Behavioral finance (Overreaction) topic

IS STOCK MARKET OVERREACTION PERSISTENT OVER TIME?

Carl R. Chen and David A. Sauer*

INTRODUCTION

A psychology study conducted by Kahneman and Tversky (1982) contends that people tend to overreact to unexpected events. Based upon this finding, DeBondt and Thaler (1985) suggest that the stock market overreacts. Constructing loser and winner portfolios, they find a performance reversal during the three year test period immediately following the three year rank period. Consequently, a contrarian investment strategy provides 25 percent abnormal returns on average. This finding is not consistent with the weakest form of market efficiency, and has gained tremendous interest and debate in academia. Chan (1988) argues that the contrarian strategy earns insignificant abnormal returns after the time-varying beta risk for the loser and winner portfolios are adjusted for. Ball and Kothari (1989) also find the same results. On the other front, Zarowin (1989 and 1990) conjectures that losers do not outperform winners after firm size and January seasonality are controlled for. Kaul and Nimalendran (1990), examining bid/ask prices for the NASDAQ stocks, also find little evidence of overreaction after extracting price measurement error caused by the bid/ask spread. DeBondt and Thaler (1987), however, re-examine the overreaction issue and conclude that the overreaction effect still exists after controlling for differences in beta and size. Their findings are reinforced by a more recent study conducted by Chopra, Lakonishok, and Ritter (1992). Therefore, controversy regarding the overreaction hypothesis continues.

Recent evidence of mean reversion in stock market returns documented in Poterba and Summers (1988), Lo and MacKinlay (1988), and Fama and French (1988) parallels the debate on the overreaction hypothesis. These studies find that the stationary component of stock returns is negatively correlated over long time horizons. Thus, information based upon prior returns is useful in predicting future returns. Recent studies in the economic literature, however, question the contention of mean reversion in stock returns. Kim, Nelson, and Startz (1991) contend that the mean reversion in

Journal of Business Finance & Accounting, 24(1), January 1997, 0306-686X

ß Blackwell Publishers Ltd. 1997, 108 Cowley Road, Oxford OX4 1JF, UK and 350 Main Street, Malden, MA 02148, USA. 51

* The authors are respectively, Professor of Finance and Assistant Professor of Finance at the Uni- versity of Dayton (Paper received February 1995, revised and accepted November 1995)

Address for correspondence: Carl R. Chen, Department of Economics and Finance, Univer- sity of Dayton, Ohio 45469-2240, USA.

stock returns is predominately a pre-war phenomenon. Furthermore, Richardson (1993) conjectures that mean reversion in the stock market relies upon the random walk being the true model. Given these counter arguments against mean reversion in the stock market, we seek to re-examine the overreaction hypothesis based upon the same line of reasoning. Even though mean reversion in the stock market literature focuses on the `market portfolio', while the overreaction hypothesis concentrates on the winner-loser portfolio relationship, the underlying reasoning and trading implications derived from these two parallel contentions are identical: information based upon prior performance can be used to predict future performance.

Although opponents of the overreaction hypothesis concentrate their arguments on the size effect and risk factor, all studies examine average portfolio returns over an extended period of time. In reality, if time-varying risk is an important issue in this debate, and expected market returns exhibit time-varying behavior, then time-series properties of the overreaction hypothesis should be closely scrutinized. Therefore, the purpose of this paper is to study the stability and persistence of equity market overreaction in accordance with the recent findings reported by Chopra, Lakonishok, and Ritter (1992). Not only is the re-examination of this issue important to the debate over market efficiency, it also has profound implications for the viability of the contrarian investment strategy. The rest of the paper is organized as follows: the following section presents the data sample and methodology, then empirical results are discussed, and the final section concludes.

DATA SAMPLE AND METHODOLOGY

For comparability with prior studies, we use data extracted from the monthly CRSP tape from 1926 through 1992. In order to be consistent with Chopra, Lakonishok and Ritter (CLR) (1992), we form twenty portfolios based upon the same criteria used in their study. Specifically, all stocks that are continuously listed for the prior five years are ranked on the basis of their five-year buy-and-hold returns and assigned to one of twenty portfolios. This procedure results in 58 ranking periods with the first ranking period extending from 1926 through 1930 and the last ranking period extending from 1983 through 1987. Monthly post-ranking period returns are compounded to obtain annual portfolio returns. These annual portfolio returns are then averaged over the five year post-ranking period to obtain average annual post-ranking period returns for each portfolio. The resulting post-ranking periods, following the CLR study, are five-year intervals starting with 1931 through 1935 and ending with 1988 through 1992. This procedure yields a total of 58 time-series portfolio returns for each rank portfolio (ranking period and post-ranking period) for our analysis.

52 CHEN AND SAUER

ß Blackwell Publishers Ltd 1997

Our procedure differs slightly from the CLR study in one aspect. A firm is deleted from our sample in the year it is delisted from the exchange. In contrast, CLR remove a firm from their sample in the year following delisting by substituting market returns for missing returns in the year of delisting.

To ensure comparability with prior studies, we report the average test period (post-ranking period) returns for all twenty portfolios in Table 1. As shown in Table 1, the loser (rank 1) portfolio yields an average return of 23.74 percent, while the winner (rank 20) portfolio has an average return of 12.43 percent. The loser portfolio outperforms the winner portfolio by approximately 11 percent annually over the past 66 years. These figures are slightly lower than those reported in the CLR study, but are still considered quite comparable. The slight difference could be due to the fact that our analysis includes six more years of data. Table 1 also provides strong evidence

Table 1

Average Annual Post-ranking Period Returns for Twenty Portfolios Formed on the Basis of Ranking Period Returns

Portfolio Frequency Average Annual Return (%) t-statistics

1 14,614 23.736 2 14,981 21.230 3.069* 3 15,142 20.085 4.748* 4 15,181 20.172 4.603* 5 15,304 18.997 6.408* 6 15,452 19.059 6.366* 7 15,463 18.357 7.293* 8 15,353 17.942 7.856* 9 15,428 17.110 8.226* 10 15,367 16.707 9.811* 11 15,487 16.333 10.428* 12 15,491 16.654 9.954* 13 15,557 16.599 10.056* 14 15,591 15.307 11.915* 15 15,597 15.368 11.850* 16 15,677 14.844 12.570* 17 15,665 14.484 13.078* 18 15,767 14.068 13.597* 19 15,842 12.794 15.399* 20 15,885 12.429 15.562*

Notes: Portfolio 1 is comprised of stocks with the lowest ranking-period returns (loser portfolio), and port- folio 20 is comprised of the stocks with the highest ranking-period returns (winner portfolio). Frequency represents the cumulative total number of valid firm data for each portfolio over the 58 five-year ranking periods. t-statistics test pairwise differences between return of portfolio 1 and other rank portfolios. * Denotes significant at the 1% level.

IS STOCK MARKET OVERREACTION PERSISTENT OVER TIME? 53

ß Blackwell Publishers Ltd 1997

that post-ranking period portfolio returns steadily decline as one moves from the extreme loser portfolio to the extreme winner portfolio. We also conduct t- tests to determine if returns of the rank portfolios are statistically different from the loser (rank 1) portfolio. All t-statistics are significant at the one percent level, which reinforces the prior findings of a winner-loser portfolio relationship. Returns for these twenty rank portfolios are plotted in Figure 1 which provides visual evidence of a winner-loser portfolio relationship.

EMPIRICAL ANALYSIS

How Consistent Does the Market Overreact Over Time?

Although Table 1 and Figure 1 show convincing evidence that ranking period returns are negatively correlated with post-ranking period returns over the past 66 years, it is not clear if this return reversal pattern is persistent over time. Alternatively, is this performance reversal dominated by outcomes found only during certain periods of time? To examine the time-series property of the overreaction hypothesis, we compute the loser and winner portfolio returns for each post-ranking period. The results yield 58 post- ranking returns for each portfolio. Since the contrarian strategy calls for the purchase of the loser portfolio and the sale of the winner portfolio, we compute

Figure 1

Whole Period

54 CHEN AND SAUER

ß Blackwell Publishers Ltd 1997

the return differences between these two portfolios for the so-called `arbitrage portfolio returns'. Thus, the arbitrage portfolio returns represent abnormal returns obtained from taking a long position in the loser portfolio and a short position in the winner portfolio. As indicated in Table 1, the average gain of such a strategy over the past 66 years averages approximately 11 percent. We plot the 58 time-series arbitrage portfolio returns in Figure 2. As

expected, returns to the arbitrage portfolio are actually quite volatile over time. Returns to the arbitrage portfolio experience significant `losses' immediately after the Great Depression period, and recover handsomely in the late 1930s and early 1940s. During the 15 year period between the mid 1940s and late 1950s, the arbitrage portfolio earns almost no returns at all. While the abnormal returns pattern is quite stable during the decade of the 1960s, volatility increases again in the 1970s after the energy crisis, and negative abnormal returns are observed after the mid 1980s. Since `consistent overreaction' is an important factor for the contrarian strategy to be successful, our preliminary results cast doubt on the effectiveness of trading strategies that rely on the overreaction hypothesis.

Overreaction During Various Time Regimes

Although Kim, Nelson and Startz (1991) argue that mean reversion in the stock market is predominately a pre-war phenomenon, Figure 2 suggests that

Figure 2

Returns of Arbitrage Portfolio

IS STOCK MARKET OVERREACTION PERSISTENT OVER TIME? 55

ß Blackwell Publishers Ltd 1997

an investment strategy based upon the overreaction hypothesis produces different results over time. We therefore examine performance of twenty rank portfolios over four intuitively apparent regimes. The first subperiod covers seventeen five year ranking (post-ranking) periods starting 1926^30 (1931^ 35) and ending 1942^46 (1947^51). This subperiod approximately corresponds to the pre-war period. The second subperiod includes thirteen five year ranking (post-ranking) periods starting 1943^47 (1948^52) and ending 1955^59 (1960^64). This subperiod corresponds to the post-war and Korean War periods. The third subperiod has fifteen five year ranking (post- ranking) periods which begins 1956^60 (1961^65) and ends 1970^74 (1975^ 79). This subperiod is hereafter termed the pre-energy-crisis period. Finally, the fourth subperiod encompasses thirteen five year ranking (post-ranking) periods that starts 1971^75 (1976^80) and ends 1983^87 (1988^92). This subperiod is named the post-energy-crisis era.1 Table 2 exhibits returns of twenty rank portfolios based upon sample partitioning. Average annual post- ranking period returns for twenty rank portfolios are formed on the basis of ranking period returns. Therefore, portfolio 1 is comprised of stocks with the lowest ranking period returns, and portfolio 20 is comprised of stocks with the highest ranking period returns. The overreaction hypothesis is most evident during the pre-war period. Not only does the loser portfolio outperform the winner portfolio by 25 percent (0.38^0.13), but the portfolio returns also steadily decline over the portfolio ranks. This parallels the results found in Kim, Nelson and Startz (1991) which re-examines the mean reversion in market portfolio returns. We also conduct t-tests to examine if returns of portfolios 2 through 20 are significantly different from that of the rank 1 portfolio. T-statistics strongly suggest that portfolio returns do decline steadily over the portfolio ranks.

The relationship between winner-loser portfolio performance becomes ambiguous during the post-war periods of the 1940s and 1950s. The loser portfolio earned only three percent above the winner portfolio and returns to rank portfolios are all quite similar irrespective of portfolio rank. The corresponding t-statistics indicate that only four out of nineteen portfolios (portfolios 7, 8, 9 and 20) have statistically different returns from that of the rank 1 portfolio. This represents a sharp contrast to the results found in the pre-war period.

Overreaction, however, becomes evident again during the pre-energy-crisis regime (1960s and 1970s). Not only does the loser portfolio outperform the winner portfolio by a wide margin of 18 percent (0.232^0.053), a pattern of steady decline in returns over portfolio ranks is also evident. Pairwise t- statistics are all significant at the one percent level which further reinforces the notion of stock market overreaction during this subsampling period. The winner-loser relationship, nevertheless, weakens substantially during the post-energy-crisis era. Most of the rank portfolios performed equally well. In effect, nine portfolios outperformed the loser (rank 1) portfolio. T-statistics

56 CHEN AND SAUER

ß Blackwell Publishers Ltd 1997

Table 2

Average Annual Post-ranking Returns for Twenty Portfolios Formed on the Basis of Ranking Period Returns

Portfolio Pre-war t-statistics 1940^1950s t-statistics Pre-energy-crisis t-statistics Post-energy-crisis t-statistics

1 0.37952 ^ 0.18942 ^ 0.23242 ^ 0.19729 ^ 2 0.27464 4.03* 0.18304 0.43 0.18473 3.31* 0.22117 ÿ1.81*** 3 0.22900 6.18* 0.17747 0.84 0.18392 3.42* 0.21350 ÿ1.36 4 0.26933 4.38* 0.17464 1.08 0.16585 4.87* 0.21318 ÿ1.29 5 0.21975 6.65* 0.17385 1.15 0.16446 5.01* 0.20564 ÿ0.75 6 0.23250 6.10* 0.16922 1.51 0.15432 5.78* 0.21196 ÿ1.34 7 0.22582 6.31* 0.16177 2.13** 0.15030 6.06* 0.20231 ÿ0.45 8 0.19443 7.90* 0.16643 1.77*** 0.14682 6.06* 0.20653 ÿ0.83 9 0.19094 7.98* 0.15388 2.79* 0.13689 7.25* 0.19976 ÿ0.23

10 0.19438 7.99* 0.16943 1.54 0.12143 8.43* 0.19150 0.53 11 0.18138 8.63* 0.17082 1.41 0.11467 9.05* 0.19281 0.42 12 0.18398 8.52* 0.16820 1.62 0.12022 8.58* 0.19682 0.04 13 0.18308 8.62* 0.17816 0.85 0.11035 9.35* 0.19873 ÿ0.13 14 0.15945 9.66* 0.17327 1.25 0.10160 10.02* 0.18385 1.26 15 0.15737 9.85* 0.17313 1.24 0.10236 9.93* 0.18610 1.05 16 0.15617 9.78* 0.17410 1.17 0.09399 10.64* 0.17942 1.68*** 17 0.13638 10.91* 0.17820 0.84 0.08561 11.28* 0.18285 1.33 18 0.14051 10.66* 0.18016 0.69 0.07861 11.75* 0.17404 2.14** 19 0.13327 11.33* 0.17586 1.01 0.05702 13.32* 0.16095 3.36* 20 0.12773 11.23* 0.15831 2.31** 0.05307 13.27* 0.16625 2.75*

Notes: Results based upon four subperiods. T-statistics test pairwise differences between return of portfolio 1 and other rank portfolios. *, **, and *** denote significance at the 1%, 5%, and 10% level, respectively.

IS S T O C K

M A R K E T O V E R R E A C T IO

N P E R S IS T E N T O V E R T IM

E ?

57

ß B lackw

ellP u b lish

ers L td

1997

Figure 3

Pre-war Period

Figure 4

1940^1950s

58 CHEN AND SAUER

ß Blackwell Publishers Ltd 1997

Figure 5

Pre-energy-crisis

Figure 6

Post-energy-crisis

IS STOCK MARKET OVERREACTION PERSISTENT OVER TIME? 59

ß Blackwell Publishers Ltd 1997

reveal that only five portfolios have returns which are statistically different from that of portfolio 1. One of the five portfolios even has a sign reversal. These observations are reinforced in Figures 3 through 6, which plot returns of twenty rank portfolios during the four aforementioned subperiods. To summarize, evidence presented in Table 2 and Figures 3 through 6 suggests that the stock market overreaction hypothesis prevails in the pre-war period and the decade preceding the energy-crisis, but not during the post-war and post-energy-crisis periods.

While examination of the winner-loser portfolio relationship during subperiods casts doubt on the consistency of the overreaction hypothesis, standard deviation of returns for each rank portfolio based upon time-series data provides yet another piece of information pertinent to the time-series property of the overreaction hypothesis which has not been examined in prior studies. First, we computed the time-series standard deviation for each rank portfolio during the whole sampling period following equation (1):

�i�p;q� � Pq

t�p�rit ÿ�ri�2 qÿ p

" #1=2 �1�

where rit represents five year post-ranking period returns at time t for regime i; �ri is the average post-ranking period returns during regime i, and p and q are the starting year and the ending year for regime i, respectively.2 Results are displayed in column 1 of Table 3. We also plot these results in Figure 1 along with the rank portfolio returns data. It is quite obvious that although the loser portfolio has the highest mean return during the post-ranking period, it also has the highest standard deviation. This result implies that a loser portfolio during the ranking period is not a `consistent' winner portfolio during the post-ranking period. It is also very interesting to note that the standard deviation persistently declines as the portfolio rank increases and then increases again when moving toward the extreme winner portfolio. Therefore, we observe a U-shaped pattern of standard deviations of rank portfolios. A ranking period winner (loser) portfolio does not consistently become a post- ranking period loser (winner) portfolio.

We also examine the time-series standard deviations of twenty rank portfolios based upon sample partitioning. Results based on four time regimes are reported in columns 2 through 5 of Table 3. They are also plotted in Figures 3 through 6 along with returns data. Without exception, the ranking period loser portfolios (i.e., post-ranking period winner portfolios) all reveal a much higher standard deviation than other rank portfolios. More strikingly, all of the standard deviations suggest a U-shaped pattern over twenty rank portfolios with the exception of, perhaps, the pre-war period which has the strongest winner-loser portfolio relationship. The U-shaped standard deviation pattern imples that one becomes less certain that a ranking period winner (loser) portfolio will consistently be a loser (winner) portfolio in

60 CHEN AND SAUER

ß Blackwell Publishers Ltd 1997

successive time periods. In effect, it suggests that the mid-rank portfolios (e.g., rank 12) are most likely to be mid-rank portfolios again over time.

To further support our contention, we investigate the following regression equations:

�j � ���RNj ��j; �2�

�j � ���RNj � ��RNj�2 ��j: �3� Where �j represents the standard deviation of rank portfolio j, RNj is the ordinal rank value, and �j represents random shocks. Equation (2) tests the linear relationship between �j and RNj, and equation (3) tests for the U- shaped property of the time-series standard deviations. Time-series standard deviations exhibit a significant U-shaped pattern if both � and � coefficients are statistically significant. Since overlapping data are used, we employ robust estimator models following Hansen and Hodrick (1980) and White (1980), which adjust for both serial correlation and conditional heteroscedasticity. Regression results for the four subperiods and the whole sample period are reported in Table 4.

Table 3

Time-series Standard Deviations of Average Annual Post-ranking Period Returns for Twenty Portfolios: Results for Both the Whole Period and Four

Subperiods

Portfolio Whole Pre-war 1940^1950s Pre-energy- Post-energy- Period Period crisis crisis

1 0.230563 0.341872 0.077284 0.161642 0.117936 2 0.158249 0.229163 0.064708 0.130300 0.110748 3 0.134216 0.192444 0.048561 0.123154 0.096245 4 0.139987 0.200179 0.040340 0.118566 0.084095 5 0.119975 0.168269 0.050930 0.115477 0.078520 6 0.117655 0.166428 0.042481 0.101521 0.077712 7 0.117746 0.154589 0.044963 0.116130 0.085366 8 0.102447 0.135326 0.035773 0.113083 0.069611 9 0.100426 0.133274 0.041175 0.101892 0.068083

10 0.099259 0.117890 0.032246 0.108566 0.082513 11 0.092321 0.114075 0.046320 0.098915 0.057629 12 0.086229 0.105004 0.050855 0.091203 0.053357 13 0.088352 0.107417 0.045496 0.087528 0.059738 14 0.084100 0.096781 0.044626 0.088594 0.063191 15 0.080218 0.088134 0.048455 0.091242 0.050628 16 0.081851 0.094179 0.047305 0.083290 0.058086 17 0.080660 0.071947 0.046699 0.095174 0.059913 18 0.085964 0.084112 0.054384 0.096174 0.065659 19 0.091586 0.076829 0.056261 0.106999 0.075756 20 0.099475 0.088557 0.053317 0.119790 0.088474

IS STOCK MARKET OVERREACTION PERSISTENT OVER TIME? 61

ß Blackwell Publishers Ltd 1997

Without exception, R2s improve dramatically as the (RNj) 2 variable is

added to the linear equation. All of the � coefficients are statistically significant at the 0.001 level with the correct sign. The improvement is most evident for the 1940^1950s subperiod. Without (RNj)

2, the � coefficient is not significant and the R2 value is a mere two percent. With (RNj)

2 added, however, both � and � coefficients are statistically significant, and the R2 value increases from two percent to 60 percent. Therefore, we conclude that not only is the winner-loser relationship inconsistent over the four time regimes, it is also unstable within the subsampling periods as suggested by the U-shaped pattern of standard deviations.

Is the Overreaction Phenomenon a Manifestation of Market Cycles?

The time-series property of arbitrage portfolio returns displayed in Figure 2 suggests that the instability of the arbitrage portfolio performance may be

Table 4

Regression Results of: (1) �j = � + �(RN)j + �j, and

(2) �j = � + �(RN)j + �(RNj) 2 + �j

Time Regimes and � � � R2

Equation No.

Pre-war (1) 0.2397 ÿ0.009657 0.76 (10.4)* (ÿ5.43)*

Pre-war (2) 0.3024 ÿ0.02674 0.000813 0.91 (30.89)* (ÿ9.05)* (5.80)*

1940^1950s (1) 0.0512 ÿ0.000245 0.02 (6.49)* (ÿ0.43)

1940^1950s (2) 0.0701 ÿ0.0054 0.00246 0.60 (18.8)* (ÿ5.47)* (5.32)*

Pre-energy-crisis (1) 0.1288 ÿ0.002037 0.43 (14.6)* (ÿ2.42)**

Pre-energy-crisis (2) 0.1578 ÿ0.00995 0.0003768 0.82 (35.72)* (ÿ7.69)* (6.26)*

Post-energy-crisis (1) 0.0963 ÿ0.002007 0.42 (10.48)* (ÿ2.30)**

Post-energy-crisis (2) 0.1268 ÿ0.01036 0.000397 0.85 (41.81)* (ÿ8.82)* (7.11)*

Whole period (1) 0.1587 ÿ0.004685 0.60 (9.51)* (ÿ3.47)*

Whole period (2) 0.20669 ÿ0.01776 0.000623 0.88 (37.77)* (ÿ10.06)* (7.35)*

Notes: t-statistics are in parentheses. * and ** denote significance at the 0.1% and 5% level, respectively.

62 CHEN AND SAUER

ß Blackwell Publishers Ltd 1997

related to market cycles. To examine this point further, we computed market risk premiums for each of the 58 five-year post-ranking periods. Market risk premiums are defined as the difference between the risk-free rate (three- month T-bill rate of return) and the equally weighted CRSP return. Monthly returns are first compounded to obtain annual returns, and the annual returns are averaged over the five-year post-ranking period.

Arbitrage portfolio returns and market risk premiums are plotted in Figure 7. A clear positive relationship between the arbitrage portfolio returns and market risk premiums emerge. The following explanation becomes plausible: During economic downturns, losers go down faster and deeper than winners. On the other hand, losers go up faster than winners during economic upturns. During periods of economic stability, losers perform just as well as winners, and there are little abnormal profits for the arbitrage portfolio. This reasoning is in line with the dynamics of time-varying betas and nonstationary expected market risk premiums. This interpretation is also consistent with the observed `size effect' found in the overreaction literature (e.g., Zarowin, 1989 and 1990), because losers are more likely to be smaller firms. Zarowin finds that the overreaction effect becomes insignificant after the size effect is controlled for. Although a later study by Chopra, Lakonishok and Ritter (1992) finds an overreaction effect when the size effect is taken into consideration, they also find that the overreaction effect is much stronger in small firms than in large firms.

Figure 7

Arbitrage Portfolio vs. MRP

IS STOCK MARKET OVERREACTION PERSISTENT OVER TIME? 63

ß Blackwell Publishers Ltd 1997

To test our arguments statistically, we consider the following regression model based upon the CAPM framework:

��RLt ÿ Rft�ÿ�Rwt ÿRft�� � ����Rmt ÿ Rft�� ut: �4� Equation (4) can be further reduced to:

�RLt ÿ Rwt�� ����Rmt ÿRft�� ut; �5� where RLt is the loser's return, Rwt is the winner's return, Rmt represents the market return, and Rft measures the risk-free rate. The dependent variable in equation (5) is thus the arbitrage portfolio return, and the independent variable is the market risk premium. Based upon the CAPM framework, � is a measurement of the beta risk differential between the loser and winner portfolios, and � is a measurement of abnormal performance of the arbitrage portfolio. If the arbitrage portfolio obeys the efficient market rule implied by the CAPM framework, then we expect a significant � coefficient and an insignificant � coefficient. Fifty-eight post-ranking period returns in conjunction with the Hansen and Hodrick (1980) and White (1980) models are employed in the time-series analysis. The regression results can be summarized as follows:

(RLtÿRwt) =ÿ0.004413 + 0.92657 (RmtÿRft), (ÿ0.075) (2.45)**

R2 = 0.38.

The intercept term (i.e., � coefficient) is a miniscule ÿ0.004413 and is not statistically significant. On the other hand, the � coefficient is close to unity and is statistically significant at the 0.05 level with a t-statistic of 2.45.3 Simply put, the arbitrage portfolio earns no abnormal returns after the risk differential between the loser and winner portfolios is factored into the analysis. This result is entirely consistent with the efficient market predictions if the CAPM appropriately describes the returns generating process.

CONCLUSIONS

Using the monthly CRSP tape, we re-examine the overreaction hypothesis posited by DeBondt and Thaler (1985 and 1987), and reinforced by Chopra, Lakonishok and Ritter (1992) employing data from 1926 to 1992. This study differs from prior research in that we examine the time-series properties of the loser and winner portfolios. The main findings of our paper are:

(1) Returns obtained from the contrarian investment strategy utilizing the overreaction concept are not time-stationary. More specifically, there are periods when the contrarian strategy earns tremendous profit (e.g., during the recovering years of the Great Depression), periods when the

64 CHEN AND SAUER

ß Blackwell Publishers Ltd 1997

strategy earns negative profit (e.g., the Great Depression years and the early 1980s), and extended periods when the strategy earns no abnormal profits at all (e.g., from mid 1940s to mid 1950s). If consistent performance is a prerequisite for the contrarian strategy to work well, then this strategy fails its first test.

(2) We partition the whole sampling period into four time regimes. The overreaction hypothesis is most evident during the pre-war subperiod which is consistent with the findings of a seemingly unrelated study conducted by Kim, Nelson and Startz (1991). The winner-loser portfolio relationship becomes ambiguous during the post-war subperiod of 1940^1950s. Although this relationship resumes during the pre-energy-crisis subperiod, it is substantially weakened again during the post-energy-crisis era.

(3) Time-series standard deviations of rank portfolios follow a U-shaped pattern, which suggests that extreme portfolios are less likely to remain extreme portfolios over successive time periods than, say, for a mid- rank portfolio to become a mid-rank portfolio again. This result reinforces the contention that the overreaction phenomenon is not consistent over the four time regimes examined. The viability of a trading strategy based upon the volatile overreaction hypothesis is thus questionable.

(4) We also investigate the relationship between the arbitrage portfolio returns and market risk premiums. The results suggest a strong positive relationship. Using a CAPM framework, the arbitrage portfolio's abnormal returns disappear after the market factor is incorporated into the model. This finding supports Chan's contention that a portfolio selection procedure based upon the overreaction hypothesis picks very risky losers when the expected market risk premium is high and less risky losers when the expected market risk premium is low.

NOTES

1 The division of our sample into four specific time regimes is not ad hoc for a few reasons. First, Figure 2 suggests the possible existence of four distinctive time regimes; second, World War II and energy-crisis periods are frequently considered by economists as turning points of economic structural changes; and third, the division results in four time regimes of approximately the same length.

2 Because rit follows a moving average process, standard deviations are probably underestimated since a moving average process smooths out extreme values. The underestimates, however, are consistent over various rank portfolios. Therefore, cross-portfolio comparisons are still valid.

3 Our estimate of the slope coefficient is comparable to Ball and Kothari (1980), and Chopra, Lakonishok, and Ritter (1992), but considerably larger than Zarowin (1990). The smaller estimate found in Zarowin is due to his use of monthly data instead of annual data.

IS STOCK MARKET OVERREACTION PERSISTENT OVER TIME? 65

ß Blackwell Publishers Ltd 1997

REFERENCES

Abarbanell, J.S. and V.L. Bernard (1992), `Tests of Analysts' Overaction/Underreaction to Earnings Information as an Explanation for Anomolous Stock Price Behaviour', Journal of Finance, Vol. 47, No. 3 (July), pp. 1181^208.

Ball, R. and S.P. Kothari (1989), `Nonstationary Expected Returns: Implications for Tests of Market Efficiency and Serial Correlations in Returns', Journal of Financial Economics, Vol. 25, No. 1, pp. 51^74.

Brown, K.C. and W.V. Harlow (1988), `Market Overreaction: Magnitude and Intensity', Journal of Portfolio Management, Vol. 14, No. 2 (Winter), pp. 6^13.

Chan K.C. (1988), `On the Contrarian Investment Strategy', Journal of Business, Vol. 61, No. 2, pp. 147^63.

Chen, N.F. (1991), `Financial Investment Opportunities and the Macroeconomy', Journal of Finance, Vol. 46, No. 2 (June), pp. 529^54.

Chopra, N., J. Lakonishok and J.R. Ritter (1992), `Measuring Abnormal Performance: Do Stocks Overreact?', Journal of Financial Economics, Vol. 31, No. 2, pp.235^68.

DeBondt, W.F.M. and R.H. Thaler (1985), `Does the Stock Market Overreact?', Journal of Finance, Vol. 40, No. 3 (July), pp. 793^805.

________________________ ________________________ (1987), `Further Evidence on Investor Overreaction and Stock Market Seasonality', Journal of Finance, Vol. 42, No. 3 (July), pp. 557^82.

Fama, E.F. and K.R. French (1988), `Permanent and Temporary Components of Stock Prices', Journal of Political Economy, Vol. 96, No. 2, pp. 246^73.

Hansen, L.P. and R.J. Hodrick (1980), `Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis', Journal of Political Economy, Vol. 88, No. 5, pp. 829^ 53.

Kahneman, D. and A Tversky (1982), `Intuitive Prediction: Biases and Corrective Procedures', in D. Kahneman, P. Slovic and A. Tversky (eds.), Judgement Under Uncertainty: Heuristics and Biases (New York: Cambridge University Press.)

Kaul, G. and M. Nimalendran (1990), `Price Reversals: Bid-Ask Errors or Market Overreaction?', Journal of Financial Econometrics, Vol. 28, No. 1/2 (December), pp. 67^94.

Kim, M.J., C.R. Nelson and R. Startz (1991), `Mean Reversion in Stock Prices? A Reappraisal of the Empirical Evidence', Review of Economic Studies, Vol. 58, No. 195, pp. 515^28.

Lo, A.W. and A.C. MacKinlay (1988), `Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test', Review of Financial Studies, Vol. 1 No. 1, pp. 41^ 66.

________________________ ________________________ (1990), `When Are Contrarian Profits Due to Stock Market Overreaction?', Review of Financial Studies, Vol. 3, No. 2, pp. 175^206.

Poterba, J.M. and L.H. Summers (1988), `Mean Reversion in Stock Prices: Evidence and Implications', Journal of Financial Economics, Vol. 22, No. 1, pp. 27^59.

Richardson, M. (1993), `Temporary Components of Stock Prices: A Skeptic's View', Journal of Business and Economics Statistics, Vol. 11, No. 2 (April), pp. 197^207.

Seyhun, H.N. (1990), `Overreaction or Fundamentals: Some Lessons From Insiders' Response to the Market Crash of 1987', Journal of Finance, Vol. 45, No. 5 (December), pp. 1363^88.

Stein, J. (1989), `Overreaction in the Options Market', Journal of Finance, Vol. 44, No. 4 (September), pp. 1011^24.

White, H. (1980), `Heteroscedasticity-consistent Covariance Matrix Estimator and Direct Test for Heteroscedasticity', Econometrica, Vol. 48, pp. 817^38.

Zarowin, P. (1989), `Short-Run Market Overreaction: Size and Seasonality Effects', Journal of Portfolio Management, Vol. 15, No. 3 (Spring), pp. 26^9.

________________________ (1990), `Size, Seasonality, and Stock Market Overreaction', Journal of Financial and Quantitative Analysis, Vol. 25, No. 1 (March), pp. 113^26.

66 CHEN AND SAUER

ß Blackwell Publishers Ltd 1997

Copyright of Journal of Business Finance & Accounting is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use.