University of Amsterdam
UvA
Master Thesis
MSc Finance
A.A.2016/2017
“Shorting Winners: an
Attention-Adjusted Momentum Strategy”
Student: Chiara Di Leone 11085134
Supervisor: Florian Peter
Statement of originality
This document is written by Chiara Di Leone who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Table of contents
1. Introduction 5
2. Literature Review 7
3. Data 11
3.1 Data sources and data preparation 11
3.2 Descriptive statistics 12
4. Methodology and results 18
4.1 Hypothesis, sample split and variables definition 18
4.2 First results 19
4.3 Trading strategies 23
4.3.1 Betting against winners (BAW) 24 4.3.2 Attention-adjusted betting against winners and testing for alpha differences 25
5. Robustness checks 27
6. Conclusions 31
7.Additional tables 33
Shorting Winners: an Attention-Adjusted Momentum
Strategy
ABSTRACT
Momentum strategy has been shown to be effective in generating abnormal returns. Stocks with high past twelve months gains tend to keep the positive performance going forward, while the opposite happens for past losers. This research shows how for certain categories of high past returns stocks, standard momentum strategy generates negative returns instead. Stocks which are difficult to short and in the “spotlight” tend to have future negative returns, diminishing the overall profitability of a simple momentum strategy within the best past performers’ portfolio. Overpriced stocks are proxied by low levels of institutional ownership paired with increased interest in shorting them. We contribute to the overpricing corrected momentum strategy by additionally sorting the stocks based on the level of attention received, using the analysts consensus on buy percentage recommendations as a proxy. This thesis proposes a long-short momentum strategy which goes short on the overpriced and in the “spotlight” winners, and long on the remaining others. The long-short strategy generates abnormal returns which cannot be explained by common risk factors. Robustness checks are provided by performing both an independent and a conditional portfolio sorting.
1. Introduction
Momentum is one of the most sought after market anomalies, that is a trading strategy seeking to exploit the positive autocorrelation of past returns by buying past winners and selling past losers.
Jegadeesh and Titman (1993) have shown how momentum is one of the most predictable and consistent market anomalies. Although this strategy has been demonstrated to work well based on empirical evidence, researchers have been struggling to find the theoretical and behavioral explanations to the phenomenon, leaving momentum as an unanchored strategy . While empirical findings alone are enough to implement a successful momentum 1
strategy, pointing out the root causes could be useful to build a more robust strategy and give more insights into investors’ behavior.
The main goal of this thesis is to test whether limited attention and short constrains can generate bubbles on a stock level within the best past year stocks performers.
In order to do so, this research starts from fundamentals of behavioral psychology, moving to existing findings within behavioral finance and ultimately succeeds to reconcile the behavioral literature with the momentum one. It is important to underline this study has been focusing on the winners (top performing stocks) only.
Behavioral psychology research has shown individuals can only handle a certain amount of information at a given time , hence they tend to focus on information which are subject to 2
their immediate attention (such as news, geographical proximity and a number of other factors) , while disregarding the ones which are far from their access. Furthermore, 3
empirical psychology shows how individuals are subject to the so self attribution bias, which occurs when investors, for instance, attribute their trading successes to their own abilities while discarding their failures as others’ responsibilities Self attribution bias has
1An unanchored strategy is a trading strategy not based on (or anchored to) fundamentals, but on the analysis
of ex -post empirical data, see Lou et al (2016)
2This may seem obvious, but classical asset pricing models assume that individuals can have
access and process all the available information at a certain time.
3See “Limited attention, information disclosure, and financial reporting”
been pointed out to be the main drive of the momentum phenomenon by positively 4
skewing investors’ beliefs after trading outcomes while contributing to overpricing.
Moreover, Daniel et al(2016) provide the empirical and theoretical background necessary to identify constrained winners . The hypothesis behind the overpricing is that it is 5
possible to identify difficult to short stocks, short them and optimize strategy’s returns. The literature backed theory states that investor’s trading behavior based on recent news, can be driven by overreaction, rather than changes in fundamentals. Starting from the overreaction hypothesis, this research adds a further behavioral interpretation of the “single stocks bubble” by introducing a measure for attention.
This thesis shows how attention bias among difficult to short winners, others factors being equal, could contribute to stock-level overpricing. Intuitively, investors are more exposed to information coming from firms which are bigger in size and heavily traded, as Hong et al(2000) show. If analysts’ consensus on that specific firm which is in the “spotlight” is positive, it is reasonable to assume that investors will be more eager to buy that stock instead of an equally valuable one, just because of its information accessibility. This attention induced behavior is likely to generate temporary overpricing.
Measuring attention in this context is no easy task. Most of the extant literature has been focusing on size, analysts coverage and trading volume as proxies . While this can be a 6
valuable approach in most scenarios, when analysing the returns of past winners, we find that size, coverage and trading volume alone are not suited for detecting attention-driven stock level bubbles . Trading volume proxies attention in general, which can be either positive or negative, while this thesis is only interested in the positive kind of attention (buy trades). Likewise, analysts coverage can be both buy or sell recommendations, while we are only interested in buy ones. Instead, we find sorting the sample for both buy analysts consensus, proxied by buy percentage, to be a balanced approach.
By splitting the sample in high buy percentage consensus recommendation stocks and low ones this research introduces an intuitive (yet incomplete) measure for investors’ exposure to positive market news on a particular stock at a specific time. We argue that
over-exposure paired with strong positive consensus could represent a further source of overreaction. While consensus analysts recommendation can be truly justified by changes
4 See Stein et al(2009)
5Meaning high performing stocks in the top quintile based on the past 12 months returns, which
show a high change and short interest paired with a low level of institutional ownership.
in the underlying stock’s value, the consequent increase in trading volume and buy orders, could, nonetheless, lead to mispricing in the short run. 7
The resulting analysis provides average abnormal excess returns of 2.95%, which represents a 0.74% extra excess abnormal return when compared to the “Overpriced Winners” methodology.
After presenting the triple sorting and the sample splitting results, the causal relationship between the variables defined will be tested. In order to do so, the cumulative excess returns will be regressed on the 3 Fama French risk factors and other independent variables controlling for endogeneity. Moreover, the results will be subject to robustness checks by sorting the portfolios conditionally instead of independently.
2. Literature Review
This research brings together extant literature on momentum strategies, investor’s sentiment ,short interest and institutional ownership. Selected studies on these topics provide the theoretical, empirical and behavioral foundations necessary to analyze excess returns of a modified momentum strategy.
Classical financial literature holds that market returns can be explained by the 8
market efficiency hypothesis.On the other hand, empirical data show that this is not quite the case: equity premium puzzle and other discrepancies of market behavior with classical theory have been puzzling researchers and leave room for further investigation. Alternative explanations are provided by behavioral finance, which, broadly speaking, argues that investors’ cognitive biases and sentiment do affect securities prices causing modest to large swings from fundamental values.
The momentum phenomenon has been one of the most observed and researched market anomalies during the past decades, yet the full explanation for the perpetuating of returns predictability (positive forward returns among past winners and negative forward
7 Chaudhuri et al (2010)
8 Referring to the strand of literature historically originated from Hayek (1945) and perpetuated
returns among past losers) presents a challenge to classical asset pricing theories. This research is putting strands of behavioral and asset pricing literature together in order to build a trading strategy which optimizes momentum strategy returns, given behavioral biases.
On momentum and beliefs
In “Returns to buying losers and selling winners: implications for stock market efficiency” (1993), Jegadeesh and Titman show that excess returns generated by a
long-short trading strategy cannot be fully explained by idiosyncratic risk, nor can they be justified by delayed price reaction to common factors. This study is a cornerstone in asset management since it analysed the causal relationship between known market factors and momentum phenomenon, failing to find a meaningful and complete explanation for the excess returns in traditional metrics used by researchers so far. These findings originated a considerable strand of literature with main contributions from
On this regard, the Stein et al(2009) suggest overconfidence and self attribution bias to be the main causes of momentum, followed by crash events. Overconfidence is defined by Stein as the overweighting of more accessible information as opposite to public information and self attribution bias as the asymmetric shift in investors’ confidence following investing outcomes. According to Stein et al(2009) when traders are
overconfident, it can be observed a short term return autocorrelation(bubble) followed by a long term return reversal (crash). Experimental behavioral psychology, in fact, argues that individuals tend to overreact to dramatic news events, in contrast with Bayesian logic. Bondt and Thaler in 1985 test these hypothesis showing in their empirical study that overreaction is indeed a source of mispricing.
Baker et al(2006) show that investors’ sentiment and beliefs about the future influence returns differently based on different classes of assets (i.e. high vs low growth stocks, dividend stocks etc). This research is relevant when analyzing the cross section of momentum returns and correct for different assets’ characteristics in order to obtain consistent estimates.
This strand of literature provides the necessary underpinning to sustain the hypothesis that stocks with a high past return are (or have been) potentially more sensitive to momentum effect and, hence, potential overpricing.
On attention and analyst coverage
In “A tale of two Anomalies: the implications of investor attention for price and earnings momentum” Hou et al (2007) present strong results suggesting that investors attention significantly influences both price and earnings momentum. According to this study, when investors’ attention is low, meaning their exposure to news are limited, information tends to be incorporated more slowly into the stock’s price, generating underreaction and consequent higher price momentum profits.
Specularly, when investors are over-exposed to information, they tend to overreact, also based on the overweighting of information deriving from overconfidence. In this scenario, price momentum gains will be lower and the stock will be subject to overpricing. In the context of this thesis, the focus is on positive past performance stocks only, therefore the Hou et al (2007) findings will be leveraged in order to detect stock-level and attention based bubbles regarding positive information only. While Hou et al use trading volume as a proxy for attention, it doesn’t seem like an appropriate choice in this research, since trading volume proxies for both optimistic and pessimistic kind of behavior, while we are only interested in overreaction.
More authors have been investigating how attention interfaces with trading behavior and profits predictability: Brennan(1995), Daniel(1998) and Bernard(1990) to name a few.
On Institutional Ownership and short interest
Despite empirical evidence shows that behavioral biases are definitely a plausible drive of prices fluctuations, traditional financial literature argues that these prices fluctuations are not to be permanent nor long term due to the presence of rational investors which will systematically exploit mispricing.
The main contribution of Stambaugh et al (2016) has been providing the empirical and theoretical grounds necessary to discredit the classic argument against behavior-induced price swings. They show that constraints such as low level of institutional holdings causes informed investors not to be able to short stocks. The inability to short stocks causes the prices to move away from fundamentals for a considerable amount of time. In this thesis, the low level of institutional ownership for a certain stock will be hence used as a proxy for inability to short and (plausible) overpricing.
Asquith et al (2005) provide the empirical foundations to back up the hypothesis that stocks who have simultaneously low institutional ownership and high short interest are
difficult to short and earn lower returns than easier to short counterparts. These findings confirm the intuition that mispricing can be due to short sell constraints and consequent slower price discovery.
Moreover, Rapach et at(2015) argue that short interest is the strongest known predictor for aggregate stocks returns since “It outperforms a host of popular return predictors both in sample and out of sample, with annual R2 statistics of 13% and 11%, respectively. In addition, short interest can generate utility gains of over 300 basis points per annum for a mean-variance investor”.
It is relevant to also discuss the large line of literature on disagreement. Starting with Miller et al (1977) who show how short sales constraints paired with large divergence of opinion, generate lower forward returns, than unconstrained stocks. Disagreement is, in this instance, proxied by high standard deviation of returns. A later paper by Sorescu (2016) stresses the importance of these two instances need to be met simultaneously as one alone is not a strong predictor of low future risk adjusted returns.
The cornerstone of this thesis is the work of Daniel et al(2016). “Overpriced winners” puts together literature on disagreement, institutional ownership and momentum anomaly in order to elaborate a momentum strategy adjusted for difficult-to short stocks. Similarly to Daniel’s work, this thesis starts from fundamentals of behavioral finance in delayed reaction and disagreement in order to construct the first portfolio sorting based on past 12 months cumulative returns. Just like Daniel’s portfolios are sorted given
institutional ownership and change in short interest, that is past winners which indicates strong boundaries to arbitrage. At this point, a betting against (BAW) (constrained) 9
winners strategy is implemented, so that the classical momentum strategy expected returns are improved. Although this long-short momentum strategy yields significant returns, it is possible to notice some shortcomings of the research, such as a lack of a measure for other behavioral biases and a not convincingly monotonic returns distributions across quintiles. We noticed one of the most relevant behavioral bias which has been left out to be attention, hence this is added as a new factor able to further expand Daniel’s work by adding an original contribution.
3. Data
3.1 Data sources and data preparation
Data regarding monthly cumulative returns are from CRSP monthly securities database and contain permno, historical cusip (ncusip) and ticker as firms identifiers. All the information in the sample range from October 1988 to December 2016 and all stocks traded on the US markets are taken into consideration, with the only adjustment of excluding the ones with a negative market capitalization. CRSP monthly returns are used to calculate the 12 previous months cumulative returns, excluding the most recent month (t-12 till t-1), following Daniel et al (2016) methodology. Based on the past eleven months cumulative returns, stocks are now ranked into quintiles. The resulting portfolios are equally weighted and will later be triple sorted based on their percentage of institutional ownership and change in short interest.
Institutional ownership data comes from Thomson Reuters 13-F database, which provides the percentage of institutional ownership for each firm in the sample with a 3 months frequency. Since the CRSP data has a monthly frequency, the Thomson’s variables are collapsed from a quarterly to a monthly level and the monthly percentage of
institutional ownership is calculated multiplying it for the number of shares outstanding. This data preparation step is necessary in order to correctly merge the Thomson data with the CRSP data. The merge variables are CRSP ncusip (historical cusip) with Thomson cusip and date (being the last day of each month).
Short interest data is provided by Compustat database and it can be found in the supplementary short interest file. It provides the percentage of short interest for each month for each stock, which, together with low percentage of institutional ownership, provides a proxy for “difficult to short” stocks (Daniel et al 2016). Short interest data have gvkey, ticker and other firm identifiers, while nor PERMNO nor cusip are provided. This lack of commonality between CRSP/Thomson and Compustat firms identification, provides a challenge for the datasets merging. The Compustat/CRSP database, while providing a link-table between different identifiers, does not provide monthly cumulative returns. The merging problem has been resolved as follows: first the short interest file is downloaded with gvkey as firm identifier; then the Compustat/CRSP merged file is download providing the link-table between gvkey and permno; at this point the original CRSP file is merged with the “Compustat/CRSP merged” file, providing a correct link between identifiers; lastly the compustat/CRSP merged plus the original CRSP file are merged with the short
interest file using gvkey and date as merging variables. Moreover, short interest data refers to the 15th of the month instead of the last day of the month, hence, the “splitadjdate” variable is taken into account. The change in short interest rate is calculated as the difference between the short interest rate today (in month t=0) and the same value eleven and a half months ago (month t=-12 until month= t-1). It is appropriate to point out that the half month is missing due to the end of the month date adjustment, creating a 15 days date discrepancy.
Data on the Fama French factors and on the risk free rate are downloaded from Compustat and provide the monthly risk free rate along with the smb, hml, umd which will be useful to run the FF regression on the modified momentum strategy excess returns. The data is monthly and refers to the entire sample, so the merging variable refers only to the last day of the month.
The IBES database provides information on consensus analysts’
recommendations and are divided in either “buy” or “sell” percentages indications for each stock during each month. The analysts’ consensus on whether to buy or sell a certain stock is used as a proxy for how “popular” a certain stock is at a certain time. The buy
percentage will be used to proxy investors’ attention to a specific stock.
3.2 Descriptive statistics
Table 1 shows the month t+1 forward cumulative excess returns within each quintile. Each quintile is sorted based on the historical lagged 12 months cumulative excess returns. Row 1 shows the first quintile (losers) of stocks for the entire sample period where the average monthly cumulative returns are -0.54% for both mean and median with a standard deviation of 0.23.
Table 1
Regular momentum strategy. Forecasts for month t+1
This table contains 1 month average forward returns for each momentum quintile.Stocks are sorted into quintiles based on their past 12 months excess returns, excluding the most recent month. Column 2 (mean of returns) reports the average of the 1 month forward cumulative excess returns for each quintile. Column 3 (median) reports the median of the 1 month forward cumulative excess returns, while column 4 (standard deviation) reports the standard deviations. Returns are sorted from row 1 (low past returns) till row 5 (high past returns).
omentum quintiles
M Mean of returns t+1 edianM t+1 tandard deviationS t+1
Low returns -0.54 -0.54 0.23
2 -0.17 -0.16 0.19
3 0.04 0.03 0.21
4 0.29 0.25 0.29
High Returns 2.46 0.81 6.12
Row 5 shows statistics regarding the top performers (winners) where the average
cumulative returns is equal to 2.46%, with a median of 0.81%. By looking at the averages across the table, from the bottom until the top quintile, it can be observed that the
distribution is rather monotonic and that, consistent with the momentum hypothesis, in expectations, past winners tend to perform better than past losers. Hence the traditional momentum strategy based on shorting past losers and buying past winners seems to be profitable. Across all quintiles it can be observed that the standard deviation ranges from 0.19 (second quintile) to 6.12 (fifth quintile), suggesting that going long on past winners, historically, forecasts high returns, yet generate a rather volatile outcome.
Table 2 shows portfolios characteristics for all 25 winners portfolios within the entire sample (1988-2016).
Table 2: Characteristics of triple sorted winners portfolios
This table reports some characteristics of the 25 equally weighted winners portfolios during the month of portfolio formation. The triple sorting is defined by first dividing the stocks into quintiles based on their past 12 months lagged returns, excluding the most recent month. Hence, portfolios are again sorted into quintiles based on the percentage of institutional ownership and the percentage of change in short interest (independently). In panels A to D the columns show the levels of change in short interest from 12.5 months ago until the month of portfolio formation (% I.O.), while the rows show the percentage of institutional ownership (Δ % short interest). Panel A shows the number of stocks within each triple sorted winners portfolio. Panel B reports the average percentage of change in short interest, along with the row and the column totals. Panel C shows the average percentage of percentage of institutional ownership. Panel D shows the average values of SIRIO (short interest/percentage of institutional ownership) across the 15 winners
portfolios. In Panel E, rows show the stocks’ sizes measured by market capitalization, while the columns report the percentage of institutional ownership (% I.O.). The values reported in panel E show the average percentage of institutional ownership.
Panel A: Number of stocks winners High % I.O. 4 3 2 Low % I.O. low % short interest Δ 37 36 30 51 62 2 40 24 25 24 37 3 38 35 27 12 23 4 52 66 31 37 19 high % short interest Δ 18 12 32 29 28
Panel B: average percentage of change in short interest winners Average of % change in short interest High % I.O. 4 3 2 Low % I.O low % short interest Δ -13.39 -0.72 -20.97 -8.87 -11.24 2.00 -0.04 -0.04 -0.03 -0.02 -0.02 3.00 -0.02 -0.01 -0.01 -0.01 0.00 4.00 -0.01 0.00 0.00 0.00 0.00 high % short interest Δ 13.74 2.09 0.09 7.45 3.63
Panel C: average percentage of institutional ownership
High % I.O. 4 3 2 Low % I.O low % short interes Δ 0.57 0.30 0.21 0.15 0.06 2 0.54 0.30 0.21 0.15 0.07 3 0.56 0.29 0.25 0.12 0.06 4 0.54 0.29 0.21 0.15 0.06 high % short interes Δ 0.50 0.29 0.21 0.14 0.07
Panel D: average levels of SIRIO
Average of SIRIO
High % I.O. 4 3 2 Low % I.O. low % short interest Δ 0.05 3.49 3.50 22.20 73.24 2 0.12 13.19 51.18 84.23 196.67 3 0.75 24.09 31.12 62.05 174.23 4 4.85 6.06 20.10 31.21 353.42 high % short interest Δ 2.01 13.19 70.21 91.24 255.49
Panel E: levels of institutional ownership (market capitalization)
Low market cap
2 3 4 High market cap
Low %I.O. 0.06 0.07 0.08 0.08 0.07 2 0.14 0.14 0.15 0.15 0.16 3 0.21 0.21 0.21 0.21 0.21 4 0.30 0.29 0.28 0.29 0.30 High % I.O. 0.45 0.55 0.56 0.45 0.58
Panel A refers to the number of stocks within each triple sorted portfolio, which is rather heterogenous across the sample, ranging from a minimum of 12 to a maximum of 66. The overpriced winners portfolio (right-bottom), which is the one presenting low institutional ownership and high change in short interest, shows a total of 28 stocks. Panel B shows the average percentage of change in short interest across the triple sorted portfolios. It can be observed that the percentage of short interest increases with the change in short interest quintiles, contributing to show the good quality of the triple sorting. There is no apparent correlation between the change in short interest and the level of institutional ownership.
Panel C reports the average percentage of institutional ownership across winners for the entire sample. Ranging from a maximum of 0.57 to a minimum of 0.06, the distributions is rather clean and shows how percentage of institutional ownership is decreasing within the quintiles, maintaining a stable level across the change in short interest quintiles, once again, suggesting a lack of correlation between the two variables.
In Panel D, the average levels of SIRIO are shown. The change in short interest to institutional ownership ratio is increasing in decreasing institutional ownership and
increasing change in short interest, as expected. The distribution of the ratio is rather monotonic, ranging from a minimum of 0.12 to a maximum of 255.49 in the right bottom portfolio.
In Panel E the distribution of levels of institutional ownership across quintiles based on market capitalization (used as a proxy for size) for winners is shown. It can be noticed that institutional ownership increases consistently with market capitalization, suggesting a strong positive correlation between the two variables. This correlation is relevant in order to back up the assumption that, since stocks which present high levels of institutional ownership are also stocks which are bigger in size, it is reasonable to assume that these stocks will be in the news more than stocks with a lower level of institutional ownership, therefore they will be potentially more subject to attention-driven overreaction.
4. Methodology and results
This section provides the core hypothesis lineup and the essential information about the main variables construction.
hypotheses:
(i) stocks which have high past returns, low levels of institutional ownership and high level of change in short interest are subject to high disagreement and difficult to short.
(ii) constrained winners’ stocks which are difficult to short earn low to negative forward returns when compared with unconstrained ones.
(iii) constrained winners which are greatly exposed to investor’s attention are more subject to overpricing
In order to test the above hypotheses, the following methodology is implemented.
First, the excess monthly returns are calculated for each firm across the panel data, then the entire universe of stocks is divided into quintiles based on their past year’s performance. Following Lou et al(2015) all stocks with negative market capitalization are dropped. Cumulative excess returns are now calculated using the monthly sum of returns for a specific firm starting from the previous 12 months until the time of portfolio
formation, excluding the most recent month. In formulas:
et 1 ag1) 1 ag2)... 1 ag )
r 12= ( + l + ( + l + ( + l T − 1
Where lagtis the lag between month t − t−1from the month of portfolio formation untilt
the 12th previous month, excluding the most recent month
Similarly, the risk-free cumulative is defined as:
f 1 ag rf1) 1 ag rf2)... 1 ag )
r = ( + l + ( + l + ( + l rfT − 1
So that the cumulative excess returns will be:
xcess returns et rf
E !2= r 12− 12
In order to triple sort the cumulative returns ranked portfolios, it is necessary to calculate the change in short interest within the same time frame considered for the
cumulative returns. Since short interest is the number of investors (more precisely the number of sell requests) who are willing to short a specific stock at a certain point in time, this number needs to be adjusted for the number of shares outstanding so that the ratio will be consistent across all different company sizes.
In formulas:
hort Interest Short Interest 00 Δ%SIR = S t−12− t* 1
Following Daniel et at(2016), SIRIO (short interest ratio ΔSIR) is calculated. A SIRIO which is larger than 1 would indicate that the demand for shorting is larger than the supply. hence , SIRIO is an alternative measure for difficult to short stocks where the cost of research and lending is greater than the potential gain of shorting the stocks.
IRIO
S = Δ%SIR /%Institutional ownership
4.2 First results
Consistent with literature findings, this thesis shows how momentum strategy indeed does generate abnormal excess returns as shown by table 1.in table 1 historically (12 months) high performing stocks (winners, bottom row) do show positive forward returns with an average of 2.46% and a median of 0.81%, while past losers underperform with a mean and median of -0.54%.
Furthermore, consistent with overpriced winner we find that the betting against winners (BAW) strategy potentially outperforms the regular momentum strategy. Table 10
3 shows the 25 winners portfolios triple sorted based on their level of institutional
ownership and change in short interest. It can be observed how moving from the left to the right and from top to bottom, that is from high level of institutional ownership to low ones and from low levels of change in short interest to high ones, excess returns tend to
gradually be lower and/or negative. In particular, the right bottom portfolio shows
forecasted excess returns equal to -2.81%, contrasting with 2.29% excess returns of the top left quintile. The row and the column differences are reported with robust t-statistics in parenthesis. For the bottom right portfolio the difference between low and high
institutional ownership excess returns equals to -4.44% with t-statistics equal to -6.24, resulting in a 99% confidence interval. Within the same portfolio, the difference between high and low short interest is significant at a 90% confidence level with a value of -2.86% and a t-statistic of -2.49.
Table 3: average 12 months excess returns across triple sorted winners
This table shows the mean excess returns of the 25 triple sorted portfolios for the month after portfolio formation. Portfolios are first sorted into quintiles based on their 12 months lagged excess returns (excluding the most recent month), then they are sorted again into quintiles based on their level of institutional ownership and change in short interest. Rows and columns report the percentage change in short interest and the percentage of
institutional ownership for each forecasted portfolio. Last row and last column show the row and the column difference between high and low levels of change in short interest and low and high percentage of institutional ownership. Robust t-statistics are shown in
parenthesis. The level of significance is shown by the number of stars. 1 star refers to 90%, 2 stars to 95% while 3 stars shows 99% confidence interval.
High % I.O. 4.00 3.00 2.00 Low % I.O. low-high low % short interes Δ 2.29 1.11 0.67 0.96 0.05 -2.24** (-2.43) 2.00 1.63 1.86 1.06 0.00 -0.34 -1.97** (-1.94) 3.00 1.85 1.16 0.02 -0.22 -1.34 -3.19*** (-3.56) 4.00 1.23 1.75 0.07 0.32 -1.87 -3.1 (-1.05) high % short interes Δ 1.63 1.02 0.60 0.14 -2.81 -4.44*** (-6.24) high-low -0.66 (-0,98 ) -0.09* (-1.35) -0.07 (-0.02) -0.82* (-1.00) -2.86** (-2.49)
It can be further observed how not only the right bottom quintile is
are mostly significantly negative. This findings push the thesis to search for more
sophisticated ways of further distinguishing overpriced winners based on behavioral biases (attention in this case).
In order to measure how attention impacts momentum strategy we further split the triple sorted winners portfolios into 2 sub-samples of which one being low recommended (below median) stocks and another one being high recommended stocks (above median), based on the median. Results of the sample split are shown in table 4. The left side of table 4 shows the excess returns and the change short and size quintiles for highly recommended stocks, that is the above median stocks for buy percentage recommendation consensus, where the median is 56.25%. Specularly, the right side shows the excess returns and the change in short interest quintiles for low buy recommendation stocks identified as the below median for buy percentage recommendations consensus.
Table 4: above and below buy percentage median sample split of excess returns
This table shows the excess cumulative lagged 12 months returns for for the 25 triple sorted portfolios. Portfolios are first sorted into quintiles based on their 12 months lagged excess returns (excluding the most recent month), then they are divided again into quintiles based on their level of institutional ownership and change in short interest. At this point, the sample is split in 2 parts: “high buy % “shows the excess returns for stocks which have a lower than median buy percentage analysts recommendation, while “low buy%” shows the distribution of returns for stocks which are above buy percentage median. “Low-high buy %” column, shows the difference between the overpriced portfolios (right-bottom) in low and high buy percentage. T-statistics are shown in parenthesis. 1 star refers to 90%, 2 stars to 95% while 3 stars shows 99% confidence intervals.
High buy % Low buy % High %I.O. 4 3 2 Low %I.O. High % I.O. 4 3 2 Low % I.O. Low-high Buy % low 0.91 0.44 0.06 0.71 -0.30 1.38 0.6 6 0.6 1 0.25 1.41 1.71* (1.54) 2 1.29 0.09 0.31 0.08 -0.33 0.34 0.7 7 0.7 5 -0.0 8 0.01 -0.34** (1.98) 3 0.90 0.72 -0.01 -0.10 -1.41 0.44 2.1 3 0.0 3 -0.1 2 0.10 1.51 (0.48) 4 0.54 0.60 0.13 -0.54 -1.99 1.15 1.4 4 0.0 4 0.20 -0.93 1.06* (1.87) High 0.96 0.61 0.09 2.48 -2.01 1.01 0.3 8 0.1 4 0.05 -1.00 1.01* (1.86)
The main goal of this sample split is to delve deeper into the composition of returns, given high and low attention levels. In particular, it aims to spot those winners which show high levels of change in short interest paired with a low level of institutional ownership and receive an above median positive analyst coverage. For these reasons, only the low institutional ownership column differences between low and high analysts buy recommendations are tested. It can be noticed that for highly recommended stocks the overall returns distribution is more negative than below recommendation percentage ones.
For the bottom right portfolios (the worse winners performers) this difference between the 2 samples equals to 1.01% and is significant at a 90% confidence interval (t=1.86). Another positive significant difference of 1.71% is shown in the top right
portfolio of table 4. These findings confirm hypothesis (iii), although the table does not yet provide a causal explanation of the results, but a mere correlation. On the other end, in the 3rd quintile row difference in table 4 is negative (meaning that the highly recommended stocks perform significantly better than the low recommended ones). These puzzling findings call for an investigation of the causal relationship between the attention measure and the forward returns of the momentum strategy.
4.3 Trading strategies
4.3.1 Betting against winners (BAW)
Following Daniel et al(2016) and based on the findings reported in the previous section, the BAW trading strategy is built. BAW (Table 5) goes long on all the triple sorted winners portfolios showed in table 3 equally, except on the overpriced ones shown in the right bottom corner of table 3. This strategy yields an excess return of 2.15% with a t-statistic of 1.34, significant at a 90% confidence level as shown in table 5 (first column).
Table 5: regression of excess returns of long-short betting against winners strategy
Table 5 shows the regression coefficients of the excess returns of the BAW (betting against winners) strategy , which goes short on the low institutional ownership and high change in 11
short interest stocks, and long on the other winners.
Column 1 reports the CAPM regression of the excess cumulative returns on the market risk free rate. Column 2 shows the Fama French 3 factors regression coefficients. Column 3 shows the 3 Fama French factors plus buy percentage recommendation. Robust t-statistics are shown in parenthesis and levels of significance are denoted by stars: 1 star refers to 90%, 2 stars to 95% while 3 stars shows 99% confidence interval.
dependent variable: excess returns of long-short betting against winners strategy
(1) (2) (3)
hml 2.63 2.08
(0.25) (0.34)
smb -1.78** -1.40*
(1.99) (1.32)
risk free rate -0.52** -0.40* -0.37* (-2.21) (-1.30) (-1.65) Buy percentage -2.63** (-2.98) Constant 2.15* 2.21*** 1.98** (1.34) (3.89) (2.04) Adjusted R2 0.00009 0.00302 0.01043
In column 2, the excess returns are regressed on the 3 Fama French factors model. Although the returns seem to be exposed to negative market risk rate throughout all 3
specifications seem to be significantly influenced by both SMB (with a value of -1.78% to -1.40%, suggesting that returns co-vary with small stocks) and rf (with values of -0.52% and -0.40%) ,the constant remains significant and almost unchanged in column 2 with a value of 2.21%, showing that the returns of this strategy cannot be fully explained by common risk factors.
On the other hand, when introducing the attention measure in specification 3 (buy percentage), it can be noticed that, although remaining significant, the alpha drops to a 1.98%. In the last specification “buy percentage” is negative and significant (-2.63% with t=-2.98) suggesting that the returns of the betting against winners are not particularly robust with respect of this measure of investor attention and are, in fact, negatively exposed to it. These findings lead the research to the next step, which is an attention adjusted BAW strategy.
4.3.2 Attention-adjusted betting against winners and testing for alpha
differences
This thesis implements a momentum trading strategy which goes long on all winners and short on difficult to short and highly exposed to investor attention winners. 12
Table 6 shows the results of regressing the excess returns of this strategy on well-known factors. The constant is significant with a value of 2.93% (first column).
Table 6: regression of excess returns of attention-adjusted betting against winners long-short strategy
Table 6 shows the coefficients relative to the regressions having the 12 months lagged excess returns as the dependent variable. These returns are the outcome of shorting stocks which present a high change in short interest jointly with a low level of institutional ownership and have been positively recommended by analysts, above median. Column 1 shows the constant and the market risk free rate. Column 2 shows the constant and the 3 Fama French factors coefficients. The last row shows the adjusted R squared. Robust t-statistics are shown in parenthesis and significance of the coefficients is denoted by stars: 1 star refers to 90%, 2 stars to 95% while 3 stars shows 99% confidence interval.
dependent variable: excess returns of attention-adjusted BAW strategy
(1) (2)
hml 3.24*
(1.79)
smb -1.64*
(1.68)
risk free rate -0.32* -0.27 (-1.48) (-0.34)
Constant 2.93** 2.95***
(2.90) (6.74)
Adjusted R2 0.00010 0.0002
The difference between the attention adjusted BAW trading strategy introduced in this thesis and the Daniel et al (2016) version of the BAW is equal to 0.74% (2.95%-2.21% in both specifications 2) and significant (t=2.54) at a 95% confidence interval. These
findings show how the attention-adjusted BAW momentum strategy significantly outperforms the standard BAW one.
5. Robustness checks
In order to assess the robustness of the findings above, the triple sorting sampling is performed conditionally instead of independently as follows.
First, the universe of stocks is divided into quintiles based on their past 12 months lagged excess cumulative returns. Conditional on that, the portfolios are now divided again into quintiles given their percentage of institutional ownership. Hence, the 5x5 portfolios matrix is split into quintiles conditional on their level of institutional ownership by their level of change in the short interest percentage.
Results are shown in the seventh section of this work (“7. Additional tables”). Both descriptive statistics and stocks characteristics remain fundamentally unchanged and significant when compared to the independent triple sorting,proving the quality and robustness of the data and methodology.
Moreover, in order to show the composition of the excess returns of the long-short BAW strategy, the returns relative to the long-short strategy are regressed separately on the Fama French 3 factors and on the attention (Table 7, panels A and B).
Table 7 Panel A shows the excess returns of the short portfolio across 3 different specifications. The first column shows the constant and the market risk free rate coefficient . It can be observed that in all 3 specifications the constant remains negative and significant ranging from -1.09% (second regression) to -1.84% (first regression). These findings show how low institutional ownership and high change in short interest stocks do indeed forecast negative significant forward returns, even when adjusted for common factors.
Panel B shows the same values for the long portfolio. In this case, the constant is positive and significant throughout the 3 specifications, although less positive than the overpricing-adjusted excess returns. Alpha ranges from 1.04% to 1.15% and remains significant despite showing exposure to some of the Fama French factors. Intuitively, by going long on all winners (panel B), and short on all overpriced winners (panel A), the resulting constant should be the difference of these two. This holds substantially true,
although small differences can be due to different portfolio composition in terms of stocks characteristics and other factors.
Table 7, panel A: regression of excess returns of low institutional ownership and high
change in short interest winners
This table reports the regression coefficients relative to the lagged 12 months excess returns as the dependent variable. In column 1 the coefficient of the market risk-free rate and the constant are shown. Column 2 shows the coefficients relative to the Fama French 3 factors model and the constant. Specification 3 reports the Fama French 3 factors along with the buy percentage (measure of attention) coefficient. Robust t-statistics are shown in parenthesis and the significance level is denoted by stars:1 star refers to 90%, 2 stars to 95% while 3 stars shows 99% significance levels.
Table 7 Panel A
Dependent variable: excess returns of low institutional ownership and high change in short interest for winners
(1) (2) (3) hml -0.62 -1.87 (-0.59) (-0.38) smb 2.39* 3.40 (1.74) (0.22)
risk free rate 0.25** 0.98* 0.90* (2.79) (1.91) (-1.65) Buy percentage -2.63** (-2.98) Constant -1.84* -1.09*** -1.11** (1.93) (4.51) (2.04) Adjusted R2 0.00003 0.00023 0.00872
Table 7, Panel B: Regression of cumulative excess returns for all winners
Table 7 shows the regression coefficients relative to the excess 12 months lagged returns of the classic momentum strategy for winners. Specification 1 reports the constant and the coefficient relative to the market risk free rate. Column 2 shows the constant and
coefficients relative to the 3 Fama French factors regression Column 3 shows the constant and the coefficients relative to the 3 Fama French factors as well as the buy percentage (measure for attention) coefficient. The bottom row shows adjusted R squared. Robust t-statistics are shown in parenthesis and the significance of the results are denoted by stars:1 star refers to 90%, 2 stars to 95% while 3 stars show 99% confidence intervals .
Table 7 Panel B
dependent variable: excess returns for all winners
(1) (2) (3)
hml 2.64* 2.85**
(1.75) (2.08)
smb -2.97** -1.93*
(1.89) (1.22)
risk free rate -1.08* -0.74* -0.19* (-1.21) (-1.70) (-1.09) Buy percentage -2.74*** (-6.43) Constant 1.09** 1.04*** 1.15** (1.98) (4.38) (2.04) Adjusted R2 0.00004 0.00974 0.00414
It can be argued that the Fama French factors and the level of buy percentage recommendation are not the only variables that can explain returns, therefore there can be a case for endogeneity. On this matter, this thesis takes the results from Daniel et al (2016) and other similar researches, while not introducing other risk factors mainly due to the lack of data and the short time frame. Overall, this research focuses on the Fama French factors only given their dominance in the asset pricing theory literature and their frequent use by researchers.
6. Conclusions
This research starts by replicating the empirical framework designed by Daniel et al(2016) which provides a method for identifying short constrained and optimism driven stocks within a momentum strategy. Historically, financial asset pricing literature has argued that the changes in prices for momentum strategies has been driven by fundamental changes in the underlying stock value. Daniel et al show how these changes are mostly of behavioral nature by identifying difficult to short stocks. Securities which show low percentage of institutional ownership paired with high past returns and high levels of change in short interest, tend to perform negatively going forward.
In this instance, overpriced winners have average significant excess returns of -2.81% and -1.84% when adjusted for common risk factors. The Betting Against Winners (BAW) Daniel’s strategy is proven to be effective in the sample taken into account by this research, yielding excess returns for the long-short portfolio equal to 2.21% when
regressed on common factors.
What still remains a puzzle in Daniel et al (2016) is the root cause of investors’ optimism which drives overpricing in constrained winners. Consistent with behavioral finance literature on the topic, this thesis argues that a major behavioral factor which drives momentum optimism might be investor attention.
This research introduces a simple measure for investor attention and proceeds to perform an additional above and below median sample split based on the percentage of buy recommendations consensus among analysts. The attention-adjusted BAW strategy yields results equal to 2.95% ( adjusted for common risk factors) and 90% significant. The difference between the standard BAW and the attention-adjusted BAW is significant and equal to 0.74%. The results are robust, given the alternative conditional portfolio sorting provided in the robustness checks section where differences remain significant.
Although results have been proven to be well grounded, in line with extant literature and statistically significant it is appropriate to point out some limitations of this research. First of all this thesis only focuses on winners: in order to gain a broader
understanding a more comprehensive analysis should be carried on, which includes the rest of the quintiles. Moreover, the attention measure provided by this research is in terms of quality (positive coverage) and we infer that high institutional ownership and bigger company size are a proxy for volume of coverage, which might not always be true. Moreover, since it is expensive and sometimes even prohibitive to short the overpriced winners, the empirical feasibility of these strategies remains to be assessed.
All in all, this research succeeds into further investigating how portfolios
composition within the momentum strategy interfaces with behavioral biases by discussing the increasingly relevant role of investor attention in asset pricing theory.
7.Additional tables
Table R.1 : Characteristics of triple sorted winners portfolios with conditional sorting
This table reports some characteristics of the 25 equally weighted winners portfolios during the month of portfolio formation. The triple sorting is defined by first grouping the stocks into quintiles based on their past 12 months lagged returns, excluding the most recent month. Hence, portfolios are again divided into quintiles based on the percentage of institutional ownership and, conditional on the latter they are divided into quintiles given the percentage of change in short interest (conditional sorting). In panel A1 to D1 the columns show the levels of change in short interest from 12.5 months ago until the month of portfolio formation (% I.O.), while the rows show the percentage of institutional ownership (Δ % short interest) . Panel A1 shows the number of stocks within each triple sorted winners portfolio. Panel B1 reports the average percentage of change in short interest, along with the row and the column totals. Panel C1 shows the average percentage of percentage of institutional ownership. In Panel E, rows show the stocks’ sizes measured by market capitalization, while the columns report the percentage of institutional
ownership (% I.O.). The values reported in panel E 1 show the average percentage of institutional ownership.
Panel A.R
% short interest
Δ High %
I.O.
4 3 2 Low % I.O.
low % short interestΔ 30 42 33 50 52
2 29 19 25 28 32
3 19 32 27 24 13
4 49 61 31 32 19
high % short interestΔ 27 19 25 26 23
Panel B.R: average percentage of change in short interest winners
Average of % change in short interest High % I.O. 4 3 2 Low % I.O low % short interest Δ -14.19 -0.92 -10.87 -8.27 -12.34 2.00 -0.09 -0.08 -0.20 -0.06 -0.09 3.00 -0.05 0.00 -0.01 -0.01 0.00 4.00 1.00 0.00 0.00 0.00 0.00 high % short interest Δ 10.02 2.75 0.09 6.02 4.13
Average of I.O. % High % I.O. 4 3 2 Low % I.O low % short interest Δ 0.51 0.31 0.20 0.15 0.02 2 0.54 0.30 0.21 0.15 0.07 3 0.59 0.28 0.21 0.19 0.09 4 0.52 0.20 0.21 0.21 0.06 high % short interest Δ 0.50 0.29 0.21 0.14 0.07
Panel D.R: levels of institutional ownership (market capitalization)
Low market cap 2 3 4 High market cap Low %I.O. 0.08 0.05 0.07 0.02 0.05 2 0.13 0.12 0.12 0.19 0.17 3 0.19 0.29 0.29 0.22 0.23 4 0.20 0.26 0.28 0.26 0.37 High % I.O. 0.21 0.54 0.49 0.43 0.61
Table 3.R: average 12 months excess returns across triple sorted winners with conditional sorting
This table shows the mean excess returns of the 25 triple sorted portfolios for the month after portfolio formation. Portfolios are first sorted into quintiles based on their 12 months lagged excess returns (excluding the most recent month), then they are sorted again into quintiles based on their level of institutional ownership and, based on the latter, on change in short interest (conditional sorting). Rows and columns report the percentage change in short interest and the percentage of institutional ownership for each forecasted portfolio. Last row and last column show the row and the column difference between high and low levels of change in short interest and low and high percentage of institutional ownership. Robust t-statistics are shown in parenthesis. The level of significance is shown by the number of stars. 1 star refers to 90%, 2 stars to 95% while 3 stars shows 99% confidence interval. High % I.O. 4.00 3.00 2.00 Low % I.O. low-high low % short interes Δ 2.31 1.14 0.61 0.86 0.02 -2.29 (-1.21) 2.00 1.65 1.83 1.06 0.05 -0.29 -1.94 (-1.01) 3.00 1.89 1.19 0.03 -0.29 -1.12 -3.01* (-1.56) 4.00 1.26 1.62 0.17 0.30 -1.27 -2.53** (-2.05) high % short interes Δ 1.63 1.05 0.51 0.18 -2.01 -3.64* (-1.89) high-low -0.68 (-0,18 ) -0.09* (-1.31) -0.10 (-0.09) -0.68** (-2.76) -2.03*** (-8.49)
Table 4.R: above and below buy percentage recommendations median sample split of excess returns with conditional sorting
This table shows the excess cumulative lagged 12 months returns for for the 25 triple sorted portfolios. Portfolios are first sorted into quintiles based on their 12 months lagged excess returns (excluding the most recent month), then they are divided again into quintiles based on their level of institutional ownership and, conditional on the latter they are sorted based on the change in short interest. At this point, the sample is split in 2 parts: “high buy % “shows the excess returns for stocks which have a lower than median buy percentage analysts recommendation, while “low buy%” shows the distribution of returns for stocks which are above buy percentage median. “Low-high buy %” column, shows the difference between the overpriced portfolios (right-bottom) in low and high buy percentage only. T-statistics are shown in parenthesis. 1 star refers to 90%, 2 stars to 95% while 3 stars shows 99% confidence intervals.
High buy % Low buy % High %I.O . 4 3 2 Low %I.O. High % I.O. 4 3 2 Low % I.O. Low-high Buy % Low 0.96 0.46 0.09 0.72 -0.33 1.32 0.6 3 0.6 6 0.24 1.42 - 2 1.74 0.05 0.33 0.09 -0.63 0.36 0.7 9 0.7 8 -0.0 6 0.05 - 3 0.96 0.77 -0.03 -0.14 -1.21 0.49 2.1 5 0.0 3 -0.1 5 0.13 - 4 0.53 0.60 0.15 -0.52 -1.98 1.12 1.7 2 0.0 3 0.23 -1.21 - High 0.97 0.69 0.07 1.98 -1.89 1.00 0.3 5 0.1 9 0.02 -0.71 2.6*** (3.94)
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