Contrarian Investment, Extrapolation, and Risk

Transcription

1 THE JOURNAL OF FINANCE * VOL. XLIX, NO. 5 * DECEMBER 994 Contrarian Investment, Extrapolation, Risk JOSEF LAKONISHOK, ANDREI SHLEIFER, ROBERT W. VISHNY* ABSTRACT For many years, scholars investment pressionals have argued that value strategies outperform market. These value strategies call for buying stocks that have low prices relative to earnings, dividends, book assets, or or measures fundamental value. While re is some agreement that value strategies produce higher returns, interpretation why y do so is more controversial. This article provides evidence that value strategies yield higher returns because se strategies exploit suboptimal behavior typical investor not because se strategies are fundamentally riskier. FOR MANY YEARS, SCHOLARS investment pressionals have argued that value strategies outperform market (Graham Dodd (94) Dreman (977)). These value strategies call for buying stocks that have low prices relative to earnings, dividends, historical prices, book assets, or or measures value. In recent years, value strategies have attracted academic attention as well. Basu (977), Jaffe, Keim, Westerfield (989), Chan, Hamao, Lakonishok (99), Fama French (99) show that stocks with high earnings/price ratios earn higher returns. De Bondt Thaler (985, 987) argue that extreme losers outperform market over subsequent several years. Despite considerable criticism (Chan (988) Ball Kothari (989)), ir analysis has generally stood up to tests (Chopra, Lakonishok, Ritter (99)). Rosenberg, Reid, Lanstein (984) show that stocks with high book relative to market values equity outperform market. Furr work (Chan, Hamao, Lakonishok (99) * Lakonishok is from University Illinois, Shleifer is from Harvard University, Vishny is from University Chicago. We are indebted to Gil Beebower, Fischer Black, Stephen Brown, K. C. Chan, Louis Chan, Eugene Fama, Kenneth French, Bob Haugen, Jay Ritter, Ren6 Stulz, two anonymous referees for helpful comments to Han Qu for outsting research assistance. This article has been presented at Berkeley Program in Finance, University California (Berkeley), Center for Research in Securities Prices Conference, University Chicago, University Illinois, Massachusetts Institute Technology, National Bureau Economic Research (Asset Pricing Behavioral Finance Groups), New York University, Pensions Investments Conference, Institute for Quantitative Research in Finance (United States Europe), Society Quantitative Analysts, Stanford University, University Toronto, Tel Aviv University. The research was supported by National Science Foundation, Bradley Foundation, Russell Sage Foundation, National Bureau Economic Research Asset Management Research Advisory Group, National Center for Supercomputing Applications, University Illinois. 54

2 54 The Journal Finance Fama French (99)) has both extended refined se results. Finally, Chan, Hamao, Lakonishok (99) show that a high ratio cash flow to price also predicts higher returns. Interestingly, many se results have been obtained for both United States Japan. Certain types value strategies, n, appear to have beaten market. While re is some agreement that value strategies have produced superior returns, interpretation why y have done so is more controversial. Value strategies might produce higher returns because y are contrarian to "naive" strategies followed by or investors. These naive strategies might range from extrapolating past earnings growth too far into future, to assuming a trend in stock prices, to overreacting to good or bad news, or to simply equating a good investment with a well-run company irrespective price. Regardless reason, some investors tend to get overly excited about stocks that have done very well in past buy m up, so that se "glamour" stocks become overpriced. Similarly, y overreact to stocks that have done very badly, oversell m, se out--favor "value" stocks become underpriced. Contrarian investors bet against such naive investors. Because contrarian strategies invest disproportionately in stocks that are underpriced underinvest in stocks that are overpriced, y outperform market (see De Bondt Thaler (985) Haugen (994)). An alternative explanation why value strategies have produced superior returns, argued most forcefully by Fama French (99), is that y are fundamentally riskier. That is, investors in value stocks, such as high bookto-market stocks, tend to bear higher fundamental risk some sort, ir higher average returns are simply compensation for this risk. This argument is also used by critics De Bondt Thaler (Chan (988) Ball Kothari (989)) to dismiss ir overreaction story. Wher value strategies have produced higher returns because y are contrarian to naive strategies or because y are fundamentally riskier remains an open question. In this article, we try to shed furr light on two potential explanations for why value strategies work. We do so along two dimensions. First, we examine more closely predictions contrarian model. In particular, one natural version contrarian model argues that overpriced glamour stocks are those which, first, have performed well in past, second, are expected by market to perform well in future. Similarly, underpriced out--favor or value stocks are those that have performed poorly in past are expected to continue to perform poorly. Value strategies that bet against those investors who extrapolate past performance too far into future produce superior returns. In principle, this version contrarian model is testable because past performance expectation future performance are two distinct separately measurable characteristics glamour value. In this article, past performance is measured using What we call "naive strategies" are also sometimes referred to as "popular models" (Shiller (984)) "noise" (Black (986)).

3 Contrarian Investment, Extrapolation, Risk 54 information on past growth in sales, earnings, cash flow, expected performance is measured by multiples price to current earnings cash flow. We examine most obvious implication contrarian model, namely that value stocks outperform glamour stocks. We start with simple onevariable classifications glamour value stocks that rely in most cases on measures eir past growth or expected future growth. We n move on to classifications in which glamour value are defined using both past growth expected future growth. In addition, we compare past, expected, future growth rates glamour value stocks. Our version contrarian model predicts that differences in expected future growth rates are linked to past growth overestimate actual future growth differences between glamour value firms. We find that a wide range value strategies have produced higher returns, that pattern past, expected, actual future growth rates is consistent with contrarian model. The second question we ask is wher value stocks are indeed fundamentally riskier than glamour stocks. To be fundamentally riskier, value stocks must underperform glamour stocks with some frequency, particularly in states world when marginal utility wealth is high. This view risk motivates our tests. We look at frequency superior ( inferior) performance value strategies, as well as at ir performance in bad states world, such as extreme down markets economic recessions. We also look at betas stard deviations value glamour strategies. We find little, if any, support for view that value strategies are fundamentally riskier. Our results raise obvious question how higher expected returns on value strategies could have continued if such strategies are not fundamentally riskier? We present some possible explanations that rely both on behavioral strategies favored by individual investors on agency problems plaguing institutional investors. The next section article briefly discusses our methodology. Section II examines a variety simple classification schemes for glamour value stocks based on book-to-market ratio, cash flow-to-price ratio, earnings-to-price ratio, past growth in sales. Section II shows that all se simple value strategies have produced superior returns motivates our subsequent use combinations measures past expected growth. Section III n examines performance value strategies that are defined using both past growth current multiples. These two-dimensional value strategies outperform glamour strategies by approximately 0 to percent per year. Moreover, superior performance value stocks relative to glamour stocks persists when we restrict our attention to largest 50 percent or largest 0 percent stocks by market capitalization. Section IV provides evidence that contrarian strategies work because y exploit expectational errors implicit in stock prices. Specifically, differences in expected growth rates between glamour value stocks implicit in ir

4 544 The Journal Finance relative valuation multiples significantly overestimate actual future growth rate differences. Section V examines risk characteristics value strategies provides evidence that, over longer horizons, value strategies have outperformed glamour strategies quite consistently have done particularly well in "bad" states world. This evidence provides no support for hyposis that value strategies are fundamentally riskier. Finally, Section VI attempts to interpret our findings. I. Methodology The sample period covered in this study is from end April 96 to end April 990. Some our formation strategies require 5 years past accounting data. Consequently, we look at portfolios formed every year starting at end April 968. We examine subsequent performance or characteristics se portfolios for up to 5 years after formation using returns data from Center for Research in Security Prices (CRSP) accounting data from COMPUSTAT (including research file). The universe stocks is New York Stock Exchange (NYSE) American Stock Exchange (AMEX). A key question about this sample is wher results for stock returns are contaminated by significant look-ahead or survivorship bias (Banz Breen (986) Kothari, Shanken, Sloan (99)). The potentially most serious bias is due to COMPUSTAT's major expansion its database in 978, which increased its coverage from,700 NYSE/AMEX firms large National Association Securities Dealers Automated Quotation (NASDAQ) firms to about 6,000 firms. Up to 5 years data were added retroactively for many se firms. As Kothari, Shanken, Sloan (99) point out, this raises prospect a look-ahead bias. Particularly among firms that start out small or low priced, only those that perform well are added to database. Hence, as one goes to lower lower market valuation firms on COMPU- STAT, one finds that population is increasingly selected from firms having good 5-year past performance records. This could potentially explain positive association between low initial valuation future returns. The potential bias toward high returns among low valuation firms is driven by data for first 5 or so years that firm appears on COMPUSTAT. Our results potentially suffer from same bias. However, our methodology differs from those in or recent studies in ways that should mitigate this bias. First, many strategies we focus on require 5 years past data to classify firms before we start measuring returns. This means that we do not use returns for first 5 years that firm appears on COMPU- STAT to evaluate our strategies. But se first 5 years returns is where look-ahead bias in returns is found. Second, we study only NYSE AMEX firms. The major expansion COMPUSTAT largely involved adding We form portfolios in April to ensure that previous year's accounting numbers were available at time formation.

5 Contrarian Investment, Extrapolation, Risk 545 (successful) NASDAQ firms. Finally, we also report results for largest 50 percent firms on NYSE AMEX. The selection bias is less serious among se larger firms (La Porta (99)). Within each our portfolios, we equally weight all stocks compute returns using an annual buy--hold strategy for Years +, +,..., +5 relative to time formation. If a stock disappears from CRSP during a year, its return is replaced until end year with return on a corresponding size decile portfolio. At end each year, portfolio is rebalanced each surviving stock gets same weight. For most our results, we present size-adjusted returns as well as raw returns. To adjust portfolio returns for size, we first identify, for every stock in sample, its market capitalization decile at end previous year. We n construct a size benchmark return for each portfolio as follows. For each stock in portfolio, replace its return in each year with an annual buy--hold return on an equally weighted portfolio all stocks in its size decile for that year. Then equally weight se returns across all stocks in original portfolio. The annual size-adjusted return on original portfolio is n computed as return on that portfolio minus return on that year's size benchmark portfolio. In addition to returns for various portfolios, we compute growth rates multiples for accounting measures such as sales, earnings, cash flow. All accounting variables are taken from COMPUSTAT. Earnings are measured before extraordinary items, cash flow is defined as earnings plus depreciation. Let us illustrate our procedure for computing growth rates using case earnings growth from Year -4 to Year - relative to portfolio formation. We consider portfolio that invests $ in each stock at end Year -4. This fixes proportion each firm owned at /(market capitalization), where market capitalization is calculated at end Year -4. We n calculate earnings per dollar invested that are generated by this portfolio in each Years -4 - as follows. For each stock in portfolio, we multiply total firm earnings by proportion firm owned. We n sum se numbers across all stocks in portfolio for that year divide by number stocks in portfolio. Computing growth rates from se numbers is complicated by fact that earnings ( cash flows) are negative for some entire portfolios for some years. This makes it impossible to compute average earnings growth rate from period -4 to period - as average (-4, -) growth rates across all formation periods since, for some formation periods, base Year -4 earnings is negative. Even without negative earnings years, se year-to-year growth rates are highly volatile because base year's earnings were sometimes very close to zero. This makes year-by-year averaging growth rates unreliable. To deal with se problems, we average Year -4 Year - portfolio Obviously, re is no such problem for sales. However, for symmetry we use same methodology to compute growth rates sales, earnings, cash flow.

6 546 The Journal Finance earnings across all formation periods before computing growth rates. Hence, earnings growth rate from Year -4 to Year - is computed as (AE( ) - AE( 4))/AE( 4) where AE( ) AE( 4) are just averages across all formation periods portfolio earnings in Years In this fashion, we compute growth rate in earnings, cash flow, sales for each portfolio for each year prior postformation. Finally, we compute several accounting ratios, such as cash-flow-to-price earnings-to-price. These ratios are also used to sort individual stocks into portfolios. For se classifications, we consider only stocks with positive ratios cash flow-to-price or earnings-to-price because negative ratios cannot be interpreted in terms expected growth rates.4 For purposes or than classifying individual stocks into portfolios, se ratios are computed for entire equally weighted portfolios ( n averaged across all formation periods) without eliminating individual stocks in portfolio that have negative values for variable. For example, we compute cash flow-toprice ratio for each stock n take average over all stocks in portfolio. This gives us cash flow per $ invested in portfolio where each stock receives same dollar investment. II. Simple Value Strategies Table I, A presents returns on a strategy that has received a lot attention recently (Fama French (99)), namely book-to-market strategy. We divide universe stocks annually into book-to-market (B/M) deciles, where book value is taken from COMPUSTAT for end previous fiscal year, market value is taken from CRSP as market value equity at portfolio formation time. In general, we focus on longhorizon returns ( up to 5 years) on various strategies. The reason for looking at such long horizons is that we are interested in performance alternative investment strategies over horizons suitable for long-term investors. Moreover, we assume annual buy hold periods in contrast to monthly buy hold periods assumed in most previous studies. Because various market microstructure issues as well as execution costs, our procedure produces returns that are closer to those that investors can actually capture. We defer statistical testing return differences across value glamour portfolios to 4While we would ultimately like to say something about future returns firms with negative earnings, not including m here should not be viewed as a source bias. As long as our strategy is feasible, in sense that it constructs portfolios based on characteristics that were observable at time portfolio formation (see our discussion on look-ahead biases), estimated differences in returns should be viewed as an unbiased measure actual return differences between subsets firms that are all part set firms with positive earnings. While a strategy that incorporates negative earnings firms may produce different returns, this is quite a different strategy from one that we are studying. In our regression in Table IV, we do include firms with negative earnings or cash flow by separately including a dummy variable for negative earnings or cash flow along with actual E/P ratio or C/P ratio if numerator is positive.

7 Contrarian Investment, Extrapolation, Risk 547 Table VI where year-by-year return differences are reported starting in April 968 ending in April 990. In A Table I, we present returns for Years through 5 after formation (R through R5), average annual 5-year return (AR), cumulative 5-year return (CR5), size-adjusted average annual 5-year return (SAAR). The numbers presented are - averages across all formation periods in sample. The results confirm extend results established by Rosenberg, Reid, Lanstein (984), Chan, Hamao, Lakonishok (99), Fama French (99). On average over postformation years, low B/M (glamour) stocks have an average annual return 9. percent high B/M (value) stocks have an average annual return 9.8 percent, for a difference 0.5 percent per year. If portfolios are held with limited rebalancing described above, n cumulatively value stocks outperform glamour stocks by 90 percent over Years through 5. Adjusting for size reduces estimated return differences between value glamour stocks somewhat, but differences are still quite large. The size-adjusted average annual return is - 4. percent for glamour stocks.5 percent for value stocks, for a difference 7.8 percent. The natural question is: what is B/M ratio really capturing? Unfortunately, many different factors are reflected in this ratio. A low B/M may describe a company with a lot intangible assets, such as research development (R & D) capital, that are not reflected in accounting book value because R & D is expensed. A low B/M can also describe a company with attractive growth opportunities that do not enter computation book value but do enter market price. Also, a natural resource company, such as an oil producer without good growth opportunities but with high temporary prits, might have a low B/M after an increase in oil prices. A stock whose risk is low future cash flows are discounted at a low rate would have a low B/M as well. Finally, a low B/M may describe an overvalued glamour stock. The point here is simple: although returns to B/M strategy are impressive, B/M is not a "clean" variable uniquely associated with economically interpretable characteristics firms. Arguably, most important such economically interpretable characteristics are market's expectations future growth past growth se firms. To proxy for expected growth, we use ratios various measures pritability to price, so that firms with lower ratios have higher expected growth. The idea behind this is Gordon's formula, which states that P = D(+ )/(r - g), where D(+ ) is next period's dividend, P is current stock price, r is required rate return on stock, g is expected growth rate dividends (Gordon Shapiro (956)). A similar formula applies to cash flow earnings. For example, to get an expression in terms cash flow, we write D(+ ) = pc(+ ), where C(+ ) is next period's cash flow p, payout ratio, is constant fraction cash flow paid out as dividends. We can n write P = pc( + )/(r - g) where growth rate g for dividends is also growth rate for cash flow on assumption that dividends are proportional to cash flow. A similar formula

8 548 The Journal Finance Table I Returns for Decile Portfolios Based on One-Dimensional Classifications by Various Measures Value At end each April between , 0-decile portfolios are formed in ascending order based on B/M, C/P, E/P, GS. B/M is ratio book value equity to market value equity; C/P is ratio cash flow to market value equity; E/P is ratio earnings to market value equity, GS refers to preformation 5-year average growth rate sales. The returns presented in table are averages over all formation periods. Rt is average return in year t after formation, t =. 5. AR is average annual return over 5 postformation years. CR5 is compounded 5-year return assuming annual rebalancing. SAAR is average annual size-adjusted return computed over 5 postformation years. The glamour portfolio refers to decile portfolio containing stocks ranking lowest on B/M, C/P, or E/P, or highest on GS. The value portfolio refers to decile portfolio containing stocks ranking highest on B/M, C/P, or E/P, or lowest on GS. Value A: B/M R, R R R R AR CR SAAR B: C/P R, R R R R AR CR SAAR would apply to earnings but with a different payout ratio. According to se expressions, holding discount rates payout ratios constant,5 a high cash flow-to-price (C/P) firm has a low expected growth rate cash flow, while. a low C/P firm has a high expected growth rate cash flow, similarly for ratio earnings-to-price (E/P).6 While assumption a constant 5In Section V, we compare risk characteristics, hence appropriate discount rates, various portfolios. 6An alternative approach is to use analysts' forecasts to proxy for expectations future growth. This approach is used by La Porta (99).

9 Contrarian Investment, Extrapolation, Risk 549 Table I-Continued Value C: E/P R, R R R R AR CR SAAR Value D: GS R, R R R R AR CR SAAR growth rate for dividends strict proportionality between cash flow (or earnings) dividends are restrictive, intuition behind Gordon's formula is quite general. Differences in C/P or E/P ratios across stocks should proxy for differences in expected growth rates.7 B Table I presents results sorting on ratio C/P. High C/P stocks are identified with value stocks because ir growth rate cash flow is expected to be low, or, alternatively, ir prices are low per dollar cash flow. Conversely, low C/P stocks are glamour stocks. On average, over 5 postformation years, first-decile C/P stocks have a return 9. percent per annum, whereas tenth-decile C/P stocks have an average return 0. percent per annum, for a difference percent. The 5-year cumulative returns are 54. percent 49.4 percent, respectively, for a difference 95. percent. On a size-adjusted basis, difference in returns is 8.8 percent per annum. Sorting on C/P thus appears to produce somewhat 7 We use current cash flow earnings rar than one-period-ahead numbers because we require our investment strategies to be functions observable variables only.

10 550 The Journal Finance bigger differences in returns than sorting on B/M ratios. This is consistent with idea that measuring market's expectations future growth more directly gives rise to better value strategies.8 Anor popular multiple, studied by Basu (977), is E/P. Table I, C presents our results for E/P. On average, over 5 postformation years, first-decile E/P stocks have an average annual return.4 percent tenth-decile E/P stocks have an average annual return 9.0 percent, for a difference 7.6 percent. On a size-adjusted basis, difference in returns is 5.4 percent per annum. Low E/P stocks underperform high E/P stocks by a fairly wide margin, although difference is not as large as that between extreme B/M or C/P deciles. One possible reason for this is that stocks with temporarily depressed earnings are lumped toger with wellperforming glamour stocks in high expected growth/low E/P category. These stocks with depressed earnings do not experience same degree poor future stock performance as glamour stocks, perhaps because y are less overpriced by market. An alternative way to operationalize notions glamour value is to classify stocks based on past growth rar than by expectations future growth. We measure past growth by growth in sales (GS) since sales is less volatile than eir cash flow or earnings, particularly for stocks in extreme portfolios that we are most interested in. Specifically, for each company for each Years -, -,..., -5 prior to formation, we calculate GS in that year. Then, for each year, we rank all firms by GS for that year. We n compute each firm's weighted average rank, giving weight 5 to its growth rank in Year -, weight 4 to its growth rank in Year -, etc. Finally, we form deciles based on each stock's weighted average sales growth rank. This procedure is a crude way to both pick out stocks with consistently high past GS, to give greater weight to more recent sales growth in ranking stocks.9 Table I, D presents results for GS strategy. On average, over 5 postformation years, portfolio firms in lowest decile past sales growth earns an average return 9.5 percent per annum portfolio firms in highest decile earns an average return.7 percent per annum. On a size-adjusted basis average annual abnormal returns are. percent for low GS strategy -.4 percent for high GS strategy. These magnitudes are not as dramatic as those for B/M C/P strategies, neverless spread in returns is sizeable. In this section, we have largely confirmed extended results ors. A wide variety simple value strategies based on classification firms by a single fundamental variable produce very large returns over -year period April 968 to April 990. In contrast to previous work, our 8 La Porta (99) shows that contrarian strategies based directly on analysts' forecasts future growth can produce even larger returns than those based on financial ratios. 9 We have also tried a procedure in which we equally weight ranks for all 5 years past sales growth obtain very similar results.

11 Contrarian Investment, Extrapolation, Risk 55 strategies involve classifying firms based on fundamentals n buying holding for 5 years. In next section, we explore more sophisticated two-dimensional versions se strategies that are designed to correct some misclassification firms inherent in a one-variable approach. For example, low E/P stocks, which are supposedly glamour stocks, include many stocks with temporarily depressed earnings that are expected to recover. The two-dimensional strategies next section are formulated with an eye toward more directly exploiting possible mistakes made by naive investors. III. Anatomy a Contrarian Strategy A. Performance Contrarian Strategies Much psychological evidence indicates that individuals form ir predictions future without a full appreciation mean reversion. That is, individuals tend to base ir expectations on past data for individual case y are considering without properly weighting data on what psychologists call "base rate," or class average. Kahneman Tversky (98, p. 47) explain: One basic principles statistical prediction, which is also one least intuitive, is that extremeness predictions must be moderated by considerations predictability... Predictions are allowed to match impressions only in case perfect predictability. In intermediate situations, which are course most common, prediction should be regressive; that is, it should fall between class average value that best represents one's impression case at h. The lower predictability closer prediction should be to class average. Intuitive predictions are typically nonregressive: people ten make extreme predictions on basis information whose reliability predictive validity are known to be low... To exploit this flaw intuitive forecasts, contrarian investors should sell stocks with high past growth as well as high expected future growth buy stocks with low past growth as well as low expected future growth. Prices se stocks are most likely to reflect failure investors to impose mean reversion on growth forecasts. Accordingly, we define a glamour stock to be a stock with high growth in past high expected future growth. A value stock must have had low growth in past be expected by market to continue growing slowly. In this section, we continue to use high ratios C/P (E/P) as a proxy for a low expected growth rate. Table II, A presents results for strategy that sorts on both GS C/P. Since we are sorting on two variables, sorting stocks into decides on each variable is impractical. Accordingly, we independently sort stocks into three groups (() bottom 0 percent, () middle 40 percent, () top 0 percent) by GS by C/P, n take intersections resulting

12 55 The Journal Finance Table II Returns for Portfolios Based on Two-Dimensional Classifications by Various Measures Value At end each April between , 9 groups stocks are formed. The stocks are independently sorted in ascending order into groups (() bottom 0 percent, () middle 40 percent, () top 0 percent) based on each two variables. The sorts are for 5 pairs variables: C/P GS, B/M GS, E/P GS, E/P B/M, B/M C/P. C/P is ratio cash flow to market value equity; B/M is ratio book value equity to market value equity; E/P is ratio earnings to market value equity; GS refers to preformation 5-year average growth rate sales. The returns presented in table are averages over all formation periods. Rt is average return in year t after formation, t =. 5. AR is average annual return over 5 postformation years. CR5 is compounded 5-year return assuming annual rebalancing. SAAR is average annual size-adjusted return computed over 5 postformation years. Depending on two variables being used for classification, value portfolio eir refers to portfolio containing stocks ranked in top group () on both variables from among C/P, E/P, or B/M, or else portfolio containing stocks ranking in top group on one those variables in bottom group () on GS. The glamour portfolio contains stocks with precisely opposite set rankings. A: C/P GS Value C/P GS R, R R R R AR CR SAAR B: E/P GS Value E/P GS R, R R R R AR CR SAAR

13 Contrarian Investment, Extrapolation, Risk 55 Table IT-Continued C: B/M GS Value B/M GS R, R R R R AR CR SAAR D: E/P B/M E/P B/M Value R, R R R R AR CR SAAR E: B/M C/P B/M C/P Value R, R R R R AR CR SAAR from two classifications. Because classifications are done independently, extreme glamour (high GS, low C/P) value portfolios (low GS, high C/P) contain greater than average numbers stocks, since GS C/P are negatively correlated.

14 554 The Journal Finance In an average postformation year in this sample, glamour portfolio had a return.4 percent, value portfolio had a return. percent, for a difference 0.7 percent per year. Over 5 postformation years, cumulative difference in returns is 00 percent. On a size-adjusted basis, difference in returns is 8.7 percent per year. As Figure illustrates, both C/P GS contribute a great deal explanatory power in se bivariate classifications. For example, low C/P stocks with low past sales growth, which we don't define as glamour stocks, have an average annual future return 6. percent, but low C/P stocks with a high past sales growth, which we do define as glamour stocks, have an average annual future return only.4 percent. Table II, B presents return results for a classification scheme using both past GS E/P ratio. The average annual difference in returns over 5-year period between two extreme portfolios is. percent per year, which cumulatively amounts to 04. percent over 5 years. As with C/P GS, (E/P, GS) strategy produces substantially higher returns than eir E/P or GS strategy alone. For example, among firms with lowest E/P ratios, average annual future return varies from 0.9 percent for firms with highest past sales growth to 8. percent for those with lowest past sales growth. Even more so than for C/P, using an E/P strategy seems to require differentiating between stocks Five-Year Return 0~ ~ _ CR Portfolios 0 ~~~~~~~~~~ /.S Portfolios Figure. Compounded 5-year return for portfolios formed on basis C /P GS. At end each April between , 9 groups stocks are formed. The stocks are independently sorted in ascending order into groups (() bottom 0 percent, () middle 40 percent, () top 0 percent) based on each two variables: cash-flow-to-price (C/P) growth-in-sales (GS). Returns presented are compounded 5-year postformation returns assuming annual rebalancing for se 9 portfolios.

15 Contrarian Investment, Extrapolation, Risk 555 with depressed earnings expected to recover true glamour firms.0 Once this finer classification scheme is used, two-dimensional strategy based on E/P generates returns as high as those produced by twodimensional strategy based on C/P. Table II, C presents results for portfolios classified by B/M GS. The results show that GS has significant explanatory power for returns even after sorting by B/M. For example, within set firms whose B/M ratios are highest, average difference in returns between low sales growth high sales growth subgroups is over 4 percent per year (. versus 6.8 percent). A similar result holds for or two groups sorted by B/M. Note that se results do not appear to be driven by role superimposed GS classification in creating a more precise partition firms by B/M. The B/M ratios across GS subgroups are not very different. s D E Table II present results for (B/M, E/P) (B/M, C/P), respectively. Once again, results confirm usefulness more precise classification schemes. For example, among firms with lowest C/P ratios, future returns vary substantially according to B/M ratios. Future returns vary from 0. percent per year for true glamour firms, to 8.6 percent per year for firms with low ratios C/P but high B/M ratios. Most likely, B/M ratio adds information here because it proxies for past growth, which is useful in conjunction with a measure expected future growth. The results this subsection can be summarized interpreted as follows. First, two-dimensional value strategies, in which firms are independently classified into subgroups according to each two fundamental variables, produce returns on order 0 to percent per year higher than those on similarly constructed glamour strategies over April 968 to April 990 period. Second, results suggest that value strategies based jointly on past performance expected future performance produce higher returns than more ad hoc strategies such as that based exclusively on B/M ratio. B. Do These Results Apply As Well to Large Stocks? Even though we have shown that superior returns to value strategies persist even after adjusting for size, returns on such strategies might still be driven by smaller stocks. Larger firms are greater interest for implementable trading strategies, especially for institutional investors. Larger firms are also more closely monitored, hence might be more efficiently priced. Finally, look-ahead survivorship biases discussed by Banz Breen (986) Kothari, Shanken, Sloan (99) should be less important for larger stocks. Table III presents a summary version Table II for subsample consisting largest 50 percent our NYSE/AMEX firms. The results 0 This probably results from greater year-to-year percentage swings for earnings than for cash flows.

16 556 The Journal Finance are similar to those obtained for whole sample. For example, using (C/P, GS) classification scheme, difference in average annual sizeadjusted returns between value glamour portfolios is 8.7 percent, exactly same as for entire sample. Using (E/P, GS) classification Table III Returns for Portfolios Based on Two-Dimensional Classifications for Largest 50 Percent Stocks At end each April between , 9 subgroups largest 50 percent stocks by market capitalization are formed. The stocks are independently sorted in ascending order into groups (() bottom 0 percent, () middle 40 percent, () top 0 percent) based on each two variables. The sorts are for 5 pairs variables: C/P GS, B/M GS, E/P GS, E/P B/M, B/M C/P. C/P is ratio cash flow to market value equity; B/M is ratio book value equity to market value equity; E/P is ratio earnings to market value equity; GS refers to preformation 5-year average growth rate sales. The returns presented in table are averages over all formation periods. AR is average annual return over 5 postformation years. CR5 is compounded 5-year return assuming annual rebalancing. SAAR is average annual size-adjusted abnormal return computed over 5 postformation years. Depending on two variables being used for classification, value portfolio eir refers to portfolio containing stocks ranked in top group () on both variables from among C/P, E/P, or B/M, or else portfolio containing stocks ranking in top group on one those variables in bottom group () on GS. The glamour portfolio contains stocks with precisely opposite set rankings. A: C/P GS Value C/P GS AR CR SAAR B: E/P GS Value E/P GS AR CR SAAR C: B/M GS Value B/M GS AR CR SAAR

17 Contrarian Investment, Extrapolation, Risk 557 Table III-Continued D: E/P B/M E/P B/M Value AR CR SAAR E: B/M C/P B/M C/P Value AR CR SAAR scheme, this difference is 8. percent per year, compared to 7.7 percent per year for entire sample. Raw return differences between value glamour portfolios are slightly lower for large-firm subsample because extra return to value firms from ir smaller average size is not present in that subsample. Value glamour firms are essentially same size in large firm subsample. We have also done analysis for largest 0 percent stocks, which effectively mimics S&P 500, get a very similar spread returns between glamour value stocks. The conclusion is clear: our results apply to largest stocks as well. C. Regression Analysis Previous analysis has identified a variety variables that can define glamour value portfolios. In this section, we ask which se variables are significant in a multiple regression. Table IV presents results regressions raw returns for each stock on characteristics stocks that we have identified. Recall that in our analysis we have portfolio formation periods. We run regressions separately for each postformation year, starting with + ending with +5. Thus, for postformation Year +, we run separate cross-sectional regressions in which dependent variable is annual return on stock i independent variables are characteristics stock i observed at beginning year. Then, using Fama-MacBeth (97) procedure, coefficients for se cross-sectional regressions are averaged t-statistics are computed. We applied same procedure for Years +, +, + 4, + 5 after formation. The results presented in Table IV are for Year +.

18 558 The Journal Finance Table IV Regression Returns on Characteristics for All Firms At end each April between , we compute for every firm in sample -year holding-period return starting at end April. We n run cross-sectional regressions with se returns for each formation period as dependent variables. The independent variables are () GS, preformation 5-year weighted average rank sales growth; () B/M, ratio end previous year's book value equity to market value equity; () SIZE, end April natural logarithm market value equity (in millions); (4) E/P +, equal to E/P- ratio previous year's earnings to end--april market value equity-if E/P is positive- to zero if E/P is negative; (5) DE/P, equal to if E/P is negative, zero if E/P is positive; (6) C/P +, equal to C/P- ratio previous-year's cash flow to end--april market value equity-if C/P is positive- zero if C/P is negative; (7) DC/P, equal to if C/P is negative, zero if C/P is positive. The reported coefficients are averages over formation- periods. The reported t-statistics are based on time-series variation coefficients. Mean t-statistic Int. GS B/M SIZE E/P + DE/P C/P + DC/P Mean t-statistic.67. Mean t-statistic Mean t-statistic Mean t-statistic Mean t-statistic Mean t-statistic Mean t-statistic Mean t-statistic We use ratios C/P E/P in regression analysis. However, for some stocks se ratios are negative, hence cannot be plausibly interpreted as expected growth rates. We deal with this problem in same way as Fama French (99). Specifically, we define variables C/P + E/P +, which are equal to zero when C/P E/P are negative, are equal to C/P E/P when y are positive. We also include in regressions dummy variables, called DC/P DE/P, which take value when C/P or E/P are negative, respectively, zero orwise. This approach enables us to treat observations with negative E/P C/P differently from observations with positive E/P C/P.

19 Contrarian Investment, Extrapolation, Risk 559 The first result emerging from Table IV is that, taken separately, each GS, B/M, E/P, C/P, although not SIZE, have statistically significant predictive power for returns. These results are in line with Fama French (99), although on a st-alone basis C/P not B/M is most significant variable. When we use dependent variables in combination, weakness B/M relative to C/P, E/P, GS begins to emerge, its coefficient drops significantly. For example, when GS, C/P, B/M are included in same regression, first two are significant, but B/M is not. In fact, coefficient on B/M is essentially zero. Similarly, when GS, E/P, B/M are included in same regression, E/P GS are significant, but B/M is not. The variables that st out in multiple regressions are GS C/P. IV. A Test Extrapolation Model So far we have shown that strategies contrarian to extrapolation earn high abnormal returns relative to market to extrapolation strategies. We have not, however, provided any direct evidence that excessive extrapolation expectational errors are indeed what characterizes glamour value stocks." In this section, we provide such evidence. The essence extrapolation is that investors are excessively optimistic about glamour stocks excessively pessimistic about value stocks because y tie ir expectations future growth to past growth. But if investors make mistakes, se mistakes can presumably be detected in data. A direct test extrapolation, n, is to look directly at actual future growth rates compare m to past growth rates to expected growth rates as implied by multiples. Table V presents some descriptive characteristics for our glamour value portfolios regarding ir valuation multiples, past growth rates, future growth rates. A reveals that value portfolios had much higher ratios fundamentals to price. We interpret se ratios in terms lower expected growth rates for value stocks. B shows that, using several measures past growth, including earnings, cash flow, sales, stock return, glamour stocks grew substantially faster than value stocks over 5 years before portfolio formation. Finally, C shows that over 5 postformation years relative growth fundamentals for glamour stocks was much less impressive. Indeed, over Years + to + 5 relative to formation growth rates fundamentals for value portfolio were ten higher. This deterioration relative growth rates glamour stocks compared to In ir study contrarian strategies based on past stock returns, De Bondt Thaler (987) provide some evidence for expectational errors view. The one exception is for E/P ratio using B/M classification scheme. Apparently, because large number stocks with temporarily depressed earnings in highest B/M decile, E/P ratio for this group is extremely low. This result goes away when looking at top two deciles toger or when looking at top decile within largest 50 percent our firms.

20 560 The Journal Finance Table V Fundamental Variables, Past Performance, Future Performance Value Stocks : At end each April between , 0-decile portfolios are formed based on ratio end--previous-year's book value equity t end--april market value equity. Numbers are presented for first (lowest B/M) tenth (highest B/M) deciles. These portfolios are denoted Value, respectively. : At end each April between 968 ad 989, 9 groups stocks are formed. The stocks are independently sorted in ascending order into groups () bottom 0 percent, () middle 40 percent, () top 0 percent) based on C/P, ratio cash flow X market value equity, GS, preformation 5-year weighted average sales growth rank. Numbers are presented for (C/P, GS), bottom 0 percent by C/P top 0 percent by GS, for (C/P, GS,) top 0 percent by C/P bottom 0 percent b GS. These portfolios are denoted Value, respectively. All numbers in table are averages over all formation periods. E/P, C/P, S/P, D/P, B/M, SIZE, defined below, use end--april market value equity preformation year accounting numbers. E/P is ratio earnings to market value equity. S/P is rato sales to market value equity. D/P is ratio dividends to market value equity. B/M is ratio book value to market value equity. SIZE is total dollar value equity (in millions). AEG(,J) is geometric average growth rate earnings for portfolio from year i to year j. ACG( j) ASGQ, i) are defined analogously for cash flow sales, respectively. RETURNI" 0) is cumulative stock return on portfolio over years prior to formation. I Value Value B/M B/M0 C/P, GS C/P, GS, A: Fundamental Variables E/P C/P S/P D/P B/M SIZE B: Past Performance-Growh Rates Past Returns AEG( 5, ) ACG(5, ) ASG(_5,O RETURN>S, ) C: Future Performance AEG(0,5) ACG(T,5) ASG(05) AEG(5) ACG(,5) ASG(,5)

21 Contrarian Investment, Extrapolation, Risk 56 past relative growth expected future relative growth is explored more systematically below. To interpret differences in financial ratios such as C/P E/P in terms expected growth rates, we come back to Gordon's formula (Gordon Shapiro (956)). Recall that for cash flow, this formula can be rewritten as pc(+ )/P = r - g, where C(+ ) is one period ahead cash flow, P is current stock price, r is required rate return on stock, g is expected growth rate cash flow, p, payout ratio for cash flows, is constant fraction cash flows received as dividends. An identical formula applies for earnings, under assumption that dividends are also some fixed fraction earnings. Taken literally, se formulas imply that, holding discount rates payout ratios constant, we can directly calculate differences in expected growth rates based on differences in C/P or E/P ratios. Because assumptions behind se simple formulas are restrictive (e.g., constant growth rates, strict proportionality dividends, cash flows earnings, identical payout ratios across stocks, etc.), we do not calculate exact estimates differences in expected growth rates between value glamour portfolios. Instead, we choose to analyze differences in past growth, valuation multiples future growth rates in a way that is more robust with respect to departures from se assumptions. However, idea behind this analysis is same. We ask wher large differences in C/P E/P ratios between value glamour stocks can be justified by differences in future growth rates. We start with data for portfolios classified according to (C/P, GS). As we know already, past growth glamour stocks by any measure was much faster than that value stocks. For example, over 5 years before portfolio formation, annual growth rate cash flow for glamour portfolio was.0 percent compared to 7.8 percent for value portfolio. The difference in cash flow multiples between value glamour portfolios suggests that market was expecting se growth differences to persist for many years. A dollar invested in value portfolio was a claim to 7.9 cents in a current cash flow while a dollar invested in glamour portfolio was a claim to only 8 cents current cash flow. Ignoring any differences in required rates return (this possibility is examined in Section V), se large differences in C/P would have to be justified eir by big differences in payout ratios between value glamour firms or else by an expectation very different growth rates over a long period time. A quick look at respective dividend yields on value glamour portfolios suggests that difference was not due to differences in payout ratios. A dollar invested in value portfolio was a claim to.9 cents in current dividends, while a dollar invested in glamour portfolio brought in only.4 cents in dividends. These differ by roughly same factor as for C/P. While cash flow payout ratios were slightly higher for glamour stocks (0.75 versus 0.40), this does not account for most difference in C/P. We estimate se payout ratios by dividing D/P by C/P.

22 56 The Journal Finance Under assumption that payout ratios discount rates were approximately equal, at some future date expected cash flows per current dollar invested must have been higher for glamour portfolio than for value portfolio. Accordingly, we can ask how many years it would take for cash flows per dollar invested in glamour portfolio (0.080) to equal cash flows value portfolio (0.79), assuming that differences in past cash flow growth rates persisted (i.e.,.0 versus 7.8 percent). The answer turns out to be approximately years. If we do same calculations using D/P ratios to take account differences in payout ratios, it would have taken approximately 9 years for dividends per dollar invested in glamour portfolio (currently 0.04) to catch up to those value portfolio (currently 0.09), assuming that past growth rate differences persisted. Note that this equality is on a flow basis not on a present-value basis. Equality on a present-value basis would require an even longer time period over which glamour firms should experience superior growth. We can now compare se implied growth expectations to actual cash flow growth experienced by glamour value portfolios. Over first 5 years after formation, cash flows glamour portfolio grew by. percent per year versus 5. percent for value portfolio. Hence, cash flow per dollar invested grew from initially to 0.6 at end Year 5, while for value portfolio cash flow per dollar invested grew from 0.79 to 0.60, still leaving a large gap in cash flow returns between two portfolios in Year 5. More importantly, superior postformation growth is driven almost entirely by higher growth in first to postformation years. From Year + to +5 postformation, annual cash flow growth rates were percent for glamour value, respectively. While market correctly anticipated higher growth in very short-term, persistence se higher growth rates seems to have been grossly overestimated.4 If growth rates after Year 5 were comparable to growth rates observed over Years + to + 5, n, after 0 years, cash flows per dollar on glamour portfolio would be only 0.4 compared to for value. These data are consistent with idea that market was too optimistic about future growth glamour firms relative to value firms. A similar conclusion emerges from an analysis earnings numbers. Over 5 years before portfolio formation, growth rate earnings per dollar invested for glamour portfolio was 4. percent versus 8. percent for value portfolio. At formation, E/P ratio for glamour was compared to 0.4 for value. This difference in E/P ratios does not appear to be driven by differences in earnings payout ratios since payout ratio for value was actually somewhat higher than for glamour (0.4 versus 0.6). Once again, we can examine postformation growth rates to see wher higher postformation growth for glamour could justify its lower initial E/P ratio. Here numbers are even more dramatic than for cash flow. Over 5 postforma- 4 The result that growth rates earnings are highly mean reverting is not new. Little (96) shows this quite clearly in his pathbreaking article.

23 Contrarian Investment, Extrapolation, Risk 56 tion years, cumulative growth in earnings per dollar initial investment was almost identical for two portfolios. Earnings growth averaged 8.9 percent per year for glamour versus 8.6 percent per year for value. While growth in first to years was higher for glamour, this was reversed over following years. If investors expected superior growth glamour firms to persist (as suggested by differences in E/P ratios), data indicate that y significantly overestimated future growth rate differences between glamour value stocks. Analogous results for portfolios classified according to B/M are also presented in Table V. We focus only on numbers for cash flow because E/P ratios for extreme decile portfolios are so low as to make an expected growth computation somewhat questionable. For example, E/P ratio for decile 0 (value) was only 0.004, indicating a high proportion firms with temporarily depressed earnings. Because cash flows are less volatile less ten negative, C/P ratios are much better behaved. For glamour portfolio (B/M), C/P was equal to versus 0.7 for value portfolio (B/M0). These numbers are quite similar to those for (C/P, GS) portfolios. Presumably, this difference in C/P reflects, at least in part, market's expectation that superior growth glamour firms would continue. Over previous 5 years cash flow for glamour portfolio had grown at.7 percent per year while cash flow growth for value portfolio had been -. percent per year. Estimated cash flow payout ratios for glamour value firms were quite similar ( , respectively). Hence, differential payout ratios alone could not justify much difference in C/P ratios. Postformation cash flow numbers indicate that glamour stocks indeed outgrew value stocks over 5 years after formation, but that this is due to much higher growth at beginning postformation period. In last years postformation period, cash flows for value portfolio actually grew faster (. percent per year versus 8.6 percent per year). In sum, at end 5 years cash flow per initial dollar invested rose from to 0.07 for glamour portfolio from 0.7 to 0.4 for value portfolio. If cash flow growth rates over Years + to + 5 postformation were any indication growth rates after Year 5, cash flow return on glamour stocks did not get any closer to that for value stocks. These results mirror those for (C/P, GS) classification. They are consistent with view that superior postformation return on value stocks are explained by upward revisions in expectations about relative growth rates value versus glamour stocks. Contrary to assertions Fama French (99, Section V), market was likely to learn about its mistake only slowly over time since its expectation higher relative growth for individual glamour firms was ten confirmed in short-run but n disconfirmed only in longer run. Hence, we do not necessarily expect to see a clear spike in returns or E/P ratios. In this respect, motivation behind contrarian strategies explored in this article is quite different from that for strategies explored by Jegadeesh Titman (99), Bernard Thomas (989), Givoly

24 564 The Journal Finance Lakonishok (979). The momentum-based strategies those articles rely on market's short-term failure to recognize a trend. In contrast, superior returns to value strategies documented here seem to be driven by market's unwarranted belief in continuation a long-term trend its gradual abonment that belief. In summary, evidence in Table V is consistent with extrapolation model. stocks have historically grown fast in sales, earnings, cash flow relative to value stocks. According to most our measures, market expected superior growth glamour firms to continue for many years. In very short-run, expectations continued superior growth glamour stocks were on average born out. However, beyond first couple years, growth rates glamour stocks value stocks were essentially same. The evidence suggests that forecasts were tied to past growth rates were too optimistic for glamour stocks relative to value stocks. This is precisely what extrapolation model would predict. In this respect, evidence in Table V goes beyond customary evidence on returns in that it shows a relationship between past, forecasted, actual future growth rates that is largely consistent with predictions extrapolation model. V. Are Contrarian Strategies Riskier? Two alternative ories have been proposed to explain why value strategies have produced higher returns in past. The first ory says that y have done so because y exploit mistakes naive investors. The previous section showed that investors appear to be extrapolating past too far into future, even though future does not warrant such extrapolation. The second explanation superior returns to value strategies is that y expose investors to greater systematic risk. In this section, we examine this explanation directly. Value stocks would be fundamentally riskier than glamour stocks if, first, y underperform glamour stocks in some states world, second, those are on average "bad" states, in which marginal utility wealth is high, making value stocks unattractive to risk-averse investors. This simple ory motivates our empirical approach. To begin, we look at consistency performance value glamour strategies over time ask how ten value underperforms glamour. We n check wher times when value underperforms are recessions, times severe market declines, or orwise "bad" states world in which marginal utility consumption is high. These tests do not provide much support for view that value strategies are fundamentally riskier. Finally, we look at some traditional measures risk, such as beta stard deviation returns, to compare value glamour strategies. Table VI Figure present year-by-year performance value strategy relative to glamour strategy over April 968 to April 990

25 Contrarian Investment, Extrapolation, Risk 565 Table VI Year-by-Year Returns: Value- : At end each April between , 0-decile portfolios are formed based on ratio previous-year's cash flow to end--april market-value equity (C/P). For each portfolio, -, -, 5-year holding-period returns are computed. For each formation period, reports difference in -, -, 5-year return between highest C/P (value) lowest C/P (glamour) portfolios. : At end each April between , 9 groups stocks are formed as follows. All stocks are independently sorted into groups (() bottom 0 percent, () middle 40 percent, () top 0 percent) by ratio previous-year's cash flow to end--april market-value equity (C/P) by preformation 5-year weighted average rank--sales growth (GS). The 9 portfolios are intersections resulting from se independent classifications. For each portfolio, -, -, 5-year holding period returns are computed. For each formation period, reports difference in -, -, 5-year return between lowest GS, highest C/P (value) highest GS, lowest C/P (glamour) portfolios. : At end each April between , 0-decile portfolios are formed based on ratio end--previous-year's book value equity to end--april market value equity (B/M). For each portfolio, -, -, 5-year-holding-period returns are computed. For each formation period, reports difference in -, -, 5-year return between highest B/M (value) lowest B/M (glamour) decile portfolios. The last two rows respectively report arithmetic mean across periods t-statistic for test hyposis that difference in returns between value glamour is equal to zero. These t-statistics are based on stard errors computed according to Hansen Hodrick (980). (C/P: 9, 0 -,) (C/P-GS:, -,) (B/M: 9, 0 -,) -Year -Year 5-Year -Year -Year 5-Year -Year -Year 5-Year Average t-statistic

26 566 The Journal Finance Pet P, D P R PD R PD P D R D P D -0 I I I I I I I I I I I I I i l l l l l l l Year Figure. Year-by-year returns: Value minus glamour. At end each April between , 9 groups stocks are formed. The stocks are independently sorted in ascending order into groups (() bottom 0 percent, () middle 40 percent, () top 0 percent) based on each two variables: cash-flow-to-price (C/P) growth-in-sales (GS). The value portfolio consists those stocks in highest C/P groups lowest GS group. The glamour portfolio consists those stocks in lowest C/P group highest GS group. The numbers presented are annual buy--hold returns for value portfolio minus returns for glamour portfolio. Annual buy--hold returns are calculated beginning at end April for given year. R indicates NBER recession years, D indicates years in which CRSP equally weighted index declined in nominal terms. period. We consider differences in cumulative returns between deciles (9, 0) (, ) for C/P B/M, between groups (, ) (, ) for (C/P, GS) over -, -, 5-year holding horizons starting each year in sample (968, 969, etc.). The arithmetic mean across years for each horizon is reported at bottom each column along with t-statistics for test hyposis that difference in returns between value glamour portfolios is equal to zero. Stard errors for t-tests involving overlapping - 5-year horizons are computed using method Hansen-Hodrick (980), assuming annual MA() MA(4) processes, respectively. The results show that value strategies have consistently outperformed glamour strategies. Using a -year horizon, value outperformed glamour in 7 out years using C/P to classify stocks, in 9 out years using C/P GS, in 7 out years using B/M ratio. As we move to longer horizons, consistency performance value strategy relative to glamour strategy increases. For all three classification schemes, value portfolio outperforms glamour portfolio over every 5-year horizon in sample period.

27 Contrarian Investment, Extrapolation, Risk 567 These numbers pose a stiff challenge to any risk-based explanation for higher returns on value stocks. Consider (C/P, GS) classification. Over a -year horizon, value strategy underperformed glamour strategy in only two instances. In those instances, magnitude value strategy's underperformance was small relative to its mean outperformance 46.4 percent. Over any 5-year horizon in sample, value strategy was a sure winner. Even for a one-year horizon, downside this strategy was fairly low. To explain se numbers with a multifactor risk model would require that relatively few instances underperformance value portfolio are tightly associated with very bad states world as defined by some payf relevant factor. Put anor way, covariance between negative realizations value minus glamour return this payf-relevant factor should be high risk-premium associated with that factor should also be quite high. While it is difficult to reject a risk-based explanation which relies on an unspecified multifactor model, we can examine a set important payfrelevant factors that are likely to be associated with large risk premia. If, after examining association between negative relative returns to value this set factors, we are unable to make sense higher average returns on value strategies, we can conclude that a risk-based explanation is unlikely to work except by appealing to large risk premia on factors that are a priori lesser payf relevance. In examining payf relevant factors, we do not restrict ourselves to tightly parameterized models such as Sharpe-Lintner model or consumption Capital Asset Pricing Model (using consumption data) which are too likely to lead to rejection risk-based explanations. For example, we do not assume that beta is appropriate measure exposure to market factor. Instead, we proceed nonparametrically examine performance value strategies in extreme down markets. Moreover, we allow for possibility that distribution stock returns does not provide a complete characterization good bad states world. Barro (990) ors find that, while stock market is useful in predicting economic aggregates such as GNP growth, R is only around 0.4 in post-war subperiod. Some evidence on performance value glamour strategies in bad states world can be gleaned from Table VI Figure. According to National Bureau Economic Research, re were four recessions during our sample period: a mild one from December 969 to November 970, a very deep one from November 97 to March 975, also significant ones from January 980 to July 980 July 98 to November 98. An examination Table VI shows that value strategy did about same or somewhat better than glamour just before during 970 recession, did much better around severe recession 97 to 975, did somewhat worse in 979 to 980, did significantly better in 98 to 98.5 It is implausible 5 Recall that returns are computed starting at end April year listed through April following year.

28 568 The Journal Finance to conclude from this that value strategies did particularly badly in recessions, when marginal utility consumption is especially high. A second approach is to compare performance value glamour portfolios in worst months for stock market as a whole. Table VII, presents performance our portfolios in each 4 states world; 5 worst stock return months in sample based on equally weighted index, remaining 88 negative months or than 5 worst, positive months or than 5 best, 5 best months in sample. The average difference in returns between value glamour portfolios for each state is also reported along with t-statistics for test that difference returns is equal to zero. The results in this table are fairly clear. Using both B/M (C/P, GS) classification schemes, value portfolio outperformed glamour portfolio in market's worst 5 months. For example, using (C/P, GS) classification, value portfolio lost an average 8.6 percent its value in worst 5 months, whereas glamour portfolio lost 0. percent its value. Similarly, using both classification schemes, value portfolio on average outperformed glamour portfolio index in next worst 88 months in which index declined. Using (C/P, GS) classification, value portfolio lost.5 percent in se months when index experiences a mild decline, compared to.9 percent for glamour portfolio. percent for index itself. So value strategy did better when market fell. The value strategy performed most closely to glamour strategy in positive months or than best 5. In very best months, value strategy substantially outperformed glamour strategy index, but not by as much as it does when market fell sharply. Some care should be taken in interpreting se mean differences for positive market return months, however, given low t-statistics. Overall, value strategy performed somewhat better than glamour strategy in all states significantly better in some states. If anything, superior performance value strategy was skewed toward negative market return months rar than positive market return months. The evidence in Table VII, thus indicates that value strategy did not expose investors to greater downside risk. Table VII, provides numbers analogous to those in except now states world are realizations real GNP growth.6 The data are quarterly, so that we have 88 quarters in sample. These quarters are classified into 4 states world; worst 0 quarters, next worst 4 quarters, best 0 quarters, next best 4 quarters. The quarterly returns on various glamour value portfolios are n matched up with changes in real GNP for one quarter ahead, since evidence indicates that stock market leads GNP by approximately one quarter. Average quarterly returns for each portfolio are n computed for each state. 6 In an earlier draft this article we included results using change in unemployment rate. The results are quite similar to those for GNP growth.

29 Contrarian Investment, Extrapolation, Risk 569 The results in mirror basic conclusions from ; namely, value strategy has not been fundamentally riskier than glamour strategy. For both classification schemes, value strategy performed at least as well as glamour strategy in each 4 states substantially better in most states. Unlike results in, re was some tendency for relative returns on value to be higher in good states than in bad states, especially for extreme good states. Roughly speaking, value stocks could be described as having higher up-market betas lower down-market betas than glamour stocks with respect to economic conditions. Importantly, while value strategy did disproportionately well in extreme good times, its performance in extreme bad times was also quite impressive. Performance in extreme bad states is ten last refuge those claiming that a high return strategy must be riskier, even when conventional measures risk such as beta stard deviation do not show it. The evidence indicates some positive relation between relative performance value strategy measures prosperity, but re are no significant traces a conventional asset pricing equilibrium in which higher returns on value strategy are compensation for higher systematic risk. Finally, for completeness, Table VIII presents some more traditional risk measures for portfolios using our classification schemes. These risk measures are calculated using annual measurement intervals over postformation period, because problems associated with use preformation period data (Ball Kothari (989)). For each our portfolios, we have annual observations on its return in year following formation, hence can compute stard deviation returns. We also have corresponding returns on value-weighted CRSP index risk-free asset, hence can calculate a beta for each portfolio. First, betas value portfolios with respect to value-weighted index tend to be about 0. higher than betas glamour portfolios. As we have seen earlier, high betas probably come from value stocks having higher "up-market" betas,'7 that, if anything, superior performance value strategy occurs disproportionally during "bad" realizations stock market. Even if one takes a very strong pro-beta position, difference in betas 0. can explain a difference in returns only up to percent per year (assuming a market risk premium 8 percent per year) surely not 0 to percent difference in returns that we find. Table VIII also presents average annual stard deviations various portfolio returns. The results show that value portfolios have somewhat higher stard deviations returns than glamour portfolios. Using (C/P, GS) classification, value portfolio has an average stard deviation returns 4. percent relative to.6 percent for glamour portfolio. Three remarks about se numbers are in order. First, we have already shown that, because its much higher mean return, value 7 De Bondt Thaler (987) obtain a similar result for ir contrarian strategy based on buying stocks with low past returns.

30 570 The Journal Finance Table VII Performa Portfolios in Best Worst Times : All months in sample are divided into 5 worst stock return months based on equally weighted index (W5), remaining 88 negative months or than 5 worst (N88), positive months or than 5 best (P), 5 best months (B5) in sample. la: At end each April between , 9 groups stocks are formed as follows. All stocks are independently sorted into groups (() bottom 40 percent, () middle 40 percent, () top 0 percent) by ratio previous year's cash flow to end--april market value equity (CP) by preformation 5-year weighted average rank sales growth (GS). The 9 portfolios are intersections resulting from se independent classifications. For each portfolio (changing every April), A presents its average return over W5, N88, P, B5 months. B: At end each April between , 0-decile portfolios are formed based on ratio end--previous-year's book value equity to end--april market value equity (B/M). For each portfolio (changing every April), B presents its average return over W5, N88, P, B5 months. s A B have same structure, but states are defined in terms best worst quarters for GNP growth. All quarters in sample are divided into 4 sets: 0 quarters lowest real GNP growth during sample period, 4 next lowest real GNP growth quarters, 4 next worst growth quarters, 0 highest real GNP growth quarters. In A, value portfolio contains stocks ranking in top group on C/P in bottom group on GS. The portfolio contains stocks ranking in bottom group on C/P in top group on GS. In B, Value portfolio contains stocks ranking in top two deciles on B/M. The portfolio contains stocks ranking in bottom two deciles on B/M. The right-most column contains t-statistic for testing hyposis that difference in returns between Value portfolios is equal to zero. : Portfolio Returns across Best Worst Stock Market Months A Value C/P Value- GS Index (, -,) t-statistic W N P B , B Value- Value B/M Index (9,0 -,) t-statistic W N P B

31 Contrarian Investment, Extrapolation, Risk 57 Table VII-Continued : Portfolio Returns across Best Worst GNP Growth Quarters A Value C/P Value- GS GNP (, -,) t-statistic Worst Next worst Next best Best B Value- Value B/M GNP (9,0 --,) t-statistic Worst Next worst Next best Best

32 57 The Journal Finance Table VIII Traditional Risk Measures for Portfolios For each portfolio described below, we compute, using year-after--formation returns as observations, its beta with respect to value-weighted index. Using formation periods, we also compute stard deviation returns stard deviation size-adjusted returns in year after formation. : At end each April between , 0-decile portfolios are formed based on ratio previous-year's cash flow to end--april market value equity (C/P). For each decile portfolio, presents its beta, stard deviation returns, stard deviation size-adjusted returns defined above. : At end each April between , 9 groups stocks are formed as follows. All stocks are independently sorted into groups (() bottom 0 percent, () middle 40 percent, () top 0 percent) by ratio previous-year's cash flow to end--april market value equity (C/P) by preformation 5-year weighted-average rank sales growth (GS). The 9 portfolios are intersections resulting from se independent classifications. For each group stocks, presents its beta, stard deviation returns, stard deviation size-adjusted returns defined above. : At end each April between , 0-decile portfolios are formed based on ratio end--previous year's book value equity to end--april market value equity (B/M). For each decile portfolio, presents its beta, stard deviation returns, stard deviation size-adjusted returns defined above. Equally Weighted C/P Index / Stard deviation Stard deviation size-adjusted return

33 Contrarian Investment, Extrapolation, Risk 57 Table VIII-Continued Equally C/P Weighted GS Index, Stard deviation Stard deviation size-adjusted return Equally Weighted B/M Index I Stard deviation Stard deviation size-adjusted return

34 574 The Journal Finance strategy's higher stard deviation does not translate into greater downside risk. Second, higher stard deviation value stocks appears to be due largely to ir smaller average size, since stard deviation size-adjusted returns is virtually same for value glamour portfolios. But results in Table III suggest that, by focusing on larger value stocks, investors could still get most extra return from value stocks without this higher stard deviation. The extra return on a portfolio large value stocks cannot refore be explained by appealing to its higher stard deviation. Finally, difference in stard deviation returns between value glamour portfolios (4. versus.6 percent per year) is quite small in comparison to difference in average return (0 percent per year). For example, over 96 to 988 period extra return on S & P 500 over T-bills was approximately 8 percent per year, while average stard deviation on S & P 500 was percent compared to percent for T-bills. In comparison to reward-to-risk ratio for stocks vis-a-vis T-bills, reward-to-risk ratio for investing in value stocks is extremely high. A risk model based on differences in stard deviation cannot explain superior returns on value stocks. VI. Summary Interpretation Findings The results in this article establish (in varying degrees detail) three propositions. First, a variety investment strategies that involve buying out--favor (value) stocks have outperformed glamour strategies over April 968 to April 990 period. Second, a likely reason that se value strategies have worked so well relative to glamour strategies is fact that actual future growth rates earnings, cash flow, etc. glamour stocks relative to value stocks turned out to be much lower than y were in past, or as multiples on those stocks indicate market expected m to be. That is, market participants appear to have consistently overestimated future growth rates glamour stocks relative to value stocks. Third, using conventional approaches to fundamental risk, value strategies appear to be no riskier than glamour strategies. Reward for bearing fundamental risk does not seem to explain higher average returns on value stocks than on glamour stocks. While one can never reject "metaphysical" version risk story, in which securities that earn higher returns must by definition be fundamentally riskier, weight evidence suggests a more straightforward model. In this model, out--favor (or value) stocks have been underpriced relative to ir risk return characteristics, investing in m has indeed earned abnormal returns. This conclusion raises obvious question: how can 0 to percent per year in extra returns on value stocks over glamour stocks have persisted for so long? One possible explanation is that investors simply did not know about m. This explanation has some plausibility in that quantitative

35 Contrarian Investment, Extrapolation, Risk 575 portfolio selection evaluation are relatively recent activities. Most investors might not have been able, until recently, to perform analysis done in this article. Of course, advocacy value strategies is decades old, going back at least to Graham Dodd (94). But such advocacy is usually not accompanied by defensible statistical work hence might not be entirely persuasive, especially since many or strategies are advocated as well. Anor possible explanation is that we have engaged in data snooping (Lo MacKinlay (990)) have merely identified an ex post pattern in data. Clearly, se data have been mined in sense that ors have looked at much se same data before us. On or h, we think re is good reason to believe that cross-sectional return differences reported here reflect an important economic regularity rar than sampling error. First, similar findings on superior returns value strategies have been obtained for several different time series. Davis (994) finds similar results on a subsample large U.S. firms over period 9 to 960. Chan, Hamao Lakonishok (99) find similar results for Japan. Capaul, Rowley, Sharpe (99) find similar results for France, Germany, Switzerl, United Kingdom, as well as for United States Japan. Second, we have documented more than just a cross-sectional pattern returns. The evidence suggests a systematic pattern expectational errors on part investors that is capable explaining differential stock returns across value glamour stocks. Investor expectations future growth appear to have been excessively tied to past growth despite fact that future growth rates are highly mean reverting. In particular, investors expected glamour firms to continue growing faster than value firms, but y were systematically disappointed. La Porta (99) shows that a similar pattern expectational errors returns on value strategies obtains when growth expectations are measured by analysts' 5-year earnings growth forecasts rar than by financial ratios such as E/P or C/P. The evidence on expectational errors supports view that cross-sectional differences in returns reflect a genuine economic phenomenon. We conjecture that results in this article can best be explained by preference both individual institutional investors for glamour strategies by ir avoidance value strategies. Below we suggest some reasons for this preference that might potentially explain observed returns anomaly. Individual investors might focus on glamour strategies for a variety reasons. First, y may make judgment errors extrapolate past growth rates glamour stocks, such as Walmart or Microst, even when such growth rates are highly unlikely to persist in future. Putting excessive weight on recent past history, as opposed to a rational prior, is a common judgment error in psychological experiments not just in stock market. Alternatively, individuals might just equate well-run firms with good investments, regardless price. After all, how can you lose money on Microst or Walmart? Indeed, brokers typically recommend "good" companies with "steady" earnings dividend growth.

36 576 The Journal Finance Presumably, institutional investors should be somewhat more free from judgment biases excitement about "good companies" than individuals, so should flock to value strategies."8 But institutional investors may have reasons ir own for gravitating toward glamour stocks. Lakonishok, Shleifer, Vishny (99b) focus on agency context institutional money management. Institutions might prefer glamour stocks because y appear to be "prudent" investments, hence are easy to justify to sponsors. stocks have done well in past are unlikely to become financially distressed in near future, as opposed to value stocks, which have previously done poorly are more likely to run into financial problems. Many institutions actually screen out stocks financially distressed firms, many which are value stocks, from universe stocks y pick. Indeed, sponsors may mistakenly believe glamour stocks to be safer than value stocks, even though, as we have seen, a portfolio value stocks is no more risky. The strategy investing in glamour stocks, while appearing "prudent," is not prudent at all in that it earns a lower expected return is not fundamentally less risky. Noneless, career concerns money managers employees ir institutional clients may cause money managers to tilt towards "glamour" stocks. Anor important factor is that most investors have shorter time horizons than are required for value strategies to consistently pay f (De Long et al. (990) Shleifer Vishny (990)). Many individuals look for stocks that will earn m high abnormal returns within a few months, rar than 4 percent per year over next 5 years. Institutional money managers ten have even shorter time horizons. They ten cannot afford to underperform index or ir peers for any nontrivial period time, for if y do, ir sponsors will withdraw funds. A value strategy that takes to 5 years to pay f but may underperform market in meantime (i.e., have a large tracking error) might simply be too risky for money managers from viewpoint career concerns, especially if strategy itself is more difficult to justify to sponsors. If a money manager fears getting fired before a value strategy pays f, he will avoid using such a strategy. Importantly, while tracking error can explain why a money manager would not want too strong a tilt toward eir value or growth, it does not explain why he would not tilt slightly toward value given its apparently superior risk/return prile. Hence, se horizon tracking error issues can explain why money managers do not more aggressively "arbitrage" differences in returns across value glamour stocks, but y cannot explain why such differences are re in first place. In our view, such return differences are ultimately explained by tendency investors to make judgmental errors perhaps also by a tendency for institutional investors to actively tilt toward glamour to make ir lives easier. 8 According to Dreman (977), pressional money managers are also quite likely to suffer from se biases.

37 Contrarian Investment, Extrapolation, Risk 577 Are anomalous excess returns on value stocks likely to persist? It is possible that over time more investors will become convinced value being a contrarian with a long horizon returns to value strategies will fall. Perhaps recent move into disciplined quantitative investment strategies, evaluated based only on performance not on individual stock picks, will increase dem for value stocks reduce agency problems that result in picking glamour stocks. Such sea changes rarely occur overnight, however. The time-series cross-country evidence support idea that behavioral institutional factors underlying higher returns to value stocks have been pervasive enduring features equity markets. Perhaps most interesting implication conjecture that institutional investors gravitate toward glamour stocks is that this may explain ir inferior performance. In an earlier article, we focused on striking underperformance pension fund money managers relative to market index (Lakonishok, Shleifer, Vishny (99b)). The large difference in returns on glamour value stocks can, at least in principle, explain why money managers have underperformed market by over 00 basis points per year before accounting for management fees. By looking at actual portfolios institutional money managers, one can find out wher y have been overinvested in glamour stocks underinvested in value stocks. We plan to do that in a follow-up article. REFERENCES Ball, R., S. Kothari, 989, Non-stationary expected returns: Implications for tests market efficiency serial correlation returns, Journal Financial Economics 5, Banz, R., W. Breen, 986, Sample dependent results using accounting market data: Some evidence, Journal Finance 4, Barro, R., 990, The stock market investment, Review Financial Studies, 5-. Basu, S., 977, Investment performance common stocks in relation to ir price earnings ratios: A test efficient market hyposis, Journal Finance, Bernard, V., J. Thomas, 989, Post-earnings announcement drift: Delayed price response or risk premium, Journal Accounting Research 7 (Supplement), -6. Black, F., 986, Noise, Journal Finance 4, Brown, S., W. Goetzmann, S. Ross, 99, Survivorship bias in autocorrelation long-term memory studies, Mimeo, New York University, Columbia University Yale University, September. Capaul, C., I. Rowley, W. Sharpe, 99, International value growth stock returns, Financial Analysts Journal, January/February, 7-6. Chan, K., 988, On contrarian investment strategy, Journal Business 6, Chan, L., Y. Hamao, J. Lakonishok, 99, Fundamentals stock returns in Japan, Journal Finance 46, Chopra, N., J. Lakonishok, J. Ritter, 99, Measuring abnormal performance: Do stocks overreact?, Journal Financial Economics, Davis, James, 994, The cross-section realized stock returns: The pre-compustat evidence, Journal Finance 49, De Bondt, W., R. Thaler, 985, Does stock market overreact?, Journal Finance 40,

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