本章导读 本章讲（尤其是个人）投资者的交易行为。§11.1 概览：三个核心问题 + 个人投资者数据集（Odean 大型折扣经纪商、消费者金融调查、瑞典/芬兰、中国）。§11.2 处置效应 (disposition effect)：过早卖盈利股、过久持亏损股，\(\text{PGR}/\text{PLR}>1\) (11.1)(11.2)（Odean 1998），多国多市场出现；理性解释（均值回归、固定权重）失败；行为解释（前景理论、实现效用 Barberis-Xiong 2012、认知失调）；注 11.1（参考点为零？个股为框架？）。§11.3 相对评价 (relative evaluation)：与组合内他股比较（图 11.1 圆圈错觉）；差异放大 Hsee 1999、排序与注意力 Hartzmark 2015（最差/最好股更易被交易，图 11.2；字母序稳健性图 11.3）。§11.4 跨多股的框架：刻意回避重访输家 Strahilevitz et al. (2011)（图 11.4）；滚动心理账户 Frydman et al. (2018)（再投资日处置效应消失，图 11.5）。§11.5 分散不足：太少资产 / 反对冲（熟悉度偏差、本土偏差 French-Poterba 1991、Huberman 2001）/ 天真分散 Benartzi-Thaler 2001（401k 均分）。§11.6 过度交易：过度自信致交易过多、损害业绩 Barber-Odean 2000（图 11.6）；性别与过往经验。图 11.1–11.6 已转述。

核心问题与数据集 / Core questions and data sets 关于投资者交易行为，通常问三个重要问题：(1) 投资者如何决策？(2) 其决策过程如何影响其交易？(3) 投资者交易行为如何影响市场？个人投资者的交易行为之所以重要：尽管个体规模小，但在加总后能以系统性方式对市场产生巨大影响；即便在某些情形下个人投资者无法影响市场，其金融决策对于决定其消费、最优退休储蓄计划等仍然重要。与个人投资者交易相关的经典数据集：Terrance Odean 大型折扣经纪商数据集（不算很新，但仍能用来提出有力的新观点）；消费者金融调查 (Survey of Consumer Finance)（含个人投资者持仓的调查型数据，但无每只股票的具体仓位，故某些研究不可用）；瑞典/芬兰数据（取得需若干步骤，且因这些国家在全球金融上不重要而需论证使用合理性）；中国数据（有 APP 使用的新颖数据；中国个人投资者仍占主导，是检验行为理论的天然实验室）。There are typically three important questions about investor trading behavior: (1) How do investors make decisions? (2) How does their decision-making affect their trading? (3) How do investor trade behaviors impact the market? Individual investors' trade behaviors are important because: although individually small in size, in aggregation they can have a huge impact on the market in a systematic way; and even if individual investors cannot affect the market in some cases, their financial decisions are still important for determining their consumption decisions, optimal retirement saving plans, etc. The classical data sets related to individual investor trading: Terrance Odean's Large Discount Brokerage Data Set (not a very new data set, but can still be used to make powerful novel points); the Survey of Consumer Finance (contains survey-type data of individual investors' holdings, but no specific positions on each stock, so it cannot be used in certain research); Swedish/Finnish Data (takes some steps to get, and needs to justify using them since these countries are not financially important in the global context); Chinese Data (has some novel data on app usage; individual investors still dominate in China, so it's a natural lab for behavioral theories).

处置效应及其度量 / The disposition effect and its measure 处置效应指投资者倾向过早卖出盈利股、过久持有亏损股这一实证事实。具体地，若 \(\frac{\text{PGR}}{\text{PLR}}>1\) 则存在处置效应，其中 PGR 为已实现盈利比例、PLR 为已实现亏损比例，由 Odean (1998) 定义为The disposition effect refers to the empirical fact that investors tend to sell winning stocks too early and hold losing stocks too long. In particular, the disposition effect is present if \(\frac{\text{PGR}}{\text{PLR}}>1\), where PGR is the proportion of gains realized and PLR the proportion of losses realized, defined by Odean (1998) as

$$\text{PGR}=\frac{\text{no. of realized gains}}{\text{no. of realized gains}+\text{no. of paper gains}}\tag{11.1}$$

$$\text{PLR}=\frac{\text{no. of realized losses}}{\text{no. of realized losses}+\text{no. of paper losses}}\tag{11.2}$$

处置效应在多国多类市场出现：Odean (1998) 美股；Grinblatt & Keloharju (2001) 芬兰股市；Feng & Seasholes (2005) 中国股市；Genesove & Mayer (2001) 美国房地产；Locke & Mann (2005) 美国期货；Hartzmark & Solomon (2012) 体育博彩。The disposition effect appears in many types of markets in many countries: Odean (1998) the U.S. equity market; Grinblatt & Keloharju (2001) the Finnish equity market; Feng & Seasholes (2005) the Chinese equity market; Genesove & Mayer (2001) the U.S. real estate market; Locke & Mann (2005) the U.S. futures market; Hartzmark & Solomon (2012) sports betting.

理性解释失败 / Rational explanations fail (1) 均值回归信念：投资者相信当前收益好则未来收益会差（均值回归），故现在卖出，并持有亏损股、盼其未来上涨。但此解释行不通，因为个人投资者的持有期通常约一年；在如此短的期间内动量存在（赢家继续涨、输家继续跌），故表现出处置效应的投资者实际是在逆动量而行，根本不理性。(2) 固定组合权重：投资者想在组合中保持各资产固定比例，故卖掉一点赢家、买入一点输家。但这不合理，因为数据中（如 Odean 数据集）个人投资者通常清仓（全卖）其盈利头寸，根本不像再平衡。(1) Mean-reversion belief: investors believe returns will be bad in the future if current returns are good (mean-reversion), so they sell the stock now and hold losing stocks in the hope its price will rise in the future. However, this explanation doesn't go through, since the holding period of individual investors is typically about one year; in such a short period momentum is existent (winners keep going up and losers keep going down), so investors showing the disposition effect are actually going against momentum, not rational at all. (2) Fixed portfolio weights: investors want to keep a fixed fraction of each asset in their portfolio, so they sell winners a bit and buy losers a bit. However, this doesn't make sense since in the data (e.g. Odean's data set) individual investors usually liquidate (sell it all) their winning positions, which doesn't look like rebalancing at all.

行为解释与注 11.1 / Behavioral explanations and Remark 11.1 前景理论：投资者对每笔盈亏窄框定，有损失厌恶的价值函数，故在盈利区风险厌恶、在亏损区风险偏好（见 Odean 1998）。实现效用 (realization utility)：投资者对每笔盈亏窄框定，实现盈利时有一阵正效用、实现亏损时有一阵负效用（见 Barberis & Xiong 2012）。认知失调：投资者对每笔盈亏窄框定，不愿承认当初买该股的决定是错的，因为这会造成认知失调（负效用）（见 Zuchel 2001、Chang et al. 2016、Hartzmark & Solomon 2012）。注 11.1：上述经典处置效应的讨论假设参考点为零（盈 vs 亏）、且以每只个股为框架（即为每只股开一个独立心理账户、平仓时关闭）。两个值得深挖的问题：(1) 零是正确的参考点吗？(2) 个股是正确的框架吗？Prospect theory: investors use narrow framing for each gain/loss and have a loss-averse value function, so they are risk averse in the gains area and risk-loving in the losses area (see Odean 1998). Realization utility: investors use narrow framing for each gain/loss and have a burst of positive utility when realizing a gain and a burst of negative utility when realizing a loss (see Barberis & Xiong 2012). Cognitive dissonance: investors use narrow framing for each gain/loss and don't want to admit that their initial decision on that stock was a mistake since it would cause cognitive dissonance (disutility) (see Zuchel 2001, Chang et al. 2016, Hartzmark & Solomon 2012). Remark 11.1: the discussion above on the classical disposition effect assumes the reference point is zero (gain vs loss) and that the framing is for each individual stock (basically open an individual mental account for each stock, and close it when the position is liquidated). Two questions worth a deeper dig: (1) Is zero the right reference point? (2) Is the individual stock the right framing?

相对评价及其特征 / Relative evaluation and its characteristics 相对评价的基本思想是：投资者通过把某只股票与组合中其他股票（或临近替代品）比较来评价它的表现。这一思想可直观说明：图 11.1 中两个橙色圆圈大小完全相同，却因与相邻蓝色圆圈的比较而看起来很不同。相对评价有几个特征：差异放大 (heightened difference)——当选项被联合评价时，选项间差异的感知幅度被放大（见心理学论文 Hsee et al. 1999）。排序与注意力吸引 (ordering and attention-grabbing)——排序中的极端情形（最顶与最底）往往吸引最多注意。Diecidue & Wakker (2001) 讨论秩相关决策；Tversky & Kahneman (1992) 指出人们倾向聚焦极端；Hartzmark (2015) 表明个人投资者与共同基金都倾向对组合中（按过去收益）最差与最好的股票交易更多、对中间股票交易更少（数据：个人用 Odean 大型折扣经纪商数据、共同基金用 Thompson-Reuters 持仓数据）。结果（图 11.2）：组合中顶部输家与顶部赢家的卖出概率更高，个人与共同基金皆然。作为稳健性检验，作者还尝试按公司名字母排序这一替代排序，结果依然成立（图 11.3）。The basic idea of relative evaluation is that investors evaluate a given stock's performance by comparing it with other stocks (or nearby alternatives) in the portfolio. This idea can be visually illustrated: in Figure 11.1 the two orange circles are exactly the same size but look very different due to the comparison with the adjacent blue circles. There are several characteristics in relative evaluation: heightened difference — the perceived magnitude of difference between options is enlarged when the options are evaluated jointly (see the psychology paper Hsee et al. 1999). Ordering and attention-grabbing — extreme cases in an ordering (top and bottom) tend to attract the most attention. Diecidue & Wakker (2001) discuss rank-dependent decision making; Tversky & Kahneman (1992) point out people tend to focus on extremes; Hartzmark (2015) shows both individual investors and mutual funds tend to trade more on the worst and best stocks (in terms of past returns) in their portfolio and less on the middle stocks (data: Odean's Large Discount Brokerage data for individual investors, Thompson-Reuters holdings data for mutual funds). Result (Figure 11.2): the probability of sale is higher for the top losers and top winners in the portfolio, true for both individual investors and mutual funds. As a robustness check, the author also tries an alphabetical ordering by company name as the alternative ordering, and the result is still there (Figure 11.3).

图 11.1–11.3（已转述 / Figures 11.1–11.3, paraphrased） 图 11.1（相对评价）：黑底上两组图——左侧一个橙色圆被六个大蓝圆环绕、右侧同样大小的橙色圆被几个小蓝圆环绕；两个橙圆实际等大，却因周围参照不同而显得左小右大，直观展示相对/对比评价。图 11.2（按排名的卖出概率）：(a) 个人投资者、(b) 共同基金，横轴为组合内股票按持有期收益的排名（从"最差"到"最好"），纵轴卖出概率（线性概率模型系数）；两图均呈 U 形——最差与最好两端的卖出概率最高、中间最低。图 11.3（按公司名字母排序）：回归表，被解释变量为"是否卖出"的虚拟变量，"First name/Last name"为该股在投资者组合中字母序是否排首/末的指示变量；三列分别给出首与次首、末与次末、以及首/末与其余之差——字母序两端同样更易被卖出。Figure 11.1 (relative evaluation): on a black background, two groups — on the left an orange circle surrounded by six large blue circles, on the right an orange circle of the same size surrounded by several small blue circles; the two orange circles are actually equal in size but appear smaller (left) and larger (right) due to the different surrounding references, visually demonstrating relative/contrast evaluation. Figure 11.2 (probability of sale by ranks): (a) individual investors, (b) mutual funds, the horizontal axis the rank of stocks in the portfolio by holding-period returns (from "Worst" to "Best"), the vertical axis the probability of sale (coefficients from a linear probability model); both panels are U-shaped — the probability of sale is highest at the worst and best extremes and lowest in the middle. Figure 11.3 (alphabetical ordering by company name): a regression table with the dependent variable a dummy for whether a sale occurs, and "First name/Last name" indicators for whether the stock is top/bottom ranked alphabetically in the investor's portfolio; the three columns give the difference between the first and second, the last and second-to-last, and the first/last vs the rest — the alphabetical extremes are also more likely to be sold.

回避重访输家与滚动心理账户 / Avoiding revisiting losers and rolling mental accounts 刻意回避重访输家：Strahilevitz et al. (2011) 发现投资者倾向重访自己此前赚钱并卖出的股票，却不愿重访此前亏钱的股票。他们还发现：在那些想重访的前赢家股票中，若该股自上次卖出后一直下跌，则更可能被重新买入。一个可能解释是：投资者不喜欢"过早卖出赢家股"这一事实；为避免承认此前过早卖出，他们倾向更不愿买回自上次卖出后一直在涨的赢家股（图 11.4）。滚动心理账户：Frydman et al. (2018) 发现投资者并非每卖一只股就简单关闭其心理账户；相反，若在卖出旧股的同时买入新股（再投资），他们会把旧的心理账户滚动到新股的心理账户，即把旧的盈亏带到新账户。如此一来，账户被滚动时投资者就不会因关闭账户而感到实现的痛苦或快乐。一个可检验的预测是：处置效应在再投资日消失，而在清仓日（只卖旧股、不买新股）清晰存在（图 11.5）。这与"实现亏损无负效用"一致。他们还表明再投资改善了交易表现；并通过实验室实验进一步确认再投资因果地降低处置效应、改善交易。Intentionally avoiding revisiting losers: Strahilevitz et al. (2011) find investors tend to revisit a stock that they earned money and sold previously, but they don't like to revisit stocks on which they lost money before. They also find that among those previous winner stocks they would like to revisit, they are more likely to repurchase the stock if it has been going down since it was sold last time. One possible explanation: investors don't like the fact that they have sold a winner stock too early; to avoid admitting that immature selling happened before, they tend to be less likely to buy back the winning stocks that have been going up since sold last time (Figure 11.4). Rolling mental accounts: Frydman et al. (2018) find investors don't simply close the mental account for every stock when it's sold; instead, if they buy a new stock simultaneously as they sell an old stock (reinvestment), they roll over the old mental account to the new stock's mental account, i.e. bring the old profit/loss over to the new account. In this way investors won't feel the realization pain or gain from closing the mental account when it's rolled. One testable prediction is that the disposition effect disappears on reinvestment days while it's clearly there on liquidation days (only selling the old stock and not buying a new one) (Figure 11.5). This is consistent with no disutility from realizing a loss. They also show reinvestment improves trading performance, and a laboratory experiment further confirms reinvestment causally reduces the disposition effect and improves trading.

图 11.4、11.5（已转述 / Figures 11.4, 11.5, paraphrased） 图 11.4（重购风险率作为原始收益的函数，1992–1996）：横轴为该股上次卖出时的原始收益，纵轴重新购买的风险率（hazard rate）；"自卖出后下跌"线整体高于"自卖出后上涨"线——前赢家若此后下跌更易被买回、若此后上涨则更不易被买回。图 11.5（再投资日的处置效应）：两组柱（"已实现盈利比例"与"已实现亏损比例"）——清仓日（约占 69% 观测）处置效应为 8.1%（t=19.72），显著为正；再投资日（约占 31% 观测）为 −0.8%（t=−1.42），不显著——再投资日处置效应消失。Figure 11.4 (repurchase hazard rate as a function of original return, 1992–1996): the horizontal axis is the original return when the stock was last sold, the vertical axis the hazard rate of repurchase; the "down since sold" line is overall above the "up since sold" line — a previous winner is more likely to be bought back if it went down afterwards and less likely if it went up. Figure 11.5 (disposition effect on reinvestment days): two pairs of bars ("proportion of gains realized" vs "proportion of losses realized") — on liquidation days (about 69% of observations) the disposition effect is 8.1% (t=19.72), significantly positive; on reinvestment days (about 31% of observations) it is −0.8% (t=−1.42), not significant — the disposition effect disappears on reinvestment days.

分散不足的三种表现 / Three manifestations of insufficient diversification 分散化的思想是：投资者应在不同资产类别中持有大量不同的头寸，以分散特质风险，并对冲其他收入来源（如劳动收入）的潜在风险。但人们并不总这样做：(1) 资产太少：人们倾向只持有极少数资产，承担了不必要的特质风险。(2) 反对冲 (anti-hedge)：人们不能有效对冲其他风险——倾向投资熟悉的股票（熟悉度偏差）；倾向只买国内股票（国际分散不足，即本土偏差）。例如 French & Poterba (1991) 表明国内股权投资占整体股权投资的比例：美国 94%、日本 98%、英国 82%。本土偏差甚至在国内市场内部也成立：Huberman (2001) 表明在美国，投资者倾向买本地电话公司的股票、而非服务其他地区的电话公司。(3) 天真分散 (naive diversification)：人们天真地把钱平均分配给所有选项、甚至不去研究每个选项。Benartzi & Thaler (2001) 表明人们在固定缴款计划（401k）下用一种"傻规则"分配投资：若 401k 提供 10 只基金，投资者就简单地各投 10%，不管这些基金的性质如何。The idea of diversification is that investors should have a large number of different holdings in different asset classes to diversify idiosyncratic risks and hedge against potential risks in other income sources, such as labor income. However, people don't always do this: (1) Too few assets: people tend to hold a very small number of assets and bear unnecessary idiosyncratic risks. (2) Anti-hedge: people don't effectively hedge against other risks — they tend to invest in familiar stocks (familiarity bias) and tend to buy domestic stocks only (insufficient international diversification, i.e. home bias). For example, French & Poterba (1991) show that domestic equity investment as a percentage of overall equity investment is 94% for the U.S., 98% for Japan, and 82% for the U.K. Home bias is even true within the domestic market: Huberman (2001) shows that within the U.S., investors tend to buy stocks of their local phone company rather than phone companies serving other regions. (3) Naive diversification: people naively allocate their money equally to all the options without even looking into each option. Benartzi & Thaler (2001) show people use a silly rule for the allocation of investment under defined contribution plans (401k): if the 401k plan offers 10 funds, investors would simply invest 10% in each fund, regardless of the nature of those funds.

过度交易及其原因 / Excessive trading and its causes 基本思想是投资者交易过多，一个重要的潜在原因是过度自信。交易过多对投资业绩有害：Barber & Odean (2000) 表明交易过多的个人投资者会因交易成本而损害自己（图 11.6）。性别与过度自信：心理学证据表明男性比女性更过度自信，且有证据表明男性比女性交易更激进、因而亏损更多。过往经验与过度自信：过去表现好的投资者（这可能只是运气）倾向交易更多。The basic idea is that investors trade too much, and one important potential reason is overconfidence. Trading too much is bad for investment performance: Barber & Odean (2000) show that individual investors who trade too much would hurt themselves due to trading cost (Figure 11.6). Gender and overconfidence: psychological evidence suggests men are more overconfident than women, and there is evidence showing men trade more aggressively than women and consequently lose more. Past experience and overconfidence: investors who perform well in the past (which potentially is just due to luck) tend to trade more.

图 11.6（个人投资者的月换手率与年收益，已转述 / Figure 11.6, paraphrased） 柱状图，横轴为按月换手率分的个人投资者五分位（从"最低换手"到"最高换手"），另加"平均个人"与"标普 500 指数基金（Vanguard Index 500）"两组；每组画灰柱（月换手率）、白柱（毛收益）、黑柱（净收益）。毛收益在各组大致相同，但月换手率越高净收益明显越低——交易成本吞噬了收益。A bar chart with the horizontal axis the individual-investor quintiles by monthly turnover (from "Low Turnover" to "High Turnover"), plus "Average Individual" and "S&P 500 Index Fund (Vanguard Index 500)" groups; each group has gray bars (monthly turnover), white bars (gross return), and black bars (net return). The gross returns are roughly the same across groups, but net returns are clearly lower when monthly turnover is higher — trading cost eats away the return.