Value Investing

Updated September, 2006

Value Premium, R.I.P.?

Among most of the world's informed investors, it has been, for quite some time, an article of faith that "value" stocks outperform "growth" stocks. To be sure, there has been extensive disagreement over just how to define "value stocks", and whether the relatively higher return on them represents additional compensation for bearing higher risk (or uncertainty), or is caused by a combination of investor irrationality and barriers to arbitrage (in which case, it represents a free lunch). However, until recently, nobody has questioned the value premium's basic existence. That has now changed, and in a quite convincing manner.

"Asset Pricing" is the term used by academic researchers to describe what many investors call "return forecasting" (obviously, since changes in prices generate returns, the two terms are synonymous). The starting point for our story is a series of recent papers by academic heavyweights that have questioned the underlying rigor (and hence accuracy) of the statistical tests that have been used to establish the value and size premiums' existence. These papers include "Testing Factor Model Explanations of Market Anomalies" by Daniel and Titman, "A Skeptical Appraisal of Asset Pricing Tests" by Lewellen, Nagel and Shanken, and "Investor Psychology and Tests of Factor Pricing Models" by Daniel, Hirshleifer and Subrahmanyam.

It was in this context that Ludovic Phalippou of the University of Amsterdam published "Can Recent Risk-Based Theories Explain the Value Premium?" He began with the observation that a large number of different risk-based asset pricing models all claimed to "explain" the value premium. He then asked, "how is it possible that so many unrelated models offer a valid explanation to one phenomenon?" His hypotheses, like the one used in other papers, was that "the statistical tests employed in these studies lacked power" to discriminate between accurate and inaccurate pricing models. His innovation was to propose a more powerful approach, and to test it in a new way. Rather than dividing a universe of stocks into smaller groups based on their size (market capitalization) and book to market ratios, he used the percentage of institutional ownership and book to market. He found that when presented with these portfolios, all the major rational/risk-based asset pricing models that claim to explain the value premium were rejected.

This strongly supported the findings in 2005 papers by Stefan Nagel ("Short Sales, Institutional Investors, and the Cross-Section of Stock Returns") and Phalippou ("Institutional Ownership and the Value Premium") that what value premium exists is concentrated in a small percentage of stocks that are primarily owned by individual, rather than institutional investors. The latter found that the value premium was statistically significant only in stocks that represented 7% of market capitalization, and decreased significantly as institutional ownership rose. Phalippou concluded that "low institutional ownership stocks are more likely to be priced by an unsophisticated marginal investor", hence, "the value premium is more likely to arise from mispricing by individual investors than it is from compensation for risk." And Nagel noted, "prices of stocks with low institutional ownership underreact to bad cash flow news and overreact to good cash flow news, consistent with the idea that short-sale constraints hold negative opinions off the market for these stocks."

More recently, Tao Shu of the University of Texas has published a paper that further strengthens these conclusions. He begins with the key insight that it is not the compostion of a stock's owners that determines its price, but the composition of the investors who are actually trading a stock. However, in line with the Nagel and Phalippou studies, Shu finds that "the costs of information acquisition play an important role in the determination of trader composition...Stocks with lower fractions of institutional trading volumes [where information acquisition is most costly] underperform stocks with higher fractions of institutional volumes... Moreover, stock market anomalies, such as return momentum...and the value premium are much stronger in stocks with lower fractions of institutional volumes." He concludes "the finding that the value premium is significantly larger in stocks whose trades are dominated by individual investors is consistent with the assumption that the value premium is associated with mispricing rather than risk, and that such mispricing is related to the trading of individual investors."

That individual investors are subject to a range of biases and other cognitive shortcomings that can lead to asset mispricing has been documented in multiple papers and books (see, for example, (Beyond Greed and Fear: Understanding Behavioral Finance and the Psychology of Investing by Hersh Shefrin). Two very recent papers provide further evidence of this sad fact. In "Advertising and Portfolio Choice", Henrik Cronqvist of Ohio State University examines the extent to which advertising by mutual fund companies ($6 billion in the U.S. alone) affects investors' decisions. He finds that fund advertising "steers people into portfolios with lower expected returns (because of higher fees) and higher risk." In "Spam Works: Evidence from Stock Touts and Corresponding Market Activity", Frieder and Zittrain show how boosting penny stocks by sending out spam emails seems to be a depressingly profitable business for those originating these schemes, with the investors who fall for them paying the price. In addition, there is ample evidence competition does not quickly eliminate less-than-perfectly rational investors from financial markets (see "Natural Selection and Financial Markets" by Hongjun Yan of London Business School).

However, the existence of these investors does not automatically mean that they will have an impact on asset prices. Historically, barriers to arbitrage has been the necessary second part of the behavioral explanation for the value premium's existence. Many papers have attempted to identify these barriers. The most common explanation has been the high levels of idiosyncratic (stock-specific) risk associated with high book to market stocks. This is risk that cannot be hedged by selling short a market or sector index; hence, it represents a real potential cost for arbitrageurs who are betting that mispricing will soon be corrected. In some cases, this cost becomes too great for arbitrageurs to pay, and mispricing (and hence the value premium) persists (see, for example, "Arbitrage Risk and the Book-to-Market Anomaly" by Ali, Hwang, and Trombley, "Costly Arbitrage and the Myth of Idiosyncratic Risk" by Jeffrey Pontiff, and "Costly Arbitrage and Idiosyncratic Risk" by Duan, Hu, and McLean).

This naturally leads to the question of whether, in the face of substantial financial market innovations (e.g., the rise of aggressive hedge funds, and the development of wider and deeper derivative markets for managing risk), arbitrage activity has increased in recent years. Two recent papers find that the barriers to arbitrage have indeed broken down, and that as a result, the value premium is disappearing. The first paper is "Do Investors Capture the Value Premium?" by Houge and Loughran. They find that over a long period, there is virtually no difference between average annual returns on small cap growth and small cap value mutual funds. The second is by Phallipou, In "Arbitrageurs and a Declining Value Premium," he finds that the value premium significantly decreased between 1963 and 2004, most likely because of an increase in arbitrage activity, particularly in those stocks with relatively lower idiosyncratic volatility. Most important, since 1984, the average value premium has not been statistically different from zero. Phalippou concludes that, on average, "the choice between value and growth funds did not matter much in the past, and should matter even less in the future."

And so it seems that, like the small cap premium before it, widespread recognition of the value premium's existence has led to its elimination, except in those cases where the potential cost of arbitraging it away is higher than the expected gain. That this has occurred should not come as a surprise - it is exactly what one would expect in a fiercely competitive market. Nor does it imply that there are no other sources of alpha still available to skilled active managers. Indeed, the rapid growth of complex quantitative alpha strategies, and the continued success of skilled fundamental stock pickers suggest that markets are still sufficiently inefficient to enable some skilled managers to succeed. As always, the truly daunting challenges lie in identifying these uniquely talented people and teams, and, perhaps even more difficult, having the courage to stick with them through the ups and downs that all successful strategies inevitably experience

Overview

Let's start with some basics. Generally speaking, people won't buy a stock unless they expect its price to go up. In this sense, all investing could be called "value investing", because nobody rationally buys a stock today if they think it will be less valuable in the future. There are, however, two broad schools of thought about how investors arrive at their expectation that the price of a stock will increase in the future.

The simplest reason a person might reasonably expect the price of a stock to increase is because he or she expects a lot of other people to buy it. The technical term for this is "momentum". As we have previously discussed, historical returns data seems to confirm that momentum investing works, at least over short periods of time (e.g., there is a statistically measurable tendency for a stock price that has risen in one month to also rise in the next one). However, investing one's money solely on the basis of a relationship in the historical data risks confusing correlation with causation, and losing money as a result. You also need a theory that explains what you observe in the historical data. As we have previously written, in the case of momentum investing, two different theories might plausibly explain the momentum effect. First, people may obtain different types of information (e.g., positive and negative information about a stock) at different times (e.g., because one is a small investor instead of a major portfolio manager). Alternatively, people may inefficiently process the new information they receive (e.g., underreacting to information which conflicts with their current opinion about a stock). In our view, these two theories in combination seem to be a plausible explanation for the short term momentum effects one observes in historical returns data for different asset classes.

The second reason a person might expect the price of a stock to increase is because he or she has conducted a "fundamental analysis" of the issuing company, and as a result believes that the current stock price is below what it is actually worth. Here's a familiar example. The current dividend on the FTSE Australia Index is 7.39. The real risk free interest rate in Australia is 3.24%. We further assume that the "correct" equity risk premium is 4.0% (that is, the additional amount of return above the risk free rate that we require in exchange for taking on the additional risk inherent in investing in equities instead of government bonds). Finally, we also assume that the dividend will grow by 4.3% per year in the future (which reflects expected labor force growth of .8%, and labor productivity growth of 3.5% per year). The formula for calculating the current value of the Index (or any stock for that matter) is Dividend divided by [(Real Risk Free Interest Rate plus Equity Risk Premium) less (Labor Force Growth plus Labor Productivity Growth)]. In numbers, it looks like this: 7.39/[(3.24%+4.00%)-(0.8%+3.5%)]. This reduces to 7.39/2.94%, which equals 251.36. As the current value of the FTSE Australia Index is 194.58, a "fundamental investor" might reasonably conclude that the index is currently undervalued, and that its price will therefore increase in the future.

Of course, this raises another good question: why would an investor rationally believe that he or she had a more accurate fundamental estimate of the true value of a stock than that held by other investors? Broadly speaking, there are three possible reasons for holding such a belief. First, our investor may believe that the information he or she has about the stock in question is superior to that available to most other investors. For example, in our Australian model, we might believe that we have a better estimate than most other investors of either the long term equity risk premium and/or the long term rate of labor productivity growth. Second, we might believe that while all investors basically have access to the same information, the model we are using to make sense of it (that is, our valuation model) is superior to the models used by most other investors (e.g., because our growth estimate takes into account both labor force growth and labor productivity growth). Third, we may believe that most other investors are subject to behavioral biases, that somehow don't affect us to the same degree (e.g., we may believe that others will systematically react more slowly than we will to news about Australia's future rate of labor productivity growth).

However, unlike the case of momentum, theories about the effectiveness of "fundamental investing" are more difficult to test with historical returns data. While it is easy to see whether or not a stock's price went up or down, there is no way to detect in the publicly available data what a wide range of different investors were originally thinking about its future value when they bought it. This basic fact has caused financial researchers to look for publicly available proxies for investors' private views about the fairness of companies' current market valuations.

Some researchers have tried to estimate future stock returns using economic factors that are widely available and theoretically easy to link to the basic stock valuation model. For example, in "Economic Forces and the Stock Market" (a working paper by Chen, Roll, and Ross), the authors try to link future stock returns to industrial production, the spread between short and long term government bond rates (the "maturity premium"), and the spread between the rates on high and low credit quality corporate bonds (the "default premium"). These variables are thought to be proxies for expected changes in cash flows as well as expected changes in required rates of return (e.g., declining industrial production and an increasing maturity premium signal an oncoming recession and decline in cash flows, while rising maturity and default premiums signal increases in the required rate of return). The results of this straightforward approach unfortunately were mixed at best.

Rather than using economic factors, an alternative approach tried to use historical returns data to predict future stock returns. The earliest and most famous example of this approach is the "Capital Asset Pricing Model" or CAPM. The theory behind this model is straightforward: since diversification eliminates the significance of company-specific risks (which offset each other in a large portfolio), the only risk factor that matters when forecasting future returns is the extent to which the return on a stock varies with the return on the overall market. This relationship is called the stock's "beta": if it is less than one, the return on a stock varies less than the return on the market, and if it is greater than one, it varies by more than the market. To forecast the future return on a company's stock, you simply estimate the future return on the market (defined as the current risk free government bond rate plus the appropriate equity market risk premium), and then multiply this times the stock's beta.

Unfortunately, the future returns forecast by the CAPM model didn't always turn out to be accurate (and gave rise to many journal articles on "the death of beta"). In their search for explanations for these "anomalies" (which, in economist speak, is anything your repeatedly encounter in reality that doesn't match the predictions of your model), researchers identified a number of systematic (that is, predictable) forecasting errors that occurred when using the CAPM approach. In their seminal papers ("The Cross Section of Expected Stock Returns", "Common Risk Factors in the Returns on Stocks and Bonds", and "Size and Book-to-Market Factors in Earnings and Returns"), Eugene Fama and Kenneth French showed how future returns on a stock could be predicted using not one, but three factors. Like the CAPM, the first of these factors was the expected return on the market as a whole. In addition to this, however, they also used risk premiums that were based on the difference between the return on small capitalization stocks less the return on large capitalization stocks (known as SML), and the difference between stocks with high book/market ratios and low book/market ratios (known as HML).

For better or worse, Fama and French's insights have now become widely used (if not widely understood) by many investors. The ratio of the book value of a company's equity (that is, the value of its assets less the value of its liabilities) to its market value (that is, the price of its stock times the number of shares outstanding) is known by many names, including (confusingly, of course) "market to book", "book to market", or "price to book". People who buy shares in companies which have high market to book ratios (or low book to market ratios, just to be confusing) have become known as "growth investors", while those that buy shares in companies with low market to book ratios (or high book to market ratios) are called "value investors."

Broadly speaking, in the popular imagination companies with high market/book ratios are assumed to have stock prices that are rising quickly, while those with low market/book ratios are assumed to represent "better value." A couple of moments thought shows that these assumptions can easily be inaccurate. Even if a company's stock price has been rising rapidly, it may still be fundamentally undervalued, depending on the assumptions you use in your valuation model. Nor is a stock with a high market/ book necessarily a momentum stock: a big write off at a company heading toward bankruptcy can temporarily produce a high market/book ratio without any increase in trading volume and price momentum in the company's shares. Similarly, a company with a low market/book might still be overvalued. Alternatively, the announcement of favorable news about the company may trigger increased trading volume and price momentum in its shares.

At this point, careful readers will be saying to themselves, "these growth and value concepts have no relationship to the two basic theories of why someone might buy a stock today in the expectation that its price will increase in the future." Or, perhaps more accurately, "my cousin Charley has no clue what he's talking about!!" Exactly. Enormous confusion has been caused as "growth" has become synonymous (in too many people's minds) with momentum investing, and "value" has become synonymous with fundamental investing.

Only in the case of the anglo-saxon economies (Australia, Canada, the UK, and the USA) does it appear that there is a reasonably high degree of correspondence between changes in the size of the annual return premium on value stocks and changes in the rate of economic growth. And even this conclusion is somewhat questionable, given the differences between some of the correlations involved.

In summary, the rational camp makes a reasonably strong, but not completely convincing case that the value premium simply reflects compensation for additional risk, and therefore should be expected to persist into the future.

The arguments of the behavioral economics camp are grounded in two fundamental assumptions. First, we as human beings face cognitive resource constraints -- when confronting a problem or decision, our attention, memory, and processing power are not unlimited. We naturally employ two strategies to conserve our limited cognitive capacity. First, we use thinking short cuts (also known as heuristics). For example, when making a decision, we will often use information that is readily available, rather than expend cognitive resources trying to identify the information we need, and then going out to find it. Similarly, in order to conserve our cognitive capacity, we tend to resist actively searching for information which contradicts the views we already hold. We also tend to underweight contradictory information if we receive it. As the old saying goes, it takes much more information to change an opinion that it does to form one in the first place.

The second way we conserve our limited cognitive resources is through the use of our emotions. They help us avoid situations that potentially could require heavy use of our limited attention, memory, and processing capacity. For example, we prefer to avoid losses, because they bother us more than gains make us happy. Similarly, we tend to avoid ambiguity because it causes us more anxiety than certainty. However, the use of heuristics and emotions is not without a cost. While they help us to conserve cognitive resources, they also tend to bias our estimates and decisions (that is, they lead to results that are different from those that one would expect from a "perfectly rational" decisionmaker).

These decision biases wouldn't be much of a problem if we could easily recognize and compensate for them. Unfortunately, the second fundamental assumption of the behavioral economics camp shows why this is much easier said than done: most of us are overconfident in the accuracy of the estimates and decisions we make. A number of writers have theorized that both of these traits -- cognitive resource conservation and overconfidence -- evolved as useful adaptations to the environment faced by primitive human beings (see, for example, "One the Evolution of Overconfidence and Entrepreneurs" by Bernardo and Welch, or "A Model of Overconfidence" by Bruce Weinberg). As such, they are "hard-wired" into our systems, and very difficult for us to change.

The behavioral theories behind the value premium are thoroughly covered in four papers: "A Unified Theory of Underreaction, Momentum Trading, and Overreaction in Asset Markets" by Hong and Stein; "A Model of Investor Sentiment" by Barberis, Shleifer, and Vishny; "Covariance Risk, Mispricing, and the Cross Section of Equity Returns" by Daniel, Hirshliefer, and Subrahamanyam; and "Prospect Theory and Asset Prices" by Barberis, Huang, and Santos. Distilled into a few sentences, the essence of the behavioral camp's argument is that investors underreact to new information which contradicts the views that they hold about a stock. For example, the price of a stock that people view as having good growth prospects will respond only slowly to the arrival of negative news that undermines this view. As a result, it will tend to overshoot its fundamental value. Similarly, the price of a stock that is viewed as having poor prospects tends to respond slowly to the receipt of good news. As a result, its market price may be well below its fundamental value. This tendency to underreact generates both momentum profits (in the first case) and value profits (in the second case). It also explains why the historical risk/return ratio on value stocks is superior to that on growth stocks. So the behavioral camp's views sound plausible in theory. But is there additional evidence?

In their paper "New Paradigm or Same Old Hype in Equity Investing", Chan, Karceski, and Lakonishok find that behavioral factors were largely responsible for the high returns on large cap growth stocks in the late 1990s. In "Book to Market Equity, Distress Ris, and Stock Returns", Griffin and Lemon demonstrate that distress risk alone can't fully explain the difference in returns between high and low book/market firms. They conclude that evidence of mispricing exists. Similarly, in "Do Stock Prices Deviate From Their Fundamental Values?", Anderson, Darrat, and Zhong find evidence of irrational investor behavior. Finally, in "The Price Impact and Survival of Irrational Traders", Kogan, Ross, Wang, and Westerfield show that it is not always possible for rational investors to exploit the mistakes of irrational investors (that is, to arbitrage away their profits, and drive them from the market). They also show how the presence of just a few irrational traders can have a large impact on stock prices.

At this point, the logic behind the behavioral arguments is almost compelling. But not quite. An important caution is raised by Mark Rubinstein in his paper "Rational Markets: Yes or No? The Affirmative Case". He begins by pointing out that "the existence of temporary predictable patterns in security returns isn't precluded in rational markets… given that saving is just delayed consumption, and given that the growth in aggregate consumption over time isn't random, we should not expect market returns to be random either…Moreover, other factors, such as short sales constraints, liquidity fluctuations, uncertainty about other investors' beliefs, and uncertainty about true values of key valuation model variables can also cause periods of predictability in market returns."

What is precluded in reasonably rational, reasonably efficient markets is the ability to profitably exploit these temporary return predictabilities. "Profitable trading strategies are by their nature self-destructive: they have a tendency to move prices against themselves as they are exploited. Eventually, they are discovered and eliminated from overuse by other investors." As proof of this proposition, he notes "the continuing underperformance over time of actively managed funds versus index funds." Clearly, active fund managers have very strong economic incentives to develop investment strategies based on the exploitation of return predictabilities . That they haven't demonstrated a consistent ability to do so is further evidence that markets are basically efficient, and that anomalies like the value premium are difficult to profitably exploit.

On balance, it appears to us that both camps' arguments make sense, and neither is wholly right or wrong about the value premium. Based on the evidence we have seen, we conclude that while most of the value premium is probably explained by higher risk, the superior risk/return tradeoff versus growth stocks probably reflects the existence of behavioral factors and market inefficiencies. We further suspect that the wide fluctuations in the annual size of the value premium reflect constant change in the relative weights applied to rational and behavioral factors. Given this, we would only recommend tilting toward broad based value indexes if a person is a long term investor (as the probability of actually realizing the value premium is high only in the long term) with a strong stomach (as the anxiety caused by watching growth indexes outperform value indexes over some periods may be too much for some people to take). If you don't meet these requirements, we believe that the best course of action is to invest in broad based equity indexes, and avoid taking "value" (or "growth"!) tilts.

Of course, this raises another good question: why would an investor rationally believe that he or she had a more accurate fundamental estimate of the true value of a stock than that held by other investors? Broadly speaking, there are three possible reasons for holding such a belief. First, our investor may believe that the information he or she has about the stock in question is superior to that available to most other investors. For example, in our Australian model, we might believe that we have a better estimate than most other investors of either the long term equity risk premium and/or the long term rate of labor productivity growth. Second, we might believe that while all investors basically have access to the same information, the model we are using to make sense of it (that is, our valuation model) is superior to the models used by most other investors (e.g., because our growth estimate takes into account both labor force growth and labor productivity growth). Third, we may believe that most other investors are subject to behavioral biases, that somehow don't affect us to the same degree (e.g., we may believe that others will systematically react more slowly than we will to news about Australia's future rate of labor productivity growth).

However, unlike the case of momentum, theories about the effectiveness of "fundamental investing" are more difficult to test with historical returns data. While it is easy to see whether or not a stock's price went up or down, there is no way to detect in the publicly available data what a wide range of different investors were originally thinking about its future value when they bought it. This basic fact has caused financial researchers to look for publicly available proxies for investors' private views about the fairness of companies' current market valuations.

Some researchers have tried to estimate future stock returns using economic factors that are widely available and theoretically easy to link to the basic stock valuation model. For example, in "Economic Forces and the Stock Market" (a working paper by Chen, Roll, and Ross), the authors try to link future stock returns to industrial production, the spread between short and long term government bond rates (the "maturity premium"), and the spread between the rates on high and low credit quality corporate bonds (the "default premium"). These variables are thought to be proxies for expected changes in cash flows as well as expected changes in required rates of return (e.g., declining industrial production and an increasing maturity premium signal an oncoming recession and decline in cash flows, while rising maturity and default premiums signal increases in the required rate of return). The results of this straightforward approach unfortunately were mixed at best.

Rather than using economic factors, an alternative approach tried to use historical returns data to predict future stock returns. The earliest and most famous example of this approach is the "Capital Asset Pricing Model" or CAPM. The theory behind this model is straightforward: since diversification eliminates the significance of company-specific risks (which offset each other in a large portfolio), the only risk factor that matters when forecasting future returns is the extent to which the return on a stock varies with the return on the overall market. This relationship is called the stock's "beta": if it is less than one, the return on a stock varies less than the return on the market, and if it is greater than one, it varies by more than the market. To forecast the future return on a company's stock, you simply estimate the future return on the market (defined as the current risk free government bond rate plus the appropriate equity market risk premium), and then multiply this times the stock's beta.

Unfortunately, the future returns forecast by the CAPM model didn't always turn out to be accurate (and gave rise to many journal articles on "the death of beta"). In their search for explanations for these "anomalies" (which, in economist speak, is anything your repeatedly encounter in reality that doesn't match the predictions of your model), researchers identified a number of systematic (that is, predictable) forecasting errors that occurred when using the CAPM approach. In their seminal papers ("The Cross Section of Expected Stock Returns", "Common Risk Factors in the Returns on Stocks and Bonds", and "Size and Book-to-Market Factors in Earnings and Returns"), Eugene Fama and Kenneth French showed how future returns on a stock could be predicted using not one, but three factors. Like the CAPM, the first of these factors was the expected return on the market as a whole. In addition to this, however, they also used risk premiums that were based on the difference between the return on small capitalization stocks less the return on large capitalization stocks (known as SML), and the difference between stocks with high book/market ratios and low book/market ratios (known as HML).

For better or worse, Fama and French's insights have now become widely used (if not widely understood) by many investors. The ratio of the book value of a company's equity (that is, the value of its assets less the value of its liabilities) to its market value (that is, the price of its stock times the number of shares outstanding) is known by many names, including (confusingly, of course) "market to book", "book to market", or "price to book". People who buy shares in companies which have high market to book ratios (or low book to market ratios, just to be confusing) have become known as "growth investors", while those that buy shares in companies with low market to book ratios (or high book to market ratios) are called "value investors."

Broadly speaking, in the popular imagination companies with high market/book ratios are assumed to have stock prices that are rising quickly, while those with low market/book ratios are assumed to represent "better value." A couple of moments thought shows that these assumptions can easily be inaccurate. Even if a company's stock price has been rising rapidly, it may still be fundamentally undervalued, depending on the assumptions you use in your valuation model. Nor is a stock with a high market/ book necessarily a momentum stock: a big write off at a company heading toward bankruptcy can temporarily produce a high market/book ratio without any increase in trading volume and price momentum in the company's shares. Similarly, a company with a low market/book might still be overvalued. Alternatively, the announcement of favorable news about the company may trigger increased trading volume and price momentum in its shares.

At this point, careful readers will be saying to themselves, "these growth and value concepts have no relationship to the two basic theories of why someone might buy a stock today in the expectation that its price will increase in the future." Or, perhaps more accurately, "my cousin Charley has no clue what he's talking about!!" Exactly. Enormous confusion has been caused as "growth" has become synonymous (in too many people's minds) with momentum investing, and "value" has become synonymous with fundamental investing.

Only in the case of the anglo-saxon economies (Australia, Canada, the UK, and the USA) does it appear that there is a reasonably high degree of correspondence between changes in the size of the annual return premium on value stocks and changes in the rate of economic growth. And even this conclusion is somewhat questionable, given the differences between some of the correlations involved.

In summary, the rational camp makes a reasonably strong, but not completely convincing case that the value premium simply reflects compensation for additional risk, and therefore should be expected to persist into the future.

The arguments of the behavioral economics camp are grounded in two fundamental assumptions. First, we as human beings face cognitive resource constraints -- when confronting a problem or decision, our attention, memory, and processing power are not unlimited. We naturally employ two strategies to conserve our limited cognitive capacity. First, we use thinking short cuts (also known as heuristics). For example, when making a decision, we will often use information that is readily available, rather than expend cognitive resources trying to identify the information we need, and then going out to find it. Similarly, in order to conserve our cognitive capacity, we tend to resist actively searching for information which contradicts the views we already hold. We also tend to underweight contradictory information if we receive it. As the old saying goes, it takes much more information to change an opinion that it does to form one in the first place.

The second way we conserve our limited cognitive resources is through the use of our emotions. They help us avoid situations that potentially could require heavy use of our limited attention, memory, and processing capacity. For example, we prefer to avoid losses, because they bother us more than gains make us happy. Similarly, we tend to avoid ambiguity because it causes us more anxiety than certainty. However, the use of heuristics and emotions is not without a cost. While they help us to conserve cognitive resources, they also tend to bias our estimates and decisions (that is, they lead to results that are different from those that one would expect from a "perfectly rational" decisionmaker).

These decision biases wouldn't be much of a problem if we could easily recognize and compensate for them. Unfortunately, the second fundamental assumption of the behavioral economics camp shows why this is much easier said than done: most of us are overconfident in the accuracy of the estimates and decisions we make. A number of writers have theorized that both of these traits -- cognitive resource conservation and overconfidence -- evolved as useful adaptations to the environment faced by primitive human beings (see, for example, "One the Evolution of Overconfidence and Entrepreneurs" by Bernardo and Welch, or "A Model of Overconfidence" by Bruce Weinberg). As such, they are "hard-wired" into our systems, and very difficult for us to change.

The behavioral theories behind the value premium are thoroughly covered in four papers: "A Unified Theory of Underreaction, Momentum Trading, and Overreaction in Asset Markets" by Hong and Stein; "A Model of Investor Sentiment" by Barberis, Shleifer, and Vishny; "Covariance Risk, Mispricing, and the Cross Section of Equity Returns" by Daniel, Hirshliefer, and Subrahamanyam; and "Prospect Theory and Asset Prices" by Barberis, Huang, and Santos. Distilled into a few sentences, the essence of the behavioral camp's argument is that investors underreact to new information which contradicts the views that they hold about a stock. For example, the price of a stock that people view as having good growth prospects will respond only slowly to the arrival of negative news that undermines this view. As a result, it will tend to overshoot its fundamental value. Similarly, the price of a stock that is viewed as having poor prospects tends to respond slowly to the receipt of good news. As a result, its market price may be well below its fundamental value. This tendency to underreact generates both momentum profits (in the first case) and value profits (in the second case). It also explains why the historical risk/return ratio on value stocks is superior to that on growth stocks. So the behavioral camp's views sound plausible in theory. But is there additional evidence?

In their paper "New Paradigm or Same Old Hype in Equity Investing", Chan, Karceski, and Lakonishok find that behavioral factors were largely responsible for the high returns on large cap growth stocks in the late 1990s. In "Book to Market Equity, Distress Ris, and Stock Returns", Griffin and Lemon demonstrate that distress risk alone can't fully explain the difference in returns between high and low book/market firms. They conclude that evidence of mispricing exists. Similarly, in "Do Stock Prices Deviate From Their Fundamental Values?", Anderson, Darrat, and Zhong find evidence of irrational investor behavior. Finally, in "The Price Impact and Survival of Irrational Traders", Kogan, Ross, Wang, and Westerfield show that it is not always possible for rational investors to exploit the mistakes of irrational investors (that is, to arbitrage away their profits, and drive them from the market). They also show how the presence of just a few irrational traders can have a large impact on stock prices.

At this point, the logic behind the behavioral arguments is almost compelling. But not quite. An important caution is raised by Mark Rubinstein in his paper "Rational Markets: Yes or No? The Affirmative Case". He begins by pointing out that "the existence of temporary predictable patterns in security returns isn't precluded in rational markets… given that saving is just delayed consumption, and given that the growth in aggregate consumption over time isn't random, we should not expect market returns to be random either…Moreover, other factors, such as short sales constraints, liquidity fluctuations, uncertainty about other investors' beliefs, and uncertainty about true values of key valuation model variables can also cause periods of predictability in market returns."

What is precluded in reasonably rational, reasonably efficient markets is the ability to profitably exploit these temporary return predictabilities. "Profitable trading strategies are by their nature self-destructive: they have a tendency to move prices against themselves as they are exploited. Eventually, they are discovered and eliminated from overuse by other investors." As proof of this proposition, he notes "the continuing underperformance over time of actively managed funds versus index funds." Clearly, active fund managers have very strong economic incentives to develop investment strategies based on the exploitation of return predictabilities . That they haven't demonstrated a consistent ability to do so is further evidence that markets are basically efficient, and that anomalies like the value premium are difficult to profitably exploit.

On balance, it appears to us that both camps' arguments make sense, and neither is wholly right or wrong about the value premium. Based on the evidence we have seen, we conclude that while most of the value premium is probably explained by higher risk, the superior risk/return tradeoff versus growth stocks probably reflects the existence of behavioral factors and market inefficiencies. We further suspect that the wide fluctuations in the annual size of the value premium reflect constant change in the relative weights applied to rational and behavioral factors. Given this, we would only recommend tilting toward broad based value indexes if a person is a long term investor (as the probability of actually realizing the value premium is high only in the long term) with a strong stomach (as the anxiety caused by watching growth indexes outperform value indexes over some periods may be too much for some people to take). If you don't meet these requirements, we believe that the best course of action is to invest in broad based equity indexes, and avoid taking "value" (or "growth"!) tilts.