lottery preferences and investor sentiment · 2017-02-16 · lottery preferences and investor...

LOTTERY PREFERENCES AND INVESTOR SENTIMENT

Benjamin M. Blaua

Abstract Prior research finds that investors have strong preferences for stocks with features that resemble lotteries. These preferences have been shown to lead to price premiums and subsequent underperformance. This study extends this growing body of literature by testing whether the underperformance of lottery-like stocks is driven by periods of high investor sentiment. The motivation for these tests is based on the idea that sentiment can directly affect the subjective probability assessments of investors. In the framework of our tests, more optimism among investors is likely to strengthen investors’ lottery preferences. Results in this study support this hypothesis as the underperformance of lottery-like stocks is primarily driven by periods of high sentiment. aBlau is an Associate Professor in the Department of Economics and Finance, in the Jon M. Huntsman School of Business at Utah State University, Logan Utah, 84322. Email: [email protected]. Phone: 435-797-2340. Fax: 435-797-2301.

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1. INTRODUCTION

While traditional asset pricing models generally assume mean-variance efficiency

(Markowitz (1952), and Sharpe (1964)), more recent research seems to indicate that some

investors will sacrifice this efficiency in order to attain portfolios with higher skewness.

Following Kahneman and Tversky (1979, 1992), Barberis and Huang (2008) use cumulative

prospect theory to demonstrate that investors will show preferences for positive skewness. If

strong enough, these preferences can influence asset prices. Empirical research seems to confirm

this theoretical prediction as some investors have preferences for portfolios that resemble

lotteries (Zhang (2005) and Mitton and Vorkink (2007)). Other studies show that assets that

resemble lotteries exhibit price premiums and subsequently underperform (Kumar (2009), Boyer,

Mitton, and Vorkink (2010), Kumar, Page, and Spalt (2011), Bali, Cakici, and Whitelaw (2011),

Green and Hwang (2012), and Boyer and Vorkink (2013)). Behavioral preferences, as discussed

in Barberis and Huang (2008), provide the most likely explanations for the underperformance of

lottery-like stocks. To the extent that this is true, we therefore hypothesize that preference-

induced underperformance will be greatest during periods of high investor sentiment.

This hypothesis is motivated by a broad stream of psychology research (Johnson and

Tverky (1983), Bower (1981), Arkes, Herren, and Isen (1988), Wright and Bower (1992), and

Mayer et al. (1992)) that contends that during periods of positive (negative) sentiment,

individuals will overweight the probability of observing favorable (unfavorable) outcomes. We

argue that lottery preferences will be magnified during periods of high investor sentiment as

some investors will assign overstated probabilities to extreme, favorable outcomes. Excess

demand by overoptimistic investors might explain the underperformance of lottery stocks during

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these periods of high sentiment. The main objective of this study is to test this simple and

intuitive hypothesis.

We closely follow three studies that empirically examine lottery preferences in financial

markets. First, Bali, Cakici, and Whitelaw (2011) proxy for lotteries by simply examining the

maximum daily return during a particular month (max return hereafter). They find that stocks

with the largest max return have the lowest expected returns, which indicates that these stocks

exhibit price premiums due to investor penchants for lottery-like returns. Second, since the

contemporaneous skewness of returns varies across time, Boyer, Mitton, and Vorkink (2010)

estimate expected idiosyncratic skewness or the expected firm-specific skewness of returns.

Consistent with the idea that investors prefer stocks with the greatest expected skewness, Boyer,

Mitton, and Vorkink (2010) observe a reliable inverse relation between expected skewness and

expected returns. Finally, we follow Kumar (2009) and Kumar, Page, and Spalt (2011) and

create an indicator variable that captures stocks with characteristics that are most likely to

resemble lotteries. Kumar (2009) provides evidence that these lottery stocks significantly

underperform non-lottery stocks. Using these three classifications for lottery-like characteristics,

we test whether the underformance observed in these studies is driven by periods of high

investor sentiment, using Baker and Wurgler’s (2007) index.

After partitioning investor sentiment into three equal states (high, medium, and low), we

find consistency with our hypothesis as the inverse relationship between expected returns and

lottery-like features is greatest during periods of strong sentiment. Our results are robust to each

of the three proxies for lottery stocks. Further, the results hold when we examine raw returns,

market-adjusted returns, and alphas from three-factor, four-factor, and five-factor models (Fama

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and French (1996), Carhart (1997), and Pastor and Stambaugh (2003)).1 We also find strong

support for our hypothesis in a more traditional multivariate framework. Using a series of Fama-

MacBeth (1973) regressions, we control for a variety of variables that have been shown to

predict next-month returns. After including these factors, we show that the negative relation

between our proxies for stock lotteries and next-month returns are strongest during periods of

high sentiment.

The results in this study provide an important contribution to the literature by first

demonstrating that variations in lottery preferences are associated with variations in investor

sentiment. Second, our findings seem to suggest that probability assessments by agents are

congruent with the sentiment of those agents. This latter contribution might be appropriately

generalized to other research areas in financial economics.

2. RELATED LITERATURE AND HYPOTHESIS DEVELOPMENT

As discussed above, our hypothesis is based on two streams of literature. The first stream

of literature focuses on deviations from the traditional mean-variance assumptions by investors

that is widely accepted in the many of the asset pricing models (Markowitz (1952), Sharpe

(1964), among others). Kahneman and Tversky (1979) model an individual’s evaluation of risk

by using a value function that is defined across a spectrum of losses and gains. They show that the

value function is concave over gains but convex over losses. When examining the distribution of

this function, Kahneman and Tversky (1979) assess transformed probabilities instead of objective

probabilities by applying a weighting mechanism to the value function described above. Results

show that, given the concavity across gains and convexity across losses, this weighting function

generally places more weight on the tails of the distribution revealing a common preference for

1 The multifactor model used throughout the study includes the market risk premium, the small-minus-big risk factor, the high-minus-low risk factor, the up-minus-down factor, and the liquidity risk factor.

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lottery-like gains. Applying this theory to asset prices, Barberis and Huang (2008) show that

investors will have penchants for stocks with positively skewed return distributions. In the

framework of more traditional asset pricing theory, these unique results imply that while investors

might intuitively focus on mean-variance efficiency, some investors are also concerned with the

skewness of the return distribution. To the extent that preferences for skewness are strong, asset

prices will be affected as demand by those with these preferences create contemporaneous price

premiums.

Mitton and Vorkink (2007) use retail brokerage accounts to show that some individual

investors intentionally underdiversify their portfolios at a sacrifice of mean-variance efficiency in

order to attain higher portfolio skewness. Since return skewness is time variant, Boyer, Mitton,

and Vorkink (2010) estimate expected idiosyncratic skewness and show that stocks with the

highest expected idiosyncratic skewness underperform other stocks. These results are robust to a

variety of multivariate tests. In annual terms, the negative return premium associated with

expected idiosyncratic skewness is approximately 8%.

Along these lines, Kumar (2009) classifies lottery stocks as those with the highest

idiosyncratic skewness, the highest idiosyncratic volatility, and the lowest share prices. These

stocks have similar characteristics to what we consider common lotteries. Kumar shows that

lottery stocks typically underperform non-lottery stocks. Using a four-factor asset pricing model,

he shows that lottery stocks generate negative alpha that is both statistically significant and

economically meaningful. For instance, lottery-type stocks underperform 4% annually, on

average.

Following this stream of research, Bali, Cakici, and Whitelaw (2011) test whether stocks

with extremely large returns predict negative returns. The idea here is that investors with

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preferences for lotteries will observe and subsequently demand stocks with extremely large

returns thus creating unusually high stock prices in the current time period and unusually low

returns in the following time period. Consistent with their hypothesis, their Fama-MacBeth (1973)

regressions, which model next-month returns as the dependent variable, show that the coefficient

on max returns ranges from -0.0434 to -0.0637 and is reliably different from zero at the .01 level.

In the analysis that follows, we follow Boyer, Mitton, and Vorkink (2010), Kumar (2009), and

Bali, Cakici, and Whitelaw (2011) and proxy for stock lotteries using expected idiosyncratic

skewness, the lottery stock identification in Kumar (2009), and max returns.

We hypothesize that investor preferences for lottery stocks, which typically explain the

underperformance discussed above, will be strongest in periods when investor sentiment is high.

This hypothesis is based on a broad psychology literature, which examines the effect of sentiment

on the assessment of subjective probabilities by agents. For instance, Johnson and Tversky (1983)

show that experimental manipulations of sentiment can affect the ability of individuals to judge

the frequency of unlikely events. Bower (1981) show that sentiment can influence an individual’s

expectations about the future weather. In a series of experiments, Arkes, Herren, and Isen (1988)

provide evidence that when a meaningful loss is not observable and participants have positive

sentiment, they exhibit more risky behavior, particularly when the probabilities of favorable

outcomes are highest.

In a more related study, Wright and Bower (1992) show that individuals with positive

sentiment were more optimistic when reporting their probabilities about future positive events.

We contend that when investor sentiment is high, investors might be more optimistic in assessing

the probabilities of observing extreme (lottery-like) stock returns in the upcoming period.

Therefore, preferences for lottery-like stocks might be stronger during periods with high investor

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sentiment thus leading to lower future performance of these types of stocks. We formally state the

null hypothesis below.

H1: The underperformance of stocks that resemble lotteries is unrelated to investor sentiment.

3. DATA DESCRIPTION

This section describes the data used throughout the analysis. From the universe of stocks

available at the Center for Research on Security Prices (CRSP), we obtain prices, volume,

returns, and shares outstanding. From Compustat, we gather the annual book-value of equity in

order to calculate book-to-market ratios. Before merging Compustat to the CRSP data, we

exclude any firm with a negative book-to-market ratio. Excluding firms with negative book-to-

market ratios reduces the likelihood that delisted firms or firms facing bankruptcy might be

biasing our results in some way. Our sample time period is from 1980 to 2010. After merging the

data from CRSP to the data from Compustat, we are left with 11,272 unique stocks and 983,637

stock-month observations.

Table 1 report statistics that describe our sample. Price is the closing monthly price

obtained from CRSP. Turn is the monthly share turnover, or the ratio of monthly trading volume

scaled by shares outstanding in percent. Beta is the CAPM beta, which is obtained in each

month by estimating the CAPM using daily returns for a rolling 6-month window. Size is the

market capitalization in (1,000s). B/M is the book-to-market ratio, which is gathered from both

CRSP and Compustat. IdioVolt is the idiosyncratic volatility, which is calculated in each month

as the standard deviation of daily residual returns where residual returns are obtained from a

daily Fama-French 4-Factor model using a rolling 6-month window. Illiq is the monthly average

of the daily Amihud (2002) illiquidity measure or the daily return (in absolute value) scaled by

dollar volume (in 100,000s). MaxRet is the daily maximum stock return during a particular

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month for an individual stock. E[IdioSkew] is the expected idiosyncratic skewness obtained from

Boyer, Mitton, and Vorkink (2010).2 LOTTERY is an indicator variable equal to one if a

particular stock has the highest (above median) idiosyncratic skewness where idiosyncratic

skewness is the skewness of daily residual 4-factor returns, the highest (above median)

idiosyncratic volatility, and the lowest (below median) share price.

Table 1 shows that the average stock in our sample has a monthly closing price of $20.62,

share turnover of 5.86%, a beta of .8423, a market cap of $2.2 billion, a book-to-market ratio of

0.488, idiosyncratic volatility of 3.18%, an illiquidity measure of 7.15, a max return of 7.54%,

and expected idiosyncratic skewness of 1.1026. We also find that 22.36% of stock-month

observations contain of indicator variable LOTTERY equal to one. We also report the standard

deviation, the 25th percentile, the median, and the 75th percentile in columns [2] through [5]. The

purpose for doing so provides some inference about the distribution of each of these variables

that will be used throughout the analysis. A couple results in Panel A are noteworthy. Both Size

and B/M do not appear to be normally distributed as the mean is markedly larger than the

median. In the analysis that follows, we simply take the natural log of these variables to provide

some normalization. The other variables seem to be normally distributed.

Table 2 extends the description of our data by reporting the summary statistics across

varying periods of investor sentiment. Monthly investor sentiment, as defined in Baker and

Wurgler (2007), is the principle component from six proxies for investor sentiment, which

include share turnover on the NYSE, the dividend premium, the closed-end fund discount, the

2 Boyer, Mitton, and Vorkink (2010) obtain expected idiosyncratic skewness from the predicted values of a regression of idiosyncratic skewness on lagged measures of idiosyncratic skewness, idiosyncratic volatility and a series of other control variables such as momentum, turnover, and indicator variables capturing exchange listing, small-cap stocks, mid-cap stocks, and Ken French industry codes.

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number and first-day returns on IPOs, and the equity share of new stock issues.3 Figure 1 shows

a time series plot of investor sentiment during our sample time period. As seen in the figure,

sentiment is highest during the technology boom and during the expansionary period during the

mid-1980s.

Following Baker and Stein (2004) and Antoniou, Doukas, and Subrahmanyam (2013), we

partition investor sentiment into three equal states: High, Medium, and Low. We then estimate

and report the means of our descriptive data across the three sentiment states. Column [1] shows

the results for the low sentiment state while columns [2] and [3] present the results for the

medium and high sentiment states. We also report (in column [4]) the difference in means

between columns [3] and [1] with corresponding p-values from pooled t-statistics testing for

significance in the differences. While the differences in column [4] are, in general, reliably

difference from zero. We do not find monotonic patterns across sentiment states for many of the

descriptive variables. The exceptions are for the variables Beta and Illiq. For instance, we show

that Beta is increasing monotonically across sentiment states suggesting that during periods with

the highest investor optimism, systematic risk is the greatest. This result is somewhat intuitive

and indirectly suggests that the comovement of stocks tends to be greatest during periods of high

investor sentiment. While outside the scope of this article, additional tests and theoretical

motivation for this initial finding might be a fruitful avenue for future research.

We also find that Amihud’s (2002) measure of illiquidity is decreasing monotonically

across sentiment states. This result is expected given the theoretical results in Baker and Stein

(2004), which predicts that liquidity improves across sentiment states. The argument for why

liquidity improves is based on the sophistication of investor participation. In periods of the

3 The monthly investor sentiment index is publicly available from Jeffrey Wurgler.

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highest sentiment, their model suggests that unsophisticated investors dominate, which results in

the few sophisticated investors being sidelined. However, since much of the market is made up

from unsophisticated investors, trading volume and liquidity are predicted to be high. We

recognize that, while outside the scope of this study, more robust tests are required before

drawing strong inferences regarding the theoretical predictions in Baker and Stein (2004). Our

simple tests in Table 2, however, provide some initial support these predictions. Again, thorough

tests of theory in Baker and Stein (2004) may provide an important contribution to the literature.

4. EMPIRICAL RESULTS

In this section, we test the hypothesis that the underperformance of stocks that resemble

lotteries is driven by periods of strong investor sentiment. This section is formatted in the

following way. We first examine next-month returns across portfolios sorted by max returns,

which is our first proxy for lottery stocks. Second, we test for a negative lottery return premium

in a traditional Fama-MacBeth (1973) framework. We then repeat this format for our second and

third proxies for lottery stocks (expected idiosyncratic skewness and Kumar’s (2009) definition

of lottery stocks). Finally we discuss several other unreported tests as they relate to the

robustness of our results.

4.1 The Max Return Premium and Investor Sentiment – Multifactor Sorts

We begin by examining various estimates of expected returns across portfolios sorted by

max returns. Table 3 presents the results from these tests. The table reports next-month returns

across quintiles that are sorted based on max returns in the current month. We report raw returns,

adjusted returns, which are the difference between raw returns and CRSP value-weighted market

returns, as well as three measures of expected returns obtained from estimating variants of the

following equation.

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Returni,t+1 – Rft+1 = α + β1MRPt+1 + β2SMBt+1 + β3HMLt+1 + β4UMDt+1 +

β5LIQt+1 + εi,t+1 (1)

The model above is a standard five-factor model where the factors are the three-factors in Fama

and French (1996) (the market risk premium (MRP), the small minus big risk factor (SMB), and

the high minus low risk factor (HML)), the momentum factor UMD, and the Pastor and

Stambaugh (2003) liquidity factor LIQ. Alphas are estimated and reported for each quintile.

Returns and alphas are equally weighted. We note that in the table, Panel A reports the results

when examining periods of low sentiment; Panel B presents the results during periods of medium

sentiment; and Panel C shows the results when examining periods of high sentiment. At the

bottom of each column, we report the difference between extreme quintiles with corresponding

p-values.

Panel A Column [1] shows that next-month raw returns are increasing monotonically

across max return quintiles. The high-minus-low difference is 1.69% and is reliably different

than zero (p-value = <.0001). Similar results are found in column [2] when we examine market-

adjusted returns. However, when we account for more commonly used risk factors, we do not

find that alphas in the lowest max return quintile is significantly different than the alphas in the

high max return quintile. This result is robust in each of the remaining columns and suggests

that the traditional negative return premium associated with max returns does not exist during

periods of low investor sentiment.

Panel B Column [1] shows the results for the medium sentiment state. Again we find

mixed results. While next-month raw returns are increasing across max return quintiles (column

[1]), the same is not true when examining next-month adjusted returns (column [2]). We do,

however, find that alphas are generally decreasing in columns [3] through [5]. These results

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seem to indicate that while the negative return premium associated with max returns is not

present during periods of low investor sentiment, the return premium is weakly observable

during periods of medium investor sentiment.

Panel C shows the results for the highest sentiment state. Consistent with our

expectation, we find that next-month returns are decreasing across max return quintiles. The

inverse relation between next-month returns and current max returns is monotonic in columns

[1], [3], [4], and [5]. Further, when examining the differences between extreme quintiles across

each panel, we uniformly find that the differences are decreasing across panels, which rejects the

null hypothesis H1 and suggests that the negative return premium associated with max returns is

driven by periods of high investor sentiment. In unreported results, we test whether the

difference between extreme quintiles at the bottom of Panel C is reliably different than the

difference at the bottom of Panel A. In each of the columns, we find that differences between

these differences are statistically significant at the 0.01 level.

4.2 The Max Return Premium and Investor Sentiment – A Fama-MacBeth (1973) Approach

Next, we continue our investigation by estimating the following equation using pooled

stock-month observations using the traditional Fama-MacBeth (1973) approach.

Reti,t+1 = β0 + β1Betai,t + β2Ln(Sizei,t) + β3Ln(B/Mi,t) + β4Momi,t + β5IdioVolti,t + β6Illiqi,t +

β7MaxReti,t + εi,t+1 (2)

The dependent variable is the raw return for each stock i in month t+1. The independent

variables include the following: Beta is the CAPM beta obtained using daily returns for a rolling

6-month window. Ln(Size) is the natural log of market capitalization. Ln(B/M) is the natural log

of the book-to-market ratio. Mom is the prior 6-month return following Jegadeesh and Titman

(2001). IdioVolt is the idiosyncratic volatility or the standard deviation of daily residual returns

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obtained from a daily Fama-French 4-Factor model using a rolling 6-month window. Illiq is the

monthly average of the daily return (in absolute value) scaled by dollar volume in $100,000.

MaxRet is the daily maximum stock return during a particular month for an individual stock. We

estimate variants of this equation and partition the time periods into the low sentiment, the

medium sentiment, and the high sentiment periods, respectively. The results reported in Table 4

are obtained by estimating a cross-sectional regression each month and then averaging both the

coefficients and the standard errors, which account for the Newey-West (1987) adjustment,

across time.

Columns [1] and [2] report the results when we include all observations. Column [1]

show that Size is negatively related to next-month returns while B/M and Mom are directly

related to next-month returns. These results are expected given the breadth of literature on the

size premium, the value premium, and the momentum premium. We also note that while the

estimate for Beta is positive, the average coefficient is not reliably different from zero. After

controlling for these factors, we find that the coefficient on max returns is negative and

significant (estimate = -0.0305, p-value = 0.004). Column [2] shows the results when we control

for idiosyncratic volatility and Amihud’s illiquidity. We note that the coefficient on Illiq is both

positive and significant, which is consistent with the idea of the illiquidity return premium

(Amihud and Mendelson (1986), Acharya and Pedersen (2005), among others). We do not find a

reliable estimate for IdioVolt. Regardless, after we control for these additional independent

variables, we still find that the variable MaxRet produces a negative and statistically significant

estimate. In economic terms, a one-standard deviation increase in max returns results in a

decrease in next-month returns of nearly 34 basis points. These findings indicate that the

negative lottery return premium is not only statistically significant, but the premium is also

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economically meaningful. Further, these results support the findings in Bali, Cakici, and

Whitelaw (2011).

Next, we replicate the analysis in columns [1] and [2] for the three sentiment states. In

general, the coefficients on the control variables are similar to those in the first two columns.4

For brevity, we only discuss the coefficients on MaxRet. First, we do not observe estimates for

MaxRet that are reliably different from zero (at the 0.05 level) in columns [3] through [6]. We

note that the estimate for MaxRet is -0.0196 in column [4] and is only marginally significant at

the 0.10 level. Consistent with our expectations, we find that the coefficient on MaxRet is

reliably negative in columns [7] and [8]. Compared to the general results in columns [1] and [2],

the coefficients in these latter columns are approximately twice as negative as the coefficients in

the former columns. In economic terms, the estimate for MaxRet in column [8] suggests that a

one standard deviation in max returns during periods of high sentiment results in a reduction in

next-month returns of nearly 58 basis points. Given that the general results we observe in the

first two columns are primarily driven by the highest sentiment state. These findings reject our

null hypothesis H1 and suggest that so-called lottery preferences are strongest in periods of high

investor sentiment.

4.3 The Expected Idiosyncratic Skewness Premium and Investor Sentiment – Multifactor Sorts

Next, we replicate the analysis in Tables 3 and 4 but instead of using max returns as our

approximation for lottery stocks, we following Boyer, Mitton, and Vorkink (2010) and use

expected idiosyncratic skewness. Table 5 shows the results for various measures of next-month

4 There are some important differences across columns [3] through [8]. First, we find that the coefficient on the variable Mom is increasing across sentiment states, which is consistent with Antoniou, Doukas, and Subrahmanyam (2013). Further, we find that the coefficient on idiosyncratic volatility is decreasing across sentiment states. While the traditional negative return premium associated with idiosyncratic volatility has been described as a puzzle (Ang et al. (2006, 2009)), we find that expected return between idiosyncratic volatility and next-month returns exists in periods with low and medium sentiment.

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equally-weighted returns across portfolios sorted by expected idiosyncratic skewness. As before,

Panels A, B, and C show the results for low, medium, and high sentiment states. The conclusions

that we are able to draw are generally similar across columns, so for brevity, we only discuss our

finding in column [5], which consists of alphas from estimating the full specification of equation

(1). Panel A shows that alphas are typically increasing across expected idiosyncratic skewness

quintiles. We note that the relation between next-month alphas and expected idiosyncratic

skewness is not monotonic. However, the difference between extreme quintiles is positive and

significant. This result suggests that while Boyer, Mitton, and Vorkink (2010) show that long-

short portfolio of expected idiosyncratic skewness generally underperforms, this is not true for

periods in the lowest sentiment state. This positive relation observed in column [5] is similar

across each column in Panel A.

Panel B shows the results for the medium sentiment state. In this medium state, we do

not find a smooth relationship between expected idiosyncratic skewness and next-month returns.

However, we do find that differences between extreme quintiles are positive and significant in

columns [1], [2], [4], and [5]. Again, these results suggest that the common negative relation

between next-month returns and expected idiosyncratic skewness is not driven by periods of

medium investor sentiment.

Panel C presents the results for the high sentiment state. Consistent with our expectation,

we find that differences between extreme quintiles are negative and statistically significant in

columns [1], [3], [4], and [5]. The underperformance of stocks with high expected idiosyncratic

skewness vis-à-vis stocks with low expected idiosyncratic skewness is 28 basis points in column

[5] and 141 basis points in column [1]. We do note, however, that next-month returns are not

monotonically decreasing across increasing skewness portfolios. As before, we test whether the

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difference between extreme quintiles at the bottom of Panel C is reliably different from the

difference at the bottom of Panel A. Although unreported, we again find that these differences-

in-differences are statistically significant at the 0.01 level. Our results in Panel C support the

findings in Boyer, Mitton, and Vorkink (2010) and are consistent with our expectation that the

underperformance of lottery-like stocks will be driven by periods with high investor sentiment.

4.4 The Expected Idiosyncratic Skewness Premium and Investor Sentiment – A Fama-MacBeth

(1973) Approach

In this subsection, we replicate Table 4 by estimating the following equation using Fama-

MacBeth (1973) regressions.

Reti,t+1 = β0 + β1Betai,t + β2Ln(Sizei,t) + β3Ln(B/Mi,t) + β4Momi,t + β5IdioVolti,t + β6Illiqi,t +

β7E[IdioSkew]i,t + εi,t+1 (3)

As before, the dependent variable is the raw return for each stock i in month t+1. Similar to the

specification in equation (2), the independent variables include the following: Beta is the CAPM

beta obtained using daily returns for a rolling 6-month window. Ln(Size) is the natural log of

market capitalization in (1,000s). Ln(B/M) is the natural log of the book-to-market ratio. Mom is

the prior 6-month return. IdioVolt is the idiosyncratic volatility. Illiq is the measure of Amihud’s

illiquidity. The independent variable of interest is E[IdioSkew], which is the expected

idiosyncratic skewness. As before, we estimate this equation using Fama-MacBeth (1973)

regressions with Newey-West (1987) adjustments to the standard errors. Similar to Table 4,

columns [1] and [2] present the results when using all observations while columns [3] through

[8] show the results when examining the low, medium, and high sentiment states.

Column [1] shows that when including Beta, Ln(Size), Ln(B/M), and Mom as control

variables, the estimate for E[IdioSkew], while negative, is not reliably different from zero

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(estimate = -0.2219, p-value = 0.224). When including both idiosyncratic volatility and

Amihud’s illiquidity as additional controls in column [2], we find a negative and significant

estimate for E[IdioSkew](estimate = -0.4451, p-value = 0.0003). These results support the

findings in Boyer, Mitton, and Vorkink (2010) and suggest that stocks with high expected

idiosyncratic skewness typically underperform. In economic terms, a one standard deviation

increase in E[IdioSkew] results in reduction in next-month returns of nearly 30 basis points.

Next, we examine the period of low investor sentiment. As before, we only discuss the

estimates for E[IdioSkew] for brevity. Without controls for illiquidity and idiosyncratic

volatility, we do not find that E[IdioSkew] produces a reliable estimate (column [3]). We do,

however, find that the estimate for E[IdioSkew] is negative and significant in column [4]

(estimate = -0.3644, p-value = 0.042). Similar results are found when we examine the medium

sentiment state in columns [5] and [6]. We note that the estimate for E[IdioSkew] in column [6]

is -0.4586 (p-value = 0.041).

In columns [7] and [8], we present our findings for the high sentiment state. Column [7]

shows that the coefficient on E[IdioSkew] is -0.6259, but only marginally significant (p-value =

0.086). When controlling for both illiquidity and idiosyncratic volatility, we find that the

estimate for E[IdioSkew] is both negative and reliably different from zero (estimate = -0.4993, p-

value = 0.026). A one standard deviation increase in E[IdioSkew] results in a 39 basis point

reduction in next-month returns suggesting that the coefficient on E[IdioSkew] is economically

meaningful. The findings in Table 6 have two noteworthy results. First, we find that the negative

estimate on E[IdioSkew] found in column [2] is decreasing monotonically across increasing

sentiment states (with controls for illiquidity and volatility). This observation is consistent with

our expectation that the underperformance caused by lottery preferences is directly related to

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investor sentiment. Second, our findings indicate that while the negative estimate for

E[IdioSkew] is decreasing across sentiment states, the negative return premium associated with

expected idiosyncratic skewness, documented in Boyer, Mitton, and Vorkink (2010), exists in

each type of sentiment state.

4.5 The Lottery Stock Premium and Investor Sentiment – Multifactor Sorts

In our final group of tests, we examine the return premium associated with what Kumar

(2009) denotes as Lottery stocks. Recall that Kumar (2009) argues that stocks with the highest

idiosyncratic skewness, the highest idiosyncratic volatility, and the lowest share prices are most

likely to resemble lotteries. As mentioned above, we have followed Kumar (2009) and

partitioned stocks into those that are considered lottery stocks (according to his definition) and

non-lottery stocks. We then report our various measures of next-month returns across both stock

categories.

Table 7 presents the results. As before, Panel A reports the results for the low sentiment

state, Panel B shows the results for the medium sentiment state, and Panel C presents the results

for the high sentiment state. In Panel A, we find that next-month raw returns are markedly larger

for lottery stocks than for non-lottery stocks. Similar results are reported when we focus on

market-adjusted returns. When we examine the alphas obtained from our different multi-factor

models, we find that the estimated alphas are approximately 2.2 times larger for lottery stocks

than for non-lottery stocks.

Panel B shows the results for the medium investor sentiment period. Again, we find that

the both next-month raw returns and next-month adjusted returns are significantly larger for

lottery stocks than for non-lottery stocks although we recognize that adjusted returns for lottery

stocks are indistinguishable from zero. While the results in column [3] shows that next-month

18

three-factor alphas are similar for both lottery and non-lottery stocks, columns [4] through [5]

show that the estimated next-month alphas are significantly larger for lottery stocks than for non-

lottery stocks. However, the differences between lottery and non-lottery stocks are substantially

smaller in Panel B than in Panel A.

Panel C presents the results for the high sentiment state. According to our hypothesis, the

negative return premium associated with lottery-type stocks (as found in Kumar (2009)) should

be most observable in this sentiment state. Consistent with our prediction, we find that each

measure of next-month returns is negative for lottery stocks while each measure of next-month

returns is positive for non-lottery stocks. Focusing on column [5], we find that after controlling

for the five risk factors specified in equation (1), the alphas associated with lottery stocks is 39

basis points less than the alphas for non-lottery stocks. This difference is reliably different from

zero (p-value = <.0001). In economic terms, the difference is also economically meaningful as it

represents a negative return premium of 4.68% annually. As before, we test whether differences

between lottery and non-lottery stocks in Panel C are statistically different from the differences

between lottery and non-lottery stocks in Panel A. Again, the unreported tests reveal that the

difference-in-differences is reliable at the 0.01 level in each of the columns. The conclusions

that we are able to draw from these findings are similar to those in Tables 3 and 5 and indicate

that the underperformance of stocks that resemble lotteries is indeed driven by periods of strong

investor sentiment.

4.6 The Lottery Stock Premium and Investor Sentiment – A Fama-MacBeth (1973) Approach

Next, we continue with the above format and test for a negative return premium

associated with lottery stocks using a traditional Fama-MacBeth (1973) approach. In particular,

we estimate the following equation using pooled stock-month data.

19

Reti,t+1 = β0 + β1Betai,t + β2Ln(Sizei,t) + β3Ln(B/Mi,t) + β4Momi,t + β5Illiqi,t +

β6LOTTERYi,t + εi,t+1 (4)

As before, the dependent variable is the raw return for each stock i in month t+1. The

independent variables have been defined previously. However, we note an important difference.

Since the independent variable of interest is the indicator variable LOTTERY, which captures

low-priced stocks with the highest idiosyncratic skewness and the highest idiosyncratic volatility,

we choose not to include idiosyncratic volatility as an additional control variable. In unreported

results, however, we generally find qualitatively similar results whether we include or exclude

idiosyncratic volatility as a control. We choose to report the results excluding idiosyncratic

volatility as an additional control because of the possibility multicollinearity bias between this

control variable and our variable of interest LOTTERY. Similar to previous tables, we estimate

variants of this equation and partition the time periods into the low sentiment, the medium

sentiment, and the high sentiment periods, respectively. We also report p-values, which are

obtained from Newey-West (1987) robust standard errors.

Table 8 presents the results from estimating equation (4). We provide the estimates with

their corresponding p-values with and without controls for Amihud’s illiquidity. The

conclusions that we are able to draw are similar so we only discuss the findings from our full

specification. We note that in column [2], the coefficient on LOTTERY is not reliably different

from zero (estimate = 0.0999, p-value = 0.546). When we focus on column [4] – the low

sentiment state, we find expectedly (given the results in the previous table) that the estimate for

LOTTERY is positive and reliably different from zero (estimate = 0.7168, p-value = 0.019). This

result suggests that during periods of low investor sentiment, there exists a positive return

20

premium on lottery stocks. Perhaps these low-priced stocks with high idiosyncratic volatility

present an unidentified risk premium that only exists in periods of low sentiment.

Columns [5] and [6] present the results for the medium sentiment state. Here we do not

find a reliable estimate for the indicator variable LOTTERY. However, in columns [7] and [8], we

find that, in the high sentiment state, the indicator variable LOTTERY produces a negative and

significant estimate whether or not we control for Amihud’s illiquidity (estimates = -0.5811, -

0.5838; p-values = 0.041, 0.040). These results again support our findings in the previous table

as well as our hypothesis that the underperformance of stocks that resemble lotteries will be

driven by periods of high sentiment. The monotonically decreasing estimates for LOTTERY

across increasing sentiment states seem to indicate that the price premiums associated with

lottery preferences (Kumar (2009), Boyer, Mitton, and Vorkink (2010), and Bali, Cakici, and

Whitelaw (2011)) are indeed driven by periods with high investor sentiment.

4.7 Robustness

We conduct a number of robustness tests and discuss the findings in this section. First,

we test whether our results are driven by something other than investor sentiment. For instance,

it is possible that our results a capturing lottery preferences across the business cycle. Using

monthly definitions of recessionary states and expansionary states given by the National Bureau

of Economic Research (NBER), we replicate our analysis for expansionary versus recessionary

states. Results from these unreported tests indicate that the underperformance of lottery-type

stocks is not necessarily driven by fluctuations in the business cycle. For instance, the Fama-

MacBeth (1973) coefficient on max returns is more negative during recessions than during

expansions. The coefficients on expected idiosyncratic skewness and lotteries are similar

between economic states. A closer examination of figure 1 provides some explanation. We find

21

that during the three periods of expansion according to the NBER (12/1982 – 7/1990, 3/1991 –

3/2001, and 11/2001 – 12/2007), investor sentiment is not unusually high. In particular, investor

sentiment decreases markedly from 1984 to 1990 and remains relatively low from 1991 until the

end of 1998. Further, investor sentiment was unusually low during the early part of the 2000s.

Alternatively, it is possible that our results could be driven by periods of high market

volatility. Results in Ang, Hodrick, Xing, and Zhang (2006) show that exposure to market-wide

volatility adversely affects expected returns. Further, they argue that during periods of high

market volatility, investors with lottery preferences might have stronger demand for stocks that

resemble lotteries. In unreported tests, we find that market-wide volatility, which we calculate as

the standard deviation of the CRSP value-weighted market index, and investor sentiment are

uncorrelated across the time series. Focusing on periods of high sentiment, our Fama-MacBeth

(1973) regressions show some evidence that the negative return premium associated with max

returns is driven by periods of high market volatility (or market volatility in the top tercile).

However, the negative return premium associated with expected idiosyncratic skewness and the

lottery indicator variable seems to be unrelated to variability in market returns. These results

suggest that, in general, our findings are robust to periods of high and low market volatility.

Finally, we test whether our results hold when conditioning on institutional ownership.

After gathering institutional holdings data at the quarterly level from 13f filings, we test whether

our findings in previous tables is stronger for stocks with less institutional ownership under the

assumption that individual investors – instead of institutional investors – are driving our results.

Again, we focus on high sentiment periods and sort stocks into terciles based on institutional

ownership. We do not find that the reliable negative return premium associated with the

22

characteristics that capture lottery stocks is related to the level of institutional ownership

indicating that our findings are robust to controls for institutional ownership.

5. CONCLUSIONS

This study develops and tests the hypothesis that the underperformance of stocks that

resemble lotteries is driven by periods of high investor sentiment. Relying on the psychology

literature that suggests that sentiment can directly affect the level of the individual’s subjective

probability assessments (Johnson and Tversky (1983), Bower (1981), Arkes, Herren, and Isen

(1988), Wright and Bower (1992), and Mayer et al. (1992)), we posit that, during periods of

strong investor sentiment, investors will assign higher probabilities of observing lottery-like

stock returns in the future. The demand for lottery-like stocks, therefore, is expected to greater

during high sentiment states than during low sentiment states.

We closely follow three studies that document preferences for lottery stocks (Kumar

(2009), Boyer, Mitton, and Vorkink (2010), and Bali, Cakici, and Whitelaw (2011)) and test

whether the observed price premiums and subsequent underperformance associated with these

preferences is driven by periods with strong investor sentiment. Consistent with our prediction,

we find strong evidence that the negative return premia for (i) stocks with the largest maximum

daily return (Bali, Cakici, and Whitelaw (2011)), (ii) stocks with the highest expected

idiosyncratic skewness (Boyer, Mitton, and Vorkink (2010)), and (iii) stocks that are classified as

lottery stocks (Kumar (2009)) is driven primarily by high sentiment states. These findings not

only provide an important contribution to the literature on lottery preferences, but our findings

are also important in light of traditional asset pricing theory that assumes investors prefer mean-

variance efficiency. In light of this theory, our findings suggest that violations of this efficiency

23

and subsequent preferences for lottery-like returns are most likely to occur during periods of high

investor sentiment.

24

REFERENCES

Acharya, V., L. Pedersen. “Asset Pricing with Liquidity Risk.” Journal of Financial Economics,

77 (2005), 375–410.

Amihud, Y. “Illiquidity and Stock Returns: Cross-Seciton and Time-Series Effects.” Journal of

Financial Markets, 5 (2002), 31–56.

Amihud, Y., and H. Mendelson. “Asset Pricing and the Bid-Ask Spread.” Journal of Financial

Economics, 17 (1986), 223–249.

Antoniou, C.; J. Doukas; and A. Subrahmanyam. “Cognitive Dissonance, Sentiment, and

Momentum.” Journal of Financial and Quantitative Analysis, 48 (2013), 245–275.

Arkes, H.; L. Herren; and A. Isen. “The Role of Potential Loss in the Influence of Affect on

Risk-Taking Behavior.” Organizational Behavior and Human Decision Processes, 41

(1988), 181–193.

Baker, M., and J. Stein. “Market Liquidity as a Sentiment Indicator.” Journal of Financial

Markets, 7 (2004), 271–299.

Baker, M., and J. Wurgler. “Investor Sentiment in the Stock Market.” Journal of Economic

Perspectives, 21 (2007), 129–151.

Bali, T.; N. Cakici; and R. Whitelaw. “ Maxing Out: Stocks as Lotteries and the Cross-Section of

Expected Returns.” Journal of Financial Economics, 99 (2011), 427–446.

Barberis, N., and M. Huang. “Stocks as Lotteries: The Implications of Probability Weighting for

Security Prices.” American Economic Review, 98 (2008), 2066–2100.

Bower, G. “Mood and Memory.” American Psychologist, 36 (1981), 129–148.

Boyer, B.; T. Mitton; and K. Vorkink. “Expected Idiosyncratic Skewness.” Review of Financial

Studies, 23 (2010), 169–202.

25

Boyer, B., and K. Vorkink. “Stock Options as Lotteries.” Forthcoming (2013), Journal of

Finance.

Carhart, M. “On Persistance in Mutual Fund Performance.” Journal of Finance, 52 (1997), 57–

82.

Fama, E., and K. French. “Multifactor Explanations of Asset Pricing Anomalies.” Journal of

Finance 51 (1996), 55–84.

Fama, E., and J. MacBeth. “Risk, Return, and Equilibrium: Empirical Tests.” Journal of Political

Economy, 81 (1973), 607–636.

Green, T.C., and B-H. Hwang. “Initial Public Offerings as Lotteries: Skewness Preference and

First-Day Returns, Management Science, 58 (2012), 432-444.

Jegadeesh, N., and S. Titman. “Profitability of Momentum Strategies: An Evaluation of

Alternative Explanations.” Journal of Finance 56 (2001), 669-720.

Johnson, E., and A. Tversky. “Affect, Generalization, and the Perception of Risk.” Journal of

Personality and Social Psychology, 45 (1983), 20–31.

Kahneman, D., and A. Tversky. “Prospect Theory: An Analysis of Decision Under Risk.”

Econometrica, 47 (1979), 263–292.

Kahneman, D., and A. Tversky. “Advances in Prospect Theory: Cumulative Representation of

Uncertainty.” Journal of Risk and Uncertainty, 5 (1992), 297–323.

Kumar, A. “Who Gambles in the Stock Market?” Journal of Finance, 64 (2009), 1889–1933.

Kumar, A.; J. K. Page; and O. G. Spalt. “Religious Beliefs, Gambling Attitudes, and Financial

Market Outcomes.” Journal of Financial Economics, 102 (2011), 671–708.

Markowitz, H. “The Utility of Wealth.” Journal of Political Economy, 60 (1952), 151–158.

26

Mayer, J.; Y. Gaschke; D. Braverman; and T. Evans. “Mood-Congruent Judgement is a General

Effect.” Journal of Personality and Social Psychology, 63 (1992), 119–132.

Mitton, T., and K. Vorkink. “Equilibrium Underdiversification and the Preference for

Skewness.” Review of Financial Studies, 20 (2007), 1,255–1,288.

Newey, W., and K. West. “A Simple, Positive Semi-Definite, Heteroskedasticity and

Autocorrelation Consistent Covariance Matrix.” Econometrica, 55 (1987), 703–708.

Pastor, L., and R. Stambaugh. “Liquidity Risk and Expected Stock Returns.” Journal of Political

Economy, 111 (2003), 642–685

Sharpe, W. “A Theory of Market Equilibrium under Conditions of Risk.” Journal of Finance 19

(1964), 425–442.

Tversky, A., and D. Kahneman. “Judgment under Uncertainty: Heuristics and Biases.” Science,

185 (1974), 1124–1131.

Wright, W., and G. Bower. “Mood Effects on Subjective Probability Assessment.”

Organizational Behavior and Human Decision Processes, 52 (1992), 276-291.

Zhang, Y. “Individual Skewness and the Cross-Section of Average Stock Returns.” Working

Paper (2005), Yale University.

27

Table 1 Summary Statistics The table reports statistics that describe the sample. Price is the closing monthly prices. Turn is the monthly share turnover, or the ratio of trading volume scaled by shares outstanding in percent. Beta is the CAPM beta obtained using daily returns for a rolling 6-month window. Size is the market capitalization in (1,000s). B/M is the book-to-market ratio. IdioVolt is the idiosyncratic volatility or the standard deviation of daily residual returns obtained from a daily Fama-French 4-Factor model using a rolling 6-month window. Illiq is the monthly average of the daily return (in absolute value) scaled by dollar volume. MaxRet is the daily maximum stock return during a particular month for an individual stock. E[IdioSkew] is the expected idiosyncratic skewness obtained from following Boyer, Mitton, and Vorkink (2010). LOTTERY is an indicator variable equal to one if a particular stock has the highest (above median) idiosyncratic skewness (skewness of daily residual 4-factor returns), the highest idiosyncratic volatility (above median), and the lowest share price (below median).

Mean Std. Deviation 25th Percentile Median 75th Percentile

[1] [2] [3] [4] [5]

Price 20.62 26.86 6.25 14.86 27.63 Turn 5.8596 20.4478 1.1875 2.9132 6.7504 Beta 0.8423 3.8344 0.3438 0.8272 1.2879 Size 2,201,121.46 12,038,943.95 42,886.00 180,834.70 821,205.75 B/M 0.4878 10.4101 0.03421 0.0606 0.1004 IdioVolt 0.0318 0.0238 0.0167 0.0255 0.0396 Illiq 0.7151 87.6594 0.0004 0.0557 0.7714 MaxRet 0.0754 0.0859 0.0327 0.0535 0.0904 E[IdioSkew] 1.1026 0.6651 0.7121 1.0542 1.4551 LOTTERY 0.2236 0.4167 0.0000 0.0000 0.0000

28

Table 2 Summary Statistics across Investor Sentiment The table reports the mean values of several stock characteristics across various periods of investor sentiment. Column [4] shows the difference in mean values between high and low periods of investor sentiment. Price is the closing monthly prices. Turn is the monthly share turnover, or the ratio of trading volume scaled by shares outstanding in percent. Beta is the CAPM beta obtained using daily returns for a rolling 6-month window. Size is the market capitalization in (1,000s). B/M is the book-to-market ratio. IdioVolt is the idiosyncratic volatility or the standard deviation of daily residual returns obtained from a daily Fama-French 4-Factor model using a rolling 6-month window. Illiq is the monthly average of the daily return (in absolute value) scaled by dollar volume. MaxRet

is the daily maximum stock return during a particular month for an individual stock. E[IdioSkew] is the expected idiosyncratic skewness obtained from following Boyer, Mitton, and Vorkink (2010). LOTTERY is an indicator variable equal to one if a particular stock has the highest (above median) idiosyncratic skewness (skewness of daily residual 4-factor returns), the highest idiosyncratic volatility (above median), and the lowest share price (below median). *, **, *** denote statistical significance at the 0.10, 0.05, and 0.01 levels, respectively.

Low Medium High High-Low

[1] [2] [3] [4]

Price 19.4050778 21.5372135 20.9326896 1.5276*** (<.0001) Turn 6.0665449 6.0714650 5.4371359 -0.6294*** (<.0001) Beta 0.8214659 0.8342438 0.8713918 0.0499*** (<.0001) Size 2113784.76 2419220.73 2069891.20 -43893.60 (0.132) B/M 6.0053175 3.8337026 4.7892538 -1.2161*** (<.0001) IdioVolt 0.0328291 0.0301309 0.0323305 -0.0005*** (<.0001) Illiq 12.2170616 4.7571428 4.4402317 -7.7768*** (0.003) MaxRet 0.0768133 0.0716736 0.0776323 0.0008*** (0.0002) E[IdioSkew] 1.1809762 1.0011978 1.1237343 -0.0572*** (<.0001) LOTTERY 0.2348 0.2175 0.2184 -0.0164*** (<.0001)

29

Table 3 Returns across Max Returns Quintiles by Investor Sentiment The table reports next-month returns across quintiles that are sorted based on max return in the current month. We report raw returns, adjusted returns, which are the difference between raw returns and CRSP value-weighted market returns, as well as three measures of expected returns obtained from estimating variants of the following equation.

Returni,t+1 – Rft+1 = α + β1(Rmt+1 – Rft+1) + β2SMBt+1 + β3HMLt+1 + β4UMDt+1 + β5LIQt+1 + εi,t+1

The model above is a standard 5-factor model where the factors are the 3-factors in Fama and French (1996), the momentum factor UMD and the Pastor and Stambaugh (2003) liquidity factor LIQ. Alphas are estimates and reported in each quintile. Panel A reports the results when examining periods of low sentiment. Panel B presents the results during periods of medium sentiment. Panel C shows the results when examining periods of high sentiment. *, **, *** denote statistical significance at the 0.10, 0.05, and 0.01 levels, respectively.

Panel A. Low Investor Sentiment – High minus Low Returns

Raw Returns Adj. Returns FF3F Alphas FF4F Alphas FF5F Alphas

[1] [2] [3] [4] [5]

Q I (LOW)

Q II

Q III

Q IV

Q V (HIGH)

Q V – Q I

0.0123 0.0150 0.0189 0.0201 0.0292

0.0169*** (<.0001)

0.0012 0.0038 0.0074 0.0079 0.0146

0.0134*** (<.0001)

0.0030 0.0039 0.0059 0.0035 0.0039

0.0009 (0.214)

0.0026 0.0036 0.0059 0.0034 0.0022

-0.0004 (0.582)

0.0026 0.0035 0.0059 0.0034 0.0030

0.0004 (0.585)

Panel B. Med Investor Sentiment

Q I (LOW)

Q II

Q III

Q IV

Q V (HIGH)

Q V – Q I

0.0108 0.0124 0.0135 0.0147 0.0157

0.0049*** (<.0001)

-0.0019 -0.0015 -0.0017 -0.0013 -0.0023

-0.0004 (0.571)

-0.0004 -0.0005 -0.0009 -0.0007 -0.0032

-0.0028***

(0.0002)

0.0007 0.0002 -0.0002 0.0004 -0.0013

-0.0020**

(0.010)

0.0007 0.0002 -0.0002 0.0004 -0.0015

-0.0022***

(0.004)

Panel C. High Investor Sentiment

Q I (LOW)

Q II

Q III

Q IV

Q V (HIGH)

Q V – Q I

0.0124 0.0098 0.0068 0.0004 -0.0137

-0.0261***

(<.0001)

0.0060 0.0063 0.0050 0.0009 -0.0085

-0.0145***

(<.0001)

0.0041 0.0021 0.0006 -0.0018 -0.0053

-0.0094***

(<.0001)

0.0042 0.0026 0.0018 0.0000 -0.0043

-0.0085***

(<.0001)

0.0044 0.0030 0.0020 0.0000 -0.0041

-0.0085***

(<.0001)

30

Table 4 Fama-MacBeth (1973) Regressions The table reports the results from estimating the following equation using a Fama-MacBeth (1973) approach.

Reti,t+1 = β0 + β1Betai,t + β2Ln(Sizei,t) + β3Ln(B/Mi,t) + β4Momi,t + β5IdioVolti,t + β6Illiqi,t + β7MaxReti,t + εi,t+1

The dependent variable is the raw return for each stock i in month t+1. The independent variables include the following: Beta is the CAPM beta obtained using daily returns for a rolling 6-month window. Ln(Size) is the natural log of market capitalization in (1,000s). Ln(B/M) is the natural log of the book-to-market ratio. Mom is the prior 6-month return. IdioVolt is the idiosyncratic volatility or the standard deviation of daily residual returns obtained from a daily Fama-French 4-Factor model using a rolling 6-month window. Illiq is the monthly average of the daily return (in absolute value) scaled by dollar volume. MaxRet is the daily maximum stock return during a particular month for an individual stock. We estimate variants of this equation and partition the time periods into the low sentiment, the medium sentiment, and the high sentiment periods, respectively. *, **, *** denote statistical significance at the 0.10, 0.05, and 0.01 levels.

All Observations Low Sentiment Medium Sentiment High Sentiment

[1] [2] [3] [4] [5] [6] [7] [8]

Intercept 3.2384*** 2.5221*** 4.6096*** 2.6312*** 2.8276*** 1.0338 2.5233** 3.5149*** (<.0001) (<.0001) (<.0001) (0.0002) (0.005) (0.149) (0.023) (<.0001) Beta 0.0548 0.0364 0.0758 -0.0071 0.1155 0.1033 -0.0058 0.0224 (0.409) (0.559) (0.545) (0.953) (0.244) (0.275) (0.960) (0.830) Ln(Size) -0.1401*** -0.0930** -0.2426*** -0.1253** -0.1161* -0.0065 -0.0762 -0.1302* (0.001) (0.010) (0.001) (0.024) (0.094) (0.907) (0.338) (0.058) Ln(B/M) 0.3553*** 0.3296*** 0.3056*** 0.2752*** 0.3364*** 0.3480*** 0.4085*** 0.3595*** (<.0001) (<.0001) (<.0001) (0.0001) (<.0001) (<.0001) (<.0001) (<.0001) Mom 0.5473** 0.3792 0.0746 -0.3161 0.8701*** 0.4676 0.6884* 0.8672** (0.015) (0.118) (0.855) (0.492) (0.006) (0.186) (0.093) (0.038) IdioVolt 0.0411 0.2010* 0.1747* -0.1827 (0.525) (0.054) (0.085) (0.125) Illiq 0.0141*** 0.0145** 0.0155** 0.0129* (0.001) (0.026) (0.045) (0.059) MaxRet -0.0305*** -0.0395*** -0.0079 -0.0196* 0.0068 -0.0167 -0.0869*** -0.0718*** (0.004) (<.0001) (0.623) (0.099) (0.701) (0.184) (<.0001) (<.0001)

31

Table 5 Returns across Expected Idiosyncratic Skewness Quintiles by Investor Sentiment The table reports next-month returns across quintiles that are sorted based on expected idiosyncratic skewness in the current month. We report raw returns, adjusted returns, which are the difference between raw returns and CRSP value-weighted market returns, as well as three measures of expected returns obtained from estimating variants of the following equation.





[1] [2] [3] [4] [5]

Q I (LOW)

Q II

Q III

Q IV

Q V (HIGH)

Q V – Q I

0.0129 0.0180 0.0161 0.0146 0.0275

0.0146*** (<.0001)

0.0019 0.0054 0.0047 0.0036 0.0132

0.0113*** (<.0001)

0.0024 0.0021 0.0017 0.0021 0.0091

0.0067*** (<.0001)

0.0021 0.0021 0.0018 0.0023 0.0088

0.0067*** (<.0001)

0.0020 0.0019 0.0019 0.0023 0.0090

0.0070*** (<.0001)


Q I (LOW)

Q II

Q III

Q IV

Q V (HIGH)

Q V – Q I

0.0107 0.0097 0.0138 0.0169 0.0172

0.0065*** (<.0001)

-0.0005 -0.0065 -0.0050 0.0006 0.0027

0.0032*** (<.0001)

0.0005 -0.0018 -0.0030 0.0008 0.0003

-0.0002 (0.782)

-0.0002 -0.0013 -0.0005 0.0021 0.0020

0.0022***

(0.003)

-0.0002 -0.0012 -0.0007 0.0013 0.0017

0.0019** (0.010)


Q I (LOW)

Q II

Q III

Q IV

Q V (HIGH)

Q V – Q I

0.0056 0.0065 0.0090 0.0088 -0.0085

-0.0141***

(<.0001)

-0.0017 0.0044 0.0065 0.0075 -0.0025

-0.0008 (0.437)

0.0001 0.0014 0.0023 0.0037 -0.0040

-0.0041***

(<.0001)

0.0008 0.0025 0.0033 0.0046 -0.0015

-0.0023***

(0.006)

0.0010 0.0025 0.0033 0.0046 -0.0018

-0.0028***

(0.001)

32


Reti,t+1 = β0 + β1Betai,t + β2Ln(Sizei,t) + β3Ln(B/Mi,t) + β4Momi,t + β5IdioVolti,t + β6Illiqi,t + β7E[IdioSkew]i,t + εi,t+1

The dependent variable is the raw return for each stock i in month t+1. The independent variables include the following: Beta is the CAPM beta obtained using daily returns for a rolling 6-month window. Ln(Size) is the natural log of market capitalization in (1,000s). Ln(B/M) is the natural log of the book-to-market ratio. Mom is the prior 6-month return. IdioVolt is the idiosyncratic volatility or the standard deviation of daily residual returns obtained from a daily Fama-French 4-Factor model using a rolling 6-month window. Illiq is the monthly average of the daily return (in absolute value) scaled by dollar volume. E[IdioSkew] is the expected idiosyncratic skewness obtained from following Boyer, Mitton, and Vorkink (2010). We estimate variants of this equation and partition the time periods into the low sentiment, the medium sentiment, and the high sentiment periods, respectively. *, **, *** denote statistical significance at the 0.10, 0.05, and 0.01 levels.


[1] [2] [3] [4] [5] [6] [7] [8]

Intercept 3.5150*** 3.4018*** 4.2477*** 3.4213*** 3.4335*** 1.9734** 2.9925** 4.4221*** (<.0001) (<.0001) (<.0001) (0.0001) (0.003) (0.028) (0.014) (<.0001) Beta 0.0345 0.0202 0.1958 0.0585 0.2293* 0.1785 -0.2348 -0.1251 (0.692) (0.789) (0.241) (0.697) (0.076) (0.122) (0.110) (0.305) Ln(Size) -0.1347*** -0.1205*** -0.2161*** -0.1548*** -0.1506** -0.0485 -0.0584 -0.1456** (0.003) (0.001) (0.001) (0.008) (0.046) (0.403) (0.482) (0.032) Ln(B/M) 0.5615*** 0.5212*** 0.5677*** 0.5034*** 0.4920*** 0.5084*** 0.6070*** 0.5445*** (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) Mom 0.5348** 0.3781 0.1085 -0.3151 0.9072*** 0.5543 0.6033 0.8007* (0.025) (0.128) (0.795) (0.499) (0.006) (0.119) (0.173) (0.070) IdioVolt -0.0037 0.1938* 0.1650 -0.2829** (0.957) (0.080) (0.169) (0.026) Illiq 0.0147*** 0.0131* 0.0159** 0.0149** (0.001) (0.051) (0.044) (0.035) E[IdioSkew] -0.2219 -0.4451*** 0.1008 -0.3644** -0.0180 -0.4586** -0.6259* -0.4993** (0.224) (0.0003) (0.698) (0.042) (0.946) (0.041) (0.086) (0.026)

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Table 7 Returns across Lottery and Non-Lottery Stocks by Investor Sentiment The table reports next-month returns by Lottery and Non-Lottery stocks, as defined in Kumar (2009), in the current month. We report raw returns, adjusted returns, which are the difference between raw returns and CRSP value-weighted market returns, as well as three measures of expected returns obtained from estimating variants of the following equation.





[1] [2] [3] [4] [5]

Lottery

Non-Lottery

Lot-NonLot

0.0261 0.0171

0.0090*** (<.0001)

0.0133 0.0051

0.0082*** (<.0001)

0.0082 0.0037

0.0045*** (<.0001)

0.0084 0.0038

0.0046*** (<.0001)

0.0085 0.0038

0.0047*** (<.0001)


Lottery

Non-Lottery

Lot-NonLot

0.0153 0.0128

0.0025*** (<.0001)

-0.0002 -0.0021

0.0019***

(0.001)

-0.0006 -0.0007

0.0001 (0.876)

0.0015 0.0000

0.0015** (0.023)

0.0014 -0.0000

0.0014** (0.035)


Lottery

Non-Lottery

Lot-NonLot

-0.0043 0.0047

-0.0090***

(<.0001)

-0.0052 0.0036

-0.0088***

(<.0001)

-0.0047 0.0012

-0.0059***

(<.0001)

-0.0015 0.0024

-0.0039***

(<.0001)

-0.0015 0.0024

-0.0039***

(<.0001)

34


Reti,t+1 = β0 + β1Betai,t + β2Ln(Sizei,t) + β3Ln(B/Mi,t) + β4Momi,t + β5Illiqi,t + β6LOTTERYi,t + εi,t+1

The dependent variable is the raw return for each stock i in month t+1. The independent variables include the following: Beta is the CAPM beta obtained using daily returns for a rolling 6-month window. Ln(Size) is the natural log of market capitalization in (1,000s). Ln(B/M) is the natural log of the book-to-market ratio. Mom is the prior 6-month return. Illiq is the monthly average of the daily return (in absolute value) scaled by dollar volume. LOTTERY is an indicator variable equal to one if a particular stock has the highest (above median) idiosyncratic skewness (skewness of daily residual 4-factor returns), the highest idiosyncratic volatility (above median), and the lowest share price (below median). We estimate variants of this equation and partition the time periods into the low sentiment, the medium sentiment, and the high sentiment periods, respectively. We note that we do not include IdioVolt as an additional regressor given that idiosyncratic volatility is included to identify the indicator variable LOTTERY. *, **, *** denote statistical significance at the 0.10, 0.05, and 0.01 levels.


[1] [2] [3] [4] [5] [6] [7] [8]

Intercept 2.7175*** 2.4410*** 3.8227*** 3.4679*** 2.6709*** 2.2853** 1.8738* 1.7386* (<.0001) (<.0001) (<.0001) (<.0001) (0.006) (0.018) (0.071) (0.092) Beta 0.0046 0.0462 0.0600 0.0600 0.0962 0.1032 -0.0050 -0.0062 (0.517) (0.499) (0.644) (0.639) (0.339) (0.303) (0.967) (0.959) Ln(Size) -0.1115*** -0.0906** -0.1859*** -0.1588*** -0.1017 -0.0730 -0.0595 -0.0493 (0.006) (0.022) (0.003) (0.009) (0.135) (0.278) (0.421) (0.501) Ln(B/M) 0.3701*** 0.3618*** 0.3145*** 0.2989*** 0.3320*** 0.3252*** 0.4418*** 0.4384*** (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) Mom 0.5795** 0.5142** -0.0504 -0.1654 0.8224** 0.7376** 0.9034 0.8918** (0.016) (0.032) (0.906) (0.702) (0.010) (0.020) (0.042) (0.044) Illiq 0.0122*** 0.0156** 0.0161** 0.0065 (0.001) (0.010) (0.025) (0.304) LOTTERY 0.1024 0.0999 0.7238** 0.7168** 0.3647 0.3675 -0.5811** -0.5838** (0.538) (0.546) (0.019) (0.019) (0.142) (0.139) (0.041) (0.040)

35

Figure 1. The figure shows Baker and Wurgler’s (2007) investor sentiment across our sample time period.

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Investor Sentiment Across Time

lottery preferences and investor sentiment · 2017-02-16 · lottery preferences and investor...

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