discussion

Contributions Carosa

Passive Investing: The Emperor Exposed?

by Christopher Carosa, CTFA

Christopher Carosa, CTFA, a member of the adjunct

faculty ofMedaille College in Buffalo, New York, has

been involved in the investment industry for more than

20 years. He is currently engaged in researching the

impact of behavioral economics on investment theory.

Mr. Carosa also serves as president of Carosa. Stanton

& DePaolo Asset Management LLC, and president and

chairman of the Bullfinch Fund Inc. a family of no-load

mutual funds.

F or some time, the academic world and the financial services industry appear to have been converging on

the virtues of passive investing versus active management. John C. Bogle, a highly regarded spokesman of indexing, conci.sely summarizes the current standard belief \\ hen he states "that the market portfolio is the mo.st sensible decision. It takes the need for JLidgment out ot \<nir decision-making; It reduces costs; it increases tax-efficiency; it avoids the need to pore o\cr past market data to figure out why the data are vv hat the}' arc.'" Bogle's comment calls to common sense. Indeed, his premise may well be used by various goxernmcnt recula- tors regarding the potential privatization of Social Security.

But u hat it Bogle's presumption is false? .'\ftcr all, most investors don't in\'est to avoid niakiny decisions. Most investors don't invest purely to reduce costs. Most investors don't invest merely to maximize tax-efficiency. Taken alone, these factors can produce irratmnal results in one's everyday life. Kor example, one can always reduce costs by l)uying the least expensive product. But what of reliabilitv? l.s it worth

Executive Summary

• Traditional studies of the passive

versus active management debate

appear to contain two flaws that can

dramatically affect results.

• The snapshot-in-time anomaly creates

period dependency, leading to incon-

sistent results.

• The equal-weighted anomaly produces

results that while statistically accurate,

fail to accurately reflect the results

experienced by actual investors.

• An analysis using rolling 12-month

returns appears to reduce, if not

eliminate, the snapshot-in-time phe-

nomenon, leading to more consis-

tent results.

• An analysis using asset-weighted per-

formance data to more accurately

it to buy a 'IA' for half price that needs to be replaced three times over the life of the alternative? More importantly, would you buy the cheapest |>ar:ichutc even though it successfully opens oiil_\' nine out ot tun times? The same could be said of tax-effi- ciency. The best way to avoid pa\'inu ta.xcs is to not earn any money. Using this logic, one uoiild never work, (jreat. You might never pay taxes, but you'd never be able to buy a TV—even the cheapest one!

So, choosing investments—just like making any other purchase decision— cannot focus on these "common sense" rules. What, then, represents the critical factor? Quite simply, it is the ability^)r, more importantly, the likelihood—of one

reflect the actual behavioral patterns

of investors appears to produce more

significant results.

An analysis of investment return data

from January 1975 through June 2004

shows active investors in U.S. equity

funds performed better than the 5&P

500 two-thirds of the time and by an

average of 2 percent annually.

Using both modern portfolio theory

and behavioral finance measure-

ments, the investors in active funds

appear to have taken less actual risk

than the index.

These results have broad implications,

not only for financial planners, but for

public policy issues such as ERiSA and

Social Security reform.

achie\'ing one's lifetime goals, or "goal-<jri- entcd target" (CX)T). In most cases, as it pertains to investments specificalK, this means earning a sufficient rate of return to pay tor one's ideal !ifesr\*lc. In vcrv straightforward terms, people invest to achieve certain positive tlnancial results.

History

Along these lines. Bogle's fundamental assumption embraces the iiiea that index mvesting provides returns that either equal or exceed active investing. Indeed, this assumption is well founded by both histori- cal data and academic research. What

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Carosa Contributions

iilmost js ;i snuill (l)ut vcr\' contni- \crsial) afterthought in 197.^ when Charles Illlis in;itter-ot-factly concluded that the commonly held tenet that pn)tes,sio[i;il si-ciirity analysts can manage portfolios that consistently outperform the market "\i|)pears to he false," hlossoined into an outright creed wlied, in 1'>S.?, William S. Cjray III wrote "the median experience of acti\'L'K [nanagetl eijiiity portfolios has been well helow (I to 2 percent) the S&P ÎKI in most years during the I'̂ T̂Os and

l9S()s."" Most sit;nif1cantK', tliis latter refer- ence appears in a hook that is rc(|Liired reading t(H" candidates for the (Chartered I inancial .\rialyst ((^I-.\) designation—the \er\" people w ho try to make a Ii\ iny l)y [licking stocks!

Perhaps the defining work was piih- lished h\ IJnrton .\lalkiel in 1995. Malkiel summarizes the current generally accepted academic principle w hen he concludes, '•.Most in\'esrors would he considtrahlv lietter oft hy |>iirchasing a low expense index fund than l)\- tr\ ing to select an active fund manager who appears to pos- sess a 'hot hand.' Since active management generall}' fails to provide excess returns and tends to generate greater tax hurdens for investors, the ad\ antage of passive manage- ment holds.'"

Hut IJogle himseit pro\ idei.1 insight as to the hiisie flaw in these types ot studies u hen he pointed out that "each and every comparison we see is period-dependent." Ave. there's the ruh!

Basic Hypothesis and Source of Data

The idea, then, is to test whether the market index beats actively managed port- tohos with enough consistency to justify index investing u.sing a mcthodolog\' that incorporates actual investment decisions as well as a practical financial planning tech- niqtie into the traditional academic analy- sis. To accomplish this, we'll use the S&P

500 performance (as provided Uv Barra) as our market proxy. While this does not rep- resent the total market, since 1933 "the !2.2 percent annual return of the SikP 5iK) has l)een exactly rhc same as the return of the total st))ck market."" The S&P 500 holds the further advantage of heing perhaps the most popular indexing choice for investors.

On the other hand, sophisticated aca- demics can riglufully express concern al)out the potential for an apples-to-oranges comparison hetueen the two data sets. To address this concern, iliscussions were held w ith other researchers u ho indicated there is no statistical difference hetween the Barra SiS:P 511(1 returns and the (Center for Research in Security Prices ((JRSP") total stock database tor the |>eriod in (]uestion (January 1975 through June 20(14). There- fore, the results ofthis study are likely to he identical whether using S^iP 500 returns or total market returns. (CRSP is a proprietary, subscription-only database generally available just to universit}' researehers.)

U,sing monthly return data, we'll meas- ure the rolling 12-month return results for the index against similar performance data for actively managed U.S. equity mutual funds. V\e chose rolling 12-nionth periods rather than calendar years lieeause, as all tlnancial advisors know, real investors— especially those «"ho regularly contribute to company retirement plans—do not limit their investment decision-making to December 3 1 of every year. Bv examining rolling 12-nionth periods, we can more accurately assess the near-term relative performance between the index and the average mutual fund. This addresses Bogle's concern by redueing—it not out- right eliminating—any period-dependent t)ias in the study.

Data regarding actively managed U.S. C(]uity mutual funds was provided by Lipper Analytics, the nation's oldest and largest provider of mutual fund perform- ance data. Since Barra S&P 500 data w ere available only from January 1975, we chose

that as our first month. .MonthU' returns were available through June 2004, To best measure the aetively managed data. Upper provided asset-weighted return data in addition to the more commonly used e(]ual-weighted return data. (The former a\"oids any skev\ ing toward smaller funds and hctrcr represents the inxestment deci- sions (if actual in\estors.) The Lipjierdata include funds that ha\'e been closed or merged, and therefore contain no sur\ i\or bias, meaning both acti\e funds anil mac- tive funds were included in this study. Nei- ther the Lipper tlata nor the Barra data include loads, commissions, or investment management fees. The Upper data reflect in\estment pertormanee net of expenses and I2h-I tees, while the Harra data, heint; index data, do not. Both funds include total return performance—that is, both capital appreciation anti rein\'estcd dividends. I'inally, the Upper data include index funds, so the Upper results will skew to some deirree {not meastirahle due to the manner in w hieh the data w as provided) toward Barra results. This means the actual \'ariance hetween actively managed funds and the index is prohal)ly greater (albeit at some unknown significance) than the ntim- l)ers reported here.

Note for those interested in duplicating tliis research: The Barra data are publicly a\'ailable on their Weh site (www.Harra. com). I he I.ipper data are available only l)y subscription, but Upper has at times (this case is one example) offered researchers a tjrant to obtain a limited amount of data. For the purposes ofthis study, it w as requested that Lipper provide monthly return data for its "US Diversified i-".t|uity (Jroup" (USDE(iroup) of mutual funds from December .'I, 1974 (this enahles you to calculate the return for the month of January 1975), through June 30, 2004. Lhe USDL Group represents data points aggregated from 15 Lipper fund class itlcations:

1. Large-Cap (Lil) Cirowth 2. LCCore

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Contributions Carosa

3. LC Value 4. Mid-Cap (MC) Growth 5. MC (.\>re 6. MC Value 7. Multi-Cap (MLC) Growth H. MLC Core 9. MLC Value

lO.Sniall-Cap(SC) Growth l l . S C C o r c 12.SCValuc l3.Iit]Uity Income i4.S&P 500 Index Objective 15,SpeeiaIty Diversified Kquicy Funds

Becau.se only a ^ e g a t e data were made available, it was impossible to perform fur- ther anatyties on the results (this might best be eondueted in future researeh). Also, the Lipper terminology for the two formats is "Average" (Lipper's term for "equal weighted") and "Dollar Weighted Average" (Li|)per\s term for "asset weighted"). Sinee Lipper's databases are usually survivor- biased, it is critically important that the retjuest specifically asks that all active and inactive funds be included.

The Results

The period from January 1975 through June 2004 represents 29 1/2 years. During this period, the equal-ueighted average annual return of all U.S. equity mutual funds—the traditional measurement tech- nique that gives smaller funds the same weight as larger funds—was ] 3.93 per- cent. Returns for the S&P 500, on the other hand, were slightly smaller: 13.73 percent. Immediately, the casual reader might hastily conclude that all previous studies purporting to show the dominance of passive investing to be in error. On the other hand, this result should not surprise those familiar with recent history in that, on average, actively managed equit)' funds have beaten the S&P 500 during the last five years. This phenomenon is just an example of Bogle's period-dependency. For example, in the 25-year period from

January 1975 through December 1999, the equal-weighted average return of all U.S. e(|uity mutual funds was 16.99 percent, lagging the index return of 17.26 pereent. So, while a longitudinal study ending in 1999 favors passive investing, a similar study ending in June of 2004 favors active investing.

But, as the astute planner recognizes, reliance on equal-weighted data betra} s the actual investment decisions made by and on behalf of clients. Think of it this way: Let's say we did an analysis on ten mutual funds. If only one mutual fund made money, the equal-weighted average return would probably be negative. On the other hand, let's say all investors invested in the one fund that made money, and not in any of the other nine funds. In this case, the asset-weighted average return would prob- ably produce positive results. What does this lead us to conclude? In this very hypo- thetical case, the asset-weighted average return suggests investors (as measured by the amount of money they invest) tend to accurately recognize and reward the better- performing fund by Investing in that fund. The equal-weighted average return sug- gests the mutual fund families were willing ro create many different kinds of equity funds, some of which will ultimately per- form poorly and fail to attract investors.

Equal-weighted returns, though meas- uring investment decisions of mutual fund portfolio managers, emphasize the business decisions of mutual fund corporate man- agement. Asset-weighted returns, on the other hand, while also measuring the investment decisions of mutual fund port- folio managers, emphasize the investment decisions of shareholders and their profes- sional advisors. Asset-weighted returns, therefore, tend to reflect the practical real- ity of the financial planning environment. As a result, an analysis of asset-weighted average returns, conducted in the same rig- orous manner of past aeademic studies, may be more meaningful to practitioners in the finaneiai services industry.

During the period from January 1975 through June 2{X}4, the geometric asset- weighted average annual return of all U.S. equit)' funds was 15.85 percent—nearl_\' 2 pereent greater than the geometric average annual return of the S&P 500 and the equal-weighted return of all U.S. equity mutual funds for the same period. Surpris- ingly, contrary to our expectations, this was not a period-dependent result. During the period from January 1975 through Deeember 1999, the geometric asset- weighted annual return of all U.S. equity funds was 19.11 percent—again nearly 2 percent better than the ec]uiva!ent S&P 500 return and greater still than the et|ual- weighted return of the same fund data for the same period.

This suggests the actual decisions made by investors and their advisors—as meas- ured by the total dollars they invested— tended tu produce better returns than either investing in the index or investing equal amounts in all U.S. equity mutual funds. This inference, as further analysis will soon reveal, contradicts the long-stand- ing belief that active deeision-making adds too little value compared with the amount of risk it introduces. As policy-makers deeide how to privatize Soeial Security, this conclusion means any rules that remove or reduce active decision-making on the part of investors may actually impede-—not protect—^those investors.

Roiling 12-Month Returns

Of course, legislative concerns aside, the practical problem of the above return analysis is that it assumes clients invested all their funds In January 1975. Would that all finaneiai planners had time machines!

Planners and their clients tend to invest periodically throughout the entire year. T o better acknowledge reality, let's take a look at the investment returns of every 12- month period from January 1975 through June 2004. There are 342 12-month periods

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ConlrihLilioiis Corosa

T A B L E 1

Percentage of 12-Month Periods Where the Asset-Weighted Return of U.S. Equity Mutual Funds Outperformed the S&P 500 in the Similar Period Index ^ No Fee [ 64.33%

Expense 20 Basis Points ^ 66.37% ^ ^^^ -

Ratio 150 Basis Points I 68.13%

during that 29 !/2-year span yielding 342 different returns. For U.S. et]uit\' funds, the arithmetic average of those 342 asset- weightetl returns was 1 7.84 percent. (We must use the arithmetic average instead of the geometric average heeause these return [leriods overlap.) Likewise, the arithmetic average of the S&P 500 in those same 342 periods uas 15.55 percent. Of interest, the standard deviation of these two samples was nearly identical—1 7.46 percent for the as.set-\veighted U.S. cquit\' mutual fiuid returns and 17.54 percent for the S&:P 500.

For advocates of modem portfolio theory, these three data points—lM)th the arithmetic anti the geometric average return a,s well as the staudari! deviation— iuiply that, w liile the universe of U.S. c(|iiity mutual funds exhibits the same risk (that is, standard (.ie\iation) us the S \ P 500, the uni\erse of U.S. eiiiiity mutual funds appears tu possess a sindificant retiim |>remium. This further implies that the more efficient jiorttolio is not the Si^P 500, but the asset-v\ eiglued collection of all U.S. ei.|uity mutual tuiuls.

For those u ho prefer using the upside/ dww nsiJe analysis more eommon In behav- ioral ectmomics, the sanu- ileductioii can be draw n. I he worst return for any given period is lower for the Sc^P 500 (-30.49 percent) versus the a.sset-weiglited average of U.S. equity mutual funds (-27..^3 per- eent). Similarly, the best return for any given period is higher for the U.S. ei|uity funds (-1-71.30 percent) versus the SivP 500 (-1-61.65 percent). These facts suggest the

equit)' funds, in aggregate, have a lower dounside aiui a higher upside for 12-month periods. Again, in using asset-weigh ted returns, the conclusion applies to the real- life investment decisions people make, not in the hypothetical instance that every person invests the identical amount of mone_\- in every U.S. equity mutual fund.

But wait, there's more! We know the mutual fund return data automatieally account for the expense ratio of those funds. I he S&P 500 data, being actual index returns, fail to account for the actual expenses incurred by index funds. 'Fhe inclusion of this expense ratio only further extends the outperforniance of U.S. etjuity funds relative to index returns. We relate this in Table I, where we indicate the per- centage of periods where the U.S. equity funds beat the index returns in three differ- ent scenarios:

1. I he raw index returu, which iiieludes no expenses

2. The scenario where index fund returns mimic the uidex returns but include a 20-basis-point expense ratio

3. The scenario w here index fund returns mimie the index returns but include a 50-basis-point expense ratio

Table 1 indicates, for any given 12- montb holding period, the asset-weighted return of all U.S. equity mutual fluids beats the S&P 500 roughly two-thirds of the time. The table also suggests that, in a manner consistent w ith the conclusions of iMalkiel, investors shouki be mindfiil w hen buying shares of iniiex funds and trv to buy those with the lowest expense ratio. (I he data provided by l.i[iper were not sufficientk- detailctl for us to make any conclusions regarding expense ratios of U.S. equity funds in general.)

Given the above data, we do not mean to suggest that U.S. equity fund returns are not correlated w ith S&P 500 returns. Indeed, a statistical analysis show s a posi- ti\ e correlation coefficient of 0.H7. There appears to be, however, a tendencv for the U.S. eijuit}' funds to either lead or lag

in discrete time periods. l*Or example. U.S. equity funds tended to lead in the late 1970s and early 1980s; again in the late I9H0S and early 1990s; and, finally, iu the most reeent five-year span. Cin the other hand, the S&P 500 tended to consis- tently lead for several short intervals in the mid-l9H0s and again in the mid-late 1990s. We attempted to correlate these periods with the general movement of the market, but the analysis showed only a slight correlation (0.28). A cursory visual review* of the market during the nearly 30-year duration (see Figure ! on page 60) hints there is a tendency for the S&P 500 to lead in late-stage bull markets and a tendency for U.S. equit\' mutual funds to lead in bear markets.

The best we can eouclude is that some- times it's better to be in aetivel\- managed funds and .sometimes it's better to l)e in passively managed S&P 500 index funds. Unlike previous researeh. we clearly cannoi conclude—or even imply—that the evi- dence show s index lnvestint; offers consis- tently better investment returns compared w irb returns offered by the entire asset- weighted U.S. equity mutual fund uni- verse.

FinalK- eomes tbe question all finaneiai planners need to know : What does this study uncover about an in\'estor's abi!it\' to meet a specific goal-oriented target (GOT)? (The C;OT represents that spe- cific rate ol return rei|uired for an in\esror to attain a particular financial goal.) How- do these series of 12-month returns stack up against a variety of (;O Fsr Fable 2 (page 60) demonstrates how both the S&P 500 and rhe equity mutual funds eompare with a \ariety of common (iO'Fs.

As 'Fable 2 clearly indieates, the asset- weighted average 12-month return for U.S. equity funds consistently betters the S&P 500 returns for similar periods. This differ- ence becomes more exaggerated as one's G O T increases. For example, when the G O I IS merely to not lose any principal (that is, 0 percent). U.S. equit_\' mutual

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Contributions Carosa

F I G U R E 1

Rolling 12-Month Returns for S&P 500 Areas Shaded in Blue Show Periods When S&P 500 Returns Lagged U.S. Equity Fund Returns

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T A B L E 2

Percentage of 12-Month Periods When Investment Returns Met or Exceeded the Indicated GOT

GOT

0%

4 %

6%

8%

10%

12%

S&P 500

80.12%

74.56%

71.05%

68.42%

65.50%

62^7% 14.875% 53.22%

16.5% 1 49.42%

U.S. Equity Mutual Funds

83.63%

78.6S%

76.02%

72^1% 69.88%

66.96%

62.28%

57.60%

funds art' just 4 percent more likely to achieve that G O T compared with the S&P 500. On the other hand, if the G O T is to double the investment every five years (that is, I4.S75 percent annually), U.S. equity mutual funds are 17 percent more likely to achieve that ( J O T com- pared with the S&P 500. In the end, it is more important for most investors to attain a certain goal-oriented target than to simply "beat the S&P 500." This par- ticular portion of the analysis reflects how people really invest, not an arbitrary target based on a market index. As a con-

sequence, the results reveal that investors have been better served with equity funds across a l)road range of CJOTs based on how they and their financial advisors implemented their actual invest- ment decisions.

How statistically significant are all these results? A simple paired two-sample t-test for means yields a t-stat of-2.62 and a P- value of 0.91 percent. (The eritical values at the 5 percent significance level are ±1.966705.) This shows we can reject the null hypothesis (that is, the hypothesis that claims there is no statistically significant differenee between the two series of returns) at most standard significance levels (ineiuding as low as 1 percent). This cer- tainty level is large enough to suggest the possibility of a statistically significant dif- ference between the U.S. equity mutual fund returns and the S&P 500 returns.

Conclusion

It has long been believed that actively man- aged portfolios underperform tbe market. This study indicates rhe more aceurate conclusion would be that there exist extended periods \\ hen the market outper-

forms aetivel}' managed U.S. e(|uity funds and extended periods when the aetively managed U.S. equity funds outperform the market. As a result, our re-examination of the passive-versus-active investing debate appears to confirm what others have hypothesized—that previous studies pur- porting to show the dominance of passive investing may have reflected the snapshot- in-time anomaly commonly found in meas- uring investment performance. The study can reach no statistically significant eonelu- sion regarding the potential correlation between these periods of overperformance and underperformance with bull and bear markets. We can anecdotally conclude there appears to be a tendency for tbe S&P 500 to beat U.S. equity funds at the top of bull markets and a tendeney for U.S. equity funds to beat the S&P 500 during bear markets.

Furthermore, and more significantl}', this study concludes, w ithin most standard significance levels (including as low as I percent), that for investment returns in rolling 12-montb periods from January 1975 through June 2004, uhen looking at actual investing patterns and not merely a hypothetical equal weighting of all mutual funds, U.S. equity funds have historically

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Suggested Web Sites

www.Barra.com

www.LipperLeaders.com

beat the S&P >()<) roughly tuo-thirds of the time. In addition, U.S. e(jiiity funJs, on avLTiigf, Lire more Hkely to meet or exceed ;in iin'esror's retiini t;irgct acrns.s ;i hroad ninge of CIO I s, and hence are more hkeiv tn earn ;i sufficicnr rate of return to fin;ince an investor's ideal litest\le. "l"hese results directly contradict the prevailing view that investors and their financial advisors are better off merely in\ esting in the market and not taking the time to researcii mutual fund investment options. I here are both practical and public policy implications of this t.li,sc<)\ery.

I'lrst. the financial ser\ ices i[idustr\' and mutual fund shareholders appear to have fxhibiteil a eonsistent track record of investing in U.S. equity funds that are niore likely to outperform the S&P .̂ 00. Recognition ofthis broad effort—and the fact that it has added value for investors— has not received much cnvcraye in aea- deniic studies. Now it looks as if u e have empirical evidence that implies the results of aetne decision-making have reaped rewards for investors. The study docs not intend to conclude that pnor investment decisions are not made. Also, it is be\ ond the scope ofthis study to suygcst which types of U.S. et[uity funds mav or may not inerease the likelihood of the investor beat- ing the S&P 500. It is the hope ofthis author that other studies, using the behav- ioral analytics described here, might fur- ther break down performance w ithin spe- cific fund categories.

Second, and perhaps ot more long-term conset]ucncc. are the public policy ramifi- cations of this study. 1 lere we refer U> both the current regulatory compliance practices of KRISA plan trustees and fidu-

eiaries. as w eil as tbe burgeoning debate on the privatization of Social Seeuritv.

Regarding the lormer, the eonckisions ofthis study, in contradicting previous studies, might cause regulatory bodies like the Department of Labor to reconsider how they define "generally accepted indus- try- practices." For example, in question- ing—if not outright rejecting—the statisti- cal dominance nt passive investing, plan trustees and other fiduciaries might uant to avoid relying solely on passive vehicles.

Regarding the latter, the [>ri\ati/.ation of Social Security, this study has profound repercussions. Witii the idea to give work- ers ownership of some p(jrtion of their Social Security savings, the goxernment finds itself in the same position as that of a 401(k) plan trustee. This stud)' reveals, l)oth in terms of the standard-deviation risk analysis of modern |iortfolio theory and the upside/dounside analysis of beha\-ioral eco- nomics, U.S. equity funds, as a whole, offer better returns with either the same or less risk than investing in the market. Again, the study does not intend to say each and every U.S. equity fund has these character- istics. Rather, the study concludes the aggregate investment decision-making of investors and their financial advisors has resulted in better returns than passively investing in the S&P .̂ 00. This holds true both over time and in nearly two-thirds of tbe .'42 12-month periods from January 1975 through June 2004. It would be diffi- cult for lawmakers to justify taking any action that would, contrary to this studv, place workers' retirement assets in harm's way by unnecessarily restricting in\est- ment choices based on a prevailing \\-isdom that could find itself turned on iis head in the near future.

Passive investing may not yet be naked, but it certainl) has fewer clothes than thought.

Endnotes

1. John C. Hogle, "The Telltale f:hart," keynote speech before tbe Morningstar Investment Forum. Chicago, II., June 26, 2002; available online from the Hogle Financial Markets Research (Center.

2. (Jharles D. FUis, "The Loser's (Same," l-innncial AnnlysTs Journal, Ju\y/August ]975: 19-26.

3. William S. CJray III, 19K3, "Portfolio

Construction: Fipiity," Munaying

Investment Portfolios, John L. Maginn and Donald L. luttlc, editors, 19^3: 402.

4. Burton (i. Malkiel, "Retui-ns from liu'esting in Fquit\- Mutual Funds, 1971 to \99]" Jinirnal of Fin-jncc, 50 (1995):

549-572.

5. Bogle, ibid. 6. Bogle, ibid. 7. These two expense ratios appear to best

represent the range of actual expense ratios based on a review of publicly available index funds.

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