THE JOURNAL OF FINANCE. VOL. XLVIII, NO.1. MARCH 1993
Returns to Buying Winners and Selling
Losers: Implications for
Stock Market Efficiency
NARASIMHAN JEGADEESH and SHERIDAN TITMAN*
ABSTRACT
This paper documents that strategies which buy stocks that have performed well in
the past and sell stocks that have performed poorly in the past generate significant
positive returns over 3- to 12-month holding periods. We find that the profitability
of these strategies are not due to their systematic risk or to delayed stock price
reactions to common factors. However, part of the abnormal returns generated in
the first year after portfolio formation dissipates in the following two years. A
similar pattern of returns around the earnings announcements of past winners and
losers is also documented.
A POPULAR VIEW HELD by many journalists, psychologists, and economists is
that individuals tend to overreact to information. 1 A direct extension of this
view, suggested by De Bondt and Thaler (1985, 1987), is that stock prices also
overreact to information, suggesting that contrarian strategies (buying past
losers and selling past winners) achieve abnormal returns. De Bondt and
Thaler (1985) show that over 3- to 5-year holding periods stocks that per-
formed poorly over the previous 3 to 5 years achieve higher returns than
stocks that performed well over the same period. However, the interpretation
of the De Bondt and Thaler results are still being debated. Some have argued
that the De Bondt and Thaler results can be explained by the systematic risk
of their contrarian portfolios and the size effect." In addition, since the
long-term losers outperform the long-term winners only in Januaries, it is
unclear whether their results can be attributed to overreaction.
*Jegadeesh is from the Anderson Graduate School of Management, UCLA. Titman is from
Hong Kong University of Science and Technology and the Anderson Graduate School of Manage-
ment, UCLA. We would like to thank Kent Daniel, Ravi Jagannathan, Richard Roll, Hans Stoll,
Rene Stulz, and two referees. We also thank participants of the Johnson Symposium held at the
University of Wisconsin at Madison and seminar participants at Harvard, SMU, UBC, UCLA,
Penn State, University of Michigan, University of Minnesota, and York University for helpful
comments, and Juan Siu and Kwan Ho Kim for excellent research assistance.
1See for example, the academic papers by Kahneman and Tversky (1982), De Bondt and
Thaler (1985) and Shiller (1981).
2See for example, Chan (1988), Ball and Kothari (1989), and Zarowin (1990). For an alternate
view, see the recent paper by Chopra, Lakonishok, and Ritter (1992).
65
66 The Journal ofFinance
More recent papers by Jegadeesh (1990) and Lehmann (1990) provide
evidence of shorter-term return reversals. These papers show that contrarian
strategies that select stocks based on their returns in the previous week or
month generate significant abnormal returns. However, since these strate-
gies are transaction intensive and are based on short-term price movements,
their apparent success may reflect the presence of short-term price pressure
or a lack of liquidity in the market rather than overreaction. Jegadeesh and
Titman (1991) provide evidence on the relation between short-term return
reversals and bid-ask spreads that supports this interpretation. In addition,
Lo and MacKinlay (1990) argue that a large part of the abnormal returns
documented by Jegadeesh and Lehmann is attributable to a delayed stock
price reaction to common factors rather than to overreaction.
Although contrarian strategies have received a lot of attention in the recent
academic literature, the early literature on market efficiency focused on
relative strength strategies that buy past winners and sell past losers. Most
notably, Levy (1967) claims that a trading rule that buys stocks with current
prices that are substantially higher than their average prices over the past 27
weeks realizes significant abnormal returns. Jensen and Bennington (1970),
however, point out that Levy had come up with his trading rule after
examining 68 different trading rules in his dissertation and because of this
express skepticism about his conclusions. Jensen and Bennington analyze the
profitability of Levy's trading rule over a long time period that was, for the
most part, outside Levy's original sample period. They find that in their
sample period Levy's trading rule does not outperform a buy and hold
strategy and hence attribute Levy's result to a selection bias.
Although the current academic debate has focused on contrarian rather
than relative strength trading rules, a number of practitioners still use
relative strength as one of their stock selection criteria. For example, a
majority of the mutual funds examined by Grinblatt and Titman (1989, 1991)
show a tendency to buy stocks that have increased in price over the previous
quarter. In addition, the Value Line rankings are known to be based in large
part on past relative strength. The success of many of the mutual funds in
the Grinblatt and Titman sample and the predictive power of Value Line
rankings (see Copeland and Mayers (1982) and Stickel (1985)) provide sug-
gestive evidence that the relative strength strategies may generate abnormal
returns.
How can we reconcile the success of Value Line rankings and the mutual
funds that use relative strength rules with the current academic literature
that suggests that the opposite strategy generates abnormal returns? One
possibility is that the abnormal returns realized by these practitioners are
either spurious or are unrelated to their tendencies to buy past winners. A
second possibility is that the discrepancy is due to the difference between the
time horizons used in the trading rules examined in the recent academic
papers and those used in practice. For instance, the above cited evidence
favoring contrarian strategies focuses on trading strategies based on either
Returns to Buying Winners and Selling Losers 67
very short-term return reversals (l week or 1 month), or very long-term
return reversals (3 to 5 years). However, anecdotal evidence suggests that
practitioners who use relative strength rules base their selections on price
movements over the past 3 to 12 months." This paper provides an analysis of
relative strength trading strategies over 3- to 12-month horizons. Our analy-
sis of NYSE and AMEX stocks documents significant profits in the 1965 to
1989 sample period for each of the relative strength strategies examined. We
provide a decomposition of these profits into different sources and develop
tests that allow us to evaluate their relative importance. The results of these
tests indicate that the profits are not due to the systematic risk of the trading
strategies. In addition, the evidence indicates that the profits cannot be
attributed to a lead-lag effect resulting from delayed stock price reactions to
information about a common factor similar to that proposed by Lo and
MacKinlay (1990). The evidence is, however, consistent with delayed price
reactions to firm-specific information.
Further tests suggest that part of the predictable price changes that occur
during these 3- to 12-month holding periods may not be permanent. The
stocks included in the relative strength portfolios experience negative abnor-
mal returns starting around 12 months after the formation date and continu-
ing up to the thirty-first month. For example, the portfolio formed on the
basis of returns realized in the past 6 months generates an average cumula-
tive return of 9.5% over the next 12 months but loses more than half of this
return in the following 24 months.
Our analysis of stock returns around earnings announcement dates sug-
gests a similar bias in market expectations. We find that past winners realize
consistently higher returns around their earnings announcements in the 7
months following the portfolio formation date than do past losers. However,
in each of the following 13 months past losers realize higher returns than
past winners around earnings announcements.
The rest of this paper is organized as follows: Section I describes the
trading strategies that we examine and Section II documents their excess
returns. Section III provides a decomposition of the profits from relative
strength strategies and evaluates the relative importance of the different
components. Section IV documents these returns in subsamples stratified on
the basis of ex ante beta and firm size and Section V measures these profits
across calendar months and over 5-year subperiods. The longer term perfor-
mance of the stocks included in the relative strength portfolios is examined in
Section VI and Section VII back tests the strategy over the 1927 to 1964
3For instance, one of the inputs used by Value Line to assign a timeliness rank for each stock
is a price momentum factor computed based on the stock's past 3- to 12-month returns. Value
Line reports that the price momentum factor.is computed by "dividing the stock's latest lO-week
average relative price by its 52-week average relative price." These timeliness ranks, according
to Value Line, are "designed to discriminate among stocks on the basis of relative price
performance over the next 6 to 12 months" (see Bernard (1984), pp. 52-53).
68 The Journal ofFinance
period. Section VIII examines the returns of past winners and past losers
around earnings announcement dates and Section IX concludes the paper.
I. Trading Strategies
If stock prices either overreact or underreact to information, then profitable
trading strategies that select stocks based on their past returns will exist.
This study investigates the efficiency of the stock market by examining the
profitability of a number of these strategies. The strategies we consider select
stocks based on their returns over the past 1, 2, 3, or 4 quarters. We also
consider holding periods that vary from 1 to 4 quarters. This gives a total of
16 strategies. In addition, we examine a second set of 16 strategies that skip
a week between the portfolio formation period and the holding period. By
skipping a week, we avoid some of the bid-ask spread, price pressure, and
lagged reaction effects that underlie the evidence documented in Jegadeesh
(1990) and Lehmann (1990).
To increase the power of our tests, the strategies we examine include
portfolios with overlapping holding periods. Therefore, in any given month t,
the strategies hold a series of portfolios that are selected in the current
month as well as in the previous K - 1 months, where K is the holding
period. Specifically, a strategy that selects stocks on the basis of returns over
the past J months and holds them for K months (we will refer to this as a
J-month/K-month strategy) is constructed as follows: At the beginning of
each month t the securities are ranked in ascending order on the basis of
their returns in the past J months. Based on these rankings, ten decile
portfolios are formed that equally weight the stocks contained in the top
decile, the second decile, and so on. The top decile portfolio is called the
"losers" decile and the bottom decile. is called the "winners" decile. In each
month t, the strategy buys the winner portfolio and sells the loser portfolio,
holding this position for K months. In addition, the strategy closes out the
position initiated in month t - K. Hence, under this trading strategy we
1
revise the weights on K of the securities in the entire portfolio in any given
month and carry over the rest from the previous month.
The profits of the above strategies were calculated for both a series of buy
and hold portfolios and a series of portfolios that were rebalanced monthly to
maintain equal weights. Since the returns for these two strategies were very
similar (the buy and hold strategies yielded slightly higher returns) we
present only the rebalanced returns which are also used in the event study
presented in Section VI.
II. The Returns of Relative Strength Portfolios
This section documents the returns of the portfolio strategies described in
the last section over the 1965 to 1989 period using data from the CRSP daily
Returns to Buying Winners and Selling Losers 69
returns file." All stocks with available returns data in the J months preced-
ing the portfolio formation date are included in the sample from which the
buy and sell portfolios are constructed.
Table I reports the average returns of the different buy and sell portfolios
as well as the zero-cost, winners minus losers portfolio, for the 32 strategies
described above. The returns of all the zero-cost portfolios (i.e., the returns
per dollar long in this portfolio) are positive. All these returns are statisti-
cally significant except for the 3-month/3-month strategy that does not skip
a week. Many of the individual t-statistics are sufficiently large to be
significant even after considering the fact that we have conducted 32 sepa-
rate tests. The probability of obtaining a single t-statistic as large as 4.28
(obtained with the 12-month/3-month strategy that skips a week) with 32
observations is less than 0.0006, as given by the Bonferroni inequality."
The most successful zero-cost strategy selects stocks based on their returns
over the previous 12 months and then holds the portfolio for 3 months. This
strategy yields 1.31% per month (shown in Panel A) when there is no time
lag between the portfolio formation period and the holding period and it
yields 1.49% per month (shown in Panel B) when there is a J-week lag
between the formation period and the holding period." The 6-month forma-
tion period produces returns of about 1% per month regardless of the holding
period. These holding period returns are slightly higher when there is a
J-week lag between the formation period and the holding period (Panel B)
than when the formation and holding periods are contiguous (Panel A).
Having established that the relative strength strategies are on average
quite profitable, we now examine one specific strategy in detail, the 6-
monthyfi-month strategy that does not skip a week between the portfolio
formation period and the holding period. The results for this strategy are
representative of the results for the other strategies.
III. Sources of Relative Strength Profits
This section presents two simple return-generating models that allow us to
decompose the excess returns documented in the last section and identify the
important sources of relative strength profits. The first model allows for
factor-mimicking portfolio returns to be serially correlated but requires indi-
4 The latest version of the CRSP daily returns file at the time this study was initiated covers
the July 1962 to December 1989 period. Monthly returns were obtained by compounding the
daily returns recorded in this data set. Since the 12-month/12-month strategy considered here
requires lagged returns data over 23 months the first full calendar year for which we could
examine portfolio returns is 1965.
5The Bonferroni inequality provides a bound for the probability of observing a t-statistic of a
certain magnitude with N tests that are not necessarily independent.
6 De Bondt and Thaler (1985) report I-year holding period returns in their tables that are
consistent with our findings here. However, they do not examine strategies based on L-year
horizons in any detail and based on their analysis of longer horizon strategies conclude that the
market overreacts.
70 The Journal ofFinance
Table I
Returns of Relative Strength Portfolios
The relative strength portfolios are formed based on J-month lagged returns and held for K
months. The values of J and K for the different strategies are indicated in the first column and
row, respectively. The stocks are ranked in ascending order on the basis of J-month lagged
returns and an equally weighted portfolio of stocks in the lowest past return decile is the sell
portfolio and an equally weighted portfolio of the stocks in the highest return decile is the buy
portfolio. The average monthly returns of these portfolios are presented in this table. The
relative strength portfolios in Panel A are formed immediately after the lagged returns are
measured for the purpose of portfolio formation. The relative strength portfolios in Panel Bare
formed 1 week after the lagged returns used for forming these portfolios are measured. The
t-statistics are reported in parentheses. The sample period is January 1965 to December 1989.
Panel A Panel B
J K= 3 6 9 12 K= 3 6 9 12
3 Sell 0.0108 0.0091 0.0092 0.0087 0.0083 0.0079 0.0084 00083
(2.16) (1.87) (1.92) (1.87) (1.67) (1.64) (1.77) (1.79)
3 Buy 0.0140 0.0149 0.0152 .0156 0.0156 0.0158 0.0158 0.0160
(3.57) (3.78) (3.83) (3.89) (3.95) (3.98) (3.96) (3.98)
3 Buy-sell 0.0032 0.0058 0.0061 0.0069 0.0073 0.0078 0.0074 0.0077
(1.10) (2.29) (2.69) (3.53) (2.61) (3.16) (3.36) (4.00)
6 Sell 0.0087 0.0079 0.0072 0.0080 0.0066 0.0068 0.0067 0.0076
(1.67) (1.56) (1.48) (1.66) (1.28) (1.35) (1.38) (1.58)
6 Buy 0.0171 0.0174 0.0174 0.0166 0.0179 0.0178 0.0175 0.0166
(4.28) (4.33) (4.31) (4.13) (4.47) (4.41) (4.32) (4.13)
6 Buy-sell 0.0084 0.0095 0.0102 0.0086 0.0114 0.0110 0.0108 0.0090
(2.44) (3.07) (3.76) (3.36) (3.37) (3.61) (4.01) (3.54)
9 Sell 0.0077 0.0065 0.0071 0.0082 0.0058 0.0058 0.0066 0.0078
(1.47) (1.29) (1.43) (1.66) (1.13) (1.15) (1.34) (1.59)
9 Buy 0.0186 0.0186 0.0176 0.0164 0.0193 0.0188 0.0176 0.0164
(4.56) (4.53) (4.30) (4.03) (4.72) (4.56) (4.30) (4.04)
9 Buy-sell 0.0109 0.0121 0.0105 0.0082 0.0135 0.0130 0.0109 0.0085
(3.03) (3.78) (3.47) (2.89) (3.85) (4.09) (3.67) (3.04)
12 Sell 0.0060 0.0065 0.0075 0.0087 0.0048 0.0058 0.0070 0.0085
(1.17) (1.29) (1.48) (1.74) (0.93) (1.15) (1.40) (1.71)
12 Buy 0.0192 0.0179 0.0168 0.0155 0.0196 0.0179 0.0167 0.0154
(4.63) (4.36) (4.10) (3.81) (4.73) (4.36) (4.09) (3.79)
12 Buy-sell 0.0131 0.0114 0.0093 0.0068 0.0149 0.0121 0.0096 0.0069
(3.74) (3.40) (2.95) (2.25) (4.28) (3.65) (3.09) (2.31)
vidual stocks to react instantaneously to factor realizations. This model is
used to decompose relative strength profits into two components relating to
systematic risk, which would exist in an efficient market, and a third
component relating to firm-specific returns, which would contribute to rela-
tive strength profits only if the market were inefficient. The second return-
generating model relaxes the assumption that stocks react instantaneously to
the common factor. This model enables us to evaluate the possibility that the
relative strength profits arise because of a lead-lag relationship in stock
prices similar to that proposed by Lo and MacKinlay (1990) as a partial
explanation for short horizon contrarian profits.
Returns to Buying Winners and Selling Losers
A. A Simple One-Factor Model
Consider the following one-factor model describing stock returns:"
71
E(ft) = 0
E(eit ) = 0
Cov(ei t , ft) = 0,
Cov(eit,ej t _ 1 ) = 0,
Vi
Vi -=/=j
(1)
where JLi is the unconditional expected return on security i, "u is the
return on security i, f t is the unconditional unexpected return on a factor-
mimicking portfolio, e it is the firm-specific component of return at time t, and
b, is the factor sensitivity of security i. For the 6-month/6-month strategy
that we consider in the rest of this paper the length of a period is 6 months.
The superior performance of the relative strength strategies documented in
the last section implies that stocks that generate higher than average returns
in one period also generate higher than average returns in the period that
follows. In other words, these results imply that:
and
where a bar above a variable denotes its cross-sectional average.
Therefore,
(2)
The above cross-sectional covariance equals the expected profits from the
zero-cost contrarian trading strategy examined by Lehmann (1990) and Lo
and MacKinlay (1990) that weights stocks by their past returns l
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