assignment代做_assignment代写价格_墨尔本assignment代写

代寫essay服務

五年專注加拿大代寫essay 信譽保證
turnitin檢測 保證原創率 高分通過

本公司成立以來,在代寫essay領域獲得了不錯的口碑,98%以上的客戶順利通過..歡迎大家進行咨詢和享受公司為你提供的全方位服務!不論你的essay有多難,deadline有多急,我們將給你帶來最專業可靠的代寫essay服務。

Order Now

Finance3017 - investment and portfolio management代寫

    Trends in the Cross-Section of Expected Stock Returns
    by
    Tarun Chordia, Avanidhar Subrahmanyam, and Qing Tong
    March 4, 2011
    Abstract
    We examine recent shifts in cross-sectional return predictability for a comprehensive sample of
    NYSE/AMEX and Nasdaq stocks, and for sub-samples of these stocks stratified by market
    liquidity. Our analysis is motivated by the notion that dramatic reductions in trading costs and the
    emergence of hedge funds in recent years should be associated with increased arbitrage activity,
    and thus greater pricing efficiency. We consider a large set of previously identified predictors,
    and find that cross-sectional predictability has decreased considerably in recent years, both
    statistically and economically. Indeed, liquid stocks have evolved to exhibit none of the well-
    known cross-sectional effects such as momentum, analyst dispersion, earnings drift, or accounting
    accruals, in recent years. Overall, the evidence is consistent with the notion that decreased trading
    costs have accompanied enhanced cross-sectional pricing efficiency of equities.
    Contacts
    Chordia  Subrahmanyam  Tong
    Voice:  +1-404-727-1620  +1-310-825-5355  +65-6828-0158
    Fax:  +1-404-727-5238  +1-310-206-5455  +65-6828-0777
    E-mail:  Tarun_Chordia@bus.emory.edu  asubrahm@anderson.ucla.edu  qingtong@smu.edu.sg
    Address:  Goizueta Business School
    Emory University
    Atlanta, GA 30322
    Anderson School
    UCLA
    Los Angeles, CA 90095-1481
    Lee Kong Chian School of Business
    Singapore Management University
    Singapore 178899
    We are grateful to the Fink Center for Investment Research at UCLA for financial assistance.
    We also thank Michael Brennan, Stuart Gabriel, Lawrence He, Sahn-Wook Huh, Igor Kozhanov,
    Fari Moshirian, Vikram Nanda, Joseph Ogden, Unyong Pyo, Samir Trabelsi, Peter Swan,
    Chunchi Wu, and seminar participants at UCLA, SUNY-Buffalo, Brock University, University
    of New South Wales, and Hong Kong University of Science and Technology, for valuable
    comments.
    Trends in the Cross-Section of Expected Stock Returns
    Abstract
    We examine recent shifts in cross-sectional return predictability for a comprehensive sample of
    NYSE/AMEX and Nasdaq stocks, and for sub-samples of these stocks stratified by market
    liquidity. Our analysis is motivated by the notion that dramatic reductions in trading costs and the
    emergence of hedge funds in recent years should be associated with increased arbitrage activity,
    and thus greater pricing efficiency. We consider a large set of previously identified predictors,
    and find that cross-sectional predictability has decreased considerably in recent years, both
    statistically and economically. Indeed, liquid stocks have evolved to exhibit none of the well-
    known cross-sectional effects such as momentum, analyst dispersion, earnings drift, or accounting
    accruals, in recent years. Overall, the evidence is consistent with the notion that decreased trading
    costs have accompanied enhanced cross-sectional pricing efficiency of equities.
    1
    Recent years have witnessed a sea change in the costs of trading in financial markets. For
    instance, Chakravarty, Panchapagesan, and Wood (2005) and French (2008) show that
    institutional commissions have declined over time. Jones (2002) as well as Chordia, Roll, and
    Subrahmanyam (2001) show that standard measures of illiquidity such as bid-ask spreads have
    also decreased substantially over time. Further, technology has facilitated algorithmic trading
    (Hendershott, Jones, and Menkveld, 2008) by institutions and online brokerage accounts have
    facilitated trading by individual investors. Another trend in financial markets is the proliferation
    of hedge funds, possibly stimulated by the exogenous decreases in trading costs. The decrease in
    trading costs is dramatic and quite unprecedented from an historical perspective. 1 Chordia, Roll
    and Subrahmanyam (2011) have argued that this decrease in trading costs has led to an explosion
    in trading volume, especially institutional trading volume, and that this has led to improvements
    in market quality.
    An unrelated paradigm shift in academic finance has been the suggestion that the cross-section of
    stock returns may be driven by behavioral as opposed to rational considerations. While Black,
    Jensen, and Scholes (1972) and Fama and MacBeth (1973) document a significant positive cross-
    sectional relation between security betas and expected returns – providing support for the capital
    asset pricing model (Sharpe (1964), Lintner (1965), and Mossin (1966)), Fama and French (1992)
    find that the relation between returns and market beta is insignificant.
    This calls into question the
    link between risk and expected returns and has led to the proliferation of the anomalies literature.
    The anomalies literature is vast and points to the importance of firm characteristics for expected
    returns. Fama and French (1992) find that firm size and the book-to-market (BM) ratio strongly
    predict future returns. Returns are negatively related to size and positively to BM. Ball and
    Brown (1968) document the post-earnings-announcement-drift (PEAD) where stocks with a high
    earnings surprise continue to outperform stocks with a low earnings surprise. Jegadeesh and
    Titman (1993) uncover a momentum effect wherein buying past winners and selling past losers
    leads to substantial abnormal returns. Sloan (1996) investigates the accruals anomaly where
    1 In its more than 200 year history, the New York Stock Exchange (NYSE) has reduced the tick size only twice:
    from an eighth to a sixteenth in June 1997 and from a sixteenth to a penny in January 2001. Technological
    improvements have allowed the NYSE to accommodate a dramatic increase in trading volumes.
    2
    stocks with greater non-cash components of earnings earn lower abnormal returns. Diether,
    Malloy, and Scherbina (2002) document the ―dispersion‖ anomaly where stocks with higher
    dispersion in analysts’ forecasts earn lower returns. Brennan, Chordia, and Subrahmanyam
    (1998) find that investments based on anomalies result in reward-to-risk ratios that are about
    three times as high as that obtained by investing in the market, and these ratios seem too large to
    be consistent with a rational model.
    On balance, it seems reasonable to assert that the evidence on the predictability of returns at least
    partially supports non-risk-based (behavioral) explanations. Several such explanations exist in
    the literature. Daniel, Hirshleifer, and Subrahmanyam (1998) suggest that overconfidence
    induces overreaction, so that extreme book-to-market ratios represent overreactions to extreme
    private signals that are later corrected. Self-attribution bias (the tendency to attribute investing
    mistakes to bad luck) ensures a continuing overreaction and slow correction that induces
    momentum. 2 Barberis, Shleifer, and Vishny (1998) suggest that naïve extrapolation from past
    growth causes stock prices to overreact and reverse, resulting in return predictability from
    fundamental/price ratios. Hong and Stein (1999) argue that momentum arises as news diffuses
    slowly over time. Grinblatt and Han (2005) argue that loss aversion can help explain
    momentum. Specifically, past winners have excess selling pressure and past losers are not
    shunned as quickly as they should be, and this causes underreaction to public information. In
    equilibrium, past winners are undervalued and past losers are overvalued. This creates
    momentum as the misvaluation reverses over time. Hirshleifer and Teoh (2003) model the
    notion that the accounting accruals effect obtains because investors have limited attention and do
    not parse accounting statements carefully enough.
    The objective of this paper is straightforward. We propose to examine how the cross-sectional
    predictability of stock returns has changed in recent years. We begin by noting that there are
    three potential reasons for the existence of the characteristic-based predictability of returns:
    1. The predictability is a result of a sustained data mining exercise over the last three decades.
    If data mining is the sole reason for the discovery of the anomalies then these anomalies
    2 For a risk based explanation of momentum, see Johnson (2002).
    3
    should dissipate upon their discovery. However, some anomalies have persisted long after
    their initial discovery. For instance, the PEAD was first documented by Ball and Brown in
    1968 and price momentum was first documented by Jegadeesh and Titman in 1993, but Fama
    (1998) finds PEAD and momentum to be the two robust anomalies and Fama and French
    (2008) find the anomalous returns associated with momentum to be pervasive.
    2. The predictability results because of the procedure for adjustment for risk in our asset pricing
    models, which may be incomplete or even incorrect. If the anomalies arise from imperfect
    risk controls we should expect intertemporal stability in the predictive power of firm
    characteristics.
    3. The predictability is a result of some unkown process (possibly involving psychological
    biases) that causes over- or under-reaction or otherwise impedes the adjustment of prices to
    new information. If this is the source of the anomalies, then increased arbitrage activity
    should eliminate the predictability. Given the steep declines in trading costs and the resulting
    increase in arbitrage activity, we expect the characteristics-based predictability to have
    diminished in recent years. Further, the diminution of predictability should be the strongest
    for the most liquid stocks, which should have higher levels of arbitrage, stimulated by lower
    trading costs. 3 An ancillary hypothesis emanates from the observation that certain financial
    institutions that have recently proliferated, such as hedge funds, are active short-sellers of
    stocks, unlike traditional institutions such as mutual funds. We expect that with an increase
    in hedge fund activity, abnormal returns to strategies that call for shorting should have
    declined in recent years.
    Our investigation reveals that cross-sectional predictability due to the anomalies has generally
    decreased in recent years. This decline has been more dramatic for liquid stocks. The decrease
    in profitability of momentum strategies is particularly noteworthy—these strategies show no
    significance for liquid stocks in recent years. Many other cross-sectional predictors such as
    share turnover,
    4
    dispersion of analyst opinion, PEAD and accounting accruals are not
    3 Chordia, Sarkar, and Subrahmanyam (2009) document that bid-ask spreads of larger, more liquid stocks
    experience a much steeper decrease as a consequence of decimalization than those of smaller, less liquid stocks. See
    also Ball and Chordia (2000).
    4 See Datar, Naik, and Radcliffe (1998), and Amihud and Mendelson (1986), for exposition of turnover and
    illiquidity as return predictors, respectively.
    4
    consistently significant in later years, and lose significance for liquid stocks. The magnitudes of
    the regression coefficients for most predictors also decline steeply, indicating sharply diminished
    economic significance in recent years. We also find that momentum strategies that call for
    shorting losers have shown a particular decline in statistical and economic significance in recent
    years. This evidence is consistent with the notions that increased liquidity has increased market
    efficiency and that institutions, such as hedge funds, that actively short-sell, contribute to
    efficiency creation.
    A recent study by Fama and French (2008) explores various cross-sectional return predictors and
    shows that the most robust anomalies are those associated with momentum and accruals.
    However, unlike our paper, their study does not focus on trends in predictability, nor on the
    relation between predictability and liquidity. Korajczyk, and Sadka (2004) document the
    relation between momentum and trading costs, but unlike us, they also do not look at
    predictability trends; further, we consider a comprehensive set of cross-sectional predictors, as
    opposed to single anomalies like momentum.
    This paper is related to a recent strand of literature that suggests that liquidity facilitates
    efficiency. 5 Our empirical results shed light on the key issue of whether decreases in trading
    costs have diminished the anomalies-based cross-section return predictability. The results are
    consistent with the economic notion that technologies and policies that reduce trading frictions
    will increase market efficiency by facilitating the movement of arbitrage capital. The results also
    suggest that since the anomalies are dynamically unstable, they may indeed represent market
    inefficiencies caused, for instance, by investor biases, since it would be difficult to argue that the
    nature of risk can change so fundamentally as to reduce the statistical and economic significance
    of virtually all the anomalies in recent years. In other words, if the anomalies are to be explained
    in the context of risk, then these explanations have to account for the decline in the anomaly
    related profits in recent years, in liquid stocks and in strategies that require short selling, which is
    a daunting challenge. Finally, the results have important implications for finance education and
    scholarship, because we believe they influence our priors on whether it is actually possible to
    5 See, for instance, Chordia, Roll and Subrahmanyam (2008) and Roll, Schwartz and Subrahmanyam (2007).
    5
    earn abnormal profits on anomalies documented by academics in the current low trading cost
    regime.
    This paper is organized as follows. The next section describes our methodology. Section II
    describes the data. Section III presents the regression results, and Section IV concludes.
    I. Methodology
    Our cross-sectional regressions follow the methodology of Brennan, Chordia, and
    Subrahmanyam (1998) (henceforth BCS) and Avramov and Chordia (2006). BCS test factor
    models by regressing individual firm risk-adjusted returns on firm-level attributes such as size,
    book-to-market, turnover and past returns. Under the null of exact pricing, such attributes should
    be statistically and economically insignificant in the cross-section. This approach avoids the
    data-snooping biases that are inherent in portfolio-based approaches (see Lo and MacKinlay
    (1990)). Moreover, the use of individual stocks as test assets is robust to the sensitivity of asset-
    pricing tests to the portfolio grouping procedure. We do, however, present the portfolio results
    as well.
    We first obtain the risk-adjusted returns, R jt * as follows:
    ?
    ?
    ? ?
    ? ? ?
    K
    k
    jk t jkt Ft jt jt
    F X R R R
    1
    1 1
    *
    ) ( ? , (1)
    where β jkt-1 is the conditional beta estimated for each stock by a first-pass time-series regression
    over the entire sample period. 6 X represents the conditioning variables, size and book-to-market
    ratio. The use of firm level attributes as conditioning variables is motivated by Gomes, Kogan
    and Zhang (2003) who develop a general equilibrium model in which firm level size and book-
    to-market ratio are correlated with the factor loadings. The Fama-French (1993) factors are used
    to adjust for risk. The risk-adjusted returns are then regressed on the equity characteristics: 
    ?
    ?
    ?
    ? ? ?
    M
    m
    jt mjt mt t jt
    e Z c c R
    1
    2 0
    *
    , (2)
    6 See Fama and French (1992) and Avramov and Chordia (2006) who argue that using the entire time series to
    estimate the factor loadings gives the same results as using rolling regressions.
    6
    where
    2 mjt
    Z
    ?
    is the value of characteristic  for security j at time t-2, with  M being the total
    number of characteristics. 7 Our procedure ensures unbiased estimates of the coefficients, c mt ,
    without the need to form portfolios, because the errors in estimation of the factor loadings are
    included in the dependent variable. The well known Fama and MacBeth (1973) estimators are
    the time-series averages of the regression coefficients,
    t c . We examine how these coefficients
    have changed over time.
    Based on well-known determinants of expected returns documented in Fama and French (1992),
    Jegadeesh and Titman (1993), and Brennan, Chordia, and Subrahmanyam (1998), the firm
    characteristics included in the cross-sectional regressions are the following:
    1) SIZE: measured as the natural logarithm of the market value of the firm’s equity in month t-2,
    2) BM: the ratio of the book value of the firm’s equity to its market value of equity, where the
    book value is calculated as in Fama and French (1992),
    3) TURN: the logarithm of the firm’s share turnover, measured as the trading volume divided
    by the total number of shares outstanding in month t-2,
    4) RET26: the cumulative return on the stock over the five months ending at the beginning of
    the previous month,
    5) RET712: the cumulative return over the 6 months ending 6 months previously,
    6) ILLIQ: The Amihud measure of illiquidity in month t-2. The Amihud (2002) illiquidity
    measure is the average daily price impact of order flow and is computed as the absolute price
    change per dollar of daily trading volume:
    ?
    ?
    ?
    it
    D
    d
    itd
    itd
    it
    it
    DVOL
    R
    D
    IlliQ
    1
    6
    10 *
    | | 1
    , where R itd is the
    return for stock i, on day d of month t, DVOL itd is the dollar trading volume of stock i, on
    day d of month t, and D it represents the number of trading days for stock i in month t. 8
    7) PRC: the price at the end of month t-2. 9
    7 The subscript t-2 on the characteristics indicates that we lag them by at two months in order to avoid biases
    because of bid-ask effects and thin trading. See BCS.
    8 While there are other measures of liquidity, the Amihud measure has the virtue of requiring only CRSP data for
    estimation, as opposed to voluminous transactions data that are only available since 1983. This measure also has
    been shown to have strong pricing effects in Amihud (2002).
    9 Miller and Scholes (1982) find that low priced stocks earn higher expected returns.
    7
    We also consider the following augmentation of the preceding characteristics. These
    characteristics are all related to information produced either by way of accounting statements or
    analyst forecasts. Since these additional characteristics cause a reduction in sample size, we use
    them in addition to the previous ones within a separate regression analysis:
    8) DISP: analyst forecast dispersion, computed as the standard deviation of the earnings-per-
    share, EPS, forecasts for the next fiscal year divided by the absolute value of the mean EPS
    forecast. This variable captures the dispersion effect of Diether, Malloy, and Scherbina
    (2002). 10
    9) SUE: the standardized unexpected earnings, computed as the most recently announced
    quarterly earnings less the earnings four quarters ago, standardized by its standard deviation
    estimated over the prior eight quarters. This is used to proxy for the earnings surprise, viz.
    Ball and Brown (1968).
    10) ACC: accounting accruals, as measured in Sloan (1996).
    In order to examine the cross-sectional variation across liquid and illiquid stocks, we also split
    the sample by the Amihud (2002) measure of illiquidity. This allows us to ask whether the
    significance of the coefficients on the characteristics is attenuated for the more liquid stocks.
    Further, we also test whether, with the advent of increasing shorting activity by hedge funds, the
    returns to shorting strategies have declined in recent years. We do this by using a dummy
    variable to flag the decile of stocks to be shorted. For instance, in the case of the momentum
    anomaly, the loser decile is flagged.
    II. Data
    The base sample includes common stocks listed on the NYSE and American Stock Exchange
    over the period January 1976 through December 2009. To be included in the monthly analysis, a
    stock has to satisfy the following criteria: (i) its return in the current month and over at least the
    10 The idea here is that short-sale constraints bind and therefore high disagreement simply reflects negative
    sentiment that is not yet in the current stock price (this general notion is usually credited to Miller, 1977).
    8
    past twelve months has to be available from CRSP, (ii) sufficient data have to be available to
    calculate market capitalization and turnover, and (iii) adequate data have to be available on the
    Compustat tapes to calculate the book-to-market ratio as of December of the previous year. In
    order to avoid extremely illiquid stocks, we eliminate stocks with month-end prices less than one
    dollar.
    The following securities are not included in the sample since their trading characteristics might
    differ from ordinary equities: ADRs, shares of beneficial interest, units, companies incorporated
    outside the U.S., Americus Trust components, closed-end funds, preferred stocks and REITs.
    We conduct the analysis for the full sample, as well as two subperiods covering 1976 to 1992,
    and, in turn, 1993 to 2009, to analyze how the cross-section of expected stock returns has
    changed in recent years. Merton (1980) has argued that we need a long time series to estimate
    first moments while estimation errors can decrease substantially when estimating second
    moments using data sampled at high frequencies. If we do not find significant coefficients in our
    regression analysis over the two subperiods it could be argued that this occurs because of
    insufficient time series data. However, we note that we have split the sample in half and we do
    find economically and statistically significant coefficients for the first subperiod but often not for
    the second subperiod. Moreover, as we shall show, the standard errors have not changed
    dramatically across the two subperiods, but the coefficient estimates have indeed declined in the
    second subperiod.
    While our base sample consists of NYSE/AMEX (henceforth, NYAM) stocks, we also consider
    Nasdaq stocks. We consider these issues separately from the NYAM sample because of the
    well-known problems associated with measuring Nasdaq turnover and the tendency for it to be
    overstated (e.g., Atkins and Dyl, 1997). The Nasdaq sample starts from 1983, since Nasdaq
    turnover is not available prior to this year. The two subperiods for Nasdaq stocks therefore
    span 1983 to 1992 and 1993 to 2009. While this implies that the first subperiod for Nasdaq
    stocks spans only ten years, we keep the breakpoint the same for NYAM and Nasdaq, because
    this keeps the time-span of the second subsample (where we expect predictability to substantially
    decrease owing to lower arbitrage costs) the same across the two groups.
    9
    Table 1 provides the summary statistics for the characteristics of the full sample as well as that of
    the two subperiods, namely, 1976-1992 and 1993-2009. Note that firm size has increased from
    the first subperiod to the second with the median firm size increasing from $0.12 billion to $0.26
    billion. However, this could be a manifestation of the fact that the market capitalizations have
    not been adjusted for inflation. The book-to-market ratio has declined over time and this decline
    is consistent with the increase in firm size. There has been an increase in turnover with the
    median (mean) turnover increasing from 3.33% (4.67%) to 5.33% (11.73%) for NYAM stocks.
    Illiquidity has declined for NYAM as well as Nasdaq stocks. While the turnover of Nasdaq
    stocks is higher, they are more illiquid than NYAM stocks. Share prices have not changed
    substantially over time.
    As mentioned earlier, we also include the characteristics related to information production,
    namely, DISP, SUE, and ACC in some of our regressions. However, these require data on
    accounting variables as well as analyst following (DISP requires at least two analysts following
    the stock). The requirement that data be available on these variables causes a considerable drop
    in sample size, so that we perform a separate analysis for this subsample. The summary statistics
    for this sample are available upon request from the authors.
    III. Results
    A. Characteristic Adjusted Returns and Fama-French Intercepts
    In Table 2, we present the characteristic-adjusted returns for the long and the short decile
    portfolios. The characteristic-adjusted returns are computed as in Fama and French (2008).
    Specifically, we sort stocks into 25 value-weighted portfolios based on size and BM, using
    NYSE breakpoints for market capitalization. We then subtract the return of the portfolio to
    which a stock belongs from its own return. If the adjustment for size and BM adequately
    controls for risk, then, under the null, the returns in Table 2 should all be zero. However, given
    that there are anomaly related profits, the decile portfolio returns in Table 2 are unlikely to be
    zero. We present the equal- and value-weighted average adjusted return of the long and the short
    portfolio for each trading strategy (momentum, value, size and turnover) as well as the long-short
    10
    hedge portfolio returns. We also present the Fama-French alphas for the hedge portfolios. Once
    again, stocks are sorted each month into decile portfolios based on the characteristic of interest.
    Then the return on the portfolio that is long the tenth decile and short the first decile is regressed
    on the three Fama and French (1993) factors. The alphas and the associated t-statistics are
    presented in the last two rows of each panel of Table 2.
    On the basis of the notion that liquidity facilitates arbitrage, the cross-section of expected stock
    returns is likely to show greater evidence of efficiency in liquid stocks. Therefore we present the
    characteristic adjusted returns as well as the Fama-French alphas separately for stocks with high
    and low liquidity. We do this by categorizing stocks each month into two groups, one whose
    Amihud illiquidity measure in that month is greater than its cross-sectional median, and the other
    whose illiquidity is lower than the cross-sectional median. The characteristic-adjusted returns,
    Fama-French alphas and t-statistics are presented in Table 2 (Panels A through D for both
    NYAM and Nasdaq stocks, as well as value- and equally-weighted portfolios). Thus, in Table
    2, we want to make two main comparisons: (i) across the two subperiods with the alternative
    hypothesis being that the characteristic based trading strategies yield lower returns in the second
    subperiod, and (ii) across the liquid and illiquid stocks with the alternative hypothesis being that
    the characteristic based trading strategies yield lower returns for the liquid stocks.
    Panel A of Table 2 presents the equally weighted results for NYAM stocks. We use two
    measures of momentum: RET26, which denotes returns over months t-6 through t-2 (short-term
    momentum) and RET712, which denotes returns over months t-12 through t-7 (long-term
    momentum). Consider the overall returns first. Both the characteristic-adjusted returns as well
    as the Fama-French alphas show that the momentum payoffs (both short-term and long-term) are
    lower in the second subperiod than in the first. For instance, the characteristic-adjusted long-
    short payoff using RET26 as the conditioning variable yields 1.4% (1.0%) per month in the first
    (second) subperiod. With RET712 as the conditioning variable the corresponding numbers are
    1.44% and 0.72% per month. This is qualitatively true also for the size effect which yields a
    statistically significant 0.59% in the first period and a statistically insignificant 0.28% per month
    in the second period. The impact of turnover is similar with a statistically significant 0.74% per
    11
    month in the first period and an insignificant 0.06% in the second. We obtain similar results,
    especially for the momentum variables, in Panel B with value-weighted characteristic based
    trading strategies. Later, we will present formal tests for the decline in anomaly returns across
    the two subperiods but the initial evidence, thus far for NYAM stocks, is consistent with the
    decline in payoffs from anomalies in recent years.
    Next we turn to the comparison between liquid and illiquid stocks. We use the Amihud
    illiquidity measure to form quintile portfolios sorted on illiquidity. ILLIQ=1 (ILLIQ=5) is the
    low (high) illiquidity portfolio. Consider the short-term momentum returns in Panel A. The
    momentum payoffs measured using either the characteristic adjusted returns or the Fama-French
    alphas for the low illiquidity portfolios are insignificant while those for the high illiquidity
    portfolios are highly significant. For instance, the characteristic adjusted return for the entire
    sample is 0.32% (1.66%) per month for the low (high) illiquidity portfolio. When conditioning
    on RET712 the corresponding numbers are 0.82% (1.38%) for the low (high) illiquidity
    portfolios. We see similar results with the size effect. None of the characteristic adjusted returns
    or the Fama-French alphas are statistically or economically significant for the low illiquidity
    portfolios while all are statistically and economically significant for the high illiquidity
    portfolios. Finally, the point estimates of the characteristic adjusted returns and the Fama-French
    alphas for the turnover-based portfolios are higher for the high illiquidity portfolios. The value-
    weighted results in Panel B present a similar picture. Thus, the results suggest that the anomaly
    profits for NYAM stocks are more pronounced in the high illiquidity portfolios.
    The results are somewhat more mixed for Nasdaq stocks in Panels C and D. In general, the
    anomaly profits are higher in the first subperiod than in the second. The one exception is the size
    anomaly for the high illiquidity stocks. Also, in general, the anomaly profits are higher for the
    more illiquid stocks, the only exception being the long-term momentum profits during the
    sample period 1983-2009. Overall the results are consistent with the notion that the anomaly
    profits have declined in recent years and are lower for the more liquid stocks.
    12
    B. Cross-Sectional Regressions
    We now turn to regression analysis to examine the extent to which the evidence from the long-
    short portfolio returns across the extreme deciles is evident in the cross-section. Panel A (B) of
    Table 3 presents the regression results for NYAM (Nasdaq) stocks for the full period as well as
    the two subperiods (using the method described in Section I). For the full sample, the
    coefficients on RET26 and RET712 at 0.38 and 0.52, respectively, are statistically significant at
    the 5% level, pointing to a strong momentum effect. The coefficient on the book-to-market ratio
    is 0.14 and is significant at the 1% level pointing to the value effect. The coefficient on turnover
    is negative suggesting that stocks with higher trading volumes earn lower returns, which is
    consistent with earlier work such as Brennan, Chordia and Subrahmanyam (1998) and Datar,
    Naik, and Radcliffe (1998). The results suggest that higher priced stocks have higher returns in
    our sample. These effects are all preserved in the first subsample from 1976-1992. In fact, the
    coefficients on the lagged returns are larger than that for the full sample.
    In the second subperiod, however, each of the momentum coefficients decline in magnitude, and
    the coefficients of RET26 as well as that of RET712 are no longer significant. We also note that
    the coefficients on firm size and on turnover are insignificant in recent years. Baker and Stein
    (2004) propose that the negative relation between turnover and future returns is due to investor
    sentiment. Investor optimism leads to higher trading volumes and, because the optimism is
    reversed out, also results in low returns during future periods. If this is the case, then the
    reduction in significance of turnover is consistent with either decreased effects of sentiment on
    volume or increased arbitrage activity taking the contrarian side of this sentiment in recent years.
    We also note that the Amihud (2002) measure of illiquidity is priced in both subperiods,
    consistent with the notion that this measure captures a genuine economic effect; namely, a
    liquidity premium. Further, the value effect is preserved in the second subperiod. Given that the
    value effect has been so well-disseminated since the work of Fama and French (1992), the fact
    13
    that it persists in the second subperiod with low trading costs is consistent with the view that it at
    least partially represents compensation for risk that is not susceptible to arbitrage forces. 11
    For Nasdaq stocks, Panel B of Table 3 indicates that for the full sample there is a strong
    momentum effect. The momentum coefficients are significantly smaller in the second subperiod,
    though the short-term momentum variable remains significant in this period. Interestingly,
    illiquidity and the book-to-market ratio are priced more strongly in the second subperiod. 12
    However, the significance of turnover and size disappears in later years.
    There is a concern that the lack of significance in the recent years is due to lack of power.
    However, we have two responses. First, we have divided the sample equally and we do find
    significant coefficients in the earlier years. Second, the standard errors are not that different
    across the two sub-periods. For instance, in Panel A for NYAM stocks, the standard error for the
    coefficient estimate of RET26 is 0.0023 (0.0029) in the first (second) subperiod; for RET712 the
    standard errors are 0.0016 (0.0019) in the first (second) subperiod; for turnover the standard
    errors are 0.00046 (0.00054) in the first (second) subperiod; for book-to-market and price the
    standard errors are actually lower in the second subperiod. Overall, the standard errors are not
    much different in the two subperiods but the coefficient estimates do decline significantly in the
    second subperiod compared to the first.
    In sum, the most noteworthy results are the reduction in the size and significance of the
    momentum coefficients and the disappearance of the turnover effect for both NYAM and Nasdaq
    stocks. We fit a simple linear trend to the monthly Fama-Macbeth coefficient estimates for
    momentum and turnover. While the results are not reported for brevity, the trend coefficients for
    11 Given the debate over whether the Fama and French (1993) factors represent risk or mispricing (Daniel and
    Titman, 1997), it is interesting to consider how the returns to the HML and SMB portfolios of Fama and French
    (1993) factors change across the two subperiods. If the returns to these factors diminish over time, it could be
    argued that they represent inefficiencies that have been arbitraged away in recent years. In fact we find that monthly
    SMB returns decrease slightly from 0.35% to 0.21%, while HML returns decrease from 0.41% to 0.37% across the
    two subperiods. However, neither of these decreases is statistically significant, so that these factor returns do not
    exhibit the same pattern as the coefficients on the cross-sectional characteristics. This is consistent with the notion
    that the Fama and French (1993) factor returns represent stable rewards to risk.
    12 The coefficient magnitudes for these variables also increase across the subperiods. We revisit this issue in the
    next subsection.
    14
    the momentum variables are negative and strongly significant, whereas the one for turnover is
    positive and significant, and these patterns obtain for NYAM as well as Nasdaq stocks. Since
    the original momentum and turnover effects enter with positive and negative coefficients,
    respectively, this is clear indication that the effects have become less material over time. The
    results are consistent with the steep decline in trading costs over recent years, which should have
    led to greater arbitrage activity and hence declines in predictability.
    C. Liquidity and the Cross-Sectional Coefficients
    To further explore the role of liquidity in cross-sectional return predictability, we now split the
    sample into stocks with high and low liquidity. We do this by dividing stocks each month into
    two groups, which represent above-median and below-median values of the Amihud illiquidity
    measure, for each of the NYAM and Nasdaq subsamples.
    13 We then run cross-sectional
    regressions separately for these two groups. Table 4 presents the results.
    Consider first the NYAM subsample in Panel A. The coefficients on past returns are lower in
    each and every case for the more liquid stocks as compared to the more illiquid stocks. This is
    true for the entire sample and for the two subperiods. In fact, the short-term momentum effect is
    not discernible for the liquid sample while the coefficient estimate for RET26 is statistically and
    economically significant in the earlier years for the illiquid stocks. The coefficient estimates for
    firm size and for the Amihud illiquidity measure are not significant for the liquid stocks but both
    the size effect and the illiquidity premium are discernible for the illiquid stocks. The coefficient
    estimates for the book-to-market ratio are also always higher for the illiquid stocks. The value
    effect is also not significant at the 5% level in the two subperiods for the liquid stocks but it is
    significant in the recent years for the illiquid stocks. The impact of turnover is similar for the
    liquid and illiquid stocks.
    13 Chordia, Sarkar,and Subrahmanyam (2009) show that larger, more liquid stocks have experienced a much steeper
    decline in spreads in recent years than smaller, less liquid ones. Ball and Chordia (2001) suggest that this is
    primarily because the tick size was more binding for more liquid companies, so that decimalization had a more
    dramatic impact on their spreads. Similarly, in our second subperiod relative to the first, the average Amihud
    measure declines by 63% (from 3.13 to 1.15) for the illiquid sample, and by 92% (from 0.035 to 0.0027) for the
    liquid sample. Thus, by stratifying our sample into liquid and illiquid subsamples in each subperiod, we not only are
    able to compare the relative price efficiency of the two subsamples within the same subperiods, but also consider
    whether the sector that experienced the greater increase in liquidity (i.e., the liquid stock sector) has become more
    efficient.
    15
    Turning now to Nasdaq stocks in Panel B, consider the illiquid sample first. With regard to the
    overall sample period, all momentum variables are significant, and there are size, value, liquidity
    and turnover effects. In the second subperiod, the momentum variables are significant and the
    size, price, liquidity, and turnover effects persist. For liquid Nasdaq stocks, the story is
    different. For the full sample during the first subperiod, there are momentum, value, and
    turnover effects but all these disappear in the second subperiod. This reduction in significance is
    not just due to an increase in the standard errors since most coefficients reverse sign and/or
    decline in magnitudes across the two sample periods. For example, the coefficients on short-
    term momentum and turnover both decline by about 80% (in absolute terms), and that on long-
    term momentum reverses sign and becomes insignificant. Thus, there is clear evidence that
    liquid Nasdaq stocks exhibit less cross-sectional predictability than illiquid ones, especially in
    recent years.
    Overall, two findings are worth noting. First, the stronger pricing of liquidity and book-to-
    market for Nasdaq stocks in later years (documented in Table 3) is prevalent only for illiquid
    stocks. Second, across the NYAM and Nasdaq samples, the findings are consistent with the
    notion that liquid stocks are more efficiently priced in the cross-section, and this phenomenon is
    particularly apparent in later years, as evidenced by the material reduction in the statistical and
    economic significance of momentum in the liquid NYAM as well as Nasdaq stocks.
    Existing explanations for price momentum fall into two general categories: time-varying
    expected returns [e.g., Conrad and Kaul (1988), Johnson (2002)], and behavioral theories [e.g.,
    Hong and Stein (1999), Barberis, Shleifer, and Vishny (1998), Daniel, Hirshleifer, and
    Subrahmanyam (1998)]. That momentum coefficients decrease in magnitude and significance
    in recent years appears to be inconsistent with the momentum phenomenon representing reward
    for risk because it seems unlikely that the inherent nature of the time variation in expected
    returns could have shifted so dramatically in the second subperiod so as to cause the remarkably
    steep decline in the coefficients in this period. If the momentum phenomenon is caused by
    investor biases that lead to underreaction of prices to information, then increased arbitrage
    16
    activity arising from decreased trading costs leads to improvements in market efficiency that
    mitigate momentum in recent years. Our results demonstrate that inefficient pricing may be
    inherently unstable, and thus can potentially be mitigated by moves that enhance liquidity, such
    as technological improvements in trading processes, and removal of artificial restrictions on
    price moves such as the minimum tick size.
    D. Information-Based Cross-Sectional Characteristics
    We now add three additional cross-sectional predictors from earlier literature: namely, dispersion
    of analyst opinion (DISP), standardized unexpected earnings (SUE), and accruals (ACC) to the
    list of predictive variables. As mentioned in the previous section, all of these variables represent
    information produced either by way of the firm through accounting statements, or by way of
    investment analysis. The addition of these variables causes an inevitable decrease in sample size
    owing to the reliance on accounting data and analyst following data through the I/B/E/S and
    Compustat databases. This is the reason why we present the results for the augmented sample
    separately from the main analysis.
    D.1 Portfolio Analysis
    We present the characteristic-adjusted returns and the Fama and French (1993) alphas on the
    long-short decile portfolios formed on the augmented set of cross-sectional characteristics,
    namely, DISP, SUE, and accruals. Stocks are sorted each month into deciles based on the
    characteristics of interest, and the resulting returns, alphas and t-statistics are presented in Table
    5, in the same format as Table 2.
    For the full NYAM sample, the equal and value-weighted characteristic-adjusted hedge portfolio
    returns for DISP (documented in Panels A and B) are significant at the 5% level only for the
    illiquid stocks. The Fama-French alphas are significant for both the illiquid and as well as the
    liquid stocks. In the case of the liquid stocks, the characteristic-adjusted hedge portfolio returns
    and the Fama-French alphas are both statistically insignificant in recent years. This pattern holds
    for PEAD as well. For instance, the value-weighted characteristic adjusted hedge portfolio
    return conditioned on earnings surprise is 0.42% (0.01%) per month in the first (second)
    17
    subperiod for the liquid stocks but it is 0.93% (1.50%) in the first (second) subperiod for the
    illiquid stocks. The accruals anomaly is significant only for the illiquid stocks and then during
    the first subperiod only.
    In the case of Nasdaq stocks the equally-weighted (Panel C) hedge portfolio returns (both
    characteristic-adjusted as well as the Fama-French alphas) are all significant for portfolios
    conditioned on analyst forecast dispersion, earnings surprise and accruals and, in general, the
    returns are higher in the first subperiod than in the second. When conditioning on liquidity, for
    the overall sample, the anomaly payoffs are higher for the illiquid stocks except for the accruals
    anomaly where it seems to be higher for the liquid stocks. In the case of accruals, the overall
    Fama-French alphas amount to -0.98% (-0.28%) per month for the liquid (illiquid) stocks.
    Surprisingly, for PEAD the payoffs are higher in the second subperiod for the illiquid stocks.
    These patterns are essentially maintained for the value-weighted Nasdaq sample in Panel D.
    Taken in totality, these results support the general notion that cross-sectional predictability based
    on analyst forecast dispersion, earnings surprises, and accounting accruals, has decreased in
    recent years. Further, we observe that these effects are weaker in liquid stocks (the exception
    being the accruals anomaly in the Nasdaq sample) in recent years. These findings are consistent
    with the conclusions from the earlier section that the cross-sectional predictability of stock
    returns has decreased materially in recent years, particularly for liquid stocks.
    D.2 Regressions
    Table 6 presents the regression results (analogous to those in Table 3) for the sample of stocks on
    which data are available for the expanded set of predictors. Keep in mind that this sample
    consists of the larger stocks because we require each stock to be followed by at least two analysts
    so as to be able to compute their forecast dispersion. In addition to the full sample analysis, we
    present results separately for the two subperiods, and as in Table 4, we stratify the sample by
    illiquid and liquid stocks in Table 8.
    18
    For NYAM stocks (Panel A of Table 6) over the full period, we see that the momentum effect is
    present but the value, turnover, liquidity, and the size effects are not evident in this subsample
    that includes the expanded list of predictors. As in earlier literature, for the full sample period,
    stocks with high analyst forecast dispersion and those with a high level of accruals earn lower
    returns and those with high earnings surprise, as measured by SUE, earn high returns. The first
    subperiod (1976-1992) preserves these features of the full sample. In the first subperiod we also
    see the impact of turnover on returns, stocks with higher turnover earn lower expected returns in
    the cross-section. In the second subperiod, none of the cross-sectional effects are apparent. It is
    not just a loss of statistical significance, as the coefficient magnitudes on SUE, accruals, and
    DISP all decline steeply in magnitude (by 72%, 77%, and 85%, respectively) in recent years.
    This is clear evidence of reduced cross-sectional return predictability in recent years.
    In the case of Nasdaq stocks (Panel B), the dispersion effect is not discernible in either of the
    subperiods. The coefficient estimate on SUE is 0.08 (t-stat=2.22) in the first period but it is
    0.019 (t-stat=1.17) in the second subperiod. Thus, PEAD seems to have dissipated in recent
    years for both the NYAM as well as Nasdaq stocks. The accruals anomaly, while significant in
    both subperiods seems to have declined considerably in recent years as evidenced by the decline
    (in absolute terms) in the coefficient estimates from -4.32 to -1.82.
    To further investigate the patterns in the cross-sectional coefficients over time, in Table 7 we
    present the slope coefficients and associated t-statistics from fitting a linear time trend to the
    coefficient estimates for momentum, DISP, SUE, and ACC from the monthly cross-sectional
    regressions. For NYAM stocks, all trend coefficients except the one for the shorter-term
    momentum variable (RET26) show evidence of a decline at the 5% level. 14 For the Nasdaq
    sample, the coefficient estimates for both the momentum variables show a decline over time at
    the 5% level and the coefficient estimates for ACC and SUE decline significantly at the 10%
    14 Note that the coefficients on DISP and ACC are negative for the full sample, so that a positive trend coefficient
    implies a reduction in their magnitudes.
    19
    level. Thus, overall, the results support the notion that cross-sectional predictability based on
    momentum, DISP, SUE, and accruals has declined in recent years. 15
    Table 8 splits the augmented sample into high and low liquidity groups. Table 4 already presents
    the results for liquid and illiquid stocks for the size, book-to-market, turnover, price, illiquidity
    and momentum anomalies. Thus, we will focus the discussion on the dispersion, PEAD and the
    accruals anomaly. Consider the NYAM stocks in Panel A of Table 8. The accruals anomaly is
    profitable for both the liquid and illiquid stocks in the first subperiod but not in the second.
    PEAD is not profitable for the liquid stocks but it is profitable for the illiquid stocks but only in
    the overall sample and in the first subperiod only. Similarly, the coefficient on analyst forecast
    dispersion is significant for illiquid stocks in the first subperiod only, while for the liquid stocks
    it is not significant at the 5% level in either of the subperiods. The results for Nasdaq stocks in
    Panel B are more mixed. The coefficient estimate of dispersion is significant for liquid stocks in
    the first subperiod but it has the wrong sign. It seems that over the period 1983-1992, the liquid
    Nasdaq stocks with high analyst forecast dispersion earn higher returns. PEAD is profitable for
    the liquid Nasdaq stocks in the first subperiod. The accruals anomaly is profitable across the
    board for the liquid stocks but only in the first subperiod for the illiquid stocks.
    Overall, there is more cross-sectional predictability in the illiquid NYAM stocks but it is
    confined to the first subperiod. In recent years there is no predictability from forecast dispersion,
    earnings surprises or accruals for the liquid or illiquid NYAM stocks. These observations are
    consistent with the general notion that liquidity promotes arbitrage activity and hence, pricing
    efficiency in the cross-section. Specifically, sharp increases in liquidity (e.g., Chordia, Roll, and
    Subrahmanyam, 2005) appear to have promoted arbitrage, thus causing an economic and
    statistical decline in the significance of these predictors in recent years.
    15 Instead of fitting a linear trend, we also perform a regression with an intercept plus a dummy for the period after
    July 2000. This dummy is intended to coincide with the imposition of Reg FD, which could mitigate price
    misreaction by reducing information asymmetry, and with decimalization (imposed January 2001), which reduced
    bid-ask spreads and made it easier to arbitrage. In the case of NYAM stocks, this dummy is positive and significant
    at the 5% level for accruals and negative and significant at the 10% level for long-term momentum, and insignificant
    in all other cases. In the case of Nasdaq stocks, the dummy is significant at the 10% level for accruals and long-term
    momentum, and at the 5% level for short-term momentum (with the signs being the same as that for NYAM stocks).
    This indicates that the post-FD and decimalization period has been accompanied by particularly reduced economic
    magnitudes of the momentum and accounting accrual effects.
    20
    E. Possible Effects of Hedge Funds
    Since hedge funds actively use short selling as a strategy, 16 the profitability of strategies that call
    for shorting should have declined in recent years with the rise of these institutions. We now
    analyze this observation in more depth. Recall that in Table 2, we presented the characteristic
    adjusted returns to the extreme decile portfolios for the various anomalies. Consider the
    equally-weighted returns for NYAM stocks in Panel A of Table 2. For the short-term
    momentum anomaly we see that the loser portfolio earns a characteristic-adjusted return of -
    0.86% (-0.44%) per month in the first (second) subperiod while the winner portfolio earns a
    return of 0.54% (0.56%) in the first (second) subperiod. Thus, the payoff from going short in the
    loser portfolio declines by about half while the payoff from the winner portfolio is practically the
    same across the two subperiods. A similar pattern obtains for the long-term momentum
    anomaly. The profits from the loser (winner) portfolio declines by 59% (39%). We see a similar
    pattern in Panel B of Table 2 for the value-weighted NYAM portfolios. We do not consider the
    size or the turnover anomaly because it should be easy to short the large stocks as well as stocks
    with high turnover. Turning to the equally-weighted Nasdaq stocks in Panel C of Table 2, we
    note a decline of 58% (4%) for the short-term momentum anomaly in the loser (winner) portfolio
    payoffs across the two subperiods. The corresponding decline in the long-term momentum
    anomaly for the loser (winner) portfolio is 65% (26%).
    Next we examine the payoffs to the analyst forecast dispersion, post-earnings announcement
    drift and the accruals anomalies. Panel A of Table 5 provides the equally-weighted payoffs to
    the extreme decile portfolios for NYAM stocks. For the dispersion anomaly, the payoff to the
    decile ten portfolio (the portfolio to be shorted) has declined by 78% as compared to 60% for the
    long portfolio. For the PEAD anomaly, the short (long) portfolio payoffs have decline by 63%
    (18%) across the two periods. The payoffs to the accruals anomaly has declined by similar
    amounts for the long and short portfolios although, in the case of Nasdaq stocks in Panel C of
    Table 5, the decline in payoffs to the short (long) portfolio is 77% (-23%).
    16 Stulz (2007) states that ―derivatives and short positions are critical in most hedge fund strategies and enable hedge
    funds to reduce mispricings more forcefully than mutual funds.‖
    21
    In general, the decline in the payoffs from going short in the loser portfolio is larger than the
    decline in the profits from going long the winner portfolio. This decline is consistent with the
    increased shorting activity of hedge funds. The results are weaker for the value-weighted
    portfolios in Panels B and D of Table 5, suggesting that it is the improvements in liquidity of the
    smaller stocks that have facilitated shorting by institutions such as hedge funds.
    We now turn to Fama-Macbeth regressions. We introduce a dummy variable for values of
    characteristics that would imply a short position. So in the case of momentum, we use a dummy
    variable for the decile of stocks with the lowest past returns. In the case of the book-to-market
    ratio we use a dummy variable for the decile of stocks with the lowest book-to-market ratio in
    the monthly cross-sectional regressions. Results are reported in Table 9.
    Consider first the NYAM stocks in Panel A. The coefficient on RET26 interacted with the
    dummy variable for the lowest decile returns is positive. With negative past returns in the lowest
    decile, a positive coefficient implies negative future returns. The main point is the decline in the
    coefficient estimate from 1.85 (t-statistic=3.65) in the first subperiod to 0.90 (t-statistic=1.74) in
    the second. Simlarly, the coefficient on RET712 interacted with the dummy variable has
    declined from 1.04 (t-statistic=2.35) to 0.42 (t-statistic=0.84) across the two subperiods. This
    decline is consistent with increased arbitrage activity leading to a decline in profits from shorting
    stocks with low past returns. The coefficient estimate of book-to-market interacted with the
    dummy variable for the lowest decile of book-to-market ratio is negative suggesting that low
    book-to-market stocks earn lower returns. 17 We see a decline in the absolute value of the
    coefficient estimate from -0.12 (t-statistic=-1.92) to -0.07 (t-statistic=-1.19) across the two
    subperiods suggesting once again that increased arbitrage activity had led to a decline in profits
    from shorting stocks with low book-to-market ratios.
    Panel B of Table 9 presents the results for the NYAM sample with the expanded set of
    characteristics (DISP, SUE, and ACC). The coefficient estimate of SUE interacted with the
    dummy variable for stocks in the lowest SUE decile is negative suggesting that stocks with low
    17 We have eliminated stocks with negative book values from the sample.
    22
    earnings surprise earn lower returns. Once again, the absolute decline in the coefficient estimate
    from -0.09 (t-statistic=-3.10) in the first subperiod to -0.06 (t-statistic=-2.18) is consistent with
    the decreased profitability from short positions in recent years. The coefficient estimate on
    analyst forecast dispersion interacted with a dummy variable indicating stocks in the highest
    dispersion decile is positive in the first subperiod. This is surprising because stocks with the
    highest dispersion, in general, earn lower returns, but this does not seem to be the case in the first
    subperiod. The coefficient estimate on accruals interacted with a dummy variables for high
    accruals is not significant.
    Panels C and D of Table 9 present results for Nasdaq stocks. We find that for the Nasdaq stocks,
    none of the interaction terms are statistically significant. In Panel C, the point estimates for the
    interaction terms do show a decline across the two subperiods, but we are unable to make any
    inferences due to the lack of significance.
    Overall, there is some evidence consistent with the notion that hedge fund short-selling activity
    has attenuated the momentum, value and earnings surprise effects, contributing to greater market
    efficiency.
    IV. Summary and Concluding Remarks
    We consider a comprehensive set of anomalies over a 34-year period, and find a sharp reduction
    in cross-sectional equity return predictability during recent years. Indeed, Fama-MacBeth (1973)
    regressions indicate that well known cross-sectional effects such as momentum, analyst
    dispersion, earnings drift, and accounting accruals, largely disappear, and the decline in
    statistical and economic significance of these predictors is sharper in more liquid stocks. Indeed,
    the sample of NYSE/AMEX stocks exhibits no evidence of any of these well-known anomalies
    in the latter half of our sample period.
    The general premise of our study is that the cross-sectional predictability of stock returns arises
    at least partly due to processes that cause over- or under-reaction (possibly due to investor
    biases) or otherwise impede the incorporation of information into prices. We conclude that such
    23
    forecastability has been decreased substantially in recent years as markets have become more
    liquid, thus facilitating arbitrage.
    One potential criticism of this study is that diminished statistical significance for the predictors in
    recent years arises due to a lack of statistical power. There are two counter-arguments to this
    line of criticism. First, many of the cross-sectional predictors are significant in the first
    subperiod but not in the second, and the second subperiod has identical (in the case of
    NYSE/AMEX stocks) or a higher (in the case of Nasdaq stocks) number of time-series
    observations. There is no a priori reason why there should be a power problem in one subperiod
    and not in the other. Furthermore, if statistical power was driving the lack of significance, we
    would expect to see it reflected in the standard errors of the estimated coefficients, but we find
    that the standard errors in most cases do not materially differ across the two subperiods while the
    regression coefficients decline substantially in the second subperiod relative to the first, so it is
    the decline in the economic significance of the predictors that drives the decrease in cross-
    sectional return predictability.
    We expect future research to be influenced by our results. For example, the decline in
    profitability of strategies based on momentum, accruals, earnings surprises, analyst forecast
    dispersion, and share turnover indicates that these cross-sectional effects are inherently unstable.
    They may have been arbitraged away in recent years. This lends support to assertions such as
    those by Fama (1998), which argue that modeling market inefficiencies may be of limited value
    since these phenomena may be arbitraged away as soon as agents become aware of them. 18 This
    observation, combined with our results, provides some guidance as to where future modeling
    efforts and regulatory attention should be focused. Our results suggest that it might be more
    fruitful to explore mechanisms that remove trading frictions and improve liquidity in markets.
    Also, the extent to which trading costs have diminished in other countries is an open question.
    18 Of course, there is the possibility that undiscovered anomalies exist. If so, our line of reasoning indicates that in
    the current regime of low transaction costs and thus strong arbitrage incentives, that new anomalies would last only
    for a fleeting period after being discovered by practitioners. This phenomenon, in turn, would cause difficulties in
    their detection by an empiricist for the very reason that they would be short-lived in nature. Therefore, there is
    reason to expect the cross-section of stock returns to continue to exhibit little, if any, evidence of predictability in
    future years.
    24
    Our analysis suggests that cross-sectional return predictability would diminish to a greater extent
    in countries that have experienced greater increases in liquidity. This hypothesis awaits rigorous
    testing in an international context.
    25
    References
    Amihud, Y., and H. Mendelson, 1986, Asset pricing and the bid-ask spread, Journal of Financial
    Economics 17, 223-249.
    Atkins, A., and E. Dyl, 1997, Market structure and reported trading volume: Nasdaq versus the
    NYSE, Journal of Financial Research 20, 291-304.
    Asness, C., T. Moskowitz, and L. Pedersen, 2009, Value and momentum everywhere, working
    paper, New York University.
    Barberis, N., A. Shleifer, and R. Vishny, 1998, A model of investor sentiment, Journal of
    Financial Economics 49, 307-343.
    Berk, J., 1995, A critique of size related anomalies, Review of Financial Studies 8, 275-286.
    Bernard, V., and J. Thomas, 1989, Post-earnings-announcement drift: Delayed price response or
    risk premium?, Journal of Accounting Research 27, 1-36.
    Black, F., M. Jensen, and M. Scholes, 1972, The capital asset pricing model: Some empirical
    tests, in M. C. Jensen, ed., Studies in the Theory of Capital Markets, pp. 79-121. (Praeger, New
    York).
    Boehme, R., B. Danielsen, and S. Sorescu, 2006, Short-sale constraints, differences of opinion,
    and overvaluation, Journal of Financial and Quantitative Analysis 41, 455-487.
    Brennan, M., T. Chordia, and A. Subrahmanyam, 1998, Alternative factor specifications,
    security characteristics and the cross-section of expected stock returns, Journal of Financial
    Economics 49, 345-373.
    26
    Chakravarty, S., V. Panchapagesan, and R. Wood, 2005, Did decimalization hurt institutional
    investors?, Journal of Financial Markets 8, 400-420.
    Chordia, T., R. Roll, and A. Subrahmanyam, 2001, Market liquidity and trading activity, Journal
    of Finance 56, 2, 501-530.
    Conrad, J., Kaul, G., 1998, An anatomy of trading strategies, Review of Financial Studies 11,
    489-519.
    Chordia, T., R. Roll, and A. Subrahmanyam, 2008, Liquidity and market efficiency, Journal of
    Financial Economics 87, 249-268.
    Chordia, T., A. Sarkar, and A. Subrahmanyam, 2009, Liquidity dynamics and cross-
    autocorrelations, forthcoming, Journal of Financial and Quantitative Analysis.
    Daniel, K., Hirshleifer, D., Subrahmanyam, A., 1998, Investor psychology and security market
    under-and overreactions, Journal of Finance 53, 1839-1885.
    Daniel, K. D., D. Hirshleifer, and A. Subrahmanyam, 2001, Overconfidence, arbitrage, and
    equilibrium asset pricing, Journal of Finance 56, 921-965.
    Daniel, K., and S. Titman, 1997, Evidence on the characteristics of cross-sectional variation in
    common stock returns, Journal of Finance 52, 1-33.
    Daniel, K., and S. Titman, 2006, Market reactions to tangible and intangible information,
    Journal of Finance 61, 1605-1643.
    Datar, V., N. Naik, and R. Radcliffe, 1998, Liquidity and stock returns: An alternative test,
    Journal of Financial Markets 1, 203-219.
    27
    Davis, J., E. Fama, and K. French, 2000, Characteristics, covariances, and average returns: 1929-
    1997, Journal of Finance 55, 389-406.
    Diether, K. B., C. J. Malloy, and A. Scherbina, 2002, Differences of opinion and the cross
    section of stock returns, Journal of Finance 57, 2113—2141.
    Fama, E., 1998, Market efficiency, long-term returns, and behavioral finance, Journal of
    Financial Economics, 49, 283-306.
    Fama, E., and K. French, 1992, The cross-section of expected stock returns, Journal of Finance
    47, 427-465.
    Fama, E., and K. French, 1993, Common risk factors in the returns on stocks and bonds, Journal
    of Financial Economics 33, 3-56.
    Fama, E., and K. French, 2008, Dissecting anomalies, Journal of Finance 63, 1653-1678.
    Fama, E., and J. MacBeth, 1973, Risk, return and equilibrium: Empirical tests, Journal of
    Political Economy 81, 607-636.
    French, K., 2008, The cost of active investing, Journal of Finance 63, 1537-1573.
    Grinblatt, M. and B. Han, 2005, Prospect theory, mental accounting, and momentum, Journal of
    Financial Economics 78, 311-339.
    Hendershott, T., C. Jones, and A. Menkveld, 2008, Does algorithmic trading improve liquidity?,
    working paper, Columbia University.
    Hirshleifer, D., and S. Teoh, 2003, Limited attention, information disclosure, and financial
    reporting, Journal of Accounting and Economics 36, 337-386.
    28
    Hong, H., Stein, J., 1999, A unified theory of underreaction, momentum trading, and
    overreaction in asset markets, Journal of Finance 54, 2143-2184.
    Jegadeesh, N., 1990, Evidence of predictable behavior in security returns, Journal of Finance 45,
    881-898.
    Jegadeesh, N., and S. Titman, 1993, Returns to buying winners and selling losers: Implications
    for stock market efficiency, Journal of Finance 48,65-92.
    Johnson, T., 2002, Rational momentum effects, Journal of Finance 57, 585-608.
    Johnson, T., 2004, Forecast dispersion and the cross section of expected returns, Journal of
    Finance 59, 1957-1978.
    Jones, C., 2002, A century of stock market liquidity and trading costs, working paper, Coluimbia
    University.
    Kim, D., and M. Kim, 2009, A multifactor explanation of post-earnings announcement drift,
    Journal of Financial and Quantitative Analysis 38, 383-398.
    Korajczyk, R., and R. Sadka, 2004, Are momentum profits robust to trading costs?, Journal of
    Finance 59, 1039-1082.
    Lesmond, D., M. Schill, and C. Zhou, 2004, The illusory nature of momentum profits, Journal of
    Financial Economics 71, 349-380.
    Lintner, J., 1965, Security prices, risk and maximal gains from diversification, Journal of
    Finance 20, 587-616.
    29
    Merton, R., 1980, On estimating the expected return on the market : An exploratory investigation,
    Journal of Financial Economics 8, 323-361.
    Miller, E., 1977, Risk, uncertainty and divergence of opinion, Journal of Finance 32, 1151-1168 .
    Miller, M., and M. Scholes, 1982, Dividends and taxes: some empirical evidence, Journal of
    Political Economy 90, 1118-1141.
    Mossin, J., 1966, Equilibrium in a capital asset market, Econometrica 34, 768-783.
    Rouwenhorst, K., 1999, Local return factors and turnover in emerging stock markets, Journal of
    Finance 54, 1439-1464.
    Sharpe, W., 1964, Capital asset prices: A theory of market equilibrium under conditions of risk,
    Journal of Finance 19, 425-442.
    Sloan, R., 1996, Do Stock Prices Fully Reflect Information in Accruals and Cash Flows about
    Future Earnings? Accounting Review 71, 289-315.
    Stulz, R., 2007, Hedge funds: Past, present, and future, Journal of Economic Perspectives 21,
    175-194.
    30
    Table 1: Summary Statistics
    This table presents the time-series averages of the cross-sectional means, medians, and standard deviations for an
    average of 3653 NYSE-AMEX and NASDAQ stocks. Size represents the market capitalization in billions of dollars.
    Turnover is the monthly share trading volume divided by shares outstanding in percent. The book-to-market ratio
    provides summary statistics for this variable after book-to-market values greater than the 0.995 fractile or less than
    the 0.005 fractile are set to equal the 0.995 and 0.005 fractile values, respectively. RET26 and RET712 are the
    cumulative returns over the second through sixth and seventh through twelfth months prior to the current month,
    respectively. Illiquidity represents Amihud measure of illiquidity. The NYSE-Amex sample period is 1976-2009
    while the Nasdaq sample period is 1983-2009.
    76-09  76-92  92-09
    Mean  Median  Std.
    Dev.
    Mean  Median  Std.
    Dev.
    Mean  Median  Std.
    Dev.
    Firm size
    ($ billions)
    1.68  0.19  7.44  0.72  0.12  2.57  2.58  0.26  12.31
    Book-to-
    market ratio
    0.79  0.61  0.95  0.89  0.73  0.84  0.71  0.49  1.05
    RET26%
    8.05
    3.79
    34.79
    8.05
    5.31
    27.38
    8.06
    2.60
    42.36
    RET712%  9.29  4.92  38.78  9.83  6.59  30.58  8.78  2.48  46.83
    Share Price
    30.09
    15.88
    21.18
    21.87
    17.01
    18.34
    37.82
    15.04
    24.32
    NYSE-AMEX
    turnover%
    8.21  6.04  9.16  4.67  3.33  5.90  11.73  5.33  12.47
    NASDAQ
    turnover%
    13.38  7.93  20.24  9.50  6.76  9.23  15.58  8.59  26.50
    NYSE-AMEX
    Illiquidity
    1.11  0.07  5.23  1.58  0.11  7.03  0.58  0.01  3.51
    NASDAQ
    Illiquidity
    2.52  0.21  9.92  3.20  0.35  10.97  2.13  0.14  9.33
    31
    Table 2: Fama-French intercepts and characteristic-adjusted returns on long-short decile portfolios.
    This table presents the characteristic-adjusted returns for the long and the short decile portfolios formed on the
    anomalies of interest. The characteristic-adjusted returns are computed as in Fama and French (2008). Specifically,
    we sort stocks into 25 value-weighted portfolios based on size and BM, using NYSE breakpoints for market
    capitalization. We then subtract the return of the portfolio to which a stock belongs from its own return. It is these
    characteristics adjusted returns that are combined to form the decile portfolios. The long-short decile portfolio is
    regressed on the three Fama and French (1993) factors to obtain the alphas. The row labeled α(10-1) reports the
    hedge portfolio alphas. RET26 and RET712 are the cumulative returns over the second through sixth and seventh
    through twelfth months prior to the current month, respectively. Size represents the logarithm of market
    capitalization in billions of dollars. BM is the logarithm of the book-to-market ratio with the exception that book-to-
    market ratios greater than the 0.995 fractile or less than the 0.005 fractile are set equal to the 0.995 and the 0.005
    fractile values, respectively. TURN represents the logarithm of turnover. ILLIQ represents the Amihud measure of
    illiquidity. ILLIQ=1 (ILLIQ=5) represents the most liquid (illiquid) quintile of stocks based on past month’s ILLIQ.
    Panel A (B) presents equal (value) weighted returns for NYSE-AMEX stocks while panel C (D) presents equal
    (value) weighted returns for Nasdaq stocks. The bold t-statistics represent significance at the 5% level or better.
    32
    Panel A: NYSE/AMEX; Equal-weighted
    RET26  RET712  SIZE  BM  TURNOVER
    76-09  76-92  93-09  76-09  76-92  93-09  76-09  76-92  93-09  76-09  76-92  93-09  76-09  76-92  93-09
    ALL
    1  -0.65  -0.86  -0.44  -0.57  -0.80  -0.33  0.44  0.61  0.27  0.02  0.08  -0.04  0.14  0.27  0.00
    10  0.55  0.54  0.56  0.51  0.64  0.39  0.01  0.02  -0.01  -0.03  -0.16  0.09  -0.26  -0.47  -0.06
    10-1  1.20  1.40  1.00  1.08  1.44  0.72  -0.43  -0.59  -0.28  -0.05  -0.24  0.13  -0.40  -0.74  -0.06
    t-stat  5.36  6.50  2.55  6.55  7.50  2.71  -2.93  -2.96  -1.27  -0.43  -1.92  0.61  -2.01  -3.45  -0.17
    α(10-1)  1.37  1.43  1.24  1.39  1.71  1.05  -0.32  -0.03  -0.48  0.06  -0.12  0.20  -0.79  -0.83  -0.66
    t-stat  4.72  5.18  2.52  6.55  6.98  3.10  -1.56  -0.13  -1.61  0.29  -0.57  0.64  -5.21  -4.39  -2.92
    ILLIQ=1
    1  -0.21  -0.23  -0.19  -0.45  -0.57  -0.33  -0.24  -0.52  0.05  0.12  0.12  0.11  -0.06  -0.08  -0.05
    10  0.11  -0.01  0.22  0.37  0.37  0.37  -0.12  -0.33  0.10  0.12  0.06  0.18  -0.13  -0.40  0.12
    10-1  0.32  0.22  0.41  0.82  0.94  0.70  0.12  0.19  0.05  0.00  -0.06  0.07  -0.07  -0.32  0.17
    t-stat  1.22  0.83  0.93  3.93  3.85  2.07  0.91  1.09  0.26  0.02  -0.44  0.38  -0.31  -1.20  0.45
    α(10-1)  0.34  0.02  0.62  1.10  1.01  1.12  0.20  0.22  0.13  -0.31  -0.21  -0.42  -0.44  -0.62  -0.20
    t-stat  1.14  0.07  1.27  4.41  3.43  2.83  1.23  1.16  0.54  -1.68  -0.98  -1.52  -2.04  -2.39  -0.60
    ILLIQ=5
    1  -0.84  -0.96  -0.72  -0.63  -0.87  -0.39  1.83  2.13  1.53  0.08  0.50  -0.33  0.27  0.51  0.03
    10  0.82  0.99  0.65  0.75  1.08  0.43  -0.07  -0.21  0.07  0.11  -0.19  0.42  -0.24  -0.24  -0.24
    10-1  1.66  1.95  1.37  1.38  1.95  0.82  -1.90  -2.34  -1.46  0.03  -0.69  0.75  -0.51  -0.75  -0.27
    t-stat  5.14  6.60  2.39  5.00  5.89  1.86  -6.20  -5.72  -3.20  0.10  -2.01  1.63  -1.87  -2.53  -0.60
    α(10-1)  1.98  2.12  1.81  1.56  1.80  1.30  -1.41  -1.07  -1.58  0.64  0.55  0.82  -0.97  -0.98  -0.85
    t-stat  5.65  5.72  3.07  5.25  4.97  2.78  -4.28  -2.63  -3.12  2.17  1.89  2.01  -3.54  -3.32  -1.87
    33
    Panel B: NYSE/AMEX;Valued-weighted
    RET26  RET712  SIZE  BM  TURNOVER
    76-09  76-92  93-09  76-09  76-92  93-09  76-09  76-92  93-09  76-09  76-92  93-09  76-09  76-92  93-09
    ALL
    1  -0.49  -0.58  -0.40  -0.71  -0.93  -0.49  0.14  0.27  0.00  -0.01  0.14  -0.15  0.03  0.03  0.02
    10  0.14  0.14  0.15  0.52  0.59  0.44  -0.03  -0.01  -0.05  -0.05  -0.21  0.11  -0.17  -0.30  -0.05
    10-1  0.63  0.72  0.55  1.23  1.52  0.93  -0.17  -0.28  -0.05  -0.04  -0.35  0.26  -0.20  -0.33  -0.07
    t-stat  2.24  2.55  1.12  4.93  5.20  2.32  -1.22  -1.60  -0.23  -0.32  -2.12  1.15  -0.81  -1.32  -0.16
    α(10-1)  0.50  0.65  0.32  1.42  1.41  1.35  -0.05  0.18  -0.19  -0.51  -0.62  -0.44  -0.49  -0.49  -0.46
    t-stat  1.43  1.70  0.57  4.77  3.68  2.98  -0.28  0.83  -0.66  -2.37  -2.59  -1.34  -2.33  -2.05  -1.37
    ILLIQ=1
    1  -0.15  -0.07  -0.22  -0.47  -0.54  -0.40  -0.20  -0.47  0.07  0.14  0.15  0.12  0.04  0.02  0.06
    10  0.16  0.14  0.19  0.41  0.43  0.39  -0.13  -0.35  0.10  0.27  0.06  0.48  -0.07  -0.40  0.25
    10-1  0.31  0.21  0.41  0.88  0.97  0.79  0.07  0.12  0.03  0.13  -0.09  0.36  -0.11  -0.42  0.19
    t-stat  1.15  0.71  0.90  3.69  3.66  1.99  0.55  0.70  0.14  1.18  -0.72  1.90  -0.42  -1.52  0.40
    α(10-1)  0.07  -0.15  0.28  1.31  0.93  1.56  0.14  0.13  0.08  -0.41  -0.39  -0.45  -0.47  -0.72  -0.17
    t-stat  0.22  -0.42  0.55  4.69  2.88  3.49  0.83  0.70  0.31  -1.83  -1.58  -1.48  -1.92  -2.77  -0.41
    ILLIQ=5
    1  -1.23  -1.52  -0.94  -1.04  -1.66  -0.43  1.48  1.78  1.18  0.00  -0.12  0.11  0.03  -0.04  0.11
    10  0.09  0.05  0.14  0.42  0.67  0.16  -0.17  -0.31  -0.03  -0.38  -1.03  0.25  -0.23  -0.51  0.07
    10-1  1.32  1.57  1.08  1.46  2.33  0.59  -1.65  -2.09  -1.21  -0.38  -0.91  0.14  -0.26  -0.47  -0.04
    t-stat  4.02  4.65  1.91  4.27  5.30  1.14  -5.78  -5.40  -2.89  -1.12  -2.35  0.26  -0.86  -1.35  -0.09
    α(10-1)  2.06  2.26  1.84  1.50  2.02  0.97  -1.14  -0.90  -1.20  0.21  0.20  0.26  -0.89  -1.03  -0.67
    t-stat  5.36  5.07  2.95  4.28  4.34  2.03  -3.57  -2.19  -2.55  0.61  0.49  0.47  -2.75  -2.82  -1.26
    34
    Panel C: NASDAQ; Equal-weighted
    RET26  RET712  SIZE  BM  TURNOVER
    83-09  83-92  93-09  83-09  83-92  93-09  83-09  83-92  93-09  83-09  83-92  93-09  83-09  83-92  93-09
    ALL
    1  -0.96  -1.35  -0.57  -0.46  -0.80  -0.28  0.60  0.10  0.86  -0.04  -0.19  0.04  0.17  0.28  0.11
    10  0.81  0.95  0.91  0.51  0.61  0.45  0.04  -0.04  0.08  0.08  -0.19  0.23  -0.33  -0.50  -0.24
    10-1  1.77  2.30  1.48  0.97  1.41  0.73  -0.56  -0.14  -0.78  0.12  0.00  0.19  -0.50  -0.78  -0.35
    t-stat  5.46  6.54  3.23  4.00  3.75  2.35  -2.18  -0.39  -2.30  0.66  -0.02  0.81  -1.30  -1.66  -0.65
    α(10-1)  1.74  1.77  1.54  1.23  1.64  0.93  -0.63  0.25  -1.19  0.46  0.39  0.63  -0.78  -0.74  -0.89
    t-stat  4.35  4.44  2.71  3.83  3.63  2.18  -1.92  0.50  -2.79  1.83  1.33  1.89  -3.13  -1.78  -2.75
    ILLIQ=1
    1  -0.61  -1.38  -0.19  -0.31  -0.87  -0.02  -0.27  -0.56  -0.12  -0.29  -0.95  0.06  0.11  0.18  0.07
    10  0.44  0.45  0.45  0.54  0.77  0.40  0.06  0.06  0.06  0.03  -0.26  0.18  -0.69  -1.31  -0.37
    10-1  1.05  1.83  0.64  0.85  1.64  0.42  0.33  0.62  0.18  0.32  0.69  0.12  -0.80  -1.49  -0.44
    t-stat  2.42  3.15  1.08  2.37  2.86  0.93  1.28  1.53  0.54  1.31  1.68  0.40  -1.77  -2.58  -0.70
    α(10-1)  1.54  1.89  1.08  0.66  1.18  0.37  0.28  0.51  0.14  0.12  0.59  0.10  -0.81  -1.31  -0.60
    t-stat  3.06  2.65  1.62  1.63  1.85  0.71  1.09  1.05  0.45  0.35  1.24  0.22  -2.51  -2.61  -1.57
    ILLIQ=5
    1  -1.20  -2.37  -0.58  -0.14  -0.43  0.01  1.99  0.78  2.63  0.17  0.21  0.14  0.18  0.47  0.03
    10  1.10  0.95  1.17  0.67  0.15  0.94  -0.38  -0.80  -0.16  0.13  -0.80  0.61  -0.11  -0.98  0.36
    10-1  2.30  3.32  1.75  0.81  0.58  0.93  -2.37  -1.58  -2.79  -0.04  -1.01  0.47  -0.29  -1.45  0.33
    t-stat  5.09  3.92  3.35  1.82  0.59  2.13  -4.99  -1.88  -4.86  -0.12  -1.41  1.09  -0.65  -1.98  0.59
    α(10-1)  1.95  2.18  1.68  0.99  0.61  1.12  -2.24  -0.29  -3.32  0.64  0.46  0.91  -0.08  -0.59  0.12
    t-stat  3.97  2.45  2.85  2.47  0.74  2.60  -4.43  -0.30  -5.96  1.87  0.68  2.18  -0.19  -0.92  0.26
    35
    Panel D: NASDAQ; Value-weighted
    RET26  RET712  SIZE  BM  TURNOVER
    83-09  83-92  93-09  83-09  83-92  93-09  83-09  83-92  93-09  83-09  83-92  93-09  83-09  83-92  93-09
    ALL
    1  -0.94  -1.06  -0.82  -0.27  -0.67  -0.05  0.34  -0.03  0.54  0.06  -0.79  0.52  -0.09  0.03  -0.16
    10  0.70  0.93  0.64  0.88  1.29  0.67  0.20  -0.04  0.33  0.02  -0.04  0.05  0.03  -0.67  0.40
    10-1  1.64  1.99  1.46  1.15  1.96  0.72  -0.14  -0.01  -0.21  -0.04  0.75  -0.47  0.12  -0.70  0.56
    t-stat  3.74  3.88  2.37  3.12  3.52  1.50  -0.52  -0.04  -0.56  -0.16  2.12  -1.22  0.28  -1.30  0.94
    α(10-1)  1.97  2.15  1.70  1.62  2.07  1.30  -0.18  0.33  -0.50  -0.46  0.41  -0.89  -0.16  -0.73  0.16
    t-stat  4.13  4.12  2.52  3.93  3.48  2.38  -0.60  0.73  -1.24  -1.32  1.19  -1.77  -0.60  -1.69  0.49
    ILLIQ=1
    1  -0.61  -1.31  -0.23  -0.19  -0.58  0.01  -0.23  -0.39  -0.15  -0.24  -0.66  -0.01  0.02  0.08  -0.02
    10  0.93  1.02  0.89  1.07  1.20  1.00  0.21  0.21  0.21  -0.47  -0.72  -0.33  -0.09  -1.17  0.48
    10-1  1.54  2.33  1.12  1.26  1.78  0.99  0.44  0.60  0.36  -0.23  -0.06  -0.32  -0.11  -1.25  0.50
    t-stat  2.99  3.27  1.62  2.95  2.80  1.75  1.74  1.45  1.11  -0.70  -0.13  -0.74  -0.19  -1.90  0.64
    α(10-1)  1.82  2.70  1.14  1.15  1.59  0.93  0.46  0.56  0.45  -0.86  -0.58  -0.88  -0.09  -0.97  0.35
    t-stat  3.21  3.33  1.52  2.45  2.34  1.49  1.66  1.13  1.36  -2.20  -1.11  -1.64  -0.22  -1.72  0.62
    ILLIQ=5
    1  -2.41  -3.54  -1.80  -1.20  -1.38  -1.10  1.66  0.73  2.16  0.06  0.31  -0.07  -0.03  0.07  -0.09
    10  0.12  -0.03  0.21  0.45  0.74  0.30  -0.39  -0.91  -0.10  -0.67  -1.41  -0.28  -0.54  -1.26  -0.16
    10-1  2.53  3.51  2.01  1.65  2.12  1.40  -2.05  -1.64  -2.26  -0.73  -1.72  -0.21  -0.51  -1.33  -0.07
    t-stat  5.52  4.24  3.69  3.13  1.81  2.73  -4.39  -1.89  -4.15  -1.96  -2.34  -0.50  -1.15  -1.60  -0.14
    α(10-1)  2.56  2.89  2.29  1.75  1.17  2.00  -1.95  -0.42  -2.84  0.01  0.27  0.05  0.03  0.07  -0.05
    t-stat  5.10  3.06  3.89  4.19  1.44  4.16  -3.93  -0.41  -5.37  0.02  0.42  0.11  0.08  0.11  -0.10
    36
    Table 3: Fama-MacBeth regression estimates with excess market return, SMB and HML as risk factors
    This table presents the time-series averages of individual stock cross-sectional OLS regression coefficient estimates.
    The dependent variable is the excess return risk-adjusted using the conditional Fama-French (1993) model.
    Conditional factor loadings are computed by conditioning on size and book-to-market ratio. Size represents the
    logarithm of market capitalization in billions of dollars. BM is the logarithm of the book-to-market ratio with the
    exception that book-to-market ratios greater than the 0.995 fractile or less than the 0.005 fractile are set equal to the
    0.995 and the 0.005 fractile values, respectively. TURN represents the logarithm of turnover. RET26 and RET712
    are the cumulative returns over the second through sixth and seventh through twelfth months prior to the current
    month, respectively. ILLIQ represents the Amihud measure of illiquidity. PRC is the logarithm of the share price.
    Panel A (B) presents the results for NYSE-AMEX (Nasdaq) stocks. All coefficients are multiplied by 100. The
    bold t-statistics represent significance at the 5% level or better.
    Panel A: NYSE and AMEX stocks only
    76-09  76-92  93-09
    mean  t-stat  mean  t-stat  mean  t-stat
    Intercept
    -0.273  -1.21  -0.722  -2.36  0.171  0.52
    RET26
    0.383  2.05  0.709  3.09  0.061  0.21
    RET712
    0.521  4.14  0.809  5.09  0.236  1.22
    SIZE
    -0.045  -2.38  -0.090  -3.23  0.000  -0.01
    BM
    0.144  4.26  0.142  2.83  0.145  3.21
    TURN
    -0.195  -5.43  -0.306  -6.60  -0.084  -1.57
    ILLIQ
    0.054  4.17  0.046  4.36  0.062  2.64
    PRC
    0.189  2.83  0.453  4.69  -0.073  -0.83
    Panel B: NASDAQ stocks only
    83-09  83-92  93-09
    mean  t-stat  mean  t-stat  mean  t-stat
    Intercept
    0.813  1.63  0.251  0.32  1.099  1.72
    RET26
    0.705  4.05  1.251  3.76  0.427  2.15
    RET712
    0.414  3.06  1.240  4.23  -0.007  -0.06
    SIZE
    -0.04  -1.03  -0.043  -0.59  -0.038  -0.85
    BM
    0.175  3.94  0.159  2.37  0.184  3.17
    TURN
    -0.144  -2.84  -0.331  -3.55  -0.048  -0.82
    ILLIQ
    0.022  0.60  -0.062  -0.60  0.065  4.35
    PRC
    -0.078  -0.70  0.038  0.24  -0.138  -0.94
    37
    Table 4: Fama-MacBeth regression estimates with excess market return, SMB and HML as risk factors for
    stocks with low and high illiquidity
    This table presents the time-series averages of individual stock cross-sectional OLS regression coefficient estimates.
    The dependent variable is the excess return risk-adjusted using the conditional Fama-French (1993) model.
    Conditional factor loadings are computed by conditioning on size and book-to-market ratio. Size represents the
    logarithm of market capitalization in billions of dollars. BM is the logarithm of the book-to-market ratio with the
    exception that book-to-market ratios greater than the 0.995 fractile or less than the 0.005 fractile are set equal to the
    0.995 and the 0.005 fractile values, respectively. TURN represents the logarithm of turnover. RET26 and RET712
    are the cumulative returns over the second through sixth and seventh through twelfth months prior to the current
    month, respectively. ILLIQ represents the Amihud measure of illiquidity. PRC is the logarithm of the share price.
    The regressions are run separately for liquid and illiquid stocks. Each month, stocks are defined as liquid or illiquid
    if their ILLIQ measure is below or above the cross-sectional median. Panel A (B) presents the results for NYSE-
    AMEX (Nasdaq) stocks. All coefficients are multiplied by 100. The bold t-statistics represent significance at the
    5% level or better.
    Panel A: NYSE and AMEX stocks only
    ILLIQ<=median  ILLIQ>median
    76-09  76-92  93-09  76-09  76-92  93-09
    mean  t-stat  mean  t-stat  mean  t-stat mean  t-stat  mean  t-stat  mean  t-stat
    Intercept -0.318  -0.76  -0.723  -1.77  0.082  0.11  1.610  2.82  1.501  2.16  1.718  1.90
    RET26  0.015  0.06  0.310  0.99  -0.277  -0.68  0.584  3.11  0.864  3.73  0.308  1.05
    RET712  0.391  2.96  0.652  3.85  0.132  0.66  0.732  3.93  1.077  4.42  0.390  1.39
    SIZE  -0.005  -0.18  -0.039  -1.21  0.029  0.64  -0.248  -4.86  -0.348  -5.11  -0.150  -1.98
    BM  0.087  2.32  0.087  1.47  0.087  1.87  0.144  3.14  0.117  1.69  0.171  2.82
    TURN  -0.270  -4.44  -0.381  -5.76  -0.160  -1.58  -0.208  -5.20  -0.339  -6.35  -0.078  -1.34
    ILLIQ  -0.589  -0.02  1.663  1.11  -2.819  -0.04  0.047  3.48  0.041  3.72  0.052  2.13
    PRC  0.045  0.78  0.221  2.42  -0.129  -1.86  0.329  3.88  0.660  5.45  0.001  0.01
    Panel B: NASDAQ stocks only
    ILLIQ<=median  ILLIQ>median
    83-09  83-92  93-09  83-09  83-92  93-09
    mean  t-stat  mean  t-stat  mean  t-stat mean  t-stat  mean  t-stat  mean  t-stat
    Intercept -0.519  -0.94  -1.521  -1.71  -0.028  -0.04  4.492  5.19  3.694  2.49  4.880  4.57
    RET26  0.547  2.67  1.189  3.06  0.232  0.99  0.938  4.57  1.409  4.01  0.710  2.82
    RET712 0.200  1.38  1.123  4.32  -0.252  -1.50  0.691  4.00  1.425  3.55  0.334  2.07
    SIZE  0.066  1.50  0.105  1.26  0.046  0.91  -0.388  -4.85  -0.342  -2.29  -0.410  -4.35
    BM  0.191  3.46  0.302  3.71  0.136  1.90  0.190  3.85  0.181  2.34  0.195  3.09
    TURN  -0.144  -2.05  -0.315  -2.95  -0.060  -0.67  -0.197  -3.37  -0.160  -1.48  -0.215  -3.11
    ILLIQ  -0.145  -0.07  0.303  0.56  -0.365  -0.13  0.036  3.03  0.030  1.66  0.038  2.53
    PRC  -0.056  -0.46  0.066  0.39  -0.116  -0.72  -0.063  -0.50  0.017  0.08  -0.101  -0.65
    38
    Table 5: Fama-French intercepts and characteristic-adjusted on long-short decile portfolios
    This table presents the characteristic-adjusted returns for the long and the short decile portfolios formed on the
    anomalies of interest. The characteristic-adjusted returns are computed as in Fama and French (2008). Specifically,
    we sort stocks into 25 value-weighted portfolios based on size and BM, using NYSE breakpoints for market
    capitalization. We then subtract the return of the portfolio to which a stock belongs from its own return. It is these
    characteristics adjusted returns that are combined to form the decile portfolios. The long-short decile portfolio is
    regressed on the three Fama and French (1993) factors to obtain the alphas. The row labeled α(10-1) reports the
    hedge portfolio alphas. DISP represents analyst forecast dispersion, computed as the standard deviation across
    analysts EPS forecasts for the next fiscal year divided by the absolute value of the mean EPS forecast. SUE is the
    standardized unexpected earnings, computed as the most recently announced quarterly earnings less the earnings
    four quarters ago, standardized by its standard deviation estimated over the prior eight quarters. ACC represents
    accruals, measured as in Sloan (1996). ILLIQ represents the Amihud measure of illiquidity. ILLIQ=1 (ILLIQ=5)
    represents the most liquid (illiquid) quintile of stocks based on past month’s ILLIQ. Panel A (B) presents equal
    (value) weighted returns for NYSE-AMEX stocks while panel C (D) presents equal (value) weighted returns for
    Nasdaq stocks. The bold t-statistics represent significance at the 5% level or better.
    Panel A: NYSE/AMEX; Equal-weighted
    DISP  SUE  ACC
    76-09  76-92  93-09  76-09  76-92  93-09  76-09  76-92  93-09
    ALL
    1  0.30  0.43  0.17  -0.30  -0.43  -0.16  0.19  0.30  0.07
    10  -0.44  -0.73  -0.16  0.54  0.60  0.49  -0.21  -0.32  -0.11
    10-1  -0.74  -1.16  -0.33  0.84  1.03  0.65  -0.40  -0.62  -0.18
    t-stat  -4.74  -6.37  -1.31  7.64  8.33  3.57  -3.52  -4.48  -1.01
    α(10-1)  -1.09  -1.43  -0.70  0.91  1.11  0.70  -0.46  -0.43  -0.40
    t-stat  -6.56  -7.13  -2.81  6.64  7.93  3.04  -3.79  -2.93  -2.22
    ILLIQ=1
    1  0.27  0.36  0.17  -0.02  -0.13  0.08  0.14  0.05  0.23
    10  -0.15  -0.34  0.04  0.18  0.28  0.06  -0.10  -0.09  -0.12
    10-1  -0.42  -0.70  -0.13  0.20  0.41  -0.02  -0.24  -0.14  -0.35
    t-stat  -1.88  -2.50  -0.39  1.41  2.57  -0.09  -1.62  -0.75  -1.47
    α(10-1)  -0.77  -1.02  -0.52  0.32  0.46  0.15  -0.28  -0.05  -0.44
    t-stat  -3.58  -3.52  -1.65  2.00  2.53  0.57  -1.79  -0.25  -1.85
    ILLIQ=5
    1  0.51  0.56  0.46  -0.68  -0.59  -0.77  0.08  -0.15  0.32
    10  -1.04  -1.04  -0.99  1.16  1.35  0.97  -0.27  -0.84  0.32
    10-1  -1.55  -1.60  -1.45  1.84  1.94  1.74  -0.35  -0.69  0.00
    t-stat  -6.74  -5.56  -4.31  8.60  7.15  5.24  -1.58  -2.74  -0.01
    α(10-1)  -1.80  -1.81  -1.75  1.85  1.93  1.73  -0.61  -0.79  -0.35
    t-stat  -7.70  -5.70  -5.27  7.92  6.79  4.72  -2.77  -2.95  -1.03
    39
    Panel B: NYSE/AMEX; Value-weighted
    DISP  SUE  ACC
    76-09  76-92  93-09  76-09  76-92  93-09  76-09  76-92  93-09
    ALL
    1  0.15  0.20  0.10  -0.15  -0.15  -0.16  0.23  0.33  0.13
    10  -0.36  -0.64  -0.08  0.16  0.33  -0.02  -0.19  -0.05  -0.32
    10-1  -0.51  -0.84  -0.18  0.31  0.48  0.14  -0.42  -0.38  -0.45
    t-stat  -2.28  -3.35  -0.50  2.28  3.05  0.64  -2.37  -2.05  -1.51
    α(10-1)  -0.98  -1.19  -0.76  0.51  0.52  0.47  -0.50  -0.32  -0.65
    t-stat  -4.25  -4.25  -2.18  3.17  2.77  1.86  -2.69  -1.54  -2.12
    ILLIQ=1
    1  0.22  0.32  0.12  -0.06  -0.10  -0.01  0.13  0.15  0.11
    10  -0.08  -0.23  0.07  0.15  0.32  0.00  -0.14  -0.05  -0.24
    10-1  -0.30  -0.55  -0.05  0.21  0.42  0.01  -0.27  -0.20  -0.35
    t-stat  -1.34  -2.04  -0.13  1.32  2.18  0.03  -1.56  -1.00  -1.20
    α(10-1)  -0.77  -0.94  -0.59  0.40  0.46  0.31  -0.44  -0.33  -0.51
    t-stat  -3.37  -3.08  -1.79  2.15  2.02  1.05  -2.41  -1.53  -1.76
    ILLIQ=5
    1  0.46  0.51  0.41  -0.54  -0.19  -0.90  -0.07  -0.29  0.14
    10  -0.95  -0.89  -0.97  0.67  0.74  0.60  -0.49  -0.86  -0.12
    10-1  -1.41  -1.40  -1.38  1.21  0.93  1.50  -0.42  -0.57  -0.26
    t-stat  -5.47  -4.28  -3.43  4.93  2.95  3.96  -1.94  -2.06  -0.80
    α(10-1)  -1.65  -1.65  -1.62  1.34  1.06  1.58  -0.69  -0.75  -0.57
    t-stat  -6.63  -4.89  -4.54  5.09  3.22  3.86  -3.05  -2.45  -1.71
    40
    Panel C: NASDAQ; Equal-weighted
    DISP  SUE  ACC
    76-09  76-92  93-09  76-09  76-92  93-09  76-09  76-92  93-09
    ALL
    1  0.83  0.72  0.88  -0.26  0.12  -0.44  0.35  0.30  0.37
    10  -0.21  -0.68  0.03  0.95  1.12  0.87  -0.41  -0.83  -0.19
    10-1  -1.04  -1.40  -0.85  1.21  1.00  1.31  -0.76  -1.13  -0.56
    t-stat  -3.91  -3.83  -2.38  6.08  2.30  6.30  -4.10  -3.00  -2.81
    α(10-1)  -1.13  -1.58  -0.91  1.33  1.32  1.30  -0.80  -0.98  -0.72
    t-stat  -4.82  -4.32  -3.30  6.86  3.53  5.77  -4.57  -3.02  -3.53
    ILLIQ=1
    1  0.83  0.45  1.03  -0.04  -0.23  0.04  0.35  1.09  -0.04
    10  0.21  -0.25  0.44  0.63  0.92  0.53  -0.67  -1.23  -0.38
    10-1  -0.62  -0.70  -0.59  0.67  1.15  0.49  -1.02  -2.32  -0.34
    t-stat  -1.63  -0.90  -1.32  2.00  1.93  1.45  -2.60  -3.47  -1.20
    α(10-1)  -0.86  -0.58  -0.97  0.82  1.15  0.65  -0.98  -1.82  -0.50
    t-stat  -2.70  -1.13  -2.48  2.77  2.16  1.80  -3.67  -3.28  -1.77
    ILLIQ=5
    1  0.63  0.47  0.71  -0.39  -0.16  -0.50  0.10  -0.66  0.49
    10  -0.25  -1.12  0.13  1.42  0.66  1.69  -0.56  -2.19  0.28
    10-1  -0.88  -1.59  -0.58  1.81  0.82  2.19  -0.66  -1.53  -0.21
    t-stat  -2.46  -2.47  -1.36  4.49  0.95  6.07  -1.80  -1.99  -0.54
    α(10-1)  -0.61  -1.00  -0.42  1.75  1.06  2.05  -0.28  -0.22  -0.42
    t-stat  -1.70  -1.92  -1.05  5.06  1.30  5.90  -0.80  -0.32  -1.55
    41
    Panel D: NASDAQ; Value-weighted
    DISP  SUE  ACC
    76-09  76-92  93-09  76-09  76-92  93-09  76-09  76-92  93-09
    ALL
    1  0.88  0.74  0.95  0.25  0.38  0.18  0.81  1.18  0.61
    10  0.22  -0.47  0.58  0.68  0.97  0.54  -0.67  -0.97  -0.51
    10-1  -0.66  -1.21  -0.37  0.43  0.59  0.36  -1.48  -2.15  -1.12
    t-stat  -2.08  -2.75  -0.87  1.51  1.20  1.02  -4.30  -4.04  -2.54
    α(10-1)  -0.95  -1.36  -0.77  0.57  1.18  0.30  -1.30  -1.73  -1.10
    t-stat  -2.99  -3.08  -1.84  2.06  2.69  0.83  -4.02  -3.50  -2.63
    ILLIQ=1
    1  0.86  0.43  1.08  0.40  -0.10  0.64  1.11  1.67  0.82
    10  0.28  -0.01  0.41  0.55  1.17  0.31  -0.67  -1.28  -0.36
    10-1  -0.58  -0.44  -0.67  0.15  1.27  -0.33  -1.78  -2.95  -1.18
    t-stat  -1.32  -0.52  -1.37  0.37  1.93  -0.81  -3.63  -3.79  -2.45
    α(10-1)  -1.06  -0.57  -1.32  0.11  1.26  -0.40  -1.81  -2.29  -1.57
    t-stat  -2.70  -0.99  -2.53  0.32  2.23  -0.97  -4.62  -3.53  -3.18
    ILLIQ=5
    1  0.62  0.66  0.60  -0.50  -0.43  -0.53  -0.25  -1.13  0.21
    10  -0.33  -1.30  0.11  1.15  1.13  1.11  -1.17  -3.19  -0.11
    10-1  -0.95  -1.96  -0.49  1.65  1.56  1.64  -0.92  -2.06  -0.32
    t-stat  -2.59  -2.94  -1.21  3.80  1.74  3.98  -2.14  -2.21  -0.74
    α(10-1)  -0.93  -1.56  -0.61  1.80  2.15  1.63  -0.36  -0.52  -0.38
    t-stat  -2.72  -2.24  -1.69  4.76  2.61  4.03  -0.89  -1.62  -1.27
    42
    Table 6: Fama-MacBeth regression estimates with excess market return, SMB and HML as risk factors,
    including analyst forecast dispersion, SUE, and accruals as firm characteristics
    This table presents the time-series averages of individual stock cross-sectional OLS regression coefficient estimates.
    The dependent variable is the excess return risk-adjusted using the conditional Fama-French (1993) model.
    Conditional factor loadings are computed by conditioning on size and book-to-market ratio. Size represents the
    logarithm of market capitalization in billions of dollars. BM is the logarithm of the book-to-market ratio with the
    exception that book-to-market ratios greater than the 0.995 fractile or less than the 0.005 fractile are set equal to the
    0.995 and the 0.005 fractile values, respectively. TURN represents the logarithm of turnover. RET26 and RET712
    are the cumulative returns over the second through sixth and seventh through twelfth months prior to the current
    month, respectively. ILLIQ represents the Amihud measure of illiquidity. PRC is the logarithm of the share price.
    DISP represents analyst forecast dispersion, computed as the standard deviation across analysts EPS forecasts for
    fiscal year 1 divided by the absolute value of the mean EPS forecast. SUE is the standardized unexpected earnings,
    computed as the most recently announced quarterly earnings less the earnings four quarters ago, standardized by its
    standard deviation estimated over the prior eight quarters. ACC represents accruals, measured as in Sloan (1996).
    Panel A (B) presents the results for NYSE-AMEX (Nasdaq) stocks. All coefficients are multiplied by 100. The
    bold t-statistics represent significance at the 5% level or better.
    Panel A: NYSE and AMEX stocks
    76-09  76-92  93-09
    mean  t-stat  mean  t-stat  mean  t-stat
    Intercept  0.278  0.88  0.117  0.28  0.434  0.92
    RET26  0.468  2.01  0.759  2.53  0.186  0.53
    RET712  0.421  2.47  0.639  2.53  0.211  0.92
    SIZE  -0.015  -0.55  -0.062  -1.78  0.031  0.78
    BM  0.005  0.09  0.036  0.51  -0.026  -0.38
    TURN  -0.072  -1.22  -0.162  -2.33  0.015  0.16
    ILLIQ  0.401  0.45  0.402  1.39  0.400  0.23
    PRC  -0.047  -0.57  0.188  1.68  -0.274  -1.80
    DISP  -0.211  -2.51  -0.372  -2.62  -0.055  -0.61
    SUE  0.026  2.66  0.043  2.89  0.010  0.77
    ACC  -1.482  -3.10  -2.327  -3.84  -0.668  -0.91
    43
    Panel B: NASDAQ stocks only
    83-09  83-92  93-09
    mean  t-stat  mean  t-stat  mean  t-stat
    Intercept  2.851  4.65  3.405  2.87  2.620  3.66
    RET26  0.612  2.61  1.400  3.11  0.283  1.04
    RET712  0.082  0.39  0.427  0.99  -0.063  -0.27
    SIZE  -0.084  -1.46  -0.179  -1.40  -0.045  -0.72
    BM  0.042  0.50  -0.140  -0.90  0.118  1.16
    TURN  -0.008  -0.10  -0.241  -1.64  0.089  0.87
    ILLIQ  -0.325  -0.64  -0.085  -0.76  -0.426  -0.59
    PRC  -0.392  -2.62  -0.233  -0.86  -0.458  -2.55
    DISP  -0.064  -0.64  0.110  0.45  -0.137  -1.38
    SUE  0.037  2.36  0.080  2.22  0.019  1.17
    ACC  -2.552  -4.40  -4.320  -3.65  -1.815  -2.79
    44
    Table 7: Trend Fits to Fama-MacBeth coefficients
    We run linear regression of the relevant Fama MacBeth coefficients on time and this table reports the slope of linear
    regression with associated t-statistics. RET26 and RET712 are the cumulative returns over the second through sixth
    and seventh through twelfth months prior to the current month, respectively. DISP represents analyst forecast
    dispersion, computed as the standard deviation across analysts EPS forecasts for the next fiscal year divided by the
    absolute value of the mean EPS forecast. SUE is the standardized unexpected earnings, computed as the most
    recently announced quarterly earnings less the earnings four quarters ago, standardized by its standard deviation
    estimated over the prior eight quarters. ACC represents accruals, measured as in Sloan (1996). All coefficients are
    multiplied by 10000. The bold t-statistics represent significance at the 5% level or better.
    NYSE/AMEX  NASDAQ
    slope  t-stat  slope  t-stat
    RET26  -0.31  -1.49  -1.03  -3.64
    RET712  -0.30  -2.01  -0.55  -2.16
    DISP  0.21  2.92  -0.10  -0.87
    SUE  -0.02  -1.98  -0.03  -1.81
    ACC  1.08  2.57  1.26  1.78
    45
    Table 8: Fama-MacBeth regression estimates with excess market return, SMB and HML as risk factors,
    including analyst forecast dispersion, SUE, and accruals, split by illiquidity levels
    This table presents the time-series averages of individual stock cross-sectional OLS regression coefficient estimates.
    The dependent variable is the excess return risk-adjusted using the conditional Fama-French (1993) model.
    Conditional factor loadings are computed by conditioning on size and book-to-market ratio. Size represents the
    logarithm of market capitalization in billions of dollars. BM is the logarithm of the book-to-market ratio with the
    exception that book-to-market ratios greater than the 0.995 fractile or less than the 0.005 fractile are set equal to the
    0.995 and the 0.005 fractile values, respectively. TURN represents the logarithm of turnover. RET26 and RET712
    are the cumulative returns over the second through sixth and seventh through twelfth months prior to the current
    month, respectively. ILLIQ represents the Amihud measure of illiquidity. PRC is the logarithm of the share price.
    DISP represents analyst forecast dispersion, computed as the standard deviation across analysts EPS forecasts for
    fiscal year 1 divided by the absolute value of the mean EPS forecast. SUE is the standardized unexpected earnings,
    computed as the most recently announced quarterly earnings less the earnings four quarters ago, standardized by its
    standard deviation estimated over the prior eight quarters. ACC represents accruals, measured as Sloan (1996). The
    regressions are run separately for liquid and illiquid stocks. Each month, stocks are defined as liquid or illiquid if
    their ILLIQ measure is below or above the cross-sectional median. Panel A (B) presents the results for NYSE-
    AMEX (Nasdaq) stocks. All coefficients are multiplied by 100. The bold t-statistics represent significance at the
    5% level or better.
    Panel A: NYSE and AMEX stocks only
    ILLIQ<=median  ILLIQ>median
    76-09  76-92  93-09  76-09  76-92  93-09
    mean  t-stat  Mean  t-stat  mean  t-stat  mean  t-stat  mean  t-stat  mean  t-stat
    Intercept -0.035  -0.04  0.821  0.76  -0.856  -0.67  1.282  1.65  1.054  1.18  1.500  1.20
    RET26  0.065  0.22  0.431  1.14  -0.286  -0.65  0.528  2.24  0.789  2.53  0.278  0.79
    RET712  0.333  1.81  0.514  1.99  0.160  0.61  0.662  2.89  1.017  2.97  0.321  1.05
    SIZE  -0.021  -0.41  -0.128  -1.80  0.081  1.06  -0.062  -0.96  -0.101  -1.23  -0.026  -0.26
    BM  0.021  0.36  0.032  0.37  0.010  0.13  -0.033  -0.47  0.051  0.55  -0.113  -1.06
    TURN  -0.100  -1.06  -0.293  -2.61  0.084  0.56  -0.062  -0.98  -0.108  -1.39  -0.017  -0.17
    ILLIQ  8.598  0.07  -7.273  -0.43  23.832  0.10  0.165  0.18  0.422  1.28  -0.081  -0.04
    PRC  0.069  0.83  0.249  2.24  -0.105  -0.85  -0.179  -1.69  0.080  0.54  -0.428  -2.86
    DISP  -0.269  -2.38  -0.297  -1.52  -0.243  -1.54  -0.371  -1.48  -1.089  -2.64  0.318  1.11
    SUE  0.010  0.76  0.030  1.70  -0.009  -0.52  0.038  2.58  0.052  2.42  0.024  1.20
    ACC  -2.011  -3.21  -2.969  -3.50  -1.092  -1.19  -1.184  -2.09  -2.255  -3.34  -0.157  -0.17
    46
    Panel B: NASDAQ stocks only
    ILLIQ<=median  ILLIQ>median
    83-09  83-92  93-09  83-09  83-92  93-09
    mean  t-stat  mean  t-stat  mean  t-stat mean  t-stat  mean  t-stat  mean  t-stat
    Intercept 0.068  0.06  -3.049  -1.20  1.117  0.86  5.339  3.09  8.698  2.77  4.559  2.28
    RET26  0.200  0.69  1.222  2.02  -0.144  -0.44  1.322  4.06  3.390  4.29  0.842  2.41
    RET712 0.153  0.61  1.004  1.55  -0.134  -0.54  0.026  0.08  0.035  0.06  0.024  0.06
    SIZE  0.077  0.89  0.321  1.47  -0.005  -0.06  -0.221  -1.46  -0.573  -1.79  -0.139  -0.82
    BM  0.113  1.09  -0.047  -0.21  0.167  1.42  -0.077  -0.58  -0.698  -2.38  0.068  0.47
    TURN  0.038  0.30  -0.126  -0.57  0.093  0.60  -0.019  -0.18  -0.291  -1.09  0.044  0.37
    ILLIQ  -26.835 -0.90  13.675  1.81  -40.475  -1.01  -0.289  -0.47  -0.036  -0.49  -0.347  -0.46
    PRC  -0.128  -0.72  -0.216  -0.59  -0.098  -0.49  -0.768  -3.69  -0.663  -1.45  -0.792  -3.39
    DISP  0.135  0.63  0.991  2.23  -0.153  -0.64  0.096  0.56  0.885  1.22  -0.087  -0.68
    SUE  0.025  1.28  0.111  2.26  -0.003  -0.16  0.048  1.60  0.063  0.88  0.044  1.34
    ACC  -2.814  -3.56  -5.187  -3.01  -2.016  -2.30  -1.565  -1.74  -3.315  -2.03  -1.158  -1.20
    47
    Table 9: Fama-MacBeth regression estimates with excess market return, SMB and HML as risk factors
    This table presents the time-series averages of individual stock cross-sectional OLS regression coefficient estimates.
    The dependent variable is the excess return risk-adjusted using the conditional Fama-French (1993) model.
    Conditional factor loadings are computed by conditioning on size and book-to-market ratio. Size represents the
    logarithm of market capitalization in billions of dollars. BM is the logarithm of the book-to-market ratio with the
    exception that book-to-market ratios greater than the 0.995 fractile or less than the 0.005 fractile are set equal to the
    0.995 and the 0.005 fractile values, respectively. TURN represents the logarithm of turnover. RET26 and RET712
    are the cumulative returns over the second through sixth and seventh through twelfth months prior to the current
    month, respectively. ILLIQ represents the Amihud measure of illiquidity. PRC is the logarithm of the share price.
    DISP represents analyst forecast dispersion, computed as the standard deviation across analysts EPS forecasts for
    fiscal year 1 divided by the absolute value of the mean EPS forecast. SUE is the standardized unexpected earnings,
    computed as the most recently announced quarterly earnings less the earnings four quarters ago, standardized by its
    standard deviation estimated over the prior eight quarters. ACC represents accruals, measured as in Sloan (1996).
    The dummy variable D is used to flag the decile of stocks that would be shorted as per the trading strategy. Panel A
    (B) presents the results for NYSE-AMEX stocks for the full (augmented) sample and panel C (D) presents the
    results for Nasdaq stocks for the full (augmented) sample.. All coefficients are multiplied by 100. The bold t-
    statistics represent significance at the 5% level or better.
    Panel A: NYSE and AMEX stocks, full sample
    76-09  76-92  93-09
    mean  t-stat  mean  t-stat  mean  t-stat
    Intercept  -0.033  -0.15  -0.340  -1.08  0.272  0.86
    RET26  0.199  1.10  0.383  1.73  0.017  0.06
    RET26*D  1.370  3.79  1.848  3.65  0.896  1.74
    RET712  0.427  3.48  0.658  4.02  0.198  1.09
    RET712*D  0.727  2.19  1.039  2.35  0.418  0.84
    BM  0.199  4.01  0.212  3.14  0.186  2.55
    BM*D  -0.097  -2.21  -0.123  -1.92  -0.072  -1.19
    SIZE  -0.050  -2.60  -0.098  -3.49  -0.002  -0.07
    TURN  -0.165  -4.78  -0.265  -5.55  -0.066  -1.35
    ILLIQ  0.056  4.33  0.047  4.52  0.065  2.75
    PRC  0.164  2.66  0.406  4.43  -0.076  -0.96
    48
    Panel B: NYSE and AMEX stocks, smaller sample with accruals, dispersion, and earnings drift
    76-09  76-92  93-09
    mean  t-stat  mean  t-stat  mean  t-stat
    Intercept  0.469  1.46  0.529  1.24  0.411  0.85
    RET26  0.302  1.31  0.440  1.47  0.169  0.48
    RET26*D  0.340  0.75  0.644  0.91  0.047  0.08
    RET712  0.434  2.58  0.660  2.67  0.217  0.95
    RET712*D  -0.072  -0.17  -0.099  -0.15  -0.046  -0.09
    BM  0.108  1.68  0.159  1.87  0.058  0.61
    BM*D  -0.131  -2.54  -0.145  -1.92  -0.117  -1.66
    SIZE  -0.023  -0.88  -0.072  -2.06  0.024  0.60
    TURN  -0.081  -1.48  -0.144  -2.18  -0.021  -0.24
    ILLIQ  0.357  0.42  0.384  1.30  0.331  0.20
    PRC  -0.034  -0.45  0.168  1.62  -0.228  -2.15
    DISP  -1.119  -1.56  -2.331  -3.65  0.050  0.04
    DISP*D  0.873  1.25  1.903  3.09  -0.120  -0.10
    SUE  0.073  4.74  0.104  4.82  0.043  1.98
    SUE*D  -0.072  -3.74  -0.087  -3.10  -0.058  -2.18
    ACC  -1.823  -3.35  -2.905  -4.07  -0.779  -0.96
    ACC*D  0.859  1.36  1.037  1.52  0.686  0.65
    49
    Panel C: NASDAQ stocks, full sample
    76-09  76-92  93-09
    mean  t-stat  mean  t-stat  mean  t-stat
    Intercept
    0.732  1.47  0.207  0.26  0.997  1.58
    RET26
    0.815  5.08  1.314  4.04  0.564  3.22
    RET26*D
    0.150  0.44  0.621  0.93  -0.088  -0.23
    RET712
    0.488  3.53  1.424  4.83  0.015  0.11
    RET712*D
    0.266  0.90  0.393  0.66  0.202  0.61
    BM
    0.248  4.24  0.247  2.89  0.249  3.23
    BM*D
    -0.092  -1.87  -0.111  -1.24  -0.082  -1.41
    SIZE
    -0.018  -0.46  -0.005  -0.07  -0.024  -0.55
    TURN
    -0.132  -2.78  -0.287  -3.42  -0.053  -0.94
    ILLIQ
    0.056  4.83  0.035  1.99  0.066  4.44
    PRC
    -0.113  -1.06  -0.059  -0.38  -0.140  -1.00
    Panel D: NASDAQ stocks, smaller sample with accruals, dispersion, and earnings drift
    76-09  76-92  93-09
    mean  t-stat  mean  t-stat  mean  t-stat
    Intercept
    1.814  2.78  1.482  1.01  1.936  2.71
    RET26
    0.446  1.83  0.927  1.78  0.270  0.99
    RET26*D
    -0.009  -0.02  2.548  2.01  -0.947  -1.56
    RET712
    -0.235  -1.20  -0.372  -0.87  -0.185  -0.85
    RET712*D
    0.330  0.75  1.340  1.12  -0.040  -0.10
    BM
    0.133  1.16  0.201  0.88  0.108  0.81
    BM*D
    -0.057  -0.56  0.076  0.27  -0.106  -1.13
    SIZE
    -0.007  -0.12  0.009  0.06  -0.013  -0.21
    TURN
    -0.012  -0.14  -0.046  -0.30  0.001  0.01
    ILLIQ
    -0.322  -0.76  0.100  0.40  -0.476  -0.84
    PRC
    -0.318  -2.13  -0.188  -0.63  -0.366  -2.12
    DISP
    -0.585  -0.71  -1.629  -1.06  -0.202  -0.21
    DISP*D
    0.530  0.66  1.933  1.30  0.015  0.02
    SUE
    0.094  3.09  0.175  2.59  0.064  1.93
    SUE*D
    -0.095  -2.42  -0.134  -1.58  -0.081  -1.84
    ACC
    -2.660  -3.26  -6.214  -3.49  -1.357  -1.52
    ACC*D
    -0.005  0.00  2.170  0.91  -0.802  -0.81
     

在線客服

售前咨詢
售后咨詢
微信號
Essay_Cheery
微信
Dueduedue论文服务-【美国论文代写】加拿大论文ESSAY代写服务 ESSAYCASE |essay代写|assignment代写|paper代写,全球在线写作中心 EasyDue™-北美地区论文作业ESSAY代写服务机构,作业代写-覆盖100+全学科 EssayBerry:美国论文ESSAY代写服务,代写essay,统计代写,代写文章 EssayWill-论文代写网|经济代写,数学,CS代写,Assignment代写 Essaymint:专注软文代写和代写作业等服务|作业代写-100%原创高分 Essay代写,论文代写,Report代写,网课代修-浩天教育 Essay代写-Assignment「免费修改」Paper代写,-51Due留学教育 Essay代写-各学科论文代写|留学作业网课代修代做|优质的代写文章的网站 Essay代写|Assignment代写|提供留学生Essay代写服务-留学写作网