“全包”投资费用的算术

· Volume 70 Number 1 PERSPECTIVES John C. Bogle This article represents a rare (if not unique) attempt to estimate the drag on mutual fund returns engendered by “all-in” investment expenses, including not only expense ratios (until now, the conventional measure of fund costs) but also fund transaction costs, sales loads, and cash drag. Compared with costly actively man-aged funds, over time, low-cost index funds create extra wealth of 65% for retirement plan investors.

I read William Sharpe’s essay “The Arithmetic of In some cases, subtle and sophisticated Investment Expenses” (2013) with interest and reasoning may be involved. More often applause (of course!). It brought to my mind (alas), the conclusions can only be justified what was likely his first article on the subject of fund by assuming that the laws of arithmetic costs—“Mutual Fund Performance”—published have been suspended for the convenience way back in 1966. In that article, Dr. Sharpe was of those who choose to pursue careers as right in his conclusion that “all other things being active managers. equal, the smaller a fund’s expense ratio, the better the results obtained by its stockholders” (p. 137). If “active” and “passive” management Sharpe’s credibility, objectivity, and quantifica- styles are defined in sensible ways, it must tion expertise are peerless. He was the 1990 recipi- be the case that (1) before costs, the return ent of the Nobel Prize in Economic Sciences and on the average actively managed dollar is now professor emeritus of finance at Stanford will equal the return on the average pas-University, where he has taught thousands of stu- sively managed dollar and (2) after costs, dents over some 43 years.

He was right again in the return on the average actively managed his 2013 article: “A person saving for retirement dollar will be less than the return on the who chooses low-cost investments could have a average passively managed dollar. These standard of living throughout retirement more assertions will hold for any time period. than 20% higher than that of a comparable inves- Moreover, they depend only on the laws of tor in high-cost investments” (p. 34). However, as addition, subtraction, multiplication and I will explain, he understated the gap in favor of division. Nothing else is required. . . . low-cost investments. Because active and passive returns are equal before cost, and because active managers The 1991 Article bear greater costs, it follows that the afterSharpe has taken up this subject often. In “The cost return from active management must be Arithmetic of Active Management” (Sharpe 1991), lower than that from passive management. he analyzed mutual fund returns and found the . . .

The proof is embarrassingly simple and same forces at work: uses only the most rudimentary notions of Statements such as [“the case for pas- simple arithmetic. sive management rests only on complex Enough (lower) mathematics. . . . and unrealistic theories of equilibrium in capital markets”] are made with alarming . . . Properly measured, the average actively frequency by investment professionals. managed dollar must underperform the average passively managed dollar, net of John C. Bogle is founder and former chief executive of the costs. Empirical analyses that appear to Vanguard Group and president of the Bogle Financial refute this principle are guilty of improper Markets Research Center. measurement. (pp. 7–8) January/February 2014 Ahead of Print 1 The 1966 Article Focusing on the issue of fees charged by bro-kers in his 1966 article, Sharpe perceptively referred Surprising as it may seem, Sharpe’s 1991 article was to the fact that the costs included in mutual fund published a quarter century after his first article on expense ratios fail to capture the all-in costs borne this subject.

Although the role of costs in shaping by fund investors: the relative performance of mutual funds was integral to my career even before I founded Vanguard One reservation is in order. Expense ratios in 1974, it took me a while to pay adequate attention as reported do not include all expenses; to that seminal article. The following are excerpts brokers’ fees are omitted. Thus the expense from Sharpe’s 1966 article: ratio does not capture all the differences in expenses among funds. It is entirely pos-Past performance [based on the ratio of sible that funds with performance superior annual fund returns to volatility in net to that predicted by the traditional expense asset values] appears to provide a basis ratio engage in little trading, thereby mini-for predicting future performance. . . . The mizing brokerage expense. It was not fea-high correlation among mutual fund rates sible to attempt to measure total expense of return suggests that most accomplish ratios for this study; had such ratios been the task of diversification rather well. used, a larger portion of the difference in Differences in performance are thus likely performance might have been explained in to be due to either differences in the ability this manner, and the apparent differences of management to find incorrectly priced in management skill might have been securities or to differences in expense smaller. (p.

134) ratios. If the market is very efficient, the funds spending the least should show the Despite the sharp decline in the commission best (net) performance. . . . The results tend rates charged by brokers, the costs of the portfolio to support the cynics: good performance transactions incurred by actively managed funds is associated with low expense ratios. . . . are substantial; fund portfolio turnover (based on aggregate industry data) has leaped almost . . . All other things being equal, the smaller fivefold since the early 1960s—from 30% to 140% a fund’s expense ratio, the better the today.2 results obtained by its stockholders. . . . In addition, Sharpe neglected to note that front-But the burden of proof may reasonably be end sales loads were a major cost. But their impact placed on those who argue the traditional on annual returns depends on the (unknowable) view—that the search for securities whose holding period of the investor.

Furthermore, front-prices diverge from their intrinsic values is end loads are far less common today; they have worth the expense required. (pp. 131–132, typically been replaced by deferred sales loads and 137­–138)1 annual fees charged by brokers and advisers. Also, there are far more pure no-load funds in the fund The Arithmetic of “All-In” Investment industry of today.

Moreover, whereas index funds are fully Expenses invested at all times, portfolios of actively managed I enthusiastically endorse Sharpe’s conclusions funds typically carry a cash position of about 5%, and his perceptive analysis, but the use of a mutual causing the funds to lose a portion of the long-term fund’s expense ratio offers only a pale approxima- equity premium. tion of the total costs paid by investors in actively Finally, for most investors, relative tax effi-managed equity funds. Using only that measure, ciency is a critically important element of total Sharpe compared the reported expense ratio costs. Funds with low expense ratios (notably, index of 1.12% for the average large-cap blend fund funds), which operate with minimal portfolio turn-(unweighted by assets) with the ratio of 0.06% over, are relatively tax efficient. Actively managed for the Vanguard Total Stock Market Index Fund. funds, with their far higher expense ratios, not only The advantage of the low-cost investment over the incur substantial transaction costs on their portfo-higher-cost investments was 1.06 percentage points lio turnover but also realize capital gains, generat-per year. In this article, I shall provide careful, if ing significant tax inefficiency. Taxes represent an inevitably imprecise, estimates of the additional additional drag on the returns earned by mutual costs that investors in actively managed equity fund investors in taxable accounts, but they are of funds incur—few, if any, of which are incurred by no immediate concern to investors in tax-deferred index fund investors. retirement plans.

2 Ahead of Print ©2014 CFA Institute In this article, I shall estimate the impact of 30 bps, which does not include certain other costs,” (1) the first three of these extra cost categories— such as the substantial market impact, which he transaction costs, cash drag, and sales loads—on did not quantify (Phillips 2013, p. 80). the net returns that funds deliver to their retirement I have been examining this issue for many years plan investors and, separately, (2) all four costs, and have shown that high turnover is negatively including excess taxes, on the returns delivered to correlated with fund performance (Bogle 2012, p. taxable fund investors. 148). In this article, I use the actual measure of fund trading: portfolio purchase of stocks plus portfolio Quantitative Imprecision sales as a percentage of fund average assets. For reasons lost in history, however, funds now cal-The issue of all-in fund costs has rarely, if ever, culate turnover as the lesser of portfolio purchases been subject to careful examination, likely because or sales as a percentage of fund average assets—a data on these costs are difficult, if not impossible, figure that obviously understates transaction activ-to quantify with precision. So, where is a businessity and is, therefore, irrelevant in the calculation of man like me (albeit one educated in economics) to total transaction costs. turn? The kind of quantitative precision that the I am also aware that because mutual fund academic community properly demands in most managers are trading largely with one another and cases is simply not possible with respect to these with other institutional fund managers, market four costs that fund investors incur over and above impact must resemble a zero-sum game for fund the expense ratio. I will provide reasonable esti- managers as a group (and their fund sharehold-mates for each based on a variety of sources and ers). Because a fund “taking a haircut” on selling data, buttressed by my industry experience. Lest I a large block of stock results in a better price for overstate the advantages of indexing, I have made the buying counterparty, I am inclined to consider these cost estimates for actively managed funds as market impact costs to be close to zero. But for conservative as possible. investors as a group, after accounting for bid–ask spreads and commissions that brokers pay to bro-Transaction Costs kers and dealers, trading obviously becomes a The first “invisible” fund costs are the transaction loser’s game. costs incurred by the funds themselves. Two aca- So for my analysis, I use an estimate that is far demic studies have produced rather different esti- more conservative than the 1.44% calculated by mates of the drain of fund trading costs in order Edelen et al. (2013) and even lower than the Haslem to calculate their annual impact on fund returns. (2006) estimates. My estimate is likely consistent One study was conducted by Dr. John A. Haslem with the expanded estimate provided by Phillips. (2006). Brokerage commissions are now required to Because precision here is impossible—and I do not be specified by equity mutual funds, and from this want to risk overstating these costs—I opt for the source, Haslem identified a performance drag on ease of “rounding” and assume just 50 bps for the fund annual returns of 39 basis points (bps). After transaction costs of actively managed funds. taking into account implicit trading costs (timing Although index funds obviously incur some delays, market impact, etc.), he estimated that the transaction costs, they are so minimal that they trading costs of actively managed funds produced have had no significant impact on the returns of an annual impact on fund returns of –60 bps. those funds. That is, the annual returns of major Edelen, Evans, and Kadlec (2013) provided large-cap index funds lag those of their target another extensive study of this issue. They exam- indices by only the amount of their expense ratios, ined the annual expenditures on trading costs meaning that net transaction costs are too small to incurred by 1,758 domestic equity funds over 1995– affect the precision with which they track their tar-2006 and calculated average annual trading costs of get indices. So, I assume zero total transaction costs 1.44%, far in excess of the average expense ratio of for the index fund.

1.19% for the funds they examined.

That surprisingly large number astonished at Cash Drag least one independent expert. Don Phillips, presi- Another additional cost is the drag of cash. Active dent of the investment research division at the funds fairly consistently carry cash in the range mutual fund data provider Morningstar, described of 5% of assets, whereas index funds are normally it as “preposterous.” But he conceded that “trading fully invested. If we assume an annual long-term is a real cost and an activity that is often counter- equity premium for stocks over cash of as little productive in asset management.” He presented his as 6%, there would be an additional 30 bp drag own estimate of annual transaction costs of “about on active fund returns. Some of the larger active January/February 2014 Ahead of Print 3 equity funds doubtless “equitize” part of this cash “A” front-end load shares carry sales loads and by holding index futures. But data on that usage 60% are sold at net asset value. are simply not available. So, I will add a cost of To further muddle the calculation of “distri-just 15 bps to account for the cash holdings of bution drag,” some individual investors are DIY active funds. (“do it yourself”) investors, incurring few, if any, extra costs. But most rely on brokers and advisers Sales Loads: Direct and Indirect who charge fees for their services. A recent survey, based on a limited sample, placed the proportion The costs paid directly by investors for fund distri-of equity fund owners in this adviser-assisted catbution are rarely, if ever, taken into account in the egory at 56% of total no-load fund sales.4 analysis of fund expenses and returns. Nonetheless, In this new environment, fees paid by inves-these expenses incurred by most mutual fund tors to brokers and investment advisers typically “retail” investors represent a major drag on fund run to about 1% per year, (indirectly) reflecting the returns. That cost was once relatively easy to esti- costs of fund share distribution. Therefore, with mate because this industry originally grew through some investors incurring almost no additional a “sales push” distribution system. From the incep- distribution costs and others subject to costs in tion of the fund industry in 1924 through the late the range of 1% or more, I will conservatively use 1970s, it was dominated by fund distributors that an average annual distribution cost of 0.5% for charged sales loads averaging about 8% of the dol- individual investors in actively managed funds, lar amount of shares purchased. (Then, few firms which includes total annual broker and adviser operated on a “no-load” basis.) costs and sales loads. Because no major index fund So in those days of yore, the math was fairly charges sales loads and because investors in tra-straightforward: For the typical investor who paid ditional index funds are largely, but not entirely, an 8% front-end load and held his shares for eight DIY investors (often in defined contribution plans years, the amortized load was 100 bps per year; for for which the sponsoring company provides the a 16-year holder, 50 bps per year. (The norm was fund menu), I take the liberty of assuming in likely closer to 100 bps.) Today, however, the distri- my basic analysis no such distribution costs for bution system has undergone a radical transforma- index funds.5 (Readers who believe that I have tion, and we can only make reasonable estimates overstated or understated the distribution costs based on limited data. for either actively managed funds or index funds First, no-load funds have soared in importance: may simply insert their own cost assumptions into They now account for almost half of long-term Table 1.) industry assets (excluding assets of institutional Note that investors in corporate defined con-funds).3 Further, the typical front-end sales load tribution (DC) plans are a major force in retirehas dropped from 8% to 5%. Also, the “retail” dis- ment plan investing and may well be subject to tribution system is rapidly changing from a front- lower distribution costs.6 But individual retirement end load model to an annual asset charge. And accounts (IRAs) have an even larger asset base ($5.4 even load funds often waive sales charges for pen- trillion versus $5.1 trillion for DC plans at the end sion plans and corporate thrift plans, as well as for of 2012).7 A significant portion of IRA assets are the registered investment advisers and brokers, who result of DC plan rollovers at retirement, and such charge their clients an annual fee, replacing the investors seem more likely to retain brokers and earlier front-end commission-based model. Recent advisers for their IRAs, incurring the distribution estimates suggest that only 40% of the traditional costs noted above.

Table 1.  All-In Investment Expenses for Retirement Plan Investors Actively Managed Funds Index Funds Index Advantage Expense ratioa 1.12% 0.06% 1.06% Transaction costs 0.50 0.00 0.50 Cash drag 0.15 0.00 0.15 Sales charges/feesb 0.50 0.00 0.50 All-in investment expenses 2.27% 0.06% 2.21% aData are from Sharpe (2013). bThe 0.50% estimate for sales charges/fees is the midpoint of the range between 0% for DIY investors and 1% for investors who pay sales loads and fees to brokers and registered investment advisers. I have chosen not to include the “service charges” for loans, withdrawals, and so forth, often paid by investors in 401(k) retirement plans.

4 Ahead of Print ©2014 CFA Institute Putting It All Together would have been accumulated in the index fund versus $561,000 in the active fund, an astonishing Table 1 details the all-in aggregate fund costs, gap of $366,000 and a 65% enhancement in capital. beginning with Sharpe’s data and then including the additional elements described previously. I will Even if we assume that the actively managed fund start by looking at these all-in costs from the per- investor incurs no distribution costs, the 40-year spective of Sharpe’s 2013 article: the tax-deferred accumulation would total $626,000. If the index retirement plan of the individual investor. fund investor incurs distribution costs of 0.5% per Note that the pervasive acceptance of present- year, the accumulation would total $824,000 and the ing expenses as a percentage of fund asset values, index fund investor would nonetheless maintain a as in Table 1, greatly diminishes the perception $198,000 advantage over the investment lifetime— of the substantial impact that costs have on fund still a 32% enhancement. annual returns. For example, assuming a 7% stock When Sharpe considered only the difference market return, the 2.27% estimated annual cost of in expense ratios for index and actively man-the actively managed funds would consume almost aged funds, he concluded that “a person saving 33% of the return, whereas the 0.06% annual cost of for retirement who chooses low-cost investments the index fund would consume less than 1% of the could have a standard of living throughout retire-return—a dramatic difference. ment more than 20% higher than that of a comparable investor in high-cost investments” (2013, p. 34). But when all-in costs—which obviously (1) Preparing for Retirement exist and (2) are substantial, whatever their precise What does this annual differential mean to an inves- amount—are considered, the assumed retirement tor who prepares for retirement by owning mutual wealth accumulation enhancement provided by funds over the long term? For illustrative purposes, the low-cost index fund as shown in Table 2 leaps I have assumed that a 30-year-old investor begins to to fully 65% higher, ranging (depending on the save for retirement at age 70, a span of 40 years, by assumptions presented in the table) from 32% to investing in a tax-deferred 401(k) or IRA plan. She 86% higher. Regardless of the assumptions used, earns $30,000 annually at the outset, and I assume the index fund would provide a truly remarkable that her compensation will grow at a 3% annual potential improvement in the standard of living for rate thereafter. In Table 2, I present a comparison retirees. For example, using my primary calcula-of the retirement plan accumulation if the investor tions and assuming a 4% annual withdrawal rate at were to invest 10% of her compensation each year retirement, the average active fund investor would in either (1) an actively managed large-cap equity receive a monthly check for $1,870 whereas the fund or (2) the Vanguard Total Stock Market Index index fund investor would receive $3,090.

Fund, the subjects of Sharpe’s 2013 analysis. The table summarizes the results over the four decades that follow. Taxes and Taxable Investors The advantage provided by the index fund is For taxable fund investors, the gap widens even substantial, and as time passes, it grows by leaps further. The high tax efficiency of the index fund and bounds. By the time retirement comes, when gains a significant advantage over the painful tax the investor in the example is 70 years old, $927,000 inefficiency of the average actively managed fund.

Table 2.  Total Wealth Accumulation by Retirement Plan Investors, Assuming a 7% Nominal Annual Return on Equities Actively Managed Fund Index Fund Index Enhancement Gross annual return 7.00% 7.00% — All-in costs 2.27 0.06 –2.21% Net annual return 4.73 6.94 +2.21 Accumulation period % Increase After 10 Years $44,000 $50,000 $6,000 13% After 20 Years 130,000 164,500 34,500 27 After 30 Years 286,000 412,000 126,000 44 After 40 Yearsa 561,000 927,000 366,000 65 aFor the DIY investor in the active fund who incurs 0% distribution costs, the accumulation would amount to $626,000. For an active fund investor who incurs the full 1% distribution cost, the accumulation would total $504,000. For the index fund investor who incurs distribution costs of 0.5%, the accumulation would total $824,000.

January/February 2014 Ahead of Print 5 Again, it is impossible to make precise calculations This rough snapshot of the annual impact of here. Therefore, for active managers and the index taxes may suggest that tax costs are inconsequen-fund, I have used as a guideline the pretax and tial. But when compounded over 40 years (as in after-tax returns provided by Morningstar for the the previous example), they bring the extra costs of 10-year period ending 30 April 2013. actively managed funds to a truly overwhelming Over this period, the total stock market index annual level of 3.02%. In Figure 1, I assume that a had an average annual return of 8.7%. The return taxable fund investor begins with a $10,000 invest-for actively managed large-cap blend funds was ment in (1) a tax-efficient index mutual fund and (2) 7.5%, of which about 75 bps was lost to taxes; the a tax-inefficient actively managed fund and simply broad market index fund lost about 30 bps to taxes.8 holds each for the subsequent four decades. So, I will use a conservative and rounded tax differ- The calculated terminal value of the active fund ential estimate of 45 bps, which likely understates grows steadily over time—$15,000 after 10 years, the extra tax costs incurred by investors in actively $22,000 after 20 years, and $48,000 after 40 years. managed funds. With taxes considered, the total The index fund grows far more swiftly, ending up all-in costs added by actively managed mutual with a value of $131,000, a remarkable enhance-funds amount to about 317 bps per year for taxable ment of $83,000, or almost 175%. Indeed, taxes are investors (Table 3). a vital consideration.9 Table 3.  All-In Fund Costs Including Tax Differential, 10 Years Ending 30 April 2013 Actively Managed Fund Index Fund Index Advantage Assumed stock market return 7.00% 7.00% — All-in costs (from Table 1) 2.27 0.06 2.21% Tax inefficiency 0.75 0.30 0.45 Total costsa 3.02 0.36 2.66 Assumed net fund return 3.98 6.64 2.66 aHere, costs (including taxes) consume 43% of the returns for the active funds, compared with 5% for the index fund.

Figure 1.  Growth of a $10,000 Investment Based on All-In After-Tax Costs, Assuming a 7% Gross Annual Return on Stocks Asset Value ($) 140,000 $131,000 120,000 100,000 80,000 60,000 $48,000 40,000 $36,000 20,000 $22,000 0 10 20 30 40 Years Index Fund (6.64%) Actively Managed Fund (3.98%) 6 Ahead of Print ©2014 CFA Institute Real vs. Nominal Returns ratios, other costs, and taxes—is a high penalty to pay for the combination of high costs and coun-So far, I have reported fund returns on a nominal terproductive movement of their money from one basis, unadjusted for the impact of inflation. But fund to another.12 investors must rely on real returns to maintain their standard of living. Although mutual funds almost exclusively report only their nominal returns, I Reconciliation believe that fund investors must consider their Now I will explore how consistent these all-in cost real returns as well. Making this adjustment has estimates are with the returns earned by large-an important negative impact on both active funds cap equity funds relative to the returns earned and index funds. by the Total Stock Market Index Fund. First, let For example, if we assume a future annual us assume, as so many academic studies indi-rate of inflation of only 2%—the approximate cate, that active equity mutual funds as a group present spread between the inflation-adjusted provide, before costs, a return equal to that of the 10-year Treasury Inflation-Protected Security and stock market itself at the same level of risk (“zero the 10-year US Treasury note itself—it reduces the alpha”). Therefore, the subtraction of direct all-in assumed nominal annual market return of 7% to fund expenses should essentially reflect the differ-a real return of 5%. Thus, the real return after all- ence between the market return and the managed in costs for actively managed funds would fall to fund return. The exercise is a bit complex because 1.98% from its nominal 3.98%, and the index fund some of the expenses I have reviewed so far are real return would fall to 4.64% from a nominal internal to the funds themselves and others are return of 6.64%.10 Compounded over 40 years, a paid directly by the fund investors. Table 4 should $10,000 initial investment in active funds would clarify this distinction. grow to just $22,000 in real terms whereas the index The concept is that the net returns achieved by fund would grow to $61,000—a nearly threefold large active funds should lag the returns earned by enhancement. These numbers may be scary and the Total Stock Market Index Fund by the amount almost unbelievable, but the data do not lie. of direct costs paid out of fund gross returns—1.77 percentage points annually. The costs of sales and Counterproductive Investor Behavior distribution fees, extra taxes, and imprudent (or opportunistic) investment behavior—another 2.15 Throughout this article, I have presented the returns percentage points in aggregate—are not included as reported by the mutual funds themselves— here because they are borne directly by the inves-essentially, the percentage change in the funds’ net tors themselves. How does that theory work in asset values, adjusted for the reinvestment of all practice? Quite nicely, as it turns out. For example, dividends and distributions. As the record makes over the two decades ending 31 December 2012, clear, however, mutual fund investors are too often the average actively managed large-cap core tempted to add to their equity holdings when mar-fund earned a compound annual return of 6.50% kets are rising, to withdraw their investments when (adjusted for survivorship bias, as described later markets tumble, and to move into funds that have in this section), falling short of the 8.3% return of performed well in the recent past only to revert to the Total Stock Market Index Fund by 1.80 percent-the mean (or below) thereafter. Such counterpro-age points per year. That shortfall is remarkably ductive investor behavior proves to be another close to the annual differential between index fund advantage for index fund investors.

For example, over the 15 years ending 30 June 2013,11 the actively managed large-cap blend funds Table 4.  Allocation of Costs of Actively evaluated by Sharpe (2013) reported an average Managed Funds (from Tables 1 and 2) annual return of 4.50%—for the funds that survived Costs Borne Costs Borne the period. But Morningstar calculated that the by Fund by Investor asset-weighted return earned by investors over the Expense ratio 1.12% — same period was just 2.59%, a “behavior gap” of Transaction costs 0.50 — 1.91 percentage points in return per year. (As it Cash drag 0.15 — happens, in this particular period, investors in the Sales charges — 0.50% Total Stock Market Index Fund exhibited moder- Tax inefficiency — 0.45 ately productive timing, earning a slightly higher Investor behavior — 1.20a annual return than the fund reported.) A loss of Total 1.77% 2.15% almost 2 more percentage points of annual return aA conservative estimate, well below the 1.91 percentage for active investors—over and above fund expense point lag realized over the past 15 years.

January/February 2014 Ahead of Print 7 direct costs and active fund direct costs of 1.77 per- section, over the 20 years ending 31 December 2012, centage points, as shown in Table 4. the underperformance of the active funds relative This near precision, I must report, is no more to the index was almost identical—1.8 percentage than a happy coincidence, simply because the cal- points per year. Broadly speaking, the reality conculations of costs and returns presented in this arti- firms the theory. cle are, as noted earlier, inevitably imprecise. Even a larger difference in the results for the past two Conclusion decades—say, plus or minus 50 bps—would none-By examining mutual fund expense ratios, Dr. theless confirm the strong relationship between Sharpe began the saga of how much the draining fund costs and fund returns. The costs are based on impact of expense ratios erodes the returns deliv-the results over the past two decades, using limited ered to fund investors over the long term. My data and some experienced judgment. Therefore, analysis in this article builds on that foundation, take this fragile precision only as proof, in prin- but I estimated the all-in costs incurred by mutual ciple, that the influence of costs must dominate the funds—expense ratios plus the other fund costs— relationship between the returns earned by active which are numerous and substantial in the case of funds and the returns earned by index funds. actively managed funds but far less numerous and One of the principal challenges in calculating less substantial for index funds. It is simply a story the average returns of the funds is the need to elim- that must be told. inate what is called “survivorship bias”—that is, to I re-emphasize the inevitable imprecision of take into account not only the returns of funds that my data, even as I reiterate that I have tried to survived a given period but also those that failed use conservative estimates—selecting the lowest to do so. Obviously, data that are not free of survi- reasonable number in each case and, in all likelivorship bias are inappropriate (after all, funds with hood, understating the confiscatory impact of the poor records are less likely to survive), but there additional transaction costs, cash drag, sales loads, are myriad methods of calculating the difference. I distribution costs, tax inefficiency, and counterpro-have found the data provided by Lipper to be quite ductive investor behavior. Others will no doubt reliable. Using its data for the two decades ending find fault with my data and estimates, and I urge 31 December 2012, for example, the surviving large- industry participants and academics alike to offer cap core funds earned an annual return of 7.86%. constructive criticism of my data, including their But, as shown above, all the funds in that category, own estimates of these costs. including those that did not survive, earned only I also urge mutual fund investors not only to 6.50%, or 1.36 percentage points less. Given the per- consider the conventional annual impact of expense sistent high failure rate of equity mutual funds,13 ratios and other costs but also to recognize how this adjustment for survivorship bias is essential. much these differences matter as time horizons Earlier studies of the relative returns of actual lengthen. In the short term, the impact of costs may mutual funds and the broad market indices confirm appear modest, but over the long run, investment the reasonableness of these estimates of the impact costs become immensely damaging to an investor’s of direct costs incurred by investors. For example, standard of living. Think long term! For those who in his book Unconventional Success: A Fundamental are investing for their retirement and for their life-Approach to Personal Investment, Yale endowment times, understanding the cost issue is vital to suc-fund manager David Swensen (2005) summarized cess in investing. An increase of 65% in the wealth research conducted by Robert Arnott, Andrew accumulated by retirement plan investors is not Berkin, and Jia Ye and reported that for the 20 years trivial! After analyzing the data over many years, ending 31 December 1998, the average actively I feel confident in reaffirming the warning that I managed fund underperformed a broad stock mar- have consistently given to fund investors over the ket index fund by 2.1 percentage points per year years: Do not allow the tyranny of compounding costs before taxes. (Numerous other studies confirm a to overwhelm the magic of compounding returns. spread in this range.) Current data also confirm a shortfall of this magnitude. As noted earlier in this This article qualifies for 0.5 CE credit.

Notes 1. Sharpe’s assignment of the “burden of proof” to fund man- 2. These turnover measures represent the total portfolio pur-agers echoes Paul Samuelson’s “Challenge to Judgment” chases and sales of equity funds each year as a percentage (1974). In that article, he demanded “brute evidence” of the of assets, not the traditional—albeit inexplicable—formula superiority of active management. As far as we know, no that is in general use today: the lesser of purchases and sales such evidence was ever produced. as a percentage of assets. My recent speech “Big Money 8 Ahead of Print ©2014 CFA Institute in Boston—The Commercialization of the ‘Mutual’ Fund leads to a far smaller capital gain tax burden, but its low Industry” details my methodology and is available at www. expense ratio, 0.06%, confiscates only 3% of income, leaving johncbogle.com. its 2.1% gross yield barely impaired.

3. Investment Company Institute, 2013 Investment Company 9. Note that taxes on both the active funds and the index fund Fact Book, 53rd ed. (2013, p. 86, Figure 5.11). are based on “pre-liquidation, after-tax returns” as provided 4. Strategic Insight, “The Strategic Insight 2012 Fund Sales by Morningstar. That is, each fund is assumed to be held Survey: Perspectives on Intermediary Sales by Distribution through the end of the period. On a post-liquidation basis Channel and by Share Class” (May 2013, p. 27). (i.e., when sold at the end of the period), the index fund 5. In Table 2, I provide a footnote that illustrates the impact on advantage still exists but is smaller. the returns of index funds assuming the same 50 bp distribu- 10. Again, relative to the assumed real return on stocks of 5%, tion cost estimate used for active funds. active fund costs would consume 60% of the return, com-6. It seems likely that many corporate DC plans (especially pared with 7% of the return of the index fund. those with substantial assets) would fall on the lower side 11. As of this writing, this is the date of the most recent and com-of the 50 bp distribution cost estimate, whereas most IRAs prehensive available Morningstar data on investor returns. (which cannot take advantage of the economies of scale 12. Alas, even the 1.98% real return for investors in actively available to large DC plans) would fall on the higher side. managed equity funds is before the (conservative) estimate of 7. Investment Company Institute, 2013 Investment Company 1.20% lost annually to counterproductive investor behavior. Fact Book, 53rd ed. (2013, p. 114, Figure 7.4). I leave it to the reader to do the subtraction.

8. The loss to taxes by active funds is increased by the capital 13. A recent study by Vanguard found that of 1,540 managed gains realized by their high turnover but reduced by their US equity funds in 1998, only 842 survived through 2012, high expense ratios, which consume almost 60% of their or barely 55% of those in existence at the beginning of the dividend income. (For 2012, gross dividend yield was 2.1%, period. In addition, only 275, or 18% of the total, both sur-the average expense ratio was 1.2%, and the net taxable yield vived and outperformed their benchmarks—further confir-was 0.9%.) In contrast, the low turnover of the index fund mation of the proven success of index funds.

References Bogle, John C. 2012. The Clash of the Cultures: Investment vs. Samuelson, Paul. 1974. “Challenge to Judgment.” Journal of Speculation. Hoboken, NJ: Wiley. Portfolio Management, vol. 1, no. 1 (Fall):17–19.

Edelen, Roger, Richard Evans, and Gregory Kadlec. 2013. Sharpe, William F. 1966. “Mutual Fund Performance.” Journal of “Shedding Light on ‘Invisible’ Costs: Trading Costs and Mutual Business, vol. 39, no. 1 (January):119–138. Fund Performance.” Financial Analysts Journal, vol. 69, no. 1 (January/February):33–44. ———. 1991. “The Arithmetic of Active Management.” Financial Analysts Journal, vol. 47, no. 1 (January/February):7–9.

Haslem, John A. 2006. “Assessing Mutual Fund Expenses and Transaction Costs.” Working paper, University of Maryland (1 ———. 2013. “The Arithmetic of Investment Expenses.” Financial May). Analysts Journal, vol. 69, no. 2 (March/April):34–41.

Phillips, Don. 2013. “Mutual Fund Urban Myths.” Morningstar Swensen, David. 2005. Unconventional Success: A Fundamental Advisor (June/July):80. Approach to Personal Investment. New York: Free Press.

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