Explaining the Value Tilt and Its Implications for Investors

    by William Reichenstein

    Explaining The Value Tilt And Its Implications For Investors Splash image

    Over the long run, returns on value stocks have exceeded returns on growth stocks. A question debated in academic and professional circles is: Why?

    This article will address this question and discuss some of its investment implications.

    Defining Value and Growth

    First of all, some definitions are in order—specifically, what is a “growth” stock and what is a “value stock?”

    Prior to about 1990, the financial profession did not use the terms “value stocks” and “growth stocks.” However, about that time, several academic studies concluded that the cross section of stock returns varied across two dimensions: “size” and what we now call “style.”

    In 1992, shortly after this literature appeared, Morningstar introduced its equity style box that separates mutual funds by size—large-cap, mid-cap, and small-cap—and by style—value, blend, and growth. Today, virtually everybody uses a similar 3x3 style classification.

    There has been little variation in the way the profession has measured a firm’s “size” through the years—a firm’s size is measured by its market capitalization, that is, stock price times number of shares of common stock outstanding.

    Until mid-2002, the profession usually classified a stock by “style” based on its price-to-book-value ratio, its price-earnings ratio, or both. Today, the profession usually measures a stock’s style by a combination of one or more valuation factors (e.g., price-to-book-value ratio, price-earnings ratio) and one or more growth factors (e.g., projected growth rate in earnings).

    Long-Term Historical Returns

    What does the historical record show about the relative performance of growth stocks and value stocks? One good illustration is indicated by the performance of the Russell indexes. The Russell 1000 index is an index of large- and mid-cap stocks, while the Russell 2000 is a small-cap index. These indexes can be split into value and growth halves.

    Over the period 1979 through 2006:

    • The Russell 1000 Value index earned 2.4% more than the Russell 1000 Growth index, and
    • The Russell 2000 Value index earned 5.1% more than the Russell 2000 Growth index. Figure 1 illustrates the advantage value stocks had over growth stocks in the Russell 1000 index for five-year holding periods ending 1983 through 2006.

    What Causes the Value Premium?

    That leads to the major question addressed by this article. Why have value stocks produced higher long-run returns?

    Figure 1.
    Historical 5-Year
    Value Premium on
    the Russell 1000
    Index: Five-Year Holding Periods
    Ending 1983–2006

    The answer to this question may help us determine whether we can expect this pattern to repeat itself in the future.

    There are two major schools of thought that try to explain why value stocks have produced higher long-run returns:

    • The “efficient markets” school, and
    • The “irrational markets” school.

    The Efficient Markets School

    The efficient markets school starts with stock price theory, and runs with it.

    Why does a growth stock sell at 25 times earnings while a value stock sells more on the order of 10 times earnings?

    In theory, a stock’s price relative to its earnings should depend upon several factors, including:

    • Its risk, and
    • Its long-run growth prospects.

    Everything else equal, a stock selling at a low price relative to its earnings (in other words, a value stock) should have a higher risk and/or lower earnings growth prospects than a stock selling at a high price relative to its earnings (in other words, a growth stock).

    The efficient markets school says that that theory holds true in the real world—in other words:

    • Stocks are fairly valued at all times, and
    • Value stocks are riskier than growth stocks.

    According to this school, the value premium—that is, the additional long-term return on value stocks—is the natural reward for bearing this additional risk.

    To use an analogy, consider that, over the long run, stocks have earned higher returns than Treasury bonds. This is natural because rational investors should not invest in stocks unless they expect to earn a higher return. Investors understand that stocks may produce lower returns over short horizons and short horizons may be a decade or longer; that is why we call stocks “riskier” than Treasuries. But over the long run, stocks should produce higher returns that Treasury bonds.

    Table 1 presents an example from the bond markets that explains why riskier securities should trade at lower valuation multiples.

    Table 1. Risk, Expected Returns, and Valuation Records
    Exxon Mobil
    Promised Yield 5.0% 6.0% 12.0%
    Expected Loss
    Due to Default
    0.0% 0.2% 4.0%
    Expected Return 5.0% 5.8% 8.0%
    Valuation Multiple:
    Price-Interest Ratio
    20x 16.7x 8.3x

    Suppose an investor wants to invest for four years and is considering investing in one of three four-year bonds:

    • A Treasury bond yielding 5%,
    • A AAA-rated Exxon-Mobil bond yielding 6%, or
    • A B-rated General Motors bond yielding 12%.

    Which bond should the investor prefer?

    The answer is: It depends upon the investor’s risk tolerance.

    Table 1 presents the expected returns for these three bonds, assuming the expected losses due to default risk are 0.2% for the Exxon-Mobil bond and 4% for the GM bond.

    Rational investors demand a higher expected return for investing in riskier assets. Therefore, the expected return increases as we go from Treasury to AAA to B-rated bonds. Theprice/interest row indicates the number of dollars investors will pay for each dollar of promised annual interest. This is similar to a price-earnings ratio in that it shows the price multiple relative to the amount in the denominator that an investor must pay for the security.

    For the Treasury bond, the investor pays 20 times annual interest payments, or $1,000/$50, for a $1,000 face value bond.

    For the Exxon-Mobil bond, the investor pays 16.7 times annual interest payments, or $1,000/$60. For the GM bond, he pays 8.3 times annual interest payments.

    This example demonstrates that the natural outcome of a market that is dominated by risk-averse investors is that higher-risk securities should trade at lower valuation multiples and offer higher expected returns than lower risk securities.

    The efficient markets school concludes that value stocks are riskier than growth stocks, and the value premium is the natural reward for bearing higher risk.

    Irrational Markets School

    The irrational markets school says that theory does not always carry over into the real world, and specifically that:

    • Individual stocks are sometimes mispriced, and
    • Overvalued stocks usually fall in the growth half and undervalued stocks in the value half of a stock index.

    According to this school, at best, only part of the additional long-run return on value stocks is attributable to their higher risk. Instead, the value premium is primarily attributable to the tendency of investors to overestimate the growth prospects of growth stocks and, therefore, to overvalue these stocks. To a lesser degree, it may be attributable to the tendency of investors to underestimate the growth prospects of value stocks and, therefore, to undervalue these stocks.

    According to the irrational markets school, financial analysts and individual investors tend to look at recent history (e.g., last five years) and project a continuation of that trend for many years to come. In general, stocks that have been growing fast are projected to continue to grow fast and, therefore, they have high price-earnings ratios today.

    In contrast, stocks that have experienced tough times in recent years are projected to experience relatively slow growth and, therefore, they have low price-earnings ratios today.

    Empirical studies suggest that individual stocks’ earnings growth rates usually revert to the mean; firms that have experienced fast earnings growth in recent years are likely to experience reduced earnings growth rates, while firms that have experienced slow earnings growth are likely to experience improving earnings growth rates.

    These studies suggest that, as a group, firms with historically fast earnings growth will likely experience a relatively small growth advantage compared to firms with historically slow earnings growth, but this advantage will likely only last for about two years.

    The irrational markets school’s story is supported by stock returns around the turn of the century. In the last half of the 1990s, growth stocks experienced fast growth. Investors, especially momentum investors, jumped on their bandwagons and drove their prices excessively high. Growth stocks’ high price-earnings ratios implied expectations of continued fast earnings growth for long horizons.

    The accompanying box below provides two good examples of what happened when great expectations collided with hard reality. Of course, two examples from one period cannot prove or disprove either school of thought. But these stocks help illustrate the irrational markets story during a period in which, with the advantage of hindsight, most of us would agree that investors collectively overvalued many growth stocks, especially Internet stocks. [I am not trying to say that it was obvious—to me or anyone else—at that time that these growth stocks were substantially overvalued. The fact that these growth stocks were selling at those prices clearly indicates that, at that time, the average investor felt they were fairly valued.]

    Great Expectations: Cisco and Sun Microsystems

    On March 31, 2000, Cisco closed at $77.31 per share. Its 1999 earnings were $0.38 per share, so its trailing price-earnings ratio was over 200.

    Cisco stock had experienced earnings per share growth rates of about 50% per year for the prior seven years. Based on Value Line forecasts at that time, its earnings were expected to continue to grow fast. Earnings were projected to average $1.45 for the 2003–2005 period, which (interpreted at the 2004 midpoint) represented a projected 31% annual growth rate for the next five years. In reality, Cisco’s earnings per share grew at 18% per year between 1999 and 2004. Although earnings growth was strong, it was below investors’ expectations. Therefore, the stock produced disappointing returns for this period.

    Another example comes from Sun Microsystems, which on March 31, 2000, closed at a split-adjusted price of $46.85 per share. Its 1999 earnings were a split-adjusted $0.355 per share, so its trailing price-earnings ratio—defined as price divided by trailing earnings—was over 130. Sun Microsystems stock had experienced earnings per share growth rates of almost 40% per year for the prior six years. Based on Value Line forecasts at that time, its earnings were expected to continue to grow at an average rate of 24% for the next five years.

    In reality, its earnings not only failed to grow, but they were negative five years later. Investors overestimated this growth stock’s growth prospects and it produced disappointing returns through 2004.

    If investors collectively overvalue some stocks then these stocks will tend to show up in the growth half of stock indexes. From simple math, stocks with prices that are too high usually have high price-earnings ratios and stocks with prices that are too low usually have low price-earnings ratios. Thus, overvalued stocks tend to land in the growth half of a stock index.

    According to the irrational markets school, the additional long-run return on value stocks is primarily attributable to the tendency for Cisco, Sun Microsystems, and other overvalued stocks to land in the growth half of a stock index and, to a lesser degree, for undervalued stocks to land in value indexes. The value premium has little to do with risk.

    Table 2. Value vs. Growth Stocks: Which Is Riskier?
    The efficient markets school argues that the value tilt is due to greater risk; the irrational markets school argues that value stocks are less risky than growth stocks and that the value tilt is due to mispricings.
      AMR (Value Stock) Yahoo (Growth Stock)
    Earnings per Share Losses (2001–2005) 28% avg annual (1998–2006)
    Revenues per Share $129.57 (2000) to $104.95 (2006) 35% avg annual (1999–2006)
    Projected Revenue Growth 3.8% (next five years) 14.5% (2007–2011)
    Projected EPS Growth 9.8% (2007–2012) 27% (2007–2011)
    Price-to-Cash-Flow Ratio
    (based on 2006 cash flows)
    5.0x 30x
    Price-Earnings Ratio
    (based on 2007 proj earnings)
    7.5x 50x
    Value Line Risk Ratings:
    Financial Strength C+ B+
    Safety 5 3
    Price Stability 5 20
    Beta Risk 2.65 1.45

    The Risk Record

    Traditional risk measures support the irrational markets school because they suggest that value stocks are less risky than growth stocks. Three common measures of risk are:

    • Standard deviation: the volatility of actual returns around the average return, with higher volatility indicating higher risk;
    • Beta: the sensitivity of returns to the stock market, with beta greater than 1.0 indicating above-average risk; and
    • Average loss in down years: the lower the average loss, the lower the risk. What does the record show?

    For 1979–2006, compared to the Russell 1000 Growth index, the Russell 1000 Value index had lower standard deviation (13.5% versus 19.6%), lower beta risk (0.79 versus 1.21), and lower average loss in down years (4.2% versus 16.5%).

    However, there are questions as to whether these traditional risk measures adequately reflect the risks of firms in financial distress. Nevertheless, these risk measures suggest that the value premium is primarily attributable to the tendency of investors to misprice stocks in the short run.

    Gleaning Today's "Record"

    The end of last century represents a period where most observers agree after the fact that growth stocks were overvalued. But it is never easy to tell whether a group of stocks are mispriced before the fact.

    For example, let’s look at two stocks today: AMR, the parent company for American Airlines, is a value stock, while Yahoo is a growth stock (summarized in Table 2).

    AMR has experienced a rough go since 9/11. It experienced substantial losses each year from 2001 through 2005. Revenues per share fell from $129.57 per share in 2000 to $104.95 in 2006. Revenues are projected to grow at 3.8% for the next five years.

    This stock has low valuation multiples. Based on 2006 cash flows, its price-to-cash-flow ratio is 5.0 and based on 2007 projected earnings its price-earnings ratio is 7.5. Its projected earnings per share growth from 2007 to 2010–2012 (interpreted at 2011) is 9.8%.

    This is a risky firm that is in financial distress. As indicators of the stock’s high risk, Value Line rates the company’s financial strength as C+, safety as 5 (lowest), price stability at 5 (lowest on a scale of 5 to 100), and beta risk at 2.65, which is more than twice as high as the market portfolio’s beta risk.

    Yahoo has been a tremendous success story in recent years. Its earnings per share increased from $0.07 in 1998 to $0.52 in 2006, or at 28% average annual growth rate. Revenues per share grew at over 35% per year since 1999. Expectations are for continued good times. Earnings and revenues per share are expected to grow at 27% and 14.5% per year through 2009–2011 (interpreted at 2010). The stock is selling at almost 30 times 2006 cash flows and at 50 times projected 2007 earnings. Value Line gives this stock lower risk ratings than AMR for the company’s financial strength (B+), safety (3, average), price stability (20), and beta risk (1.45).

    I do not want to suggest that AMR will beat Yahoo in the next few years; the value-versus-growth literature only makes predictions for portfolios and over long horizons.

    However, these examples bring home some of the debating points. Most investors would feel uneasy about investing in an airline stock, especially after their recent problems. AMR is under financial distress, and financial distress may not be reflected in the traditional measures of risk. It is easy to understand why the average investor would demand a higher expected rate of return before he or she would be willing to invest in AMR.

    Thus the efficient market’s argument that the value stock premium is a reward for bearing risk is not without merit.

    The irrational markets school would counter that portfolios of stocks like Yahoo tend to be overvalued. Investors tend to project continued good times for such glamorous stocks; proponents of the irrational markets school often refer to growth stocks as glamour stocks. This school suggests that portfolios of glamour stocks will generally produce relatively low returns because, as a group, they will not be able to match the expectations for continued strong growth rates in earnings, cash flows, and revenues that are embedded into today’s lofty price-earnings ratios, price-to-cash-flow ratios, and price-to-revenue ratios. In short, this school believes glamour stocks, as a group, have been bid up too high relative to their true prospects, and their future underperformance relative to value stocks will be due to their inability to match their rosy projections.

    Investment Implications

    There are several investment implications from this research.

    Should you tilt your portfolio toward value stocks?

    If the efficient markets school is correct, then you should not tilt your portfolio toward value stocks.

    The long-run value premium is a risk premium, and not a free lunch.

    Over long investment horizons, stocks have beaten bonds, and it is fair to say that stocks have higher expected returns today. But that does not mean that you should invest all your assets in stocks. Most investors combine bonds and stocks in their portfolios to reduce the portfolio’s risk.

    Similarly, most investors combine growth stocks and value stocks so all their stocks are not held in the value basket.

    If the irrational markets school is correct, then you should tilt your portfolio toward value stocks. Most of the long-run value premium is due to the tendency for overvalued stocks to fall in the growth half of a stock index and for undervalued stocks to fall in the value half.

    Note that the irrational markets school advocates a value tilt to the portfolio, but not a complete neglect of growth stocks.

    Do scholars recommend a value tilt?

    The merits of a persistent value tilt remain an area of professional disagreement. In an article titled “Choosing the Right Mix: Lessons From Life Cycle Funds” in the January 2007 issue of the AAII Journal, William Jennings and I examined the recommended portfolios by age at life cycle funds offered by AllianceBernstein, Fidelity, T. Rowe Price and Vanguard. None of these families of mutual funds recommended a persistent value tilt in their life cycle funds. Rather, they recommended style-neutral portfolios with roughly equal allocations to value and growth stocks for investors of all ages. Similarly, John Bogle recommends investing in low-cost, style-neutral, cap-weighted index funds (“‘Enhanced’ Index Funds: Can They Beat the Market?,” May 2007 AAII Journal).

    In “Recommended Readings: Four Books That Cover It All,” (July 2006 AAII Journal), I recommend three general investment books. The books by William Bernstein, Burton Malkiel, and Larry Swedroe each recommend a persistent value tilt. [Past Journal articles can be accessed at in the AAII Journal area.]

    Obviously, there remains professional disagreement on this important issue.

    Would it have been easy for most investors to follow a value tilt?

    The following story illustrates why many investors would have found it hard to follow a value tilt in practice.

    The irrational markets school was especially popular in the early- to mid-1990s after publication of academic articles and a reader-friendly book by Robert Haugen (“The New Finance: Overreaction, Complexity, and Uniqueness,” Pearson Prentice Hall 1992). I know one finance professor who switched his entire stock allocation to value stocks about that time. The evidence looking backward—by necessity, all empirical studies are backward-looking since they must rely on historical returns—was especially strong about that time.

    However, in what is an all-too-familiar occurrence, the successful strategy looking backward, stopped working looking forward.

    From 1994 through 1999, value stocks substantially underperformed growth stocks, with most of that underperformance due to 1998 and 1999 when the Russell 1000 Growth index beat the Russell 1000 Value index by, respectively, 20% and 24%.

    Although value stocks have beaten growth stock for the entire post-1993 period, it is not clear that a typical investor would have stuck with the value strategy, especially after growth stocks clobbered value stocks in 1998 and 1999.

    I have never asked—and dare not ask—the finance professor if he stuck with his convictions through the rough years or bailed out of his extreme value strategy at precisely the wrong time. But I suspect most investors would have bailed out of the value strategy at the wrong time.

    Attaining a Value Tilt

    Not everyone will want to tilt their stock portfolio toward value stocks. But for those who do want such a tilt, you can attain a value-tilted portfolio in at least three ways.

    First, you can fill your portfolio primarily with value stocks.

    Second, you can invest, say 80% to 90% of the U.S. stock portion of the portfolio in a traditional index fund and the other 10% to 20% in one or more traditional value funds. If this approach is taken, the value funds should be the first stock funds to hold in retirement accounts, since they would likely be less tax efficient than the traditional stock index fund.

    Third, you can invest in fundamental-based index funds. [For more on traditional index funds versus fundamental index funds, see the accompanying sidebar starting on page 12.] Or, in a slightly different twist, you might invest the stock portion of your portfolio held in retirement accounts in fundamental-based index funds, where the tax-inefficiency of these index funds should not be a concern.

    Table 3 provides information on two major providers of fundamental index funds.

    Table 3. Two Providers of Fundamental Stock Indexes
    Wisdom Tree offers two sets of fundamental exchange-traded funds (ETFs): one based on firms’ dividends and the other based on earnings.
    Research Affiliates
    Research Affiliates offers fundamental ETFs based on a combination of four fundamental-value metrics: book value of equity, cash flows, sales, and gross dividends. The RAFI U.S. 1000 index (ETF ticker: PRF) may be the best-known fundamental index.


    In my opinion, the evidence suggesting that the value premium is primarily attributable to the tendency for investors to overvalue some growth stocks (and to a lesser extent to undervalue some value stocks) may be the strongest evidence against the efficient markets hypothesis.

    If the value premium is largely attributable to such mispricing and such mispricing continues in the future, then it would pay to tilt the stock portfolio toward value stocks. Based on this evidence, I usually tilt my portfolio toward value stocks, and I have never tilted my portfolio toward growth stocks. Value stocks tend to have low valuation multiples—that is, either they trade at low multiples of earnings, book value, cash flows, and sales per share, or they are high dividend yield stocks. An individual investor could attain a value-tilted portfolio in at least three ways:

    • You could select a portfolio of individual stocks that is tilted toward stocks that meet one or more value criteria;
    • You could invest most of your portfolio in a traditional cap-weighted index fund and the remaining in a value index fund. If this strategy is chosen then the value index funds will likely be the less tax-efficient funds, so they should be the first funds to be held in retirement accounts.
    • You could invest in fundamental-based stock indexes. By their nature, these index funds will trade securities more frequently than traditional index funds. This trading may add value, but it will also result in higher transaction costs, higher expense ratios than traditional indexes, and it will be less tax efficient.
       Index Funds: Traditional vs. Fundamental-Based Indexes

    One of the big arguments that arose after the last bear market debacle is whether index fund holdings should be based on market capitalizations or whether some other weighting method should be used. How does the value premium research affect this question?

    Almost all stock indexes traditionally have been market-capitalization weighted, which means that they invest in each stock based on its market capitalization—that is, price times number of shares of common stock outstanding.

    After the 2000–2002 market plunge, however, a number of professionals argued that this traditional method of weighting stocks in an index resulted in too much emphasis on stocks whose prices were rising rapidly, which in a bull market tend to be growth stocks.

    The Traditional Index Argument

    The major argument for investing in a broad-based market-capitalization-weighted stock index is that it allows an investor to attain a well-diversified portfolio at minimal cost.

    The argument follows the efficient markets school. If markets are perfectly efficient, then cap-weighted indexing is the ultimate investment strategy. In other words, instead of trying to find undervalued securities—which would not exist in perfectly efficient markets—an individual should invest the U.S. stock portion of his portfolio in a low-cost broad-based traditional stock index fund with weightings based on firm size as measured by a stock’s market capitalization.

    The Fundamental-Weighted Index Argument

    What if markets are not particularly efficient? Suppose markets tend to get things right in the long run, but individual stock prices are heavily influenced by investor sentiment in the short run? If stocks are mispriced in the short run, then a traditional index fund may not be optimal because the changes in a stock’s price affect its market capitalization and distort this measure of firm size. Instead, a more optimal index would be one in which the firm size is defined by a more stable measure that is not tied to stock prices, such as total sales, cash flows or book values.

    Table 4 illustrates the issues. It assumes stocks are fairly valued at Time 1, but Stock A becomes overvalued at Time 2 before returning to fair valuation at Time 3. By design, the table assumes that nothing fundamentally changes within either firm except share price.

    First, consider what would happen in a traditional stock index fund. The traditional index fund is a buy-and-hold strategy.

    At Time 1, this fund is invested 60% in Stock A and 40% in Stock B, which reflects the $6 billion market cap of Stock A and $4 billion market cap of Stock B. When Stock A’s price rises from $12 to $15, the portfolio’s value rises to $11.5 billion with 65.2% (or $7.5 billion/$11.5 billion) invested in Stock A. When Stock A’s price falls back to $12, the value of the portfolio returns to $10 billion with 60% again invested in Stock A.

    Because the traditional index fund holdings are based on market capitalizations, no trades need to be made even though the prices change—the index automatically rebalances itself. The traditional index fund is tax efficient because the index manager did not buy or sell shares and, therefore, did not realize capital gains or losses that must be passed through to investors. However, a stock with an increasing stock price will become a larger percentage of the total holdings, as with Stock A when its price rose in Time 2.

    Next, consider a fundamental-based index fund that bases the stock weights on sales.

    In this example, assume Stock A has 60% of the combined sales of Stocks A and B, and the sales at the two firms do not change. At Time 1, it has the same initial portfolio as the traditional index fund. At Time 2, when Stock A’s price rises from $12 to $15, the value of the portfolio rises to $11.5 billion. Since sales at the two firms have not changed, this manager would have to rebalance the portfolio back to 60%Stock A and 40% Stock B by selling 40 million shares of Stock A and investing the proceeds into 60 million shares of Stock B. After rebalancing, this index has 460 million shares each in Stocks A and B and a combined market value of $11.5 billion.

    At Time 3, when Stock A’s price falls back to $12, the value of the portfolio would be $10.12 billion,[460m × ($12) + 460m × ($10)], as shown in the Table (before this portfolio has been rebalanced). At this time, however, the manager would have to rebalance again by selling shares of Stock B and buying shares of Stock A.

    The net result is that the fundamental-based index fund ends up with 1.2% more in portfolio value ($10.12 billion compared to $10 billion for the traditional index fund). However, this result is before considering higher transaction costs and tax implications.

    The Bottom Line: Returns After Taxes and Expenses

    An unfortunate feature of a traditional index fund is that the stocks’ weights change whenever stock prices change—even if the stock price changes do not reflect any fundamental changes within the firm. In this example, the traditional index fund’s weight in Stock A increased from 60% to 65.2% and then fell to 60%.

    The fundamental index ended with 1.2% more wealth, and this additional 1.2% was due to rebalancing when only the stock prices change.

    However, the fundamental index fund is less tax efficient, since the rebalancing results in realized capital gains that have to be distributed to the underlying investors. It also incurs more transaction costs and expenses.

    In backdating tests, fundamental index funds that base stocks’ weights on book values, cash flows, sales or dividends produced higher long-run average returns, often on the order of 2% per year. In practice, when compared to traditional index funds, fundamental-based index funds are essentially value-tilted portfolios. So, you should not be surprised to see higher gross returns on fundamental indexes. However, these higher gross returns do not take into consideration higher mutual fund expense ratios, higher transaction costs, or higher tax bills associated with these more active indexing strategies.

    Some individuals may wish to tilt their stock portfolios toward value stocks. If that is your objective, buying a fundamental index is one way to accomplish this tilt.



    "Fundamental Indexation," by Robert D. Arnott, Jason Hsu, and Philip Moore, Financial Analysts Journal, March/April 2005, pgs. 83-99.

    "Four Pillars of Investing: Lessons for Building a Winning Portfolio," by William J. Bernstein, McGraw-Hill, 2002.

    "'Enhanced' Index Funds: Can They Beat the Market?," by John C. Bogle, AAII Journal, May 2007.

    "The New Finance: Overreaction, Complexity, and Uniqueness," Robert A. Haugen,. Pearson Prentice Hall, 1992.

    "A Random Walk Down Wall Street," 8th Edition, by Burton G. Malkiel, W.W. Norton & Company, 2004.

    "The Only Guide to a Winning Investment Strategy You'll Ever Need," by Larry E. Swedroe, St. Martin Press, 2005.

    "The Successful Investor Today," Larry E. Swedroe, St. Martin's Press, 2003.

    "Contrarian Investment, Extrapolation, and Risk," Josef Lakonishok, Andrei Shleifer, and Robert W. Vishny, Journal of Finance, December 1994, pgs. 1541-1578.

→ William Reichenstein