Abstract

Notes for reading papers

• Empirical Cross-Sectional Asset Pricing
• Choosing Factors
• A five-factor asset pricing model

Empircal Cross-Sectional Asset Pricing

概述

• It is a fundamental question of financial economics whether assets with different risk exposures and characteristics are priced to earn different rates of return. I survey studies in empirical cross-sectional asset pricing that provide evidence on this question and relate the evidence to models of investor preferences and beliefs. I begin by laying out a framework that will be helpful for categorizing and interpreting empirical work in this area. (金融经济学的一个基本问题是，对 不同风险敞口和特征的资产的定价能够获得不同的回报率。 我调查了在实证横截面资产定价方面的研究， 这些研究为这个问题提供了证据，并将证据与投资者偏好和信念模型联系起来。 我首先列出一个框架，这将有助于对这一领域的实证工作进行分类和解释。)
• Stochastic discount factor (SDF): 随机贴现因子，The law of one price implies that a stochastic discount factor (SDF) exists such that (1) holds, and it can be constructed as a linear combination of the asset payoffs [Hansen and Richard (1987]). (可以被构造为资产收益的线性组合。) Researchers often look to enrich the specification of investors’ preferences or the dynamics of risks to enhance the pricing performance of models (研究人员通常希望丰富投资者偏好或风险动态的specification， 以提高模型的定价性能)
• Sentiment ( 情绪 ): Since the boundary between rational theories and sentiment approaches is fuzzy, I refrain from using the somewhat simplistic categorization of cross-sectional asset-pricing studies into “rational” and “irrational”, or “behavioral,” approaches. (我用“情绪”这个标签来描述这种预期的形成。 由于理性理论和情绪方法之间的界限是模糊的， 我避免将 cross-sectional 资产定价研究简单分类为“理性”和“非理性”或“行为”方法。)
• Frictions (摩擦): Frictions can affect the SDF in several ways. Frictions may prevent participation of some classes of investors in the market. Frictions can also give rise to risks that are of concern to investors, such as liquidity risk. ( 摩擦可以通过多种方式影响SDF。 摩擦可能会阻碍某些类别的投资者参与市场。 摩擦还可能引发投资者关注的风险，如流动性风险) Frictions also play an important role in the sentiment-based approaches in Section 5 as an explanation as to why sophisticated investors—whose beliefs may be closer to the Bayesian learning or rational-expectations benchmarks may be unable to exploit and eliminate the effects of sentiment on asset prices. (摩擦在第5节基于情绪的方法中也起着重要作用， 这解释了为什么老练的投资人的投资理念可能更接近贝叶斯学习 或理性预期基准的成熟投资者可能无法利用和消除情绪对资产价格的影响)
• Data Snooping (数据窥探): One problem that plagues cross-sectional asset pricing is that much of the empirical work in this area is inherently a search for anomalies. (困扰cross-sectional资产定价的一个问题是，该领域的许多实证工作本质上是寻找 anomalies). When researchers search over a large number of candidate predictors for predictability that is unexplained by standard models of the SDF, it is inevitable that some turn up as “significant” just by pure chance. Conventional procedures of statistical inference do not account for this search over many candidate predictors. The out-of-sample tests reviewed in Section 6 can help shed light on this problem. (当研究人员在大量候选预测因子中寻找SDF标准模型无法解释的可预测性时， 不可避免的是，一些预测因子仅仅是偶然出现的“显著性”。 传统的统计推断程序没有考虑对许多候选预测因子的搜索。第6节中回顾的样本外测试有助于阐明这个问题。).
• Market efficiency (市场有效性)： Empirical work on cross-sectional return predictability is often discussed as the study of market efficiency, but the meaning of this concept is not clearly defined, which limits its usefulness as an organizing principle. (关于cross-sectional 可预测性的实证工作经常被讨论为市场效率的研究， 但这一概念的含义没有明确定义，这限制了其作为 organizing principle 的实用性。).
• Market efficiency ( 市场有效性 ): Fama (1970) defines a (semi-strongly) efficient market as one that always “fully reflects” all available (public) information, but it is not clear whether “fully reflect” refers to the demanding notion of rational expectations (this is the view taken in Jensen (1978)), or whether the notion of market efficiency should allow for learning and adaptation (Schwert (2003) and Timmermann and Granger (2004) propose this interpretation). Frictions and risks further obscure the precise meaning of market efficiency. (Fama（1970） 将semi-strongly（半强）有效市场定义为始终“充分反映”所有 可用（公共）信息的市场，但不清楚“完全反映”是否指理性预期的苛刻概念（这是[Jensen（1978）]的观点）， 或者市场效率的概念是否应该允许学习和适应（[Schwert（2003）和Timmermann和Granger（2004）]提出了这种解释）。 摩擦和风险进一步模糊了市场效率的确切含义).
• Market efficienty ( 市场有效性 ): Jensen (1978) augments his rational-expectations definition of market efficiency by suggesting that market efficiency should be defined as the “absence of profit opportunities” from trading on public information.
  ( Jensen（1978） 通过建议将市场效率定义为公共信息交易中的“无盈利机会”， 增强了他对市场效率的理性预期定义。)
• Market efficienty ( 市场有效性 ): Yet, in a market in which sophisticated and sentiment-driven investors trade, it is possible that sentiment affects prices, yet sophisticated investors do not perceive any abnormal profit opportunities given the frictions and risks that they face. ( 然而，在一个成熟且情绪驱动的投资者交易的市场中，情绪可能会影响价格， 但成熟的投资者在面临摩擦和风险的情况下，不会察觉到任何异常利润机会。 ).
• Market efficienty ( 市场有效性 ): If one defines such a market as efficient, efficiency becomes a largely empty concept because it does not distinguish between interesting alternative hypotheses (rational expectations, learning sentiment) of how investors price assets. For these reasons, I prefer to explicitly spell out the belief-formation hypothesis that researchers work with, rather than relying on the imprecise notion of market efficiency. ( 如果将这样一个市场定义为有效市场，那么效率在很大程度上就是一个空洞的概念， 因为它没有区分投资者如何定价资产的有趣的替代假设（理性预期、学习情绪）。 出于这些原因，我更愿意明确阐述研究人员所使用的信念形成假设， 而不是依赖于不精确的市场效率概念。 )

Cross-Sectional Return Predictability

Technical Predictors ( 技术类 predictor ):

• Technical Predictors (技术类 predictor): The history of return and trading volume of a stock is a natural place to look for return predictors, and the data are easily accessible. In the practice of investment management, predictors of this kind are in the realm of “technical analysis”. (股票回报和交易量的历史是寻找回报预测因子的自然场所，数据很容易获取。 在投资管理实践中，此类预测属于“技术分析”领域).
• Technical Predictors:
  One of the most studied predictability patterns in this area is the momentum effect that entered the academic literature with Jegadeesh and Titman (1993). Jegadeesh and Titman show that stocks with high returns over the past three to twelve months (winners) outperform stocks with low recent returns (losers) over the next three to twelve months. A related phenomenon is the post earnings-announcement drift 该领域研究最多的可预测性模式之一是 [Jegadeesh和Titman（1993）]写入学术文献的动量效应。 Jegadeesh和Titman表明， 在过去三到十二个月内回报率高的股票（赢家）在未来三到十二月内表现 优于近期回报率低的股票（输家）。一个相关的现象是盈利公告后的漂移。
• Technical Predictors: Over longer horizons, in contrast, returns have a tendency to mean-revert, as shown in DeBondt and Thaler (1985) and DeBondt and Thaler (1987): Winners over the past three to five years underperform losers. Jegadeesh and Titman (2001) find that the momentum effect dies out after a holding period of about 12 months, and returns then start to revert at longer holding periods. (相比之下，在更长的时间范围内，回报率有均值回归的趋势， 如[DeBondt和Thaler（1985）]以及[DeBondt和Thaller（1987）]所示： 过去三到五年的赢家表现不如输家。[Jegadeesh和Titman（2001）]发现，动量效应 在大约12个月的持有期后消失，然后在更长的持有期内开始恢复。)

Valuation Ratios and Profitability (估值比例和盈利能力)

• A second category of predictors can be motivated within a simple present-value framework. Vuolteenaho (2000) and Cohen, Polk, and Vuolteenaho (2003) build on the log-linear present value model of Campbell and Shiller (1988) to formulate a present-value relationship in terms of the book-to-market (B/M) ratio. (第二类预测因子可以在简单的现值框架内得到。 Vulteenaho（2000年）和Cohen、Polk和Vulteinaho（2003年） 基于Campbell和Shiller（1988年）的对数线性现值模型， 以账面与市场（B/M）比率的形式建立现值关系。)

Firm Investment and Financing

• Theories of firms’ investment and financing can provide further insights about potential predictors of returns. According to the q-theory of investment, firm investment is positively related to expected profitability and negatively related to discount rates and hence future stock returns. Li, Livdan, and Zhang (2009) provide a recent exposition of this mechanism. Titman, Wei, and Xie (2004), Fama and French (2006), Anderson and Garcia-Feij´oo (2006), and Li, Livdan, and Zhang (2009) find evidence consistent with this prediction. ( 企业投资和融资理论可以提供关于潜在回报预测因素的进一步见解。 根据投资的q理论，公司投资与预期盈利能力正相关，与贴现率负相关，因此与未来股票回报率负相关。 [Li、Livdan和Zhang（2009）]最近对这种机制进行了阐述。 [Titman、Wei和Xie（2004年）]、[Fama和French（2006年）]、 [Anderson和Garcia Feij‘oo（2006）] 以及 [Li、Livdan和Zhang（2009年）] 发现了与这一预测一致的证据。)

• High-investment firms are also likely to raise external financing, while firms with low investment rates distribute capital to investors. As a result, discount rates are also negatively related to external financing (see, e.g., Li, Livdan, and Zhang (2009)). Consistent with this prediction, Daniel and Titman (2006), Fama and French (2008), and Pontiff and Woodgate (2008) construct measures of net equity issuance activity and find a negative relationship to future stock returns. (高投资公司也可能筹集外部融资，而低投资率的公司则将资本分配给投资者。 因此，贴现率也与外部融资呈负相关（见Li、Livdan和Zhang（2009））。 与此预测一致，Daniel和Titman（2006年）、Fama和French（2008年）、 Pontiff和Woodgate（2008年）构建了净股票发行活动的度量， 并发现与未来股票回报呈负相关。)

• High levels of investment and external financing also translate into higher growth. Therefore, one would expect a negative association between growth and future returns. Lakonishok, Shleifer, and Vishny (1994) document a negative relation between past sales growth and returns. Cooper, Gulen, and Schill (2008) look at growth in total assets and find a negative correlation with future returns (高水平的投资和外部融资也转化为更高的增长。 因此，人们预计增长与未来回报之间存在负关联。 [Lakonishok、Shleifer和Vishny（1994）] 记录了过去的销售增长和回报之间的负关系。 [Cooper、Gulen和Schill（2008）] 研究了总资产的增长， 发现其与未来回报呈负相关)

• Investment and growth are also related to accruals. Fairfield, Whisenant, and Yohn (2003) argue that high-growth firms tend to be high-accrual firms, suggesting that the relationship between accruals and expected returns of Sloan (1996) may be a growth effect. Lewellen and Resutek (2012) however show that investment, external financing, and accruals all have distinct roles in predicting returns. (投资和增长也与应计项目有关。[Fairfield、Whisenant和Yohn（2003）]认为， 高增长企业往往是高应计企业，这表明[斯隆（1996）]的应计利润和预期回报之间的关系可能是一种增长效应。 然而，[Lewellen和Resutek（2012）]表明，投资、外部融资和应计项目在预测回报方面都有不同的作用。)

• While q-theory is useful for identifying potential cross-sectional predictors of returns, the theory is silent about the reasons why investors price stocks to have different expected rates of return. The evidence that investment- and financing-related variables predict returns does not reveal whether priced risk under rational expectations, investor learning, or sentiment are the drivers of the discount rates that firms face in financial markets and that they respond to in their investment and financing decisions. (虽然q理论有助于识别潜在的横截面回报预测因子， 但该理论对投资者为具有不同预期回报率的股票定价的原因保持沉默。 投资和融资相关变量预测回报的证据并未揭示理性预期下的定价风险、 投资者学习或情绪是否是公司在金融市场面临的贴现率的驱动因素， 以及它们在投资和融资决策中的反应。)

Idiosyncratic risk (特殊风险)

• Theories in which idiosyncratic volatility plays a role in pricing typically predict a positive relation between idiosyncratic volatility and expected returns. For example, in Merton (1987) a positive relationship arises because investors are imperfectly diversified and demand compensation for bearing idiosyncratic volatility (特殊波动率在定价中起作用的理论通常 预测特殊波动率和预期回报之间的正关系。 例如，在Merton（1987）中，正相关关系出现， 因为投资者不完全多样化，并要求补偿承受的特殊波动)

• Empirically, Ang, Hodrick, Xing, and Zhang (2006) find the opposite result: stocks with high idiosyncratic volatility have extremely low returns. Huang, Liu, Rhee, and Zhang (2010) caution that this idiosyncratic volatility effect seems to be driven by the return reversals known to exist in one-month returns (Jegadeesh (1990)). (实证方面，[Ang、Hodrick、Xing和Zhang（2006）]发现了相反的结果：具有高特质波动率 的股票回报极低。 [Huang、Liu、Rhee和Zhang（2010）]警告称，这种特殊的波动性效应似乎是 由一个月收益中已知存在的收益反转驱动的（Jegadeesh（1990））。)

• Idiosyncratic volatility is also one of the variables used in the distress-prediction model of Campbell, Hilscher, and Szilagyi (2008) and the sign of the effect in their framework is consistent with the findings of Ang et al. (特质波动率也是[Campbell、Hilscher和Szilagyi（2008）] 的 困境预测模型中使用的变量之一， 其框架中的效应符号与Ang等人的发现一致。)

Seasonality ( 季节性 )

• One puzzling feature of cross-sectional return predicability is that it is subject to strong seasonality. Novy-Marx (2012b) offers an updated view based on recent data. He documents that many of the cross-sectional return predictors reviewed in this section have a strong January seasonal: size and value effects, for example, are concentrated in January, while momentum and profitability-related predictability is weaker in January. The research reviewed in this survey is silent about the source of this seasonality. (横截面收益率可预测性的一个令人费解的特征是它受强季节性的影响。 [Novy Marx（2012b）] 提供了基于最新数据的更新视图。 他记录了本节中回顾的许多横截面收益预测具有强烈的一月季节性： 例如，规模和价值效应集中在一月，而与动量和盈利能力相关的可预测性在一月较弱。 本次调查中回顾的研究没有提到这种季节性的来源。)

Linear Factor Models

Canonical Models

• Most empirical studies in cross-sectional asset pricing employ (log-)linear factor representations of the SDF. Typically, the SDF specifications in cross -sectional asset pricing studies are special cases of the SDF that arises in a representative-agent framework in which the representative investor has the preferences proposed by Epstein and Zin (1989), Epstein and Zin (1991), and Weil (1990). (横截面资产定价中的大多数实证研究采用 SDF 的（对数）线性因子表示。 通常，横断面资产定价研究中的 SDF 规范是代表性代理框架中出现的SDF的特例， 其中代表性投资者具有[Epstein和Zin（1989）]、[Epstein和Zin（1991）] 和[Weil（1990）]提出的偏好。)

Ad-hoc Factor Models

• The failure of the (consumption) CAPM to explain cross-sectional return predictability has prompted some researchers to resort to ad-hoc factor models. The motivation for this approach is the insight that risk factors in the SDF can be replaced by their mimicking portfolios. The most prominent example is the Fama and French (1993) three-factor model, in which the SDF is specified as a linear function of a market index return, RM, the difference in returns between portfolios of small and large stocks, SMB, and the difference in returns between portfolios of high and low B/M stocks, HML. (资本资产定价模型未能解释横截面收益的可预测性， 这促使一些研究人员求助于特殊因素模型。 采用这种方法的动机是洞察到SDF中的风险因素可以被其模拟投资组合所取代。 最突出的例子是Fama和French（1993）三因素模型， 其中SDF被指定为市场指数回报率RM、 小型和大型股票组合之间的回报差异SMB以及高B/M和低B/M股票组合之间回报差异HML的线性函数。)

Fama and French models

• Fama and French (1993) show that this model captures most of the cross-sectional variation in average returns of 25 portfolios sorted by size and B/M. (Fama和French（1993）表明，该模型捕捉了按规模和B/M排序的 25个投资组合平均回报的大部分横截面变化。)

• SMB and HML are constructed from portfolios that span the very same expected return spreads along the size and B/M dimensions that the model is trying to explain. Is the model therefore tautological? (SMB和HML是从投资组合中构建的， 这些投资组合沿着模型试图解释的规模和B/M维度跨越了非常相同的预期收益利差。 因此，这个模型是重言式的吗)

• Not entirely. The economic content in Fama and French (1993) is in the finding that the three factors explain not only cross-sectional, but also most of the timeseries variation in the size and B/M portfolios, with time-series R2 in excess of 90%. (不完全是。 Fama和French（1993）的经济内容在于发现这三个因素不仅解释了横截面， 而且还解释了规模和B/M投资组合中的大多数时间序列变化，时间序列R2超过90%。)

• This shows that small firms’ returns, for example, correlate a lot more strongly with almost-small firms’ returns than with large firms’ returns (这表明，例如，小公司的回报与几乎小公司的收益的相关性要比与大公司的回报的相关性强得多)

• However, given this strong co-movement, it is not surprising that expected returns of small firms are similar to those of almost-small firms and value stocks’ expected returns are similar to those of almost-value stocks in the way captured by the factor model; otherwise a near-arbitrage opportunity would arise. (然而，考虑到这种强烈的协同运动，小公司的预期收益与几乎小公司的相似并不令人惊讶， 价值股的预期收益在因子模型中与几乎价值股的相似；否则，将出现近乎套利的机会。)

• Absence of near-arbitrage opportunities arises in any model under minimal restrictions on preferences and beliefs (e.g., as in Ross (1976) and Cochrane and Sa´a-Requejo (2000)), and these weak restrictions hold in (plausible) models of sentiment and models of learning just as well as in rational expectations models. (在偏好和信念受到最小限制的任何模型中（如[罗斯（1976）和科克伦（Cochrane）和萨阿雷奎乔（2000）]） 都不存在近套利机会，这些弱限制在情绪模型和学习模型以及理性预期模型中同样适用。)

• Therefore, the fact that the Fama-French model explains size and B/M returns does not discriminate between these competing explanations。 (因此，Fama-French模型解释了规模和B/M回报， 这一事实并不区分这些相互竞争的解释)

• Fama and French (1993) suggest that SMB and HML could mimick pervasive priced macroeconomic risk factors. If so, then SMB and HML should explain other features of the cross-section of expected returns, too, not just size and B/M effects (Fama和French（1993）提出，中小企业和HML可以模拟普遍存在的定价宏观经济风险因素。 如果是这样，那么SMB和HML也应该解释预期收益横截面的其他特征， 而不仅仅是规模和B/M效应)

• Fama and French (1996) argue that this is the case because the three-factor model also explains the expected return variation related to earnings/price, cash-flow/price, sales growth, and long-term reversals. However, all of these variables are closely related to B/M (Fama和French（1996）认为这是因为三因素模型也解释了与收益/价格、 现金流/价格、销售增长和长期反转相关的预期回报变化。 然而，所有这些变量都与B/M密切相关)

• The one anomaly in their tests—momentum—that is not, fails to be explained by the three-factor model. (他们测试中的一个反常现象，即动量，不能用三因素模型来解释。)

• The empirical evidence accumulated since Fama and French (1996) suggests that there are other important sources of cross-sectional variation in expected returns unrelated to the Fama-French factors. Most of the cross-sectional return predictors reviewed in Section 2 have predictive power after adjusting for exposure to the Fama-French factors. (自Fama和French（1996）以来积累的经验证据表明， 与Fama-French因素无关的预期回报的横截面变化还有其他重要来源。 第2节中回顾的大多数横断面回归预测因子在调整暴露于Fama-French因素后具有预测能力。)

• To name a few, the idiosyncratic volatility anomaly (Ang, Hodrick, Xing, and Zhang (2006)), the net equity issuance effect (Daniel and Titman (2006)), and the predictability associated with gross-profitability (Novy-Marx (2012a)) are all present after risk-adjusting returns with the Fama-French factors. ( 举几个例子， 特殊波动异常（[Ang、Hodrick、Xing和Zhang（2006）]）、 净股票发行效应（[Daniel和Titman（2006）]）， 以及与总盈利能力相关的可预测性（[Novy Marx（2012a）]） 都是在使用Fama-French因素进行风险调整后出现的。 )

• Lewellen (2011) looks at portfolios sorted on a composite measure of expected returns that combines many known predictors and his portfolios exhibit large abnormal returns after adjusting for exposure to the Fama French factors. ([Lewellen（2011年）]研究了根据预期收益综合测度排序的投资组合， 该指标结合了许多已知的预测因素， 他的投资组合在调整了暴露于Fama-French因素后显示出巨大的异常收益.)

• Judging from this evidence, the Fama-French factors seem to be a convenient way of summarizing the size and value effects, but not more than that. To capture other dimensions of cross-sectional predictability, too, researchers have proposed alternative factors. (从这一证据来看，Fama-French因素似乎是总结规模和价值效应的一种方便方法， 但仅此而已。为了获取横截面可预测性的其他维度，研究人员也提出了替代因素。)

• Judging from this evidence, the Fama-French factors seem to be a convenient way of summarizing the size and value effects, but not more than that. To capture other dimensions of cross-sectional predictability, too, researchers have proposed alternative factors (从这一证据来看，Fama-French因素似乎是总结规模和价值效应的一种方便方法， 但仅此而已。为了获取横截面可预测性的其他维度，研究人员也提出了替代因素。)

• Carhart (1997) adds a momentum factor to the Fama-French model. Novy-Marx (2012a) proposes a gross-profitability factor. Hou, Xue, and Zhang (2012) construct a four-factor model with a market factor, a size factor, an investment factor, and an ROE factor.

• The use of profitability and investment-related factors is motivated by the present-value relationships and q-theoretic models discussed above in Sections 2.2 and 2.3. Of course, one must keep in mind that present value relationships and q-theory do not answer the question why investors price stocks to have these differences in expected returns. (盈利能力和投资相关因素的使用是由上述第2.2节和第2.3节中讨论的现值关系和q理论模型推动的。 当然，必须记住，现值关系和q理论并不能回答投资者为什么对股票定价以获得这些预期回报差异的问题。)

Choosing factors (Eugene F. Fama, Kenneth R. French, 2018)

概述

Fama French 6 factor models

• Our goal is to develop insights about the maximum squared Sharpe ratio for model factors as a metric for ranking asset pricing models. We consider nested and non-nested models. The nested models are the capital asset pricing model, the three-factor model of Fama and French (1993), the five-factor extension in Fama and French (2015), and a six-factor model that adds a momentum factor. The non-nested models examine three issues about factor choice in the six-factor model: (1) cash profitability versus operating profitability as the variable used to construct profitability factors, (2) long-short spread factors versus excess return factors, and (3) factors that use small or big stocks versus factors that use both. (我们的目标是深入了解模型因素的最大平方夏普比率， 作为对资产定价模型进行排名的指标。 我们考虑嵌套和非嵌套模型。 嵌套模型是资本资产定价模型、Fama 和 French (1993) 的三因子模型、Fama 和 French (2015) 的五因子扩展模型以及添加动量因子的六因子模型。非嵌套模型考察了六因子模型中关于因子选择的三个问题： （1）现金盈利能力与经营盈利能力作为构建盈利能力因素的变量， （2）多空利差因素与超额收益因素， 以及（ 3) 使用小股票或大股票的因子与同时使用两者的因子。 )

A five-factor asset pricing model (Eugene F. Fama, Kenneth R. French, 2015)

概述

Fama French 5-factor model

• Tutorials for Fama French Five Factors Model.
• A five-factor model directed at capturing the size, value, profitability, and investment patterns in average stock returns performs better than the three-factor model of Fama and French (FF, 1993). The five-factor model׳s main problem is its failure to capture the low average returns on small stocks whose returns behave like those of firms that invest a lot despite low profitability. The model׳s performance is not sensitive to the way its factors are defined. With the addition of profitability and investment factors, the value factor of the FF three-factor model becomes redundant for describing average returns in the sample we examine. (五因素模型旨在捕捉股票平均回报中的规模、价值、盈利能力和投资模式， 其性能优于 Fama 和 French 的三因素模型（FF，1993 年）。五因素模型的主要问题是 它未能捕捉到小型股票的低平均回报， 这些股票的回报表现类似于尽管盈利能力低但投资很多的公司。 该模型的性能对其因子的定义方式不敏感。随着盈利能力和投资因素的加入， FF 三因素模型的价值因素对于描述我们检查的样本中的平均回报变得多余)