本章导读 本章（全书最后一章）精读 McLean & Pontiff (2016)：研究 97 个被证明能预测横截面收益的变量在样本外与发表后的可预测性。§12.1 要点：样本外收益低 26%（统计偏差/数据挖掘）、发表后低 58%（校正统计偏差后，发表本身解释 32% 的下降）；可预测性并未在发表后完全消失（存在套利摩擦）；投资者从学术发表中学习并利用错误定价。§12.2 预测变量：97 个特征、来自 79 项研究、用公开数据，按数值/指示/三值分别构造多空组合。§12.3 实证设计：三时段（原样本期/样本后发表前/发表后）；三类解释（统计偏差、理性定价、错误定价）；基线回归 (12.1)、按类型 (12.2)、按套利成本 (12.3)（六类套利成本特征 + Corwin-Schultz 2012 价差）。§12.4 结果：图 12.1 摘要统计；(12.1) 估计图 12.2（样本外 −26%、发表后 −58%）；高样本内收益/t 值者下降更猛（图 12.3）；时段细分图 12.4；稳健性（时间趋势图 12.5、类型图 12.6、套利成本图 12.7）；交易活动图 12.8；发表后组合间相关性上升图 12.9。§12.5 贡献（首次比较样本内/外/发表后；调和 Jegadeesh-Titman 2001 与 Schwert 2003 的矛盾发现）。图 12.1–12.9 已转述（12.1 以表格重现）。

McLean & Pontiff (2016) 的核心发现 / core findings McLean & Pontiff (2016) 聚焦于 97 个被证明能预测横截面收益的变量的样本外与发表后可预测性。他们发现：样本外组合（脚注：组合为多空——同时买入收益最高的 20% 分位、卖空收益最低的 20% 分位）收益低 26%，这一下降反映统计偏差（数据挖掘）；发表后组合收益低 58%，在校正统计偏差后，发表本身解释了 32% 的异常收益下降。其中：(1) 对样本内收益更高、样本内 \(t\) 值更高的预测变量，下降更严重；(2) 对越容易套利的预测变量，发表后收益越低，而特质风险更高、流动性更低的组合则显示更高收益；(3) 已发表的预测变量在学术文章发表后彼此之间的相关性更强；(4) 该下降对一般时间趋势与时间固定效应都稳健；(5) 预测组合中的股票在发表后交易不同——组合内股票发表后交易量更大、空头一侧的股票发表后空头利益 (short interest) 更高。"可预测性在学术发表后完全消失"这一假说被拒绝——这反映市场中存在某种套利摩擦。他们因此得出结论：投资者从学术发表中学习并利用错误定价。McLean & Pontiff (2016) focus on the out-of-sample and post-publication return predictability of 97 variables shown to predict cross-sectional returns. They find: out-of-sample portfolio (footnote: the portfolio is long-short, simultaneously buying the top 20th percentile and selling the bottom 20th percentile based on each predictor) returns are 26% lower, a decline that reflects statistical bias (data mining); post-publication portfolio returns are 58% lower, and after correcting for the statistical bias, publication alone accounts for a 32% drop in abnormal returns. Among these: (1) the drop is more severe for predictors with higher in-sample returns and in-sample \(t\)-statistics; (2) post-publication returns are lower for predictors that are less costly to arbitrage, while portfolios with higher idiosyncratic risk and lower liquidity display higher returns; (3) published predictors have stronger correlations with each other after the publication of academic articles; (4) the drop is robust to a general time trend and to time fixed effects; (5) stocks in the predictor portfolios are traded differently post-publication — stocks within the portfolio have larger trading volume post-publication, and stocks on the short side have higher short interest post-publication. The hypothesis that predictability completely disappears after academic publication is rejected — this reflects that there are some arbitrage frictions in the market. They conclude that investors learn about and take advantage of mispricing from academic publications.

97 个特征及组合构造 / the 97 characteristics and portfolio construction 97 个特征：发表于经同行评审的金融、会计、经济学期刊、被证明能预测横截面收益；用公开可得数据；由 79 项不同研究识别，来源包括 Econlit 等搜索引擎（关键词"cross-section"）、书籍或其他论文的参考文献、其他金融教授的建议。并非完美复现每项研究——对某些研究，作者使用一个能抓住其要旨的特征（因 CRSP 数据集变化、或原文对计算细节描述不足）。对每个预测变量构造多空组合：若预测变量为数值型，则买入收益更高的 20% 分位、卖空收益更低的 20% 分位；若为指示型（共 16 个），则买入收益更高的指示类别、卖空收益更低的指示类别；若有三个离散值（多/空/中性；共 3 个），则按原文方式构造多空组合。The 97 characteristics: published in peer-reviewed finance, accounting, and economics journals and shown to predict cross-sectional returns; conducted with publicly available data; identified by 79 different studies, from sources including search engines such as Econlit (with the keyword "cross-section"), reference lists in books or other papers, and suggestions from other finance professors. They do not perfectly replicate each study — for some studies the authors use a characteristic that captures the gist (because of a changing CRSP data set, or insufficient description of calculation details in the original paper). For each predictor they construct a long-short portfolio: if the predictor is numeric, buy the 20th-percentile higher-return side and short-sell the 20th-percentile lower-return side; if the predictor is an indicator (16 in total), buy the indicator category with higher return and short-sell the category with lower return; if the predictor has three discrete values (long, short, neutral; 3 in total), construct a long-short portfolio in the same way as in the original paper.

三时段与三类解释 / three periods and three explanations 聚焦横截面收益可预测性。对 97 个预测变量中的每一个，考察三个时段：(1) 原研究的样本期；(2) 原研究样本之后、但研究发表之前的时段；(3) 发表后时段。对可预测性有三类解释：1. 统计偏差 (statistical bias)——由数据挖掘造成；众多聪明研究者日夜寻找好预测变量，很可能在未对多重检验适当校正的情况下找到一些样本内有效、实则虚假的预测变量；若存在统计偏差，则样本外可预测性应显著下降。2. 理性定价 (rational pricing)——反映风险的那部分可预测性；即便该可预测性被更广泛传播，它仍会持续。3. 错误定价 (mispricing)——精明投资者从发表中习得后会据以反向交易的那部分；故该部分在学术发表后应下降（甚至消失）——无摩擦时应消失，存在套利摩擦时不会消失但会衰减。The study focuses on cross-sectional return predictability. For each of the 97 predictors, it looks into three periods: (1) the original study's sample period; (2) the period after the original study's sample but before the publication of the study; (3) the post-publication period. There are three types of explanation for the predictability: 1. Statistical bias — caused by data mining; as many clever researchers try to find good predictors day and night, it's very likely they end up finding some in-sample predictors without properly adjusting for multiple testing that are indeed spurious; if there is statistical bias, the out-of-sample predictability should decline significantly. 2. Rational pricing — the part of predictability that reflects risks; even after it gets more publicity, it will still persist. 3. Mispricing — the part that sophisticated investors will trade against after they learn it from the publication; so this part should decrease (or even disappear) after academic publication — in the frictionless case it should disappear, and with arbitrage frictions it won't disappear but will decay.

三个回归模型 / the three regression models 基线回归 (12.1)：\(R_{i,t}=\alpha_i+\beta_1\cdot\text{Post Sample Dummy}_{i,t}+\beta_2\cdot\text{Post Publication Dummy}_{i,t}+e_{i,t}\)，其中 \(R_{i,t}\) 为预测变量 \(i\) 组合在第 \(t\) 月的月收益，\(\text{Post Sample Dummy}_{i,t}=1\) 当 \(t\) 在原文样本结束之后、发表之前，\(\text{Post Publication Dummy}_{i,t}=1\) 当 \(t\) 在原文发表之后。作者用可行广义最小二乘 (FGLS) 估计（预测变量收益间存在异方差、部分相关部分不相关）。\(\beta_1\) 是统计偏差的上界，因为它是统计偏差与错误定价的结合（论文以工作论文形式流传时，部分精明投资者可能已知该异象）。按类型的回归 (12.2)：\(R_{i,t}=\alpha_i+\beta_1\cdot\text{Post Publication Dummy}_{i,t}+\beta_2\cdot\text{Predictor Type Dummy}_{i,t}+\beta_3\cdot\text{Post Publication Dummy}_{i,t}\times\text{Predictor Type Dummy}_{i,t}+e_{i,t}\)，预测变量分四组：事件 (event)、市场 (market)、估值 (valuation)、基本面 (fundamentals)。按套利成本的回归 (12.3)：\(R_{i,t}=\alpha_i+\beta_1\cdot\text{Post Publication Dummy}_{i,t}+\beta_2\cdot\text{Arbitrage Cost}_i+\beta_3\cdot\text{Post Publication Dummy}_{i,t}\times\text{Arbitrage Cost}_i+e_{i,t}\)。套利成本算法：先按某特征（如规模或价差）对 CRSP 全部股票排名，按排名给每只股票赋 \(0\) 到 \(1\) 的值，取组合内全部股票该月特征的平均，再取该预测变量在样本内各月特征均值的平均。考察六类特征：1. 规模（市值）；2. 价差（按日内高低价估计的买卖价差，方法见 Corwin & Schultz 2012）；3. 美元成交量（成交股数 × 股价）；4. 特质风险（与市场和行业组合正交的日股票收益方差）；5. 股利（公司上一年付股利则为 1 的虚拟变量）；6. 指数（前五个度量的第一主成分）。Baseline regression (12.1): \(R_{i,t}=\alpha_i+\beta_1\cdot\text{Post Sample Dummy}_{i,t}+\beta_2\cdot\text{Post Publication Dummy}_{i,t}+e_{i,t}\), where \(R_{i,t}\) is the monthly return of predictor \(i\)'s portfolio in month \(t\), \(\text{Post Sample Dummy}_{i,t}=1\) if month \(t\) is after the end of the sample in the original paper but before publication, and \(\text{Post Publication Dummy}_{i,t}=1\) if month \(t\) is post-publication of the original paper. The authors use feasible generalized least squares (FGLS) for estimation (there is heteroskedasticity among predictor returns since some are correlated while others are not). \(\beta_1\) is an upper bound of the statistical bias because it's a combination of statistical bias and mispricing (some sophisticated investors may become aware of the anomaly when the paper is available as a working paper). Regression for different types (12.2): \(R_{i,t}=\alpha_i+\beta_1\cdot\text{Post Publication Dummy}_{i,t}+\beta_2\cdot\text{Predictor Type Dummy}_{i,t}+\beta_3\cdot\text{Post Publication Dummy}_{i,t}\times\text{Predictor Type Dummy}_{i,t}+e_{i,t}\), where the predictors are split into four groups: event, market, valuation, fundamentals. Regression for arbitrage costs (12.3): \(R_{i,t}=\alpha_i+\beta_1\cdot\text{Post Publication Dummy}_{i,t}+\beta_2\cdot\text{Arbitrage Cost}_i+\beta_3\cdot\text{Post Publication Dummy}_{i,t}\times\text{Arbitrage Cost}_i+e_{i,t}\). The arbitrage cost is calculated as: first rank all stocks in CRSP on a trait (e.g. size or spreads), assign each stock a value between 0 and 1 based on its rank, take the average trait of all stocks in the portfolio for that month, and then take the average of the predictor's monthly trait averages across months that are in-sample. Six categories of traits are considered: 1. Size (the market value); 2. Spreads (the bid-ask spread estimated by daily high and low prices, following the method in Corwin & Schultz 2012); 3. Dollar Volume (shares traded multiplied by stock price); 4. Idiosyncratic Risk (the variance of daily stock returns that are orthogonal to market and industry portfolios); 5. Dividends (a dummy that equals one if the firm paid a dividend during the last year); 6. Index (the first principal component of the other five measures).

基线回归结果与时段细分 / baseline results and period breakdown 由基线回归 (12.1)（图 12.2）：第 1 列——样本外组合收益低 26%（\(15.0\) 个基点 / 共 \(58.2\) 个基点）；发表后组合收益低 58%（\(33.7\) 个基点 / 共 \(58.2\) 个基点）。第 3、4 列——对样本内收益更高、样本内 \(t\) 值更高的预测变量，下降更严重（亦见图 12.3）。时段细分（图 12.4，相对样本内均值的月收益差）：样本内最后一年收益更高，暗示作者可能在某个精选时点停止取样；但样本外第一年的收益与样本内均值大致相同，又说明作者并非刻意挑停止年份（否则样本外第一年的相对收益应为负）。From the baseline regression (12.1) (Figure 12.2): Column 1 — out-of-sample portfolio returns are 26% lower (\(15.0\) bps out of \(58.2\) bps in total); post-publication portfolio returns are 58% lower (\(33.7\) bps out of \(58.2\) bps in total). Columns 3 and 4 — the drop is more severe for predictors with higher in-sample returns and in-sample \(t\)-statistics (also see Figure 12.3). Period breakdown (Figure 12.4, the difference in monthly returns relative to the in-sample mean): the last year in-sample has higher returns, implying the authors might have stopped their samples at a selected time; however, the first year out-of-sample has roughly the same return as the in-sample mean, which implies the authors were not picking the year to stop (otherwise the year-1 out-of-sample relative return should be negative).

稳健性、交易活动与相关性 / robustness, trading activity and correlations 稳健性——时间趋势与持续性（图 12.5）：Time = 1926 年 1 月之后的月数除以 100；Post-1993 为年份晚于 1993 则为 1 的指示变量；1-Month/12-Month Return 为预测变量上 1 个月/上 12 个月的收益。第 1 列负时间趋势（组合收益随时间下降）、第 3 列含时间趋势与 post-1993 虚拟、第 4 列含时间固定效应、第 5/6 列含动量；发表后下降对所有设定都稳健。稳健性——不同类型（(12.2)，图 12.6）：底行报告"该类型发表后收益是否不同于其他三类"的 \(p\) 值；发表后下降对不同类型稳健。套利成本（(12.3)，图 12.7）：末行报告 \(\beta_2+\beta_3\) 是否显著异于零；越难套利的预测变量发表后收益应越高，六类特征符号都正确、六中有五显著。交易活动（图 12.8）：Trading Volume 为成交股数、Variance 为月股票收益平方、Short interest 为做空股数/流通股数、Short-long short interest 为空头侧减多头侧的空头利益（若投资者识别错误定价，空头侧做空应多于多头侧）；组合内股票发表后交易量更大、空头侧股票发表后空头利益更高。相关性（图 12.9，预测变量收益对其他预测变量指数的回归）：In-Sample Index Return 为所有其他未发表预测组合的等权收益、Post-Publication Index Return 为所有其他已发表预测组合的等权收益；发表前收益与其他发表前收益高度相关（beta \(0.748\) 显著），发表前与其他发表后不显著相关（beta $-0.008$），发表后与其他发表前不显著相关（beta $0.748-0.674=0.074$ 近零），发表后与其他发表后高度相关（\(P\times\) Post-Publication Index Return 的交互系数为正且显著）。Robustness — time trend and persistence (Figure 12.5): Time = the number of months post-January 1926 divided by 100; Post-1993 is an indicator equal to one if the year is after 1993; 1-Month/12-Month Return is the predictor's return from the last 1/12 months. Column 1 has a negative time trend (portfolio returns declined over time), column 3 has both the time trend and the post-1993 dummy, column 4 has time fixed effects, and columns 5/6 have momentum; the post-publication decline is robust to all these settings. Robustness — different types ((12.2), Figure 12.6): the bottom row reports the \(p\)-value of the test of whether the post-publication returns of this type differ from the other three types; the post-publication decline is robust to different types. Arbitrage cost ((12.3), Figure 12.7): the last row reports whether \(\beta_2+\beta_3\) is significantly different from zero; predictors that are harder to arbitrage against should have higher post-publication returns, and all six traits have the correct sign, with five out of six significant. Trading activity (Figure 12.8): Trading Volume is shares traded, Variance is the monthly stock return squared, Short interest is shares shorted over shares outstanding, and Short-long short interest is the short interest on the short side minus that on the long side (if investors recognize mispricing, there should be more shorting on the short side than the long side); stocks within the portfolio have larger trading volume post-publication, and stocks on the short side have higher short interest post-publication. Correlations (Figure 12.9, a regression of predictor returns on an index of other predictors): the In-Sample Index Return is the equal-weighted return of all other unpublished predictor portfolios and the Post-Publication Index Return is the equal-weighted return of all other published predictor portfolios; pre-publication returns are highly correlated with other pre-publication returns (beta \(0.748\), significant), pre-publication is not significantly correlated with other post-publication (beta $-0.008$), post-publication is not significantly correlated with other pre-publication (beta $0.748-0.674=0.074$, almost zero), and post-publication is highly correlated with other post-publication (the interaction coefficient of \(P\times\) Post-Publication Index Return is positive and significant).

图 12.2–12.9（已转述 / Figures 12.2–12.9, paraphrased） 图 12.2（(12.1) 估计回归表）：Post-Sample 系数约 $-0.150$、Post-Publication 约 $-0.337$（均显著），列 3/4 加入"× 样本内均值"、"× 样本内 \(t\) 值"交互项（显著为负）。图 12.3：散点图 (a) 样本内收益、(b) 样本内 \(t\) 值（纵轴）对"发表后收益下降量"（横轴），均呈正斜率拟合线——样本内表现越强、发表后下降越大。图 12.4：按"样本内最后一年 / 样本外第 1 年 / 发表后第 1–5 年"等时段画条，纵轴为相对样本内均值的月收益差。图 12.5/12.6/12.7：分别为时间趋势/类型/套利成本的回归表。图 12.8：交易活动回归表（成交量、方差、空头利益、空头−多头空头利益）。图 12.9：相关性回归表。Figure 12.2 ((12.1) estimate regression table): the Post-Sample coefficient is about $-0.150$ and the Post-Publication about $-0.337$ (both significant), with columns 3/4 adding "× in-sample mean" and "× in-sample \(t\)-statistic" interactions (significantly negative). Figure 12.3: scatter plots of (a) in-sample return and (b) in-sample \(t\)-statistic (vertical axis) against the "decline in returns post-publication" (horizontal axis), both with positive-slope fitted lines — the stronger the in-sample performance, the larger the post-publication drop. Figure 12.4: bars by period ("last year in-sample / year 1 out-of-sample / post-publication years 1–5", etc.), the vertical axis the difference in monthly returns relative to the in-sample mean. Figures 12.5/12.6/12.7: regression tables for the time trend / type / arbitrage cost respectively. Figure 12.8: a trading-activity regression table (volume, variance, short interest, short-long short interest). Figure 12.9: a correlation regression table.

本文贡献 / contributions of this paper 此前没有研究对大样本预测变量比较其样本内收益、样本外收益与发表后收益。本文为文献提供了一致的证据，而此前研究对"发表对错误定价的影响"有相互矛盾的发现：Jegadeesh & Titman (2001) 发现高动量股的相对收益自动量论文 Jegadeesh & Titman (1993) 发表以来增加了；Schwert (2003) 则讨论了基于价值与规模因子的指数基金在这些因子被发表后不再能产生 alpha。No study had compared in-sample returns, out-of-sample returns, and post-publication returns for a large sample of predictors. This paper provides consistent evidence to the literature, which had previous studies showing contradictory findings about the publication effect on mispricing: Jegadeesh & Titman (2001) find the relative returns to high-momentum stocks have increased since the publication of the momentum paper Jegadeesh & Titman (1993); Schwert (2003) discusses that index funds based on value and size factors cannot generate alpha anymore after the publication of those factors.