CFAレベル1における定量的手法の概要

Key Topics You Need to Focus On

1. Overview of the Subject

定量的方法 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. コアトピックと重要な概念

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

モジュール 1: お金の時間的価値

• Understand interest rates and their components
• 18. これらのキャッシュフローの Effective Annual Rate (EAR)
• Master present value (PV) and future value (FV) of cash flows
• Use a financial calculator efficiently

モジュール 2: データの整理、視覚化、および説明

• 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
• Dispersion measures: range, variance, standard deviation
• Coefficient of variation
• Skewness and kurtosis
• Correlation coefficient

モジュール 3: 確率の概念

• Random variables and probability fundamentals
• Conditional vs unconditional probability
• Addition and multiplication rules
• Expected value, covariance, correlation
• Applications in portfolio return and risk
• Bayes’ formula
• Factorials, permutations, and combinations

Module 4: Common Probability Distributions

• Discrete vs continuous random variables
• Binomial distribution
• Uniform distribution
• Normal distribution
• Lognormal distribution
• Shortfall risk and Roy’s Safety-First criterion
• Discrete vs continuous compounding
• Student’s t-distribution, F-distribution
• Monte Carlo simulation

モジュール 5: サンプリングと推定

• Random sampling methods
• Sampling error and stratified sampling
• Central Limit Theorem
• Standard error of the mean
• Confidence intervals
• Resampling methods (Bootstrap, Jackknife)
• Sampling bias

モジュール 6: 仮説検定

• Hypothesis testing framework
• Null and alternative hypotheses
• One-tailed vs two-tailed tests
• Type I and Type II errors
• テスト統計量と有意水準
• p値の解釈
• 母集団パラメータの検定（平均、分散など）

Module 7: Introduction to Linear Regression

• 単純線形回帰モデル
• 従属変数と独立変数
• 回帰方程式、傾き、切片
• 横断的回帰と時系列回帰
• 回帰モデルの仮定
• 主要指標：SST、RSS、SSE、R²
• 一般的な仮説検定（F検定、t検定）
• 予測値と信頼区間
• 線形回帰モデルの拡張