CFA 一级定量方法概述

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主题概述

定量方法 is one of the most important and foundational subjects in the Chartered Financial Analyst Level I program.

This subject mainly covers core concepts such as:

• Time value of money
• Present and future value of cash flows
• Probability and statistics
• Hypothesis testing

A strong understanding of these topics will give you a major advantage when studying more advanced subjects like asset valuation and portfolio management later in the CFA program.

Although the volume of material is relatively large, Quantitative Methods is often considered a “scoring subject” because:

• The concepts are not overly tricky
• Many questions are calculation-based
• It is especially advantageous if you have a solid math background

Exam weight: Approximately 8–12% of the CFA Level I exam

2. 核心主题和重要概念

The Quantitative Methods section typically includes several modules (note: curriculum may change slightly each year). Below is a structured overview:

模块 1：货币的时间价值

• Understand interest rates and their components
• Calculate the Effective Annual Rate (EAR)
• Master present value (PV) and future value (FV) of cash flows
• Use a financial calculator efficiently

模块 2：组织、可视化和描述数据

• Types and classification of data
• Frequency distributions
• Contingency tables and confusion matrices
• Data visualization techniques
• Measures of central tendency: mean, median, mode
• Arithmetic mean vs geometric mean
• Quantiles and percentiles
• 离散度量：范围、方差、标准差
• 变异系数
• 偏度和峰度
• 相关系数

Module 3: Probability Concepts

• 随机变量和概率基础
• 条件概率与无条件概率
• 加法和乘法规则
• 期望值、协方差、相关性
• 在投资组合收益和风险中的应用
• 贝叶斯公式
• 阶乘、排列和组合

模块 4：常见概率分布

• 离散随机变量与连续随机变量
• 二项分布
• 均匀分布
• 正态分布
• 对数正态分布
• 短缺风险和罗伊的安全第一准则
• 离散复利与连续复利
• 学生t分布、F分布
• 蒙特卡洛模拟

模块 5：抽样与估计

• 随机抽样方法
• 抽样误差和分层抽样
• 中心极限定理
• 均值的标准误
• 置信区间
• 重抽样方法（自助法、切片法）
• 抽样偏差

Module 6: Hypothesis Testing

• 假设检验框架
• 零假设和备择假设
• 单尾检验与双尾检验
• 类型 I 和类型 II 错误
• 检验统计量和显著性水平
• p 值解释
• 测试总体参数（均值、方差等）

模块 7：线性回归简介

• 简单线性回归模型
• 因变量和自变量
• 回归方程、斜率和截距
• 横截面回归与时间序列回归
• 回归模型的假设
• 关键指标：SST、RSS、SSE、R²
• 常见假设检验（F 检验、t 检验）
• 预测值和置信区间
• 线性回归模型的扩展