The case for index fund investing for Swiss investors

The case for index fund investing for Swiss investors Vanguard research September 13 Executive summary. Index fund investing (indexing) refers to an investment methodology that attempts to track a specific market index (either broad or narrow) as closely as possible. This paper explores both the theory behind indexing as an investment strategy and provides evidence to support its use in investor portfolios. 1 The theory behind indexing as an investment strategy focuses on the zero-sum game: before costs, for every investment that outperforms the index of a chosen market, there has to be another one that underperforms. But once costs are taken into account, it means that low-cost index funds will have a greater probability of outperforming higher cost actively managed funds. Authors Peter Westaway, Vanguard Asset Management Charles J Thomas, Vanguard Asset Management Biola Babawale, Vanguard Asset Management Christopher Philips, The Vanguard Group, Inc. Todd Schlanger, The Vanguard Group, Inc. Important information This document is directed at investment professionals only and should not be distributed to, or relied upon, by retail investors. The value of investments, and the income from them, may rise or fall and investors may get back less than they invested. 1 Throughout this paper, when we refer to indexing, we assume a strategy that is weighted according to market capitalisation. For an evaluation of indices and the strategies that seek to track those indices, refer to Philips et al. (11) and Thomas & Bennyhoff (1). Connect with Vanguard > vanguard.ch

This theoretical result applies across all investors. But some professional active managers might claim that they are still able to perform better than other investors in the total market (for example individual retail investors). To investigate, we examine the performance of a range of funds available to Swiss investors. First, to establish a baseline, we compare the records of actively managed funds to various unmanaged benchmarks. We demonstrate that, after costs, (1) the average actively managed fund underperformed a reasonable benchmark while exhibiting greater volatility over long time periods, () reported performance statistics can deteriorate markedly once accounting for survivorship bias, and (3) that persistence of performance among past winners is no more predictable than a flip of a coin. We then explicitly compare the performance of actively managed funds with passive funds. We show how low-cost index funds result in a greater probability of outperforming higher-cost actively managed funds. As part of this discussion, we focus on some key characteristics of a well-managed index fund, noting that not all indexed strategies are created equal. We conclude that indexing can be a viable strategy for Swiss investors across a range of asset classes and regional markets.

The importance of the zero-sum game to the case for indexing The zero-sum game is a theoretical concept that forms the foundation for why indexing can serve as an attractive investment strategy. The concept of a zero-sum game starts with the understanding that at any given point in time, the holdings of all investors in a particular market aggregate to form that market (Sharpe, 1991). Because all investors holdings are represented, if one investor s positions outperform the aggregate market over a particular time period, another investor s positions must underperform, such that the valueweighted performance of all investors sums to equal the performance of the market. Of course, this holds for any market, such as foreign stock and bond markets, or even specialised markets such as commodities or real estate. The aggregation of all investors returns can be thought of as a bell curve (see Figure 1), with the benchmark return as the mean. In Figure 1, the specific market is represented by the green curve, with the market return as the black vertical line. In reality, investors are exposed to costs such as commissions, management fees, bid-ask spreads, administrative costs and, where applicable, taxes all of which combine to reduce investors realised returns over time. If these costs were to affect all investment funds equally, then the result of these costs would be to shift the investors curve to the left but to leave the shape of the bell curve unchanged. We represent this adjustment for costs with a red curve. Although a portion of the after-cost value-weighted performance continues to lie to the right of the market return, represented by the green shaded region, a much larger portion is now to the left of the market line, meaning that after costs, more than half of the value-weighted performance of investors falls short of the aggregate market return. So the smaller these additional costs are, the less this aggregate underperformance will be. This simple theoretical result is powerful because it is just as relevant in all markets, even those often thought to be less efficient, such as small-cap or emerging market equities (Waring and Siegel, 5). One potential counter argument to this powerful result is that active mutual fund managers do not represent the totality of active investors in a given market; other investors include, but are not limited to hedge funds, pension funds, separately managed account managers and holders of individual securities. So, if active fund managers were able to outperform systematically their benchmark before costs, then this might Figure 1. The impact of costs on the zero-sum game Cost of funds Figure 1. Median post-cost return of funds Probability Benchmark return Funds underperforming benchmark Funds outperforming benchmark -5-4 -3 - -1 1 3 4 5 Expected return relative to benchmark (pp) Source: The Vanguard Group, Inc. Value weighting gives proportional weight to each holding, based on its market capitalisation. Compared to equal weighting, which helps ensure against any one fund dominating the results but also implicitly makes relatively large bets on smaller constituents, value weighting more accurately reflects the aggregate equity and bond markets. 3

suffice to compensate for, or even outstrip, the harmful effects of higher costs on performance. Appendix A provides a stylised analysis of the return distributions of passively and actively managed funds which suggests that such an outcome is unlikely. But to understand what has happened in practice, empirical evidence is required for the performance of active and passive funds. The rest of the paper examines the facts and finds convincing evidence that the average active fund manager is unable to compensate for higher costs and as a consequence will still have a higher probability of underperforming relative to passively managed funds. The performance record of actively managed mutual funds Typically, the objective of an actively managed portfolio is to outperform a given benchmark. Depending on the active strategy, the target benchmark could be a traditional broad market index such as the SIX Stock Market Index or the Barclays Swiss Franc Aggregate Index or an index with a narrower objective such as the Swiss Small-cap Index. The objective could also be to generate an excess return relative to a short-term government debt instrument or to EURIBOR (i.e. an absolute return strategy). Some managers even seek to deliver outperformance while exhibiting less volatility than their targeted benchmark (so called minimum-volatility strategies). Of course every manager will go through periods where their investing style is out of favour, but over a reasonably long period of time, covering multiple market cycles and environments, a skilled active manager should be aiming to deliver positive excess returns versus their benchmark for the full time period. In fact, we will see that while the theory is appealing, the actual track record of actively managed funds is underwhelming, suggesting that an active manager with such skill is difficult to find. Data To examine how successful active managers have been in achieving these aims, we begin by examining the performance of a range of funds available to Swiss investors, focusing on a few broad investment categories; European, euro zone, Asia ex Japan, Japan, US, global, emerging markets and Swiss equity and euro diversified, dollar diversified, global and Swiss bonds. For all of our comparisons we use the open-end fund universe provided by Morningstar. Fund classifications are provided by Morningstar, as are the expense ratio, assets under management, inception date and termination date (if relevant). Fund returns are reported net of cost, however front or back end loads and taxes are unaccounted for. We exclude sector funds and specialist funds from our analysis. For our evaluation of index funds, we exclude ETFs because of the lack of adequately long back-runs of data. However, we would expect the conclusions of our results using index funds to extend to ETFs because ETFs operate with a similar objective to index funds. For funds that offer income and accumulation accounts, we use the returns for the accumulation account only except in those cases where only an income fund is listed. Similarly, for funds that include variants denominated in different currencies, we use the returns for the Swiss francdenominated fund except in those cases where only foreign currency funds are available (although the return is still reported in Swiss Franc). 3 Otherwise, we use all share classes of funds in order to capture the broadest perspective of investor performance. This approach is taken to capture the influence of differential costs on returns on otherwise identical funds. Even so, it runs the risk of over-weighting particular investment strategies. So, as a robustness check, we also present our results in Appendix B where we provide an alternative version of the analysis where we weight the returns on the fund by asset holdings, thereby only recording a return for each fund name once. Given the lesser availability of fund holdings, we have fewer results on this basis but we find the main conclusions from those results are largely unaltered. Primary findings Figure shows the relative performance of these different categories of actively managed mutual funds when evaluated over 5, 1 and 15 years versus a benchmark that is specified in the funds own prospectus. The rationale for this evaluation is straightforward; comparing all funds versus a broad market benchmark results in a mismatch of market risk factors. A small-cap manager may outperform the broad market simply because small-cap stocks in general outperformed the broad market and not because of a specific skill or management technique. In our view, comparing a small-cap manager against a small-cap benchmark addresses this mismatch and thus permits a more reasonable evaluation of outperformance. 4 3 The total returns on otherwise identical income and accumulation funds might be expected to be identical but differ slightly because of the way Morningstar choose to incorporate tax effects on dividend income. Swiss Franc returns on funds that are identical apart from their currency denomination differ because non-swiss Franc returns are usually hedged thus causing a difference with ex-post returns.

Each cell in Figure shows three things: 1 The percentage of funds in each category that survived the time period but underperformed their benchmark. Taking Swiss equities over 15 years as an example, this figure is 74%. The percentage of all funds that started the given period but either underperformed or dropped out of the sample (8% in the case of Swiss equities over 15 years). 3 The annualised excess return for the median surviving fund (-.67% for Swiss equities over 15 years). The dominant finding in Figure is that active fund managers as a group have underperformed their benchmarks across most of the fund categories and time periods considered. To take one notable example, 71% of global equity funds have underperformed their benchmarks over the ten-year period. The case for indexing is strong over shorter horizons, too, although shorter sample periods tend to produce slightly more erratic results 4. The case for indexing over even longer horizons such as fifteen years tends to be strong too although, at this horizon, relatively few funds have been in existence for the entire period so the results are less reliable due to the smaller sample size. For example, only 6 emerging market equity funds survived the full 15 years, 1 for 1 years and 5 for 5 years. We show annualised excess returns because to evaluate managers using solely the percentage of managers underperforming assumes that a manager who underperforms by.1% has achieved a result as significant as one who underperforms by 1%. Picking the example again of global equities at the ten-year horizon, the median return is 1.14% below the benchmark return. This median excess return is negative for 1 out of 1 of the broad asset categories considered at the ten-year horizon and for 9 out of 1 at the 15-year horizon. We attempt to account for survivorship bias in Figure by identifying those funds that were alive at the start of each year period but dropped out of the database at some point along the way, usually Figure. The Performance percentage of Swiss of underperforming active funds actively managed funds (using prospectus benchmark) funds 15-years 1-years 5-years Bond funds 15-years 1-years 5-years European Eurozone Asia Ex Japan Japan US Global Emerging Markets Switzerland 5% / 77% 63% / 8% 5% / 73% 6% / 7% 65% / 8% 69% / 86% 5% / 65% 74% / 8% -.8% -.76%.7% -.65% -.96% -.61%.49% -.67% 57% / 73% 47% / 69% 71% / 77% 73% / 83% 86% / 93% 71% / 85% 87% / 9% 61% / 71% -.35%.16% -1.9% -1.36% -1.74% -1.14% -1.76% -.55% 51% / 71% 3% / 59% 74% / 81% 67% / 8% 83% / 9% 71% / 8% 84% / 88% 64% / 71% -.9% 1.3% -.1% -1.5% -.% -1.89% -.31% -.84% EUR Diversified Bond USD Diversified Bond Global Bond CHF Bond 89% / 97% 95% / 98% 8% / 85% % / 9% -.91% -.79% -.67.8% 91% / 95% 8% / 9% 61%/ 67% % / 88% -.7% -.5% -.%.57% 71% / 86% 76% / 87% 49% / 57% 74% / 8% -.51% -.6%.1% -.36% Notes: Fund universe includes all share classes of funds available for sale in Switzerland, from the following Morningstar categories: Swiss equity largecap, small/mid-cap; Europe equity Europe OE: flex-cap,large-cap blend, large-cap growth, large-cap value, mid-cap, small-cap; Euro zone equity flex-cap, large-cap, mid-cap, small-cap; Asia ex Japan equity Asia ex Japan, Asia-Pacific ex Japan; Japan equity large-cap, small/mid-cap; Global flex-cap, large-cap blend, large-cap growth, large-cap value, small-cap; US equity flex-cap, large-cap blend, large-cap growth, large-cap value, mid-cap, small-cap; Emerging markets equity global emerging markets; Europe bond EUR diversified; US bond USD diversified; Global bond global un-hedged bond, global CHF-hedged bond; Swiss bonds CHF diversified. Performance is for periods ending on 31 December 1. Performance is calculated relative to prospectus benchmark. Fund performance is shown in Swiss franc terms, net of fees, gross of tax withholding, with income reinvested, based on closing NAV prices. Source: Vanguard, based on data from Morningstar. 4 For example, only 47% of euro zone funds underperform at the ten-year horizon although this is a relatively small sample of funds, and as explained below, the underperformance is influenced by survivorship bias. 5

on the grounds of closure due to underperformance. See Box A for more discussion around the performance of those funds that no longer report returns to the database. If underperforming funds drop out of the database, this will tend to exaggerate the degree to which active managers can outperform their chosen index. And this is exactly what the empirical results tend to suggest. This adjusted percentage is shown in the table after the unadjusted number followed by the upward slash. 5 For example, in the case of global equities at the ten-year horizon, the adjustment for survivorship Box A: The impact of survivorship bias on performance results While the objective of active managers is outperformance, we have demonstrated that a majority may not deliver on that objective. However an additional risk facing investors is that while there may be periods where a majority of actively managed funds outperform, an investor must still select, in advance, one of those outperforming funds and hold it for the entire period. It s only in hindsight that one can determine if they were correct or not. And this challenge often overlooks the possibility that the fund selected by the investor underperforms to the extent that it is closed down. To test the assumption that closed funds underperformed we evaluated the performance of all the funds identified by Morningstar as either being liquidated or merged into another fund. For this analysis we again looked at returns starting in January 1998. We measured the closed funds excess returns versus a broad market benchmark from January 1998 or the fund s inception (whichever was the later) up until the month-end prior to the fund s date of closure. The results are presented in Figure A-1. Clearly, a possible cause leading to the closure of these funds was relative underperformance. 6 As a result, investors selecting active management not only have to be concerned with underperformance and potentially higher volatility, but underperformance that may lead to a fund closing down, and the possibility that a new manager search may result in the selection of another poor performing fund. Figure A-1 Excess Return of Dead Funds Over Broad Market Benchmark. From Jan. 1998 to Fund Closure Annualised Excess Return Prior to Liquidation/Merger 1-1 - -3-4 -5-6 -7 European Eurozone Asia Ex Japan Japan US Global Emerging Markets Switzerland EUR Diversified Bond USD Diversified Bond Global Bond CHF Bond Middle 5% of Funds Median Displays the cumulative annualised performance of those equity and bond funds that were merged or liquidated within our sample, relative to a broad market benchmark as defined in Figure 3. We measure performance from 1 January 1998 or the fund s inception, whichever is later, and continue each fund s measurement period up until the month-end prior to it being merged or liquidated. Fund universe is as described in Figure, limited to those funds that were merged or liquidated from Jan.1998 to Dec.1. Figure displays the middle 5% distribution of these fund s returns prior to dying. Performance is measured in Swiss franc terms, net of fees, gross of tax withholding, with income reinvested. Source: Vanguard, based on data from Morningstar and MSCI. 6 5 The actual number of funds that were closed due to poor performance is likely fewer than the percentages cited in Figure. This is because some poorly performing funds are merged into other better-performing funds. An investor in such a fund would then receive the performance of the new fund provided they held on to the investment. Unfortunately there is no easy way to identify which funds were the recipients of poorly performing funds. As a result the actual survivorship adjusted percentage is most likely found between the two percentages in Figure, but closer to the adjusted value than the unadjusted value given the performance results shown in Figure A-1. 6 These results corroborate previous studies on the impact of survivorship bias. Brown and Goetzmann (1995) showed that funds tend to disappear owing to poor performance. In addition, Carhart et al. () showed that the performance impact of dead funds increases as the sample period increases.

bias takes the proportion underperforming from 71% to 85%. Indeed, after accounting for this so called survivorship bias, the degree of underperformance is increased across all categories. 7 Implications for investors While we have demonstrated the challenges with respect to outperformance, performance in terms of a lower expected return may not be the only negative outcome. For example in Figure 3 we show the average return and volatility of a market proportional portfolio of the median actively managed funds from Figure. For comparison purposes we plotted the returns and volatilities of both the equity and fixed income markets for all the regions that we have examined. In each portfolio, the median actively managed funds registered higher volatility and lower returns than the market benchmark. In other words, not only was performance poor, but investors experienced more risk to achieve that poor performance. Figure 3. Return/volatility comparisons: Median fund versus benchmark. 16% 14 1 1 Annual return 8 6 4-5 1 15 5% Annual volatility of monthly returns European Eurozone Asia Ex Japan Japan US Global Emerging Markets Switzerland EUR Diversified Bond USD Diversified Bond Global Bond CHF Bond European Index Eurozone Index Asia Ex Japan Index Japan Index US Index Global Index Emerging Markets Index Switzerland Index EUR Diversified Bond Index USD Diversified Bond Index Global Bond Index CHF Diversified Bond Index Notes: Active funds are represented by a square and are defined as in figure. We take the median of all surviving funds returns and the median of all surviving funds standard deviation of monthly returns. Broad market benchmarks are defined as: Swiss equity- MSCI Switzerland IMI, European - MSCI Europe IMI, Eurozone - MSCI Eurozone IMI, Asia ex Japan - MSCI Asia ex Japan IMI, Japan - MSCI Japan IMI, US - MSCI USA IMI, Global - MSCI All Country World IMI, Emerging - MSCI Emerging Markets IMI, CHF Diversified Bonds- Barclays Swiss franc Aggregate Index, EUR Diversified Bonds- Barclays Euro Aggregate Index, USD Diversified Bonds- Barclays US Aggregate Index, Global Bonds- Barclays Global Aggregate Index. Performance covers the ten-year period ending 31 December 1 and is expressed in Swiss franc terms, net of fees, gross of withholding tax, with income reinvested based on closing NAV prices. Source: The Vanguard Group, Inc., based on data from Morningstar, FTSE, MSCI and Barclays. 7 Once survivorship bias is accounted for, the apparent outperformance result for euro zone equities at the ten-year horizon is reversed with almost three quarters of these funds underperforming. 7

Of course while the median fund and portfolio generally underperformed their indices, investors do have the opportunity to select a fund that ranks in the upper half of all managers. Indeed Figure does indicate that there were actively managed funds that survived and outperformed their benchmark. Including such outperformers in a portfolio is the primary objective of investors who use actively managed funds. And if one were to recreate Figure 3 using top quartile funds, the results would shift in favour of the actively managed portfolios. Two critical questions therefore are: Can I pick a winning portfolio in advance? and Will the winning portfolio continue to be a winning portfolio for the entire time period for which the investor holds that portfolio? In other words, would an investor be able to select a winner from the past and expect them to continue to win in the future? For years, academics have studied whether past performance has any predictive power regarding future performance. Dating back to Sharpe (1966) and Jensen (1968), researchers have found limited or no persistence. Carhart (1997) reported no evidence of persistence in fund outperformance after adjusting for the common Fama-French risk factors (the influence of the equity market, size and style) as well as for momentum. The Carhart study reinforced the importance of fund costs and highlighted how not accounting for survivorship bias can skew results of active/passive studies in favour of active managers. More recently, in 9, Fama-French s -year study suggested that it is extremely difficult for an actively managed investment fund to regularly outperform its benchmark. To examine the consistency within the actively managed fund sector we performed an analysis that ranked all equity funds in terms of risk adjusted return for the five years ended 7. We then divided the funds into quintiles, separating out the top % of funds, the next best performing % of funds and so on. We then tracked their risk adjusted returns over the next five years (through December 1) to see how consistently they performed. If the funds in the top quintile displayed consistently superior risk adjusted returns, we would expect a significant majority to remain in the top %. A random outcome would result in approximately 17% dispersed evenly across the 6 subsequent buckets (if we assume that the possibility of a fund closing down is just as probable as any other outcome). Figure 4 displays the results for the investments of Swiss investors in active equity funds available for sale in Switzerland. Interestingly the results do not appear to be significantly different from random. While around 11.7% of the top funds remained in the top % of all funds over the subsequent five-year period, an investor selecting a fund from the top % of all funds in 7 stood a 55.7% chance of falling into the bottom 4% of all funds or seeing their fund disappear along the way. Indeed, we find that the percentage of highest quintile active funds falling to the lowest quintile or closing (38.8%) exceeds the probability that they remain in the top quintile (11.7%). Stated another way, only 11.7% achieved top quintile excess returns over both the five-years ended 7 and the five years ended 1. It is also interesting to examine the subsequent performance of those funds that were in the bottom quintile in 7. Fully 38.5% were liquidated or closed by 1 and 1% remained in the bottom quintile, while only 5.5% managed to right the ship and rebound to either of the top two quintiles. Indeed, persistence has tended to be stronger for previous losers than previous winners whereas past performance has not been a strong indicator of future success. 8

Figure 4. Rank persistence of active equity funds available for sale in the Switzerland Initial Excess Return Quintile, 5-years through Dec.7 Number of funds Notes: The far left column ranks all active Swiss equity funds based on their excess return over their respective prospectus benchmark return during the five-year period through 31 December 7. The columns going across the right of the table rank these funds according to their subsequent excess returns over the five-year period through 31 December 1. Random performance across the six subsequent possibilities (5 quintiles, plus funds that die) would infer a value of 16.67%. The fund universe includes all active equity funds available for sale in Switzerland, investing in Swiss equity, as defined in Figure. Returns are in Swiss franc terms, calculated net of fees, gross of tax witholding, with income reinvested. Source: Vanguard, based on data from Morningstar Subsequent 5-year excess return rank, through Dec.1 Highest Quintile nd Quintile 3rd Quintile 4th Quintile Lowest Quintile Liquidated/ Merged 1st 91 11.7% 17.% 15.5% 16.8% 18.9% 19.9% nd 91 1.4% 14.1% 13.4% 1.% 16.% 34.% 3rd 9 1.3% 13.4% 17.1% 14.7% 13.4% 9.1% 4th 9 7.% 1.3% 15.5% 18.3% 1.4% 36.% 5th 91 15.5% 1.% 1.7% 11.3% 1.% 38.5% Figure 5 graphs the performance of the funds that were in the top quintile in the first five year period over the subsequent five years for Swiss, European, euro zone, Asia ex Japan, japan, US, global and emerging markets equity funds. As with the Swiss equity funds, past performance has not been a strong indicator of future success; there is no systematic tendency for funds that start in the top quintile to remain there. Indeed, only the Asia ex Japan equity funds managed to achieve this result with better frequency than chance would indicate. Figure 5. Rank persistence of fund performance across regional markets 6% 5 Percentage of funds 4 3 1 Remained in top quintile Fell to nd quintile Fell to 3rd quintile Fell to 4th quintile Fell to 5th quintile Liquidated/ merged European Eurozone Asia Ex Japan Japan US Global Emerging Markets Switzerland Notes: Fund sample includes those funds that were in the top quintile of performance in the five-year period ending 31 December 7, with performance defined as the excess return over each funds prospectus benchmark. The figure displays the rank of these funds subsequent excess returns over the five-year period through 31 December 1. Random performance across the six subsequent possibilities (5 quintiles, plus funds that die) would infer a value of 16.67%. The fund universe includes all active equity funds available for sale in Switzerland, from the Morningstar categories defined in Figure. Returns are in Swiss franc terms, calculated net of fees, gross of tax witholding, with income reinvested. Source: Vanguard, based on data from Morningstar 9

This high turnover with respect to outperformance and market leadership is one reason why changing managers due to poor performance can lead to further disappointment. For example, in a wellreported 8 study, authors Amit Goyal and Sunil Wahal found that the process of replacing underperforming managers with outperforming managers within US institutional pension plans resulted in performance results far different than expected. For example, the authors evaluated the performance of both the hired and fired managers before and after the decision date. They found that following termination, the fired managers actually outperformed the managers hired to replace them by 49 basis points in the first year, 88 basis points over the first two years, and 13 basis points over the first three years. The impact of market cycles on the performance of actively managed funds Over time and over alternative evaluation windows, the percentage of funds underperforming a particular index will vary. Much of this is due to the cyclical nature of the financial markets. To supplement our analysis in Figure, we show Figure 6, which breaks the time period into bull and bear market cycles. A common perception holds that actively managed funds will outperform their benchmark in a bear market because in theory active managers can move into cash or rotate into defensive securities to avoid the worst of a given bear market. In reality, the probability that these managers will move fund assets to defensive stocks or cash at just the right time is very low. Most events that result in major changes in market direction are unanticipated. To succeed, an active manager would have to not only time the market but also do so at a cost that was less than the benefit provided. Figure 6 illustrates how the median active fund manager has performed relative to respective benchmarks across all regions across market cycles. The results clearly show that, although there are short periods in some regions where active managers have been able to outperform, in general there is no systematic tendency for them to do better at particular stages of the cycle. In order to win over time a manager must accurately time the start and end of the bear market and must accurately select winning stocks during each period. Combining these results with those from Figure, shows the challenges for long-term investors when electing to use active management. Figure 6. Percentage of active managers underperforming market during bull and bear cycles 1% 9 8 7 6 5 4 3 1 Bull Market: Jan. 1998 Aug. Bear Market: Sept. Feb. 3 Bull Market: Mar. 3 Oct. 7 Bear Market: Nov. 7 Feb. 9 Bull Market: Mar. 9 Dec. 1 European Eurozone Asia Ex Japan Japan US Global Emerging Markets Switzerland 1 Notes: Displays the percentage of surviving funds that underperform their prospectus benchmark, over the time period shown. We define bull and bear markets as a local peak or trough in the global equity market, defined as the MSCI All Country World IMI. The fund universe and categories are as defined in Figure. Returns are calculated in Swiss franc terms, net of fees, gross of tax withholding, with income reinvested. Source: Vanguard, based on data from Morningstar.

Comparing the performance of passive and active funds The results presented so far showing the average underperformance of actively managed funds would seem to be consistent with the theory of the zero-sum game explained earlier. Before costs, for every invested cent that outperforms the market there has to be a cent that underperforms. But once costs are taken into account, more funds will inevitably undershoot their desired benchmark than overshoot. Moreover, the evidence shows that the population of actively managed funds that we have examined is not able to outperform the rest of the population of investors (retail investors etc.). The earlier theoretical discussion also suggested that passive funds ought to be able to outperform actively managed funds if (a) active funds are not able on average to outperform their chosen benchmarks after costs, and (b) passive funds have lower average costs. Having demonstrated (a), we now turn to consideration of (b). There is already considerable evidence that the odds of achieving a return that outperforms a majority of similar investors is increased if investors simply aim to seek the lowest possible cost for a given strategy. For example, using evidence from US mutual funds, Financial Research Corporation evaluated the predictive value of different fund metrics, including a fund s past performance, Morningstar rating, alpha, and beta. In the study, a fund s expense ratio was the most reliable predictor of its future performance, with low-cost funds delivering above-average performances in all of the periods examined. Similar research was conducted by Vanguard. Wallick et al (11) evaluated a fund s size, age, turnover and expense ratio, finding that the expense ratio was the only significant factor in determining future alpha. Additionally, Philips & Kinniry (1) showed that using a fund s Morningstar star rating as a guide to future performance was less reliable than a fund s expense ratio. Practically speaking, a fund s expense ratio is a valuable guide (although not a sure thing) because the expense ratio is one of the few characteristics that is known in advance. Figure 7 shows the average value-weighted expense ratios for both actively and passively managed equity funds. It shows clearly that index funds generally operate with lower costs than actively managed funds. Higher expenses for actively managed funds often result from both the research process and the generally higher turnover 8 associated with the attempt to outperform a benchmark. As at 31 December 1, investors in actively managed Swiss equity funds were paying an average of approximately 1.5% annually versus.9% for index funds. An even greater cost disadvantage applies for international equity funds versus their indexed equivalents with a cost difference of 1.14% for European funds, 1.% for euro zone funds,.99% for US funds, 1.18% for global funds and 1.11% for emerging market funds. The cost disadvantage for actively managed bond funds is somewhat lower but still generally significant. Figures 8 illustrates the importance of cost on a fund-by-fund basis, displaying scatter plots for each regional investment asset category of individual fund excess returns plotted against the total expense ratio of that fund. Our earlier stylised discussion, as captured in Figure 1 and Figure A-1 Figure 7. Value-weighted expense ratios of active and passive investments Category Index Active Difference European.9 1.4-1.14 Eurozone.4 1.4-1. Asia ex Japan.6 1.9-1.3 Japan.4 1.8 -.84 US.1 1. -.99 Global.13 1.3-1.18 Emerging Markets Notes: The average TER quoted for each category of funds represents the asset-weighted average Total Expense Ratio based on information in latest available annual report at 31 December 1. Fund TERs are weighted by the share-class AUM, reflecting the typical investor s experience in that fund. Taking a simple (un-weighted) average shifts up the TERs across all groups by about bps, but does not change the finding that index funds are cheaper across all categories. The fund universe is as described in figure. Source: Vanguard, based on data from Morningstar.39 1.5-1.11 Switzerland.9 1.5 -.76 EUR Diversified Bond n/a.86 n/a USD Diversified Bond.64 1. -.36 Global Bond.6.8 -.74 CHF Bond.4.35 -.31 8 Turnover, or the buying and selling of securities within a fund, results in transaction costs such as commissions, bid-ask spreads, market impact and opportunity cost. These costs, although incurred by every fund, are generally opaque, but do detract from net returns. A mutual fund with abnormally high turnover would thus likely incur large trading costs. All else equal, the impact of these costs would reduce total returns realised by the investors in the fund. 11

in Appendix A, suggested that there ought to be a negative correlation between the excess return on a fund and the expense ratio associated with that fund. Figure 8 indeed confirms that there is a systematic tendency for funds with higher costs to suffer from lower excess returns. Figure 8. Scatter plot by asset category of fund excess annualised returns versus total expense ratio 1 5-5 -1-15 - -5-3 -35 European.5 1 1.5.5 3 3.5 4 4.5 5 8 6 4 - -4-6 Eurozone.5 1 1.5.5 3 3.5 4 4.5 5 6 4 - -4-6 -8 Asia Ex Japan.5 1 1.5.5 3 3.5 4 4.5 5 8 6 4 - -4-6 -8-1 -1 Japan.5 1 1.5.5 3 3.5 4 4.5 5 3 1-1 - -3-4 -5-6 US.5 1 1.5.5 3 3.5 4 4.5 5 1 8 6 4 - -4-6 -8 Global.5 1 1.5.5 3 3.5 4 4.5 5 8 6 4 - -4-6 -8 Emerging Markets.5 1 1.5.5 3 3.5 4 4.5 5 6 4 - -4-6 -8 Switzerland.5 1 1.5.5 3 3.5 4 4.5 5 Bonds 1.5 1.5 -.5-1 -1.5 - -.5-3 -3.5 EUR Diversified Bonds.5 1 1.5.5 3 3.5 4 4.5 5 4 3 1-1 - -3-4 USD Diversified Bonds %()#.5 1 1.5.5 3 3.5 4 4.5 5 5 4 3 1-1 - -3 Global Bonds.5 1 1.5.5 3 3.5 4 4.5 5 5 4 3 1-1 - -3-4 -5 CHF Bonds.5 1 1.5.5 3 3.5 4 4.5 5 1 Except for the Swiss funds, returns on the vertical axis are the 1-year annualised excess return over each fund s prospectus benchmark, through 31 December 1. Due to data constraints, for Swiss funds, returns on the vertical axis are the 5-year annualised excess return over each fund s prospectus benchmark, through 31 December 1. Total Expense Ratio on the horizontal axis is from the latest available annual report as at 31 December 1. Fund universe and categories are as defined in Figure. Performance is shown in Swiss franc terms, net of fees, gross of tax withholding, with income reinvested. Sources: Vanguard calculations, using data from Morningstar, Inc. Data as of 31/1/1.

Figures 9(a)-(d) display the distribution of excess returns on equity and fixed income funds relative to their prospectus benchmark index, both to the actively managed funds already examined as well as the passively managed fund universe; Figure 9(a) shows results for Swiss equities, 9(b) for European equities, 9(c) for emerging market equities and 9(d) for Swiss government bonds; other categories previously shown in Figure are not shown due to a lack of passive funds available for comparison. Also, due to the more recent introduction of passive funds into Swiss markets, such funds are not available for such a long history, so fund return distributions are only shown for the five year history. A number of striking results emerge from Figures 9(a)-(d). First, as suggested by the earlier results in Figure, the net returns of the actively managed fund universe are located to the left of the returns of their respective benchmark. Second, the wide distribution of fund returns for actively managed funds is noteworthy; so for example, in Swiss equity funds as shown in Figure 9(a), 31% of the surviving active funds delivered returns more than % below their benchmark while no index funds underperformed by that margin; on the other hand, around 1% of active funds also outperformed their benchmark by more than % (something none of the passive funds achieved). Figure 9a. The distribution of mutual fund performance: Swiss equity funds v their prospectus benchmark Distribution of annualised excess returns among Swiss Funds five-years ended 31 December 1 45 Prospectus benchmark 4 35 Number of funds 3 5 15 1 5 Merged/Liquidated Less than -8% Between -8% and -7% Between -7% and -6% Between -6% and -5% Between -5% and -4% Between -4% and -3% Between -3% and -% Between -% and -1% Between -1% and % Between % and 1% Between 1% and % Between % and 3% Between 3% and 4% Between 4% and 5% Between 5% and 6% Between 6% and 7% Between 7% and 8% More than 8% Excess return Swiss equity active funds Swiss equity index funds Notes: Displays the distribution of fund excess returns, relative to their prospectus benchmark, for the five-year period ending 31 December 1. Fund universe is as defined in Figure. Performance is shown in Swiss franc terms, net of fees, gross of tax withholding, with income reinvested. Source: Vanguard, based on data from Morningstar. 13

For European funds, in Figure 9(b), the results are even more striking with 71% of surviving active funds deviating from their benchmark by 1%, while only 6% of passive funds in this category deviated by the same margin. Similarly, for emerging market equity funds, Figure 9(c), 57% of surviving active funds underperformed their benchmark while around 1% outperformed by that amount, with one passive fund deviating by more than 1%. Finally, for diversified CHF bond funds, Figure 9(d), % underperformed by 1% or more, while 7% outperformed by that margin, and no passive funds underperformed by more than 1%. Figure 9b. The distribution of mutual fund performance: European equity funds versus their prospectus benchmark Distribution of annualised excess returns among European equity funds five-years ended 31 December 1 4 375 Prospectus benchmark 35 Number of funds 1 75 5 5 Merged/Liquidated Less than -8% Between -8% and -7% Between -7% and -6% Between -6% and -5% Between -5% and -4% Between -4% and -3% Between -3% and -% Between -% and -1% Between -1% and % Between % and 1% Between 1% and % Between % and 3% Between 3% and 4% Between 4% and 5% Between 5% and 6% Between 6% and 7% Between 7% and 8% More than 8% Excess return European equity active funds European equity index funds Notes: Displays the distribution of fund excess returns, relative to their prospectus benchmark, for the five-year period ending 31 December 1. Fund universe is as defined in Figure. Performance is shown in Swiss franc terms, net of fees, gross of tax withholding, with income reinvested. Source: Vanguard, based on data from Morningstar. 14

Several factors contribute to this wide performance distribution in addition to differences in cost and any skill the managers exhibit: the type of funds included, the benchmark used, and the time period analysed can all affect the return distribution and the conclusions drawn. For example, if managers exhibit a style or size bias over a given five-year period, the relative performance of active managers in aggregate can change substantially, depending on the relative performance of one or more market segments, such as small-cap stocks. Similarly, to the extent that different benchmarks cover different groups of securities (even in the same region), the relative performance results can vary. Figure 9c. The distribution of mutual fund performance: Emerging market equity funds versus their prospectus benchmark Distribution of annualised excess returns among emerging market equity funds five-years ended 31 December 1 Number of funds 7 65 6 55 5 3 5 15 1 5 Prospectus benchmark Merged/Liquidated Less than -8% Between -8% and -7% Between -7% and -6% Between -6% and -5% Between -5% and -4% Between -4% and -3% Between -3% and -% Between -% and -1% Between -1% and % Between % and 1% Between 1% and % Between % and 3% Between 3% and 4% Between 4% and 5% Between 5% and 6% Between 6% and 7% Between 7% and 8% More than 8% Excess return Global emerging markets active fund Global emerging markets index funds Notes: Displays the distribution of fund excess returns, relative to their prospectus benchmark, for the five-year period ending 31 December 1. Fund universe is as defined in Figure. Performance is shown in Swiss franc terms, net of fees, gross of tax withholding, with income reinvested. Source: Vanguard, based on data from Morningstar. 15

Figure 9d. The distribution of mutual fund performance: Swiss bond funds versus their prospectus benchmark Distribution of annualised excess returns among Swiss bond funds five-years ended 31 December 1 6 Prospectus benchmark 5 Number of funds 4 3 1 Merged/Liquidated Less than -8% Between -8% and -7% Between -7% and -6% Between -6% and -5% Between -5% and -4% Between -4% and -3% Between -3% and -% Between -% and -1% Between -1% and % Between % and 1% Between 1% and % Between % and 3% Between 3% and 4% Between 4% and 5% Between 5% and 6% Between 6% and 7% Between 7% and 8% More than 8% Excess return Swiss bond active funds Swiss bond index funds Notes: Displays the distribution of fund excess returns, relative to their prospectus benchmark, for the five-year period ending 31 December 1. Fund universe is as defined in Figure. Performance is shown in Swiss franc terms, net of fees, gross of tax withholding, with income reinvested. Source: Vanguard, based on data from Morningstar. By contrast, the dispersion of the passive funds is unsurprisingly much more narrow, since by construction, the managers of these funds are attempting to generate returns as close as possible to the chosen benchmark. Even so, it is too simplistic to assume that all index funds are created equal. Box B explains in more detail how the implementation of an index strategy is not as straightforward as sometimes believed and that the deviation of the return of an index fund from its benchmark should be interpreted as a reflection of inefficient fund management. It also explains the additional benefits to holding an index fund beyond simply hitting the benchmark at low cost in the form of diversification and style consistency. 16

Box B: The benefits of indexation strategies While on the surface the theory and application of indexing seems straightforward, it s not as simple as picking just any index fund. An indexed investment strategy via a mutual fund or an exchange-traded fund (ETF), for example seeks to track the returns of a particular market or market segment by assembling a portfolio that invests in the same group of securities, or a sampling of the securities, that compose the market. Indexing strategies use quantitative riskcontrol techniques that seek to replicate the benchmark s return with minimal expected deviations (and, by extension, with no expected alpha, or excess return versus the benchmark). However because the targeted benchmark incurs no expenses, inefficiencies or implementation costs, the return an investor receives in an index fund will reflect those implementation costs, (transaction costs, and other operational or trading frictions) and, therefore, should provide investors with the best proxy for the achievable or investable index return. It is thus incumbent upon an investor seeking to capture the performance of a specific benchmark to identify and then invest in an appropriate product that seeks to track that index, acknowledging that not all indexed investment strategies are created equal. Because the objective of an indexed strategy is to mimic a given benchmark as tightly as possible, any deviations from a benchmark s return over time can be an indication of inefficient management. 9 For index funds, one of the key drivers of potential deviations is the expense incurred along the way to manage the portfolio. Beyond expense ratio, some other factors that might contribute to the effectiveness of mimicking a targeted benchmark include the size of the portfolio, the number of securities in the benchmark, the liquidity of the targeted market (resulting in larger or smaller bid-ask spreads), the nature and size of the portfolio s cash-flow profile and the index strategy providers portfolio and risk management processes. The net result of the factors discussed is that an ideal index fund or ETF would have low expenses, economies of scale and an efficient and risk controlled portfolio management process. Together, these factors would permit an index fund or ETF to deliver returns very close to, if not identical to, the targeted benchmark consistently over time. Indexed investments can provide several benefits to investors. First and foremost, indexed strategies benchmarked to broad market indices can provide greater control of the risk exposures in a portfolio. For example, filling a recommended equity allocation with an actively managed fund can result in meaningfully different risk and return characteristics than the broad market. This could expose the investor to greater (or less) risk than they targeted by way of their asset allocation decision. Index funds typically are more diversified than actively managed funds, a by-product of the way indices are constructed. Except for index funds that track narrow market segments, most index funds must hold a broad range of securities to accurately track their target benchmarks, whether by replicating them outright or by a sampling method. The broad range of securities dampens the risk associated with specific securities and removes a component of return volatility. An index fund maintains its style consistency by attempting to closely track the characteristics of the index. An investor who desires exposure to a particular market and selects an index fund that tracks that market is assured of a consistent allocation. An active manager may have a broader mandate, causing the fund to be a moving target from a style point of view. 9 There are a wide range of possible causes for tracking error with some the result of government regulations. For example, in very narrow indices such as a specific stock market sector or an individual country, there may be position limits established by the relevant regulatory authorities (either FINMA in Switzerland or other national regulators in Europe) for how much of any one security can be represented in a portfolio. As such the index fund or ETF cannot replicate the targeted benchmark even if the desire is to do so. This will lead to unavoidable tracking error, but may not be indicative of a poorly managed strategy as the strategy may still reflect the most efficient investable vehicle available. 17