一、模块二概览
模块一：职业道德（Ethics） L001–L086 ✅ 已完成
模块二：数量分析（Quant） L087–L160 ← 当前
模块三：经济学（Economics）
...
二、数量分析在 CFA 三级考试中的位置
| 级别 | 权重 | 主要工具 |
|---|---|---|
| L1 | 8%–12% | TVM、DCF、概率统计基础、假设检验 |
| L2 | 5%–10% | 回归分析、时间序列、多因子模型 |
| L3 | 0%（含在组合管理中） | 模拟、风险管理工具 |
关键认知： 数量分析不是考试重点，但它是所有其他模块的语言——固收、权益、衍生品、组合管理都必须用数量工具。
三、数量分析的三大支柱
┌───────────────────────────────────┐
│ CFA 数量分析 │
└───────────────┬───────────────────┘
│
┌────────────────┼────────────────┐
▼ ▼ ▼
┌─────────┐ ┌──────────┐ ┌──────────┐
│ ① TVM │ │ ② 统计 │ │ ③ 回归 │
│ 货币时间 │ │ 概率与 │ │ 相关与 │
│ 价值 │ │ 描述统计 │ │ 推断模型 │
└────┬────┘ └────┬─────┘ └────┬─────┘
│ │ │
▼ ▼ ▼
债券定价 投资回报分析 因子研究
项目评估 风险测量 预测模型
贷款计算 假设检验 事件研究
四、为什么数量分析是"必备工具"
4.1 没有 Quant，你做不了的事
| 投资活动 | 依赖的数量工具 |
|---|---|
| 给一只债券定价 | TVM（折现现金流） |
| 判断一个基金经理是靠能力还是运气 | t 检验 |
| 预测公司利润 | 回归分析 |
| 评估投资组合风险 | 方差、协方差、Correlation |
| 做 Monte Carlo 模拟 | 概率分布 |
| 比较两个策略的收益 | 假设检验 |
4.2 CFA 考试的特点
- 不考数学推导（不需要手算回归系数）
- 考概念理解和解读（给你一个回归输出表，你能读出哪些变量显著）
- 考陷阱识别（异方差、多重共线性、自相关——这些在什么情况下出现、怎么解决）
- 计算器操作（TVM 和 DCF 靠 BA II Plus / HP 12C 计算器）
五、模块二学习路线
L087–L092 时间价值（TVM）基础
L093–L098 概率基础
L099–L104 描述统计
L105–L110 概率分布
L111–L116 抽样与估计
L117–L122 假设检验
L123–L128 相关与回归
L129–L134 多元回归
L135–L140 时间序列分析
L141–L146 模拟方法
L147–L152 技术分析
L153–L160 模块复习与模拟
六、本节课核心要点
6.1 "量化思维"三原则
原则 1：未来是不确定的 → 要用概率语言描述
原则 2：数据有噪音 → 需要统计工具分离信号和噪音
原则 3：相关 ≠ 因果 → 永远追问：这是真实关系还是巧合？
6.2 你不需要成为数学天才
CFA 数量分析的精髓不在于数学技巧，而在于：
- ✅ 读懂别人做的分析 → 别人扔给你一个回归表，你能判断是否有问题
- ✅ 提出正确的问题 → "你控制了哪些变量？""有没有异方差？"
- ✅ 避免被数字欺骗 → 知道数据挖掘（data mining）和过拟合（overfitting）的风险
- ✅ 会按计算器 → TVM 五个键（N, I/Y, PV, PMT, FV）烂熟于心
七、预热：TVM 直觉
正式课程从 L088 开始，这里先建立直觉
问题：今天的 100 元和一年后的 100 元，哪个更值钱？
答案：今天的 100 元更值钱
原因：
1. 你可以投资（赚利息）
2. 通胀会侵蚀未来购买力
3. 未来有不确定性（风险溢价）
如果你今天有 100 元，存银行一年利率 3%：
→ 一年后 = 100 × (1 + 3%) = 103 元
→ 100 元"终值"（FV）= 103 元
→ 103 元"现值"（PV）= 100 元
这就是 TVM 的全部直觉基础。明天 L088 开始正式展开。
八、测试题
1. CFA 一级考试中，数量分析（Quantitative Methods）的权重约为：
A) 20%–25%
B) 15%–20%
C) 8%–12%
D) 3%–5%
2. 货币时间价值（TVM）最直接的应用是：
A) 预测股价走势
B) 债券定价和项目评估
C) 宏观经济分析
D) 财务报表分析
3. CFA 考试对数量分析的考查特点是：
A) 要求手算复杂的回归系数
B) 重点考查概念理解、结果解读和陷阱识别
C) 纯粹考公式记忆
D) 仅在一级考试中出现
4. "量化思维"三原则不包括：
A) 未来是不确定的 → 用概率语言描述
B) 数据有噪音 → 需要统计工具分离信号和噪音
C) 投资决策只靠直觉 → 不需要数据
D) 相关 ≠ 因果 → 追问真实关系
5. 今天的 100 元和一年后的 100 元，为什么今天的更值钱？
A) 因为今天的纸币更新
B) 因为你可以投资赚取收益，且通胀和不确定性带来风险
C) 因为人们偏好延迟满足
D) 两国货币存在汇率差
答案
- C — 一级权重 8%–12%，二级 5%–10%，三级融入组合管理。
- B — TVM 的核心应用场景是折现现金流定价（债券、项目）。
- B — CFA 不考推导，考概念理解和陷阱识别。
- C — 量化思维的本质就是用数据和概率做决策。
- B — 三重原因：投资收益机会 + 通胀侵蚀 + 风险溢价。
Module 2 开始。下一课 L088：时间价值（TVM）基础
1. Module 2 Overview
Module 1: Ethics L001–L086 ✅ Complete
Module 2: Quantitative Methods L087–L160 ← Current
Module 3: Economics
...
2. Quantitative Methods Across CFA Levels
| Level | Weight | Key Tools |
|---|---|---|
| L1 | 8%–12% | TVM, DCF, probability & statistics basics, hypothesis testing |
| L2 | 5%–10% | Regression analysis, time series, multi-factor models |
| L3 | 0% (embedded in portfolio management) | Simulation, risk management tools |
Key insight: Quantitative methods are not the heaviest part of the exam, but they are the language of all other modules — fixed income, equity, derivatives, and portfolio management all require quantitative tools.
3. The Three Pillars of Quantitative Analysis
┌───────────────────────────────────┐
│ CFA Quantitative Methods │
└───────────────┬───────────────────┘
│
┌────────────────┼────────────────┐
▼ ▼ ▼
┌─────────┐ ┌──────────┐ ┌──────────┐
│ ① TVM │ │ ② Stats │ │ ③ Regress│
│ Time │ │ Prob & │ │ Correl & │
│ Value of │ │Descript. │ │Inference │
│ Money │ │ Stats │ │ Models │
└────┬────┘ └────┬─────┘ └────┬─────┘
│ │ │
▼ ▼ ▼
Bond pricing Return analysis Factor research
Project eval Risk measurement Forecasting
Loan math Hypothesis tests Event studies
4. Why Quantitative Methods Are "Essential"
4.1 What You Cannot Do Without Quant
| Investment Activity | Depends On |
|---|---|
| Pricing a bond | TVM (discounted cash flows) |
| Deciding if a fund manager has skill or luck | t-test |
| Forecasting company earnings | Regression analysis |
| Measuring portfolio risk | Variance, covariance, correlation |
| Running Monte Carlo simulations | Probability distributions |
| Comparing two strategies' returns | Hypothesis testing |
4.2 CFA Exam Characteristics
- No math derivations required (no hand-calculating regression coefficients)
- Tests conceptual understanding and interpretation (given a regression output table, can you identify which variables are significant?)
- Tests trap detection (heteroskedasticity, multicollinearity, autocorrelation — when do they occur, how to fix them)
- Calculator proficiency (TVM and DCF via BA II Plus / HP 12C)
5. Module 2 Learning Roadmap
L087–L092 Time Value of Money Basics
L093–L098 Probability Basics
L099–L104 Descriptive Statistics
L105–L110 Probability Distributions
L111–L116 Sampling & Estimation
L117–L122 Hypothesis Testing
L123–L128 Correlation & Regression
L129–L134 Multiple Regression
L135–L140 Time Series Analysis
L141–L146 Simulation Methods
L147–L152 Technical Analysis
L153–L160 Module Review & Mock
6. Core Takeaways for This Lesson
6.1 Three Principles of Quantitative Thinking
Principle 1: The future is uncertain → Describe it in probabilistic language
Principle 2: Data is noisy → Use statistical tools to separate signal from noise
Principle 3: Correlation ≠ Causation → Always ask: is this a real relationship or a coincidence?
6.2 You Don't Need to Be a Math Genius
The essence of CFA quantitative methods is not mathematical skill, but:
- ✅ Reading others' analyses → Given a regression table, can you spot the problems?
- ✅ Asking the right questions → "What variables did you control for?" "Is there heteroskedasticity?"
- ✅ Avoiding being fooled by numbers → Know the risks of data mining and overfitting
- ✅ Knowing your calculator → Master the five TVM keys (N, I/Y, PV, PMT, FV)
7. Warm-Up: TVM Intuition
Formal lessons start at L088; here we build intuition first
Question: Which is worth more — $100 today or $100 in one year?
Answer: $100 today is worth more.
Reasons:
1. You can invest it (earn interest)
2. Inflation erodes future purchasing power
3. The future is uncertain (risk premium)
If you have $100 today and deposit it in a bank at 3% annual interest:
→ One year later = $100 × (1 + 3%) = $103
→ The Future Value (FV) of $100 = $103
→ The Present Value (PV) of $103 = $100
This is the entire intuitive basis of TVM. L088 starts the formal lessons.
8. Practice Questions
1. At CFA Level I, the weight of Quantitative Methods is approximately:
A) 20%–25%
B) 15%–20%
C) 8%–12%
D) 3%–5%
2. The most direct application of the Time Value of Money (TVM) is:
A) Forecasting stock price trends
B) Bond pricing and project evaluation
C) Macroeconomic analysis
D) Financial statement analysis
3. The CFA exam's approach to testing quantitative methods is characterized by:
A) Requiring manual calculation of complex regression coefficients
B) Emphasizing conceptual understanding, result interpretation, and trap detection
C) Purely testing formula memorization
D) Only appearing in the Level I exam
4. Which is NOT one of the three principles of quantitative thinking?
A) The future is uncertain → describe it in probabilistic language
B) Data is noisy → use statistical tools to separate signal from noise
C) Investment decisions rely solely on intuition → data is unnecessary
D) Correlation ≠ causation → question whether it is a real relationship
5. Why is $100 today worth more than $100 in one year?
A) Because today's banknotes are newer
B) Because you can invest to earn returns, and inflation and uncertainty create risk
C) Because people prefer delayed gratification
D) Because of exchange rate differences between currencies
Answer Key
- C — Level I: 8%–12%, Level II: 5%–10%, Level III: embedded in portfolio management.
- B — The core application of TVM is discounted cash flow pricing (bonds, projects).
- B — CFA tests conceptual understanding and trap detection, not derivations.
- C — The essence of quantitative thinking is using data and probability for decisions.
- B — Three reasons: investment return opportunity + inflation erosion + risk premium.
Module 2 begins. Next L088: Time Value of Money (TVM) Basics