The Inefficient Market Argument for Passive Investing

Steven Thorley*

September 1999


Index fund proponents often argue in favor of passive investing because they believe that the modern U.S. equity market is informationally efficient. Market efficiency is the assertion that stock prices already reflect the best possible estimate of fair value, so there is no reason to actively buy and sell individual securities. However, for most investors, the assumption that the stock market is not efficient makes the argument for indexing even stronger. Even if prices routinely deviate from fair value, about two thirds of all active investors will underperform index funds every year. Further, if market prices are not efficient and investing is a matter of talent, then the investors in the underperforming majority will tend to be the same from year to year. Thus, indexing is preferred for most investors.

In addition to making the argument for passive investing given inefficient stock prices, this paper presents the following clarifications to conventional wisdom: 1) a high percentage of mutual funds underperforming the market index is not evidence that the market is efficient, and may in fact be evidence of an inefficient market; 2) as individuals and institutions opt out of active investing and index, the market may become more competitive, not less; 3) properly measured, about two thirds of all active investors will underperform index funds every year, independent of who chooses to actively invest, or the direction the market takes; 4) the proportion of small-cap oriented investors that must underperform small-cap indices is even higher than two-thirds, despite the fact that the small-cap sector may be less informationally efficient.

* PhD, CFA, H. Taylor Peery Professor of Financial Services, Marriott School, BYU.

Phone: (801) 422-6065 E-mail:

The Inefficient Market Argument for Passive Investing

Before picking stocks, the individual investor faces several strategic decisions, including investing style, and how much of the total portfolio to allocate to equities. The growing availability of low-cost equity index funds and ETFs adds another strategic decision: whether to invest actively or passively. Active investing, historically the only alternative available, is the process of seeking out, or hiring someone else to seek out, the best stocks to buy. Implicit in this process is the assumption that some stocks are better buys than others, and that a diligent search can ferret them out. Indexing presents an increasingly popular alternative to active investing. An indexed fund includes all stocks in proportion to their capitalization in the market. All stocks in the market are included -- there is no attempt to distinguish between good and bad investments.

The common justification for passive investing is that stock pricing in a competitive marketplace is informationally efficient. Financial economists who study the effects of competition sometimes conclude that all stocks will have the correct price all the time. The "correct price" in economic theory is defined as the best possible estimate of fair value based on currently available information. If a particular security is even slightly underpriced, diligent and ever vigilant investors will initiate buy orders that will quickly push the price up to its fair value. Similarly, the selling of overpriced stocks by informed market participants will immediately pull the price down. The controversial Efficient Market Hypothesis concludes that there is no point to fundamental or technical security analysis, because any stock is as good an investment as another. Active buying and selling of stocks by individuals will only run up brokerage commissions and waste time and energy. Turning to a professionally managed mutual fund is even worse, according to the Efficient Market Hypothesis, because of the fees required to pay well compensated experts to waste their time. (1)

In contrast, I argue for passive investing under the assumption that the stock market is not efficient, so that some investments are simply better than others. (2) The pragmatic motivation for this assumption is that it conforms to most investors' beliefs. Market rookies take up active investing based on the implicit assumption of pricing errors, while seasoned market veterans are often the most passionate critics of the Efficient Markey Hypothesis. For those inclined to accept the idea of market efficiency, it should be noted that this like most economic theory is based on the premise that people are perfectly rational, utility maximizing agents. If you have had any firsthand experience with people (or happen to be a person yourself) the assertion that people are always rational may be difficult to swallow. In fact, the growing field of behavioral finance is based on the proposition that people are consistently irrational in predictable ways.

For example, some observers argue that markets are predictably inefficient because so many market participants continue to confuse a good company with a good investment. (3) As a result, growth companies are consistently overpriced and out of favor stocks are consistently underpriced. If this is true, a simple strategy of buying low P/E or low Price to Book ratio stocks will outperform the market in the long run. Other human frailties, like the tendency to place too much weight on the most recent data, may cause investors, and thus market prices, to overreact to news. Predictable overreaction allows for a market timing strategy of buying on bad news, or buying stocks whose prices have recently dropped. On the other hand, another assertion is that all but a few investors neglect certain obscure stocks. This belief motivates basic fundamental analysis, as well as technically based momentum strategies; buying stocks whose prices have started to rise. The point is that if some investors are irrational, and the irrationality is pervasive enough, some stocks will be mispriced and the market will be inefficient. In the discussion that follows, we will assume that stock prices are sometimes wrong, and focus on the effects of the competition among investors attempting to identify these mispricings. In other words, we will acknowledge that investors compete with each other, but will assume that the competition does not make all stock prices correct all of the time.

The logic of passive investing

If the stock market is not efficient, should you be an active investor? If stock prices are sometimes wrong, then someone with the skill and expertise required to identify these market inefficiencies might do well. Consider other skill based activities, for example, a free throw competition in basketball. Suppose that you get a dollar for every shot out of ten that goes through the basket, and there is no fee to play. This is a conservative assumption with regard to the stock market because there are in fact "fees" to active investing, like transaction costs and tax inefficiencies, which we will discuss later. Like any analogy, the free-throw competition has its strengths and weaknesses, but one important characteristic of this analogy is that most players in the game will make at least some money. This is a critical characteristic, because the stock market is a "positive sum" game in the sense that investors do, on average, enjoy returns greater than the time value of their money. The compounded annual return on U.S. large-cap stocks since 1926 has been about 11 percent, as reported by Ibbotson Associates. This long-run return, in excess of the time value of money (interest rates), is a reward for risk and represents the new societal wealth that is created by the investment of capital in plant and equipment, employee coordination and training, and technological research. In contrast, sports betting and other forms of gambling are "zero-sum" games. A zero-sum game is one in which the profits of all players sum to zero. (4)

Under the no-fee-to-play condition, you should play the free throw game (and perhaps the stock market) even if your self-assessed basketball talent is marginal. But what if we add the twist that, instead of actively participating in the game, you can take the average score of those that do? Passive investing is just such a twist in the investing game, because a total market index fund contains all stocks, and all stocks have to be held by someone. This often ignored but unassailable fact has important implications. Chief among them is that in the absence of the costs of active investing, the index return over any time period must be the weighted-average performance of all active investors during that time period. (5) Thus, while investing in general is a positive-sum game, active investing is a zero sum game with respect to the alternative of indexing. One active investor's ability to outperform the index has to come at the expense of another investor's underperformance. Unlike the children in Garrison Keillor's Lake Wobegone, all investors cannot be above average.

If you were in the basketball free throw game, and were given the alternative to sit out and take the average score of the other players, what would you do? Your first thought might be to look around and make a guess at how your basketball skills compare to everyone else's. If you think your skills are lower than average (and remember, that must be half of everyone) then the smart thing to do is to not play: to take the average. But what if everyone else takes this approach? Then only those in the top-half of the skill pool will choose to play, and the average score you get by sitting on the sidelines will be based on only the top-half players. From this more rational perspective, you should only choose to play if your skills are in the top 25 percent of all potential players. But what if everyone takes this more rational perspective? Eventually no one but the very best player shoots, and everyone else gets his or her score. If everyone were perfectly rational, and not subject to overconfidence, there would be very few active investors. Thus overconfidence, perhaps the most pervasive of all investor irrationalities, is critical to market liquidity. We will return to the role of overconfidence in the marketplace toward the end of this discussion, but it should be clear that at least half, and perhaps more, of all active investors would be better off indexing.

Misconceptions about market competition

Before outlining the actual pros and cons of active investing compared to indexing, we will expose some common misconceptions about stock market competition based on the notion that active investing is a zero sum game with respect to indexing. First, remember that active investing is only a skill-based activity under the assumption that the stock market is not efficient. If stock prices always represent the best possible estimate of fair value, then outperforming the market index by actively selecting the best investments is purely a matter of luck. If active investing is a luck-based activity, a better analogy is a coin-tossing contest, not a free throw contest. Second, it is a well-publicized fact that more than half of all actively managed mutual funds underperform market indices and thus index funds. Some pundits mistakenly interpret this as evidence that the market is efficient. This is bad logic. In the absence of the costs associated with active investing, at least half of all investors will underperform the average every year, whether by luck or skill. Expressions of surprise or dismay that at least half of all managers underperform the index are similar to statements made by shocked politicians that half of all families live on less than the median income. It cannot be otherwise. The real test of market efficiency -- a luck versus skill based game -- is an investing group's consistency in performance. In fact, when a given category of investor, for instance, mutual fund managers, consistently underperforms the market by more than can be accounted for by the extra costs of active investing, then some other category of investor must be consistently outperforming the market. The percentage of actively managed mutual funds that underperform the market has been reported as high as 95 percent. (6) If this number is accurate and persists over time, then it is evidence that the market is a skill based game, and that active mutual fund managers, as a group, have below average skills. (7) If investing is a skill based game, then prices in the stock market are not efficient. (8)

Another common misconception is that active investors are better off when other investors leave the game and index. Over the last thirty years, university based business schools have become increasingly staffed by efficient market theorists. Universities now routinely turn out young investors with a passive investing bias. Some observers suggest that this increasing tendency to opt out of active investing reduces the competition to find undervalued securities, and makes those who stay in the game better off. This is bad logic. If active investing is a skill-based game, then skilled players will be worse off when lower skilled investors choose not to play. As an active investor, your ability to outperform the indexing alternative (be better than average) depends on the participation of players with below average skills. Someone has to sell the stock you want to buy at a bargain, and buy the stock you want to unload at a higher than justified price. Someone has to be wrong in order for you to be right. The exit of low skilled players from the stock market will increase competition, not reduce it, and should be viewed with dismay by active investors. The opposite effect may hold true with respect to the emergence of the Internet. Market analysts expect there to be over fourteen million online traders by the year 2002. (9) If equity investing is a skill-based game, then active investors should be encouraged by the entry of new players, particularly novices. Aspiring Warren Buffets (or Michael Jordans in the basketball analogy) should be happy to see lots of low skilled rookies join the game. Active investors need to consider the composition of the competitive environment in which they operate, not the raw number of competitors. There will be plenty of active investors, including (literally) thousands of professional investing firms and millions of individual investors, no matter how popular indexing becomes. The important concern in the money management industry is the skill level, or other comparative advantages, of the competition. In any industry, including money management, increases or decreases in the raw number of competitors is inconsequential after a sufficiently large number of players are in the game.

The costs of active management

Thus far we have ignored the extra costs associated with active investing versus passive investing. The most familiar of these (and perhaps the least important) are transaction costs, specifically, brokerage commissions and bid-ask spreads. Brokerage rates have dropped precipitously from the pre deregulation days prior to May 1975. Exhibit 1 estimates the transaction cost of active investing at a little more than one percent per year. On the other hand, passive investing through an index fund is not entirely cost free. For example, the largest U.S. index fund, the Vanguard Index Trust 500, has an annual managerial fee of 6 basis points for institutions (e.g., corporate pension plans) and 18 basis points for individuals. Unfortunately, S&P 500 based funds are not the best candidates for U.S. equity market indexing, because they only include large cap stocks, not the entire market. Because of their size, these five hundred stocks (out of the thousands of publically traded securities) represent about 70 percent of total stock market capitalization, but not all of it. Thus, S&P 500 funds do not fully index and can outperform or underperform the entire U.S. equity market by several percentage points a year, depending on the relative performance of the small-cap and large-cap sectors. To some extent, this defeats the intent and philosophy of indexing in the first place. (10) Fortunately, index funds based on the total stock market are becoming more popular and also have low fees of 20 to 30 basis points. These small annual fees cover bookkeeping expenses and occasional transaction costs associated with changes (i.e., IPOs, mergers, and acquisitions) in the broad market. Since we are concerned about the extra fees associated with active investing over passive investing, these small fees should be subtracted from the estimated active management transaction cost of a little over one percent. Thus, the correct characterization of active management transaction costs is a net fee of a little less than one percent per year.

Unfortunately, there are three other costs associated with active investing, each potentially more significant than transaction costs. First, active trading is tax inefficient compared to passive investing because the IRS defines a trade as a taxable event. Outside of tax-deferred accounts (like traditional IRAs), capital gains taxes are due every year as stocks are bought and sold under active management. Index investing defers most capital gains taxes until the investment is liquidated for consumption purposes during retirement. In other words, taxes on capital gains are deferred by a passive investment strategy, even without designating the account as an IRA. Summarizing the tax inefficiencies of active investing is difficult, because individual tax status and rates vary, as well as the tax law itself over time. Exhibit 1, however, details a quick and dirty estimate of at least one percent a year; similar to the transaction costs of active investing.

Investors often under-appreciate another cost of active investing: sub-optimal diversification. William Sharpe received the 1990 Nobel Prize in economics for proving, among other things, that if stocks are always correctly priced (i.e., if the stock market is informationally efficient), then the only perfectly diversified portfolio is the capitalization weighted portfolio of all stocks. Anything less exposes the investor to diversifiable risk that he or she could have avoided. The optimal diversification argument for indexing has not received as much press as the efficient markets argument, perhaps because most investors do not accept the pre-requisite idea of informational efficiency. In addition, applied research finds only a small difference between a well diversified portfolio of, say, twenty stocks, and the optimally diversified portfolio of all stocks. Nevertheless, Exhibit 1 suggests an active management cost estimate for undiversified risk of about one percent a year, similar to the transaction and tax costs.

The fourth and final fee associated with active investing is perhaps the most significant and the least appreciated. Successful active investors will acknowledge that analyzing and identifying the best stocks to buy requires substantial time and effort. Serious investors spend a great deal of time analyzing the large amount of data available on thousands of individual stocks, including financial statements, market trends, and industry structure. When investors hire out these research activities by buying professionally managed mutual funds, they typically pay fees of one to two percent of money under management. Full service brokers charge similar fees for stock picking advice through higher commissions than the straight transaction cost fees of discount brokers.

However, conducting these research activities your self is an even more expensive alternative. The advent of the Internet, together with improvements in telecommunications and personal computer technology, makes access to public information on companies a non-issue. Unfortunately, the information processing activity itself can be quite expensive in an opportunity-cost sense, as explained in Exhibit 1. Managing one's own investment portfolio can be compared to assuming responsibility for other professional activities like legal, tax, or medical care. Admittedly, individuals are likely to be more concerned and motivated about their own welfare, than a medical doctor or portfolio manager. The disadvantage is that individuals can seldom compete, from an opportunity-cost perspective, with a specialist's expertise and economies of scale.

In summary, there are four cost categories of active management: transaction, tax inefficiency, undiversified risk, and research. For conceptual purposes, each category can be roughly estimated at about one percent of the money invested, with a total handicap of about four percentage points per year, compared to passive investing.

The benefits of active management

We have identified the costs of active compared to passive investment management. What are the benefits? For some active investors, the benefits include the intellectual challenge and satisfaction of actively participating in, and sometimes winning, a skill-based game (or the satisfaction of being plain lucky if the market is perfectly efficient). Actively managing one's own portfolio provides a sense of independence and self-reliance. Active investing can be challenging and psychologically rewarding, while passive investing is relatively boring. However, we will assume in the following discussion that the decision to be an active investor is based on the potential for financial, not psychological, rewards.

Although the financial performance of some categories of investors, for example, mutual fund managers, are routinely reported, reliable statistics on individual investor performance are difficult to compile. Self-reported performance is almost always overstated, and privacy laws prohibit a systematic audit of individual investor results. (11) Between these two disclosure extremes are a number of other investor and investment advisory categories, for example, brokerage house recommendations tracked by the Wall Street Journal. However, even a general characterization of active management benefits, based on the performance of all categories of investors, is impossible because most of the required data is simply nonexistent. Here again, the fact that all stocks have to be held by someone allows for a better understanding of active management potential. This fact was used before to argue that the average before cost performance of all active investors each year is that year's market index return. We can also use this fact to estimate the range or distribution of active management results around the average. Since all stocks have to be held by someone, data on individual security returns on all stocks in the market place contains information on the performance of all, not just some investors. No group's performance is left out or double counted in an analysis of all the shares in the market.

The Center for Research in Security Prices (CRSP) database, from the University of Chicago, contains accurate price and dividend information on all U.S. common stocks for the last quarter century. The CRSP database also contains the number of shares outstanding for each issue over time. The shares outstanding data is essential because more investor dollars are devoted to large capitalization stocks than small capitalization stocks (for example, more people own Microsoft than Novell). Using this database, I conducted a computer simulation of ten thousand portfolios of twenty stocks for each calendar year for the past ten years. The twenty stocks for each portfolio were chosen randomly based on a probability equal to the market capitalization of the issue divided by the capitalization of the entire market at the beginning of the year. These probabilities are appropriate because index funds hold stocks in proportion to their market capitalization, and thus do not alter the portfolio composition summed across all active investors. While a computer simulation based on the entire stock market database is better than anecdotal assessments of active management benefits, the simulation does have its limitations. (12) However, the simulation's random selection of stocks in contrast to informed choice in the real world does not invalidate the basic conclusions about the performance range of all active investors. The point remains that someone had to own each of the stocks in the database. Someone thought each stock was worth including in his or her portfolio.

Figures 1 and 2 cover two recent years in the stock market, and show the number of portfolios out of ten thousand that had rounded returns at each percentage point from minus 20 to plus 50. Version A of each figure shows before-cost returns that do not account for transaction, tax inefficiency, undiversified risk, or research costs. Version B of each figure shows after-cost returns. The calendar year 1996, shown in Figure 1, was a good one for the stock market. The average before-cost return for the ten thousand simulated portfolios was 21.86 percent. This return is also, by definition, the capitalization weighted average return on all stocks, and is thus very close to the return on index funds that track the entire market. For example, the 1996 return on the Russell 3000 was 21.82 percent. The 1996 return on index funds available to individual investors was slightly less than 21.82 percent because of tracking errors and the small fees charged to manage the funds.

An assessment of the after-cost returns on the simulated active portfolios depends on which of the active management costs previously discussed apply. Four cost categories were identified, each with a rough estimate of about one percentage point a year. To ensure a conservative bias in favor of active management, we'll assume that only three of the four categories applies for any given individual. It is unclear how any investor could avoid transaction costs or undiversified risks, but the tax inefficiencies could be avoided by only trading within a tax privileged account, like a self-directed IRA. Alternatively, one could argue that the research commitment and opportunity cost issue is irrelevant because an investor has no other viable uses for his or her time (not something to be proud of). If we assume the cost of active management is three percentage points, instead of four, then the average after-cost return of the ten thousand portfolios for 1996 was 21.86 - 3 = 18.86. Under this assumption, about 67 percent (6,654 out of 10,000) of the simulated active portfolios underperformed total market index funds in 1996 on an after cost basis, as shown in Figure 1b.

The relative performance results for other years are similar to the 1996 simulation. For example, Figure 2 shows the simulation results for 1994; a bad year for the U.S. equity market with a slightly negative market-wide return. In 1994, about 72 percent of the simulated active portfolios underperformed broad based index funds on an after-cost basis. The higher percentage of underperforming funds in 1994 compared to 1996 is not due to the lower market wide return. Rather, the higher number of underperforming funds in 1994 is a result of the tighter dispersion or standard deviation of portfolio returns around the mean for that year. The standard deviation of portfolio returns was 5.22 percent in 1994, compared to 7.19 percent in 1996, shown as a thinner "bell curve" for 1994. However, the average standard deviation of portfolio returns around the mean for the last ten years has been about seven percent. This important performance statistic shows up repeatedly in the real world of active management. For example, the performance of major brokerage houses' recommended stock lists for the calendar year 1997 had a standard deviation of 6.60 percentage points, and the return standard deviation of the largest active mutual funds for 1997 was 7.63 percentage points. (13)

Using the observed seven percentage point standard deviation, and the assumed three percentage point net active management cost, we can derive a general rule of thumb about the prospects for active versus passive investing. Under the assumption that performance returns are normally distributed, these numbers dictate that 67 percent, or about two thirds, of all active investors will underperform the indexing alternative on an after cost basis each year. This calculation is based on the standard normal distribution function, f(x), where x = 3/7. (14) In terms of the basketball free-throw analogy, there is a cost to being a shooter instead of sitting back and taking the average. Because of this cost, you have to be in the top third, not just the top half, of those that choose to play, in order for active management to pay off. If we could tabulate the performance of all active individual and institutional investors, with absolutely no one left out, we would find that two thirds underperform index funds each year after costs. Of course, one could quibble about the active management cost assumptions, and thus the two thirds estimate. The percentage of underperformers might be higher, say 70 percent, or perhaps as low as 60 percent. But whatever the number is, it is fixed and immovable despite the hope and hard work of market participants. There never has been and never will be a year where the majority of all actively invested money beats the market-wide index. (15)

The one-out-of-three success rate is a good rule of thumb with respect to the general stock market. For investors who focus on small-cap stocks, only about one in four active investors can beat a small-cap index fund in any given year. The proportion of outperformers in the small-cap arena is lower because active investing in small-cap equities involves higher transaction and research costs. The relatively lower odds of success in the small-cap arena may seem to contradict the conventional wisdom that the small-cap market is less informationally efficient, so that price errors are more common. However, the percentage of players that must underperform any given index is a function of the range of performance outcomes and active management costs, not the informational efficiency of the market that the index tracks. Market efficiency only indicates whether the fixed minority proportion of outperformers are lucky or talented. In the small-cap arena, talent, rather than luck, may be a more important factor, because the small-cap market is less informationally efficient. But the mathematical logic presented above dictates that a higher percentage of players must underperform small-cap indices, compared to large-cap indices, because the active management costs in the small-cap arena are higher.

The top third

If only one-third of all active investors can actually be in the top third in terms of investment skill and expertise, what motivates the other two thirds to stay in the game? First, many investors view "the market" as an entity in and of itself, rather than the collective actions of other investors with exactly the same objective of holding only the best stocks. In other words, they do not appreciate the fact that investing takes place in a competitive environment. Such investors do not realize that in every trade, another individual, not just "the market", must be wrong in order for them to be right. They may mistakenly conceptualize the stock market as a place where everyone can be above average if they are bright and work hard enough. A second explanation for the lower two-thirds remaining in the game is that, while they understand the market is a competitive environment, they are overconfident about their own skills. Overconfidence is a well known irrationality in many contexts, and is a major topic of study in the field of behavioral finance. For example, behavioral finance researchers cite surveys showing that over 80 percent of all drivers consider their driving skills to be in the top third. In investment management, as in other areas of life, the large majority of people believe their abilities to be above average.

The discussion above motivates another important question: which investors, or investor groups, are in fact the most likely to be in the top third in terms of skill, information, or other competitive advantages? Any ranking is subjective in the absence of performance data on all investor categories, but some general conclusions are possible. The fact that public mutual funds, as a group, perform at or below the level of the after-cost computer simulation results, suggests that mutual fund managers, as a group, are not in the top third. Two other investing groups, insiders and hedge fund managers, are more likely candidates for top third status. With regard to insiders, U.S. security law restricts the investing activities of corporate officers and fiduciaries that have access to non public information. Unfortunately, the list of potential insiders includes corporate officers, public accountants, attorneys, investment bankers, corporate board members, board member's nephews and nieces, the bankers' golfing buddies, the clerical staff that supports each of these professional groups, and anyone else to whom the people mentioned above owe a favor. Given the long list of people with access to inside information, and given the amount of money at stake, insider-trading laws will never be completely effective. There are, in addition, still a number of legal ways to come by more timely information than the general investing public.

The competitive advantage of hedge fund managers is not private information, but regulatory freedom together with a substantial capital base. Hedge funds are restricted to a small number of wealthy investors in order to avoid the prudent man laws and suitability constraints imposed on more widely held public mutual funds. Regulators do not limit the types of trading activities that hedge fund managers can pursue, including long or short exposure to any domestic and international asset class, options trading, and currency speculation. Whether the freedom and market clout that hedge fund managers enjoy actually results in top third status is unclear, because their performance results are not routinely made public. But they do have, as a group, an identifiable competitive advantage. Identifying a competitive advantage that individual investors have in the market wide investing game is quite difficult, although this clearly does not dissuade individuals from active management. Ironically, a basic tenet of security analysis is that a company has to have a sustainable competitive advantage in order to qualify as a potential investment. Surprisingly few individual investors apply this same hardheaded business logic to their own activities. There are few, if any, identifiable competitive advantages that have the potential to lift small investors into the top third of all stock market participants. (16) An important question for individual investors remains unanswered: Why should they jump into a game in which their competitors have an advantage, if they can win more often than not by simply watching from the sidelines and taking the average?

The unavoidable conclusion

If prices in the stock market are not efficient, and investing is a skill-based game, then disadvantaged or low skilled investors who try to actively manage their portfolios will consistently lose to players with an advantage. If we reverse the premise of this paper and assume that the stock market is perfectly efficient, then advantages don't matter -- it's all luck -- and less-skilled players have the same one in three chance of beating the market as anyone else. In other words, market efficiency protects the less-skilled investor from consistently making bad investments because all stocks are fairly priced. There is, on the other hand, no such protection in a market where stocks are routinely mispriced. The active investing majority that underperforms the index will tend to be the same year after year. Thus, the argument for indexing is even stronger for individual investors if the stock market is not efficient. The game of poker provides, in some respects, an instructive analogy. Poker is a zero sum game, similar to active investing compared to indexing, and poker combines luck and skill, consistent with the assumption of a less than perfectly efficient market. An old adage among professional poker players applies to those deciding to participate in the active investing game. "If you don't know who the mark is, get up and leave the table, because it's you."

About two-thirds of all active investors, whose only financial justification for being active is beating the index, must fail in that objective each year. Press reports that quote the failure rate as substantially higher or lower in any given year, either track only one category of investor, or do not properly measure all active management costs. The two-thirds failure rate among all active investors is as mathematically certain as the forecast that exactly half of the workforce will earn less than the median income. It may seem unfair, but it cannot be otherwise. No amount of hope and luck (if the market is efficient) or work and skill (if it is not) can change that fact. Each individual investor should confront the question "Am I in the top third of everyone who thinks they are?" and the unavoidable answer "Probably not."

Exhibit 1: Active Management Cost Calculations

1) Transactions Cost

Pure transaction fees, in the form of reliable brokerage services, are now (1999) available for as low as $15 for any retail sized trade. For example, on a trade of three hundred shares of a $20 stock (a $6 thousand dollar trade), the $15 commission is a 0.25 percent (25 basis point) fee. Both buyers and sellers incur the fee, so the round trip or doubled brokerage fee is 50 basis points. Bid ask spreads are an equally important but less apparent element of transaction costs. Investors cannot sell shares at the same price that they are available to buy. For immediate liquidation, the market typically bids one eighth dollar below the asking price. On a $20 stock, the one eighth bid-ask spread represents another 62.5 basis points, so that the total transaction costs (brokerage fees plus bid-ask spread) are 112.5 basis points, or a little more than one full percentage point, per trade.

Loosely speaking, all common shares on the combined U.S. equity markets have a market value of about $10 trillion (1998 data). The NYSE has about $8 trillion and the NASDAQ has about $2 trillion; the other exchanges are small enough that they can be ignored. A typical day's trading volume is 600 million shares on the NYSE and 650 million on the NASDAQ, at an average share price of about $20, or about $25 billion in trading. In other words, the daily turnover rate is about 25/10,000 = 0.25 percent of market value. At this rate, complete share turnover takes 1/.0025 = 400 days, or 1.6 years based on 250 trading days a year. This represents an overall average; different securities trade either more or less frequently. Many shares are held in indexed and other non-active accounts, supporting an estimated average holding period of about one year across all active investors. Thus, the transaction cost fee of active investing can be characterized as a little more than one percentage point of assets under management per year. Of course, annual transaction costs will be higher for investors who trade more frequently than once a year.

2) Tax-inefficiency Cost

Suppose you earn the long-run equity return average of about 11 percent a year. Further, assume you are in the 28 percent tax bracket (a conservative assumption) and that all of the 11 percent return is capital gains (a liberal assumption because 2 of the 11 percent is likely to be dividend yield). If the account is actively managed so that taxes are paid each year, then the annual reinvested after-tax return is 11*(1-.28) = 7.92 percent. If, on the other hand, you passively manage the account, and reinvest the full 11 percent each year, the account will have increased by 1.1110 - 1 = 183.94 percent after 10 years. After taxes, which are due upon liquidation of the passive account, the 10 year return will be 183.94*(1-.28) = 133.42 percent, or an annualized return of 8.85 percent. The annual tax inefficiency cost is 8.85 minus 7.92, or about one percentage point. Of course this is only an example, and the actual tax inefficiencies of active management might vary from nothing, for IRA investors, to as high as 3 percent per year for a 30-year horizon and a combined federal and state tax rate of 40 percent.

3) Undiversified Risk Cost

The U.S. stock market, as experienced through an index fund, has an average annual return of about 11 percent and a standard deviation of about 16 percent. Suppose that an actively managed fund has a higher standard deviation of 20 percent, because it is not optimally diversified. Under these conditions, an index fund investor could replicate the higher risk of the active fund by borrowing an additional 25 percent of the money invested at an interest rate of 5 percent, and invest it in the index (this is referred to as a 1/1.25 = 80 percent margin position because 20 percent of the total investment is borrowed money). This leveraged investment in the index will have a standard deviation of 1.25 * 16 percent = 20 percent, just like the sub-optimally diversified active fund. The risks are now equal so that the expected returns can be compared. The expected return on the leveraged index fund is 1.25*11 - 0.25*5 = 12.5 percent; more than one percentage point higher than the active fund.

4) Research Cost

Consider an individual investor who allocates $260 thousand dollars of liquid net worth to actively self-managed stocks. Given similar allocations to the bond and money markets, and personal real estate holdings, this individual might have a net worth of one million dollars. Suppose that this investor spends 5 hours a week (260 hours a year) in evenings and weekends following the market and being informed enough about both the stocks currently held and potential acquisitions to manage the portfolio. If this research increases his or her return by 2 percentage points above the index each year, then the investor earns $20 an hour for the effort. Individuals who have acquired a million dollars in net worth can generally make more than $20 an hour, so that self-managed portfolios of this size or smaller do not meet the opportunity cost criteria. In other words, it is cheaper for most investors to "hire" a mutual fund manager, with a support team of market analysts, to do the research. Active mutual fund fees for research alone are generally over one percent of assets under management.

Appendix: Clarification of the Efficient Market Hypothesis

The Efficient Market Hypothesis (EMH), a central theme of financial economics, asserts that competition among active investors results in market prices that are always fair. The stated, and perhaps overstated, implication of the EMH that invokes the indignation of market analysts is that market research of any kind is pointless. This extreme version of the EMH is admittedly simplistic. Someone has to be the first to detect the mispricing of a stock and take advantage of it. Economists more formally propose that the marginal benefits of active research are no greater than the marginal costs for the most privileged market participants; those with access to the best information and the lowest transaction costs. The legal requirements about universal access to material information, and the low transaction costs and liquidity associated with publicly traded equity compared to other speculative markets (for example real estate or the used car market), lead economists to aim most of their efficient market rhetoric at the large-cap U.S. stock market. No one in the ivory tower suggests that the used car prices are always fair and correct.

Stock market players do not generally appreciate why economist are so enamored with efficient market theory. The reason is that informational efficiency in security prices is a key assumption behind the argument for capitalism. Fair prices in unfettered financial markets promote social welfare by ensuring that capital is allocated to its best and highest use. Scarce funding is automatically dispersed to those industries and companies most likely to produce the goods and services we all want. If stock mispricings due to overreaction, crowd psychology, or neglect, are as common as some market observers claim, then we would all be better off with a central planning committee making society's capital allocation decisions. This concept lies behind the humorous observation by Rex Sinquefield of Dimensional Fund Advisors: "I've polled everyone I know, and the only people who think that markets are not efficient are the Cubans, the North Koreans, and the active fund managers."

Perhaps the most commonly expressed concern about the EMH is the assumption of universal human rationality. In defense of the EMH, the assertion is not that all investors are rational, but that there are enough rational market participants to provide informed competition and sufficient capital and market power to assume the positions needed to eliminate stock mispricings when they occur. The proportion of rational market players needed to make the market efficient is unclear, but it probably does not require a majority. Indeed, financial economists acknowledge that most investors are not rational, or there would be a lot less trading than is observed in practice. Few people would actively trade stocks knowing that the person on the other side of the transaction may know something that they do not. If all investors were perfectly rational, volume would be reduced to "liquidity traders" (passive investors adding to or liquidating retirement accounts) and a small number of rational "information traders." The reality of high stock market volume has caused efficient market theorists to create a third category of investors called "noise traders." Fisher Black first described noise trading in his 1986 American Finance Association Presidential Address: "Noise trading is trading on noise as if it were information. People who trade on noise are willing to trade even though from an objective point of view they would be better off not trading. Perhaps they think the noise they are trading on is information. Or perhaps they just like to trade." Financial economists believe that the bulk of the trading volume in U.S. equity markets is due to noise traders.


1. The Appendix elaborates on this simplified characterization of the efficient market hypothesis. For the record, my personal belief is that while the even the modern large-cap U.S. stock market is not perfectly efficient, it is more efficient than most individual investors realize. Underpriced securities exist but are difficult to find, and performance variations from investor to investor is more a matter of luck than skill.

2. "Best" in the context of investments generally means the highest possible return with the least possible risk. The preferred trade-off between these conflicting objectives is subjective, as is the definition of risk. This discussion assumes that there is enough commonality in preferences to talk about a good or bad investment for anyone.

3. As any experienced investor knows, good (highly profitable) companies are not necessarily good (highly profitable) investments. If other investors already anticipate a company's profit potential, the stock price will reflect that belief and the future return will be mediocre at best. The return that an active trader enjoys in a stock is not based on the company's profitability, but rather on the increase or decrease in other investor's belief about the future performance of the company between the time that the stock is purchased and sold.

4. Derivative financial markets such as financial futures and options, are true zero-sum games. However, most financial economists believe that futures and options have societal value because they allow for simple risk-transfers from one party to another, and thus facilitate the operation of the primary financial markets; stocks and bonds.

5. The "weights" in this average are based on the dollars invested by each market player. The more precise concept is that the market index return must be the simple average return on all the dollars invested in the market. If small investors also happen to be the lower skilled players, then more than half of all active investors will underperform the index, even on a before cost basis.

6. For example, see "Your Money Matters" in the Wall Street Journal, February 3, 1998.

7. If accurately measured, the underperformance of mutual fund managers does not imply that individual investors are taking up the slack. Pension funds, hedge funds, and investment banking firms are the more likely candidates.

8. These very high underperformance statistics may be overstated for two reasons: (1) the lack of a risk-adjustment (many equity fund managers must hold some cash for liquidity), and (2) improperly chosen benchmarks or indices (some managers focus on small-cap stocks, and in recent years large-cap indexes have had higher returns). In other words, these statistics do not provide convincing evidence either for or against the Efficient Market Hypothesis.

9. Forecasts are made by Forester Research, Inc., as discussed in "The New Stock Traders", Business Week, May 4, 1998, and "A Nation of Stock Keepers", Time, May 11, 1998.

10. The popularity of S&P 500 indexing has caused price distortions in the past as stocks were added or deleted by the Standard and Poor's committee. Recent studies indicate that these issues are being resolved, as the growth of S&P 500 indexing is slowing and more funds are targeting broader market indices like the Russell 3000 or the Wilshire 5000.

11. Reliable information on individual investor performance is difficult, but not impossible, to compile. Recently, Brad Barber and Terrance Odean, of the University of California at Davis, were able to gain access to the trading records of 60 thousand individuals at an unnamed discount brokerage firm, as reported in their paper "The Common Stock Investment Performance of Individual Investors." (Forthcoming if the April 2000 Journal of Finance.) The individual investors' average annualized return from February 1991 to December 1996 was 15.3 percent, 1.8 percentage points below the market index return of 17.1 percent for the same period. The 15.3 percent average return includes the effects of transaction costs, but not the other costs of active management identified in this paper.

12. One important computer simulation limitation is the assumption of a twenty stock portfolio. The number of stocks influences the size of the standard deviation around the average, with a higher number of stocks in the portfolio simulation reducing the standard deviation of portfolio outcomes. The fact that the simulated portfolios are randomly created may also affect the range of portfolio outcomes depending on investors' propensity to strategically diversify.

13. Each quarter, the Wall Street Journal reports on the performance of the major brokerage houses' recommended stock lists. The February 5, 1998, edition shows the performance for fifteen firms during the calendar year 1997. The Wall Street Journal, as well as a number of other publications, also reports mutual fund results.

14. To be precise, the distribution of returns cannot be normal because they are bounded below by minus 100 percent (a complete loss). Financial economists typically assume that the distribution of returns is log-normal, but even this assumption is inconsistent with empirical studies of equity returns that find fat-tails or leptokurtosis. These technical issues do not materially affect the basic conclusions in this paper about the percentage of active investors that must underperform indexed funds.

15. Technically, this statement only refers to the investor dollars, not the investors themselves. See footnote 5.

16. Size may be the one competitive advantage of the individual investor, because large institutional investors cannot exploit pricing errors on very small or illiquid stocks. Either the market order itself will be so large that the pricing error evaporates as the order is executed, or the position taken will be too small to materially affect the bottom line of a large pool of money. The significance of this individual investor advantage is debatable, given the relatively high costs, both research and transactions, of active management in the small-cap market.