over confidence and momentum price
TRANSCRIPT
Investor Overconfidence and Momentum Effects:
A Comparative Study with Stocks
Zi Ning*
Department of Finance, University of Texas at San Antonio
Nicolas Gressis
Department of Finance, Wright State University
September 2006
*Corresponding author. College of Business, One UTSA Circle, San Antonio, TX 78249-1644. Tel.: 210-458-7392; E-mail: [email protected]
Directional Momentum Strategies: A Comparative Study with Stocks
Abstract
There is substantial evidence of short-term stock price momentum that is linked to investor behavioral biases. Different from previous momentum literature, this study considers not only the prior quarterly returns but also the patterns of monthly returns within specific quarter. With a focus on “winners” only, this paper investigates how return movements within a quarter affect the expectations of investors and thus the firms’ returns for the subsequent quarter. The evidence shows that there is indeed a differentiation of the new momentum strategies from the traditional momentum stock selection strategy. Momentum strategies that exhibit accelerating monthly returns seem to be most profitable over the entire 18-year period. However, a more minute examination of the results shows that the highest returns are generated from the late 1990s, when the whole market is experiencing what is called “irrational exuberance”. The results support the overreaction theories of short-run momentum. Also, the study provides additional evidence that momentum effects are closely related to investors’ psychology.
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I. INTRODUCTION
An extensive range of literature has documented that the stock returns are
predictable based on their past returns. Particularly, stock returns exhibit positive serial
correlation (momentum) at 3 to 12 month horizons (Jegadeesh & Titman 1993, 2001;
Chan et al., 1999). Jegadeesh and Titman (1993, 2001) report that trading strategies of
buying past winners and selling past losers realize significant positive returns over the
period of 1965-1998, with an excess return of about 1% per month.
Momentum has also been shown to be robust across international financial
markets (Rouwenhorst 1998; Griffin et al. 2002). For example, Rouwenhorst (1998)
shows that the equity markets in 12 European countries exhibit intermediate-term (3 to 12
months) return continuation from 1980 to 1995. A diversified portfolio of past medium-
term winners outperforms a portfolio of medium-term losers by more than 1 percent per
month after adjusting for risk.
However, there are substantial debates on the profitability of momentum, as well
as the sources of momentum returns. To date, no measures of risk have been found that
completely explain the profitability of momentum strategies. A number of authors have
found that a three-factor asset pricing model cannot explain the returns of the short-term
momentum but only the long-term reversal (Fama and French 1996; Grundy and Martin
2001; Lee and Swaminathan 2000). The persistence of intermediate-term momentum is
deemed as one of the most serious challenges to the asset-pricing literature.
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Korajczyk & Sadka (2004) find that transaction costs, in the form of spreads and
price impacts of trades, reduce but do not fully eliminate the return persistence of past
winner stocks. Chordia and Shivakumar (2002) show that macroeconomic instruments
for measuring market conditions can explain a large portion of momentum profits. They
argue that inter-temporal variations in the macroeconomic factors, such as dividend yield,
default spread, term spread, and short-term interest rates, are the main sources of
momentum profits. However, Cooper et al. (2004) find that the macroeconomic
multifactor model is not robust to common screens used to diminish microstructure-
induced biases.
Additionally, Lee and Swaminathan (2000) show that trading volume plays a role
in the profits to momentum strategies. Grinblatt and Moskowitz (2003) conclude that tax
environments affect the profits to momentum.
In recent years, several behavioral and cognitive biases theories have been
developed to jointly explain the short-run momentum in stock returns. Some claim that
momentum profits arise because of inherent biases in the way investors interpret
information (DeBondt & Thaler, 1985; Daniel et al.,1998; Hong & Stein, 1999).
Other authors claim that momentum in stock returns is related to the market’s
under-reaction to earnings-related information (Latane and Jones, 1979; and Bernard et
al., 1995; Chan et al., 1996, 1999). For instance, firms reporting unexpectedly high
earnings outperform firms reporting unexpectedly poor earnings. The market incorporates
the news in stock prices gradually, so prices exhibit predictable drifts. These drifts last for
3
up to a year (Chan et al., 1999). Barberis et al. (1998) also demonstrate that momentum
profits arise because investors under-react to ranking period information.
Contrary to the under-reaction theory, Daniel at al. (1998) report that the
momentum effect comes from the continuing overreaction of informed investors. When
the direction of the market is upwards, traders’ overconfidence is boosted. Their model
predicts that momentum profits are stronger following bull markets, which are attributed
to the psychological biases of traders.
Cooper et al. (2004) show that the profits from momentum strategies are tightly
linked to the state of the market. Overreactions become stronger following up markets
generating greater momentum in the short run. A momentum portfolio is profitable only
following periods of market gains, consistent with the overreaction models of Daniel et
al. (1998) and Hong and Stein (1999).
Intuitively, momentum effects should become even stronger if the overall market
is overconfident, such as the unusual years of the burst of High-tech bubble. During that
period, investors in general (both informed and uninformed) should be overoptimistic and
overreact to positive information. We thus should expect to observe stronger momentum
over that period. Using data from 1982 to 2000, the findings of this study are consistent
with such assumptions.
Also, in previous studies, it is usually the case that stock behaviors are examined
on a one-quarter or two-quarter basis. In order to better capture the ideas of momentum,
this study categorizes the momentum strategies into those that are with and without
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accelerating monthly returns within a quarter. Intuitively, momentum strategies with
accelerating monthly returns should convey more positive information for investors and
thus drive up the momentum returns. The evidence shows that this is exactly the case.
Using S&P 500 index as a benchmark, momentum strategies with accelerating monthly
returns are the obvious winners over the last sub-period, from 1996-2000. Yet, there is no
distinct difference in terms of returns among the four momentum strategies over the
period from 1982 to 1996 and S&P 500 index. It appears that an over-optimistic market
tends to drive up the momentum effects. Such findings indicate that psychological factor
is closely linked to the momentum effects.
The remainder of the paper is organized as follows: Section II provides a brief
description of data, sample, and methodology, the stock selection rules defined,
compared and contrasted. Section III documents the findings and analysis. Section IV
concludes the paper.
II. METHODOLOGY
RATIONALE
In the prior momentum studies, it is very common that all stocks are ranked into
deciles of stocks based on their past 3-month or 6-month rate of return compound return.
However, such ranking may not catch the essence of momentum in that stocks may
exhibit different degrees of momentum within the formation period. The traditional
momentum approach assumes that all stocks in the decile portfolio are homogeneous in
momentum, which may increase the probability of losing economically significant
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information. Intuitively, the patterns of momentum within the formation period should
differentially affect investors’ expectations (Akhbari et al., 2006).
Let’s illustrate above arguments graphically. Here, it is necessary to out that only
stocks with positive return in the past quarter are considered. Let the sequence of intra-
quarter security prices be P0, P1, P2 where P0 (P2) is the beginning (end) of quarter
price.
Figure 1. The possible patterns of monthly returns that produce the same quarterly return are illustrated.
Intuitively, patterns 2 and 3 do not reflect the momentum idea in terms of trend
continuation. Thus, although all three price patterns produce the same quarterly return,
investors are likely to have more preferences patters 1 over patterns 2 and 3 in that
pattern 1 denotes more positive information. In addition to positive ROR, the monthly
returns are all positive. Figure 2 provides a more detailed illustration of pattern 1.
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Figure 2. Intra-formation period monthly return sub-patterns.
Intuitively, price acceleration over time should be a desirable feature for
momentum investors. Thus, in figure 2, the first sub-pattern is likely more attractive than
the other sub-patterns. The investors will expect on average higher subsequent returns
from securities exhibiting this sub-pattern than from the others. The primary goal of this
paper is to find out if the portfolio consisting of stocks selected by such investment
strategy generates above the average returns in a bull market. An appealing feature of this
study is that it considers not only momentum upon formation period but also the intra-
quarterly changes of the price patterns within the formation period as applied to the
construction of common stock portfolios.
This study limits the analysis to winners alone, referring to those stocks with the
highest rate of return (ROR). The existing literature indicates that a larger share of the
abnormal returns (without trading costs) to the long/short strategy is due to the short
positions in past losers. Thus, before trading costs, winners-only investing strategy is
conservative, as it leads to lower abnormal returns (Korajczyk & Sadka, 2004).
7
SAMPLE CONSTRUCTION
The stocks are selected and evaluated on a quarterly basis. The sample data comes
from the Center for Research in Security Prices (CRSP) database. Both the CRSP
monthly and quarterly returns files are used, which included all domestic, primary stocks
listed on the New York (NYSE), American (AMEX), and Nasdaq stock markets. All
stocks priced below $10 are excluded at the beginning of the holding period so as to
ensure that “the results are not driven primarily by small and illiquid stocks or by bid-ask
bounce” (Jegadeesh and Titman, 2001).The deletion of low-priced stocks also lower the
magnitude of the sample variability. The data extends from October 1982 to September
2000, totally 72 quarters. The following is a description of the working procedures.
First, at the end of each quarter, all stocks are ranked in ascending order on the
basis of their compound returns in the past 3 months. Then, stocks are selected based on
the four selection rules describe below. The top ten stocks that meet the requirement for
each strategy are grouped into one of the four portfolios accordingly. Thus, a total of
forty stocks are selected in each quarter. The selection rules are not easily met
particularly for strategy D. Portfolios are rebalanced for each quarter. Very likely
another forty stocks are selected for the subsequent quarter. There are a total of 288
portfolios over the study period. Each portfolio is held for three months, following the
ranking quarter. The average mean of quarterly returns are calculated and reported for
each portfolio/strategy for the subsequent quarter.
8
STOCK SELECTION RULES
Four stock selection rules are discussed here, namely, strategies A, B, C and D.
A. Strategy A
According to this traditional momentum strategy, stocks are ranked from top to
bottom based on its past quarterly compound return. Mathematically, the strategy can
be expressed as follows
Max(1+Rt-1)(1+Rt-2)(1+Rt-3)
where Rt-i ( i=1,2,3) is the return on a stock in the past three months. Simply put,
portfolio A comprises the ten stocks with the largest ranking period returns.
B. Strategy B
For this specific strategy, inequality ratios imply that the chosen stock’s price
undergoes acceleration in certain months during the past quarter. It can be
mathematically written as
Max(1+Rt-1)(1+Rt-2)(1+Rt-3)
subject to
Rt-1> 0, Rt-2> 0, Rt-3> 0 and 111
2
1>
++
−
−
t
t
RR , 1
11
3
2>
++
−
−
t
t
RR
C. Strategy C
In this case, it is assumed that more recent return movements convey more
information than less recent ones. Hence, investors pay more attention to Rt-1 and Rt-2
9
than to Rt-3 and, who would prefer to select the stock that exhibits price acceleration
over the two most recent months. Mathematically, this strategy is shown as follows
Max(1+Rt-1)(1+Rt-2)(1+Rt-3)
subject to
Rt-1> 0, Rt-2> 0, Rt-3> 0 and 111
2
1>
++
−
−
t
t
RR
D. Strategy D
This strategy selects only stocks with increasing monthly price acceleration over the
past three months. It is the most difficult one to implement due to the strict selection
criteria. It is expressed as follows
Max(1+Rt-1)(1+Rt-2)(1+Rt-3)
subject to
Rt-1> 0, Rt-2> 0, Rt-3> 0 and 2
1
11
−
−
++
t
t
RR > 1
11
3
2>
++
−
−
t
t
RR
After the first round of screening, stocks that meet the criteria of particular
strategy are put into the appropriate portfolio accordingly. It is found that the ROR for
some stocks are missing in the subsequent quarter. Thus, the prices and returns of the
delisted stocks are obtained from CRSP individually. Very likely, those companies have
been either merged by other companies or simply went bankrupt. For all strategies other
than Strategy A, if less than 10 stocks meet the requirements, a certain percentage of
money would be invested in 3-month U.S. treasury bills. This situation is most likely to
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happen in strategy D. Lastly, the mean returns of strategy portfolios are calculated, in
which way comparisons can be made among the four momentum strategies.
III. RESULTS
RAW RETURNS
This section documents the returns of the strategy portfolio described in the
previous section. Table I reports the mean, or the subsequent “realized” quarterly returns
from following each of the four momentum strategies over the 72 periods. It is
emphasized that the decision on which stock to invest in is made every quarter based on
return information provided by the previous three months.
The basic assumption in all computations is that at the beginning of each quarter
studied the investor puts an equal amount of money, supposed $1 into each common
stock, under the assumption that all dividends are reinvested in the month paid.
Table I presents terminal value over the post-formation period, which shows the
evolution of wealth over the entire sample period and the sub-periods. The findings
suggest that almost all momentum strategies (with the exception of strategy C)
outperform the market.
Particularly, the analysis is motivated by the fact that typical momentum strategy
with accelerating monthly returns (strategy B) prove to be very profitable over the 18-
year period. Supposed we put $1 at the beginning of holding period, we would have
received nearly $25 by the end of holding period, more than double of the returns from
S&P 500 portfolios.
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Table I
Terminal Value of $1 Invested in Momentum Strategy Portfolios by Periods
The momentum strategy portfolios are formed based on 3-month lagged returns and held for 3 months. The stocks are ranked in ascending order on the basis of 3-month lagged returns. The momentum strategy portfolios are formed immediately after the lagged returns are measured for the purpose of portfolio formation. The terminal value of $1 invested in portfolios for strategies A, B, C and D are presented in this table. The sample period is October 1982 to September 2000. Strategy A Strategy B Strategy C Strategy D S&P500 Panel A 1982.10-2000.9 15.91 24.75 9.80 14.66 11.93 Panel B 1982.10-1991.9 2.41 2.24 2.28 2.41 3.22 1991.10-2000.9 6.59 11.04 4.29 6.09 3.70 Panel C 1982.10-1987.3 1.47 1.59 1.40 2.17 2.42 1987.4-1991.9 1.64 1.41 1.63 1.11 1.33 1991.10-1996.3 4.81 2.86 3.47 2.80 1.66 1996.4-2000.9 1.37 3.87 1.24 2.17 2.23
Figure 3-9 visually illustrates the performance of momentum portfolios over the
18-year period, the two 9-year sub-periods and four 4.5-year sub-periods.
Terminal Value of $1 Invested from 1982.10-2000.9
05
1015202530
1982
1984
1985
1986
1987
1989
1990
1991
1992
1994
1995
1996
1997
1999
2000
Time
Term
inal
Val
ue o
f $1
Inve
sted
Strategy A Strategy B Strategy C Strategy D Return S&P
Figure 3. The cumulative return for strategy A, B, C, D and S&P over the entire 18-year period.
12
Terminal Value of $1 Invested from 1982.10-1991.9
00.5
11.5
22.5
33.5
1982
1983
1984
1985
1985
1986
1987
1988
1988
1989
1990
1991
Time
Term
inal
Val
ue o
f $1
Inve
sted
Strategy A Strategy B Strategy C Strategy D Return S&P
Figure 4. The cumulative return for strategy A, B, C, D and S&P for the first 9-year sub-period.
Terminal Value of $1 Invested from 1991.10-2000.9
02468
101214
1991
1992
1992
1993
1993
1994
1994
1995
1995
1996
1996
1997
1997
1998
1998
1999
Time
Term
inal
Val
ue o
f $1
Inve
sted
Strategy A Strategy B Strategy C Strategy D Return S&P
Figure 5. The cumulative return for strategy A, B, C, D and S&P for the second 9-year sub-period.
Figures 6-9 revisit the comparative wealth behavior of the momentum strategies
under consideration over four intervals.
13
Terminal Value of $1 Invested From 1982.10-1987.3
0
0.5
1
1.5
2
2.5
3
1982
1983
1983
1984
1984
1985
1985
1986
1986
Time
Term
inal
Val
ue o
f $1
Inve
sted
Strategy A Strategy B Strategy C Strategy D Return S&P
Figure 6. The cumulative return for strategy A, B, C, D and S&P for the first 4.5-year sub-period.
Terminal Value of $1 Invested from 1987.4-1991.9
0
0.5
1
1.5
2
1987 1987 1988 1988 1989 1989 1990 1990
Time
Term
inal
Val
ue o
f $1
Inve
sted
Strategy A Strategy B Strategy C Strategy D Return S&P
Figure 7. The cumulative return for strategy A, B, C, D and S&P for the second 4.5-year sub-period.
14
Terminal Value of $1 Invested from 1991.10-1996.3
0
1
2
3
4
5
6
1991 1992 1993 1994 1994 1995
Time
Term
inal
Val
ue o
f $1
Inve
sted
Strategy A Strategy B Strategy C Strategy D Return S&P
Figure 8. The cumulative return for strategy A, B, C, D and S&P for the third 4.5-year sub-period.
Terminal Value of $1 Invested from 1996.4-2000.9
0
1
2
3
4
5
1996 1996 1997 1997 1998 1998
Time
Term
inal
Val
ue o
f $1
Inve
sted
Strategy A Strategy B Strategy C Strategy D Return S&P
Figure 9. The cumulative return for strategy A, B, C, D and S&P for the fourth 4.5-year sub-period.
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The sub-period evidence gives a better picture of the performances of momentum
strategies under study. Generally speaking, strategy B has an outstanding performance
over the entire sample period. However, over the first sub-period from 1982-1991, all
momentum strategies produce progressively inferior wealth performance relative to S&P
500 portfolio. Over the second sub-period from 1991-2000, strategy B and D are the clear
winners, which perform much better than strategy A, C and S&P 500 portfolio.
As the attention is drawn to the shorter time intervals, we find that it is over the
sub-period from 1996-2000 that has a significant influence on the terminal wealth of all
investing strategies. Typical momentum strategy B substantially outperform S&P500
index.
Such findings are not coincident. In a no-load mutual fund study done by Akhbari
et al. (2006), similar portfolio construction strategies are employed. It is found that only
in the past few years of the 1990s, when the stock market bubble burst, did the
momentum strategy B clearly exhibit superior performance. Both evidences from the no-
load mutual funds and stocks confirm the hypothesis that momentum effects are at least
partially related to investor behaviors.
RISK-ADJUSTED RETURNS
The Jensen-alpha
The model that is being adopted to incorporate risk is the standard Sharpe-Lintner
Capital Asset Pricing Model (CAPM) (1967). The risk-adjusted returns are estimated as
the intercepts from the following model regression:
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R - F = α + β (M – F) + ε
where R is the return on the portfolios under consideration, M is the market index, F is
the risk-free rate, α is the excess stock return and ε is the residual rate of return. I
In evaluating the performance of the momentum strategies, the S&P 500 portfolio
is used as the benchmark. The related variables in this study are defined as: R is the
quarterly rate of return for portfolio A, B, C and D, F is the three-month U.S. Treasury
bill rate constructed from one-month bill rates, M is the S&P 500 portfolio rate of return.
The models are estimated by regressing the mean of returns for each holding
period for strategies A, B, C and D separately. Table IV shows the estimation results for
each portfolio for the 18-year horizon.
Table II
CAPM Regressions Explain Quarterly Excess Returns on Momentum Strategies. This table reports the risk-adjusted returns of momentum portfolios based on strategy A, B, C and D. This table reports the intercepts from Jensen CAPM alpha. The sample period is October 1982 to September 2000. The t statistics are reported in parentheses. Jensen Alpha Beta Strategy A 0.059 -0.494 (1.92) (-1.24) Strategy B 0.048 - 0.176 (2.19) (-0.62) Strategy C 0.037 -0.071 (1.49) (-0.22) Strategy D 0.039 -0.158 (1.92) (-0.60)
For strategies A and D, the estimated α is positive and significant at the 10 %
level. For strategy B, it is highly significant at 5% level. All the βs are slightly negative,
but none of them is statistically significant.
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Several reasons may explain the result. First, the stock market is extremely
volatile and heterogeneous than mutual funds. Second, stocks that exhibit momentum
may catch more attention from investors, creating more volatility. They are affected by
such short- term macro-economy variables such as interest rate, federal money dealing,
and fiscal policy that affect all securities as well as some internal indicators such as the
company’s profits and sales, day-by-day performance, and analyst report. As more
attention is being paid, investors may overreact to these factors. Lastly, the small sample
size might also be a reason. The strategy portfolios consisted of only 10 stocks out of
4,000 to 6,000 stocks in each quarter and the sample is not very typical; whereas, the
S&P 500 portfolio better represents the whole market performances considering its large
sample size. One major reason that limit us from constructing portfolios with more stocks
is due to the strict stock selection rules applied to strategy D.
IV. CONCLUSION
Optimism is contagious. The late 1990s are certainly a period of over- optimism
in the US. General investors tend to overreact to positive information, such as stocks with
positive returns, particularly those with accelerating returns.
This study applies the concept of patterned momentum to stocks, assuming
monthly price movements within a quarter contains valuable importation. Reasonably,
the intra-formation period return behavior differentially influences investors’
expectations.
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The results indicate that the recent record of stock prices do project future prices
and produce generous profits over the 18-year period from 1982-2000. The more nuanced
classification of recent return performance differentiates among alternative price growth
patterns. The findings show that the year of 1996-2000 is a critical period that typical
momentum strategy performs best, when the whole market is experiencing “irrational
exuberance”.
This paper contributes to the current literature by demonstrating the psychological
aspect of momentum effect, which is consistent with the over-reaction models of Daniel
et al. (1998) and Hong and Stein (1999).
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