THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE DEPARTMENT OF FINANCE

Transcription

1 THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE DEPARTMENT OF FINANCE Active or Passive Management: Fee and Risk Adjusted Returns for U.S. Domestic Equity Mutual Funds During a Period of Economic Recession JACOB WILLIAM OCHROCH SPRING 2016 A thesis submitted in partial fulfillment of the requirements for baccalaureate degrees in Finance and French and Francophone Studies with honors in Finance Reviewed and approved* by the following: Peter Iliev Assistant Professor of Finance Thesis Supervisor Brian Davis Clinical Associate Professor of Finance Honors Adviser * Signatures are on file in the Schreyer Honors College.

2 i ABSTRACT This thesis studies the Sharpe Ratios (1966) and alphas from the Fama-French threefactor model of 75 U.S. domestic equity mutual funds from one of three categories over the period of January 2007 through January Ideally, this study will determine whether, under certain ideal conditions as laid out by previous scholars, funds with active managers could outperform indexed (passively managed) mutual funds within the same asset class category. The funds fall into one of three categories: Indexed/Passively managed funds, actively managed funds with no load fees, and actively managed funds with load fees. Operating under the assumption that investors are rational and seek the highest returns for a given level of risk, this thesis studies on approximately the 25 largest funds by Assets Under Management (AUM), as investor rationality implies the largest funds are in fact the funds with highest returns as they attract the most investors. This thesis studies these funds through the time period of January 2007 through January 2013 because it was a period of large scale economic recession and recovery, and this would meet one of the hypothetical ideal scenarios for active management laid out by previous scholars. Based on the findings of this study, rational investors should generally avoid active funds with load fees, as they detract from net returns beyond the fund manager s ability to achieve excess returns. While in a few cases, active management with no load can in fact return higher fee adjusted returns for the investor than passive management, this was not a widespread phenomenon, nor was is true in the majority of scenarios, nor was the sample size significant enough to say definitively that the results are widely applicable. Likewise, these higher returns could be an anomalous event specific to this five-year period. Therefore, while not definitive

3 ii proof, the findings of this paper support weak market efficiency and investment in passive management funds.

4 iii TABLE OF CONTENTS LIST OF FIGURES... iii LIST OF TABLES... iv ACKNOWLEDGEMENTS... v Chapter 1 Introduction... 1 Passive vs. Active Mutual Funds... 1 Load vs. Non-Load Mutual Funds... 3 The Efficient Market Hypothesis and Investor Rationality... 5 The Sharpe Ratio... 8 The Carhart Four-Factor Model Chapter 2 Literature Review Duties of the Independent Director in Open-End Mutual Funds (1972) Mutual Fund Flows and Performance in Rational Markets (2002) Incentive Fees and Mutual Funds (2003) The Structure of Mutual Fund Charges (1996) Mutual Fund Performance (1966) Can Mutual Funds Outguess the Market? (1966) Chapter 3 Methodology Theory Other Calculations Chapter 4 Results Cumulative Returns, Standard Deviation, and Sharpe Ratios Alpha Analysis Chapter 5 Large Growth Load vs. Non Load Funds Chapter 6 Conclusion Appendix A Mutual Funds Investment Class, Expenses Ratios, and AUM Appendix B Fama- French Data for the Period of January 1, 2007 through December 3,

5 iv Appendix C Annualized Returns (adjusted for load fees when applicable) Appendix D Fama-French Alphas for Each Fund BIBLIOGRAPHY... 51

6 v LIST OF FIGURES Figure 1. Total Fund Class Allocation as of Source: Bloomberg... 7 Figure 2. Average Expense ratio of Funds by Type of Fund as of Source: Bloomberg 7 Figure 3. The Markowitz Frontier, and the Linear Sharpe Ratio... 9 Figure 4. Load Fund Alphas Figure 5. No Load Fund Alphas Figure 6. Index Fund Alphas Figure 7. Comparison of Large Cap Growth Actively Managed Funds... 38

7 vi LIST OF TABLES Table 1. Buy and Hold Returns, Std. Dev., and Sharpe Ratios of Index Funds 1/1/ /1/ Table 2. Buy and Hold Returns, Std. Dev., and Sharpe Ratios of No-Load Funds 1/1/ /1/ Table 3. Buy and Hold Returns, Std. Dev., and Sharpe Ratios of Load Funds 1/1/ /1/ Table 4 Welch T-test statistics... 37

8 vii ACKNOWLEDGEMENTS I would like to thank my thesis supervisor, Peter Iliev, for your time and effort in guiding my research and topic, as it was essential in completing this study. I would also like to thank my honors advisor, Brian Davis for all of your help and discussion in choosing my topic after my semester abroad. A special thanks to my family for you love and support, both throughout my life and especially in in the past year. You have always encouraged me to excel, to succeed with excellence, and to question why. I cannot thank you all enough for ingraining in me my drive to succeed. Lastly, I would like to thank Simranjeet Singh, for your help in saving me many, many hours with your help programming regressions into excel.

9 1 Chapter 1 Introduction Passive vs. Active Mutual Funds The research for this study started with different styles of fund management and fee structures. Overall, mutual funds fall into one of three categories based upon multiple criterion. The first, and most basic of the differentiating factors of a mutual funds is whether it is actively or passively managed. This is the most rudimentary and simultaneously, fundamentally important determination to differentiate funds. Passive funds will track and index (such as the S&P 500 or a large cap index, etc.) and, in the vast majority of scenarios, have the lowest expense ratios, the details of which upon shortly. Active funds have managers who analyze the market with the intention of finding undervalued securities and profiting off the difference on behalf of investors in exchange for a fee. All United States equity based mutual funds experience expenses, which lower net investor returns. These fees fall into one of two categories: operating fees and transaction fees. All mutual funds incur operating fees, which include management fees (usually based on assets under management (AUM), 12b-1 fees, and administrative costs. On average, management fees range from 0.5% to 1% of the total net AUM. Although some funds exceed this range. These fees go directly to the fund s investment advisor. 12b-1 fees are paid out of fund assets for shareholder distribution and shareholder service expenses, and are named as such after the ruling by the Securities and Exchange Commission (SEC) that permits funds to charge these fees.

10 2 Without adopting 12b-1, funds would still be permitted to charge shareholder expense fees, but would not be permitted to charge distribution fees. Should a fund choose not to adopt 12b-1 and still charge a shareholder expense fee, it would be included in the administrative costs. Shareholder service expenses go to employees to answer investor questions and to provide shareholders with all pertinent information regarding their personal investments. Distribution fees include fees paid to brokers to market and sell fund shares, promoting the fund, and the printing and mailing of the fund prospectus (a document with the key attributes of the fund sent to current and prospective investors). The Financial Industry Regulatory Authority (FINRA) limits shareholder service fees and distribution expenses to.25% and.75% respectively of the fund s average AUM per annum. The aggregation of these costs divided by the fund s annual average net AUM represents the fund s expense ratio of the fund. This statistic is a percentage of the funds average net AUM, tends to range from.2% to 2%, and is one of the fund s key statistics. It is worth noting that while not all funds expense ratios fall in this range, all funds that were a part of this study did. The final classification of general fund expenses are transaction fees. These fees, with few exceptions, tend to only occur in actively managed funds, where the investor is charged a fixed amount every time the manager moves fund assets, operating under the assumption that the active management of fund assets will earn the investor a high enough return such that the investor makes money on the asset movement even after the transaction fee is taken into account, and the manager makes money on the transaction fee. In this ideal scenario, everyone involved in the transaction profits. However, as seen historically and in this paper, that is not always the case.

11 Load vs. Non-Load Mutual Funds 3 The second major differentiation of mutual funds is whether the fund has a transaction fee commonly referred to as a load. These fees are almost exclusively associated with actively managed funds, as load fees compensate the fund manager for his or her expertise and work in picking securities to earn excess returns for the investor. The catch being that the extra fees hurt net investor returns. However, this does not mean that all active funds have load fees. As one might guess based on the classification, non-load mutual funds charge investors only the standard operating fees that apply to all investors, foregoing the extra transaction fees charged by loaded mutual funds, the details of which will be explained momentarily. The eschewing of transaction fees by non-loaded mutual funds leads, with few exceptions, to lower expenses for the investor, and therefore higher returns for a given level of risk. Loaded mutual funds, on the other hand, charge shareholders extra transaction fees known as loads, which falls into one of two classifications: front-end loads or back-end loads. Front-end loads are a commission charged to the investor upon initial purchase of fund shares and is limited to 8.5% of initial investment. This effectively reduces investor return by lowering initial investment by the amount of the load. By way of example, if an investor purchased $100,000 worth of shares in a mutual fund with a 5% front end load, they would effectively be purchasing $95,000 worth of shares and paying a $5,000 commission fee for the privilege of investing in the fund. This of course lowers net investor returns, as the investor must invest more initially, hold the investment for a longer period, or take on more risk in order to achieve the same level of returns. In this study, I use the Morningstar load-adjusted return equation to adjust net investor returns for the transaction fees of load funds. The equation is as follows: RI,A =RP*(1-L)

12 Where 4 RI,A= the load adjusted return RP = the return of the fund over the pre-determined period before load fees L = the total load fees (regardless of front or back loading) Back-end loads, commonly referred to as redemption fees, are incurred by the investor upon sale of fund shares, and normally charged as a percentage of the Net Asset Value (NAV) of the investor s holdings. These fees tend to start very high if the investor wishes to withdraw their funds within a certain period, but diminish the longer the investor holds the fund. These fees are designed more to encourage the investor to hold the fund for as long as possible, as the shorter holding period will result in higher redemption fees. Conventional wisdom suggests that it makes sense to pay a professional manager a premium for his or her expertise in obtaining higher returns, as they, if anyone, would have the expertise to find mispriced securities and capitalize on the arbitrage. However, upon further review, this would inherently disobey the Efficient Market Hypothesis (EMH), which states that no manager (or human being for that matter) can, within the realm of legal possibilities, have any information that everybody has access to. The EMH suggests that market securities are priced based on all legally available information, which therefore implies that all securities are priced at either exactly the proper market value, or are so close to their exact market value that the extra work, fees, and asset allocation required to have the mispricing lead to profit make doing so infeasible, as the price will almost instantaneously correct itself. Furthermore, if even weak market efficiency holds, then it is nearly impossible for anybody to beat the market, especially on a fee adjusted basis.

13 5 Therefore, as stated above, the main three classifications of funds in this study are as follows: 1. Passively managed funds 2. Actively managed funds with no load fees 3. Actively managed funds with load fees There are several arguments in favor of load fees in mutual funds outlined by Berk and Green as well as many others in the papers found in the bibliography (Berk, 2002). However there are two that are, in my opinion, most pertinent to this study. The first and most apparent reason is the concept that the managers most adept at picking mispriced securities will flock to manage the funds with the highest fees, which gets them higher compensation for their abilities. The other major advantage of load fees, especially rear loads, is that they discourage quick outflows and encourage leaving money in the fund, which allows the manager more flexibility in managing fund assets and could be highly beneficial to investors and managers alike. Particularly in an economic crisis. The Efficient Market Hypothesis and Investor Rationality The efficient market hypothesis, as originally proposed by Professor Eugene Fama, (Fama, 1970) proposes that it is impossible to beat the market for a given level of returns over an extended period of time, as securities prices will always reflect all of the information that is legally available to the open market, thus making the only legal method of achieving higher returns being to take on more risk. The academic financial community has, on a highly

14 consistent basis, concluded that markets are at the very least, weakly efficient. Another 6 important concept to understanding the theory of mutual fund investment and allocations is investor rationality. A concept that states that the investor will act in such a way as to create the maximum amount of utility or benefit for his or her self. The academic financial community has, on a highly consistent basis, concluded that markets are at the very least, weakly efficient, and that investors mostly behave rationally. This study started with a rather simple conundrum: if investors are rational, they will always invest in securities that net the highest return; and if markets are at least weakly efficient (follow the EMH), then active management will not be able to outperform indices consistently enough to make active management worthwhile for investors without access to insider information. That said, active and, more obviously, loaded mutual funds still exist and thrive today. If the investor fell in line with the investor rationality theory, he or she will always act out of personal self-interest. In this scenario, that would mean achieving the highest level of return for his or her desired level of risk. Therefore, based on the widely accepted theories of market efficiency and investor rationality, conventional wisdom would state that actively managed funds, or at the very least actively managed funds with high expense ratios, would have died out. This is because if the EMH is true, no active managers could beat the market on a fee-adjusted basis on behalf of fund investors. If the investor was rational, this would lead them to invest in other, lower fee (and therefore higher return) assets. Yet actively managed funds are still widely used today. This raised the question of why investors continue to invest with active managers. By extension, what incentives or benefits does active management offer the investor that passive management cannot or does not supply?

15 7 Figure 1. Total Fund Class Allocation as of Source: Bloomberg Figure 2. Average Expense ratio of Funds by Type of Fund as of Source: Bloomberg Figure one shows the total assets allocated to all U.S. equity Index, load, and non-load mutual funds as of December 1, 2012, in a period of economic recovery after a major financial crisis, when markets had just started to show consistent recovery and investors were highly wary of where their money

16 8 was going. Given the information available at the time, it makes sense that based on the average expense ratios seen in figure two, along with the poor equity returns over the period of the study, that investors flocked rather heavily to index funds, where at the very least, they would pay smaller fees. However, this raises a question in investor rationality: if passive funds returns are comparable to active funds of both types with smaller fees, why have active funds, or loaded funds at the very least, survived? A question further detailed later in this paper. The Sharpe Ratio The Sharpe ratio was created by Professor William F. Sharpe in 1966 (Sharpe, 1966), and is now widely used in financial analysis of portfolio and asset valuation. At its core, the Sharpe ratio is a measurement of a financial asset s returns beyond a risk free rate per unit of risk. In general, the risk free rate used to adjust for excess returns of the asset is the return of a one-month U.S. Treasury bill. In this study, the risk free rate used is the average return of a one-month U.S. Treasury bill from January 1, 2007 through December 1, The Sharpe ratio itself is as follows: Sharpe Ratio = (R p-r f/ σ p) Where: R p = the return of the asset or portfolio R f = the risk free rate of return σ p = the standard deviation of the returns of the asset The numerator of the equation (R p-r f) shows the asset s excess returns above the risk free rate. Another description for the Sharpe ratio is the extra return the investor gets to compensate him or her for taking on extra risk beyond the risk free rate, as the investor always has to option to invest risk free and achieve that level of return on his or her investment. In some scenarios, several of which are in this study, the numerator of the Sharpe ratio is negative. This is the result of highly negative equity returns during

17 9 the recession, and represents the additional returns that investors could have gained by pulling their funds from risky assets and investing in the risk free asset instead. The standard deviation of returns of the risky asset measure the volatility of asset s returns relative to its average performance. By benchmarking each risky asset to the same risk free rate, and then the respective risk of the asset itself, the Sharpe ratio allows investors to compare different risky assets on a risk-adjusted basis, making all assets comparable on an even scale. This means, generally speaking, that a high Sharpe ratio shows that the asset has historically performed well on a risk-adjusted basis, while assets with low Sharpe ratios have performed less well or poorly on a risk adjusted basis. Figure 3. The Markowitz Frontier and the Linear Sharpe Ratio As seen in figure three, the individual assets, when invested properly, combine into the bullet shaped horizontal parabola called the efficient frontier or the Markowitz frontier. The best possible capital allocation line (CAL) drawn from its y intercept, which is equal to the risk free rate, to the point tangent to the efficient frontier that creates the steepest slope of the CAL. The slope on the CAL is the Sharpe Ratio. Rational investors will never invest in a portfolio or asset that is not on the CAL, as this would result in lower returns for the same level of risk or a higher level of risk for the same level of returns.

18 The Carhart Four-Factor Model 10 The Carhart four-factor model, developed by Mark Carhart (Carhart 1997), extends upon the Fama-French 3 factor model developed by Professors Eugene Fama and Kenneth French. The Fama- French three-factor model is an extension of the Capital Asset Pricing Model (CAPM) that provides a market, and historical prediction of asset returns based upon three factors: the market (also in CAPM), size, and value (Fama, 1993). The Carhart four-factor model simply expands upon this by adding a momentum factor to the Fama-French model. For this study, I have chosen to use the Carhart four-factor model and incorporates momentum as a factor, given that the period covered in this study is defined by its large swings in market volatility. The four factors of the Carhart model control for different mutual fund investment styles, which can include large, medium, or small cap companies, all of which could be mixed with and investment style based on value, growth, or a blend of the two. These factors are then risk adjusted using a beta (β) for each individual factor. These betas for these factors are determined by running a multiple linear regression of the asset s historical returns over the given period over the market, size, value, and momentum from Kenneth French s website containing all historical data on the factors (French, Data Library). These figures are also in appendix B. The following shows the Carhart formula: R i= +R f+ MKT RP MKT+ HML RP HML+ SMBRP SMB+ mom RP Mom Where: measures the returns of the fund that are not explained by the model R F measures the rate of return on risk free assets R i measures the return of the fund RP M measures the risk premium (return of the market minus the risk free rate) of the market RP SMB measures the risk premium of the SMB (small minus big) factor RP HML measures the risk premium of the HML (high minus low) factor

19 RP Mom measures the risk premium of the momentum factor 11 M measures the historical beta of the market factor SMB measures the historical beta of the SMB factor HML measures the historical beta of the HML factor Mom measure the historical beta of the Mom factor. For the risk free rate used in this analysis, to remain consistent with the rest of the study, was the average return of one-month U.S. Treasury bills over the period of the study. Historical represents the asset s volatility as compared to a benchmark index. Therefore an asset with a of one has historically moved one basis point (one hundredth of a percent) with its respective benchmark (normally an index such as the S&P 500) for each basis point that the benchmark moves. Therefore, historically, if the S&P 500 went up 3% over the past day, this same asset with a β of one would have also moved up 3% for that day. The market factor calculation is based on a hypothetical scenario where an investor could invest in all available risky assets in the market, and therefore calculates what risk premium an investor would require to invest in a portfolio with all risky assets. Therefore, for the purposes of this study MKT adjusts for the relative risk of a particular fund to the entirety of the equity market. The size factor is based on the total market capitalizations of all stocks traded on the New York Stock Exchange (NYSE), Arca Major Market Index (AMEX), and NASDAQ indices and is represented by the RP SMB factor in the equation. This is calculated by taking the average monthly returns of the companies with the 1/3 smallest market capitalization minus the average monthly returns of companies with the 1/3 largest market capitalization. This can be expressed using the following formula: SMB = (1/3 smallest value + 1/3 smallest blend + 1/3 smallest growth) (1/3 largest value + 1/3 largest blend + 1/3 largest growth))

20 12 The value factor is calculated based on the book-to-market ratios of all of the underlying assets of the NYSE, AMEX, and NASDAQ indices and is represented by the RP HML variable in the Fama-French equation. The variable is calculated by subtracting the average returns of 30% lowest book to market ratio assets in small and large cap funds from the average returns of the 30% highest book to market ratio assets among small and large cap firms, and can be represented with the following formula: HML = (30% highest HML Small Value returns + 30% highest HML large value returns) (30% lowest HML small growth + 30% lowest HML large growth). The momentum factor accounts for the concept that if an asset has largely performed well in recent periods is more likely to continue to do well in the short term than to reverse course. This phenomenon, driven by the supply and demand pressure for the asset, occurs when many investors all attempt to buy or sell certain securities over a period. As more investors buy an asset, the price will rise with demand until such a time as investors feel the asset is overpriced, and sell the asset, which floods the market with excess supply, driving the price back down. This concept applies to domestic equity mutual funds directly, as their underlying assets are comprised of stocks, and the underlying assets are either picked via an algorithm to match fund investment style and indices (in the case of index funds) or by a fund manager based on investment style and expected performance of the asset. Stocks with more upward momentum or in the case of widespread economic recession, less downward momentum hypothetically could attract active managers, as they would have greater ability to choose individual stocks. In theory, this could give active managers an advantage over indexed funds in a period of recession, when momentum is highly negative. Lastly, the represents the difference between the model s predicted return for the fund and the fund s actual returns. Alpha is calculated as follows: R i (Fama-French expected return) = A positive alpha indicates that a fund outperformed its expected returns based on a Fama-French analysis, and may, but does not necessarily; indicate that a fund manager successfully allocated funds

21 based on expertise outside of the Fama-French model in order to achieve higher returns than expected. 13 The positive alpha could also be a result of many different factors, including the investment style of the fund or factors outside of the manager s control. The manager also may have simply gotten lucky, and produced above expected returns anomalously. On the contrary, a negative means that the fund underperformed its expected returns based on the three factor analysis, and could suggest that the fund manager, in a lack of expertise or due to an error, underperformed or misallocated fund assets to in order to fall short of fund expected returns. That said, the negative alpha might also be attributed to any of the alternative factors listed above for a positive alpha. Regardless, due to their higher expenses, actively managed funds, and to an even greater extent, load funds, necessitate higher returns than their passively managed counterparts in order to compensate and make it profitable for investors to allocate their limited resources to active funds. The in the Fama- French three-factor model may prove to be an indicator of a fund manager s ability to actively select the underlying securities of a fund. This study should at least suggest whether the alpha factors could be correlated with manager ability.

22 14 Chapter 2 Literature Review Duties of the Independent Director in Open-End Mutual Funds (1972) The first article under review, titled "Duties of the Independent Director in Open-End Mutual Funds." This paper opens with a brief analysis of the Investment Company Act of 1940, designed to protect investors from widespread abuses of funds such as inadequate capital structures, fraud on investors, insider dealings, and even theft from fund treasuries. This act, which required funds to report their capital structure, earnings, income, etc. caused a massive boom in the mutual fund industry from due to the increased accountability and investor confidence. While this vastly ameliorated the moral hazard problem of actively managed funds, it did not eliminate all of the problems. A major problem that remains is the agency problem, or misalignment of incentives and interests, between the investment adviser and the fund itself wherein the investors want the highest possible returns whereas the investment manager is incentivized by the compensation structure to be highly active and gain raw size. Hence the need for an independent director to serve as an overall watchdog for misconduct and breach of contract. This becomes especially important when considering the fact that many fund managers manage several funds, which often cause conflicts of interests that can hurt investors financially. Again, while the Investment Company Act has addressed these issues in part by requiring specific duties of directors to oversee the fund management and provide a check on the adviser in order to properly align the adviser with investor goals. Unfortunately, the act proved

23 15 disappointing, with most of the regulations being circumvented through loopholes allowing the independent director to be somewhat less than independent, and allowing for the continuation of agency problems. While a solution was eventually found in holding advisers financially accountable for breaches of contract or abuse of investor capital, the struggle to align advisers with their investors remains in a state of imperfect resolution. Which begs the question that will prove a major motif in this paper: given the lower fee adjusted returns and agency problems, why would a rational investor entrust their money to an actively managed fund? This leads us into our next paper, Mutual Fund Flows and Performance in Rational Markets (2). Mutual Fund Flows and Performance in Rational Markets (2002) In Johnathan Berk and Richard Green s paper Mutual Fund Flows and Performance in Rational Markets, the authors discuss an explanation regarding what were previously considered anomalous positive returns in active funds previously attributed to luck. According to Berk and Green, these anomalous returns are caused by the competitive market for capital provision and allocation. Furthermore, they go on to say that this competitive market, along with decreasing returns to scale in active funds, is also a large reason why actively managed funds underperform their similar passively managed counterparts. They do however; postulate that differential ability between different fund managers is both real and rewarding, as there exists a strong relationship between past performance and inflows of capital to the fund, consistent with roughly 80% of active managers who at least earned their fees in returns for the investor. This implies investor rationality in seeking higher returns. The paper goes on to question why fund managers are so highly compensated for their inability to outperform the market, again raising the question

24 16 of why investors would invest in an actively managed fund. Moreover, by logical extension, why actively managed funds have survived if markets are truly rational. Berk and Green even go so far as to say [the data raises] questions about the rationality of investors who place money with active managers despite their apparent inability to outperform passive strategies. (pg.1) Berk and Green continue to say that the best active managers have marketable abilities in choosing securities, and would want to go where they are most highly rewarded. Yet if all performance can be attributed to luck, there should be no rewards for this talent. Yet that is clearly not the case, as active managers are often handsomely rewarded. The authors postulate that when investors compete for superior returns in an active market, they are actively ensuring that superior returns is unobtainable. Meaning that the lack of performance in the active market implies simply that the market is highly competitive, rather than the fact that gathering information about performance is wasteful, active manager ability is inconsequential or unrewarded, or that chasing higher returns is a fruitless endeavor. In this paper s attempt to find the opportune setup of an active fund to maximize investor returns, one consideration based on this paper was to test the risk and fee adjusted returns by reducing the competition in the active field by either transferring large amounts of capital to the passive industry or other hypothetical scenarios to simulate lesser competition. However, this proved infeasible, as there was no realistic way to simulate a lack of market competition, since investors have always sought higher returns since the inception of capital markets. In regards to constructing a hypothetical ideal scenario for maximizing returns in an actively managed fund, it will be imperative to include the conclusion of Berk and Green s study that rational models for active management considering managerial talent is a scarce resource that experiences diminishing marginal returns with increases in the scale of fund operations. Moreover, that this model is consistent with a high

25 level of skill amongst active managers. A theory that points to questions regarding properly 17 incentivizing these highly skilled managers, a topic discussed in detail in several papers found in the bibliography below. Incentive Fees and Mutual Funds (2003) Perhaps the most supportive piece of Berk and Green s claims is Incentive Fees and Mutual Funds written by Edwin J. Elton, Martin J. Gruber, and Christopher R. Blake in the Journal of Finance. As evidenced in the title, this piece discusses how incentive fees correlate to fund performance against a given benchmark. Primarily, incentive fees align manager and investor incentives, reducing agency problems and moral hazard from the manager, as both groups profit from superior performance. It follows that in this incentive structure, the best managers would gravitate toward investment funds with incentive fees that would allow them to profit more from managing these funds. This is consistent with Berk and Green s hypothesis that the investors will rationally flock to the best managers, investing more money with them until the diminishing returns from growing operations brings the excess returns to zero. Still, up until that point, the fund s assets under management will grow as investors want to place more money with the best managers, who will inevitably flock to funds with the highest incentive structures, most aligning the manager s interest with the fund shareholders. Given the consistency in the logic and proof of the theories, it stands to reason that in constructing an ideal hypothetical scenario for active fund returns that both Elton, Gruber, and Blake s theory be incorporated alongside Berk and Green s proposal to ensure the best possible outcome. In continuing with Elton, Gruber, and Blake s research, they explore the phenomenon of the superior nature of incentive

26 18 funds to comparable non incentive funds, citing that as of 1999, incentive fee funds represented roughly 1.7% of total bond and stock funds while holding roughly 10.5% of total assets in that category. Which, operating under the assumption that investors are rational, implies that incentive fee funds outperform non-incentive fee funds, resulting in the disparity between total number of incentive fee funds and total assets under management held by incentive fee funds seen in this paper. Also noteworthy is the way in which these fees are structured. These fees are designed as a mix of fixed and variable fees designed such that the total fee paid out to the fund manager is never negative. Therefore, while the manager s incentives are aligned better with the investors, he/she still is paid for achieving negative or below benchmark returns. Furthering investors incentives to selectively choose their fund manager. In the conclusion of this paper, Elton, Gruber, and Blake highlight that on average incentive fee funds do not earn positive or negative incentive fees. But internal managers do tend to have more control over the fee structure, allowing them to earn slightly larger fees. However that doesn t mean that they have higher fees than non-incentive funds, in fact quite the opposite, as incentive funds on average have lower expense ratios than comparable non-incentive funds; luring investors with superior managers as well as lower expenses. That said, even though incentive funds tend to have positive excess returns, they do not normally outperform their benchmark because they have a beta of less than one, but still generally greater than the beta of non-incentive fee funds. Thus limiting returns relative to the benchmark. Regardless, incentive fee funds consistently outperform nonincentive fee funds on a risk-adjusted basis, despite being slightly riskier. However, it is still unclear whether this is due to skilled managers adopting incentive fees to advertise their skills or because the fees supply extra motivation. Still, Elton, Gruber, and Blake brought up an

27 interesting point of internal managers compared to externally sourced managers, a topic 19 discussed in much further detail in Tarun Chordia s The Structure of Mutual Fund Charges. The Structure of Mutual Fund Charges (1996) In The Structure of Mutual Fund Charges, Chordia explores the reasoning behind the diversity in investment strategies and fees within open-end mutual funds. The first model discussed is a fee structure wherein the manager charges a fee that is a fraction of the increase in the investor s wealth. Furthermore, funds will charge a fee (otherwise known as loading or a redemption fee) for investors to remove their money from the fund, thus allowing the manager to invest in less liquid assets and increasing their assets under management, a standard number upon which many fees are structured. Therefore, load fees can be used to discriminate between investors with different probabilities of redeeming their capital investment, making load fees a method for nonlinear discrimination in the model set by Chordia for this study. This study predicts that funds without back loaded or redemption fees have a higher redemption rate than those without those fees, that closed end funds are more likely to hold more illiquid assets. In the context of this paper, the findings of this study will determine whether loaded or non-loaded funds provide superior returns for investors. While common wisdom would dictate that less fees would create greater returns for the investor, Chordia makes the argument that with redemption and back loaded fees, it may be possible for funds to invest in lower liquidity products of similar risk for higher returns,. Especially when considering that the mutual fund helps investors lower liquidity risk in the first place, offsetting the lack of liquidity in loaded funds to a certain, though inexact degree. While front end load fees can be used to discriminate between investors with

28 20 different probabilities of redemption, redemption (back end load fees) can dissuade the investor entirely from pulling their funds and tend to be more effective than front load fees in that regard. In conclusion, Chordia surmises that redemption rates are likely to be higher in no load funds than redemption rated in load funds, and that no load funds must hold more liquid assets than funds with load fees. Continuing to propose the possibility that active funds cannot beat their benchmark. Extrapolating Chordia s concept, and assuming investor rationality, investors will (and should) be looking to invest in the most efficient portfolio. As discussed further in William Sharpe s paper Mutual Fund Performance. Mutual Fund Performance (1966) In Mutual Fund Performance, William Sharpe (inventor of the Sharpe ratio) discusses efficient capital allocation as it pertains to mutual funds. Postulating, as an extension of Jack L. Treynor s theory of predictors of mutual fund performance, which we will discuss in further detail later in this review, that the portfolio analyst s jobs are to a) translate predictions about security performance into predictions of portfolio performance and b) selecting the efficient portfolio from the mass of possible portfolio. While the security analyst s job is to provide predictions on the performance of the underlying securities. Leaving the task of choosing the most desirable portfolio from the list of efficient portfolios to the investment manager. In the context of mutual funds, managers are responsible for at least the security and portfolio analysis. However, investment theory cannot definitively say that the fund is responsible for investment management, as the fund cannot anticipate the preferences of each investor. Leaving that decision to the rational investor. Sharpe continues to theorize; much like Blake and Green, that

29 21 the reason detecting mispriced securities is so difficult is not that fund managers are not good at their job but quite the opposite. Concluding that market efficiency is strong enough that fund managers are so effective at securities pricing that the market price is almost universally accurate. Given these conditions, Sharpe hypothesizes that fund managers that engage in trying to actively pursue mispriced securities may (and historically does) provide investors with lower returns for relative risk after costs than a passively managed fund. Assuming market efficiency, Sharpe proposes that the tasks of the mutual fund still encompass security and portfolio analysis with a slight change in focus. Wherein security analysis is now focused on evaluating the correlation between the returns of diverse securities and portfolio analysis is focused on diversification and selecting a portfolio with the proper risk factor. This allows for differentiation between funds based upon the intentional or unintentional difference in volatility of returns based on the manager s selection of portfolios of varying risk. Therefore, according to Sharpe s hypothesis, in the long term the only cause for difference in performance would be continued expenditure of fund assets in searching for mispriced securities. More commonly referred to as active management. If proven true, this would re-ignite the question: why would rational investors allocate any capital to actively managed funds? As Sharpe explains, fund performance is measured by expected returns (Ei) and variability of returns quantified by the standard deviation (σ i). In tests of his theory, Sharpe ran test on returns and variability of 34 open-end funds from ranking them by their ex post statistics Ai for returns and Vi for variability. The results showed how the differences in fund performances could be roughly approximated from short term to long term based on the correlation of the underlying assets. To conclude, Sharpe states that this measurement of fund performance is highly valid despite precluding the identification of differences in performance based upon differences in objectives

30 and risk aversion. Rather that differences in fund performance can be largely explained by 22 differences in expense ratios, and that in a highly efficient market, good managers focus on diversification and risk management. Spending little time and money on identification and discovery of mispriced securities. This further affirms the theory set forth by Jack L. Treynor in his paper Can Mutual Funds Outguess the Market? While Sharpe acknowledges the possibility that past performance has an effect on fund returns, as proposed by Berk and Green, he proposes that the burden of proof remains with those who argue in favor of active management. Can Mutual Funds Outguess the Market? (1966) In Can Mutual Funds Outguess the Market? (16) Jack L. Treynor and Kay K. Mazuy analyze the historical ability of fund managers to predict major market movements, and built upon Tryenor s previous work with market efficiency and security evaluation. Furthermore, Treynor and Mazuy go into a detailed analysis of the responsibilities of fund managers largely aligning with the description proposed by Sharpe in Mutual Fund Performance. Treynor and Mazuy then take manager responsibility a step further, asking what steps should a manager take to protect himself from scrutiny that he or she should have anticipated a major market move, or even whether the shareholder has the right to question his decision. Treynor and Mazuy are operating under the understanding that a manager s ability to outguess the market means anticipating market rises and falls and adjusting their portfolios accordingly. Their definition of which is changing the volatility of the portfolios they manage to match market scenarios, investing in low volatility securities such as bonds in times of economic downturn and vice versa when anticipating an economic boom. To measure performance, Treynor and Mazuy used Arthur

31 Wiesenberger s formula of to asset value per share at the end of the period, adjusted to reflect 23 reinvestment of all capital gains distributions, add dividends per share paid during the period from investment income, similarly adjusted; divide the total by the starting per share asset value. Hence, if year over year the funds returns are plotted against the rate of return for a comparable index, a line fitting the pattern is called a characteristic line, and if such a line shares a slope with the index for years in which the market goes down, the line will be straight and constant. In which case the tangent of the line reveals the fund s sensitivity to market movements. This formula will prove helpful in my attempt to find ideal market scenarios for active management. Using this methodology, one should be able to evaluate the effectiveness of certain managers, which could be cross referenced with which managers receive incentive fees such as those discussed in Berk and Green s Incentive Fees and Mutual Funds, which could provide valuable insight as to whether Berk and Green s theory that better managers flock to funds with incentive fees. However, if the manager, like most in real life, guess wrong sometimes and correctly at other times, the characteristic line is no longer straight, and has several inefficient points. Treynor and Mazuy hypothesize that in a realistic scenario where fund managers cannot always accurately predict market movements, the best method for managers to outguess the market and create value for their investors is to vary fund volatility in such a way that the characteristic line is concave upward; giving the fund returns some semblance of convexity. Treynor and Mazuy studied the ten-year period from , but felt that their study was applicable to any decade. They base this hypothesis on the fact that historic characteristic lines have remains largely the same over time. In addition, given that historically management has predicted market volatility correctly more often than incorrectly; the characteristic line tends to be curved, with the degree of convexity depending on how heavily management gambles on its predicted market movements. This characteristic line, in conjunction with the theories proposed by the other authors in this review and, to a slightly lesser degree, the authors in the bibliography below whose pieces did not make it into this review, could lead to an interesting study on the convexity of the characteristic line of different forms of active funds, and how they compare to passive funds when

32 24 considering large scale market movements. This unfortunately proved to be infeasible, as the majority of data regarding characteristic lines was behind paywalls that were not available for this study. Nonetheless, their analysis of the role of an active manager in changing the volatility (and therefore the convexity) of the portfolio depending on market conditions is important to understanding the success or failure of a manager in outperforming the market.

33 25 Chapter 3 Methodology Theory In accordance with the vast majority of academic literature to date, this study assumes weak market efficiency and imperfect investor rationality for the purposes of explanation and data selection. Therefore, assuming investor rationality, this study looks at the 22 largest index mutual funds, the 25 largest actively managed non-loaded funds, the 25 largest loaded mutual funds, and 3 major U.S. indices, all chosen by size based upon assets under management (AUM). While the original effort was to find 25 of each type of fund, after these, the AUM numbers dropped significantly, and including these funds would shake the basis of investor rationality. These funds represent investor rationality, as one could assume that the largest funds would be those to which investors flocked to due to the best overall returns in their respective categories for a given level of risk. All of the funds in this study are domestic U.S. equity funds from each of the following categories: 1) Index Funds 2) No Load Active Funds 3) Load active funds (many of which have front and rear loads/redemption fees) From there, the study compares these funds relative returns, fee adjusted returns, and Fama-French Alphas to determine which methods achieve the highest returns for investors. Furthermore, since most academic literature suggests that active management is, overall, inferior

34 to index or passive funds on a fee-adjusted basis, I have taken the study one-step further. 26 According to Johnathan Berk and Richard Green, in their paper Mutual Fund Flows and Performance in Rational Markets, described skilled active management is a scarce resource that experiences diminishing marginal returns as investors flock to the funds with the highest returns, which explains the otherwise anomalous short spirts of active outperformance of the market. Sharpe also concludes in his paper Mutual Fund Performance that the reason active managers cannot consistently outperform the market is not due to lack of ability but instead because managers are, for the most part, all excellent. He further hypothesizes that securities prices are often only mispriced for fractions of a second if they are ever mispriced at all, and that the work and attention necessary to detect mispriced securities and capitalize on them would end up necessitating fees that would make the practice too expensive to justify the returns to the investor anyway. That said, Michael Pollock in his paper Investing in Funds & ETFs: A Monthly Analysis --- The Case for the Active Mutual-Fund Manager --- Investors Have Flocked to Index Funds, but There Are Still Some Scenarios Where the Hands-on Way Might Make More Sense argues that in certain scenarios, (mainly if you own stocks for income, if you expect high volatility, or a large scale market downturn) it makes sense for an investor to place their money with an active manager. As a compilation of these theories, this study tests whether, assuming market efficiency and investor rationality, and in an ideal scenario for active management (according to Pollock), actively managed funds could outperform passive funds on a fee adjusted basis from January 1, December 3, The period of the great recession through the beginning of the economic recovery. While there are a few shortcomings to this data, such as the fact that all of the largest funds at the time survived the crisis, therefore not taking into account the fund deaths that took place during the time period, as well as a highly volatile risk free rate (was as

35 high as 5% in 2007 and has been near 0 since 2008), and the small sample size relative to the 27 massive amount of funds available, this study should be able to conclude if the largest funds of any one type give the highest returns to investors. If Green, Sharpe, Treynor, and Mazuy are correct, then passive funds should still reign as the best return for a given level of risk. However, if investor rationality holds to an extreme degree, and Pollock is correct, then it may be that actively managed mutual funds will in fact outperform index funds through a period of economic crisis. Other Calculations In order to conduct this study, I required the following statistics in the given time period for each fund: monthly returns, annualized monthly returns, annualized standard deviation, and load fees for the relevant funds. From these statistics, I could calculate fund Sharpe ratios, CAPM and Fama-French expected returns and alphas, and load adjusted returns. The first step in this study was obtaining historical prices of all funds and indices included in the study. From there, I calculated monthly returns by subtracting each month s price by the previous month s price and dividing by the previous month s price. For example: (February, 2007 Price January, 2007 Price)/January Price = February 2007 monthly returns To annualize these returns, I could have simply multiplied the average of monthly returns by 12. Representing the arithmetic average of monthly returns. This method is commonly referred to as a cumulative return, and is easy and efficient, but is an imperfect method for representing the overall return of an investor who bought a security at the beginning of a period of more than a year. Therefore, in this study, I calculated the annual returns of the funds using a geometric average, commonly referred to as a buy and hold return, which smooths the volatility of the security and more accurately represents the

36 28 overall returns of an investor who invests in the fund at the beginning of the period of study and holds it through the end of the period. To calculate the geometric average: [(Pn/P0)^(1/n)]1 Where Pn = The price of the security at the end of the period P0 = The price of the security at the beginning of the period N = the number of periods (in this study, n= 6 years) After calculating annualized returns, I used Microsoft excel to calculate the standard deviation of monthly returns of each individual fund and multiplied that number by the square root of 12. From there I calculated each no-load fund s Sharpe ratio by subtracting annual (fund returns annualized risk free rate)/ annualized standard deviation. 1 For load funds, I used the same formula using the funds load-adjusted returns instead. 1 For Sharpe ratio equation please see section of Introduction

37 Chapter 4 29 Results Cumulative Returns, Standard Deviation, and Sharpe Ratios. Based upon data stretching from the beginning of the great recession in 2007 through the beginning of the economic recovery at the end of 2012, the buy and hold returns, as calculated by the geometric average of monthly returns throughout the aforementioned period suggests that Pollock is in fact correct. As seen in tables one, two, and three below, as well as appendix, the returns for January 1, 2007 through December 3, 2012 suggest that Pollock may have been correct. When adjusted for load fees, actively managed load funds and non-load funds outperformed indexed funds on based on returns and standard deviation, and therefore Sharpe ratio as well. While active load funds did slightly outperform no-load funds in terms of volatility, the extra returns on no-load funds gives the no load funds a higher average Sharpe ratio, therefore making it a better investment strategy through a period of deep economic recession and recovery. As stated earlier in this paper, the Sharpe ratio is perhaps the most important measure of returns on a financial asset as it allows for the risk-adjusted comparison of different financial securities. Because of this, the data below suggests that while load funds still do not outperform all available funds in the market, they do, in Pollock s ideal scenario, outperform their Indexed counterparts.

38 Table 1. Buy and Hold Returns, Std. Dev., and Sharpe Ratios of Index Funds 1/1/ /1/ Index Funds Ticker Annualized Geometric Return Annual Std. Dev Sharpe Ratio Morningstar Classification VTSMX 2.40% 18.38% Large Growth VINIX 2.07% 17.76% Large Blend VGTSX -0.30% 23.16% Large Blend VFINX 1.95% 17.76% Large Blend FUSEX 1.92% 17.76% Large Blend VIMSX 2.89% 21.15% Mid Blend NAESX 3.92% 23.24% Small Blend VITNX 1.45% 18.37% Large Blend VEXMX 3.55% 22.11% Small Growth FSTMX 2.34% 18.33% Large Blend VIGRX 4.22% 18.15% Large Growth VGSIX 0.41% 30.87% Mid Growth PREIX 1.81% 17.75% Large Blend VTMGX -1.19% 22.39% Large Blend SWPPX 2.04% 17.69% Large Blend VIVAX 0.12% 18.33% Large Value FSEMX 3.69% 21.44% Small Growth VISVX 2.27% 23.37% Small Value VISGX 5.42% 23.70% Small Growth TIEIX 1.00% 18.45% Large Blend NOSIX 1.83% 17.85% Large Blend RUI 0.12% 18.13% Index RUT 1.00% 22.89% Index RUA 0.19% 18.42% Index SPY 1.98% 17.71% ETF Average 1.88% 20.21% Table 2. Buy and Hold Returns, Std. Dev., and Sharpe Ratios of No-Load Funds 1/1/ /1/2012 Active No Load Funds Ticker Annualized Geometric Return Annual Std. Dev Sharpe Ratio Morningstar Classification FCNTX 4.37% 16.27% Large Growth DODGX -0.50% 20.54% Large Blend VGHCX 5.39% 14.01% Large Growth VPMCX 4.09% 17.41% Large Growth VWNFX 1.20% 18.06% Large Value PRGFX 3.62% 18.99% Large Growth

39 31 FLPSX 4.36% 19.53% Middle Blend FDGRX 5.95% 19.77% Large Growth TRBCX 4.08% 19.13% Large Growth VDIGX 4.33% 14.03% Large Blend HACAX 4.15% 17.58% Large Growth RPMGX 6.40% 19.99% Mid Growth TRVLX 1.81% 20.09% Large Value PRFDX 1.62% 18.58% Large Growth MADVX 3.93% 15.53% Large Value FBGRX 3.93% 15.53% Large Growth VEIPX 3.22% 15.99% Large Value VWNDX 0.06% 19.85% Large Blend FMAGX -0.53% 21.76% Large Growth OAKMX 4.03% 19.89% Large Blend PRNHX 7.23% 20.73% Mid Growth DFLVX 0.62% 22.52% Large Value DFQTX 2.10% 20.28% Large Blend SEEGX 5.59% 18.72% Large Growth VHCOX 3.59% 20.21% Large Growth Average 3.38% 18.60% Table 3. Buy and Hold Returns, Std. Dev., and Sharpe Ratios of Load Funds 1/1/ /1/2012 Active Load Funds Load Adjusted Annualized Standard Load Adjusted Front Rear Morningstar Classification Ticker return deviation Sharpe ratio load load L AGTHX 2.27% 17.87% % 0.00% 5.75% Large Growth AWSHX 1.75% 16.12% % 0.00% 5.75% Large Value AIVSX 1.38% 16.44% % 0.00% 5.75% Large Blend ANCFX 2.65% 18.48% % 0.00% 5.75% Large Blend AMCPX 2.92% 17.94% % 0.00% 5.75% Large Growth AMRMX 2.60% 14.49% % 0.00% 5.75% Large Value MFEBX 0.93% 17.35% % 4.00% 4.00% Large Value FNIAX 3.62% 16.46% % 0.00% 5.75% Large Growth FRDPX 2.11% 15.49% % 0.00% 5.75% Large Blend MLAAX 4.31% 19.16% % 0.00% 5.50% Large Growth TEMTX -0.65% 16.48% % 1.00% 1.00% Large Value JAMCX 3.26% 18.39% % 0.00% 5.75% Mid Blend ANEFX 2.95% 19.40% % 0.00% 5.00% Large Growth JVLAX -0.25% 18.32% % 0.00% 4.75% Large Value LCEAX 1.25% 19.40% % 0.00% 5.75% Large Value

40 32 JUEAX 3.19% 18.32% % 0.00% 5.50% Large Growth SHRAX 2.48% 16.77% % 0.00% 5.50% Large Growth NYVTX 1.19% 18.99% % 0.00% 5.75% Large Blend FKGRX 5.95% 18.47% % 0.00% 5.50% Large Growth ACSTX 2.26% 19.67% % 0.00% 5.50% Large Value SVAAX 1.26% 13.70% % 0.00% 5.50% Large Value JVAAX 8.88% 19.16% % 0.00% 5.75% Large Value DDVAX 3.16% 16.12% % 0.00% 5.75% Large Value ITHAX 4.31% 18.47% % 1.00% 1.00% Large Growth VAFAX 3.99% 17.78% % 0.00% 5.50% Large Growth Average 2.71% 17.57% % 0.24% 5.16% Alpha Analysis It is clear that these data points suggest that Pollock s theory of active management in times of economic volatility and steep downturn. Furthermore, now that the study has established the potential validity of Pollock s theory, we can now use the alpha variable to test the concept that alpha factor of the Fama-French analysis could indicate manager ability. With a positive alpha showing a manager s skill in picking underlying securities and a negative alpha showing a managers ineptitude in doing so. Whereas in an index fund a positive or negative alpha tells nothing of the non-existent manager and simply shows if the fund over or underperformed the market based on the Fama- French Factors.

41 FUND ALPHAS FCNTX DODGX VGHCX VPMCX VWNFX PRGFX FLPSX FDGRX TRBCX VDIGX HACAX RPMGX TRVLX PRFDX MADVX FBGRX VEIPX VWNDX FMAGX OAKMX PRNHX DFLVX DFQTX SEEGX VHCOX Avg ALPHA VALUE Figure 4. Load Fund Alphas Load Fund Alphas FUND TICKERS Figure 5. No Load Fund Alphas No Load Alphas FUND TICKERS

42 FUND ALPHAS VTSMX VINIX VGTSX VFINX FUSEX VIMSX NAESX VITNX VEXMX FSTMX VIGRX VGSIX PREIX VTMGX SWPPX VIVAX FSEMX VISVX VISGX TIEIX NOSIX RUI RUT RUA SPY Avg Figure 6. Index Fund Alphas 34 Index Fund Alphas FUND TICKERS Above in figures four through six as well as in the data of appendix D we see that actively managed funds seemed to have higher alphas than both its no-load and indexed peers. While it is worth noting that the average alpha of the no load funds was brought down by three or four highly negative outliers, it remains, clear that the alpha factors of the load funds is widely superior. As seen by the fact that 12 of the 25 no load funds experienced negative alphas over the period of the study while only two load funds experienced negative values over the same period. While this does support Pollock s theory that the best managers flock to where they get paid most, there is no definitive way to prove the highly positive alphas in load funds was caused by the manager, and given the sample size, could still be attributable to the anomalous returns that Sharpe and Treynor often cite. Also worth mentioning: because index funds have no manager picking the underlying securities, it is significantly more subject to market momentum and widespread upticks and downturns, and momentum is not a factor considered in the Fama-

43 French model, but was later added in the Carhart four factor model. While this is a common 35 argument in favor of active management, the majority of academic literature states that if an investor plans to stay in the market for an extended period, such as one would in a retirement investment account or when saving for a child s college education, etc. that passive management enjoys higher net returns. Even considering widespread market downturns, investors would be better off riding out recessions in passive funds in order to avoid fees, as their overall returns to investors tend to be higher. Regardless, all data in this study supports Pollock s theory of active management in times of economic volatility as well as Elton, Gruber, and Blake s theory that the best managers flock to the funds with the highest fees that get them the most pay. A theory that, as stated in the literature review above, is highly controversial. In order to test the statistical legitimacy of the results of the alpha factor, this study conducted a Welch T test. This test assumes that the underlying stock prices, and therefore the mutual fund prices, are independent of each other as well as individually distributed. The calculation starts with the null hypothesis henceforth referred to as the null: μ load = μ non load = μ index These tests must be run independently, and will therefore be done three separate times. In order to prove or disprove the null, one must first calculate a T value, calculated as: Where = The average of the first sample (in this case alphas of one type of fund) = The average of the second sample (in this case alphas of one type of fund)

44 & represent the average of the alphas of the population of all mutal funds in the given asset category, however based on the null we assume these cancel out in the equation above 36 & represent the variances of the alphas of the sample and & represent the number of funds in each sample category After achieving a T value, the study requires a calculation for the degrees of freedom of the test, calculated and represented by the r variable with the same underlying statistics as follows: Then, given your T stat and degrees of freedom, you calculate a t score at a given level of confidence, which I have chosen at 95%, or 2.5% in each tail of the normal distribution. If my T stat has a greater absolute value than the t score given the calculated degrees of freedom and preset confidence level, the null hypothesis of the population of all mutual fund alphas being equal will be rejected, and the study can say at a 95% level of confidence that the entire population of fund alphas across the different types of funds was different over the period of the study After running these tests, the values for comparing index and non-load funds, index and load funds, and load vs non-load funds are in the following table:

45 Table 4 Welch T-test statistics 37 Stat Description Load and NL Index and Load Index and NL SQRT(Numerator) ----> E E E-05 Numerator > E E E-10 Denominator----> E E E-11 Degree of Freedom T Stat = t Therefore, given that T stats for all three of the comparisons have a significantly higher absolute value than the respective t score at a 95% confidence interval, the findings of this study conclude with 95% confidence that the difference in the alpha values of all index funds vs. all non-load funds vs all load funds over the period of this study should be statistically different.

46 Chapter 5 Large Growth Load vs. Non Load Funds 38 Amongst the many potential explanations for the difference in fund performance, specifically between the two forms of active management, perhaps most obvious guess would be the Morningstar investment styles of funds. However, the most common investment style amongst both forms of active management in the top 25 mutual funds by assets under management was large growth. That the fund invested in underlying assets with a large market cap and high growth. Therefore, one could argue that one of the main reasons for active management s outperformance of index funds throughout this study was due to the style of investment best suited to an economic recession. However, this paper does not have enough data to speak to the validity of the argument. Within actively managed large cap growth funds, as seen from the following graph, deviates even further from common investment wisdom. Figure 7. Comparison of Large Cap Growth Actively Managed Funds 0.2 Load V. Non-Load funds Average Returns Avg. Annual Std. Dev Avg. Sharpe ratio Avg. Alpha Load Funds Non Load Funds Note 1. All load fund data, including returns, Sharpe ratio, and alpha adjusted to include load fees.

47 39 The graph above shows that if an investor had placed funds in only large cap growth active funds over the period of this study, he or she would have achieved a higher risk adjusted return for their investment. While the non-load funds would achieve a slightly higher return on a buy and hold basis, the excess risk involved significantly lowers the Sharpe ratio, making the large cap growth load mutual funds a superior risk adjusted investment, even after accounting for loads in calculations. Furthermore, this limited sample of large cap growth funds suggests that within this narrow style of investments, managers who receive a load fee do in fact have superior ability to pick underlying assets to those who run funds without a load fee. Although as discussed in the previous section of this paper that is not definitively true, as other reasons that this study did not explore could be contributing to these results.

48 40 Chapter 6 Conclusion This study produced results that were in some ways consistent with previous studies and in other way entirely different. This study shows that load funds do not, even under what Pollock describes as ideal circumstances for active management, outperform actively managed no load funds, as managers tend to be unable to perform so well as to out-earn their fees on a consistent basis. However, this study also found, against most conventional wisdom, that active funds, both load and no-load, outperform index funds through a period of high volatility and economic recession. While the data from this study suggests that active management is superior in this particular economic scenario, it does not provide definitive proof. This study did not isolate fund investment style, fund families, or account for different methods of expected return such as CAPM, or the Carhart Four Factor Model. Therefore, while the results are indicative but not definitive, overall the results of this study support the theory that active managers do in fact have an ability to allocate fund assets in a superior fashion than simply allocating to an index. However, due to load fund s inability to outperform no load funds on a fee adjusted basis, this study concludes that investors are not compensated with higher, or high enough returns to justify paying load fees and were best off investing in no-load mutual funds during periods of large scale economic recession and high volatility. In the future, derivations of this study could deviate from this study in several ways. One could extend the period of the study to observe a longer period of time that includes the great recession, to see if the inclusion of a more stable economic period suggests passive or active management. Further studies might also isolate funds in one square of the Morningstar style box, in order to determine which

49 investment style netted investors the best returns over the period, although such a study would require 41 more index funds in various categories in order to prove statistically significant.

50 42 Appendix A Mutual Funds Investment Class, Expenses Ratios, and AUM Ticker Fund Type Expense Ratio AUM (Millions AGTHX Active Loaded 0.65% $ 123, AWSHX Active Loaded 0.58% $ 70, AIVSX Active Loaded 0.59% $ 66, ANCFX Active Loaded 0.61% $ 65, AMCPX Active Loaded 0.68% $ 41, AMRMX Active Loaded 0.58% $ 32, MFEBX Active Loaded 1.61% $ 32, FNIAX Active Loaded 0.92% $ 24, FRDPX Active Loaded 0.92% $ 15, MLAAX Active Loaded 0.99% $ 14, TEMTX Active Loaded 1.80% $ 13, ANEFX Active Loaded 0.79% $ 13, JVLAX Active Loaded 1.08% $ 12, NYVTX Active Loaded 0.86% $ 11, DDVAX Active Loaded 0.98% $ 9, ITHAX Active Loaded 1.09% $ 8, VAFAX Active Loaded 1.08% $ 7, LBSAX Active Loaded 1.02% $ 7, PEEAX Active Loaded 1.05% $ 7, IHGIX Active Loaded 1.02% $ 6, ACGIX Active Loaded 0.83% $ 6, SGRAX Active Loaded 1.18% $ 6, MITTX Active Loaded 0.71% $ 6, PLGJX Active Loaded 0.97% $ 6, FCNTX Active Non-Loaded 0.71% $ 102, DODGX Active Non-Loaded 0.52% $ 50, VGHCX Active Non-Loaded 0.34% $ 47, VPMCX Active Non-Loaded 0.40% $ 43, VWNFX Active Non-Loaded 0.34% $ 42, PRGFX Active Non-Loaded 0.67% $ 41, FLPSX Active Non-Loaded 0.79% $ 37, FDGRX Active Non-Loaded 0.87% $ 36, TRBCX Active Non-Loaded 0.71% $ 29,132.69

51 VDIGX Active Non-Loaded 0.32% $ 25, HACAX Active Non-Loaded 0.64% $ 25, RPMGX Active Non-Loaded 0.77% $ 22, TRVLX Active Non-Loaded 0.81% $ 21, PRFDX Active Non-Loaded 0.66% $ 21, MADVX Active Non-Loaded 0.69% $ 19, FBGRX Active Non-Loaded 0.88% $ 19, VEIPX Active Non-Loaded 0.26% $ 18, VWNDX Active Non-Loaded 0.39% $ 15, FMAGX Active Non-Loaded 0.68% $ 14, OAKMX Active Non-Loaded 0.85% $ 14, PRNHX Active Non-Loaded 0.79% $ 13, DFLVX Active Non-Loaded 0.27% $ 13, DFQTX Active Non-Loaded 0.22% $ 13, SEEGX Active Non-Loaded 0.90% $ 13, VHCOX Active Non-Loaded 0.45% $ 12, VTSMX Index 0.16% $ 332, VINIX Index 0.04% $ 185, VGTSX Index 0.19% $ 178, VFINX Index 0.16% $ 171, FUSEX Index 0.09% $ 86, VIMSX Index 0.20% $ 61, NAESX Index 0.20% $ 50, VITNX Index 0.04% $ 37, VEXMX Index 0.22% $ 35, FSTMX Index 0.10% $ 29, VIGRX Index 0.22% $ 46, VGSIX Index 0.26% $ 51, PREIX Index 0.27% $ 24, VTMGX Index 0.09% $ 50, SWPPX Index 0.09% $ 20, VIVAX Index 0.23% $ 18, FSEMX Index 0.10% $ 14, VISVX Index 0.23% $ 10, VISGX Index 0.23% $ 9, TIEIX Index 0.05% $ 9, NOSIX Index 0.11% $ 6, SPY Index 0.09% $ 170, Note 2 All values and styles directly from Bloomberg terminals 43

52 Appendix B 44 Fama- French Data for the Period of January 1, 2007 through December 3, 2012 FF3F Mkt-RF SMB HML ######## ######## ######## /4/ /1/ /2/ /1/ /1/ /2/ /1/ /1/ /3/ ######## ######## ######## /1/ /1/ /1/ /1/ /2/ /1/ /1/ /1/ /3/ ######## ######## ######## /1/ /2/ /1/ /1/ /3/ /1/ /1/ /1/ /4/ ########

53 ######## ######## /1/ /3/ /1/ /1/ /1/ /1/ /2/ /2/ /2/ ######## ######## ######## /2/ /1/ /1/ /2/ /1/ /1/ /3/ /1/ /2/ ######## ######## ######## /4/ /1/ /2/ /1/ /1/ /2/ /1/ /1/

54 AGTHX AWSHX AIVSX ANCFX AMCPX AMRMX MFEBX FNIAX FRDPX MLAAX TEMTX JAMCX ANEFX JVLAX LCEAX JUEAX SHRAX NYVTX FKGRX ACSTX SVAAX JVAAX DDVAX ITHAX VAFAX Average Cumulative Geometric return Appendix C 46 Annualized Returns (adjusted for load fees when applicable) Load Adjusted Fund Returns 9.00% 8.00% 7.00% 6.00% 5.00% 4.00% 3.00% 2.00% 1.00% 0.00% -1.00% Fund Ticker Active No-Load Cumulative Fund returns 9.00% 8.00% 7.00% 6.00% 5.00% 4.00% 3.00% 2.00% 1.00% 0.00% -1.00%