this results from the fact that hedge funds are not required to disclose information about their risks and returns. Consequently, empirical studies of the hedge fund industry are based on limited hedge fund data. Even though Chan et al. (2007) conclusions and methodology are prone to dispute among economists and academics, they have been largely accepted in the literature (eg., Garbaravicius and Dierick, 2005; Rajan, 2006; Kambhu et al., 2007; Lo, 2008a; Aggarwal and Jorion, 2010; Billio et al., 2010; Bisias et al., 2012).
3. Data and methodology
At the beginning, data for publicly traded banks is collected. Using the University of Chicago’s Center for Research in Security Prices (CRSP) database, I gather monthly total returns for all stocks with SIC codes 6000-6199, which represent the banking sector. The period of study is from September 2007 to July 2009. The motivation for selecting this time frame is to give a representation of the events that were taking place during a period of financial distress, the recent Financial Crisis. In addition, I use monthly returns for different hedge fund indexes and S&P 500. The data for the hedge fund indexes is collected from Barclay Hedge databases.
Firstly, I construct bank indexes using the publicly traded banks’ monthly
returns. The returns of the indexes will further be used as proxies for the banking sector. The index return can be defined as the change in value of a portfolio over some holding period. This return can be calculated as a weighted average of the returns of individual securities in the portfolio. To construct these indexes, I use:
∑ ∑
for each month t; where w is the weight applied and r is the return of each security n. The first index constructed is the equally weighted index. In an equally weighted index each security in the portfolio is given an equal weight, regardless of its market
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capitalization or economic size. Thus, , for all n. Furthermore, I construct a value weighted index. For the value weighted portfolio I assigned the total market value of each security as its weight. The market value of a security can be defined as the product of its price and the number of shares outstanding. The value weighted index is monthly rebalanced in order to weight most heavily the securities that have higher market value during each month.
Following the collection of the data and the construction of bank indexes, I examine the data on hand. Figure 1 shows a plot of the monthly returns of the equally and the value weighted bank indexes, and the S&P 500. Firstly, as we can note in the graph, the value weighted index is shown to be more volatile than the equally weighted bank index and the S&P 500. This means that larger banking institutions were more volatile than the smaller and medium sized institutions that did not perish during the crisis period. In addition, it can be noted that the series are consistent with the mean reversion theory for both bank indexes and the S&P 500. The theory suggests that returns will eventually move back towards the mean. This is customary with stock returns. In Figure 2 it can be observed that the mean of the three indexes stays very close to 0.
Figure 2 also shows the descriptive statistics of the data. It is observed that both bank indexes exhibit positive skewness. In contrast, the S&P 500 has a negative skew. This could be an indication of tail risk exposure. Tail risk refers to the possibility of a portfolio moving more than three standard deviations from its mean. However, kurtosis, which is a more direct measure of tail risk, has a value below 3 for every index. A normal distribution exhibits a kurtosis with a value of 3, and values less than this represent thinner tails in the distribution. Nevertheless, inferences about the distribution with a relatively small sample, as the one used in this study, can prove to be misleading when high order moments, such as kurtosis, are taken into account. Thus, it is likely that these are not true representations of their real value, and might lead to wrong
conclusions about the shape of the distribution. According to Wheeler (1995), we should not care much about these statistics when the sample is relatively small, since they are dependent on sample size.
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Figure 1. Monthly returns of bank indexes and S&P 500
Figure 2. Descriptive statistics of the bank indexes and S&P 500
Variable Observations Mean Std. Dev. Min Max Skewness Kurtosis Equally Weighted Index 23 -.021949 .0799634 -.1543761 .1420374 .2109255 2.692972 Value Weighted Index 23 -.00341 .1209342 -.2028376 .2659448 .3132163 2.617602 SP500 Index 23 -.0150189 .0673478 -.1694245 .0939251 -.340592 2.546251 -. 2 -. 1 0 .1 .2 .3
Jul 2007 Jan 2008 Jul 2008 Jan 2009 Jul 2009
Month-Year
Value Weighted Index Equally Weighted Index S&P 500 Index
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Figure 3 illustrates a plot of the monthly returns of the 13 different hedge fund indexes used in my study. The description of each hedge fund index is shown in Figure 4. As displayed by the graph, the Emerging Markets Index and the Equity Short Bias Index appear to have greater volatility than the rest. However, in Figure 5 it is shown that the Emerging Market Index has the greatest volatility. In Figure 5, I present the descriptive statistics of the hedge fund indexes. As noted, these returns also exhibit mean reversion with mean values very close to 0. It is also obvious the heterogeneity that exists in the historical risk and returns of the different categories of hedge fund investment styles. For instance, the mean returns range from a low -1.04% for
Distressed Securities to a high 1.44% for Equity Short Bias. The volatility ranges from a low 1.28% for Equity Market Neutral to a high 6.12% for Emerging Markets. As
expected, the Equity Market Neutral exhibits the lowest volatility, which is due to the fact that investors that use this strategy combine long and short positions in order to hedge against market factors, and consequently, eliminate volatility. Additionally, Emerging Markets is usually considered to be relatively risky due to the fact that it involves additional political, economic and currency risks.
As opposed to the bank indexes, the majority of the hedge fund indexes exhibit negative skewness. Barclay Hedge Fund, Convertible Arbitrage, Distressed Securities, Emerging Markets, Equity Long Short, Equity Market Neutral, Event Driven, Fixed Income Arbitrage, Merger Arbitrage, Multi Strategy and Equity Long Bias have
skewness coefficients less than 0. Again, this property could imply that there is tail risk exposure. Fixed Income Arbitrage has the lowest value, with a skewness of -2.21. This is no surprise, since this investment style is known to generate consistent profits, with occasional extreme losses. Furthermore, the three indexes that exhibit the lowest skewness also have the largest kurtosis. Fixed Income Arbitrage, Convertible Arbitrage and Multi Strategy exhibit kurtosis of 8.52, 4.95 and 4.39, respectively. As noted, several of the hedge fund indexes have a kurtosis greater than 3. In general, this would imply that they have fatter tails than a normal distribution, as it is common for hedge fund returns due to the high exposure to multiple risks. However, the previous discussion applies in this case as well; given the size of the sample, estimates of high order moments may lack reliability.
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The previous to last column of Figure 5 shows the correlations of the hedge fund indexes with the S&P 500. As Chan et al. (2007) remark, these correlations were
historically low since investors discovered that hedge funds offer greater diversification benefits than many traditional asset classes. However, as discussed by Garbaravicius and Dierick (2005), during stressed conditions many hedge funds start to take similar positions in order to avoid risky strategies. While looking for less risk, hedge funds move similarly to the traditional markets, as observed during the Russian default and near-collapse of Long Term Capital Management in 1998. Likewise, Garbaravicius and Dierick (2005) noted that correlations were increasing during the years leading to the Financial Crisis. In order to make a comparison, I also look at the correlations of the hedge fund indexes with the S&P 500 for the years 2005 and 2006. This can be observed in the last column of Figure 5. As expected, the majority of the hedge fund indexes had considerably greater correlations with the S&P 500 during the years of the crisis, which could imply that hedge funds decreased their risk-taking and took similar positions to the traditional market. Furthermore, this feature might result in a
multicollinearity problem for some of the regressions that I intend to use, since several explanatory variables have strong relationships. This will likely produce high R2’swith low values for the t-statistics, and coefficients may have opposite signs. Nevertheless, the regressions will produce unbiased estimates. Additionally, in order to avoid
specification errors by dropping variables, it might be best to accept the fact that there is multicollinearity present in certain regressions and be aware of the consequences.
In order to assess the existence of multicollinearity in the regressions, I use as a diagnostic, the variance inflation factor (VIF). The VIF is calculated for each
explanatory variable by doing a linear regression of that predictor on all the other predictors. Then, the R2 is obtained from that regression; and the VIF equals 1/(1-R2). The VIF name derives from the fact that it estimates how much the variance of a coefficient is inflated due to the linear dependence with the other predictors. Following Allison (2012), I acknowledge that multicollinearity is present in a regression when the VIF has a value greater than 2.50.
18 Figure 3. Monthly returns of hedge fund indexes
Figure 4. Description of Barclay Hedge hedge fund indexes
Barclay Hedge Fund Index
Measure of the average return of all hedge funds in the Barclay database, with the exception of Funds of Funds. The index is the arithmetic average of the returns of all the funds that have reported that month.
Convertible Arbitrage Index
Strategy identified by hedge investing in the convertible securities of a company. A common investment is to take a long position in the convertible bond and short the common stock of the same company. Positions are designed to generate profits from the fixed income security as well as the short sale of the stock, while
protecting principal from market moves. Distressed Securities
Index
Non-traditional strategy in which fund managers invest in debt, equity or trade claims of companies in financial distress or already in default. The securities of companies in distressed or defaulted situations typically trade at substantial discounts to par value due to difficulties in analyzing a proper value for such securities, lack of street coverage, or simply an inability on behalf of traditional investors to accurately value such claims or direct their legal interests during restructuring proceedings.
Emerging Markets Index Strategy that involves equity or fixed income investing in
-. 1 5 -. 1 -. 0 5 0 .0 5 .1
Jul 2007 Jan 2008 Jul 2008 Jan 2009 Jul 2009
Month-Year
Barclay Hedge Fund Index Convertible Arbitrage Index Distressed Securities Index Emerging Markets Index Equity Long/Short Index Equity Market Neutral Index
Event Driven Index Fixed Income Arbitrage Index
Global Macro Index Merger Arbitrage Index
Multi Strategy Index Equity Long Bias Index
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emerging markets around the world. Since many emerging
markets do not allow short selling, nor offer viable futures or other derivative products with which to hedge, emerging market
investing often employs a long-only strategy.
Equity Long/Short Index Directional strategy that involves equity-oriented investing on both the long and short sides of the market. The objective is not to be market neutral. Managers have the ability to shift from value to growth, from small to medium to large capitalization stocks, and from a net long position to a net short position. Managers may use futures and options to hedge. The focus may be regional or sector specific.
Equity Market Neutral Index
Investment strategy that is designed to exploit equity market inefficiencies and usually involves being simultaneously long and short matched equity portfolios of the same size within a country. Market neutral portfolios are designed to be either beta or currency neutral, or both. Well-designed portfolios typically control for industry, sector, market capitalization, and other exposures. Leverage is often applied to enhance returns.
Event Driven Index Strategy defined as “special situations” investing designed to capture price movement generated by a significant pending corporate event such as a merger, corporate restructuring, liquidation, bankruptcy or reorganization.
Fixed Income Arbitrage Index
The arbitrageur aims to profit from price anomalies between related interest rate securities. Most managers trade globally with a goal of generating steady returns with low volatility. This category includes interest rate swap arbitrage, US and non-US government bond arbitrage and forward yield curve arbitrage.
Global Macro Index Managers carry long and short positions in any of the world's major capital or derivative markets. These positions reflect their views on overall market direction as influenced by major
economic trends and/or events. The portfolios of these funds can include stocks, bonds, currencies, and commodities in the form of cash or derivatives instruments. Most funds invest globally in both developed and emerging markets.
Merger Arbitrage Index Funds typically invest simultaneously long and short in the companies involved in a merger or acquisition. Risk arbitrageurs are typically long the stock of the company being acquired and short the stock of the acquirer. By shorting the stock of the acquirer, the manager hedges out market risk, and isolates his exposure to the outcome of the announced deal.
Multi Strategy Index Funds are characterized by their ability to dynamically allocate capital among strategies falling within several traditional hedge fund disciplines. The use of many strategies, and the ability to reallocate capital between them in response to market
opportunities, means that such funds are not easily assigned to any traditional category.
Equity Long Bias Index Managers are typically considered long-biased when the average net long exposure of their portfolio is greater than 30%.
Equity Short Bias Index Managers take short positions in mostly equities and derivatives. The short bias of a manager's portfolio must be constantly greater
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than zero to be classified in this category.
Figure 5. Descriptive statistics of the hedge fund indexes
Variable Observations Mean Std. Dev. Min Max Skewness Kurtosis Corr. with S&P 500 Corr. S&P 500 Jan.2005- Dec.2006 Barclay Hedge Fund Index 23 -.0026435 .0332544 -.0841 .0557 -.6333514 3.319535 0.8321 0.7198 Convertible Arbitrage Index 23 .0003043 .0467633 -.1376 .0714 -1.226753 4.947872 0.6526 0.3594 Distressed Securities Index 23 -.010387 .0355646 -.0881 .0563 -.2680173 2.631692 0.7365 0.4866 Emerging Markets Index 23 -.0054435 .0612037 -.1564 .1107 -.3976186 3.268877 0.8362 0.6538 Equity Long Short Index 23 -.0007826 .0215485 -.0492 .038 -.3811479 2.618511 0.7818 0.6594 Equity Market Neutral Index 23 .0004696 .0128472 -.0287 .0234 -.4564123 2.743004 -0.0706 0.2555 Event Driven Index 23 -.0005783 .0272486 -.0572 .0523 -.0615745 2.552335 0.7533 0.6772 Fixed Income Arbitrage Index 23 -.0088348 .034993 -.1355 .0246 -2.21238 8.523067 0.6042 -0.0414 Global Macro Index 23 .0044478 .0195251 -.0327 .0387 .1550376 2.416923 0.4253 0.5907 Merger Arbitrage Index 23 .0024957 .0148303 -.036 .0231 -.9857697 3.377962 0.7156 0.6588 Multi Strategy Index 23 -.0003783 .0288312 -.0762 .0388 -1.278839 4.392754 0.6415 0.5494 Equity Long Bias Index 23 -.0054478 .0463404 -.118 .0665 -.5647413 2.943966 0.9012 0.7984 Equity Short Bias Index 23 .0144 .0468867 -.0612 .1227 .5462304 2.690977 -0.8782 -0.8885
Before continuing with the regressions, I check that the time series data are stationary. As it is conventional for stock returns, we can observe in the graphical illustrations that the returns for the S&P 500, bank and hedge fund indexes do not follow any trend. To the extent that index returns are essentially the change in the total value over some period of time, we can say that potential trends are removed by taking first differences. Furthermore, since a random walk is a non-mean reverting process that can move away from the mean in a positive or negative direction, we can also say that
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the series do not follow a random walk. Instead, the series are stationary. Nevertheless, I prove the stationarity of the series by performing a Dickey Fuller test for all the
variables. The null hypothesis of the test is that the variable contains a unit root, or equivalently, that it follows a random walk. In this case, under the null hypothesis the series has a zero drift parameter. The alternative is that the variable was generated by a stationary process. The results showed that we can reject the null hypothesis of a unit root for all the variables at the 10% significance level. Similarly, we can reject the null at the 5% level for all but one variable. In addition, we can reject the null at the 1% level for the majority of the variables.
Given the stationarity of the series, we can safely say that the data will not produce unreliable or spurious results. Now, I can continue with the regressions.
Following Chan et al. (2007), firstly, I regress the Equally Weighted Bank Index on the S&P 500 with its first two lags. The S&P 500 is used as the market risk factor.
Subsequently, I regress the Equally Weighted Bank Index on the S&P 500 with its first two lags, and a hedge fund index with its corresponding first two lags. Similarly, I perform equivalent regressions using each hedge fund index at a time, for a total of 14 regressions. The objective of these regressions is to potentially provide some insight into links between certain hedge fund styles and the banking industry. Additionally, I use the Value Weighted Bank Index as the dependent variable, and perform equivalent regressions.
4. Empirical results
Figure 6 displays the regressions of the monthly Equally Weighted Bank Index returns on the S&P 500 and various hedge fund index returns, from September 2007 to July 2009. The first column shows the regression of the Equally Weighted Bank Index on the S&P 500 and its first two lags. As it can be noted, contemporaneous S&P 500 returns are significant at the 1% level. This suggests that banks were exposed to market risk during the period of study. In fact, the coefficient suggests that banks and the S&P 500 were moving very close together. However, in contrast to Chan et al. (2007), lagged S&P 500 returns are not significant at the 1% or at the 5% levels. In the aforementioned article, the authors assert that a significant result of the lagged S&P 500 returns suggest that banks had illiquidity exposure. This analysis is analogous to the one pertaining to
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hedge fund returns and serial correlation that the authors make in a previous section of the paper. In short, they claim that serially correlated hedge fund or asset returns imply that there exists illiquidity exposure. However, that discussion is not within the scope of my study. Following the same line of thought, nevertheless, we can say that I found no supporting evidence to claim that banks had illiquidity exposure during the period of study (even if it is common knowledge the fact that illiquidity reigned over this period).
The next 13 columns contain regressions of the Equally Weighted Bank Index on the S&P 500 and its first two lags, and additionally, each of the 13 hedge fund indexes and the first two lags, respectively. Before continuing, I inspect the relation of the independent variables in each regression in order to address the problem of
multicollinearity. After calculating the VIF of each explanatory variable in every regression, I acknowledge that several regressions suffer from multicollinearity.
The second column contains a regression that uses Barclay Hedge Fund Index (and its first two lags) as an explanatory variable. In this case, the regression suffered from multicollinearity. Yet, the contemporaneous Barclay Hedge Fund Index is statistically significant at the 5% level, implying that banks were exposed to the hedge fund index. This is somewhat unexpected due to the fact that, given multicollinearity, the standard errors are larger than the actual, and consequently, the t-statistics are low. However, the effect is uncertain given that multicollinearity produces regression coefficients that may be different to their true values and/or signs. For this reason, this relationship should be treated with care.
Similarly, columns 6 and 13 show regressions with multicollinear predictors that produce statistically significant coefficients at the 5% level for the contemporaneous Equity Long Short Index and Equity Long Bias Index, respectively. In addition,
columns 11 and 12 show regressions with statistically significant coefficients at the 5% level for the contemporaneous Merger Arbitrage Index and Multi Strategy Index, respectively. In contrast to the former, these regressions did not produce multicollinear predictors. Hence, the coefficients are more reliable in these regressions. Both of these coefficients have negative values, implying that these hedge fund styles were moving in opposite directions to banking institutions during the financial crisis.
The least significant hedge fund indexes for explaining the Equally Weighted Bank Index are Distressed Securities and Global Macro (columns 4 and 10,
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respectively). Nevertheless, the regression that contains Distressed Securities as an explanatory variable showed that it suffered from multicollinearity. This implies that due to the larger standard errors, the t-statistic has a small value. Not surprisingly, Global Macro was the most uncorrelated to the banking sector during the crisis period. According to Casano (2010), this strategy usually has low correlation to equities; and it differentiated itself from other strategies in terms of outperforming the equity markets and diversifying risks of institutional portfolios during the financial crisis. These managers carry positions that reflect their views on overall market direction as
influenced by major economic trends and events. Another hedge fund index that proves to be very insignificant for explaining the Equally Weighted Bank Index is the Fixed Income Arbitrage. The regression that contains this hedge fund index does not suffer from multicollinearity, implying that the insignificance of the coefficient is not misleading. However, this is not surprising due to the fact that this index is usually categorized under market neutral strategies. The managers who follow the Fixed Income Arbitrage strategy trade globally with the goal of generating steady returns with low volatility.
The most notable result in Figure 6 is illustrated in column 7. In this regression, which showed explanatory variables free from multicollinearity, the contemporaneous Equity Market Neutral Index is significant at the 1% level. Also, it is remarkable the fact that this regression has the highest adjusted R2, with a value of 84%. This implies that Equity Market Neutral yields the highest explanatory power. It is quite surprising the fact that this particular index provides the highest explanatory power among all the hedge fund indexes, given that the objective of this strategy is to avoid exposures to market movements.
In general terms, the regressions in Figure 6 proved to have high explanatory power, with adjusted R2’s ranging from 66% to 84%, even if we discard the regressions with collinear predictors. Inspecting again the first column, it is apparent that S&P 500 provides most of the explanatory power. However, the adjusted R2 increases in the regressions that hedge fund indexes are added. This implies that hedge fund indexes do in fact provide explanatory power, even if it is small. With an adjusted R2 value of 84%, we can conclude that the regression in column 7 provides the highest explanatory power.
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Figure 6. Regressions of monthly equally weighted bank index returns on the S&P 500 and various hedge fund index returns
Equally Weighted Bank Index
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) SP500 0.976 1.511 1.097 1.110 1.392 1.497 1.009 1.254 1.058 1.160 1.330 1.134 1.735 1.460 (5.55)** (5.08)** (4.96)** (3.25)** (4.28)** (6.26)** (7.67)** (3.63) ** (5.23) ** (6.27) ** (6.03) ** (5.29) ** (4.85) ** (4.17) ** SP500(1) 0.075 0.138 0.107 0.217 0.032 0.270 -0.020 0.211 0.076 0.071 0.193 0.140 0.250 0.051 (0.38) (0.53) (0.55) (0.82) (0.11) (1.17) (0.15) (0.83) (0.38) (0.36) (0.85) (0.73) (0.76) (0.14) SP500(2) -0.105 -0.072 -0.373 -0.289 -0.031 0.059 0.081 -0.044 -0.280 0.099 -0.202 -0.276 -0.225 -0.356 (0.58) (0.21) (1.81) (0.74) (0.08) (0.21) (0.62) (0.11) (1.24) (0.51) (0.86) (1.25) (0.52) (1.05) Barclay Hedge Fund -1.419 (2.56)* Barclay Hedge Fund (1) 0.061 (0.11) Barclay Hedge Fund (2) 0.041 (0.06) Convert. Arbit. -0.733 (1.99) Convert. Arbit. (1) 0.304 (0.67) Convert. Arbit. (2) 0.448 (1.14) Dist. Secur. -0.854 (1.36) Dist. Secur. (1) 0.285 (0.44) Dist. Secur. (2) 0.416 (0.74) Emerg. Markets -0.576 (1.72) Emerg. Markets (1) 0.097 (0.29) Emerg. Markets (2) -0.016 (0.04) Equity -1.968
25 Long Short (2.87)* Equity Long Short (1) -0.673 (0.99) Equity Long Short (2) -0.407 (0.52) Equity Market Neutral -2.593 (4.25)** Equity Market Neutral (1) -0.895 (1.54) Equity Market Neutral (2) -0.306 (0.51) Event Driven -0.977 (1.48) Event Driven (1) -0.211 (0.31) Event Driven (2) 0.036 (0.04) Fixed Income Arb. -0.619 (1.61) Fixed Income Arb. (1) 0.511 (1.37) Fixed Income Arb. (2) 0.385 (1.06) Global Macro -0.868 (1.38) Global Macro (1) -0.603 (1.02) Global Macro (2) -1.128 (1.91) Merger Arb. -2.449
26 (2.57) * Merger Arb. (1) -0.757 (0.85) Merger Arb. (2) 0.308 (0.32) Multi Strat. -1.184 (2.60) * Multi Strat. (1) 0.247 (0.52) Multi Strat. (2) 0.514 (1.00) Equity Long Bias -1.396 (2.79) * Equity Long Bias (1) -0.001 (0.00) Equity Long Bias (2) 0.215 (0.37) Equity Short Bias 0.769 (1.58) Equity Short Bias (1) 0.018 (0.04) Equity Short Bias (2) -0.332 (0.70) Cons. -0.004 0.000 -0.004 -0.004 -0.001 0.005 -0.004 0.002 -0.003 0.011 0.006 -0.005 0.001 -0.007 (0.38) (0.04) (0.43) (0.38) (0.10) (0.48) (0.45) (0.14) (0.27) (0.89) (0.46) (0.42) (0.05) (0.57) Obs. 21 21 21 21 21 21 21 21 21 21 21 21 21 21 Adj. R2 0.66 0.72 0.76 0.68 0.66 0.75 0.84 0.65 0.72 0.71 0.74 0.75 0.74 0.66 Durbin-Watson d-stat. 1.549 1.393 2.060 1.708 1.347 1.403 2.046 1.453 1.909 1.473 1.826 1.685 1.500 1.762
Absolute value of t-statistics in parentheses
* significant at 5% level; ** significant at 1% level
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As opposed to Figure 6, Figure 7 shows the corresponding regression results for the Value Weighted Bank Index. As in the previous case, we can observe in the first column that the contemporaneous S&P 500 returns are significant at the 1% level. In this case, the results suggest that larger banking institutions were exposed to market risk during the period of study. The lagged coefficients are not significant. Again, this implies, according to Chan et al. (2007), that there is little illiquidity exposure. In this case, it is more plausible than in the previous the fact that there is little illiquidity
exposure given that the Value Weighted Bank Index consists mostly of the largest banks and bank holding companies.
There is a remarkable feature in the next 13 columns of Figure 7 that must be noted. Similarities among hedge fund indexes that produced insignificant coefficients emerge. Firstly, columns 2, 4, 5, 8 and 14 exhibit the coefficients for Barclay Hedge Fund, Distressed Securities, Emerging Markets, Event Driven and Equity Short Bias, respectively. These hedge fund indexes proved to be highly correlated to S&P 500, and consequently, presented a multicollinearity problem in their corresponding regressions. As noted above, this implies that t-statistics are lower than their true value. For this reason, inferences regarding these regressions should not be conclusive. Secondly, Convertible Arbitrage and Fixed Income Arbitrage (columns 3 and 9) also exhibit insignificant coefficients. This is not surprising due to the fact that both styles follow market neutral strategies in which the objective is to search for arbitrage or relative value opportunities and to avoid market exposures. Lastly, Global Macro (column 10) is not significant given that this strategy outperformed other investment strategies by maintaining low correlation to equities during this period.
Columns 6 and 13 show the results for the regressions using Equity Long Short and Equity Long Bias, respectively, as explanatory variables. Again, it should be noted that, even when both regressions presented multicollinearity problems, these two hedge fund indexes produced significant coefficients at the 5% level. The same result can be noted in Figure 6, implying that both large and smaller banking institutions were exposed to these two hedge fund strategies during the crisis. Similarly, column 12 exhibits a significant coefficient at the 5% level for the contemporaneous Multi Strategy.
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The two hedge fund indexes that provide most of the explanatory power in this set of regressions are Equity Market Neutral and Merger Arbitrage (columns 7 and 11, respectively) with significant coefficients at the 1% level. Additionally, the regressions that used these two strategies as predictors produced the highest adjusted R2’s, with values of 82% and 80%, respectively. The majority of the regressions in Figure 7 produced higher adjusted R2 values than the regressions showed in Figure 6. This could imply that large banking institutions have more in common with the majority of the hedge fund indexes. However, by inspecting the first column of Figure 7, it can be noted that S&P 500 seems to be providing the additional explanatory power. By taking this feature into account, it can be observed that more hedge fund indexes provided higher explanatory power to the Equally Weighted Bank Index, implying that smaller banks were more exposed during this period.
The last row of Figures 6 and 7 show the results for the Durbin Watson d-statistic, which tests for autocorrelation in the error terms. The null hypothesis of the test is that there is no first order autocorrelation. The d-statistic can take values between 0 and 4, with null d equal to 2. As shown in both figures, the d-statistics for all the regressions were far from the extremes and closer to a value of 2. In all cases, we fail to reject the null hypothesis at the 5% level. Additionally, I perform the Breusch Pagan/ Cook Weisberg test for heteroskedasticity. The null hypothesis is that the variance of the error terms is constant. Likewise, we fail to reject the null in all cases.
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Figure 7. Regressions of monthly value weighted bank index returns on the S&P 500 and various hedge fund index returns
Value Weighted Bank Index
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) SP500 1.542 2.258 1.812 2.060 1.980 2.209 1.607 1.929 1.737 1.776 2.078 1.892 2.635 1.979 (5.99)** (4.96)** (5.18)** (4.01)** (3.95)** (5.91)** (7.59)** (3.82) ** (5.34) ** (6.53) ** (7.06) ** (6.12) ** (4.92) ** (3.77) ** SP500(1) 0.085 0.274 0.084 0.287 0.251 0.366 -0.039 0.260 0.172 0.150 0.281 0.155 0.385 0.048 (0.30) (0.68) (0.27) (0.72) (0.56) (1.02) (0.18) (0.70) (0.54) (0.52) (0.92) (0.56) (0.79) (0.09) SP500(2) 0.062 0.171 -0.195 0.288 0.178 0.276 0.309 0.106 0.003 0.294 -0.211 -0.069 -0.029 -0.474 (0.23) (0.33) (0.60) (0.49) (0.31) (0.64) (1.47) (0.18) (0.01) (1.03) (0.67) (0.22) (0.04) (0.94) Barclay Hedge Fund -1.801 (2.12) Barclay Hedge Fund (1) -0.248 (0.29) Barclay Hedge Fund (2) -0.015 (0.02) Convert. Arbit. -1.134 (1.94) Convert. Arbit. (1) 0.605 (0.84) Convert. Arbit. (2) 0.294 (0.48) Dist. Secur. -1.497 (1.58) Dist. Secur. (1) 0.378 (0.39) Dist. Secur. (2) -0.445 (0.52) Emerg. Markets -0.526 (1.02) Emerg. Markets (1) -0.239 (0.46) Emerg. Markets (2) -0.005 (0.01) Equity Long -2.515
30 Short (2.35)* Equity Long Short (1) -0.998 (0.94) Equity Long Short (2) -0.511 (0.42) Equity Market Neutral -3.528 (3.59)** Equity Market Neutral (1) -1.014 (1.09) Equity Market Neutral (2) -0.776 (0.80) Event Driven -1.460 (1.52) Event Driven (1) -0.163 (0.16) Event Driven (2) 0.125 (0.09) Fixed Income Arb. -0.915 (1.48) Fixed Income Arb. (1) 0.235 (0.39) Fixed Income Arb. (2) 0.295 (0.51) Global Macro -1.459 (1.58) Global Macro (1) -1.312 (1.50) Global Macro (2) -1.207 (1.39) Merger Arb. -3.972 (3.13) **
31 Merger Arb. (1) -1.149 (0.96) Merger Arb. (2) 1.144 (0.90) Multi Strat. -1.920 (2.93) * Multi Strat. (1) 0.479 (0.69) Multi Strat. (2) 0.333 (0.45) Equity Long Bias -1.966 (2.63) * Equity Long Bias (1) -0.115 (0.16) Equity Long Bias (2) 0.213 (0.25) Equity Short Bias 0.680 (0.94) Equity Short Bias (1) 0.009 (0.01) Equity Short Bias (2) -0.832 (1.17) Cons. 0.027 0.036 0.030 0.025 0.033 0.041 0.029 0.036 0.028 0.049 0.040 0.030 0.036 0.029 (1.61) (1.94) (1.79) (1.46) (1.60) (2.29)* (2.23)* (1.63) (1.61) (2.65) * (2.34) * (1.93) (2.04) (1.48) Obs. 21 21 21 21 21 21 21 21 21 21 21 21 21 21 Adj. R2 0.68 0.72 0.74 0.68 0.65 0.74 0.82 0.67 0.69 0.73 0.80 0.77 0.75 0.67 Durbin-Watson d-stat. 2.113 2.084 2.544 1.924 2.137 1.966 2.403 1.871 2.577 2.413 2.197 2.024 2.010 2.383
Absolute value of t-statistics in parentheses
* significant at 5% level; ** significant at 1% level
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Given that my assessment of multicollinearity determined that it exists in some of the previous regressions, decisive statements may not be surely reliable. For this reason, I go further in aims to eliminate the problem. Then, I group the previously used hedge fund indexes, by assigning equal weights to each one of them, and construct new ones that are not highly correlated with S&P 500. The new indexes are grouped by the similarities of the strategies used. For instance, hedge funds that generally intend to anticipate market movements and provide high returns proportionate with the high risks and leverage they use are said to follow directional strategies. On the contrary, hedge funds that follow neutral strategies generally look for arbitrage and relative value opportunities in order to exploit price discrepancies. Additionally, their objective is to avoid exposure to market-wide movements.
In this context, I construct three indexes, and I call them: Directional Strategies Index, Neutral Strategies Index and Event Driven/Equity Biases Index, which have correlations of 0.66, 0.61 and 0.63, respectively, with the S&P 500. Directional Strategies Index contains the following previously used indexes: Global Macro and Equity Long Short. Similarly, Neutral Strategies is formed by Convertible Arbitrage, Equity Market Neutral and Fixed Income Arbitrage. Lastly, Event Driven/Equity Biases Index contains Distressed Securities, Merger Arbitrage, Equity Long Bias and Equity Short Bias. This last newly constructed index is a combination of hedge funds that follow event driven strategies and equity biases. Event driven strategies usually carry positions with medium volatility and low to medium leverage. The name derives from the fact that these funds obtain most of the profits by investing in companies that undergo special “events”, e.g., bankruptcies, mergers and acquisitions. The equity biases, in turn, maintain net short (long) exposures to the market and attempt to obtain profits when the market declines (rises). Next, I follow equivalent dynamics to the previously performed regressions.
Figure 8 shows regressions for the Equally Weighted Bank Index. It can be noted that Neutral Strategies provide the highest explanatory power, with the most significant coefficient at the 1% level and the highest adjusted R2value of 79%, implying that smaller banking institutions have higher exposure to market neutral strategies. However, by looking back at Figure 6, it can be noted that Equity Market Neutral is most likely providing the higher explanatory power, since it is contained in
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the Neutral Strategies Index. Additionally, Directional Strategies also seem to provide some explanatory power.
In Figure 9 I illustrate similar regressions for the Value Weighted Bank Index. These regression results show that larger banks are exposed to the three different hedge fund indexes at the 5% level. Directional Strategies seem to provide similar explanatory power in both cases. Once again, Neutral Strategies seem to provide higher explanatory power for the Equally Weighted bank Index. However, new insights emerge. We must observe that Event Driven/Equity Biases is significant for larger banks but not for smaller ones, and also the adjusted R2 is higher by 7%. Bearing in mind that Event Driven/Equity Biases contains the Merger Arbitrage hedge fund index, and going back to Figures 6 and 7, we can acknowledge the fact that this index has a much greater effect on large banking institutions.
Similar to the previous figures, the last row of Figures 8 and 9 show the Durbin Watson d-statistic. Likewise, we fail to reject the null hypothesis at the 5% level in all cases. Also, we fail to reject the hypothesis that the variance of the error terms is constant, in all cases.
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Figure 8. Regressions of monthly equally weighted bank index returns on the S&P 500 and newly constructed hedge fund index returns
Equally Weighted Bank Index
Directional Strategies Neutral Strategies Event Driven/Equity
Biases SP 500 1.373 1.195 1.191 (6.61)** (6.13)** (4.06)** SP 500 (1) 0.191 0.105 0.299 (0.93) (0.61) (1.26) SP 500 (2) 0.208 -0.208 -0.034 (0.92) (1.07) (0.10) Directional Strat. -1.608 (2.36)* Directional Strat. (1) -0.950 (1.45) Directional Strat. (2) -1.172 (1.66) Neutral Strat. -1.511 (3.07)** Neutral Strat. (1) 0.729 (1.37) Neutral Strat. (2) 0.293 (0.57) Event Driven/Equity Biases -2.279 (1.82) Event Driven/Equity Biases (1) -0.157 (0.13) Event Driven/Equity Biases (2) 0.272 (0.22) Constant 0.013 -0.003 0.003 (1.06) (0.32) (0.20) Observations 21 21 21 Adjusted R2 0.75 0.79 0.68 Durbin-Watson d-stat. 1.468 1.779 1.521
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Figure 9. Regressions of monthly value weighted bank index returns on the S&P 500 and newly constructed hedge fund index returns
Value Weighted Bank Index
Directional Strategies Neutral Strategies Event Driven/Equity
Biases SP 500 2.07 1.915 2.250 (6.67)** (6.06)** (5.77)** SP 500 (1) 0.315 0.141 0.411 (1.03) (0.51) (1.31) SP 500 (2) 0.441 0.040 0.597 (1.31) (0.13) (1.34) Directional Strat. -2.293 (2.25)* Directional Strat. (1) -1.634 (1.67) Directional Strat. (2) -1.342 (1.27) Neutral Strat. -2.077 (2.60)* Neutral Strat. (1) 0.812 (0.94) Neutral Strat. (2) 0.062 (0.07) Event Driven/Equity Biases -4.538 (2.73)* Event Driven/Equity Biases (1) -0.279 (0.18) Event Driven/Equity Biases (2) -1.671 (1.02) Constant 0.051 0.031 0.052 (2.83)* (2.02) (2.65)* Observations 21 21 21 Adjusted R2 0.75 0.76 0.75 Durbin-Watson d-statistic 2.307 2.465 1.770
Absolute value of t-statistics in parentheses
