An examination of the
Preface
With this thesis my university career has officially been completed. As probably the last ‘doctoraal’ student I have many good memories of my time in Groningen. Memories of classes filled with men – are there no women interested in finance? - and long hours of studying. But more importantly, memories of a sparkling social life and gaining knowledge about equity markets in practice. I am looking forward to exploring the world of finance even further.
I want to thank my supervisor dr. A. Plantinga for his advice and support. His enthusiasm for finance is contagious and I hope he will infect many more students with his ‘virus’.
Abstract
This paper examines the performance of U.S. equity funds during 1991-2006. There exists a large variation in return among mutual funds. Selecting the best mutual fund is an important, but difficult process. Our research makes a contribution in simplifying the selection process. An extensive examination of 3891 regression analyses leads to the conclusion that the risk of the mutual fund, defined by the Fama and French [1993] 3-factor model, does not solely explain the return of the fund. Statistically significant abnormal returns exist.
Contents
1. Introduction
51.1 The Capital Asset Pricing Model 5
1.2 The Fama and French [1993] 3-factor model 6
1.3 The examination of abnormal returns 9
1.3.1 Diversification and non-systematic risk 9
1.3.2 The effect of expenses on performance 12
1.3.3 Portfolio turnover of mutual funds 15
1.4 Overview 16
2. Data
173. Methodology
203.1 Fama and French [1993] 3-factor model: performance measurement 20 3.2 Fama and French [1993] 3-factor model: risk measurement 21
3.3 The examination of abnormal returns 22
4. Results
244.1 Abnormal returns of individual mutual funds 24
4.2 Risk of individual mutual funds 28
4.3 The effect of international diversification 29
4.4 Factors related to the abnormal returns of mutual funds 30
5. Conclusion and discussion
34Appendix
37A1 Robustness measures for the Fama and French [1993] 3-factor analysis 37
A2 Risk, t-statistics and r2 for individual mutual funds 39
A3 Robustness measures for the cross-sectional regression analysis 48
1. Introduction
Investors can choose to invest in various stocks. However, they can also decide to invest in a mutual fund containing a few or more of these stocks. One reason why many investors choose to invest in mutual funds is because mutual funds are diversified, which leads to a reduction of variability. A second reason is that professional investment managers, who claim to have more knowledge about the markets they invest in, manage the mutual funds. Both reasons should, in theory, lead to higher risk-adjusted performance.
Choosing a mutual fund is not easy. The mutual fund industry has grown tremendously. There are many funds to choose from with very different qualities, including management,
investment style and geographical allocation. How can one select the best mutual fund? There are large return differences found among mutual funds. For example, the USD yearly return in 2006 was 24.0% for the ABN Amro Latin America Equity Fund and –2.1% for the Corngest Asia fund.1 This means that selecting the best mutual fund of these two would have led to a substantial increase in performance in a short period. Indeed, making a well-informed decision is important and difficult. This leads to the main question of this paper: what causes certain mutual funds to excel in their performance compared to other funds?Or better said: which variables influence theperformance of a mutual fund?
1.1 The Capital Asset Pricing Model
The basis of mean-variance modern portfolio theory is created by Markowitz [1957]. Working forward on this basis, the Capital Asset Pricing Model (CAPM) was more or less simultaneously developed by Sharpe [1964], Lintner [1965] and Mossin [1966]. According to the CAPM the differences in return among mutual funds can only be explained by their risk. Beta can be used as a measure for risk. The CAPM assumes that investors want to be
rewarded for taking on extra non-diversifiable risk. Therefore, the higher the beta, the higher the required expected return of the asset.
Actual returns can vary from the expected returns calculated under the assumptions of the CAPM. Jensen’s alpha represents the difference between the actual and expected return and can be interpreted as the under- or overperformance of an asset. According to Jensen
[1968] a naïve random selection buy and hold strategy can be expected to have a Jensen’s alpha of zero. For a manager with forecasting abilities Jensen’s alpha is expected to be positive, while Jensen’s alpha is expected to be negative for managers with unsuccessful forecasting attempts. Jensen [1968] examined the performance of mutual funds during 1945-1964 and found only small abnormal returns. Most mutual funds are unable to beat the market.2
1.2 The Fama and French [1993] 3-factor model
According to the CAPM only risk, measured by beta, determines the expected return of an asset. However, in practice, other variables also seem to influence the average return of a stock. These patterns in average stock returns are not explained by the Sharpe [1964], Lintner [1965] and Mossin [1966] CAPM and therefore called anomalies. Fama and French [1996] argue that the following anomalies exist: size, book-to-market equity, earnings/price, cash flow/price, leverage, past sales growth, long-term past return and/or short-term past return. Beta does not seem to explain the cross-section of average stock return, however the combination of size and book-to-market equity seems to absorb most of the other CAPM average-return anomalies according to Fama and French [1996]. Fama and French [1992] suggest that book-to-market equity and size are proxies for distress of a firm, signalling poor prospects, and can be included in the CAPM as systematic risk. Therefore, Fama and French [1993] extend the CAPM into a 3-factor model adding the variables market-to-book equity and size. Opinions about this model are mixed as it is well used, but also criticized.3 Just as the CAPM, the Fama and French [1993] 3-factor model can be used for stocks as well as mutual funds.
The value (book-to-market equity) and size effect were documented many years before Fama and French [1993] decided to add these anomalies to the CAPM as systematic risk. The value effect was first documented by Stattman [1980], while Banz [1981] was the first to document the size effect.
2 The research of Jensen [1968] is criticized for using an insufficient amount of annual returns for the regression
analysis.
Stattman [1980] found a relation between average U.S. stock returns and book-to-market equity. Later on, Rosenberg, and Reid and Lanstein [1985] among others found the same value effect in the United States. Fama and French [1992] investigated these matters further and concluded that the value effect persisted over time, which led them to suggest that book-to-market equity can be seen as systematic risk. The research of Chen, Hamao and Lakonishok [1991] made it evident that the value effect does not only exist in the U.S., but also in Japan. This gave rise to the question if the relation between average stock returns and book-to-market equity might be a worldwide phenomenon. Fama and French [1998] provide evidence that this is indeed the case as they find value premiums in twelve of thirteen major markets around the world. Also, the higher returns for value stocks exist in developed as well as in emerging markets.
Banz [1981] was the first to document that size adds to the explanation of the cross-section of average stock returns provided by market betas. Average returns on small stocks are too high given their beta estimates, and average stock returns on large stocks are too low. Fama and French [1992] find a negative relation between average U.S. stock returns and size (market equity) for the period 1962-1990. This relation persists no matter which other explanatory variables are in the regressions and therefore the size effect is robust in the 1963-1990 returns on NYSE, AMEX and NASDAQ stocks. Chen, Hong, Huang and Kubik [2004] find evidence that fund size erodes returns, before and after fees and expenses, for U.S. equity mutual funds during 1962-1999.
In contrast, Grinblatt and Titman [1989] find mixed evidence of the size effect using a small sample of funds from 1974-1984. Droms and Walker [1994] find that asset size is not related to performance using data of international equity mutual funds during the period 1971-1990. However, in a more recent study, Droms and Walker [1995] examine this issue further. They find evidence that is consistent with the CAPM: portfolios of smaller funds appear to be more risky and because larger funds are more broadly diversified, risk and asset size should be inversely related. According to Droms and Walker [1995] large funds appear better able to manage their portfolio risk.
In theory, large mutual funds could have an advantage over small funds if the size advantage would mean that they have more resources available for research. However, as explained above, large mutual funds underperform small funds. There are various hypotheses given for this impact of size on average returns, among which liquidity problems, diseconomies of scale and differences in stock-picking abilities.
Perold and Salomon [1991], and Lowenstein [1997] suggest that a large asset base erodes fund performance because of trading costs associated with liquidity or price impact. A lack of liquidity might cause slower portfolio adjustments for larger funds. Or it might force larger funds to invest in its not-so-good ideas because it is impossible to invest more in its good ideas.
Chen, Hong, Huang and Kubik [2004] argue that organizational diseconomies related to hierarchy costs may play a role in addition to the liquidity in the diseconomies of scale. Berk and Green [2004] agree with this hypothesis and argue thatdiseconomies of scale in money management make it difficult for large funds to outperform smaller funds. There are many types of organizational diseconomies that lead to various hypotheses on why small funds outperform larger funds. Bureaucracy and related coordination costs are one example addressed by Williamson [1988]. Another set of diseconomies comes from the influence-cost literature (Milgrom and Roberts [1988]). Hierarchy costs are seen as yet another set of diseconomies of scale (Aghion and Tirole [1997], Stein [2002]). In large organizations with hierarchies, agents need to fight for their ideas to be implemented. If information cannot be directly verified by anyone other than the agent who produces it (for example investment ideas about local stock), that agent might have a harder time convincing others of his ideas. Small organizations without these hierarchy problems therefore outperform larger ones. Chen, Hong, Huang and Kubik [2004] find that consistent with the hierarchy costs hypothesis, small funds are significantly better in their investment choices regarding local stock. Another implication of hierarchy costs is that funds that are managed by one manager don’t have these information problems and perform better than funds managed by many managers. Chen, Hong, Huang and Kubik [2004] find evidence, consistent with this hypothesis, that solo-managed funds outperform co-solo-managed funds and are better at picking local stock.
1.3 The examination of abnormal performance
In this paper the Fama and French [1993] 3-factor model will be used to calculate Jensen’s alpha for Morningstar U.S. equity funds for the periods 1991-1994, 1995-1998, 1999-2002 and 2003-2006. Returns of mutual funds vary greatly and we examine whether this can be explained solely by the risk of the mutual fund. If Jensen’s alpha is significantly different from zero, the mutual fund is able to earn significant abnormal returns in excess of (or below) the market-required return for a fund of a given riskiness. We examine if there are indeed abnormal returns found among mutual funds. If so, what causes these abnormal returns? Can it be (partially) explained by other factors than the forecasting abilities of a mutual fund manager as claimed by Jensen [1968]?
The abnormal returns of the U.S. mutual funds are examined in a cross-sectional regression analysis. We assume that the size, earnings/price, cash flow/price, book-to-market equity, leverage, past sales growth, long-term past return and/or short-term past return anomalies are captured by the Fama and French [1993] 3-factor model as claimed by Fama and French [1996]. Therefore we will not include these factors in our cross-sectional regression analysis. We examine if there is a relation between the abnormal returns and the non-systematic risk, net expense ratio and portfolio turnover of the mutual funds.
Furthermore, we examine if there are any significant differences found between mutual funds that are well diversified or have limited international diversification.
1.3.1 Diversification and non-systematic risk
According to the CAPM assets have systematic and non-systematic risk. Systematic risk is market risk and can not be diversified away. Non-systematic risk is the risk that is unique to the asset and can be diversified away. The diversification effect of two assets is stronger when these assets have a lower correlation. If assets move more into opposite directions the
variability of the portfolio (standard deviation) containing these assets will be reduced more. The market portfolio has systematic risk, but no non-systematic risk. The performance of mutual funds is often compared with the market portfolio, however, this is problematic because the market portfolio is not directly observable. Therefore, indexes are used as
benchmarks. Mutual fund managers can choose to replicate the index (passive investing) or to try to beat the index (active investing). There are some constraints attached to passive
index. When the portfolio is not rebalanced in the same way as the index, a tracking error exists. If mutual fund managers have excellent skills, active investing leads to a higher performance. In order to beat the market index managers can decide to adjust the weights of certain stocks and/or to adjust the amount of stock in their portfolio. These two adjustments have implications for the non-systematic risk of the portfolio. It is possible that large weights in certain stock add more stock-specific (non-systematic) risk than can be diversified away. Also, reducing the number of stock in the portfolio can increase the non-systematic risk. For example, Statman [1987] argues that at least 30 stocks are needed to achieve an optimal variance reduction. For all of the above reasons, we expect that there is a relation between abnormal returns and non-systematic risk. Therefore, we include the non-systematic risk in our cross-sectional regression analysis.
Grinold [1989] argues that the added value (alpha) of active investing depends on the manager’s skill and the manager’s opportunity to add value. The manager’s opportunity to add value is determined by the number of securities in the manager’s universe. A manager of a global mutual fund will have more opportunities to add value than a manager of a mutual fund investing nationally.
Furthermore, past research has shown that international diversification of equity portfolios leads to diversification gains.4 Low correlations between assets lead to stronger diversification effects. Solnik [1976] shows that an internationally diversified portfolio has only half of the risk of a portfolio diversified with only U.S. stock. Thus, international diversification should in theory lead to diversification gains and gains in abnormal return.
The correlation structure of the international equity markets is not constant during time. This means that the benefit of international diversification is subject to change. Recent studies have shown that international correlation increases during high-volatility down markets.5 This is a time when the investor needs diversification the most. But according to Goetzmann, Lingfeng and Rouwenhorst [2005] the investment opportunity set expands when the time correlations of major markets increase, meaning that there are still international diversification benefits which mostly lie in emerging capital markets. Furthermore, Campbell et. al. [2002] find evidence that the correlation breakdown can be partly explained by
econometrical assumptions of bivariate normality of correlation estimates. And even though
4 See Grubel [1968], Levy and Sarnat [1970], Solnik [1974], Grauer and Hakansson [1987], Eldor, Pines, and
Schwartz [1988], DeSantis and Gerard [1997], among others.
5 See Solnik, Boucrelle and LeFur [1996], Goetzmann, Lingfeng and Rouwenhorst [2005], Longin and Solnik
the globalisation of equity markets in the previous years could lead to higher correlations, Ang and Bekaert [2002] find that the benefits of international diversification are still significant under most circumstances.
Under the classical CAPM risk reduction can be measured by the reduction in the standard deviation of return. The ease of a simple risk measure does not exist anymore with the use of the Fama and French [1993] 3-factor model. The Fama and French [1993] 3-factor model has added two components of systematic risk to the CAPM. The risk of the mutual fund now consists of size, value (market-to-equity) and market risk. If mutual funds “load up” on size and value stocks, they can create a portfolio with higher risk than the market portfolio (and therefore a higher expected return), but not necessarily a higher standard deviation. Simply looking at the standard deviation of the portfolio return gives a wrong picture in the Fama and French [1993] 3-factor world.
Despite of the diversification potential of investing internationally, a home bias makes investors under invest in foreign stock. Information asymmetries (for example language barriers and transparency problems)6, government restrictions, foreign taxes, and fees and transaction costs are the most common explanations for this home bias.7
Information asymmetries can have a deep impact on performance. Some mutual funds claim that a concentrated strategy gives them comparative advantage over other mutual funds due to the difficulty of finding information in an inefficient market. This might boost
performance even more than the gains of extra diversification. Kacperczyk, Sialm and Zheng [2005] study the relation between the industry concentration and the performance of actively managed U.S. mutual funds from 1984-1999. Their results indicate that, on average, more concentrated funds perform better after controlling for risk and style differences using various performance measures. This finding suggests that managers perform better when
concentrating on a few industries. Therefore, one can question if concentrating on one country might also lead to increased performance.
In addition to being unable to concentrate management attention, the effect of distance adds to the disadvantages of going global. Malloy [2005] examines the effect of distance on the accuracy of equity analyst’ forecasts and recommendations. Malloy [2005] provides evidence that local analysts are significally more accurate than other analysts. The results
suggest that local analysts have an information advantage over other analysts, which leads to better performance. This local advantage exists especially for small stocks and stocks located in remote areas. In Malloy’s research, local analysts do not outperform other analysts simply as a result of covering fewer stocks or through increased specialisation. This effect of distance exists between countries but also within a country. For example, Coval and Moskowitz [1999] show that U.S. domestic portfolio funds are geographically biased toward the home of the fund.
Language barriers are another part of the information asymmetries. Hau [2001] finds that foreign traders in non-German-speaking financial centers have lower trading profits in their trading of German blue-chip stocks. Chan, Covrig and NG [2005] find that when a host country is more remote from the rest of the world and has a different language, foreign investors will invest less in this country.
Information disadvantages may be stronger for non-transparent countries. Gelos and Wei [2005] examine if country transparency affect international portfolio investment. They distinguish between government (data transparency and macroeconomic policy transparency) and corporate transparency and find that funds systematically invest less in less transparent countries.
Foreign taxes and government restrictions are also a common explanation for the home bias. In addition, they influence the size of the market of a country. For example, favourable banking and tax laws explain the large equity market of Luxembourg. Mutual fund industries are larger in countries where mutual fund investors’ rights are better protected with stronger rules, laws, and regulations.8
1.3.2 The effect of expenses on performance
Costs of fund ownership have always been a trivial subject. Funds with high returns before costs might suddenly not do so well after costs are deducted. Actively managed funds incur higher trading costs than passively managed funds. Costs are an important subject to take into account when choosing a mutual fund. In our cross-sectional regression analysis we examine whether there is a relation between the abnormal performance and net annual expense ratios of U.S. equity funds during 1991-2006.
Fund fees differ from fund to fund and across countries. In the U.S. we can distinguish two different costs of holding a mutual fund: the net expense ratio and distribution fees. We will only include the net expense ratio in the cross-sectional regression analysis. The total annual net expense ratio includes all annual expenses levied by a fund on its investors, covering investment management (management fees), administration, servicing, transfer, agency, audit, legal and 12b-1 fees etc. The expense ratio is expressed as a percentage of the fund’s assets. If the fund’s assets are small, the expense ratio can be quite high because the fund must meet its expenses from a restricted asset base. Conversely, as the net assets of the fund grow, the expense ratio should ideally decrease as expenses are spread across the wider asset base. The expense ratio excludes distribution charges such as front-end or back-end loads paid when entering or exiting the fund, as well as ongoing or annual distribution fees that are charged separate from the fund charges.
Since 1980, mutual funds have been permitted to deduct 12b-1 distribution fees from the fund’s assets. This has to be specified in the mutual fund’s prospectus. A mutual fund with 12b-1 fees is authorized to pay commissions to selling agents. Since 1993 there has been an annual cap on the 12b-1 charges placed at 75 basis points. However, there is also an annual service fee of 25 basis points allowed, which effectively raises the combined fee to 1 percent. In addition, only U.S. funds with a fee below 25 basis points can call itself a no-load fund. Theoretically the 12b-1 fees could give selling agents an incentive to sell additional shares, which could lead to economies of scale and lower costs to the investors. However, research contradicts this as 12b-1 funds have higher expense ratios9 and lower net investment returns10.
The relationship between net expense ratios and performance can be either positive or
negative based on two contradicting hypotheses. The relation can be positive if higher charges imply better management, better facilities and resources and actively traded funds with excess returns that outweigh the additional transactions cost and other expenses incurred. However, the majority of the research shows no11 or a negative relation between net performance and expense ratios. Expense ratios have an impact on the wealth of a fund, but more importantly they decrease the net performance of investors. Carhart [1997] finds a negative relation of net expense ratios to net performance, which is consistent with the finding of Dahlquist,
Engstrom and Soderlind [2000] of a negative relation between administrative fees and
9 Ferris and Chance [1987], Ferris and Chance [1991], Trzcinka and Zweig [1990], McLeod and Malhotra [1994]
and report that 12b-1 funds carry higher expense ratiosthan non-12b-1 funds
performance. Wermers [2000] finds that U.S. equity mutual funds do outperform the market (CRSP index) in 1962-1994 before expenses and transaction costs and have good stock-picking talent and style. However, after expenses and transaction costs, the mutual funds underperform the CRSP index due to lower average returns on non-stock holdings and expense ratios (incl. the transactions costs) of the funds.
Let’s take a closer look at the management fees which are part of the net expense ratio. Are some managers indeed better than others and are higher management fees in place? Chevalier and Ellison [1999] find large return differences in the U.S. between managers, but most of these can be explained by behavioural differences between managers and by selection biases and therefore not by ability, effort or knowledge of the manager. However, they do find that managers who attended higher-SAT undergraduate institutions have systematically higher risk-adjusted excess returns. Daniel et. al. [1997] have examined whether portfolio managers successfully time their portfolio weightings on stock characteristics and whether managers can select stocks that outperform the average stock having the same characteristics. According to their research of U.S. equity funds from 1975-1994, mutual funds have some selection ability, but no timing ability. This would imply that if Jensen [1968] is correct assuming abnormal returns depend on managers forecasting abilities, we can expect to find small positive abnormal returns.
Khorana, Servaes and Tufano [2006] examine mutual fees around the world. They focus on management fees, total expense ratios and total shareholder charges (which include loads). They find that different prices are charged for the same product in different countries. Furthermore, all of the above three fees are lower when a fund is sold across borders due to the foreign competition. Also, fees are lower in countries with stronger investor protection. However, when a fund is distributed in more countries, fees become higher as it is expensive to be registered in multiple countries.
Droms and Walker [1994] find that returns are not related to whether a fund is load or no-load, whereas Carhart [1997] finds that load funds underperform compared to no-load funds.
1.3.3 Portfolio turnover of mutual funds
Some mutual funds trade more than others. It is possible that some managers simply trade too much based on noise or that they trade too much due to higher risk-taking in order to prevent loosing their job (Khorana [1996]). But it is also possible that these managers are better skilled and therefore see more good investment opportunities. In this case, one could expect actively managed funds to outperform passively managed funds due to better selection and timing abilities of the manager. Thus, we expect portfolio turnover to be related to manager’s abilities and to explain part of the abnormal returns of U.S. mutual funds. For this reason portfolio turnover is included in the cross-sectional regression analysis. Note that even when actively managed funds see more good investment opportunities, the additional return still has to outweigh the additional trading costs in order to provide a gain to the investor.
Prior research on the relation between portfolio turnover and performance shows mixed results. Droms and Walker [1994] find no relation between turnover rates and investment performance in their sample of international equity mutual funds during the period 1971-1990, while Carhart [1997] finds a negative relation in his sample of U.S. equity funds during 1962-1993.
funds as well as low-turnover funds have stock-picking abilities, however, the stock-picking skills of high turnover funds are marginally better.
1.4 Overview
In this paper the performance of U.S. equity funds during 1991-2006 is examined. In chapter 2 and chapter 3 respectively, the data and methodology is explained. The result of our
research is presented in chapter 4. Returns of mutual funds vary greatly and in chapter 4.1 and 4.2 we examine whether this can be explained by solely the risk of the mutual fund, calculated under the Fama and French [1993] 3-factor model. We examine if there are indeed significant abnormal returns and mutual funds make more/less return than required.
2. Data
We collect information on U.S. equity funds for the period January 1991 - December 2006 from Morningstar. The data consists of monthly returns in U.S. dollars, geographical allocations on a monthly basis, annual net expense ratios, and annual turnover rates. The Morningstar U.S. equity fund monthly returns are not adjusted for sales charges (such as front-end loads, deferred loads and redemption fees). The returns do account for management, administrative, 12b-1 fees and other costs automatically deducted from fund assets.The annual turnover is the lesser of purchases or sales (excluding all securities with maturities of less than one year) divided by the average monthly net assets. The annual net expense ratio includes 12b-1 fees, management fees, administrative fees, operating costs, and all other asset-based costs incurred by the fund. Portfolio transaction fees, or brokerage costs, as well as initial or deferred sales charges are not included in the expense ratio.
The monthly risk-free and market returns are provided by Fama and French, as well as the Fama and French one-month SMB and HML factors.12 The risk-free return is the one-month Treasury bill rate (from Ibbotson Associates) and the market return is calculated as the value-weighted return on all NYSE, AMEX, and NASDAQ stocks (from CRSP).
Morningstar data exhibits survivorship bias, which causes average (abnormal) returns to be inflated. Elton et al. [1996] show that average performance measures are inflated between 0.40% and 1% per year, depending on the sample period. In contrary, CRSP data includes all mutual funds, but return data is missing for many. This so-called omission bias also inflates average return data upwards according to Elton et. al. [2001].
The original dataset of Morningstar is edited in order to eliminate the existence of multiple fund classes. Averages are calculated for the known data.
In order to allow for some variations in risk levels, we divide our database into periods of four years: January 1991 - December 1994, January 1995 - December 1998, January 1999 - December 2002, and January 2003 - December 2006. Average annual net expense ratios and annual turnover rates are calculated for these periods. In order to get net expense ratios and turnover rates on a one-month basis we divide the annual ratios by twelve. Funds with lacking data for a certain period are discluded from our period’s sample. We require the mutual funds to have all 48 monthly returns to be included in our period’s sample.
Furthermore, for each period the sample is divided into well internationally diversified US mutual funds (diversified) and US mutual fund with only limited international
diversification (non-diversified). We define a mutual fund as well diversified when it has a maximum of 80% invested into one region. We have divided the world into 4 regions using the definition of Morningstar: Americas, greater Europe, greater Asia, and the rest of the world (including the Middle East, Afrika and Australasia). We use average geographical allocations for the whole 4-year period in order to categorize the mutual funds. Note that our definition implies that an U.S. mutual fund with an allocation of 90% in Japan is also
categorized as non-diversified.
Our international allocation ratio is based on the research of Solnik, Boucelle and Le Fur [1996]. Solnik, Boucelle and Le Fur [1996] use 20% allocated in non U.S. stocks as the optimal international allocation, because most U.S. pension funds have a goal of investing 20% in non-U.S. stocks. Instead of just focusing on U.S. or non-U.S. stocks, we divide the world into more regions. We assume this raises the accuracy of our research, because international diversification benefits are obtained when the correlations of markets between regions are lower than the correlations of markets within one region.
Table 1 shows the summary statistics of our data. Monthly returns among mutual funds vary greatly, with a minimum of –47.97% and a maximum of 60.89% during the period 1991-2006. From 1999 to 2002 average monthly returns are far lower than during the other periods. The burst of the internet bubble in 2001 caused a downward pressure on returns.
Turnover rates vary greatly as well, between zero and 1860.25%. Morningstar defines a turnover ratio of 100% as considerable buying and selling, while a turnover ratio of 20% or 30% would indicate a buy-and-hold strategy. Average annual turnover rates are highest during the 1999-2002 period, but for all of the periods the average annual turnover ratio would indicate considerable buying and selling according to the definition of Morningstar.
Annual net expense ratios vary between zero and the extreme amount of 29.46%. Average annual net expense ratios have risen during 1991-2002, but seem to be decreasing a bit during 2003-2006.
Table 1
Mutual fund database summary statistics
The table reports monthly returns, annual turnover and annual net expense ratios for the Morningstar database of U.S. equity funds during 1991-2006. The mutual funds are divided into well diversified funds (diversified) and funds with only limited international diversification (non-diversified) for each period. Diversified mutual funds have a maximum of 80% of their stock invested in one region. The monthly returns are not adjusted for sales charges (such as front-end loads, deferred loads and redemption fees), but do account for management, administrative, 12b-1 fees and other costs automatically deducted from fund assets. The annual turnover is the lesser of purchases or sales (excluding all securities with maturities of less than one year) divided by the average monthly net assets. The expense ratio expresses the percentage of assets deducted each fiscal year for fund expenses, including 12b-1 fees, management fees, administrative fees, operating costs, and all other asset-based costs incurred by the fund. Portfolio transaction fees, or brokerage costs, as well as initial or deferred sales charges are not included in the expense ratio. The average for the whole period 1991-2006 is calculated as the weighted average of the four periods 1991-1994, 1995-1999, 1999-2002, and 2003-2006.
1991-2006 1991-1994 1995-1998 1999-2002 2003-2006 Total funds - 119 484 1,315 1,973 Diversified - 12 86 249 412 Non-diversified - 107 398 1,066 1,561 Monthly return (%) Average 0.99 1.11 1.62 0.04 1.47 Average (diversified) 1.02 0.98 1.66 0.03 1.49 Average (non-diversified) 0.99 1.12 1.61 0.04 1.47 Minimum -47.97 -9.42 -31.00 -47.97 -25.07 Maximum 60.89 14.01 46.79 60.89 23.09 Annual turnover (%) Average 90.50 72.31 82.37 97.66 88.82 Average (diversified) 84.90 68.64 75.15 101.89 77.14 Average (non-diversified) 91.86 72.72 83.93 96.67 91.91 Minimum 0.00 4.55 0.00 3.51 1.00 Maximum 1860.25 302.50 1732.84 1392.75 1860.25
Annual expense ratio (%)
Average 1.4616 1.2822 1.3887 1.5101 1.4580
Average (diversified) 1.5182 1.3052 1.4321 1.5870 1.5008
Average (non-diversified) 1.4479 1.2796 1.3793 1.4921 1.4467
Minimum 0.0000 0.1975 0.1500 0.0000 0.0000
3. Methodology
3.1 Fama and French [1993] 3-factor model: performance measurement
Returns of mutual funds vary greatly and we will examine whether this can be explained
solely by the risk of the mutual fund. We will use the Fama and French [1993] 3-factor model
as our model of performance measurement. The Fama and French [1993] 3-factor model has added two forms of systematic risk to the classical CAPM. If Jensen’s alpha is significantly different from zero, the actual return of the mutual fund significantly differs from the market-required return for a fund of a given riskiness. We will examine if there are indeed abnormal returns found among mutual funds. And if so, a cross-sectional regression analysis will examine which variables influence these abnormal returns. Furthermore, we will divide our sample into well diversified funds and mutual funds with limited international diversification in order to examine the effect of international diversification.
The Fama and French [1993] 3-factor model will be used to calculate one-month Jensen’s alpha for Morningstar U.S. equity funds for the periods 1991-1994, 1995-1998, 1999-2002 and 2003-2006:
(Rpt – Rft) = p + p (Rmt – Rft) + sp SMBt + hp HMLt + pt t = 1, 2, ..T (1)
where Rpt is the monthly return of the mutual fund, Rft is the monthly risk-free rate of return,
Rmt is the monthly return of the market, p the one-month Jensen’s alpha of the mutual fund, p beta of the mutual fund, pt the random error term, and SMB and HML the monthly return
on value-weighted, zero-investment, factor-minimizing portfolios for size and book-to-market equity respectively.
The Fama and French factors are constructed using returns of size and book-to-market portfolios. SMB (small minus big) is the average return on the three small portfolios minus the average return on the three big portfolios. HML (high minus low) is the average return on the two value portfolios minus the average return on the two growth portfolios.
) ( 3 1 ) ( 3 1 SV SN SG BV BN BG SMB= + + − + + (2) ) ( 2 1 ) ( 2 1 SV BV SG BG HML= + − + (3)
where SV is small value, SN is small neutral, SG is small growth, BV is big value, BN is big neutral and BG is big growth portfolio.13
3.2 Fama and French [1993] 3-factor model: risk measurement
One can expect mutual funds to be diversified because of the simple fact that mutual funds hold multiple assets and it is interesting to examine whether there is indeed this reduction in non-systematic risk. In order to outperform the market, mutual fund managers adjust the weightening and/or amount of stock in their portfolio, which can lead to a slight increase in non-systematic risk. In our cross-sectional regression analysis we will examine the relation between the abnormal returns and the non-systematic risk of the mutual fund. In addition, it is especially interesting to examine the effect of international diversification.
Under the assumption of the Ordinary Least Squares (OLS) method that the explanatory variables and the error terms are independent (cov( t,xt) =0), formula (4) represents the risk of an asset. The risk of an asset can be divided into a systematic and a non-systematic
component. Under the Fama and French [1993] 3-factor model var( i) is the non-systematic
risk component and remaining part of formula (4) is the systematic risk component.
var(Rpt – Rft) = p2 var(Rmt – Rft) + sp2 var(SMBt) + hp2 var(HMLt) + var( p) (4)
2 psp cov(Rmt – Rft , SMBt) + 2 php cov (Rmt – Rft , HMLt) +
2hpsp cov(HMLt , SMBt)
where var(Rpt – Rft) is the variance of the excess portfolio return, var(Rmt – Rft) is the variance
of the excess market return, var(SMBt) the variance of the SMB factor, var(HMLt) the
variance of the HML factor, cov(Rmt – Rft , SMBt) the covariance of excess market return and
SMB, cov (Rmt – Rft , HMLt) the covariance of the excess market return and HML, cov(HMLt ,
SMBt) the covariance of HML and SMB, and p the beta of the portfolio, and sp and hp the
coefficients of the SMB and HML explanatory variables for the portfolio respectively.
An implicit assumption of the OLS method is that the explanatory variables are not correlated with one another. Therefore, adding or removing a variable from the OLS regression equation does not cause the values of the coefficients of other variables to change. In this case, the covariances in equation (4) will be equal to zero. However, in practice, explanatory variables usually have small correlations for which the OLS method can still be used with only a small loss of precision.
3.3 The examination of abnormal returns
The abnormal returns of the mutual funds, represented by Jensen’s alpha, are examined further. What causes these abnormal returns? Can it be (partially) explained by other factors than the forecasting abilities of a mutual fund manager as claimed by Jensen [1968]? In order to try to answer these questions, we conduct a cross-sectional regression analysis. We assume that the size, earnings/price, cash flow/price, book-to-market equity, leverage, past sales growth, long-term past return and/or short-term past return anomalies are captured by the Fama and French [1993] 3-factor model as claimed by Fama and French [1996]. Therefore we will not include these factors in our cross-sectional regression analysis.
p = 0 + 1 EXPp + 2 TRp + 3 SQEp+ p (5)
where p is one-month Jensen’s alpha of the mutual fund, EXPp the annual net expense ratio
of the mutual fund divided by 12 months, TRp the annual turnover ratio of the mutual fund
divided by 12 months, SQEp the one-month standard deviation of the non-systematic risk of the mutual fund (the square of var( i) from formula (4)), p the random error term, with p the
pth mutual fund, and
4. Results
4.1 Abnormal returns of individual mutual funds
Using Morningstar monthly returns of U.S. equity funds we re-examine the work of Jensen [1968] and calculate Jensen’s alpha for each mutual fund. However, instead of using the classical CAPM as Jensen did, we use the Fama and French [1993] 3-factor model. The Fama and French [1993] 3-factor model has added two components of systematic risk to the CAPM. Returns of mutual funds vary greatly and we will examine whether this can be explained by
solely the risk of the mutual fund. If Jensen’s alpha is significantly different from zero, the
mutual fund is able to earn significant abnormal returns in excess of (or below) the market-required return for a fund of a given riskiness. Furthermore, we will examine if there are any significant differences found between well diversified mutual funds and mutual funds with limited international diversification.
We have divided our database into periods of four years. For each period the mutual funds are divided into diversified and non-diversified funds. This leaves us with eight samples: 1991-1994 diversified, 1991-1991-1994 diversified, 1995-1998 diversified, 1995-1998 non-diversified, 1999-2002 non-diversified, 1999-2002 non-non-diversified, 2003-2006 non-diversified, and 2003-2006 non-diversified. This means that for each mutual fund Jensen’s alpha is calculated for each period (containing sufficient data) resulting in a total of 3891 regression analyses. We find a relatively high amount of heteroskedasticity and a smaller amount of leptokurtosis and autocorrelation in our data sample, see appendix A1. The OLS method assumes that the errors are homoskedastic, uncorrelated and normally distributed (skewness: 0 and kurtosis: 3). When this is not the case and the OLS method is still used, this has consequences for the accuracy of the regression results.
reducing our sample size from four years (48 monthly returns) to three years (36 monthly returns) is not an acceptable option.
Heteroskedasticity means that errors change systematically with one of the
explanatory variables. This implies that the coefficient estimates under the OLS method are correct, but the standard errors and t-statistics are not accurate. In order to deal with the heteroskedasticity and autocorrelation, we use a robust least squares measure. We use the Newey and West [1987] method for heteroskedasticity and autocorrelation (both of unknown form) consistent standard errors to conduct our 3891 regression analyses.
Graph 1 shows the abnormal returns, represented by the constant in formula (1), of each sample. There are insufficient diversified mutual funds for the period 1991-1994 to make any significant conclusions about this sample. The one-month Jensen’s alpha has many far
outliers. There are also relatively large differences between funds. Alpha roughly varies between -3% and 2%, which is high on a one-month basis.
The market portfolio has an alpha of zero. Table 2 shows hypothesis tests for the variables of formula (1). A simple hypothesis test is conducted to examine whether the
average alpha (H0: =0) of the mutual funds differs statistically significantly from zero. Table 2 shows that alpha is significantly different from zero on a 1%-level for the period 1995-2006. Only during the years 1991-1994 abnormal returns are not significant. There is clear evidence that mutual funds exhibit abnormal returns for the period 1995-2006, although the average abnormal returns are positive as well as negative.14 During 1991-1994 the abnormal returns are positive, during 1995-1998 negative, during 1999-2002 positive and during 2003-2006 they are negative. The regression analyses have a high R squared15, which means that the risk of the mutual fund explains a large part of the return. But, solely the risk of the mutual fund, according to the Fama and French [1993] 3-factor model, does not explain the large variation in returns among mutual funds. The evidence makes us wonder if there is a systematic force behind the highly significant abnormal returns during 1995-2006. In chapter 4.4 we examine what causes the abnormal returns.
Jensen [1968] found smaller alphas, but he used the classical CAPM and calculated the alpha’s with yearly returns. He found alphas between –0.080% and 0.058% with an
average of –0.011%. The majority of the mutual funds do not have an alpha that is statistically significant from zero. Jensen’s research of the performance of mutual funds during 1945-1964
shows that the great majority of the mutual funds are unable to outperform the market.
However, his work is criticised for using an insufficient amount of annual observations for the regression analysis. But more recent research also finds limited or no statistically significant alphas in contrary to our findings.16
Graph 1
Abnormal returns of individual mutual funds
US equity mutual funds are examined during 1991-2006. The data is divided into four periods. Each period the mutual funds are sorted into well diversified funds and funds with limited international diversification.
Diversified funds have a maximum of 80% invested into one area. Non-diversified funds are noted with a #. Alpha is the intercept in formula (1) and is the abnormal return of a mutual fund compared to the return calculated under the Fama and French [1993] 3-factor model. The boxplots show the mean, median and far outliers of alpha per period. The Newey-West heteroskedasticity and autocorrelation consistent method is used for the regression.
-4
-3
-2
-1
0
1
2
3
199
1-1
994
199
1-1
994
#
199
5-1
998
199
5-1
998
#
199
9-2
002
199
9-2
002
#
200
3-2
006
200
3-2
006
#
16 Droms and Walker [1994] examined international equity funds during 1981-1990, Droms and Walker [1995]
Table 2
Hypothesis testing for abnormal returns and risk components
The market portfolio has an alpha, SMB, HML and error term of zero and a beta of one. A simple hypothesis test is conducted per sample to examine whether the average beta of the mutual funds differs statistically significantly from one (H0: =1) and the average alpha (H0: =0), average s (H0: s=0), average h (H0: h=0) and average SQEp
(H0: SQEp =0) differ significantly from zero. The , , s, h and SQEp are calculated under the Fama and French [1993] 3-factor model represented by formula (1). Each period
the U.S. mutual funds are sorted into well diversified funds and funds with limited international diversification. Diversified funds have a maximum of 80% invested into one area. Non-diversified funds are noted with a #.
Abnormal returns Systematic risk Non-systematic risk
Period Average (%) T-statistic (H0: =0)
Average T-statistic (H0: =1) Average s T-statistic (H0: s=0) Average h T-statistic (H0: h=0) Average SQEp (%) T-statistic (H0: SQEp =0) 1991-1994 -0.0386 -0.3923 0.8466 -2.2256** 0.1560 1.8606* 0.01826 0.2523 1.8302 6.8742*** 1991-1994 # 0.0257 1.0657 0.9429 -2.4928** 0.1988 5.9941*** -0.0028 -0.1095 1.6934 14.5324*** 1995-1998 -0.2010 -3.6216*** 0.9297 -4.0529*** 0.1989 6.6757*** 0.0227 0.6203 1.7646 19.4875*** 1995-1998 # -0.2648 -9.0378*** 0.9466 -7.2668*** 0.2236 13.7757*** 0.0237 1.3035 1.7874 29.9622*** 1999-2002 0.1120 4.0428*** 0.9675 -2.0330** 0.1918 11.2633*** 0.1503 6.1815*** 2.5317 32.9504*** 1999-2002 # 0.1264 9.9361*** 0.9682 -4.6696*** 0.1945 24.5472*** 0.1436 12.1114*** 2.4568 60.5085*** 2003-2006 -0.0470 -2.8247*** 0.9972 -0.3103 0.2005 10.9264*** 0.1278 6.7596*** 1.4305 30.9997*** 2003-2006 # -0.0589 -7.2709*** 0.9873 -2.9038*** 0.2206 24.0700*** 0.1177 12.0089*** 1.3820 57.3134***
4.2 Risk of individual mutual funds
There is clear evidence that mutual funds exhibit significant abnormal returns during the years 1995-2006, although the average abnormal returns are positive as well as negative. Thus,
solely the risk of the mutual fund, according to the Fama and French [1993] 3-factor model,
does not explain the large variation in returns between mutual funds during these years. The riskiness of the mutual fund depends on its systematic and non-systematic risk. According to the Fama and French [1993] 3-factor model the systematic risk of a mutual fund can be measured by , s and h. The non-systematic risk is represented by the standard deviation of the error terms.
Appendix 2 shows the boxplots of , s and h and the non-systematic risk of the mutual fund, represented by formula (1). There are insufficient diversified mutual funds for the period 1991-1994 to make any conclusions about this sample. Table 2 shows the hypothesis tests of the variables of formula (1). A simple hypothesis test is conducted to examine whether the average beta of the mutual funds differs statistically significantly from one (H0: =1) and the average s (H0: s=0), average h (H0: h=0) and average SQEp (H0: SQEp =0)
differ significantly from zero. Table 2 shows that the average beta of the mutual funds is lower than one for all periods. The mutual funds have lower market risk than the market portfolio. There is a significant positive size effect found for all of the periods. The value effect is mostly positive, but only significant during the years 1999-2006. Mutual funds seem to “load up” on size and/or value stocks.
Table 2 shows that the non-systematic risk is statistically significant from zero on a 1%-level for all of the periods examined. This is consistent with the hypothesis that mutual funds adjust the weightening and amount of stock in order to beat the market, which leads to a slight increase in non-systematic risk. Table 3 divides the risk of the mutual funds into
Table 3
Risk components of the excess portfolio return
Diversified mutual funds have a maximum of 80% invested into one area. Non-diversified mutual funds are noted with a #. The risk of the portfolio is decomposed into a systematic and a non-systematic risk component, see formula 4. The total portfolio risk is the average of the variance of the excess portfolio return for all mutual funds in the sample. The systematic risk component is the average of the systematic risk of all mutual funds per sample. The systematic risk of a mutual fund is p2 var(Rmt – Rft) + sp2 var(SMBt) + hp2 var(HMLt) + 2 psp cov(Rmt – Rft , SMBt) + 2 php cov(Rmt – Rft , HMLt) + 2hpsp cov(HMLt , SMBt). The non-systematic risk is the
average of the variance of the error term (var( p)) for all the mutual funds in the sample. In parentheses is the
percentage of systematic or non-systematic risk of the total portfolio risk.
Period Total portfolio risk (%) Systematic risk (%) Non-systematic risk (%)
1991-1994 12.4339 8.3047 (66.8%) 4.1292 (33.2%) 1991-1994# 14.8089 10.5018 (70.9%) 4.3071 (29.1%) 1995-1998 21.7726 17.9617 (82.5%) 3.8109 (17.5%) 1995-1998# 23.6495 19.0417 (80.5%) 4.6078 (19.5%) 1999-2002 43.6222 35.7489 (82.0%) 7.8733 (18.0%) 1999-2002# 43.6473 35.8560 (82.1%) 7.7913 (17.9%) 2003-2006 12.6463 9.7249 (76.9%) 2.9214 (23.1%) 2003-2006# 12.5597 9.7430 (77.6%) 2.8167 (22.4%)
4.3 The effect of international diversification
Each period the mutual funds are divided into well internationally diversified funds and funds with limited international diversification. Mutual funds that are well diversified on an
international basis invest a maximum of 80% in one region. The world is divided into four regions, which implies that international diversification benefits are obtained when the correlations of markets between regions are lower than the correlations of markets within one region.
Table 4 shows equality tests of the averages (H0: 1= 2) of the variables of formula (1) between the diversified and the non-diversified funds per period. The equality tests test if there are statistically significant differences for the average alpha, average beta, average s, average h and average non-systematic risk. Table 4 shows that there are no statistically
significant differences between diversified and non-diversified mutual funds, despite our strict definition of international diversification. This contradicts the view that international
diversification leads to diversification gains17. The non-systematic risk is not statistically significantly different and there are also no statistically significant differences in systematic risk.
Our results also contradict the hypothesis of Grinold [1989] that the value added (alpha) by the manager depends on the number of securities the manager can invest in.
17 See Solnik [1974], Solnik [1976] Grubel [1968], Levy and Sarnat [1970], Grauer and Hakansson [1987],
Although global funds have more opportunities to add value, they do not add more value than funds investing on a national basis. With our definition of international diversification there are no abnormal return gains. International diversification does not lead to diversification or abnormal return gains, which explains the home bias seen in practice.
Table 4
Testing for the effect of international diversification
Each period the mutual funds are divided into well internationally diversified funds and funds with limited international diversification. Mutual funds that are well diversified on an international basis invest a maximum of 80% in one region. Equality tests for means are performed to examine the effect of international
diversification. Equality tests are performed for the average alpha, average beta, average s, average h and the average standard deviation of the error terms (non-systematic risk) of formula (1).
Abnormal returns Systematic risk Non-systematic risk
Period
T-statistic for average alpha (H0: 1= 2)
T-statistic for average beta (H0: 1= 2) T-statistic for average s (H0: 1= 2) T-statistic for average h (H0: 1= 2) T-statistic for average SQEp
(H0: 1= 2)
1991-1994 0.8130 1.3347 0.4154 0.2602 0.3800
1995-1998 0.9365 0.9555 0.6574 0.2374 0.1688
1999-2002 0.4876 0.0389 0.1458 0.2442 0.81554
2003-2006 0.6627 1.0236 1.0000 0.4686 0.9230
*** 1% significance, ** 5% significance, * 10% significance
4.4 Factors related to the abnormal returns of mutual funds
Returns of mutual fund vary greatly and it appears that this can not be solely explained by the risk of the fund as assumed by the Fama and French [1993] 3-factor model. During our whole period (1991-2006) abnormal returns are found, which are significant on a 1%-level during the years 1995-2006. This evidence makes us question if there are (systematic) factors influencing the abnormal return of a mutual fund.
analysis. We examine if there exists a relation between the abnormal return and non-systematic risk, net expense ratio and portfolio turnover of the mutual funds. The cross-sectional regression analysis is redone for each period divided into samples of diversified and non-diversified funds.
The OLS method assumes that the errors are homoskedastic, uncorrelated and normally distributed (with a skewness of 0 and a kurtosis of 3). Our data exhibits heteroskedasticity and leptokurtosis, see appendix A3. The sample size is already large and removing extreme
residuals is not an acceptable option, therefore we make no adjustments to deal with the leptokurtosis. In order to deal with the heteroskedasticity and small amount of autocorrelation we use a robust least squares method. We use the Newey and West [1987] method for
heteroskedasticity and autocorrelation (both of unknown form) consistent standard errors to conduct our cross-sectional regression analysis.
Table 5
Cross-sectional regression analysis for abnormal returns
The cross-sectional regression analysis (see formula (5)) examines the relation between the abnormal returns and the expense ratio, turnover ratio and non-systematic risk. The average abnormal return is the average one-month alpha of all mutual funds in one sample. The expense ratio is the average annual net expense ratio for the period divided by 12. The turnover ratio is the average annual turnover ratio for the period divided by 12. The non-systematic risk is the standard deviation of the error terms (on a one-month basis). Internationally diversified funds have a maximum of 80% invested in one area. Non-diversified mutual funds are noted with a #. The standard errors are in parentheses. The Newey-West method for heteroskedasticity and autocorrelation consistent standard errors is used for the regression analyses.
Cross-sectional regression analysis Period Average abnormal return (%) Number of funds in sample
Constant Net expense
Table 5 shows the results of the cross-sectional regression analysis, represented by formula (5), between the abnormal returns and the net expense ratio, turnover ratio and non-systematic risk. There is an insufficient amount of diversified mutual funds for the period 1991-1994. For this reason we will exclude this sample from our conclusions.
Table 5 shows a negative relation between the net expense ratio and the abnormal returns, which is consistent with the results of other research.18 This negative relation is significant on a 5%-level for the years 1991-1994 and 1999-2006. The average net annual expense ratios are slightly higher for diversified mutual funds, as can be seen in table 1. The coefficient of the expense ratio in table 5 is also higher for diversified funds. This raises the question if expense ratios between diversified and non-diversified mutual funds are
statistically different. Table 6 tests for equality of average net expense ratios between diversified and non-diversified mutual funds and shows that the null hypothesis of equality can not be rejected.
There exists either a positive or a negative relation between the abnormal return and the portfolio turnover. During 1991-2002 the relation is positive, but during 2003-2006 the relation is negative. The relation is highly significant (1% level) for the years 1995-1998 and 2003-2006. Past research also shows mixed results. On the one hand, a positive relation exists when managers are skilled and see many investment opportunities.19 This could explain the positive relation during 1991-2002. On the other hand, a negative relation exists when
managers simply trade too much based on noise.20 It is also possible that managers are skilled and see good investment opportunities, but the additional trading costs do not outweigh the additional returns. If trading costs explain the negative relation during 2003-2006 we would expect the portfolio turnover to be the highest during this period. The summary statistics of our data in table 1 shows that this is not the case as the portfolio turnover is the highest during 1999-2002. Therefore, managers have probably traded too much based on noise during 2003-2006.
The results in table 5 show a statistically significant relation on the 5%-level between the abnormal returns and the non-systematic risk of the mutual funds during the whole period 1991-2006. However, there is a positive relation found during the years 1991-1994 and 1999-2006 and a negative relation during 1995-1998. The positive relation can be explained by the
18 See Carhart [1997], Dahlquist, Engstrom and Soderlind [2000], and Wermers [2000] among others. 19 Grinblatt and Titman [1989], Dahlquist, Engstrom and Soderlind [2000], Wermers [2000], Chen, Jegadeesh
and Wermers [2000] find a positive relation between performance and turnover.
20 Droms and Walker [1994] find no relation between performance and turnover, while Carhart [1997] finds a
theory that managers trying to beat the market adjust the weightening and amount of stock in their portfolio which (slightly) increases non-systematic risk. During 1995-1998 these
attempts to add value were apparently not successful.
The explanatory power of our model is relatively high. Between 11.1% and 38.3% of the abnormal return is explained by our model. There are no striking effects of international diversification, in contrary to the hypotheses that the manager’s opportunity to create abnormal returns depends on the number of securities in the manager’s universe (Grinold [1989]) and that international diversification leads to diversification gains21.
Table 6
International diversification and expense ratios
Each period the U.S. mutual funds are divided into well diversified funds and funds with limited international diversification. Mutual funds that are well diversified on an international basis invest a maximum of 80% in one region. An equality tests for means is performed to examine if average monthly expense ratios are different for diversified versus non-diversified mutual funds. The monthly expense ratio is the average net annual expense ratio during the period divided by 12.
Period T-statistic for average
expense ratio (H0: 1= 2)
1991-1994 0.1838
1995-1998 0.9148
1999-2002 1.3189
2003-2006 1.6433
*** 1% significance, ** 5% significance, * 10% significance
21 See Grubel [1968], Levy and Sarnat [1970], Solnik [1974], Grauer and Hakansson [1987], Eldor, Pines, and
5. Conclusion and discussion
Choosing a mutual fund is not easy. Qualities of mutual funds vary greatly and there are large return differences found among mutual funds. Our research makes a contribution towards simplifying the selection process for mutual funds. Selecting the best mutual fund can lead to a substantial increase in return. According to the CAPM these return differences can be explained by solely the risk of the mutual fund. The higher the risk of the mutual fund, the higher the expected return required by investors. We examine whether the large variation in returns among U.S. equity funds during 1991-2006 can indeed be explained by the risk of the mutual funds. We use the Fama and French [1993] 3-factor model where systematic risk is represented by size, value and market risk. Our extensive examination consisting of 3891 regression analyses indicates that mutual funds have lower market risk than the market portfolio, but “load up” on size and/or value stocks.
Actual returns vary from the expected returns calculated under the assumptions of the Fama and French [1993] 3-factor model. These abnormal returns are statistically significant from zero for the years 1995-2006. This result differs from the result found by Jensen [1968] and other researchers who examine more recent time periods22. They find that most mutual funds are unable to beat the market. Further research is needed to examine whether the internet bubble has triggered this change in abnormal returns. We find clear evidence that mutual funds exhibit abnormal returns, although the abnormal returns are positive as well as negative. Solely the risk of the mutual fund does not explain the large variation in returns among mutual funds.
What causes these abnormal returns? We conduct a cross-sectional regression analysis between the abnormal returns and the portfolio turnover, expense ratio and non-systematic risk of the mutual fund. We assume that the size, earnings/price, cash flow/price, book-to-market equity, leverage, past sales growth, long-term past return and/or short-term past return anomalies are captured by the Fama and French [1993] 3-factor model as claimed by Fama and French [1996]. Therefore we will not include these factors in the cross-sectional regression analysis. Furthermore, the effect of international diversification is examined.
According to Jensen [1968] abnormal returns are expected to be positive for managers with forecasting abilities, while it is expected to be negative for managers with unsuccessful
forecasting attempts. Consistent with this theory, we expect a relation between abnormal returns and portfolio turnover. There exist a highly statistically significant relation between portfolio turnover and abnormal returns for two of the four periods examined. During the years 1995-1998 this significant relation is positive, which is consistent with the hypothesis that managers are skilled and see many investment opportunities23, while it is negative during the years 2003-2006, which indicates that managers trade too much based on noise24.
Past research25 has provided evidence for a negative relation between net expense ratios and abnormal returns. Our results are consistent with these findings. We find negative relations for all of the years examined, of which half are significant. Higher expenses provide a downward pressure on net performance. Also, during all of the years there exists a
statistically significant (5% level) relation between the non-systematic risk and the abnormal returns of the mutual funds. This is consistent with the hypothesis that in order to beat the market, managers adjust the weightening and amount of stock in their portfolio, which increases non-systematic risk.
Despite our strict definition of international diversification, we find no diversification gains in investing internationally. This contradicts the well-accepted theory that investing on an
international basis leads to diversification gains.26 The non-systematic risk and systematic risk of the well diversified mutual funds and funds with limited international diversification show no statistically significant differences. We have defined that well internationally diversified mutual funds invest a maximum of 80% in one region. The world is divided into four regions, which implies that international diversification benefits are obtained when the correlations of markets between regions are lower than the correlations of markets within one region. Further research is needed to show if correlations between regions are indeed lower than correlations within one region. In addition, further research is needed to examine if the use of the Fama and French factors and market and risk-free return based on U.S. stock returns biases our research of mutual funds that invest (partially) outside the United States.
International diversification does not lead to gains in abnormal return. This result contradicts the theory of Grinold [1989] that the value added (alpha) by the manager depends
23 Grinblatt and Titman [1989], Dahlquist, Engstrom and Soderlind [2000], Wermers [2000], Chen, Jegadeesh
and Wermers [2000] find a positive relation between performance and turnover.
24 Droms and Walker [1994] find no relation between performance and turnover, while Carhart [1997] finds a
negative relation.
25 See Carhart [1997], Dahlquist, Engstrom and Soderlind [2000], and Wermers [2000] among others.
26 See Grubel [1968], Levy and Sarnat [1970], Solnik [1974], Grauer and Hakansson [1987], Eldor, Pines, and
on the number of securities the manager can invest in. Although internationally diversified funds have more opportunities to add value, they do not add more value than funds with limited international diversification. Apparently there is nothing to be gained by diversifying internationally, no diversification gains and no abnormal return gains, which explains the home bias27seen in practice.
There is a significant relation found with abnormal returns for all of the three variables. The explanatory power of our cross-sectional regression analysis between abnormal returns and expense ratios, turnover ratios and non-systematic risk is relatively high. Up to 38.3% of the abnormal returns are explained by our model. However, the results indicate that another force behind the abnormal returns is still to be discovered. We suggest an expansion of our model with measures for the timing and selection abilities of mutual fund managers.
27 See Gehrig [1993], Brennan and Cao [1997], and Kang and Stulz [1997], Lewis [1999], Hau [2001], Tesar and
