Part II 导读 / Part II overview Part II 行为金融（Ch 8–12）：行为金融可大致定义为"任何未被标准的、价格由理性主体在无摩擦市场中决定的模型完全刻画的东西"，但并无权威定义——只要是在回答一个重要的金融问题，是否"行为"其实并不那么重要。Ch 8 有效市场假说 (EMH) 与其检验；Ch 9 对 EMH 的表观违背（弱式/半强式异象）；Ch 10 心理学；Ch 11 投资者交易行为；Ch 12 学术研究与股票收益可预测性（McLean–Pontiff 2016）。

本章导读 §8.1 前 EMH 时代：1960 年代前的两类投资法——基本面分析（Benjamin & Dodd 1934）与技术分析。§8.2 有效市场假说 (EMH)：价格充分反映所有可得信息，\(P_t=\mathbb{E}_t[\sum_\tau CF_{t+\tau}/(1+R)^{t+\tau}]\) (8.1)；Fama (1970) 三种形式——弱式（历史价格/收益）、半强式（所有公开信息）、强式（公开 + 私有信息）。§8.3 用供求解读 EMH：供给短期固定，价格波动只反映需求侧的信息变化，无新信息则总需求平坦；三种辩护（人人理性 / 非理性者相互抵消即噪声交易者 / 深口袋套利者）。§8.4 EMH 的检验：直接检验受联合假设问题困扰（拒绝 EMH 可能只是模型错误）；间接检验（事件研究 Fama et al. 1969，940 次股票拆分，半强式 EMH，图 8.1），但仍有"用哪个收益模型"的问题。图 8.1 已转述。

EMH 的数学表述与三种形式 / EMH formula and three forms 数学上，EMH 意味着资产的实际价格 \(P_t\) 应等于其基本价值（由所有未来现金流的折现之和定义）：Mathematically, the EMH implies that the actual price of an asset \(P_t\) should be equal to its fundamental value, defined by the sum of all discounted future cash flows:

$$P_t=\mathbb{E}_t\!\left[\sum_{\tau=1}^{\infty}\frac{CF_{t+\tau}}{(1+R)^{t+\tau}}\right]\tag{8.1}$$

其中 \(CF_{t+\tau}\) 为 \(t+\tau\) 时的现金流、\(R\) 为基于风险的收益率（更一般地可随时间变化）。Fama (1970) 讨论三种市场有效性：(1) 弱式 (weak form)——历史价格与收益已高效纳入当前价格（换言之，历史价格与收益不能用于预测未来收益）；(2) 半强式 (semi-strong form)——所有公开可得信息已高效纳入当前价格；(3) 强式 (strong form)——所有公开与私有信息都已高效纳入当前价格。若 EMH 成立，则除信息输入外，没有任何东西能改变价格。where \(CF_{t+\tau}\) is the cash flow at time \(t+\tau\) and \(R\) is the risk-based return that can be more generally time-varying. Fama (1970) discusses three types of market efficiency: (1) weak form — past prices and returns are efficiently included in the current price (in other words, past prices and returns cannot be used to predict future returns); (2) semi-strong form — all publicly available information is efficiently included in the current price; (3) strong form — all public and private information is efficiently included in the current price. If EMH is true, then nothing other than information input can change the prices.

平坦的总需求及其三种辩护 / flat aggregate demand and its three justifications 把资产价格 \(P_t\) 看作市场出清价格。供给：证券由特定公司供给，合理假设其短期供给固定。需求：既然供给固定，价格波动就只能反映需求侧的波动；EMH 简单假设所有价格波动都是信息变化的结果，故只要没有新信息，价格就完全不变——即无新信息到达时，证券的总需求应是平坦的。辩护：平坦的总需求看似是个疯狂的假设，需要论证。通常有三种辩护：(1) 人人理性——每个投资者都与"价格应该是多少"完全一致：价格低于公认价就人人买入、高于就人人卖出，价格调整到恰好等于公认价，总需求基于供求保持恒定。(2) 有人理性、有人非理性，但非理性者相互抵消——投资者信念存在对称结构，过度悲观与过度乐观的非理性者对总需求与市场价格的影响净为零；这些非理性投资者被称为噪声交易者 (noise traders)（脚注：把非理性投资者假设为噪声交易者并不是有吸引力的建模假设，因为我们更关心人们某些系统性有偏的行为及其影响）。(3) 深口袋套利者——套利者有近乎无限的资金与资源去利用价格偏离，直到价格回到理性价；若这种套利力量足够大，EMH 支持者便认为市场价格仍高效反映信息、别无其他（脚注：这一想法的一大问题是，套利者有时会把事情弄得更糟，而非纠正市场）。Consider the asset price \(P_t\) as the market-clearing price. Supply: a security is supplied by a specific firm, and we reasonably suppose its supply is fixed in the short term. Demand: since supply is fixed, price fluctuations must only reflect fluctuations on the demand side; EMH simply assumes all price fluctuations are results of information changes, so as long as no new information is available the price should not change at all — i.e. the aggregate demand for a security should be flat when there is no arrival of new information. Justification: a flat aggregate demand seems like a crazy assumption and certainly needs justifications. Typically there are three: (1) Everyone is rational — every investor agrees exactly with what the price should be: everyone buys if the price goes below the commonly agreed price and everyone sells if it goes above, so the price adjusts to exactly equal the commonly agreed price and aggregate demand is constant based on the supply-demand story. (2) Some people are rational and some are not, but the irrational investors cancel out — there is a symmetric structure of investors' beliefs such that overly pessimistic and overly optimistic irrational investors net to zero impact on aggregate demand and the market price; these irrational investors are called noise traders (footnote: assuming irrational investors are noise traders is not an attractive modeling assumption, because we are more interested in some potentially systematically biased behaviors people have and the impacts of those biases). (3) Deep-pocket arbitrageurs — arbitrageurs have an almost infinite amount of money and resources to take advantage of a price deviation until it goes back to the rational price; if such arbitraging force is large enough, EMH advocates believe the market price still efficiently reflects the information and nothing else (footnote: a big problem of this idea is that sometimes arbitrageurs make it a lot worse, rather than correcting the market).

直接检验与联合假设问题 / Direct testing and the joint hypothesis problem 直接检验：直接检验 (8.1)。这很难，因为永远不可能找到完美的现金流预测模型与完美的基于风险的折现因子模型。直接检验常受联合假设问题 (joint hypothesis testing problem) 困扰：做检验时总要提出一个折现因子与现金流预测模型，而所提模型不保证正确；于是"用所提模型检验 EMH"实际上是在联合检验 EMH 与所提模型。若检验拒绝了 EMH，其实并非真的拒绝 EMH，而是拒绝了"EMH 与所提模型都正确"这一联合假设。简言之，直接检验中的拒绝可能只是模型错误的结果，并不能说明 EMH 的有效性。Direct testing: directly test (8.1). This is hard because it's always impossible to figure out a perfect model for cash flow forecast and a perfect risk-based model for the discount factor. Direct testing often suffers from the joint hypothesis testing problem: when conducting the tests, people always need to propose a model for discount factors and cash flow forecasts, and the proposed models are not guaranteed to be correct; so when testing EMH with the proposed models, it's actually testing jointly the EMH and the proposed model. If the test rejects EMH, it's not really rejecting EMH but actually rejecting the joint hypothesis that both EMH and the proposed model are correct. In short, rejection in direct testing may be a result of a false model, not saying anything about the validity of EMH.

间接检验：事件研究 Fama et al. (1969) / Indirect testing: the event study 间接检验：对折现率（收益）的基线模型做假设，但不预测未来现金流。例如 Fama et al. (1969) 做了一项事件研究（首个事件研究），对 940 次股票拆分检验半强式 EMH。事件研究（脚注：更多细节见 He 2019a 第 18.10 节）：先选一个模型（脚注：Fama et al. 1969 选的是 CAPM）来预测预期收益 \(\mathbb{E}_t[R_{i,t+1}]\)；设事件发生在第 \(t\) 天，记 \(t\) 到 \(t+1\) 的实际收益为 \(\tilde R_{i,t+1}\)；定义股票 \(i\) 的异常收益 \(AR_{i,t+1}=\tilde R_{i,t+1}-\mathbb{E}_t[R_{i,t+1}]\)；对每只股票算此异常收益，再在横截面上取平均以估计事件异常收益。半强式 EMH 认为：股票拆分作为纯粹"装饰性"的变动，在其发生并成为公开信息后不应再对价格有影响。Fama et al. (1969) 找到相当扎实的证据支持半强式 EMH：经历拆分的股票通常是在拆分前数月已累积多期良好收益者，而拆分发生后股票不再有任何超额收益——市场已高效纳入拆分信息（图 8.1）。Indirect testing: make assumptions about a baseline model for the discount rate (returns), but don't forecast future cash flows. For example, Fama et al. (1969) conduct an event study (the first event study), on 940 stock splits to test the semi-strong-form EMH. The event study (footnote: see more details in subsection 18.10 in He 2019a): first pick a model (footnote: the model picked by Fama et al. 1969 is CAPM) to predict the expected return \(\mathbb{E}_t[R_{i,t+1}]\); suppose the event takes place on day \(t\), and denote the actual return from \(t\) to \(t+1\) by \(\tilde R_{i,t+1}\); define the abnormal return of stock \(i\) by \(AR_{i,t+1}=\tilde R_{i,t+1}-\mathbb{E}_t[R_{i,t+1}]\); then for each stock calculate this abnormal return and take an average across the cross-section of stocks to estimate the event abnormal return. The semi-strong EMH suggests a stock split, as a totally cosmetic change, should not have an impact on the price after it happened and became public information. Fama et al. (1969) find pretty solid evidence to support the semi-strong EMH: the stocks which experienced a split were typically those that had accumulated many periods of good returns in the months before the split happened, and after the split took place the stocks no longer had any excess returns — the market has efficiently included the information of the splits (Figure 8.1).

间接检验仍有问题 / Indirect testing still has issues 收益模型有很多（CAPM、APT、C-CAPM 等），并不清楚到底该用哪个来预测 \(\mathbb{E}_t[R_{i,t+1}]\)。这尤其麻烦，因为任何"用某个特定收益模型拒绝 EMH"的研究，仍然逃不开联合假设问题的批评。There are many models for returns (CAPM, APT, C-CAPM, etc.), and it's not clear which model should be used for predicting \(\mathbb{E}_t[R_{i,t+1}]\). This is particularly problematic because any research that rejects EMH with a particular model for returns is still subject to the critique of the joint hypothesis testing problem.

图 8.1（股票拆分前后的收益，已转述 / Figure 8.1, paraphrased） 两面板均以"相对拆分月的月份数"（−29 到 +30）为横轴。(a) CAPM 平均残差：拆分前（负月份）平均异常收益为正、逐月累积，拆分月（0）后基本回落到 0 附近。(b) CAPM 累积平均残差：累积异常收益在拆分前持续上升、在拆分月附近走平——拆分后不再有超额收益，印证半强式 EMH 已把拆分信息纳入价格。Both panels have "month relative to split" (−29 to +30) on the horizontal axis. (a) Average residual in CAPM: the average abnormal return is positive and accumulates month by month before the split (negative months), and basically falls back to around 0 after the split month (0). (b) Cumulative average residual in CAPM: the cumulative abnormal return keeps rising before the split and flattens out around the split month — there are no excess returns after the split, confirming that the semi-strong EMH has incorporated the split information into the price.