Over Confidence And Momentum Price

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 mediumterm 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 microstructureinduced 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

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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 intraquarter 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 intraquarterly 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).

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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.

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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

1 + Rt − 1 1 + Rt − 2 > 1, >1 1 + Rt − 2 1 + Rt − 3

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

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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

1 + Rt − 1 >1 1 + Rt − 2

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

1 + R t − 1 1 + Rt − 2 > >1 1 + Rt − 2 1 + Rt − 3

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 18year 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 Panel A 1982.10-2000.9 Panel B 1982.10-1991.9 1991.10-2000.9 Panel C 1982.10-1987.3 1987.4-1991.9 1991.10-1996.3 1996.4-2000.9

Strategy B

Strategy C

Strategy D

S&P500

15.91

24.75

9.80

14.66

11.93

2.41 6.59

2.24 11.04

2.28 4.29

2.41 6.09

3.22 3.70

1.47 1.64 4.81 1.37

1.59 1.41 2.86 3.87

1.40 1.63 3.47 1.24

2.17 1.11 2.80 2.17

2.42 1.33 1.66 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.

30 25 20 15 10 5 0 19 82 19 84 19 85 19 86 19 87 19 89 19 90 19 91 19 92 19 94 19 95 19 96 19 97 19 99 20 00

Terminal Value of $1 Invested

Terminal Value of $1 Invested from 1982.10-2000.9

Time 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.

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3.5 3 2.5 2 1.5 1 0.5

19 91

19 90

19 89

19 88

19 88

19 87

19 86

19 85

19 85

19 84

19 83

0

19 82

Terminal Value of $1 Invested

Terminal Value of $1 Invested from 1982.10-1991.9

Time 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.

14 12 10 8 6 4 2 0 19 91 19 92 19 92 19 93 19 93 19 94 19 94 19 95 19 95 19 96 19 96 19 97 19 97 19 98 19 98 19 99

Terminal Value of $1 Invested

Terminal Value of $1 Invested from 1991.10-2000.9

Time 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.

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3 2.5 2 1.5 1 0.5

19 86

19 86

19 85

19 85

19 84

19 84

19 83

19 83

0 19 82

Terminal Value of $1 Invested

Terminal Value of $1 Invested From 1982.10-1987.3

Time 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

Terminal Value of $1 Invested from 1987.4-1991.9

2 1.5 1 0.5 0 1987

1987

1988

1988

1989

1989

1990

1990

Time 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.

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Term inal Value of $1 Invested from 1991.10-1996.3

Terminal Value of $1 Invested

6 5 4 3 2 1 0 1991

1992

1993

1994

1994

1995

Time 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

Terminal Value of $1 Invested

5 4 3 2 1 0 1996

1996

1997

1997

1998

1998

Time 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 noload 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.

Strategy A Strategy B Strategy C Strategy D

Jensen Alpha 0.059 (1.92) 0.048 (2.19) 0.037 (1.49) 0.039 (1.92)

Beta -0.494 (-1.24) - 0.176 (-0.62) -0.071 (-0.22) -0.158 (-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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