Please Provide a 2 to 3 page article review for each, there attached on this question. Your discussion should include a brief summary (including the big ideas or major points of the article) along with some synthesis of the ideas and some of your own thoughts. You should draw any parallels with your textbook readings (Investments, Bodie and Kane 9th Edition) or with current events. This assignment is due on Sunday, August 16, 2015 at 11:59 pm. Have fun studying.

Financial Analysts Journal Volume 70 Number 1 2014 CFA Institute PERSPECTIVES The Arithmetic of \"All-In\" Investment Expenses 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 managed 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 Investment Expenses\" (2013) with interest and applause (of course!). It brought to my mind what was likely his first article on the subject of fund costs\"Mutual Fund Performance\"published way back in 1966. In that article, Dr. Sharpe was right in his conclusion that \"all other things being equal, the smaller a fund's expense ratio, the better the results obtained by its stockholders\" (p. 137). Sharpe's credibility, objectivity, and quantification expertise are peerless. He was the 1990 recipient of the Nobel Prize in Economic Sciences and is now professor emeritus of finance at Stanford University, where he has taught thousands of students over some 43 years. He was right again in his 2013 article: \"A person saving for retirement who chooses low-cost investments could have a standard of living throughout retirement more than 20% higher than that of a comparable investor in high-cost investments\" (p. 34). However, as I will explain, he understated the gap in favor of low-cost investments. The 1991 Article Sharpe has taken up this subject often. In \"The Arithmetic of Active Management\" (Sharpe 1991), he analyzed mutual fund returns and found the same forces at work: Statements such as [\"the case for passive management rests only on complex and unrealistic theories of equilibrium in capital markets\"] are made with alarming frequency by investment professionals. John C. Bogle is founder and former chief executive of the Vanguard Group and president of the Bogle Financial Markets Research Center. In some cases, subtle and sophisticated reasoning may be involved. More often (alas), the conclusions can only be justified by assuming that the laws of arithmetic have been suspended for the convenience of those who choose to pursue careers as active managers. If \"active\" and \"passive\" management styles are defined in sensible ways, it must be the case that (1) before costs, the return on the average actively managed dollar will equal the return on the average passively managed dollar and (2) after costs, the return on the average actively managed dollar will be less than the return on the average passively managed dollar. These assertions will hold for any time period. Moreover, they depend only on the laws of addition, subtraction, multiplication and division. Nothing else is required. . . . Because active and passive returns are equal before cost, and because active managers bear greater costs, it follows that the aftercost return from active management must be lower than that from passive management. . . . The proof is embarrassingly simple and uses only the most rudimentary notions of simple arithmetic. Enough (lower) mathematics. . . . . . . Properly measured, the average actively managed dollar must underperform the average passively managed dollar, net of costs. Empirical analyses that appear to refute this principle are guilty of improper measurement. (pp. 7-8) January/February 2014\twww.cfapubs.org 13 Financial Analysts Journal The 1966 Article Surprising as it may seem, Sharpe's 1991 article was published a quarter century after his first article on this subject. Although the role of costs in shaping the relative performance of mutual funds was integral to my career even before I founded Vanguard in 1974, it took me a while to pay adequate attention to that seminal article. The following are excerpts from Sharpe's 1966 article: Past performance [based on the ratio of annual fund returns to volatility in net asset values] appears to provide a basis for predicting future performance. . . . The high correlation among mutual fund rates of return suggests that most accomplish the task of diversification rather well. Differences in performance are thus likely to be due to either differences in the ability of management to find incorrectly priced securities or to differences in expense ratios. If the market is very efficient, the funds spending the least should show the best (net) performance. . . . The results tend to support the cynics: good performance is associated with low expense ratios. . . . . . . All other things being equal, the smaller a fund's expense ratio, the better the results obtained by its stockholders. . . . But the burden of proof may reasonably be placed on those who argue the traditional viewthat the search for securities whose prices diverge from their intrinsic values is worth the expense required. (pp. 131-132, 137-138)1 The Arithmetic of \"All-In\" Investment Expenses I enthusiastically endorse Sharpe's conclusions and his perceptive analysis, but the use of a mutual fund's expense ratio offers only a pale approximation of the total costs paid by investors in actively managed equity funds. Using only that measure, Sharpe compared the reported expense ratio of 1.12% for the average large-cap blend fund (unweighted by assets) with the ratio of 0.06% for the Vanguard Total Stock Market Index Fund. The advantage of the low-cost investment over the higher-cost investments was 1.06 percentage points per year. In this article, I shall provide careful, if inevitably imprecise, estimates of the additional costs that investors in actively managed equity funds incurfew, if any, of which are incurred by index fund investors. 14\twww.cfapubs.org\b Focusing on the issue of fees charged by brokers in his 1966 article, Sharpe perceptively referred to the fact that the costs included in mutual fund expense ratios fail to capture the all-in costs borne by fund investors: One reservation is in order. Expense ratios as reported do not include all expenses; brokers' fees are omitted. Thus the expense ratio does not capture all the differences in expenses among funds. It is entirely possible that funds with performance superior to that predicted by the traditional expense ratio engage in little trading, thereby minimizing brokerage expense. It was not feasible to attempt to measure total expense ratios for this study; had such ratios been used, a larger portion of the difference in performance might have been explained in this manner, and the apparent differences in management skill might have been smaller. (p. 134) Despite the sharp decline in the commission rates charged by brokers, the costs of the portfolio transactions incurred by actively managed funds are substantial; fund portfolio turnover (based on aggregate industry data) has leaped almost fivefold since the early 1960sfrom 30% to 140% today.2 In addition, Sharpe neglected to note that frontend sales loads were a major cost. But their impact on annual returns depends on the (unknowable) holding period of the investor. Furthermore, frontend loads are far less common today; they have typically been replaced by deferred sales loads and annual fees charged by brokers and advisers. Also, there are far more pure no-load funds in the fund industry of today. Moreover, whereas index funds are fully invested at all times, portfolios of actively managed funds typically carry a cash position of about 5%, causing the funds to lose a portion of the long-term equity premium. Finally, for most investors, relative tax efficiency is a critically important element of total costs. Funds with low expense ratios (notably, index funds), which operate with minimal portfolio turnover, are relatively tax efficient. Actively managed funds, with their far higher expense ratios, not only incur substantial transaction costs on their portfolio turnover but also realize capital gains, generating significant tax inefficiency. Taxes represent an additional drag on the returns earned by mutual fund investors in taxable accounts, but they are of no immediate concern to investors in tax-deferred retirement plans. 2014 CFA Institute The Arithmetic of \"All-In\" Investment Expenses In this article, I shall estimate the impact of (1) the first three of these extra cost categories transaction costs, cash drag, and sales loadson the net returns that funds deliver to their retirement plan investors and, separately, (2) all four costs, including excess taxes, on the returns delivered to taxable fund investors. Quantitative Imprecision The issue of all-in fund costs has rarely, if ever, been subject to careful examination, likely because data on these costs are difficult, if not impossible, to quantify with precision. So, where is a businessman like me (albeit one educated in economics) to turn? The kind of quantitative precision that the academic community properly demands in most cases is simply not possible with respect to these four costs that fund investors incur over and above the expense ratio. I will provide reasonable estimates for each based on a variety of sources and data, buttressed by my industry experience. Lest I overstate the advantages of indexing, I have made these cost estimates for actively managed funds as conservative as possible. Transaction Costs The first \"invisible\" fund costs are the transaction costs incurred by the funds themselves. Two academic studies have produced rather different estimates of the drain of fund trading costs in order to calculate their annual impact on fund returns. One study was conducted by Dr. John A. Haslem (2006). Brokerage commissions are now required to be specified by equity mutual funds, and from this source, Haslem identified a performance drag on fund annual returns of 39 basis points (bps). After taking into account implicit trading costs (timing delays, market impact, etc.), he estimated that the trading costs of actively managed funds produced an annual impact on fund returns of -60 bps. Edelen, Evans, and Kadlec (2013) provided another extensive study of this issue. They examined the annual expenditures on trading costs incurred by 1,758 domestic equity funds over 1995- 2006 and calculated average annual trading costs of 1.44%, far in excess of the average expense ratio of 1.19% for the funds they examined. That surprisingly large number astonished at least one independent expert. Don Phillips, president of the investment research division at the mutual fund data provider Morningstar, described it as \"preposterous.\" But he conceded that \"trading is a real cost and an activity that is often counterproductive in asset management.\" He presented his own estimate of annual transaction costs of \"about 30 bps, which does not include certain other costs,\" such as the substantial market impact, which he did not quantify (Phillips 2013, p. 80). I have been examining this issue for many years and have shown that high turnover is negatively correlated with fund performance (Bogle 2012, p. 148). In this article, I use the actual measure of fund trading: portfolio purchase of stocks plus portfolio sales as a percentage of fund average assets. For reasons lost in history, however, funds now calculate turnover as the lesser of portfolio purchases or sales as a percentage of fund average assetsa figure that obviously understates transaction activity and is, therefore, irrelevant in the calculation of total transaction costs. I am also aware that because mutual fund managers are trading largely with one another and with other institutional fund managers, market impact must resemble a zero-sum game for fund managers as a group (and their fund shareholders). Because a fund \"taking a haircut\" on selling a large block of stock results in a better price for the buying counterparty, I am inclined to consider market impact costs to be close to zero. But for investors as a group, after accounting for bid-ask spreads and commissions that brokers pay to brokers and dealers, trading obviously becomes a loser's game. So for my analysis, I use an estimate that is far more conservative than the 1.44% calculated by Edelen et al. (2013) and even lower than the Haslem (2006) estimates. My estimate is likely consistent with the expanded estimate provided by Phillips. Because precision here is impossibleand I do not want to risk overstating these costsI opt for the ease of \"rounding\" and assume just 50 bps for the transaction costs of actively managed funds. Although index funds obviously incur some transaction costs, they are so minimal that they have had no significant impact on the returns of those funds. That is, the annual returns of major large-cap index funds lag those of their target indices by only the amount of their expense ratios, meaning that net transaction costs are too small to affect the precision with which they track their target indices. So, I assume zero total transaction costs for the index fund. Cash Drag Another additional cost is the drag of cash. Active funds fairly consistently carry cash in the range of 5% of assets, whereas index funds are normally fully invested. If we assume an annual long-term equity premium for stocks over cash of as little as 6%, there would be an additional 30 bp drag on active fund returns. Some of the larger active January/February 2014\twww.cfapubs.org 15 Financial Analysts Journal equity funds doubtless \"equitize\" part of this cash by holding index futures. But data on that usage are simply not available. So, I will add a cost of just 15 bps to account for the cash holdings of active funds. Sales Loads: Direct and Indirect The costs paid directly by investors for fund distribution are rarely, if ever, taken into account in the analysis of fund expenses and returns. Nonetheless, these expenses incurred by most mutual fund \"retail\" investors represent a major drag on fund returns. That cost was once relatively easy to estimate because this industry originally grew through a \"sales push\" distribution system. From the inception of the fund industry in 1924 through the late 1970s, it was dominated by fund distributors that charged sales loads averaging about 8% of the dollar amount of shares purchased. (Then, few firms operated on a \"no-load\" basis.) So in those days of yore, the math was fairly straightforward: For the typical investor who paid an 8% front-end load and held his shares for eight years, the amortized load was 100 bps per year; for a 16-year holder, 50 bps per year. (The norm was likely closer to 100 bps.) Today, however, the distribution system has undergone a radical transformation, and we can only make reasonable estimates based on limited data. First, no-load funds have soared in importance: They now account for almost half of long-term industry assets (excluding assets of institutional funds).3 Further, the typical front-end sales load has dropped from 8% to 5%. Also, the \"retail\" distribution system is rapidly changing from a frontend load model to an annual asset charge. And even load funds often waive sales charges for pension plans and corporate thrift plans, as well as for registered investment advisers and brokers, who charge their clients an annual fee, replacing the earlier front-end commission-based model. Recent estimates suggest that only 40% of the traditional \"A\" front-end load shares carry sales loads and 60% are sold at net asset value. To further muddle the calculation of \"distribution drag,\" some individual investors are DIY (\"do it yourself\") investors, incurring few, if any, extra costs. But most rely on brokers and advisers who charge fees for their services. A recent survey, based on a limited sample, placed the proportion of equity fund owners in this adviser-assisted category at 56% of total no-load fund sales.4 In this new environment, fees paid by investors to brokers and investment advisers typically run to about 1% per year, (indirectly) reflecting the costs of fund share distribution. Therefore, with some investors incurring almost no additional distribution costs and others subject to costs in the range of 1% or more, I will conservatively use an average annual distribution cost of 0.5% for individual investors in actively managed funds, which includes total annual broker and adviser costs and sales loads. Because no major index fund charges sales loads and because investors in traditional index funds are largely, but not entirely, DIY investors (often in defined contribution plans for which the sponsoring company provides the fund menu), I take the liberty of assuming in my basic analysis no such distribution costs for index funds.5 (Readers who believe that I have overstated or understated the distribution costs for either actively managed funds or index funds may simply insert their own cost assumptions into Table 1.) Note that investors in corporate defined contribution (DC) plans are a major force in retirement plan investing and may well be subject to lower distribution costs.6 But individual retirement accounts (IRAs) have an even larger asset base ($5.4 trillion versus $5.1 trillion for DC plans at the end of 2012).7 A significant portion of IRA assets are the result of DC plan rollovers at retirement, and such investors seem more likely to retain brokers and advisers for their IRAs, incurring the distribution costs noted above. Table 1. \u0007All-In Investment Expenses for Retirement Plan Investors Expense ratioa Transaction costs Cash drag Sales charges/feesb All-in investment expenses Actively Managed Funds 1.12% 0.50 0.15 0.50 2.27% Index Funds 0.06% 0.00 0.00 0.00 0.06% Index Advantage 1.06% 0.50 0.15 0.50 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. 16\twww.cfapubs.org\b 2014 CFA Institute The Arithmetic of \"All-In\" Investment Expenses Putting It All Together Table 1 details the all-in aggregate fund costs, beginning with Sharpe's data and then including the additional elements described previously. I will start by looking at these all-in costs from the perspective of Sharpe's 2013 article: the tax-deferred retirement plan of the individual investor. Note that the pervasive acceptance of presenting expenses as a percentage of fund asset values, as in Table 1, greatly diminishes the perception of the substantial impact that costs have on fund annual returns. For example, assuming a 7% stock market return, the 2.27% estimated annual cost of the actively managed funds would consume almost 33% of the return, whereas the 0.06% annual cost of the index fund would consume less than 1% of the returna dramatic difference. Preparing for Retirement What does this annual differential mean to an investor who prepares for retirement by owning mutual funds over the long term? For illustrative purposes, I have assumed that a 30-year-old investor begins to save for retirement at age 70, a span of 40 years, by investing in a tax-deferred 401(k) or IRA plan. She earns $30,000 annually at the outset, and I assume that her compensation will grow at a 3% annual rate thereafter. In Table 2, I present a comparison of the retirement plan accumulation if the investor were to invest 10% of her compensation each year in either (1) an actively managed large-cap equity fund or (2) the Vanguard Total Stock Market Index Fund, the subjects of Sharpe's 2013 analysis. The table summarizes the results over the four decades that follow. The advantage provided by the index fund is substantial, and as time passes, it grows by leaps and bounds. By the time retirement comes, when the investor in the example is 70 years old, $927,000 would have been accumulated in the index fund versus $561,000 in the active fund, an astonishing gap of $366,000 and a 65% enhancement in capital. Even if we assume that the actively managed fund investor incurs no distribution costs, the 40-year accumulation would total $626,000. If the index fund investor incurs distribution costs of 0.5% per year, the accumulation would total $824,000 and the index fund investor would nonetheless maintain a $198,000 advantage over the investment lifetime still a 32% enhancement. When Sharpe considered only the difference in expense ratios for index and actively managed funds, he concluded that \"a person saving for retirement who chooses low-cost investments could have a standard of living throughout retirement more than 20% higher than that of a comparable investor in high-cost investments\" (2013, p. 34). But when all-in costswhich obviously (1) exist and (2) are substantial, whatever their precise amountare considered, the assumed retirement wealth accumulation enhancement provided by the low-cost index fund as shown in Table 2 leaps to fully 65% higher, ranging (depending on the assumptions presented in the table) from 32% to 86% higher. Regardless of the assumptions used, the index fund would provide a truly remarkable potential improvement in the standard of living for retirees. For example, using my primary calculations and assuming a 4% annual withdrawal rate at retirement, the average active fund investor would receive a monthly check for $1,870 whereas the index fund investor would receive $3,090. Taxes and Taxable Investors For taxable fund investors, the gap widens even further. The high tax efficiency of the index fund gains a significant advantage over the painful tax inefficiency of the average actively managed fund. Table 2. \u0007Total Wealth Accumulation by Retirement Plan Investors, Assuming a 7% Nominal Annual Return on Equities Actively Managed Fund Gross annual return Index Fund Index Enhancement 7.00% 7.00% All-in costs 2.27 0.06 -2.21% Net annual return 4.73 6.94 +2.21 Accumulation period After 10 Years After 20 Years After 30 Years After 40 Yearsa $44,000 130,000 286,000 561,000 $50,000 164,500 412,000 927,000 $6,000 34,500 126,000 366,000 % Increase 13% 27 44 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\twww.cfapubs.org 17 Financial Analysts Journal Again, it is impossible to make precise calculations here. Therefore, for active managers and the index fund, I have used as a guideline the pretax and after-tax returns provided by Morningstar for the 10-year period ending 30 April 2013. Over this period, the total stock market index had an average annual return of 8.7%. The return for actively managed large-cap blend funds was 7.5%, of which about 75 bps was lost to taxes; the broad market index fund lost about 30 bps to taxes.8 So, I will use a conservative and rounded tax differential estimate of 45 bps, which likely understates the extra tax costs incurred by investors in actively managed funds. With taxes considered, the total all-in costs added by actively managed mutual funds amount to about 317 bps per year for taxable investors (Table 3). This rough snapshot of the annual impact of taxes may suggest that tax costs are inconsequential. But when compounded over 40 years (as in the previous example), they bring the extra costs of actively managed funds to a truly overwhelming annual level of 3.02%. In Figure 1, I assume that a taxable fund investor begins with a $10,000 investment in (1) a tax-efficient index mutual fund and (2) a tax-inefficient actively managed fund and simply holds each for the subsequent four decades. The calculated terminal value of the active fund grows steadily over time$15,000 after 10 years, $22,000 after 20 years, and $48,000 after 40 years. The index fund grows far more swiftly, ending up with a value of $131,000, a remarkable enhancement of $83,000, or almost 175%. Indeed, taxes are a vital consideration.9 Table 3. \u0007All-In Fund Costs Including Tax Differential, 10 Years Ending 30 April 2013 Actively Managed Fund 7.00% 2.27 0.75 3.02 3.98 Assumed stock market return All-in costs (from Table 1) Tax inefficiency Total costsa Assumed net fund return Index Fund 7.00% 0.06 0.30 0.36 6.64 Index Advantage 2.21% 0.45 2.66 2.66 aHere, costs (including taxes) consume 43% of the returns for the active funds, compared with 5% for the index fund. Figure 1. \u0007Growth 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 0 10 20 30 40 Years Index Fund (6.64%) 18\twww.cfapubs.org\b Actively Managed Fund (3.98%) 2014 CFA Institute The Arithmetic of \"All-In\" Investment Expenses Real vs. Nominal Returns So far, I have reported fund returns on a nominal basis, unadjusted for the impact of inflation. But investors must rely on real returns to maintain their standard of living. Although mutual funds almost exclusively report only their nominal returns, I believe that fund investors must consider their real returns as well. Making this adjustment has an important negative impact on both active funds and index funds. For example, if we assume a future annual rate of inflation of only 2%the approximate present spread between the inflation-adjusted 10-year Treasury Inflation-Protected Security and the 10-year US Treasury note itselfit reduces the assumed nominal annual market return of 7% to a real return of 5%. Thus, the real return after allin costs for actively managed funds would fall to 1.98% from its nominal 3.98%, and the index fund real return would fall to 4.64% from a nominal return of 6.64%.10 Compounded over 40 years, a $10,000 initial investment in active funds would grow to just $22,000 in real terms whereas the index fund would grow to $61,000a nearly threefold enhancement. These numbers may be scary and almost unbelievable, but the data do not lie. Counterproductive Investor Behavior Throughout this article, I have presented the returns as reported by the mutual funds themselves essentially, the percentage change in the funds' net asset values, adjusted for the reinvestment of all dividends and distributions. As the record makes clear, however, mutual fund investors are too often tempted to add to their equity holdings when markets are rising, to withdraw their investments when markets tumble, and to move into funds that have performed well in the recent past only to revert to the mean (or below) thereafter. Such counterproductive investor behavior proves to be another advantage for index fund investors. For example, over the 15 years ending 30 June 2013,11 the actively managed large-cap blend funds evaluated by Sharpe (2013) reported an average annual return of 4.50%for the funds that survived the period. But Morningstar calculated that the asset-weighted return earned by investors over the same period was just 2.59%, a \"behavior gap\" of 1.91 percentage points in return per year. (As it happens, in this particular period, investors in the Total Stock Market Index Fund exhibited moderately productive timing, earning a slightly higher annual return than the fund reported.) A loss of almost 2 more percentage points of annual return for active investorsover and above fund expense ratios, other costs, and taxesis a high penalty to pay for the combination of high costs and counterproductive movement of their money from one fund to another.12 Reconciliation Now I will explore how consistent these all-in cost estimates are with the returns earned by largecap equity funds relative to the returns earned by the Total Stock Market Index Fund. First, let us assume, as so many academic studies indicate, that active equity mutual funds as a group provide, before costs, a return equal to that of the stock market itself at the same level of risk (\"zero alpha\"). Therefore, the subtraction of direct all-in fund expenses should essentially reflect the difference between the market return and the managed fund return. The exercise is a bit complex because some of the expenses I have reviewed so far are internal to the funds themselves and others are paid directly by the fund investors. Table 4 should clarify this distinction. The concept is that the net returns achieved by large active funds should lag the returns earned by the Total Stock Market Index Fund by the amount of direct costs paid out of fund gross returns1.77 percentage points annually. The costs of sales and distribution fees, extra taxes, and imprudent (or opportunistic) investment behavioranother 2.15 percentage points in aggregateare not included here because they are borne directly by the investors themselves. How does that theory work in practice? Quite nicely, as it turns out. For example, over the two decades ending 31 December 2012, the average actively managed large-cap core fund earned a compound annual return of 6.50% (adjusted for survivorship bias, as described later in this section), falling short of the 8.3% return of the Total Stock Market Index Fund by 1.80 percentage points per year. That shortfall is remarkably close to the annual differential between index fund Table 4. \u0007Allocation of Costs of Actively Managed Funds (from Tables 1 and 2) Expense ratio Transaction costs Cash drag Sales charges Tax inefficiency Investor behavior Total Costs Borne by Fund 1.12% 0.50 0.15 1.77% Costs Borne by Investor 0.50% 0.45 1.20a 2.15% aA conservative estimate, well below the 1.91 percentage point lag realized over the past 15 years. January/February 2014\twww.cfapubs.org 19 Financial Analysts Journal direct costs and active fund direct costs of 1.77 percentage points, as shown in Table 4. This near precision, I must report, is no more than a happy coincidence, simply because the calculations of costs and returns presented in this article are, as noted earlier, inevitably imprecise. Even a larger difference in the results for the past two decadessay, plus or minus 50 bpswould nonetheless confirm the strong relationship between fund costs and fund returns. The costs are based on the results over the past two decades, using limited data and some experienced judgment. Therefore, take this fragile precision only as proof, in principle, that the influence of costs must dominate the relationship between the returns earned by active funds and the returns earned by index funds. One of the principal challenges in calculating the average returns of the funds is the need to eliminate what is called \"survivorship bias\"that is, to take into account not only the returns of funds that survived a given period but also those that failed to do so. Obviously, data that are not free of survivorship bias are inappropriate (after all, funds with poor records are less likely to survive), but there are myriad methods of calculating the difference. I have found the data provided by Lipper to be quite reliable. Using its data for the two decades ending 31 December 2012, for example, the surviving largecap core funds earned an annual return of 7.86%. But, as shown above, all the funds in that category, including those that did not survive, earned only 6.50%, or 1.36 percentage points less. Given the persistent high failure rate of equity mutual funds,13 this adjustment for survivorship bias is essential. Earlier studies of the relative returns of actual mutual funds and the broad market indices confirm the reasonableness of these estimates of the impact of direct costs incurred by investors. For example, in his book Unconventional Success: A Fundamental Approach to Personal Investment, Yale endowment fund manager David Swensen (2005) summarized research conducted by Robert Arnott, Andrew Berkin, and Jia Ye and reported that for the 20 years ending 31 December 1998, the average actively managed fund underperformed a broad stock market index fund by 2.1 percentage points per year before taxes. (Numerous other studies confirm a spread in this range.) Current data also confirm a shortfall of this magnitude. As noted earlier in this section, over the 20 years ending 31 December 2012, the underperformance of the active funds relative to the index was almost identical1.8 percentage points per year. Broadly speaking, the reality confirms the theory. Conclusion By examining mutual fund expense ratios, Dr. Sharpe began the saga of how much the draining impact of expense ratios erodes the returns delivered to fund investors over the long term. My analysis in this article builds on that foundation, but I estimated the all-in costs incurred by mutual fundsexpense ratios plus the other fund costs which are numerous and substantial in the case of actively managed funds but far less numerous and less substantial for index funds. It is simply a story that must be told. I re-emphasize the inevitable imprecision of my data, even as I reiterate that I have tried to use conservative estimatesselecting the lowest reasonable number in each case and, in all likelihood, understating the confiscatory impact of the additional transaction costs, cash drag, sales loads, distribution costs, tax inefficiency, and counterproductive investor behavior. Others will no doubt find fault with my data and estimates, and I urge industry participants and academics alike to offer constructive criticism of my data, including their own estimates of these costs. I also urge mutual fund investors not only to consider the conventional annual impact of expense ratios and other costs but also to recognize how much these differences matter as time horizons lengthen. In the short term, the impact of costs may appear modest, but over the long run, investment costs become immensely damaging to an investor's standard of living. Think long term! For those who are investing for their retirement and for their lifetimes, understanding the cost issue is vital to success in investing. An increase of 65% in the wealth accumulated by retirement plan investors is not trivial! After analyzing the data over many years, I feel confident in reaffirming the warning that I have consistently given to fund investors over the years: Do not allow the tyranny of compounding costs to overwhelm the magic of compounding returns. This article qualifies for 0.5 CE credit. Notes 1. Sharpe's assignment of the \"burden of proof\" to fund managers echoes Paul Samuelson's \"Challenge to Judgment\" (1974). In that article, he demanded \"brute evidence\" of the superiority of active management. As far as we know, no such evidence was ever produced. 20\twww.cfapubs.org\b 2. These turnover measures represent the total portfolio purchases and sales of equity funds each year as a percentage of assets, not the traditionalalbeit inexplicableformula that is in general use today: the lesser of purchases and sales as a percentage of assets. My recent speech \"Big Money 2014 CFA Institute The Arithmetic of \"All-In\" Investment Expenses in BostonThe Commercialization of the 'Mutual' Fund Industry\" details my methodology and is available at www. johncbogle.com. 3. Investment Company Institute, 2013 Investment Company Fact Book, 53rd ed. (2013, p. 86, Figure 5.11). 4. Strategic Insight, \"The Strategic Insight 2012 Fund Sales Survey: Perspectives on Intermediary Sales by Distribution Channel and by Share Class\" (May 2013, p. 27). 5. In Table 2, I provide a footnote that illustrates the impact on the returns of index funds assuming the same 50 bp distribution cost estimate used for active funds. 6. It seems likely that many corporate DC plans (especially those with substantial assets) would fall on the lower side of the 50 bp distribution cost estimate, whereas most IRAs (which cannot take advantage of the economies of scale available to large DC plans) would fall on the higher side. 7. Investment Company Institute, 2013 Investment Company Fact Book, 53rd ed. (2013, p. 114, Figure 7.4). 8. The loss to taxes by active funds is increased by the capital gains realized by their high turnover but reduced by their high expense ratios, which consume almost 60% of their dividend income. (For 2012, gross dividend yield was 2.1%, the average expense ratio was 1.2%, and the net taxable yield was 0.9%.) In contrast, the low turnover of the index fund leads to a far smaller capital gain tax burden, but its low expense ratio, 0.06%, confiscates only 3% of income, leaving its 2.1% gross yield barely impaired. 9. Note that taxes on both the active funds and the index fund are based on \"pre-liquidation, after-tax returns\" as provided by Morningstar. That is, each fund is assumed to be held through the end of the period. On a post-liquidation basis (i.e., when sold at the end of the period), the index fund advantage still exists but is smaller. 10.\tAgain, relative to the assumed real return on stocks of 5%, active fund costs would consume 60% of the return, compared with 7% of the return of the index fund. 11.\tAs of this writing, this is the date of the most recent and comprehensive available Morningstar data on investor returns. 12.\tAlas, even the 1.98% real return for investors in actively managed equity funds is before the (conservative) estimate of 1.20% lost annually to counterproductive investor behavior. I leave it to the reader to do the subtraction. 13.\tA recent study by Vanguard found that of 1,540 managed US equity funds in 1998, only 842 survived through 2012, or barely 55% of those in existence at the beginning of the period. In addition, only 275, or 18% of the total, both survived and outperformed their benchmarksfurther confirmation of the proven success of index funds. References Bogle, John C. 2012. The Clash of the Cultures: Investment vs. Speculation. Hoboken, NJ: Wiley. Samuelson, Paul. 1974. \"Challenge to Judgment.\" Journal of Portfolio Management, vol. 1, no. 1 (Fall):17-19. Edelen, Roger, Richard Evans, and Gregory Kadlec. 2013. \"Shedding Light on 'Invisible' Costs: Trading Costs and Mutual Fund Performance.\" Financial Analysts Journal, vol. 69, no. 1 (January/February):33-44. Sharpe, William F. 1966. \"Mutual Fund Performance.\" Journal of Business, vol. 39, no. 1 (January):119-138. Haslem, John A. 2006. \"Assessing Mutual Fund Expenses and Transaction Costs.\" Working paper, University of Maryland (1 May). Phillips, Don. 2013. \"Mutual Fund Urban Myths.\" Morningstar Advisor (June/July):80. . 1991. \"The Arithmetic of Active Management.\" Financial Analysts Journal, vol. 47, no. 1 (January/February):7-9. . 2013. \"The Arithmetic of Investment Expenses.\" Financial Analysts Journal, vol. 69, no. 2 (March/April):34-41. Swensen, David. 2005. Unconventional Success: A Fundamental Approach to Personal Investment. New York: Free Press. January/February 2014\twww.cfapubs.org 21 Financial Analysts Journal Volume 70 Number 1 2014 CFA Institute The Limits to Arbitrage and the Low-Volatility Anomaly Xi Li, Rodney N. Sullivan, CFA, and Luis Garcia-Feijo, CFA, CIPM The authors found that over 1963-2010, the existence and trading efficacy of the low-volatility stock anomaly were more limited than widely believed. For example, they found no anomalous returns for equal-weighted long-short (low-risk minus high-risk) portfolios and that alpha is largely eliminated when omitting lowpriced stocks from value-weighted long-short portfolios. Furthermore, performance of long-short portfolios was significantly reduced by high transaction costs, reflecting the finding that the abnormal returns were concentrated among low-liquidity and smaller stocks. Amplifying liquidity needs, the anomalous excess returns quickly reversed, requiring frequent rebalancing. The authors' findings have meaningful implications for implementing low-risk equity portfolio strategies. I n what is sometimes referred to as the \"low-risk\" or \"low-volatility\" anomaly, researchers have discovered a provocative empirical inverse connection between future stock returns and various measures of stock return variability, including total return volatility, idiosyncratic volatility, and beta. Documented empirical evidence has shown that future stock returns of low-return-variability portfolios outperform those of high-return-variability portfolios in both US and international markets (see, e.g., Ang, Hodrick, Xing, and Zhang 2006, 2009; Blitz and van Vliet 2007; Clarke, de Silva, and Thorley 2010; Baker, Bradley, and Wurgler 2011; Frazzini and Pedersen, forthcoming; Li, Sullivan, and Garcia-Feijo, forthcoming 2015). These findings run counter to our economic intuition because economic theory predicts that higher expected return compensates for higher expected risk. Garcia-Feijo, Kochard, Sullivan, and Wang (2013) suggested that the so-called low-risk anomaly might more accurately be called the highrisk anomaly given that the anomalous historical returns are found primarily among stocks in the Xi Li is managing partner at XL Partners, Boston, and an assistant professor at Hong Kong University of Science and Technology. Rodney N. Sullivan, CFA, is head of publications at CFA Institute, Charlottesville, Virginia. Luis Garcia-Feijo, CFA, CIPM, is assistant professor of finance at Florida Atlantic University, Davie. Editor's Note: Rodney N. Sullivan, CFA, is editor of the Financial Analysts Journal. He was recused from the referee and acceptance processes and took no part in the scheduling and placement of this article. See the FAJ policies section of cfapubs.org for more information. 52\twww.cfapubs.org\b highest-risk quintile. They demonstrated that the historical performance of low-risk investing is strikingly cyclical, driven largely by swings in the relative valuation levels of low-risk and high-risk stocks and by the varying investor appetite for momentum-driven investing. Taken together, these findings motivated us to further investigate the properties of this anomalous low-volatility effect. In our study, we explored anomalous \"lowrisk\" returns to better understand the underlying economics of low-volatility stock outperformance. In particular, we explored whether the abnormal returns associated with the persistent low-volatility anomaly can be captured over time in practice or are somehow subsumed by limits to investors' arbitraging them away. To accomplish this objective and gain additional insight into the seemingly powerful association between historical volatility and future returns, we examined the role of portfolio rebalancing and transaction costs in the persistence of the low-risk anomaly and in attempts to extract profits from the anomaly. Specifically, we examined portfolio-rebalancing requirements and the impact of associated transaction costs on the returns to zerocost (low-risk minus high-risk) portfolios formed on the basis of various low-volatility measures. Discussion of findings. We found that investors' ability to extract the excess returns of zero-cost portfolios that are based on both idiosyncratic volatility (IVOL) and the estimated CAPM (capital asset pricing model) beta is limitedlikely a surprising result for many observers. In particular, we found that the excess returns of the low-risk, zero-cost portfolios are short lived because they are present only in month t + 1 and are largely subsumed by 2014 CFA Institute The Limits to Arbitrage and the Low-Volatility Anomaly high transaction costs. Moreover, we found that the anomalous returns of value-weighted portfolios are largely eliminated when low-priced (under $5) stocks are omittedand are completely absent from equal-weighted portfolios. Our results are based on a series of tests in which we separated the universe of US stocks into high- and low-liquidity segments and then related the performance of these liquidity segments to the zero-cost, IVOL-based portfolio. In conducting this analysis, we determined whether the abnormal returns of our zero-cost, volatilitybased portfolios persist beyond the first month and whether the excess returns are concentrated in the low-liquidity segment. Such a finding would imply that traders will necessarily experience relatively high transaction costs in attempting to extract excess returns. The Low-Volatility Anomaly Of the many possible approaches to measuring the low-volatility effect, the literature follows two primary paths: one that uses one month of daily returns (Ang et al. 2006, 2009) and one that uses a longer period (36 months or 60 months) of monthly returns (Clarke et al. 2010). Risk is typically measured by either idiosyncratic volatility or beta. In our study, we used all the various low-volatility measures in testing the efficacy of investors' attempts to arbitrage the low-volatility effect away. We first explored the low-volatility trading strategy as used by Ang et al. (2006, 2009), who found that stocks with high IVOL in one month have low returns the next month. In discovering this onemonth volatility effect, Ang et al. (2006, 2009) formed value-weighted portfolios by buying low-IVOL stocks and selling high-IVOL stocks (based on their IVOL ranking in the prior month) and holding the portfolios for one month. Their portfolios generated statistically significant excess returns over time, and these returns held when controlling for a variety of factors, including the well-known size and style effects of Fama and French (1993).1 We tested this portfolio trading strategy with both value-weighted and equal-weighted portfolios. We then tested the strategy by using idiosyncratic volatility estimates over 36 months (IVOL36) and 60 months (IVOL60) as well as holding the portfolios for one month. Finally, we also formed portfolios by assigning stocks on the basis of the magnitude of their estimated CAPM beta (BETA). Researchers' curious findings about volatility return patterns have spurred important research contributions aimed at a better understanding of the low-volatility anomaly. For example, in implementing a trading strategy, traders must obviously consider available liquidity. In our study, we attempted to ascertain the extent to which liquidity affects the viability of implementing various low-volatility trading strategies.2 We also tried to determine whether the IVOL anomaly derives from investor mispricing or from systematic market riskan important distinction for investors. Should the anomaly be related to systematic risk, then the excess returns could be viewed as arising from some, as yet unknown, common risk factor(s). For instance, Merton (1987) offered an explanation for why investors would demand higher returns for taking on higher IVOL. He explained that IVOL is positively related to expected return when investors cannot fully diversify their portfolios. Therefore, investors demand a higher return from companies with higher IVOL to compensate for imperfect diversification. Ang et al. (2009) found that the IVOL anomaly extends to numerous countries and is highly correlated with that found in the United States. They argued that such an effect could be driven by latent systematic risks. Specifically, they showed that abnormal returns generated by IVOL-based portfolio strategies in international markets strongly co-move with those in the US markets, suggesting a common risk factor: \"The large commonality in co-movement . . . suggests that broad, not easily diversifiable factors lie behind this effect\" (p. 2). The co-movement finding implies that the returnpredictive power of idiosyncratic risk is likely due to some pervasive risk factor. Similarly, Clarke et al. (2010) argued that IVOL (and total volatility) should be considered an additional equity market risk factor that investors should incorporate into portfolio construction. Interestingly, the empirical evidence in Ang et al. (2009) and Clarke et al. (2010) runs counter to the prediction by Merton (1987). The excess return, however, may be unrelated to systematic risk. Instead, it may be driven by a mispricingperhaps associated with an imperfection such as investor irrationality, perhaps somehow connected with IVOL. In exploring the competing risk versus mispricing explanations of the low-volatility anomaly, Li, Sullivan, and Garcia-Feijo (forthcoming 2015) traced the observed low-volatility return's link to market mispricing. Those findings suggest that the highly anomalous returns to IVOL portfolios, as identified in the literature, cannot be viewed as compensation for factor risk. In the case of mispricing, the profit opportunity may be ephemeral as investors come to understand their cognitive error and arbitrage away any excess return. Or the mispricing could be more lasting, supported over time by the high costs of arbitraging away the anomalous returns and perhaps even by some behavioral considerations. January/February 2014\twww.cfapubs.org 53 Financial Analysts Journal Focusing on market beta, Black (1972) offered a theoretically consistent interpretation of why lowrisk stocks do so well relative to high-risk stocks. He showed that such borrowing restrictions as margin requirements may cause low-beta stocks to outperform. More recently, Baker et al. (2011) proposed that behavioral considerations, including the structure of institutional client mandates, discourage arbitrage activity that would otherwise eliminate the low-volatility effect. These two explanations may provide insight into why the low-volatility effect has persisted for so many years despite being highly recognized. Data and Sample We obtained our stock return data from the CRSP monthly stock return files for July 1963 through December 2010. For delisted companies, the CRSP monthly return file does not include the returns from the delisting month unless the delisting date is at the end of the month. We fetched the returns in the delisting month and the market capitalization on the delisting date from the CRSP daily return files and combined those returns with the delisting returns to create the effective delisting month returns. If the delisting was for performance-related reasons, however, we set the delisting return equal to -55% for trading on NASDAQ or -30% for the NYSE and Amex. We concentrated on measuring idiosyncratic risk with respect to the Fama-French three-factor model. Specifically, we measured IVOL as the standard deviation of the residuals from the Fama- French three-factor model by regressing the daily returns of individual stocks in excess of the onemonth T-bill rate, Ri,t - Rf,t, on the daily returns to the common factors of size and book-to-market ratio. In other words, for each stock i, we performed the following time-series regression: ( ) Ri ,t R f ,t = ai + bi RM ,t R f ,t + si SMBt + hi HMLt + i ,t , (1) where RM,t - Rf,t, SMB, and HML represent the Fama-French market, size, and value factors, respectively. Following Ang et al. (2006), we required a minimum of 17 observations for model estimation. With this requirement, we omitted the most illiquid stocks from our results, thus minimizing the likelihood that our results are biased toward stocks that trade infrequently. We measured IVOL36 and IVOL60 similarly as the standard deviation of the residuals from regressions of monthly excess returns on the Fama- French three-factor model, using 36 months (or at least 12, depending on availability) or 60 (at least 54\twww.cfapubs.org\b 24). We further measured low risk as the estimated beta (bi) from the CAPM market model: ( ) Ri ,t R f ,t = ai + bi RM ,t R f ,t + i ,t , (2) where the dependent variable is the monthly excess return of an equal- or value-weighted portfolio. Beta is computed monthly by regressing excess returns on the CRSP value-weighted index over the prior 60 months (a minimum of 24 months). Measures of Volatility and Liquidity As a tool to better gauge the data in our analysis, Table 1 provides a summary of distribution and correlation statistics for the key variables. To examine trading strategies based on low volatility, we began by forming quintile portfolios on the basis of the level of IVOL, which allowed us to explore the average return variation among the various IVOL quintile portfolios, including a zero-cost IVOL portfolio (lowest-IVOL quintile minus highest-IVOL quintile). We tested the performance of these portfolios over periods subsequent to their formation. To accomplish this task, we applied a commonly used rank portfolio test while controlling for the well-known Fama-French (1993) effects of size and style. In particular, our portfolio formation strategy was based on an estimation period of N months (for our purposes, we focused on N = 1, 36, and 60), and we held these value-weighted portfolios over M months. At month t, we computed risk from regressions (Equation 1 and Equation 2) on data over the previous N months. We then constructed value-weighted and equal-weighted portfolios on the basis of these risk measures and held these portfolios for up to 12 months. Because we found that the zero-cost IVOL portfolio is meaningfully profitable only in the first month (discussed later), we concentrated the bulk of our analysis on the onemonth holding period strategy (M = 1), whereby we simply sorted stocks into quintile portfolios on the basis of their level of IVOL, IVOL36, IVOL60, or BETA and held the portfolios for one month. The portfolios were rebalanced each month. We first report the average intercept (alpha) results from our Fama-French (1993) three-factor quintile regression portfolios, as sorted on IVOL (N = 1), IVOL36 (N = 36), and IVOL60 (N = 60) and adjusted for the effects of size and style. The dependent variables are the IVOL-based portfolio returns in excess of the risk-free rate.3 Using several empirical measures of liquidity, we explored the efficacy of the IVOL trading strategy (see Stoll 2000). For our first measure, we used the average stock price per share in the month prior to portfolio formation. It is well known that stocks with a market value of less than $5 a 2014 CFA Institute 1.00 14.38 14.52 17.65 10.58 6.36 0.10 -0.01 -0.03 0.19 -0.02 NonZEROR Amihud DVOL IVOL60 Price 0.46 IVOL36 BETA 0.48 IVOL Daily Correlation Variable Mean Std. dev. Quartile 3 Median Quartile 1 IVOL Daily (%) 0.06 -0.04 -0.11 -0.02 0.28 0.94 1.00 12.97 8.84 15.99 10.76 7.34 IVOL36 (%) 0.06 -0.04 -0.12 -0.02 0.31 1.00 12.92 8.28 15.98 10.87 7.48 IVOL60 (%) Table 1. \u0007 Summary Statistics, July 1963-December 2010 -0.01 0.02 0.10 -0.09 1.00 1.17 0.80 1.57 1.10 0.68 BETA 0.00 0.01 0.02 1.00 23.86 658.47 24.73 13.02 5.35 Average Price ($) -0.04 0.05 1.00 80.56 20.00 95.24 85.71 71.43 Average NonZEROR (%) 1.00 0.00 6.54 131.71 1.22 0.14 0.01 Average Amihud 1.00 179.97 2,875.00 26.14 3.52 0.55 Average DVOL ($ millions) The Limits to Arbitrage and the Low-Volatility Anomaly January/February 2014\twww.cfapubs.org 55 Financial Analysts Journal shareso-called penny stockspossess meaningfully less liquidity for trading purposes and are subject to market manipulation versus nonpenny stocks (see, e.g., Bradley, Cooney, Dolvin, and Jordan 2006). For our second liquidity measure, we proxied transaction costs (e.g., bid-ask spread and commissions) as the proportion of trading days with nonzero returns (see Lesmond, Ogden, and Trzcinka 1999).4 We measured the incidence of nonzero returns as the percentage of days in the prior month that a stock has a nonzero return (NonZEROR). The idea behind NonZEROR is that a security with high transaction costsand thus low liquiditywill have less price movement and more zero-return days than a security with low transaction costs and high liquidity. The underlying premise is that the marginal trader will trade only when the marginal benefit of the information signal exceeds the costs of trading; otherwise, the security will have a zero return. In short, NonZEROR takes on smaller values for lower levels of liquidity. For our third liquidity measure, we used dollar volume (DVOL), defined as the product of the daily closing share price and share volume, to proxy for the ease with which arbitrageurs can accumulate and liquidate trading positions. Higher values of DVOL suggest greater amounts of available liquidity, meaning that arbitrageurs can more easily transact. Finally, we applied the Amihud (2002) illiquidity measure, which is calculated for each stock i in every month as follows: 1 1, 000, 000 Return t Amihudit = , (3) t t Pricet Volumet where t is a positive-volume trading day in the month the measure is calculated. Note that a higher value for the Amihud illiquidity measure signifies higher illiquidity because a particular dollar volume traded is associated with a relatively strong price movement. We calculated all our measures of expected transaction costs during the same month in which we measured IVOL or BETA. Table 1 presents summary statistics for our measures of volatility (IVOL, IVOL36, IVOL60, and BETA) and our measures of liquidity (average price, DVOL, Amihud, and NonZEROR). The daily IVOL is multiplied by the square root of the number of trading days in a month to make it comparable to the other (monthly) volatility measures. As Table 1 shows, in comparing each measure of volatility, we can see large changes in the level of volatility, with Quartile 3's volatility approximately double that of Quartile 1. Likewise, in comparing each liquidity metric for Quartiles 1 and 3, we see 56\twww.cfapubs.org\b meaningful changes in each liquidity level. In the bottom portion of Table 1, we can see that the average correlations between our four liquidity metrics are quite low, with near-zero correlations between our various measures of volatility and all our liquidity metrics. Estimating Low-Risk Anomalous Returns Table 2 reports the average alpha of each quintile portfolio, indicating the return-predictive power of IVOL for various months following portfolio formation. Column 1 shows the value-weighted alpha for month t + 1 over the full sample period, 1963-2010. We can see that the stocks in the highestranked IVOL quintile portfolio underperform all other month t + 1 quintile portfolios. Interestingly, this average alpha is relatively unchanged for the three lowest-ranked risk quintiles and declines for the two highest-ranked risk quintiles. The underperformance of that highest-ranked IVOL portfolio is meaningful compared with the three lowest-ranked IVOL quintiles, each posting nearzero average excess returnsall statistically insignificant from zero. Although the average alpha of Quintile 4, at -0.30%, is lower than that of the three lowest-IVOL quintiles, it is still higher than that of the highest-IVOL quintile. These results are consistent with the IVOL anomalythe notion that portfolios formed with low-IVOL stocks outperform their high-IVOL counterparts in the following month. We then focused our attention on the more interesting zero-cost quintile spread portfolio, which seeks to arbitrage the difference between the lowestranked and highest-ranked quintiles. As shown in Table 2 (last row of column 1), the factor-adjusted, zero-cost portfolio has a statistically significant average alpha of 1.19% for 1963-2010, suggesting that current-month IVOL has a significant negative relationship with the one-month post-formation (t + 1) return. These results again demonstrate that currentmonth low-IVOL stocks outperform high-IVOL stocks in the following month, a finding consistent with Ang et al. (2006, 2009). Interestingly, however, as shown in columns 2-4 of Table 2, the observed outperformance monotonically declines during succeeding months after portfolio formation. That is, in extending our tests to include holding periods beyond the first two months following portfolio formation, we found that current-month IVOL has no meaningful relationship with stock returns in periods beyond the second month.5 Empirically then, the excess returns of the IVOL anomaly all occur in the first month or two following portfolio formation. 2014 CFA Institute The Limits to Arbitrage and the Low-Volatility Anomaly Table 2. \u0007 Abnormal Returns for IVOL-Based Portfolios: Monthly Regressions of IVOL Quintile Portfolio Returns, July 1963-December 2010 Month t + 1 (1) 0.08* Month t + 2 (2) 0.46*** Month t + 3 (3) 0.52*** Month t + 12 (4) 0.37** 2 (1.87) 0.07 (2.60) 0.50** (3.04) 0.62*** (2.10) 0.44** 3 (1.13) 0.09 (2.30) 0.54** (2.82) 0.64** (2.09) 0.55** 4 (1.09) -0.30** (1.98) 0.32 (2.46) 0.63** (2.11) 0.60* 5 (-2.35) -1.11*** (0.94) -0.31 (1.96) 0.13 (1.92) 0.30 1-5 (-5.90) 1.19*** (-0.80) 0.77** (0.35) 0.39 (0.83) 0.06 (6.04) (2.54) (1.22) (0.21) Rank 1 Notes: Quintile 1 (5) corresponds to the quintile companies with the lowest (highest) IVOL characteristic; 1 - 5 is the difference portfolio between the lowest- and highest-ranked quintile portfolios, or the quintile spread portfolio. Returns are expressed in percentages. Heteroskedasticityconsistent t-statistics (White 1980) are in parentheses. *Significant at the 10% level. **Significant at the 5% level. ***Significant at the 1% level. In short, we found that the IVOL effect is short lived, effectively requiring traders to adjust portfolio holdings at least every other month to have a reasonable chance at producing alpha. Such frequent rebalancing naturally raises questions about the impact of transaction costs and liquidity constraints. Our results have thus far ignored the impact of these crucially important components on the success of any trading strategy. We then analyzed this issue in some detail. Our results, presented next, led us to conclude that transaction costs and liquidity constraints create significant barriers to traders' ability to effectively implement an IVOL-based trading strategy. In particular, we found that the various IVOL-based trading strategies we explored are profitable only for those subsamples in which transaction costs and liquidity constraints are significantly greater. We report our zero-cost portfolio results for each quintile portfolio, indicating the returnpredictive power of our three definitions of risk for various months following portfolio formation. Table 3 shows the alpha results for various holding period months, t + M, where M = 1, 2, 3, or 12, as well as for our three definitions of risk and for both value-weighted and equal-weighted portfolios. Results are for the full sample period, 1963-2010. Table 4 reports zero-cost portfolio results for various sample periods, different definitions of risk, and both value-weighted and equal-weighted portfolios. As shown in Tables 3 and 4, we draw conclusions similar to those discussed earlier concerning these various dimensions. Specifically, several noticeable trends emerge from an exploration of the data. First, results for average alpha are somewhat weaker with equal-weighted portfolios, a finding consistent across all periods and risk definitions. Second, Table 3 reports results for holding periods of up to 12 months, showing that the observed zero-cost alpha monotonically declines rapidly in months following portfolio formation for all measures of risk: Current-month risk has no meaningful relationship with stock returns in periods beyond the second month. On the basis of this finding and our other findings discussed herein, we chose to focus on understanding transaction costs for only the t + 1 period in conducting additional analyses in our study. Third, our alternative definitions of volatility (IVOL36 and BETA) generally present somewhat reduced average alphas versus IVOL for both value-weighted and equal-weighted portfolios.6 Fourth, the low-risk effect has been noticeably weaker since 1990, and the global financial crisis in 2008 had little impact on our long-term findingsthat is, the average alpha results for 1991-2007 and 1991-2010 are quite similar, except for value-weighted returns based on IVOL. Our finding of weaker results after 1990 could be a result of improved market efficiency, reflecting January/February 2014\twww.cfapubs.org 57 Financial Analysts Journal Table 3. \u0007 Abnormal Returns for Low-Risk-Based Portfolios: Monthly Regressions of Zero-Cost Quintile Portfolio Returns for Month t + M, July 1963-December 2010 (t-statistics in parentheses) Month t + M Zero Cost Equal Weighted Value Weighted Zero Cost (P