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PhD-Course/book/Asset Pricing/Theoretical AP/cards/part1/CARA 效用 - 常绝对风险厌恶.md

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+---
+orphan: true
+---
+
+# CARA 效用 - 常绝对风险厌恶
+
+导航：[Asset Pricing index](../../../index.md) · 来源：[01_Single_Period_Models](../../01_Single_Period_Models.md)
+
+
+:::{admonition} Definition (Definition)
+CARA 效用写作
+
+$$
+u(w)=-e^{-\alpha w},\qquad \alpha>0.
+$$
+
+:::
+
+## 性质
+
+$$
+-\frac{u''(w)}{u'(w)}=\alpha,
+$$
+
+即绝对风险厌恶不随财富变化。
+
+## 经济含义
+
+- 没有 wealth effect。
+- 最优风险暴露不依赖初始财富。
+- 与正态分布结合时，常可化成均值—方差问题。

PhD-Course/book/Asset Pricing/Theoretical AP/cards/part1/CRRA 效用 - 常相对风险厌恶.md

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+---
+orphan: true
+---
+
+# CRRA 效用 - 常相对风险厌恶
+
+导航：[Asset Pricing index](../../../index.md) · 来源：[01_Single_Period_Models](../../01_Single_Period_Models.md)
+
+
+:::{admonition} Definition (Definition)
+CRRA 效用写作
+
+$$
+u(w)=\frac{w^{1-\rho}}{1-\rho},\qquad \rho\neq 1,
+$$
+当 $\rho=1$ 时，退化为
+
+$$
+u(w)=\log w.
+$$
+
+:::
+
+## 性质
+
+$$
+-\frac{wu''(w)}{u'(w)}=\rho,
+$$
+
+即相对风险厌恶不随财富变化。
+
+因此
+
+$$
+\alpha(w)=-\frac{u''(w)}{u'(w)}=\frac{\rho}{w},
+\qquad
+\frac{d\alpha(w)}{dw}=-\frac{\rho}{w^2}<0,
+$$
+
+所以 CRRA implies DARA.
+
+## 经济含义
+
+- 对“按财富比例缩放”的风险态度不变。
+- 常用于跨期消费和增长模型。
+- 因为 $\alpha(w)=\rho/w$ 随财富上升而下降，所以它蕴含 DARA（decreasing absolute risk aversion，递减绝对风险厌恶）。

PhD-Course/book/Asset Pricing/Theoretical AP/cards/part1/二次效用 - Mean-Variance 基础.md

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+---
+orphan: true
+---
+
+# 二次效用 - Mean-Variance 基础
+
+导航：[Asset Pricing index](../../../index.md) · 来源：[01_Single_Period_Models](../../01_Single_Period_Models.md)
+
+
+:::{admonition} Definition (Definition)
+二次效用常写作
+
+$$
+u(w)=-\frac12(w-\zeta)^2,
+$$
+通常要求 $w<\zeta$，以保证边际效用为正。
+
+:::
+
+## 性质
+
+若
+
+$$
+u(w)=-\frac12(w-\zeta)^2,
+$$
+
+则
+
+$$
+\begin{aligned}
+E[u(\tilde w)]
+&= -\frac12E[(\tilde w-\zeta)^2] \\
+&= -\frac12\Big(E[\tilde w^2]-2\zeta E[\tilde w]+\zeta^2\Big) \\
+&= -\frac12\Big(\operatorname{Var}(\tilde w)+E[\tilde w]^2-2\zeta E[\tilde w]+\zeta^2\Big) \\
+&= -\frac12\operatorname{Var}(\tilde w)-\frac12\big(E[\tilde w]-\zeta\big)^2.
+\end{aligned}
+$$
+
+故
+
+$$
+\max E[u(\tilde w)]
+\Longleftrightarrow
+\max \Big\{E[\tilde w]-\frac{1}{2}(E[\tilde w]-\zeta)^2-\frac12\operatorname{Var}(\tilde w)\Big\},
+$$
+
+因此只要期望收益与方差的组合相同，效用排序就等价于 mean-variance preferences。
+
+## 局限
+
+它蕴含 IARA（绝对风险厌恶随财富上升），通常被认为不够现实。

PhD-Course/book/Corporate Finance/attachments/AharonySwary1980.md

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+# Reading Note: Aharony and Swary (1980)
+
+<a href="../01_Empirical_Corporate_Finance.html">Back to the main note</a>
+
+## 1. Core Question
+Do dividend announcements contain information about future cash flows, as reflected in announcement-window CARs?
+
+## 2. Figure / Evidence
+![[Pasted image 20260421200909.png]]
+
+$$
+\begin{aligned}
+\Delta d<0 &\Longrightarrow CAR \downarrow \\
+\Delta d>0 &\Longrightarrow CAR \uparrow
+\end{aligned}
+$$
+
+## 3. Interpretation
+- dividend decrease：公告前后 $CAR$ 明显下跌，市场把减息视为坏消息。
+- dividend increase：公告前后 $CAR$ 明显上升，市场把加息视为好消息。
+- 这支持 signaling 解释；dividend change 是 management 对 future cash flow 的公开信号，但不等于 dividend change 机械预测 future earnings。
+
+## 4. Notes
+- Use this card for the slide / table screenshot and any extra annotation.

PhD-Course/book/Corporate Finance/attachments/AllenMichaely2003.md

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+# Reading Note: Allen and Michaely (2003)
+
+<a href="../01_Empirical_Corporate_Finance.html#sec-allen-michaely-2003">Back to the main note</a>
+
+## 1. Core Question
+How much of dividend policy and dividend recipient composition can be explained by tax clientele, and how much is left once transaction costs and trading opportunities are taken into account?
+
+## 2. Main Point
+- Dividend taxation can create different after-tax payoffs across investor types.
+- But actual holder composition is not perfectly segmented by tax rate.
+- Ex-dividend day trading and transaction costs weaken a clean clientele split.
+
+## 3. Reading Frame
+- Use this card for any figure or slide that illustrates:
+  - shareholder composition
+  - tax clientele
+  - ex-dividend day trading
+  - transaction-cost frictions
+
+## 4. Figure Slots
+
+## 5. Notes
+- Keep the main note concise.
+- Add screenshots or paper figures here when needed.

PhD-Course/book/Corporate Finance/attachments/BakerWurgler2002.md

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+---
+title: "Market Timing and Capital Structure"
+year: 2002
+journal: "Journal of Finance"
+author: "Malcolm Baker and Jeffrey Wurgler"
+contribution: "提出 market timing theory：公司在高估值时发行 equity、低估值时回购 equity，长期资本结构因此带有历史市场择时的痕迹。"
+tags: [CapitalStructure, MarketTiming, EquityIssuance, Repurchase, Empirical]
+type: Course
+---
+
+# Reading Note: Baker and Wurgler (2002)
+
+## 1. Core Question
+这篇文章问的不是“STO 为什么有最优杠杆”或“PO 为什么先内后外”，而是：
+
+- 公司是否会系统性地在股价高时发股、股价低时回购？
+- 如果会，这种 market timing 会不会长期留在 capital structure 里？
+
+## 2. Why This Paper Matters
+前面的文献已经给了两类经典解释：
+
+- **STO / trade-off**: leverage 由税盾和困境成本共同决定
+- **PO / pecking order**: leverage 由内部资金优先和信息不对称决定
+
+Baker and Wurgler 增加的是第三条机制：
+
+- **Market timing**: 资本结构是历史上多次择时发行的累积结果
+
+所以你图里的三张 slide 不是重复 STO/PO，而是在补充一个新维度：
+
+1. leverage 和 market-to-book 的关系为什么是负的
+2. 这种关系为什么更像 equity issuance timing，而不只是 distress
+3. repurchase side 是否也有同样的 timing 证据
+
+## 3. Main Channels
+
+### 3.1 Equity issuance timing
+当 market-to-book 高时，公司股票价格相对更“贵”：
+
+- 发行 equity 更划算
+- 发行后 leverage 被动下降
+- 这种下降会积累成长期低杠杆
+
+### 3.2 Repurchase timing
+当 market-to-book 低或公司被低估时：
+
+- 公司更容易回购股票
+- 回购会提高 leverage
+- 这与 equity issuance 形成对称关系
+
+### 3.3 Persistent capital structure effect
+如果公司长期在高估值时发股、低估值时回购：
+
+- 当前 leverage 会和历史 market-to-book 强相关
+- 这解释了为什么资本结构不是只看当期最优，而是包含历史路径依赖
+
+## 4. Evidence Moved to Part 1
+这部分正文已经移动到 <a href="../01_Empirical_Corporate_Finance.html#section-bw02">Part</a>，这里仅保留入口。
+
+- 主讲义中的对应部分现在按三张图整理了 SEO、prior return、undervaluation index 的证据
+- 如果需要完整的课内读法和图注解释，以 Part 1 为准
+
+## 5. Relation to Other Papers
+
+### 5.1 Rajan and Zingales (1995)
+- RZ95 先证明：国际样本里 leverage 的相关性很稳定
+- 但它并没有把 market-to-book 的负相关完全解释为哪一种理论
+- 在这门课的读法里，RZ95 提供的是 market timing 的前置证据
+- Baker and Wurgler 进一步把这条负相关整理成 historical market timing 的核心经验动机
+
+### 5.2 Frank and Goyal (2009)
+- FG09 说：大样本里 trade-off 更稳，但 profitability 等变量并不完全符合简单 trade-off
+- Baker and Wurgler 则补充：market-to-book 那一块，可能不是 trade-off 或 pecking order，而是 timing 效应
+
+### 5.3 SEO and repurchase literatures
+这篇不是从零开始，而是把已有 long-run return evidence 组织成同一个解释框架：
+
+- **Ritter (1991)**, **Loughran and Ritter (1995)**, **Spiess and Affleck-Graves (1995)**: equity issues 之后长期表现偏弱
+- **Ikenberry, Lakonishok and Vermaelen (1995)**: repurchases 之后长期表现偏强
+- **Peyer and Vermaelen (2009)**: open market repurchases 也有类似 undervaluation / long-run return 证据
+
+这些论文共同支持的不是 STO 或 PO，而是：
+
+- 公司在高估值时发股
+- 在低估值时回购
+- 资本结构因此带有历史 timing 的痕迹
+
+## 6. Main Conclusion
+这篇文章的核心结论可以简化成一句话：
+
+> capital structure is the cumulative outcome of past attempts to time the equity market.
+
+也就是说：
+
+- STO 解释“杠杆为什么有目标”
+- PO 解释“为什么融资顺序不同”
+- **Baker and Wurgler 解释“为什么历史发行时点会长期留在资本结构里”**
+
+## 7. Course Use
+- 这篇是 market timing 理论的经典入口
+- 和 RZ95、FG09、SEO / repurchase literatures 放在一起看，逻辑最完整
+- 相关课堂笔记：<a href="../01_Empirical_Corporate_Finance.html#section-papers">Part 1 papers section</a>
+
+## 8. Symbol List
+
+| Symbol / Term | Meaning |
+| :--- | :--- |
+| leverage | 资本结构指标；公司债务占比 |
+| market-to-book | 市值与账面价值比，常被用来衡量估值高低或 market timing 环境 |
+| equity issue | 增发 / SEO，发行新股融资 |
+| repurchase | 回购，尤其是 open market repurchase |
+| cumulative abnormal returns | 长期超额收益 |
+| undervaluation index | 低估程度指标；高值通常对应更强的回购后正收益 |
+| large equity issuers | 历史上大量发股的公司，Baker-Wurgler 里是关键分组 |

PhD-Course/book/Corporate Finance/attachments/FarreMensaMichaelySchmalz2014.md

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+# Reading Note: Farre-Mensa, Michaely and Schmalz (2014)
+
+<a href="../01_Empirical_Corporate_Finance.html#sec-farre-mensa-2014">Back to the main note</a>
+
+## 1. Core Question
+This review asks what the main empirical determinants of dividend policy are, and how much of payout behavior can be explained by investor demand, taxes, agency frictions, signaling, and lifecycle effects.
+
+## 2. Main Channels
+- investor demand
+- taxes
+- agency
+- signaling
+- lifecycle
+
+## 3. Reading Frame
+- The review is useful as a map of payout determinants rather than a single clean identification exercise.
+- Dividends and repurchases should be read together when the goal is to understand payout policy.
+- The card is intentionally left open for figures and slide screenshots.
+
+## 4. Notes
+- Add any figures from the review or the lecture slides here.
+- Keep the main note concise; use this card for images and longer annotations.