Essays on Mutual Fund Performance

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(2) Ekonomi och samhälle Economics and Society Skrifter utgivna vid Svenska handelshögskolan Publications of the Hanken School of Economics. Nr 301. David Humberto González Osorio. Essays on Mutual Fund Performance. Helsinki 2016.

(3) Essays on Mutual Fund Performance. Key words: Mutual Fund Performance. © Hanken School of Economics & David Humberto González Osorio, 2016. David Humberto González Osorio Hanken School of Economics Department of Finance and Statistics P.O.Box 287, 65101 Vaasa, Finland. Hanken School of Economics ISBN 978-952-232-310-1 (printed) ISBN 978-952-232-311-8 (PDF) ISSN-L 0424-7256 ISSN 0424-7256 (printed) ISSN 2242-699X (PDF). Juvenes Print – Suomen Yliopistopaino Oy, Tampere 2016.

(4) i. in nomine Patris, et Filii, et Spiritus Sancti..

(5) ii. PREFACE I would like to thank my supervisor, Professor Johan Knif for his support and guidance. I thank Professor Kenneth Hogholm for giving me advice and direction. Thank you Johan and Kenneth for allow me to teach and assist in several courses during my years at Hanken. The experience I have accumulated is invaluable. I thank the external reviewers of the Dissertation, Professor Wolfgang Bessler and Professor Timo Rothovius. Your insightful comments help me to improve in great manner my research. I am especially grateful with the Department of Finance at Hanken, the Hanken Foundation and the WCEFIR fund for supporting me financially during this quest. I am thankful to fellow students and Professors at the Department for spending some time reading earlier versions of the manuscripts and given valuable comments in the internal seminars. Thanks to Mujahid, Ihsan, Annand, Hilal, Nader, Saint, Nasib, Gbenga, Mo, Fredrik, and Jesper. I thank my siblings, Sandra and Andrés, for their continued support and for encourage me to not give up. Thanks to my mom for her wisdom and faith. Thanks to my late father for inspiring me. Thanks to Mariana and Nicolás for giving me the strength to overcome my weaknesses. Special thanks to Rocío, my lovely wife. Thank you for believe in me. I truly appreciate your sacrifices while you join me in this journey far from home. Finally, thanks God for bringing me to the end of this stage in my life..

(6) CONTENTS FIRST PART BACKGROUND, METHODOLOGY AND FINDINGS 1 INTRODUCTION.......................................................................................1 2 LITERATURE OVERVIEW ...................................................................... 4 3 THE MUTUAL FUND INDUSTRY IN THE U.S...................................... 6 4 MUTUAL FUND PERFORMANCE AND PERSISTENCE .................... 10 5 NETWORKS IN FINANCE ...................................................................... 11 6 CENTRALITY MEASURES .....................................................................13 7 MUTUAL FUND NETWORK .................................................................. 17 8 SUMMARY OF ESSAYS ......................................................................... 24 8.1. The effect of network characteristics on mutual fund performance .................24. 8.2. Performance persistence and the mutual fund network ...................................24. 8.3. Empirical analysis on mutual funds herd behavior using a network approach25. REFERENCES ............................................................................................ 27 SECOND PART THE ESSAYS 1 THE EFFECT OF NETWORK CHARACTERISTICS ON MUTUAL FUND PERFORMANCE…………………………………………………………………………....33 2 PERFORMANCE PERSISTENCE AND THE MUTUAL FUND NETWORK…………………………………………………………………………………….95 3 EMPIRICAL ANALYSIS ON MUTUAL FUND HERD BEHAVIOR USING A NETWORK APPROACH………………………………………………..…127.

(7) FIRST PART BACKGROUND, METHODOLOGY AND FINDINGS.

(8) 1. 1. INTRODUCTION. There is plenty of research on mutual fund performance. Various questions have been raised and some have been answered although not all researchers concur with the findings. The US is without hesitation the most studied market. The abundance of data and general presumption about good data quality have helped researchers to evaluate hypotheses about how financial markets work. Two examples are the test of the efficient market hypothesis and the evaluation of performance in the mutual fund industry. As Chang and Lewellen (1984) mentioned, collective performance is relevant to the efficient market hypothesis while individual funds performance is relevant for evaluating the performance of the mutual funds. In the literature the question of whether actively managed mutual funds perform better than index funds has been studied extensively; if actively managed funds charge higher fees than passive funds, an investor should expect higher returns, net of expenses from actively managed funds. If actively managed funds cannot outperform the market, there is no obvious reason to invest in those funds. Solving questions regarding performance of mutual funds is not an easy task and there is no agreement on how to measure performance. Since the early 1960s numerous measures have been proposed; in some cases, studies have reached contradictory conclusions, depending on the performance measurements utilized. Perhaps the most interesting phenomenon that researchers have investigated is the existence of persistent outperformance and therefore, whether “gifted” managers exist that can transform stones into gold: are there alchemist fund managers that can consistently outperform the market and create wealth at will? More to the point how we can find them? To obtain an answer we need to know when a stone can be considered gold or just a stone. But establishing outperformance depends on different issues, one of which is how performance is measured. Other concerns are related to how performance is calculated. Performance can be calculated for individual funds or portfolios. When the time horizon varies, different results have been proved; and the results also depend on the type of funds included in the assessment; such as dead funds, new funds, and small funds. Many other factors can be considered too. Later in this introductory chapter, a brief review of the previous literature helps to illustrate some of the challenges that researchers have faced when studying mutual fund performance. Evidence of outperformance is not necessarily explained by the existence of talented managers. Under the assumption that all managers have equally access to the same information, funds can outperform the market simply because of luck. The idea that information is available for free to all participants in the market creates a paradox: why should an investor spend money gathering information, researching, and analyzing it when the result is not an advantage? An advantage should exist and funds with an informational advantage should produce better returns. Because investigating mutual fund performance is a very competitive field in financial research, finding anything new to say is a challenge. In this dissertation, we elaborate on some observations made by Brown and Goetzmann (1995). The authors found that on a year-by-year basis, funds are usually consistent winners or losers but sometimes reversals occur. According to the authors, one reason that could explain those reversals is that “…persistence is correlated across managers. Consequently, it is likely due to a common strategy that is not captured by standard stylistic categories or risk.

(9) 2. adjustment procedures.” 1 They suggested that future research should investigate “… issues of cross-fund correlation…”2 In that sense, to address the issue of performance in the mutual fund industry, it must be very helpful to use a network approach based on cross-fund correlation to calculate metrics that can help to describe the existence of common features not captured by common factors. Even though Brown and Goetzmann (1995) were interested in the study of mutual fund persistence, we consider it important to investigate initially how measures of the mutual fund network are related to abnormal performance in mutual funds. Previous studies have found that measurements of performance adjusted by risk factors are explained by some fund characteristics, like size, age, expenses and turnover. In the first essay of this dissertation we argue that performance is also explained by other features of the funds related to informational linkages. Grossman (1976) showed that in order to have incentives to collect information, traders should be able to hide it from other traders. We argue that managers with different types of information will invest differently. In the same line of argument, managers with access to only free public information and poor private information should behave similarly, and their investments should perform close to the market, while managers of the type that holds quality private information should outperform the market. In that sense, funds with similar type of information will be correlated. We propose that informational linkages can be approximated by measurements of centrality in a network of mutual funds. Centrality of a fund in the network, as explained later, can be interpreted as a measure of how closely correlated the returns of a fund are to other funds in the market. In the second essay we build on the foundations of the first essay to include measures of the mutual fund network in order to establish a link between persistence and correlation across funds. If there are informational linkages, those connections could help to test for persistence. The reasoning is simple. Suppose that a number of funds have access to similar private information and assume that managers will interpret that information in the same way. Then, we expect that the returns of those funds will be correlated to each other; if the returns of those funds were correlated by luck, it is expected that in the next period, those linkages will disappear. However, when those linkages remain from one period to another, we can consider that the returns of the funds are not correlated by chance and we expect to find persistence. Finally, we consider how correlation across funds can help to explain herd behavior in the mutual fund industry. The third essay argues that an aggregate centrality measure in the network of mutual funds could signal the existence of herd behavior in the market. This dissertation specifically studies performance in the mutual fund industry utilizing a network approach to address the following three questions. Do the characteristics of the mutual fund network help to explain the performance of mutual funds? Is the position of a mutual fund in the network related to persistence of abnormal performance of the fund? Do changes in the structure of the network of mutual funds signal the presence of herd behavior? Individually, the essays contribute to the study of mutual funds by adding a newer perspective to the field of finance. The three essays endorse the idea that the network of 1. Brown and Goetzmann (1995:680). 2. Brown and Goetzmann (1995:680).

(10) 3. mutual funds shaped by different frequencies contains information that certainly plays a part in answering the questions proposed. Specific characteristics of the network of mutual funds are related to performance, while centrality of a mutual fund is related to persistence of abnormal performance and changes in average degree centrality signal the presence of herd behavior..

(11) 4. 2. LITERATURE OVERVIEW. Since the early 1960s, researchers have studied the mutual fund industry extensively. The main concern about testing for performance was to find the proper approach to measure performance. Innovations related to the formulation of the asset-pricing model led to developments in the study of mutual fund performance. Friend and Vickers (1965) proposed and developed tests for measuring performance based on performance and risk. Similarly, Treynor (1965) suggested a measure of performance that accounts for the volatility of the fund and Sharpe (1966) tested the performance measure proposed by Treynor (1965). Jensen (1968) used a measure of performance ߙ௝ from the equation ܴ෨௝௧ െ ܴி௧ ൌ ߙ௝ ൅ ߚ௝ ሾܴ෨ெ௧ െ ܴி௧ ሿ ൅ ‫ݑ‬෤௝௧ ; Jensen (1969) proposed a model to evaluate performance in portfolios such as those held by mutual funds and based his model on the work of Lintner (1965) and Sharpe (1964). A common result of most of those initial studies was to find no evidence against the acceptance of the classic asset-pricing model; the existence of positive alphas was ruled out. In addition, the work by Jensen (1969) found that the asset pricing model holds, and therefore, outperformance of mutual funds can be dismissed. In the 1970s, as mentioned by Malkiel (1995), the efficient market hypothesis was broadly accepted and the acknowledgement that past information did not help to predict future movements of stock prices was implied. Carlson (1970) found no evidence of outperformance and found that outperformance depends on the definition of market and the time period. In the 1980s, some studies found evidence of market timing ability; Henriksson and Merton (1981) and Henriksson (1984) are some examples. The latter found no evidence of market timing during 1968–1980. Chang and Lewellen (1984) found that some managers have market timing ability but there was no evidence of collective outperformance. Studies like Grossman and Stiglitz (1980) elaborated on the issue of information and efficient markets; they argued that the cost of information is in conflict with the idea of efficiency in the market. The importance of the benchmarks used to estimate performance was evaluated by Lehmann and Modest (1987). They argued that the measure of performance is sensible to the asset-pricing model and different benchmarks have a significant effect on measuring performance. In addition, Grinblatt and Titman (1994) evaluated different benchmarks to calculate performance and found a significant effect depending on the benchmark. According to their results, funds on average have negative performance, which is significantly related to turnover but not to size, expense ratios, management fees, and load. In a previous study, Connor and Korajczyk (1991) found that measures of performance are influenced by size. Survivorship bias is an issue that has been widely discussed in the literature. Nowadays, most studies need to have settled this issue by using datasets free of survivorship bias. Malkiel (1995) found that the effect of survivorship bias is significant in the results; the author found no evidence of outperformance. Brown and Goetzmann (1995) studied performance persistence with a dataset partially free of survivorship bias. They established that the time period of study affects the results and that there is relative performance persistence. Interestingly, they found a correlation in winning strategies explained by unknown common factors. In that sense, links in the mutual fund network based on correlation in returns can be considered an approximation to those related factors..

(12) 5. Some studies have found that investing in funds that outperform the previous year results in a winning strategy. Hendricks and Zeckhauser (1993) found that during 1975– 1988, funds that had outperformed the previous year were likely to outperform the next year; good advice would have been to abstain from investing in funds that perform poorly the year before. In addition, Goetzmann and Ibbotson (1994) using data for 1976–1988 found evidence of a successful repeat-winner strategy. Like Grinblatt and Titman (1992) mentioned, the industry gives a lot of consideration to past indicators in order to assess future performance, and thus, it is relevant to evaluate how past performance is related to future performance. The authors proved the existence of positive persistence in mutual fund performance. Elton, Gruber, and Blake (1996) found evidence of predictive past performance, revealing that expenses are related to performance. Carhart (1997) argued that persistence in returns is explained by the 1-year momentum effect. In addition, performance is negatively related to expenses, turnover, and load fees. Grinblatt and Titman (1989a) proposed an alternative measure of performance. The authors investigated abnormal returns using gross returns and found evidence of outperformance. They explained that this occurs because skillful managers should charge higher fees; however, outperformance disappears with net returns (Grinblatt and Titman, 1989b). Similarly, Ippolito (1989) found evidence of outperformance before load charges and no evidence of any effect from expenses and turnover in performance. Contrary to this finding, Elton, Gruber, Das, and Hlavka (1993) found that the metric used by Ippolito (1989) mistakenly did not account for the performance of non-S&P assets. The authors used a new metric and found evidence of underperformance. In addition, higher fees and turnover are related to underperforming funds. Ippolito (1993) critically reviewed some studies on mutual fund performance and argued that performance of actively managed funds does not differ significantly from index funds. In the same way, Wermers (2000) claimed that most research shows actively managed funds on average underperform passively managed funds; however, some studies have found that funds sharing some characteristics outperform their benchmarks. Wermers (2000) found that portfolios held by mutual funds outperform the market; portfolios net of costs and expenses underperform the market owing in part to lower return of non-stock holdings. The author found that funds with high turnover hold stocks with higher average returns. According to Cuthbertson, Nitzsche, and O’Sullivan (2010), there are two main avenues of research related to mutual fund performance; one is linked to debating the existence of positive abnormal performance obtained by investors, and the other is concerned with the identification beforehand of abnormal performance and its persistence. More recently, researchers, like Carhart (1997), have estimated performance using factor models, which include a market factor, a size factor, a book-to-market factor, and a momentum factor. Fama and French (2015) proposed a factor model that does not include a momentum factor but includes two additional factors: difference in returns for portfolios with robust and weak profitability, and returns of a portfolio representing the difference between conservative and aggressive stocks. In this dissertation, we use the Carhart (1997) factor model to estimate performance; in addition, in the first essay, we use Fama and French (2015); the results obtained using both models help to achieve robustness of the results..

(13) 6. 3. THE MUTUAL FUND INDUSTRY IN THE US. According to Rouwenhorst (2004), the beginnings of the mutual fund industry can be traced back to Holland. At the end of the 18th century, Amsterdam was a vibrant financial center where the securities of dozens of companies were traded and governments obtained financing at low rates. The first mutual fund was established by a broker in order to give small investors access to a diversified portfolio. Nowadays mutual funds serve the same purpose; they represent a safe strategy for small investors to gain access to diversified and liquid portfolios. Initially, the main investments in such portfolios were foreign government bonds, bank bonds, and plantation loans3. After the initial fund, several others were established in Holland, some with relative success4. Almost a century passed before the first mutual fund was established in the United Kingdom (UK) while in the United States (US), investment trusts started at the end of the 19th century. Since then, the importance of mutual funds in the asset portfolio of US households has increased notably. These days, investment companies in the US include exchange-traded funds (ETFs), close-end funds, unit investment trusts (UIT), and open-end funds, also known as mutual funds (Investment Company Institute, 2015). During the 20th century, the bulk of investment companies were mutual funds and still are; however, in recent years, ETFs have gained popularity and have increased as a proportion of the total assets of investment companies (Figure 1). At the end of 2014, mutual funds represented more than 85% of the assets hold by investment companies. Mutual funds are characterized by the fact that they issue redeemable shares that investors can sell to the fund at their net asset value (NAV)5. Close-end funds differ from mutual funds because the number of shares issued is fixed even though additional shares can be issued in the secondary market. Shares of close-end funds are listed on stock exchanges and trade at market value. As shown in Figure 1, the amount of assets invested in close-end funds is small, less than 2% of the total assets of investment companies. ETFs can be bought and sold on an intraday basis on stock exchanges at prices determined by the market. Most ETFs are open-end funds. Market prices for these funds differ from the NAV of the fund for different reasons, mainly because of changes in supply and demand. Managers of ETFs are obliged to make daily disclosures about the investments made by the funds, and thus, market participants can estimate deviations of the market value of the fund from its components. UITs are a hybrid type of investment companies that have a predetermined termination date and redeemable shares usually issued in fixed numbers. As seen in Figure 1, UIT funds represent a minuscule proportion of investment companies. In addition, mutual funds can be classified according to the type of investments made by the fund (domestic equities, equities in international markets, fixed income, municipal According to Rouwenhorst (2004), in July 1774, an investment vehicle called Eendragt Maakt Magt was established with the aim of investing in a diversified portfolio. The investment was open to the public with a total of 2,000 shares.. 3. Rouwenhorst (2004) wrote that in 1779, Abraham van Ketwich, the broker who established the first mutual fund, founded the Concordia Res Parvae Crescunt fund, which existed for 114 years, and according to the author, may be the mutual fund that has existed for the longest period.. 4. NAV is calculated as the ratio between the market value of the investments of the fund (net of liabilities) and the number of shares issued by the fund.. 5.

(14) 7. bonds, etc.). Furthermore, mutual funds can be divided into actively and passively managed funds. Decisions by managers of active funds are expected to have a positive impact on fund performance; ordinarily it is thought that managers either have better information than the market or are skillful professionals who can interpret in a better way the information available in the market. On the other hand, managers of passive funds do not need to spend time trying to beat the market because their objective is to construct a portfolio that resembles some benchmark. In this research, we focus on US actively managed funds that invest in domestic equities.. 12%. 98% 96% 94%. 8%. Mutual Funds. 92% 6%. 90% 88%. 4% 86% 2%. Closed-end Funds, ETF and UIT. 10%. 84% 0%. Mutual Funds. Closed-end funds. ETF. 2013. 2014. 2012. 2011. 2010. 2009. 2008. 2007. 2006. 2005. 2003. 2004. 2001. 2002. 1999. 2000. 1997. 1998. 1996. 82%. UIT. Figure 1 Investment Companies. Total Net Assets by Type. Source: Calculations based on data from the Investment Company Institute (2015) and the Federal Reserve Board (2015)..

(15) 8. In the US, for most of the 20th century, shares owned by households in mutual funds represented less than 2% of their financial assets. The participation of mutual funds in households’ assets increased notably after 1985 (Figure 2). During the last decades, the mutual fund industry has grown remarkably, increasing its participation in the total assets held by households from 6% to almost 12% (Figure 3). 14%. 12%. 10%. 8%. 6%. 4%. 2%. Mar-14. Mar-12. Mar-10. Mar-08. Mar-06. Mar-04. Mar-02. Mar-00. Mar-98. Mar-96. Mar-94. Mar-92. Mar-90. Mar-88. Mar-86. Mar-84. Mar-82. Mar-80. Mar-78. Mar-76. Mar-74. Mar-72. Mar-70. Mar-68. Mar-66. Mar-64. Mar-62. Mar-60. Mar-58. Mar-56. Mar-54. Mar-52. 0%. Mutual Fund Assets as % of household financial assets. Figure 2. Participation of mutual fund assets in the total financial assets households. 1952Q1 – 2014Q4.. Share of mutual fund assets held by households. 50%. 12% 11%. 45%. 10% 40% 9% 35% 8% 30% 7% 25%. 6%. 20% 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014. 5%. Mutual fund assets as % of household financial assets. Source: Calculations based on data from the Federal Reserve Board (2015).. Share of mutual fund assets held by households Mutual fund assets as % of household financial assets. Figure 3 Share of mutual fund assets held by households and participation of mutual fund assets in the total financial assets households. Source: Calculations based on data from Investment Company Institute (2015) and the Federal Reserve Board (2015)..

(16) 9. Articles. Mutual Fund Assets as % of household financial assets. 2012. 2009. 2006. 2003. 2000. 0%. 1997. 0. 1994. 2%. 1991. 10. 1988. 4%. 1985. 20. 1982. 6%. 1979. 30. 1976. 8%. 1973. 40. 1970. 10%. 1967. 50. 1964. 12%. 1961. 60. 1958. 14%. 1955. 70. 1952. Number of Articles in last 5 years in the Journal of Finance. While the importance of mutual funds in the US economy has been augmented, the academic interest in the industry has also increased. This interest is reflected in the number of research articles published in academic journals. An approximation is shown in Figure 4, which presents articles related to mutual funds published in the Journal of Finance since 1952. The trend is clear; since the early 1990s, the number of articles has increased steadily, with some interruptions, like the global financial crisis.. % of household financial assets. Figure 4 Number of articles published in the Journal of Finance during the last five years related with mutual funds and participation of mutual fund assets in the total of households financial assets. 1952–2014. Source: American Finance Association (2015) and the Federal Reserve Board (2015)..

(17) 10. 4. MUTUAL FUND PERFORMANCE AND PERSISTENCE. Actively managed funds work under the assumption that talented managers can produce outperforming returns. The question then arises: do actively managed funds outperform the market? Studies like Elton, Gruber, Das, and Hlavka (1993), Malkiel (1995), Barras, Scaillet, and Wermers (2010), and Fama and French (2010) found that on average, actively managed funds underperform the market. Nonetheless, there are funds that outperform the market. Researchers have studied whether those funds persist in their behavior but the conclusions differ. Examples of studies that have found evidence of persistence are Kacperczyk, Sialm, and Zheng (2005), Malkiel (1995), and Kosowski, Timmermann, Wermers, and White (2006). To investigate persistence, authors have used varied approaches, like contingency tables and recursive portfolios. An issue with persistence is that abnormal performance could occur as a result of luck and is not necessarily driven by talented managers. Studies like Barras, Scaillet, and Wermers (2010) and Fama and French (2010) investigated abnormal performance while controlling for luck. We measure abnormal performance as ߙ௜ in a four-factor model proposed by Carhart (1997), ܴ௜௧ െ ܴ௙௧ ൌ ߙ௜ ൅ ߚ଴௜ ൫ܴ௠௧ െ ܴ௙௧ ൯ ൅ ߚଵ௜ ܵ‫ܤܯ‬௧ ൅ ߚଶ௜ ‫ܮܯܪ‬௧ ൅ ߚଷ௜ ‫ܯܱܯ‬௧ ൅ ߝ௜௧ where ܴ௜௧ is the return on fund i in month t, ܴ௙௧ is the risk-free rate in month t, ܴ௠௧ is the market return in month t, ܵ‫ܤܯ‬௧ represents the return on a factor mimicking portfolio for size, ‫ܮܯܪ‬௧ is the variable that mimics the portfolio for book-to-market equity, and ‫ܯܱܯ‬௧ represents the factor that mimics a portfolio for 1-year momentum in stock returns; ߝ௜௧ is the error term. There is abnormal positive performance when ߙ௜ ൐ Ͳ and underperformance when ߙ௜ ൏ Ͳ. When ߙ௜ ൌ Ͳ, there is no abnormal performance. In that context, persistence occurs when ߙ௜ǡ் ൐ Ͳ or ߙ௜ǡ் ൏ Ͳ is repeated for a while. Persistence can be positive or negative. Persistence is positive when ߙ௜ǡ் is always positive or always negative for sequential periods, T+1, … ,T+j. Persistence is negative when ߙ௜ǡ் is positive in T and negative in T+1 or negative in T and positive in T+1..

(18) 11. 5. NETWORKS IN FINANCE. Theory of networks has been used increasingly to solve problems in fields like mathematics, physics, sociology, biology, and economy. A network can be a very useful approach to deal with sets of vast amounts of data. Insightful use of network analysis reduces the complexity of the problem while highlighting the most relevant information. The use of a network approach has proved a useful tool when analyzing different problems in finance as long as they help to reduce the complexity of datasets while keeping the most relevant information available. Allen and Babus (2008) mentioned five topics for which the theory of networks has been used in finance: systemic risk, interbank market, investment decisions, securities, and mutual monitoring. In addition, Nagurney (2008) offered a detailed overview on the uses of networks to solve optimization problems in finance and to study equilibrium in financial systems. Furthermore, some authors have investigated issues in the mutual fund industry by using network analysis. Pareek (2009) defined a network by studying similar stocks included in the portfolio of different funds. The author checked correlated trading and the interaction between location and stock ownership. He evaluated how the information is distributed in the network by using information diffusion measures and centralization measures. Cohen, Frazzini, and Malloy (2008) assumed that managers of mutual funds and executives of traded companies belong to a social network if they attended the same academic institution. The authors found that the portfolio of investments in linked companies outperform investments in non-linked companies. Han and Yang (2011) analyzed the role of social networking in the mutual fund industry by using a rational expectations model. They found that social communications have two contrary effects. On the one hand, if participants are better informed then markets are more efficient; on the other hand, since the information acquired through social networks is free, investors are willing to buy less information, and therefore, markets are less efficient. Hong, Kubik, and Stein (2005) studied the effect of word-of-mouth communication in the composition of portfolios. They found that mutual fund managers tend to buy or sell a stock if other managers in the same city do the same. The authors present different explanations, such as word-of-mouth communication and managers looking at the same news channels or reading the same local papers. Regardless of the format, the idea is that investors receive buying signals from someone close to them. Cohen, Coval, and Pástor (2005) evaluated performance by monitoring managers’ decisions. When decisions resemble those of skilled managers, then the manager should be skilled. A network is a representation of a set of nodes or vertices connected by links. Those connections can be directed or undirected and can have a value that represents a weight, a distance, or a flow. In a network of banks, links could represent flows of interbank funds. In this case, links will have a direction. The analysis of such a network could be derived in conclusions about the stability of the network when a bank disappears. In a network of mutual funds, connections between them may represent a social linkage between their managers. Managers that previously studied at the same university or worked for the same company are linked in the network. The analysis of such a network could result in connected funds that behave similarly. A network is convenient when the problem requires finding the shortest path between two nodes, defining the importance of a node in the network, or measuring the resilience of the network in order to determine the sustainability of a system..

(19) 12. An approach of particular interest for this dissertation was employed by Boginski, Butenko, and Pardalos (2005), Kim, Kim, and Ha (2007), and Heimo, Kaski, and Saramäki (2009). In those studies, the authors built networks for the stock market by defining links between stocks using the coefficient of correlation of returns. A connection between two stocks in a given period exists when the coefficient of correlation between returns of the stocks is larger than a predefined threshold. The resulting network is undirected, and the links do not represent distance or flows but merely a relationship. This approach is highly dependent on the threshold chosen. Central to this dissertation is the definition and construction of the mutual fund network using coefficients of correlation between returns of funds. Another important aspect is the use of centrality measures. In the next sections of this chapter, we define some centrality measures and construct the network of mutual funds for 1992–2007. We describe the network of mutual funds and explore it using different thresholds and centrality measures..

(20) 13. 6. CENTRALITY MEASURES. To understand how to calculate centrality, we propose an example of an undirected network, ‫ ܩ‬ൌ ሾܰǡ ‫ܮ‬ǡ ‫ܣ‬ሿ represented in Figure 5; the network has 12 nodes, ܰ ൌ ሾ‫ݒ‬ଵ ǡ ‫ݒ‬ଶ ǡ ǥ ǡ ‫ݒ‬ଵଶ ሿ, which are connected by 12 links, ‫ ܮ‬ൌ ሾ݁ଵ ǡ ݁ଶ ǡ ǥ ǡ ݁ଵଶ ሿ. An adjacency matrix A, which represents the network, is shown in Table 1; the element ܽ௜௝ ൌ ͳ if nodes i and j are connected and ܽ௜௝ ൌ Ͳ if they are not. We calculate four centrality measures: degree, betweenness, closeness, and eigenvector centrality. The degree of the node ‫ݒ‬௜ corresponds to the number of nodes connected to ‫ݒ‬௜ and is calculated as the sum of the row or column i in the adjacency matrix ௡. ‫ݐ݊݁ܥܦ‬௩೔ ൌ ෍ ܽ௜௝ ௝ୀଵ. A relative measure of degree that takes into account the size of the network is ‫ݐ݊݁ܥܦ‬௩ᇱ ೔ ൌ. σ௡௝ୀଵ ܽ௜௝ ݊െͳ. Ǥ. Betweenness of ‫ݒ‬௞ is defined as ௡. ௡. ‫ݐ݊݁ܥܤ‬௩ೖ ൌ ෍ ෍ ௜ୀଵ ௝ୀଶ. ݃௜௝ ሺ‫ݒ‬௞ ሻ ǡ ݂‫ ݅ݎ݋‬൏ ݆ ݃௜௝. where ݃௜௝ corresponds to the number of geodesics connecting ‫ݒ‬௜ and ‫ݒ‬௝ ; a geodesic is defined as the shortest path connecting i and j. According to Lewis (2009:25), a path is a sequence of connected nodes in G; in the case of nodes ‫ݒ‬ଶ and ‫ ଺ݒ‬, there are only two paths between them, ܲ௩మ ௩ల ൌ ሼሺ݁଻ ǡ ݁ଽ ǡ ݁ଵଵ ሻǡ ሺ଼݁ ǡ ݁ଵଵ ሻሽ, and the shortest path or geodesic is the one that includes only two links ሺ଼݁ ǡ ݁ଵଵ ሻ, as shown in Figure A2. The number of geodesics between ‫ݒ‬௜ and ‫ݒ‬௝ that include one link to ‫ݒ‬௞ is ݃௜௝ ሺ‫ݒ‬௞ ሻ; for example, ݃ଶǡ଺ ሺ‫ݒ‬ଽ ሻ ൌ ͳ and ݃ଶǡ଺ ሺ‫ݒ‬ଵ଴ ሻ ൌ Ͳ, because there is only one geodesic between ‫ݒ‬ଶ and ‫ ଺ݒ‬, and the geodesic includes only ‫ݒ‬ଽ . In the case of ‫ݒ‬ଷ ǡ ‫ݒ‬ହ ǡ ‫ ଺ݒ‬ǡ ‫ ଻ݒ‬ǡ ‫ ଼ݒ‬, and ‫ݒ‬ଵଶ , betweenness is 0 because there is no path between two nodes that includes those vertices; in the case of ‫ݒ‬ଵଵ , betweenness is 10 because there is only one minimum path between every other node and ‫ݒ‬ଵଶ , and all of them pass by ‫ݒ‬ଵଵ . According to Freeman (1978:224), betweenness centrality can achieve a maximum value of ሺ݊ଶ െ ͵݊ ൅ ʹሻΤʹ, and then, the relative measure of betweenness is defined by. ‫ݐ݊݁ܥܤ‬௩ᇱ ೖ ൌ. ݃௜௝ ሺ‫ݒ‬௞ ሻ ൰ ݃௜௝ ǡ ݂‫ ݅ݎ݋‬൏ ݆ ଶ ݊ െ ͵݊ ൅ ʹ. ʹ ൬σ௡௜ୀଵ σ௡௝ୀଶ. The closeness centrality of ‫ݒ‬௜ is the inverse of the distance from ‫ݒ‬௜ to every other node, ‫ݐ݊݁ܥ݈ܥ‬௩೔ ൌ. ͳ Ǥ σ௡௝ୀଵ ݀൫‫ݒ‬௜ ǡ ‫ݒ‬௝ ൯.

(21) 14. The distance ݀൫‫ݒ‬௜ ǡ ‫ݒ‬௝ ൯ is the length (number of edges) in the geodesic that connects ‫ݒ‬௜ and ‫ݒ‬௝ ; then, the distance between nodes ‫ݒ‬ଵ and ‫ ଺ݒ‬is 3; in Table 2, closeness is calculated step by step for vertices ‫ݒ‬ଵ and ‫ ଼ݒ‬. A standardized measure of closeness is ݊െͳ Ǥ σ௡௝ୀଵ ݀൫‫ݒ‬௜ ǡ ‫ݒ‬௝ ൯. ‫ݐ݊݁ܥ݈ܥ‬௩ᇱ ೔ ൌ. Finally, eigenvector centrality refers to the eigenvector of the adjacency matrix calculated for the largest eigenvalue; the eigenvector centrality can be interpreted as a weighted measure of how close one node is to all the nodes in the network. In this study, the centrality measures that we use are normalized, and then, the size of the network will not affect the level of any centrality measure. In Table 3, the centrality measures for all the nodes in the network are presented.. v6. v7 e11. e9. v 10. e12 v9 e10. e7. e8 v2. v8. e6. v5. v1. v3. e4. e5 e3. v 12. v 11 e1. v4 e2. Figure 5 Example of an undirected network.

(22) 15. Table 1. ‫ݒ‬ଵ ‫ݒ‬ଶ ‫ݒ‬ଷ ‫ݒ‬ସ ‫ݒ‬ହ ‫଺ݒ‬ ‫଻ݒ‬ ‫଼ݒ‬ ‫ݒ‬ଽ ‫ݒ‬ଵ଴ ‫ݒ‬ଵଵ ‫ݒ‬ଵଶ. ‫ݒ‬ଵ 0 1 1 1 1 0 0 0 0 0 0 0. Adjacency matrix for network in Figure 5. ‫ݒ‬ଶ 1 0 0 0 0 0 0 0 1 1 0 0. ‫ݒ‬ଷ 1 0 0 0 0 0 0 0 0 0 0 0. ‫ݒ‬ସ 1 0 0 0 0 0 0 0 0 0 1 0. ‫ݒ‬ହ 1 0 0 0 0 0 0 0 0 0 0 0. ‫଺ݒ‬ 0 0 0 0 0 0 0 0 1 0 0 0. ‫଻ݒ‬ 0 0 0 0 0 0 0 0 1 0 0 0. ‫଼ݒ‬ 0 0 0 0 0 0 0 0 1 0 0 0. ‫ݒ‬ଽ ‫ݒ‬ଵ଴ ‫ݒ‬ଵଵ ‫ݒ‬ଵଶ 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0. v6. v6 e11. e9. v 10. e11 v9. v9. e7. e8. v2. v2. Figure 6 Paths between nodes ࢜૛ and ࢜૟. Table 2. Closeness centrality for nodes ࢜૚ and ࢜ૡ in Figure 5. Distance to ‫ݒ‬ଵ ‫ݒ‬ଶ ‫ݒ‬ଷ ‫ݒ‬ସ ‫ݒ‬ହ ‫ݒ ଼ݒ ଻ݒ ଺ݒ‬ଽ ‫ݒ‬ଵ଴ ‫ݒ‬ଵଵ ‫ݒ‬ଵଶ ‫ݒ‬ଵ 0 1 1 1 1 3 3 3 2 2 2 3 ‫ ଼ݒ‬3 2 4 4 4 2 2 0 1 2 5 6. ƶ. Closeness. Relative Closeness. 22 35. 0.045 0.029. 0.500 0.314.

(23) 16. Table 3. ‫ݒ‬ଵ ‫ݒ‬ଶ ‫ݒ‬ଷ ‫ݒ‬ସ ‫ݒ‬ହ ‫଺ݒ‬ ‫଻ݒ‬ ‫଼ݒ‬ ‫ݒ‬ଽ ‫ݒ‬ଵ଴ ‫ݒ‬ଵଵ ‫ݒ‬ଵଶ. Centrality measures for network in Figure 5. Degree. Relative Degree. Betweeness. Relative Betweeness. Closeness. Relative Closeness. Eigenvector. 4 3 1 2 1 1 1 1 5 2 2 1. 0.36 0.27 0.09 0.18 0.09 0.09 0.09 0.09 0.45 0.18 0.18 0.09. 37 30 0 18 0 0 0 0 27 0 10 0. 0.67 0.55 0.00 0.33 0.00 0.00 0.00 0.00 0.49 0.00 0.18 0.00. 0.5 0.5 0.34 0.39 0.34 0.31 0.31 0.31 0.44 0.39 0.31 0.24. 5.5 5.5 3.74 4.29 3.74 3.41 3.41 3.41 4.84 4.29 3.41 2.64. 0.33 0.48 0.12 0.15 0.12 0.21 0.21 0.21 0.56 0.39 0.06 0.02.

(24) 17. 7. MUTUAL FUND NETWORK. We estimate the mutual fund network utilizing monthly data from the CRSP SurvivorBias-Free US Mutual Fund Database. We construct a uniform sample that includes only actively managed equity funds investing in the US. For example, we construct the mutual fund network for 1992–2007. The purpose of this section is to explain how the network, central to this dissertation, is built and how its main characteristics could have repercussions for the expected results. We establish a link between two funds if the coefficient of correlation is above a minimum value (ߛ : threshold). Depending on that threshold, the number of nodes in the network will differ (Figure 7). A threshold below 0.66 will include more than 80% of the potential nodes in the network while a threshold above 0.8 will include less than 43% of the potential nodes in the network; if the threshold is equal to 0.9, the network will include only 20% of the potential nodes in the network. In order to obtain robustness in the estimation, we calculate two different networks using two thresholds for the coefficient of correlation: ߛ ൌ ͲǤ͸ and ߛ ൌ ͲǤͺ. 1. 0.07 38%. 43% 0.9. 0.06 0.8. 0.05. 0.7 0.6. 0.04. 0.5 0.03. 0.4. Cumulative frequency. % of vertices given a level of coef. of correlation. 19%. 0.3. 0.02. 0.2 0.01 0.1 0. -0.20 -0.16 -0.12 -0.08 -0.04 0.00 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 0.36 0.40 0.44 0.48 0.52 0.56 0.60 0.64 0.68 0.72 0.76 0.80 0.84 0.88 0.92 0.96 1.00. 0. Coefficient of Correlation Frequency. Inverse Cumulative Freq.. Cumulative Freq.. Figure 7 Distribution of Coefficients of Correlation for mutual fund returns (1992-2007). In the case of the network estimation, the edge density7 diminishes as expected when the correlation threshold ߛ increases (Figure 8). Higher levels of ߛ will result in less links in A threshold equal to 0.6 means that a link between two mutual funds (nodes) exists only if the coefficient of correlation among returns of the funds is above 0.6.. 6. 7 Edge density refers to the observed number of edges as a proportion of the maximum possible number of edges in an undirected network. Given an undirected network, ܰሺ‫ݐ‬ሻ ൌ ሾ‫ݒ‬ଵ ǡ ‫ݒ‬ଶ ǡ ǥ ǡ ‫ݒ‬௡ ሿ is.

(25) 18. the network. For ߛ ൏ ͲǤ͸, the edge density will reduce at a slower pace than for ͲǤ͸ ൏ ߛ ൏ ͲǤͻͷ. This means that for values of ߛ ൐ ͲǤ͸, the structure of the network should not vary significantly. We expect that measurements of the network, like degree distribution, will not change. However, the degree distribution in the network will change with values of ߛ ൐ ͲǤ͸ (Figure 9). For values of ߛ ൐ ͲǤͻ, the distribution resembles a power law8, which is characteristic of complex networks, like the world wide web; a power-law distribution indicates that only few nodes are highly connected (hubs) while most of the nodes have a low degree. It is expected that the results will be different depending on the chosen ߛ. A high level of ߛ implies that the centrality measures will focus mostly on the tails of the distribution.. 1 0.9 0.8. Edge density. 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0. 0.10. 0.20. 0.30. 0.40. 0.50 0.60 Correlation threshold. 0.70. 0.80. 0.90. 0.99. Figure 8 Edge density of the US mutual fund network (1992 – 2007) according to correlation threshold ࢽ.. the set of nodes and ‫ܮ‬ሺ‫ݐ‬ሻ ൌ ሾ݁ଵ ǡ ݁ଶ ǡ ǥ ǡ ݁௠ ሿ is the set of links between nodes; density is defined by ‫ܦ‬ሺ‫ݐ‬ሻ ൌ ݉Τሺ݊ ‫ כ‬ሺ݊ െ ͳሻΤʹሻ. The degree of the nodes in a network follows a power-law distribution when the probability of a node with degree = k decreases exponentially when k increases. ܲሺ݇ሻ̱݇ ିఛ . See Boginski, Butenko, and Pardalos (2005).. 8.

(26) 19. 90. 45. Ȗ = 0.6. Ȗ = 0.7. 40. 70. 35. 60. 30 Frequency. Frequency. 80. 50 40. 30. 25 20 15. 20. 10. 10. 5. 0. 0 0. 500. 1000. 1500. 2000. 2500. 0. 500. 1000. Degree. 60. 2500. Ȗ = 0.85. 90 80 70 Frequency. 40 Frequency. 2000. 100. Ȗ = 0.8. 50. 30 20. 60 50 40 30 20. 10. 10 0. 0 0. 500. 1000. 1500. 2000. 0. 2500. 500. 1500. 1000 Degree. Degree. 100. 800. Ȗ = 0.9. 90 80. Ȗ = 0.95. 700. 600. 70 60. Frequency. Frequency. 1500 Degree. 50 40. 500 400 300. 30 200. 20. 100. 10 0. 0 0. 500. 1000 Degree. 1500. 0. 200. 400. 600. 800. 1000. Degree. Figure 9 Frequency of degree in the US mutual fund network (1992 – 2007) according to correlation threshold ࢽ.. The use of different values of ߛ does not result in major changes in the relationship between the estimated centrality measures (Figure 10). Given the positive and almost linear relationship between degree and eigenvector, we consider that both variables contain equivalent information. The same can be inferred about closeness centrality and degree centrality. In the case of betweenness centrality and degree centrality, the relationship is not linear, and we consider that both variables contain additional information. In that sense, to estimate equation (2), we separately use four measures of centrality (degree, closeness, betweenness, and eigenvector) for the US mutual fund network calculated with ߛ ൌ ͲǤ͸ and ߛ ൌ ͲǤͺ. When we estimate a new network with different Ǆ, the centrality measures change in different magnitude for each node, and the variation is slightly different for the four centrality measures (Figure 11). Thus, we expect that the results in the estimation of equation (2) will not vary much for each measure of centrality, with the exception of betweenness. In addition, the change in the centrality measures when ߛ varies affects the relationship between the centrality measures and the estimated alphas (Figure 12)..

(27) 1. 1. 0.4. 0.5. 0.6. 0.7. 0.8. 0.9. 0. 0. 0.2. 0.2. 0.4 0.6 Closeness centrality. 0.4 0.6 Closeness centrality. 0.8. 0.8. 1. 1. 1. 0. 0.1. 0.2. 0.3. 0.4. 0.5. 0.6. 0.7. 0.8. 0.9. 1. 0. 0.1. 0.2. 0.3. 0.4. 0.5. 0.6. 0.7. 0.8. 0.9. 0. 0. 0.0005. 0.0005. Figure 10 Relation between centrality measures in the US mutual fund network (1992 – 2007) with ࢽ ൌ ૙Ǥ ૟ and ࢽ ൌ ૙Ǥ ૡ. 0 0.035. 0.035. 0 0.03. 0.03. 0.1. 0.025. 0.025. 0.1. 0.015 0.02 Eigenvector centrality. 0.015 0.02 Eigenvector centrality. 0.2. 0.01. 0.01. 0.2. 0.005. 0.005. 0. 0.1. 0.2. 0.3. 0.4. 0.5. 0.6. 0.7. 0.8. 0.3. 0. 0. 1 0.9. 0.3. 0.4. 0.5. 0.6. 0.7. 0.8. 0.9. 1. 0. 0.1. 0.2. 0.3. 0.4. 0.5. 0.6. 0.7. 0.8. Degree centrality Degree centrality. Degree centrality. Degree centrality. Degree centrality Degree centrality. 0.9. 0.001 Betweeness centrality. 0.001 Betweeness centrality. 0.0015. 0.0015. 0.002. 0.002. 20.

(28) Ȗ= 0.8. 1. 0. 0.000. 0.005. 0.010. 0.015. 0.020. 0.025. 0.030. 0.035. 0. 0.1. 0.2. 0.3. 0.4. 0.5. 0.6. 0.7. 0.8. 0. 0.005. 0.4. Ȗ=0.6. 0.01. Ȗ=0.6. 0.015. 0.6. 0.02. Eigenvector centrality. 0.2. Degree centrality. 0.025. 0.8. 0.03 0.035. 1 0.3. 0.0000 0.0000. 0.0005. 0.0010. 0.0015. 0.0020. 0.0025. 0.0030. 0.3. 0.4. 0.5. 0.6. 0.7. 0.8. 0.9. 1. 0.0005. 0.4. 0.5. Ȗ= 0.6. 0.7. 0.8. 0.0010. Ȗ=0.6. 0.0015. 0.0020. Betweeness centrality. 0.6. Closeness centrality. 0.9. 0.0025. Figure 11 Variation in centrality measures in the US mutual fund network (1992 – 2007) for ࢽ ൌ ૙Ǥ ૟ and ࢽ ൌ ૙Ǥ ૡ. Ȗ= 0.8. Ȗ= 0.8 Ȗ= 0.8. 0.9. 0.0030. 1. 21.

(29) 1. 1. 0.9. 0.9. 0.8. 0.8. 0.7. 0.7 Degree centrality. Degree centrality. 22. 0.6 0.5 0.4. 0.6 0.5 0.4. 0.3. 0.3. 0.2. 0.2. 0.1. 0.1. 0 -0.05. -0.04. -0.03. -0.02. -0.01. 0. 0.01. 0 -0.05. 0.02. -0.04. -0.03. -0.02. 1. 0.9. 0.9. 0.8. 0.8 Closeness centrality. Closeness centrality. 1. 0.7 0.6. 0.4. 0.4. -0.03. -0.02. -0.01. 0. 0.01. 0.3 -0.05. 0.02. -0.04. -0.03. 0.005. 0.005. 0.004. 0.004. 0.003. 0.002. 0.001. -0.02. 0. 0.01. 0.02. 0.002. 0.001. -0.04. -0.03. -0.02. -0.01. 0. 0.01. 0.000 -0.05. 0.02. -0.04. -0.03. -0.02. -0.01. 0. 0.01. 0.02. -0.01. 0. 0.01. 0.02. Alpha. 0.035. 0.035. 0.030. 0.030. 0.025. 0.025. Eigenvector centrality. Eigenvector centrality. -0.01. 0.003. Alpha. 0.020 0.015 0.010 0.005 0.000 -0.05. 0.02. Alpha. Betweeness centrality. Betweeness centrality. Alpha. 0 -0.05. 0.01. 0.6 0.5. -0.04. 0. 0.7. 0.5. 0.3 -0.05. -0.01 Alpha. Alpha. 0.020 0.015 0.010 0.005. -0.04. -0.03. -0.02. -0.01 Alpha. 0. 0.01. 0.02. 0.000 -0.05. -0.04. -0.03. -0.02 Alpha. Figure 12 Relation between centrality measures in the US mutual fund network (1992 – 2007) and estimated alpha for Ǆ = 0.6 and Ǆ = 0.8.

(30) 23. The estimation of the mutual fund network varies depending on Ǆ; a key issue is to set Ǆ. A larger level of Ǆ helps to reduce the size of the database and focuses the centrality measure on highly connected funds; a smaller level of Ǆ will not differentiate much between highly connected funds and isolated funds. An alternative is to use a link that reflects the distance between two funds; that distance can be constructed using the coefficient of correlation. In that case, centrality does not depend on an arbitrary level of Ǆ..

(31) 24. 8. SUMMARY OF ESSAYS. This PhD thesis consists of three single authored essays. Following there is an overview of each one of the essays and a succinct discussion including the contribution to the literature. 8.1. The effect of network characteristics on mutual fund performance. This study investigates how the characteristics of the US mutual fund network affect the performance of mutual funds. Our interest is to study actively managed funds. We assume that mutual funds are related, and this relationship can be established by calculating the coefficient of correlation for the returns. We are not interested in the particular source of the relationships that create connections. Our concern is about the effect of those connections on the performance of the funds. We presuppose that most of the fund managers make decisions based on public information. Returns of the majority of the funds will be close to the market. In some cases, some followers will imitate skilled managers. In other cases, managers will share information acquired by belonging to the same social networks. We consider that the link between two funds can be established by the coefficient of correlation. We calculate a network in which mutual funds are nodes linked to each other dependent on the level of the coefficient of correlation between returns. Initially, we define the link between two nodes with a measure of distance calculated with the coefficient of correlation. In addition, we use another approach to establish a link between two nodes. Two nodes are connected by a link when the coefficient of correlation is above some threshold. The network is calculated for the entire period and for subsamples. We characterize the network using centrality measures that attempt to identify important nodes in the network. In the study, we use monthly data from the CRSP database. The dataset is constructed using US equity mutual funds with returns net of management expenses from 1992 to 2007. The funds included are open, non-institutional, actively managed, and domestically focused. A four-factor asset-pricing model is used to calculate risk-adjusted returns for each fund. The marginal effect that centrality has on performance is estimated while controlling for expenses, volume of assets, and turnover. We expect that degree centrality and average distance will affect the performance of the fund. Funds with a low level of connections, that is, low centrality, will likely have abnormal returns. The results indicate that after controlling for age, size, turnover, and inactivity, there is a significant relationship between performance and average distance as well as centrality. The study contributes to the discussion on mutual fund performance by testing the relationship between performance and centrality in the network of mutual funds. 8.2. Performance persistence and the mutual fund network. This study investigates how performance persistence is affected by cross-correlation in mutual funds. We utilize the network approach to that end. We use traditional methods.

(32) 25. to estimate persistence and we test for changes in the estimation of persistence when we include measures of centrality and survival ratio in the tests. Researchers are not only concerned about the existence of funds that outperform the market but also with whether those funds have any other outstanding characteristics as time goes by. The use of contingency tables is a common technique to measure how likely it is that a winner or outperforming fund today will outperform tomorrow. Statistics calculated with this technique measure if there is positive or negative persistence. Positive persistence occurs when a winner or loser fund is likely to repeat its behavior in the next period. On the contrary, negative persistence arises when a winner or loser fund is not likely to be a winner or loser again. There is no persistence when previous performance is not linked to future performance. In that sense, another way to test for persistence is to run a regression in which abnormal performance is a function of lagged abnormal performance. In this case, there is evidence of persistence when the parameter for lagged performance is significant. Recursive portfolios are a third common method to probe persistence. The use of this technique requires the construction of portfolios based on the performance of funds in the previous period. In every period of the sample, the portfolio is rebalanced. The returns for the top and bottom portfolios are compared to check for persistence. Several studies, like Brown and Goetzmann (1995), Malkiel (1995), Elton, Gruber, and Blake (1996), Cohen, Coval, and Pastor (2005), Kacperczyk, Sialm, and Zheng (2005), and Kosowski, Timmermann, Wermers, and White (2006), found that funds present persistence in their returns. We construct the mutual fund network using the coefficient of correlation for returns of the funds for every year between 1999 and 2012. We calculate the centrality and survival ratio for every fund in the network. We expect that nodes with low levels of centrality will most likely outperform or underperform the market. In that sense, in the case of persistence, this will probably occur with funds that have low centrality. In addition to centrality, we expect that the survival ratio, a measure of how stable the connections for a fund are, will help to indicate which funds present persistence with more accuracy. The study finds that centrality and performance are related. Contingency tables and cross-sectional regression show evidence that centrality affects performance persistence. The approach of rebalanced portfolios shows that low levels of centrality are related with top performers and low performers, but without enough significance. The relationship between performance and survival ratio is less clear; on one hand, contingency tables and rebalanced portfolios show no indication of any effect; on the other, the crosssectional regression indicates that the survival ratio has significant effects on performance. 8.3. Empirical analysis on mutual fund herd behavior using a network approach. We study herding in the mutual fund market. The choice of an investor to buy or sell shares in a company should be the result of a rational process that involves the collection and analysis of private information. However, in some cases, the investor chooses to follow other investors or recommendations made by analysts..

(33) 26. Researchers test for the existence of herding and how it affects the market. Two common measures to test for herding are cross-sectional absolute deviation of returns (CSAD) and cross-sectional standard deviation of returns (CSSD). In this study, we investigate herding using CSAD and CSSD. We include network measures to study herding in the mutual fund market. In order to measure herding, we use the average degree centrality for all the funds in the sample. The results indicate that mutual funds show herd behavior and that lagged degree centrality helps to explain herding in the mutual fund market..

(34) 27. REFERENCES Allen, F. and A. Babus, 2008. Networks in Finance. Wharton Financial Institutions Center. Working Paper Series No. 08-07. August 2008. American Finance Association, 2015. Articles Search Criteria: mutual fund. Downloaded on 8.apr.2015. http://www.afajof.org/view/search.html?q=mutual+ fund&submitSearch=Submit Barras, L., O. Scaillet and R. Wermers, 2010. False Discoveries in Mutual Fund Performance: Measuring Luck in Estimated Alphas. The Journal of Finance, Vol. 65, No. 1, 179-216. Brown, S.J. and W.N. Goetzmann, 1995. Performance Persistence. The Journal of Finance, Vol. 50, No. 2, 679-698. Boginski, V., S. Butenko and P. M. Pardalos, 2005. Statistical analysis of financial networks. Computational Statistics & Data Analysis, Vol. 48, No. 2, 431-443. Carhart, M. M., 1997. On Persistence in Mutual Fund Performance. The Journal of Finance, Vol. 52, No. 1, 57-82. Cohen, R.B., J.D. Coval and L. Pastor, 2005. Judging Fund Managers by the Company They Keep. The Journal of Finance, Vol. 60, No. 3, 1057-1096. Cohen, L., A. Frazzini and C. Malloy, 2008. The Small World of Investing: Board Connections and Mutual Fund Returns. The Journal of Political Economy, Vol. 116, No. 5, 951-979. Cuthbertson, K., D. Nitzsche and N. O'Sullivan, 2010. Mutual Fund Performance: Measurement and Evidence. Financial markets, institutions & instruments, Vol.19, No. 2, 95 -187. Elton, E. J., M. J. Gruber, S. Das and M. Hlavka, 1993. Efficiency with Costly Information: A Reinterpretation of Evidence from Managed Portfolios. The Review of Financial Studies, Vol. 6, No. 1, 1-22. Fama, E. F. and K. R. French, 2010. Luck versus Skill in the Cross-Section of Mutual Fund Returns. The Journal of Finance, Vol. 65, No. 5, 1915-1947. Fama, E. F. and K. R. French, 2015. A five-factor asset pricing model. Journal of Financial Economics, Vol. 116, No. 1, 1-22. Federal Reserve Board, 2015. Financial Accounts of the United States Z.1 files Downloaded on 2.apr.2015 from, http://www.federalreserve.gov/ releases/z1/Current/data.htm.

(35) 28. Freeman, L.C., 1978/79. Centrality in Social Networks. Conceptual Clarification. Social Networks, Vol. 1, No. 1, 215-239. Friend, I. and D. Vickers, 1965. Portfolio selection and investment performance. The Journal of Finance, Vol. 20, No. 3, 391-415. Han, B. and L. Yang, 2011. Social Networks, Information Acquisition, and Asset Prices. McCombs Research Paper Series No. FIN-02-11. Heimo, T., K. Kaski and J. Saramäki, 2009. Maximal spanning trees, asset graphs and random matrix denoising in the analysis of dynamics of financial networks. Physica A, Vol. 388, 145-156. Hong, H., J. D. Kubik and J. C. Stein, 2005. Thy Neighbor’s Portfolio: Word-of-Mouth Effects in the Holdings and Trades of Money Managers. The Journal of Finance, Vol. 60, No. 6, 2801-2824. Ippolito, R. A., 1989. Efficiency With Costly Information: A Study of Mutual Fund Performance, 1965-1984. The Quarterly Journal of Economics, Vol. 104, No. 1, 123. Ippolito, R. A., 1993. On Studies of Mutual Fund Performance. Financial Analysts Journal, Vol. 49, No. 1, 42-50. Investment Company Institute, 2015. Investment Company Fact Book. 55th edition. Downloaded from http://www.ici.org/pdf/2015_factbook.pdf on 27.may.2015. Jensen, M. C., 1968. The performance of mutual funds in the period 1945-1964. The Journal of Finance, Vol. 23, No. 2, 389-416. Jensen, M. C., 1969. Risk, the pricing of capital assets, and evaluation of investment portfolios. Journal of Business, Vol. 42, No. , 167-247. Kacperczyk, M., C. Sialm and L. Zheng, 2005. On the Industry Concentration of Actively Managed Equity Mutual Funds. The Journal of Finance, Vol. 60, No. 4, 1983-2011. Kim, K., S. Y. Kim and D. H. Ha, 2007. Characteristics of networks in financial markets. Computer Physics Communications, Vol. 177, 184–185. Kosowski, R., A. Timmermann, R. Wermers and H. White, 2006. Can Mutual Fund "Stars" Really Pick Stocks? New Evidence from a Bootstrap Analysis. The Journal of Finance, Vol. 61, No. 6, 2551-2595. Lewis, T. G., 2009. Network Science. Hoboken, New Jersey: John Wiley & Sons, Inc..

(36) 29. Lintner, J., 1965. Security prices, risk, and maximal gains from diversification. The Journal of Finance, Vol. 20, No. 4, 587-615. Malkiel, B. G., 1995. Returns from Investing in Equity Mutual Funds 1971 to 1991. The Journal of Finance, Vol. 50, No. 2, 549-572. Nagurney, A., 2008. Networks in Finance. In: D. Seese, C. Weinhardt and F. Schlottmann, eds, The Handbook on Information Technology and Finance. Berlin: Springer, 383-420. Pareek, A, 2009. Information Networks: Implications for Mutual Fund Trading Behavior and Stock Returns. Working Papers, Rutgers University. Rouwenhorst, K. G., 2004. The Origins of Mutual Funds. Yale ICF Working Paper No. 04-48 Sharpe, W. F., 1964. Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. The Journal of Finance, Vol. 19, No. 3, 425-442. Sharpe, W. F., 1966. Mutual fund performance. The Journal of Business, Vol. 39, No. 1, 119-138. Treynor, J. L., 1965. How to rate management of investment funds. Harvard Business Review, Vol. 43, No. 1, 63-75. Wermers, R., 2000. Mutual Fund Performance: An Empirical Decomposition into Stock-Picking Talent, Style, Transactions Costs, and Expenses. The Journal of Finance, Vol. 55, No. 4, 1655-1695..

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(38) SECOND PART THE ESSAYS.

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(40) 33. The effect of network characteristics on mutual fund performance. David H. González-Osorio1. May 5, 2016. Abstract We investigate the effect that cross-correlation across mutual funds has on performance. We calculate a US mutual fund network based on coefficients of correlation. Monthly data from the CRSP database is used to construct a survivorship unbiased sample of US equity mutual funds with returns net of management expenses from 1992 to 2015. The funds included are open, non-institutional, actively managed, and domestically focused. Risk-adjusted returns are calculated using factor models proposed by Fama and French (1993, 2015) and Carhart (1997). We build a network in which mutual funds are nodes linked to each other depending on measures based on coefficients of correlation between their monthly returns for periods of 6 years; for each fund in the network, we calculate average distance and degree centrality. We estimate the marginal effect of average distance and centrality in the performance of the funds while controlling for expenses, turnover, size, and age of the fund. The results indicate that the importance of a fund in the network measured by the average distance and degree centrality has a non-negligible effect on the risk-adjusted performance of the fund. In particular, funds with large absolute values of alpha are not relatively close to all the funds in the network. Evidence of centrality positively related to the absolute value of alpha indicates that when larger values of alpha are excluded from the estimation, funds relatively close to all other funds will have larger alphas.. Keywords: mutual fund performance, networks in finance.. 1Hanken. School of Economics. Departament of Finance and Statistics, P.O. Box 287, 65101 Vaasa, Finland. Phone +358 (0)40 3521766. Email: [email protected].

(41) 34. 1. INTRODUCTION. The US mutual fund industry has been studied widely in finance; the existence of actively managed mutual funds raises questions about the presence of abnormal returns and how to find funds with skillful and well-informed managers. Most questions that researchers have addressed are related to how actively managed funds behave when they are compared with the market and how those funds can be regarded as outperforming; if the actively managed funds do not outperform the market, investors will do better investing in index funds. Several studies (Elton, Gruber, Das, and Hlavka, 1993; Malkiel, 1995; Wermers, 2000; Barras, Scaillet, and Wermers, 2010; Fama and French, 2010) have found that, on average, funds underperform the market. However, some other studies investigating persistence have found that managers outperform the market consistently. For instance, in Kosowski, Timmermann, Wermers, and White (2006), the authors controlled for luck by using a bootstrap technique, and they found that there are skillful managers that consistently outperform the market. In Barras, Scaillet, and Wermers (2010), the authors used a measure of false discoveries to isolate lucky funds and found evidence of funds that outperform the market persistently. James and Karceski (2006) studied the differences in performance between institutional funds and retail funds, concluding that on average, returns in both types of funds are similar. Gil-Bazo and Ruiz-Verdú (2009) found that underperforming mutual funds have higher fees than outperforming ones. Researchers have investigated how some characteristics of mutual funds influence their own performance. Sharpe (1966) found that differences in performance among funds can be explained by expense ratios; however, Ippolito (1989) found that both expenses and turnover were unrelated to performance. Elton, Gruber, Das, and Hlavka (1993) critiqued the measure of performance used by Ippolito (1989) and found that performance is indeed related to expenses and turnover. Carhart (1997) found that performance of US mutual funds is influenced by size, expense ratios, turnover, and load fees. The results show that performance is significant and negatively related with expense ratio but the relationship with size is negative and non-significant. Kacperczyk, Sialm, and Zheng (2005) estimated the relationship between industry concentration and fund performance, including other fund characteristics. They found a negative and significant relationship between fund performance and expense ratio, and with the age of the fund. The relationship with size is negative but not significant. Otten and Bams (2002) estimated how characteristics of European mutual funds affect performance and established a positive and strong relationship with assets (size), a negative relationship with age, and a negative and strong relationship with expenses. We verify that performance is positively related to size; however, this relationship is not strongly significant through the whole sample. The results indicate a negative relationship between the expenses ratio and performance, which is in line with previous findings. We find that the relationship with turnover is not significant in most of the sample. The relationship with age is negative and significant. The relationships lose significance in the last two subsamples, which include the global financial crisis and postcrisis periods..

(42) 35. 2. NETWORKS IN FINANCE. To the best of our knowledge, the analysis of mutual fund performance using a network of mutual funds based on coefficients of correlation has not been undertaken before. Nevertheless, some researchers have studied stock markets using networks; we construct the stock market network with nodes representing stocks and links between stocks defined by coefficients of correlation of returns. Mantegna (1999) investigated stocks in the US market and defined a measure of closeness between two stocks based on the coefficient of correlation among returns. Boginski, Butenko, and Pardalos (2005) also studied the US stock market; they did not use a measure of closeness, but instead drew a link between two stocks when the coefficient of correlation between returns of the stocks surpassed a threshold. Heimo, Kaski, and Saramäki (2009) calculated the network for the New York Stock Exchange using 116 stocks; they defined a link using a threshold for the coefficient of correlation among returns. Kim, Kim, and Ha (2007) used a similar approach to construct a stock market network for South Korea. These studies were mostly interested in studying the properties of the networks, like stability and the distributions that characterize the degree2 of the nodes. In addition, some studies have focused on trading networks in stock markets. For instance, Ozsoylev, Walden, Yavuz, and Bildik (2012) attempted to identify the underlying informational network in the Istanbul stock market. Adamic, Brunetti, Harris, and Kirilenko (2010) built a network with buyers and sellers connected by transactions and estimated how patterns of trading were affected by the flow of information. They calculated the most important metrics of the network and found that returns were highly correlated with volatility, volume, duration, and market liquidity. Jiang and Zhou (2010) constructed a network with stock trading information for the Shenzhen Stock Exchange and showed the main characteristics of the network. In their study, nodes represent investors and transactions represent links between seller and buyer. The authors constructed the network on a daily basis, and found that the largest component3 includes at least 95% of the investors and the network follows a power-law degree distribution4, which means that there is a low proportion of nodes with high degree in the network; nodes with high degree in a network are referred to as hubs. Cohen, Frazzini, and Malloy (2008) studied whether social networks can help analysts to outperform the market on their recommendations. The authors investigated how social relationships could affect the way financial information is acquired. In that sense, they constructed a network with linkages that exist between sell-side analysts and executives in companies that attended the same academic institutions. They found that those ties are related to outperforming recommendations. Larcker, So, and Wang (2013) constructed a boardroom network among listed companies in the US. In the network, two companies are connected if there is at least one The degree of a node in a network corresponds to the number of links that connect the node with any node in the network.. 2. 3 Jiang and Zhou (2010) defined a “component” in the network as “a part… in which two arbitrary nodes are connected by at least one path, while there are no edges connecting two different components.” The largest component has the most nodes in the network. 4 According to Boginski, Butenko, and Pardalos (2005), the degree of the nodes in a network follows a power-law distribution when the probability that a node has a degree, k, decreases exponentially when k increases. ܲሺ݇ሻ̱݇ ିఛ ..

(43) 36. common member. The authors found that firms with well-connected boards outperform firms with boards that are not well connected. The use of a network approach to analyze the stock market and the mutual fund industry is not uncommon. The approach provides additional information that helps to clarify unanswered questions in finance. In this study, we construct a network of mutual funds following Boginski, Butenko, and Pardalos (2005), Kim, Kim, and Ha (2007), and Heimo, Kaski, and Saramäki (2009). We use correlations between mutual fund returns to identify links between mutual funds. Previous studies have assumed physical closeness (living in the same city, working with the same company, studying in the same university, etc.) in order to build networks using fund managers, executives of companies, and analysts as nodes. A common characteristic of the studies mentioned is the assumption that a link exists because managers, executives, or analysts share relevant information. In this study, we consider that managers of funds have access to public information and some of them have access to the same private information; it is not the focus of this study to learn how information travels from one person to another or to different people from the same source. In this study, we assume there are informational relationships implicit within the mutual fund network. However, instead of the particular ways in which information links are built, we consider that two funds with similar historical returns share similar sources of information; therefore, it is expected that both are connected in the network. We consider that metrics calculated for the network can help to explain performance. In this study, we focus on the closeness and centrality of a fund, which can be regarded as how well connected the fund is in the market. We construct a network of mutual funds by establishing connections between funds based on correlations between returns. We assume that a network exists because managers construct portfolios based on public information and different types of private information, and in some cases, by imitating the behavior and strategies of other managers with successful skills. We anticipate that the location of the fund in the network will affect the performance of the fund. A highly connected fund or a fund closer to all other funds will perform closer to the market average while funds with a low number of connections or far from other funds will likely outperform or underperform the market. In addition, it is expected that the number of links will be higher for funds with long history while funds with few observations (newer and short-lived funds) will have lower numbers of links5. Dead funds will have lower connections and are expected to underperform the market 6. In this study, we analyze the performance of mutual funds and how this is affected by the importance of the fund in the mutual fund network. The results indicate that after controlling for age, size, expenses, and turnover there is a significant relationship between performance and connectedness. This study contributes to the existing literature about mutual fund performance by constructing a network of mutual funds based on coefficients of correlation among returns of mutual funds. Average distance and centrality measures derived from the 5 This is also explained by the fact that periods used to estimate the network might be longer than the age of some funds.. In this case, we do not differentiate between funds that disappear because they are dissolved and funds that are merge with other funds.. 6.

(44) 37. network of mutual funds include additional information that has not been considered by the previous literature. In addition, this study contributes to the literature by finding a relationship between fund connectedness and performance..

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