Quantitative Methods- Exam Ready Notes

CFA Level 1 : Quantitative Methods

1. Rates and Returns / Time Value of Money

Interest Rate Components

Formula:

Nominal Rate = Real risk-free rate + Inflation premium + default risk premium +Liquidity premium + maturity premium

Interest Rate Structure Diagram

Time Value of Money (TVM)

Timeline for TVM Problems

Annuities and Perpetuities

Annuity:

Ordinary Annuity: Payments occur at the end of each period (most common in loans, bonds).

Annuity Due: Payments occur at the beginning of each period (e.g., rent).

Perpetuity: Payment for infinite life

2.Statistical Concepts and Market Returns

Measures of Central Tendency

Measures of Dispersion

3. Organizing, Visualizing, and Describing Data

Graphical Tools

• Histogram: Visualizes frequency distribution.
• Boxplot: Shows median, quartiles, outliers.
• Scatter Plot: Reveals correlation between two variables.

Scatter Plot Examples

Log-normal vs Normal Distribution

4. Probability Concepts and Distributions

Probability Rules

Distributions

• Discrete: Binomial, Poisson
• Continuous: Normal, lognormal, uniform

Normal Distribution Curve

5. Sampling and Estimation

• Sampling Methods: Simple random, stratified, cluster, convenience, judgmental.
• Central Limit Theorem: Sample means approach normality as sample size increases.
• Standard Error:

6. Hypothesis Testing

Key Steps

1. State null and alternative hypotheses.
2. Select significance level, usually 0.05.
3. Choose test statistic (z, t, chi-square, F).
4. Define decision rule.
5. Calculate statistic and make decision.

Types of Errors:

• Type I: Reject when true (false positive).
• Type II: Fail to reject when false (false negative).

Hypothesis Testing Flowchart

7. Parametric vs Non-Parametric Tests

• Parametric: Assume normal distribution, test means/variances (z, t, F, chi-square).
• Non-Parametric: No distribution assumption, use ranks/signs (Wilcoxon, Mann-Whitney).

8. Simple Linear Regression

Model:

Goodness-of-Fit:

• R-squared (R² ): % of Y explained by X
• Standard Error of Estimate (SEE):

9. Simulation Methods

• Monte Carlo Simulation: Repeated random sampling to estimate outcomes.
• Bootstrapping: Resampling with replacement to estimate statistics.

Simulation Flow

10. Big Data and Machine Learning (Intro)

• Big Data: Large, complex datasets.
• Machine Learning: Algorithms that learn from data.
• Applications: Forecasting, risk management, trading.

11. Key Formula Summary Table

Visual Learning Tips

• Use timelines for TVM problems.
• Draw box-plots and histograms to understand distributions.
• Sketch normal curves and shade areas for probability questions.
• Map out regression lines and scatter plots for relationships.
• Practice with flowcharts for hypothesis testing and simulation