Should You Invest in "Value Indexes"?

"Value" and "Growth" investing are two of the world's most frequently mentioned, yet poorly understood investment concepts. We extensively discussed our views about growth investing in our December, 2001 issue. This month, we're going to take an equally hard look at value investing.

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.

While this insight alone is no doubt satisfying to many of us, we are still left with the question of what to do when faced with Fama and French's key findings. Based on reported returns data, it is unarguable that over long periods of time, the returns on high book/market (value) stocks are greater than those on low book/market (growth) stocks. For example, the following table shows the average annual difference between the returns on "value" stocks contained in the Morgan Stanley Capital International Indexes for different countries versus those on "growth" stocks over the twenty five years between 1976 and 2000. While value stocks have higher returns over the long term, the high standard deviations show that this is certainly not the case every year.

The key question we have to ask ourselves is whether or not this historical data justifies making a tilt toward investing in value oriented equity indexes instead of broad market equity indexes.

However, before we can answer this question, we have to address two other issues. First, we need to develop a clear understanding of why value stocks have earned better risk adjusted returns than growth stocks in the past. Once we have done this, our second task is to ask ourselves whether or not in light of this theory we can reasonably expect the value premium to continue to exist in the future.

Unfortunately, the theoretical basis for the existence of the value premium is currently one of the most hotly debated issues in academic finance. Broadly speaking, the different views break down into two camps. The "rational economics" camp believes that markets are basically efficient, and that the value premium exists because value stocks are riskier than growth stocks. The "behavioral economics" camp believes that markets are inefficient because many investors are less than perfectly rational. In their view, the value premium is an example of the mispricing this causes. Because this issue is critical, let's take a closer look at some of the key arguments put forth by these two camps.

The key challenge faced by the rationalists is defining the nature of the risk or risks for which the value premium represents compensation. In "The Value Spread" (by Cohen, Polk, and Vuolteenaho), the authors start with the valuation model we have already described, and note that "both the required rate of return and the expected rate of cash flow growth play a role in determining the market price of a firm's stock, and thus its book/market ratio." They then undertake an analysis to see what percentage of the variation between high and low book/market firms is caused by variation in their expected rates of return, and what percentage is caused by variation in their expected rates of cash flow growth. They find that the former accounts for only 20% to 25% of the variation in book/market ratios, while the latter accounts for 75% to 80%. In other words, at the level of individual stocks, a high book/market ratio (that is, characterization as a value stock) has much more to do with lower expected cash flow growth than it does with a higher required rate of return. On the other hand, they also find that when individual stocks are aggregated together (e.g., into an index), differences in cash flow growth expectations for individual stocks tend to cancel each other out, and most variation in the index level book/market ratio is caused by variation in the required rate of return. This leads them to conclude that "if the cross section of book/market ratios is largely driven by rational differences in cash flow growth expectations, the conclusion that aggregate book/market ratios are exclusively driven by irrational investor sentiment is perhaps premature."

In "An Empirical Investigation of Risk and Return Under Capital Market Imperfections", Hahn and Lee make a similar point. Their research found that bond maturity and default premiums were just about as good as Fama and French's size and value premiums at predicting future asset prices. Like Chen, Roll, and Ross, they see these factors as proxies for changing expectations about future economic growth (which would affect companies' cash flows) and the risks that they face. Specifically, they cite the example of two firms with equal book values and equal amounts of debt. One firm, has a much higher market value than the other one. In effect, this means that the "value" firm (that is, the one with the high book/market ratio) is more highly leveraged than the growth firm (in terms of the ratio of debt to the market value of equity), and therefore faces a greater risk of financial distress (e.g., bankruptcy) if economic growth turns negative.

This point of view is supported by two other research papers. In "News Related to Future GDP Growth as a Risk Factor in Equity Returns", Maria Vassalou found that a factor that captured news about expected future GDP growth, together with an expected market return factor, did as good a job of forecasting future equity returns as Fama and French's three factor model (which, as you recall, uses expected market return, along with size and book/market based risk premiums to estimate future stock returns). In "The Value Premium", Lu Zhang shows how value firms find it harder to reduce their use of capital (and debt) during a downturn relative to growth firms, because value firms tend to use their capital less productively than growth firms. As a result, during an economic downturn value firms find it more difficult than growth firms to sell their assets to raise the funds needed for debt reduction. As a result, value firms are more likely to experience financial problems when the economy is in a recession.

If you accept the rationalists' arguments about the nature of the factors that give rise to the value premium, then it is easy to see why you would expect it to persist in the future: value stocks will continue to be riskier than growth stocks, and will therefore continue to generate higher returns. Unfortunately, the rationalists' arguments aren't quite as convincing as they first appear.

One of the biggest objections to their views is that (as shown above) value stocks appear to offer a better risk/return trade-off than growth stocks. This would not be the case in an efficient market where the higher return on value stocks was simply compensation for a higher level of risk.

Two additional challenges to the rationalists' views are presented in "The Cross Section of Common Stock Returns: A Review of the Evidence and Some New Findings" by Hawawini and Keim. "First, the evidence indicates that the relationship between returns and variables like firm size and the book/market ratio is typically significant only during the month of January. If the premium is compensation for risk, is there reason to believe the market is systematically more risky in January than during the rest of the year? Second, if the size and book/market premia are compensation for additional risks that are priced in the context of an international asset pricing model under conditions of integrated international capital markets, then the premia should be correlated (that is, move together) across markets, in much the same way that the market risk premium is significantly correlated across markets. Inconsistent with this hypothesis, we find that the premia correlations are insignificant across the 17 international markets in our sample. If these premia are uncorrelated across international markets, is it reasonable to characterize them as compensation for risk?"

Similarly, if the value premium in fact represents compensation for being more exposed to the risk of an economic downturn, then you would expect to see roughly similar correlations across countries between the annual size of the value premium (that is, the difference in the year's return on value stocks less the return on growth stocks) and the correlations across countries in their real rates of GDP growth. In other words, the difference in the size of the value premium between two countries should be closely related to the difference in their respective rates of economic growth. As you can see in the table below, we did this analysis, and found that this generally wasn't the case.

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.

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