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  • 1. Mutual Fund Indexing versus Active Management Redux Rich Fortin New Mexico State University Stuart Michelson* Stetson University Contact author: Stuart Michelson, Stetson University, 421 N. Woodland Blvd, Unit 8398, Deland, Florida 32723, 386-822-7376, Fax: 386-822-7446, smichels@stetson.edu
  • 2. Abstract Indexing versus Active Mutual Fund Management Redux The purpose of this paper is to reexamine the relative investment performance of mutual funds that are actively managed versus an index approach over various fund classifications through time. Since actively managed funds have cost and tax disadvantages, do they perform well enough to outperform index funds? For overall parametric tests, we find that index funds outperform actively managed funds for the Growth/Income and Equity/Income (GIEI) and the balanced fund (AAB) categories and both bond fund categories while actively managed Aggressive Growth and Growth (AGG),Specialty Equity (SP), Small Company Equity (SCE), and International Stock (IS) fund categories significantly outperform the index over study period. The nonparametric tests provide overall results favoring index funds with the Sign Test indicating that Index funds outperform actively managed funds for all categories, except for SP and AGG funds. 2
  • 3. Indexing versus Active Mutual Fund Management Redux PURPOSE The purpose of this paper is to reexamine the relative investment performance of mutual funds that are actively managed versus indexing over various fund classifications over time. Since actively managed funds have cost and tax disadvantages, do they perform well enough to outperform index funds? Is there a benefit to active fund management over investing in passive index funds? MOTIVATION The relative benefits of active versus passive mutual fund management has been debated in the popular press and examined in the literature over the last few years. In support of active fund management, we observe that there are thousands of investment professionals involved in active mutual fund management and billions of dollars invested in these funds, which suggests that there must be benefits accruing to supposedly rational investors in these funds. There have been several recent articles in the popular press that indicate that actively managed funds have outperformed index funds. An article in USA Today (Waggoner, January 2005) states that actively managed funds beat the S&P 500 index funds for the seventh consecutive year. An article in the Wall Street Journal (Lauricella & Gullapalla, January 2006) indicates that in 2005, actively managed funds outperformed their indexes for five out of nine fund categories. Alternatively, popular press articles also argue against actively managed funds. An article in the Wall Street Journal (Clements, February 2006) states that “the odds of beating the market over the long run are so slim that it isn’t worth the effort.” Also in the Wall Street Journal, Lieber (February 2006) states that “it’s hard for any investor to consistently beat most market indexes over several years. Over decades, it’s nearly impossible.” Empirical evidence demonstrates the advantages of indexing over active management. Malkiel (1996) shows that over the past 25 years, about 70% of active equity managers have been outperformed by the S&P 500 Stock Index. Bogle (1995) notes similar results. He argues that index funds allow investors to buy a portfolio of securities with minimal expense and significant tax savings. Additionally, Fortin & Michelson (September 2002) find that index funds outperformed actively managed funds in six out of eight equity and bond categories. There is current research that supports active mutual fund investing. Elton, Gruber and Blake (1996) show that their portfolio of high-alpha actively managed funds outperform the Vanguard S&P Index fund. Wermers (2000) finds that equity mutual funds outperform the market by 1.3% per year, although expenses and transaction costs reduce this benefit to essentially zero. Waggoner (2005) states that small-cap funds and value funds have performed better than the S&P 500 index over the past five years. Lauricella and Gullapalli (2006) maintain that in most years active small-company stock funds will surpass their target index. Chen, Noronha, and Singal (2006) show that index fund investors lose value when securities are changed in index funds. Fortin and Michelson (2005) find that actively managed international funds (except for Europe funds) outperform their respective indexes. There is additional evidence that supports the advantages of indexing over active management. Elton, Gruber and Blake (1996) state that since index funds are available at a low cost and there are a variety of index funds available to address most investor risk preferences, the index funds are likely to outperform an active fund of similar risk, so why would an investor select an actively 3
  • 4. managed fund? Bogle (2000) demonstrates that an index fund has a 350 basis point advantage over the average equity mutual fund, due to management expenses, brokerage costs, sales charges, and tax advantages. Arnott, Berkin, and Ye (2000) find that the Vanguard 500 Index fund outperforms the average equity mutual fund and the effect is enhanced when taxes are considered. Malkiel (1996) shows that over the past 25 years, about 70% of active equity managers have been outperformed by the S&P 500 Stock Index. Gruber (1996) and Bogle (1995) argue that index funds allow investors to buy a diversified selection of securities with minimal expense and significant tax savings. “It’s often the case that about half the funds can beat the index in any given year, Malkeil says. But it’s not the same half each year (Waggoner 2005).” Bogle (2005) shows that index funds outperformed actively managed funds by 2.8% before-tax and 4.1% after-tax over the 20 period from 1983 to 2003. It appears that the recent market environment brings this question to the forefront once again. This research will investigate the performance of index funds relative to actively managed funds across eight equity and bond categories over the past 29 year period. This study is an update and extension of a prior paper by Fortin and Michelson (2002) in that a more recent and longer time period is covered. HYPOTHESIS This study tests the hypothesis that actively managed mutual funds have significantly outperformed (underperformed) index funds over the study period, 1977-2005. This research examines both total returns and after-tax total returns. This analysis includes eight classes of mutual fund categories, including five categories of equity funds, two categories of bond funds, and one category of balanced funds. DATA The mutual fund data used in this study is from the January 2006 Morningstar Principia Pro Plus for Mutual Fundsi. This database contains historical information of over 20,000 mutual funds through December 31, 2005 year-end. Data and information are provided on investment objective, total return, income and capital gain distributions, annual expense ratios, fund size, load, and turnover. This study groups the funds into eight broad investment categories: Aggressive Growth & Growth (AGG), Growth/Income & Equity/Income (GIEI), Specialty Equity (SP), Small Company Equity (SCE), Corporate Bond (CB), Government Bond (GB), International Stock (IS), Asset Allocation & Balanced (AAB). The comparison index funds include: Vanguard Index 500, Vanguard Total Bond Index, Vanguard Small Cap Index, Vanguard Total International Index, and Vanguard Balanced Index. These index funds were selected because of their more complete return series over the study period and the fact that the Vanguard Group was the first investment company to initiate index funds over 29 years ago. The final sample contains 15,193 funds with 103,998 annual return data points.ii The actively managed fund categories were matched with index funds that most closely approximated the investment objective of the funds. A consideration in the selection of the comparison index fund was that the index fund had a return series long enough to perform statistical tests. The funds were matched as follows. The Aggressive Growth & Growth, Growth/Income & Equity/Income, and Specialty Equity funds were matched with the Vanguard Index 500 fund. Small Company Equity funds were matched with the Vanguard Small Cap Index fund. The Corporate Bond and Government Bond funds were matched with the Vanguard Total 4
  • 5. Bond Index fund. The International Stock funds were matched with the Vanguard Total International Index fund. The Asset Allocation & Balanced funds were matched with the Vanguard Balanced Index fund.iii METHODOLOGY The methodology employed to test the hypothesis of significant differences in mutual fund returns involve a comparison of the cross sectional mean (median) mutual fund returns each year and over the 29-year period. These tests are performed across investment classifications. The returns relationship is investigated by segmenting the sample by fund category and testing the mean (median) differences in fund returns between the index funds and each category. Both parametric and non-parametric statistical tests are used where applicable. Tests are performed on both a before- and after-tax basis. Since annual total returns (calculated assuming reinvestment of all dividends and capital-gain distributions) are provided by Morningstar, an important variable for individual investors is the after-tax total return. This calculation involved estimating the historical marginal tax rates on ordinary income and capital gains. This paper uses the marginal tax rates provided in Exhibit 1 of Siegel and Montgomery [Winter 1995]. Because tax rates are heterogeneous, they chose an arbitrary single taxpayer earning $75,000 in “earned” (noninvestment) income in 1989 dollars. This level of income was deflated (inflated) by the Consumer Price Index (CPI) for earlier (later) years. They argue that this investor would be typical of individuals with sizable investment portfolios subject to tax. Since our data starts in 1977, we use the Siegel and Montgomery marginal tax rates on ordinary income and capital gains from 1977 through the end of their study in 1993. For the years 1994 through 2005, we utilize tax code information on the ordinary income and capital gains rates and adjust earned income by the CPI for each year. After-tax returns for a given mutual fund in a given year are computed by adjusting the total return for the taxes that would have been paid on the dollar income and capital-gain distributions for that year.iv There is a slight upward bias in this after-tax return computation since Morningstar includes both short-term and long-term capital gains in its yearly dollar-per- share capital-gain figure. The short-term capital-gain distributions should be subject to the higher ordinary income- tax rates, but it was not possible to make this adjustment. The differences between before- and after-tax returns presented in this article are thus slightly smaller than would actually be expected. EMPIRICAL RESULTS Table 1, panel A provides summary descriptive statistics for each of the eight investment categories and Table 1, panel B provides similar information for the five comparison index funds. The expense ratio is the total fund expenses expressed as a percentage of fund assets. Total fund expenses include all management and administrative fees, 12b-1 distribution fees and all other asset-based costs incurred by the fund, except brokerage costs. Sales charges (front or deferred loads) are not included in the expense ratio. Fund size is the total net assets of the fund (in millions of dollars). Turnover, as defined by the SEC, is computed by taking the lesser of purchases or sales (excluding all securities with maturities of less than one year) as a percentage of average fund assets. Return is the yearly total return computed based upon changes in fund net asset value (NAV) assuming reinvestment of all income and capital gain distributions. Returns are net of the funds expense ratio and brokerage costs, but are not adjusted for front or deferred loads. The number of observations (N) is the total number of non- missing observations for each variable. N is often different for the five variables because data is missing in the Morningstar database more often for some variables than others. Table 1 5
  • 6. provides a broad overview of the total return, after-tax total return, turnover, expense ratio, and size variables for the funds across investment classifications. The second column of Table 1A provides the years and comparison index fund for each category that were used for the analysis. Notice that each of the category comparison periods is different due to differing lives of the respective index funds, so the following discussion should be read with that in mind. Continuing with Table 1A, the total return (/after-tax total return) was highest for the equity funds and lowest for the bond funds. The Specialty Equity (12.33% / 11.25%) and Small Company Equity (13.06% / 11.93%) funds were the leading equity funds. The lowest total return category was Government Bond funds (5.54% / 3.89%). Reviewing the comparison index funds in Table 1B, note that there is no data for the Vanguard Total International Index fund for turnover and expense ratio. This index fund is a “fund of funds” and, thus, this data is not available. Continuing with Table 1B, the Vanguard Small Cap Index fund (13.40% / 11.31%) had the highest total return. The Vanguard Total International Index fund (7.85% / 7.26%) and the Vanguard Total Bond Index fund (7.28% / 5.11%) had the lowest total returns. Growth/Income & Equity/Income funds had the lowest turnover (67.97%), while Government Bond funds (195.07%) and Specialty Equity funds (169.10) had the highest turnover. As anticipated, the index funds had lower turnover ratios than their comparison fund categories. The Vanguard Small Cap Index fund (63.61%) had the highest turnover, while the Vanguard Index 500 (11.64%) had the lowest turnover. Unexpectedly, the Vanguard Total Bond Index fund (47.44%) had a relatively higher turnover. Expense ratios were highest for International Stock funds (1.81%) and Specialty Equity funds (1.69%) and lowest for Government Bond funds (1.02%). As expected, the comparison index funds had, overall, lower expense ratios. The Vanguard Small Cap Index fund (0.71%) had the highest expense ratio and the Vanguard Total Bond Index and Vanguard Balanced Index funds (0.21%) had the lowest expense ratios. The largest funds were Growth/Income & Equity/Income ($789.60 million) and AA and Balanced ($498.50 million). The smallest category was Specialty Equity funds ($231.19 million). The index funds were generally much larger than their peer comparison funds. The largest index fund was the Vanguard Index 500 ($26,179 million) and the smallest was the Vanguard Small Cap Index fund ($1,398 million). [Insert Tables 1A and 1B here] Table 2 presents the paired comparison t-tests for total return (left panel) and after-tax total return (right panel) for each of the eight fund categories overall, with respect to their comparison index funds. We take the index fund return minus the active fund return and then compute a paired comparison t-test based upon this value. Therefore, a positive mean return indicates that the index fund outperformed the average actively managed fund. The statistical results performed on the differences in returns appear to reflect skewed distributions when comparing the mean and median returns values. We, therefore, compute the nonparametric sign test to determine if there is a significant difference in the number positive versus negative differences in returns (Index minus Active fund). All fund categories, except GIEI and Corporate Bonds showed a significant difference in returns (at the .0001 level) between the index funds and the actively managed funds for total return. Interestingly, four equity categories exhibit a negative relationship for total return, indicating the actively managed funds significantly outperformed the index funds over the full comparison period. The Aggressive Growth & Growth, Specialty Equity, Small Company Equity, and International Stock funds exhibited this negative relationship (note that the IS funds only contained nine years of data). After-tax total returns exhibited similar relationships as before-tax returns, except that the GIEI and Corporate Bond funds were significant (and positive). 6
  • 7. The nonparametric sign test provides overall support for indexing. All categories are significant and only two (Aggressive Growth/Growth and Specialty Equity) show significantly more negative than positive returns (based on a one-tailed test at the 0.0001 level) for both total return and after-tax total return. The nonparametric results provide additional evidence that index funds outperform actively managed funds for all categories, except for AGG and Specialty Equity funds. [Insert Table 2 here] Tables 3A and 3B present the results of the same paired comparison t-test for each of the eight fund categories on a year-by-year basis for total return and after-tax total return. Over all categories and time periods, 147 out of 176 differences in total returns and after-tax total returns are significant. The table below shows how many total returns are significantly positive (index fund outperforms) versus significantly negative (actively managed fund outperforms). Number Significantly Positive & Negative from Table 3A Total Return AGG GIEI SP SCE CB GB IS AAB Positive 14 15 10 7 9 13 2 9 Negative 14 11 11 14 9 1 5 3 Number Significantly Positive & Negative from Table 3B After-Tax Total Return AGG GIEI SP SCE CB GB IS AAB Positive 12 14 10 8 9 12 3 8 Negative 14 12 12 13 9 2 5 4 Three of the eight total return categories show that index funds outperformed actively managed funds in the majority of years (the AGG and CB categories were split) while active management outperformed indexing in the majority of years in three categories (SP, SCE, and IS). For after- tax returns three of eight index categories outperformed, one was tied (CB), and four active fund categories outperformed the indexes (AGG, SP, SCE, and IS). This summary provides additional evidence that, at least in a majority of years, Small Company Equity, Specialty Equity, and International Stock funds outperform the index funds on a before and after-tax basis. Fortin and Michelson (2002) also found similar total return results for these funds. In addition, it appears that the results in Table 3 are sensitive to market cycles. This is an important point to consider when making investment decisions because the overall results presented in Table 2 hide this tendency. [Insert Table 3 here] We understand that there is an obvious survivorship bias in these results. Since our study period encompasses 29 years, there will be a number of mutual funds that perform poorly and disappear from our sample in the later years. As such, this bias favors active fund management over indexing and any indexing (active) advantage would be greater (less) than reported. This bias thus favors the hypothesis that index funds outperform the actively managed funds for those two fund categories (AGG and CB) that had the same number of significant positive and 7
  • 8. negative fund years. Therefore, an argument that index funds outperform actively managed funds could be more strongly stated than the results imply. Conclusion Parametric Test Sign Test Parametric Test by Years No. of Active No. of Index No. of Active No. of Index No. of Active No. of Index Funds that Funds that Funds that Funds that Funds that Funds that Outperforms Outperform Outperforms Outperform Outperforms Outperform Tie Equtiy Funds Total Return 4 1 2 3 3 1 1 After-Tax Total Return 4 1 2 3 4 1 0 Bond Funds Total Return 0 2 0 2 0 1 1 After-Tax Total Return 0 2 0 2 0 1 1 AAB Funds Total Return 0 1 0 1 0 1 After-Tax Total Return 0 1 0 1 0 1 This paper provides further evidence on the debate on the benefits of mutual fund indexing and whether actively managed funds perform as well as index funds. The table above provides an overall summary. We find that index funds outperform actively managed funds for one equity and one balanced fund category (GIEI and AA Balanced) and both bond fund categories under the parametric tests. However, the parametric tests also show that actively managed Aggressive Growth/Growth (AGG), Specialty Equity (SP), Small Company Equity (SCE), and International Stock (IS) funds significantly outperform the index over the study period. The nonparametric tests indicate an overall index fund advantage. The Sign Test establishes that Index funds outperform actively managed funds for all categories, except for SP and AGG funds. These results are similar to, though not as strong as, Fortin and Michelson (2002). As a final comment, if geometric (time weighted) returns are computed over the various yearly periods in Table 3A and B, all five actively managed equity fund categories outperform index funds on a before-tax basis and all except GIEI on an after-tax basis. The index funds outperform for both bond fund categories and the AA Balanced category on both a before-tax and after-tax basis. Since investors are primarily concerned with their terminal wealth position, these results suggest that an equity (bond) indexing strategy would under (over) perform active management, at least for the average fund over the time period examined. The specific geometric compound annual returns for each category are noted below: Category Active TR Active ATTR Index TR Index ATTR AGG 13.45 11.45 12.06 10.41 GIEI 12.17 9.72 12.06 10.41 SP 14.4 12.48 12.06 10.41 CB 7.14 4.74 7.15 4.99 GB 6.24 4.24 7.15 4.99 SCE 14.62 13.03 11.71 9.69 IS 8.17 7.37 5.87 5.29 AAB 8.14 6.63 8.99 7.89 A number of caveats are also in order. 1) Note that this study does not consider either front or deferred loads. 2) This study does not take into account a risk/return tradeoff. We have examined returns by category and a number of funds with lower returns might actually have a 8
  • 9. better risk/return tradeoff than the market because they have lower risk than the market. 3) These tests do not consider persistence of fund superiority over the passive index fund. Any fund that does consistently outperform the market index tends to be averaged out in our cross- sectional methodology. 4) This study uses the Morningstar classification of funds to determine the mutual fund investment category. A fund manager may actively change the funds risk/return profile to achieve higher returns. This would cause the fund to be grouped in the incorrect investment category. 9
  • 10. References Arnott, R., A. Berkin, and J. Ye, (2000), “How Well Have Investors Been Served in the 1980’s and 1990’s?” The Journal of Portfolio Management, 26(4), Summer 2000, pp. 84-91. Bogle, J., April, 1995, "The Triumph of Indexing," The Vanguard Group, pp. 1-45. Bogle, J., 2005, “The Relentless Rules of Humble Arithmetic,” Financial Analysts Journal, 61(6), p. 22-35. Bogle, J., December, 2000, "What Can Active Managers Learn from Index Funds?," The Vanguard Group, from a speech present to the Bullseye 2000 Conference in Toronto, Canada. Chen, H., G. Noronha, and V. Singal, 2006, “Index Changes and Losses to Index Fund Investors,” Financial Analysts Journal, 62(4), p. 31-46. Clements, J., 2006, “Investing Like the Pros Do: Combining Index Funds With Alternative Strategies,” The Wall Street Journal, (February 8, 2006) p. C1. Elton, E.J., M.J. Gruber, and C.R. Blake, 1996, “The Persistence of Risk-Adjusted Mutual Fund Performance,” Journal of Business, Vol. 69, No. 2, pp. 133-157. Fortin, R. and S. Michelson, 2002, “Indexing Versus Active Mutual Fund Management,” Journal of Financial Planning, Vol. 15, No. 9, pp. 82-94. Fortin, R. and S. Michelson, 2005, “Active International Mutual Fund Management; Can Managers Beat the Index?,” Managerial Finance, 31(1), pp. 41-51. Gruber, M.J., July, 1996, “Another Puzzle: The Growth in Actively Managed Mutual Funds,” The Journal of Finance, Vol. 51, No. 3, pp. 783-810. Lauricella, T.and D. Gullapalli, 2006, “In Humans vs. Indexes, the Duel Continues,” The Wall Street Journal, (January 6, 2006) p. C1. Lieber, R., 2006, “Finding an Index-Fund Genius,” The Wall Street Journal, (February 25, 2006), p. C1. Malkiel, B., April 22, 1996, "Not So Random," Barron’s, p. 55. Principia Pro Plus, Operations Manual, Morningstar Mutual Funds, Chicago, IL, January 2006. Siegel, B. and D. Montgomery, 1995, “Stocks Bonds and Bills after Taxes and Inflation,” Journal of Portfolio Management, Winter 1995, pp. 17-25. Waggoner, J., 2005, “Managed Funds Top S&P 500 Index Again,” USA Today, (January 4, 2005) p. B1. Wermers, R., (2000), “Mutual Fund Performance: An Empirical Decomposition into Stock Picking Talent, Style, Transactions Cost, and Expenses,” The Journal of Finance, 55(4), August 2000, pp.1655-1703. 10
  • 11. Table 1 - Panel A - Summary Descriptive Statistics for Mutual Fund Categories Fund Total AT-Total Expense Category Category Variable Return Return Turnover Ratio Net Assets 1 AGG N 31553 31553 28529 22769 25631 Years 1977-2005 Mean 9.83 8.8 101.33 1.48 490.49 Vang Index Index 500 Std Dev 21.67 21.35 129.19 0.75 2452.32 Median 9.96 9.03 74 1.35 56.1 2 GIEI N 13144 13144 11914 9403 10406 Years 1977-2005 Mean 10.04 8.56 67.97 1.25 789.6 Vang Index Index 500 Std Dev 15.29 14.95 65.31 0.54 3307.94 Median 10.08 8.91 54 1.16 90.25 9 Spec Equity N 8874 8874 8293 6693 7287 Years 1977-2005 Mean 12.33 11.25 169.1 1.69 231.19 Vang Index Index 500 Std Dev 28.8 28.48 411.46 0.61 758.28 Median 11.54 10.32 70 1.63 40.3 8 SCE N 8609 8609 7889 6572 7188 Years 1977-2005 Mean 13.06 11.93 93.38 1.57 274.68 Vang Small Index Cap Index Std Dev 24.37 24.14 80.71 0.98 983.22 Median 11.65 10.46 77 1.45 61.25 5 Corp Bond N 14003 14003 12832 10501 11509 Years 1987-2005 Mean 6.15 4.22 144.55 1.08 364.38 V. Total Index Bond Index Std Dev 7.83 7.69 190.74 0.51 1326.66 Median 5.18 3.54 89 0.95 75.5 6 Govt Bond N 7267 7267 6730 5496 5873 Years 1987-2005 Mean 5.54 3.89 195.07 1.02 397.17 V. Total Index Bond Index Std Dev 5.20 4.93 252.93 0.49 1177.72 Median 5.60 3.74 118 0.9 80.4 3 Int'l Stock N 11304 11304 10277 8324 9376 Years 1997-2005 Mean 11.67 10.99 93.98 1.81 411.82 V. Total Intl Index Index Std Dev 26.78 26.67 85.22 0.66 1902.76 Median 13.5 12.88 74 1.75 42 AA 4 Balanced N 9234 9234 8321 6654 7599 Years 1993-2005 Mean 7.26 6.05 86.45 1.29 498.5 Index V. Bal. Index Std Dev 12.09 11.9 90.54 0.62 2087.8 Median 7.23 6.09 64 1.21 55.7 11
  • 12. Table 1 - Panel B - Summary Descriptive Statistics Index Funds Fund Total AT-Total Expense Category Category Variable Return Return Turnover Ratio Net Assets Vanguard Index Index 500 N 29 29 28 28 29 Mean 13.18 11.5 11.64 0.25 26179 Std Dev 15.78 15.53 9.85 0.08 35060.79 Median 16.22 14.38 7.5 0.21 4345.3 Vanguard Small Cap Index Index N 29 29 28 28 29 Mean 13.4 11.31 63.61 0.71 1398.34 Std Dev 19.58 19.07 38.58 0.57 1949.45 Median 18.12 14.95 45.5 0.29 131.1 Vanguard Total International Index Index N 9 9 8 9 9 Mean 7.85 7.26 4371.69 Std Dev 21.7 21.62 3621.66 Median 15.57 14.92 2919.8 Vanguard Balanced Index Index N 13 13 12 12 13 Mean 9.54 8.44 26.67 0.21 2379.37 Std Dev 11.32 11.2 7.63 0.01 1538.07 Median 10 8.75 26.5 0.2 2990.4 Vanguard Total Bond Index Index N 19 19 18 19 19 Mean 7.28 5.11 47.44 0.21 6999.58 Std Dev 5.32 5.16 16.38 0.03 7392.7 Median 8.26 5.85 46.5 0.2 2952.8 12
  • 13. Table 2 - Paired Comparison T-Statistics - Fund Category Compared to (Index - Active Fund): Comparison using Total Return Variable Comparison using After-Tax Total Return Variable Category Category Variable Vang. Index 500 Category Category Variable Vang. Index 500 1 AGG Mean -1.249 1 AGG Mean -0.926 Years 1977-2005 Prob. 0.0001 Years 1977-2005 Prob. 0.0001 N 31,553 Median -0.24 N 31,553 Median -0.12 No. Pos. 15,355 Sign Test* 0.0001 No. Pos. 15,546 Sign Test* 0.0096 2 GIEI Mean 0.0437 2 GIEI Mean 0.703 Years 1977-2005 Prob. 0.5934 Years 1977-2005 Prob. 0.0001 N 13,144 Median 0.29 N 13,144 Median 0.68 No. Pos. 6,839 Sign Test* 0.0001 No. Pos. 7,183 Sign Test* 0.0001 9 Spec Equity Mean -3.748 9 Spec Equity Mean -3.341 Years 1977-2005 Prob. 0.0001 Years 1977-2005 Prob. 0.0001 N 8,874 Median -2.17 N 8,874 Median -1.89 No. Pos. 3,960 Sign Test* 0.0001 No. Pos. 4,017 Sign Test* 0.0001 Vang. Small Vang. Small Category Category Variable Cap Index Category Category Variable Cap Index 8 SCE Mean -0.8788 8 SCE Mean -0.8254 Years 1977-2005 Prob. 0.0001 Years 1977-2005 Prob. 0.0001 N 8,609 Median 0.39 N 8,609 Median 0.9 No. Pos. 4,460 Sign Test* 0.0009 No. Pos. 4,656 Sign Test* 0.0001 Vang. Total Vang. Total Category Category Variable Bond Index Category Category Variable Bond Index 5 Corp Bond Mean 0.0669 5 Corp Bond Mean 0.2234 Years 1987-2005 Prob. 0.3019 Years 1987-2005 Prob. 0.0005 N 14,003 Median 0.51 N 14,003 Median 0.44 No. Pos. 8,293 Sign Test* 0.0001 No. Pos. 8,283 Sign Test* 0.0001 6 Govt Bond Mean 1.008 6 Govt Bond Mean 0.797 Years 1987-2005 Prob. 0.0001 Years 1987-2005 Prob. 0.0001 N 7,267 Median 1.07 N 7,267 Median 0.86 No. Pos. 5,336 Sign Test* 0.0001 No. Pos. 5,139 Sign Test* 0.0001 Vang. Total Int'l Vang. Total Int'l Category Category Variable Index Category Category Variable Index 3 Int'l Stock Mean -2.106 3 Int'l Stock Mean -2.0199 Years 1997-2005 Prob. 0.0001 Years 1997-2005 Prob. 0.0001 N 11,304 Median 0.68 N 11,304 Median 0.72 No. Pos. 5,955 Sign Test* 0.0001 No. Pos. 5,964 Sign Test* 0.0001 Vang. Balanced V. Balanced Category Category Variable Index Category Category Variable Index 4 AA Balanced Mean 0.6589 4 AA Balanced Mean 0.881 Years 1993-2005 Prob. 0.0001 Years 1993-2005 Prob. 0.0001 N 9,234 Median 0.8 N 9,234 Median 0.85 No. Pos. 5,298 Sign Test* 0.0001 No. Pos. 5,388 Sign Test* 0.0001 *Sign test one-tailed probability that the difference is significantly positive (Index - Active Fund)
  • 14. Table 3A - Paired Comparison T-Test Comparison Fund Category Compared to (Index - Active Fund)(Mean): Year Comparison Variable: Total Return Spec Corp Govt AA Fund Cat AGG GIEI Equity SCE Bond Bond Int'l Stock Balanced 1977 -12.137* -6.292* -20.560* -4.492 na na na na 1978 -9.331* -2.485* -5.678* -14.446* na na na na 1979 -15.464* -4.008* -52.093* 2.982 na na na na 1980 -6.733* 5.881* -12.808* 4.637 na na na na 1981 -3.741* 7.197* 5.121 -1.691 na na na na 1982 -7.257* -4.671* -4.601 19.934* na na na na 1983 0.058 -0.118 5.227* -8.206* na na na na 1984 9.667* 0.730 9.369* -18.319* na na na na 1985 1.956* 3.327* 11.428* -6.988* na na na na 1986 3.778* 0.909* -1.469 -10.359* na na na na 1987 2.518* 2.129* -3.532 -3.422* -0.095 0.099 na na 1988 1.135* 0.041 7.539 4.219 -3.140* 0.212 na na 1989 2.876* 7.491* 3.641* -11.343* 5.580* 1.083* na na 1990 1.635* 1.108* 5.291* -6.571* 8.602* -0.066 na na 1991 -9.638* 1.510* 1.385 -3.430* -8.987* 1.135* na na 1992 -1.853* -2.033* 0.827 2.367* -3.610* 0.972* na na 1993 -3.423* -3.095* -18.180* 1.008 -3.265* 1.862* Na -3.186* 1994 2.898* 2.022* 2.847* -0.396 0.521* 0.285 Na 1.178* 1995 5.729* 5.701* 8.770* -2.110* 1.213* 3.024* Na 4.198* 1996 3.595* 2.451* 3.128* -2.380* -3.185* 0.320* Na 0.861* 1997 9.140* 5.330* 17.798* 2.773* -0.846* 1.280* -6.257* 4.490* 1998 8.166* 13.669* 18.780* -3.767* 3.430* 1.380* 8.987* 5.134* 1999 -13.315* 9.518* -8.537* -15.167* -3.695* -0.339* -22.087* 2.570* 2000 -6.962* -13.337* -21.117* -6.548* 7.482* 0.948* -0.147 -4.180* 2001 0.928* -5.874* 0.005 3.065* 3.376* 1.622* -4.044* 0.990* 2002 0.708* -3.303* -4.415* -0.026 4.548* -0.234 -0.826* 0.773* 2003 -3.435* 1.148* -11.534* 2.916* -7.649* 2.124* 0.361 -0.434 2004 -0.589* -0.961* -4.647* 3.739* -1.302* 1.474* 2.361* 0.5452* 2005 -2.433* -1.208* -7.383* 0.541* 0.264* 0.580* -2.067* -0.542* Notes: * indicates significance at 5% level or better
  • 15. Table 3B - Paired Comparison T-Test Comparison Fund Category Compared to (Index - Active Fund)(Mean): Year Comparison Variable: After-Tax Total Return Spec Corp Govt AA Fund Cat AGG GIEI Equity SCE Bond Bond Int'l Stock Balanced 1977 -12.728* -5.765* -20.265* -7.014 na na na na 1978 -9.922* -1.926* -5.625* -18.676* na na na na 1979 -16.089* -3.666* -51.383* 0.665 na na na na 1980 -7.671* 5.806 -12.695* 1.524 na na na na 1981 -3.645* -6.133* 5.977 1.340 na na na na 1982 -7.562* -3.777* -4.856 16.094* na na na na 1983 -0.247 0.259 4.108 -9.744* na na na na 1984 9.340* 1.418* 9.017* -16.972* na na na na 1985 -0.0135 2.620* 9.694* -7.811* na na na na 1986 3.558* 1.295* -3.202* -10.826* na na na na 1987 5.751* 5.415* -1.573 -3.392* 0.566 0.055 na na 1988 0.729 0.5544 6.866* 5.356* -2.778* 0.142 na na 1989 3.523* 8.469* 3.475* -14.802* 5.949* 1.114* na na 1990 1.924* 1.831* 5.290* -6.308* 8.962* -0.104 na na 1991 -8.617* 2.354* 1.922 -3.188* -8.459* 1.040* na na 1992 -1.191* -1.098* 1.199 3.228* -3.325* 0.840* na na 1993 -2.217* -1.737* -17.078* 1.280 -2.909* 1.673* na -2.250* 1994 3.495* 2.803* 3.142* -0.225 0.653* 0.179 na 1.524* 1995 7.385* 7.137* 9.732* -1.127 1.321* 2.909* na 4.799* 1996 5.508* 4.438* 4.399* -2.030* -2.966* 0.207* na 1.917* 1997 10.938* 7.449* 19.305* 3.347* -0.675* 1.105* -5.299* 5.554* 1998 9.008* 14.971* 19.440* -4.640* 3.538* 1.211* 9.266* 5.889* 1999 -12.004* 10.741* -7.627* -16.191* -3.514* -0.585* -21.302* 3.240* 2000 -5.212* -12.079* -19.843* -7.362* 7.647* 0.689* 0.826* -3.271* 2001 0.884* -5.536* 0.310 3.300* 3.540* 1.359* -4.273* 0.869* 2002 0.409* -3.360* -4.375* -0.0998 4.591* -0.558* -1.203* 0.492 2003 -3.786* 1.060* -11.518* 2.890* -7.432* 1.856* -0.025 -0.703* 2004 -0.8196* -0.950* -4.518* 4.219* -1.217* 1.175* 2.070* 0.3573* 2005 -2.381* -0.847* -7.030* 1.392* 0.327* 0.3446* -1.899* -0.531* Notes: * indicates significance at 5% level or better 15
  • 16. ENDNOTES i See References for version. ii Note that the total number of mutual funds represents totals over different time periods. For example AGG funds were examined over 1977 through 2005 and IS were reviewed over the years 1997 through 2005. iii The index funds represent specific segments of the market. The Vanguard Index 500 fund reflects the S&P 500 Index, the Vanguard Total Bond fund reflects the Lehman Brothers Aggregate Bond Index, the Vanguard Small Cap fund reflects the Russell 2000 Index, the Vanguard Total International fund reflects the MSCI European, Pacific and Emerging Markets Indices, and the Vanguard Balanced fund reflects the combination of the Wilshire 5000 and the Lehman Brothers Aggregate Bond Index. iv More specifically, the ending net-asset value from the prior year is multiplied by one plus the decimal return for the current year. Then the computed tax on the ordinary income and capital-gain distributions for the year are subtracted from this appreciated net-asset value to give an after-tax net-asset value. After-tax total returns are then computed by dividing the after-tax net-asset value by the ending net-asset value from the prior year and subtracting one.