Quantitative Methods Notes for CFA Level 1

1. Rates and Return (TVM)

Unpack the essentials of Time Value of Money (TVM), an essential finance concept for the CFA Level 1 exam. From interest rates to the world of annuities, you’ll learn all you need to become a TVM wizard.

• Understanding Interest Rates: Dive into the world of interest rates, learning about their components and how to interpret them as required rate of return, discount rate, and opportunity cost.
• Future Value of a Single Cashflow: Explore the time-centric nature of single cash flows, honing your skills in calculating future value and effective annual rates, and understanding the power of continuous compounding.
• Present Value of a Single Cashflow: Master the reverse concept of future value, learning to calculate present value for different compounding scenarios and frequencies.
• Series of Cash Flows: Get your hands on the calculation of future values of multiple cash flows, be they regular or uneven, and learn to adjust payments and timelines accordingly.
• Annuities: Unearth the intricacies of annuities and perpetuities, understanding their differences and learning to calculate their present values.
• Measures of Return. Dive into multi-period returns and understand various ways to calculate average return, including arithmetic mean, geometric mean, and money-weighted return.
• MWRR and TWRR. Dive into the nuances of portfolio return measurement, focusing on the Money Weighted Rate of Return (MWRR) and Time Weighted Rate of Return (TWRR), essential for evaluating investment performance accurately.

2. The Time Value of Money in Finance

Dive into the world of finance with a clear understanding of how the time value of money (TVM) influences investments in fixed income and equity instruments. You’ll uncover the magic of interest rates and time on your returns, master dividend-based valuation models, and learn how the principle of cash flow additivity serves as the foundation for financial instrument valuation and market equilibrium.

• Time Value of Money in Fixed Income: Discover the impact of interest rates and time on bond investments.
• Time Value of Money in Equity Instruments: Learn to value stocks using dividend-based models and understand growth rates and P/E ratios.
• Cash Flow Additivity: Explore how the present value of future cash flows determines the valuation of securities.

3. Statistical Measures of Asset Returns

Dive into the world of data analysis, exploring everything from types and organisation of data to correlation. This captivating course will provide a comprehensive guide to organising, visualising, and describing data.

• Data Types and Data Organisation: Understand the difference between numerical and categorical data, cross-sectional and time series data, and structured and unstructured data.
• Summarising and Visualising Data: Discover the process of summarising and visualising data, including distinguishing between population and sample, creating frequency distributions, and using data visualisation tools.
• Measures of Central Tendency: Learn about measures of central tendency such as mean, mode, and median, and how to visualise your data using box and whisker plots.
• Measures of Dispersion: Get acquainted with measures of dispersion, including range, mean absolute deviation, and variance, and learn how these metrics can help in investment risk decisions.
• Skewness and Kurtosis in Returns Distributions: Explore the concepts of skewness and kurtosis in returns distributions, understanding normal distributions, asymmetry, and peakedness.
• Covariance and Correlation: Delve into the world of covariance and correlation, learning to calculate and interpret them, and visualising relationships using scatter plots.

4. Probability Trees and Conditional Expectations

Welcome to the exciting domain of probability. From understanding basic definitions to advanced techniques like Bayes’ formula, this guide will help you conquer Probability Concepts.

• Definitions in Probability Concepts: Learn about random variables, events, and odds, and explore different methods to determine probabilities, such as empirical, subjective, and a priori.
• Joint Probability and Total Probability Rule: Gain knowledge about conditional and joint probability, master the total probability rule, and the multiplication and addition rules for calculating probabilities.
• Expected Values and Variance: Become proficient in expected values and variance, understanding how to handle conditional expected values to improve your forecasts and financial decisions.
• Bayes’ Formula: Grasp the magic of Bayes’ Formula, and learn how to update probabilities, which will boost your problem-solving skills in investment scenarios.
• Principles of Counting: Understand counting principles and their application in probability, learning to use multiplication rules, factorials, and multinomial formulas, and improve your skills in permutations and combinations.

5. Portfolio Mathematics

Step into the intriguing world of common probability distributions. This guide will walk you through portfolio return, discrete random variables, continuous random variables.

• Portfolio Return and Variance, Covariance and Correlation: Understand the dynamics of portfolio return and risk, diving into the concepts of variance, covariance, and correlation that are key to analysing and managing investment portfolios.
• Discrete Random Variables: Uncover the secrets of discrete random variables and grasp uniform and binomial distributions, learning how to apply these to track errors and stock price movements.
• Continuous Random Variables: Get acquainted with continuous random variables and delve into continuous uniform, normal, and lognormal distributions, understanding confidence intervals, the z-table, and Roy’s safety-first ratio.
• Portfolio Risk Measures: This lesson offers a straightforward approach to understanding the quantitative tools essential for portfolio management.

6. Simulation Methods

Unlock the mysteries of simulation methods in finance, where you’ll get hands-on with lognormal distributions to understand asset price movements and dive into Monte Carlo simulations to forecast stock option prices.

• Lognormal Distributions: See how financial markets favor the optimistic side of growth, making asset predictions more realistic.
• Monte Carlo Simulation: Learn about the Monte Carlo simulation, a computer-based technique, its role in evaluating stock option price movements, its applications in finance, and become aware of its limitations and alternatives like historical simulation.

7. Estimation and Inference

Dive into the fascinating realm of sampling and estimation. This guide will take you on a journey through sampling methods, point and interval estimates, resampling methods, and biases in sampling.

• Sampling and Central Limit Theorem: Master the world of sampling methods and the central limit theorem, learning to make inferences about population parameters using sample statistics.
• Point and Interval Estimates: Grasp the properties of estimators (Consistent, Unbiased, Efficient) and differentiate between point estimates and confidence intervals.
• Resampling Methods: Explore the world of resampling methods, focusing on the bootstrap and jackknife techniques, to estimate the sampling distribution of a statistic.
• Biases in Sampling: Learn about the potential biases in sampling, including large sample sizes, data snooping bias, sample selection bias, and time-period bias, and how to mitigate their effects.

8. Hypothesis Testing

Delve into the fascinating world of Hypothesis Testing, a cornerstone of statistical decision-making. This journey explores the steps of the hypothesis testing procedure, various types of hypothesis tests concerning the mean and variance. By the end, you’ll be well-equipped to make robust, data-driven decisions.

• Hypothesis Testing Procedure: Embark on the 7-step hypothesis testing process, differentiating between null and alternative hypotheses, and reinforcing your understanding with practical examples.
• Hypothesis Tests Concerning the Mean: Understand hypothesis testing around the mean, whether for a single mean or comparing two means.
• Hypothesis Tests Concerning Variance: Delve into hypothesis tests relating to variance, learning about the chi-square test for single populations and the F-test for comparing two populations.

9. Parametric and Non-Parametric Tests of Independence

Continuing with Hypothesis Testing, we have a deep dive into tests of correlation, and tests of independence using contingency tables.

• Hypothesis Tests Concerning Correlation: Explore the nuances of hypothesis tests for correlation, from the parametric Pearson correlation coefficient to non-parametric tests like the Spearman rank correlation test.
• Test of Independence Using Contingency Tables: Learn to perform a test of independence using contingency tables, a crucial tool for analyzing relationships between categorical or discrete variables.

10. Simple Linear Regression

Embark on an exciting exploration of Linear Regression, where you’ll delve into the world of dependent and independent variables, regression model analysis, hypothesis tests for slope coefficients, and various functional forms for simple linear regression. By the end, you’ll be well-equipped to analyze data and draw meaningful insights from regression models.

• Simple Linear Regression: Dive into the realm of dependent and independent variables, and discover how to estimate and apply the parameters of the model effectively.
• Measures of Goodness-of-Fit: Navigate regression analysis by learning the secrets of ANOVA, components of the regression model, and the application of SEE and R-squared.
• Hypothesis Tests on Slope Coefficient: Enhance your statistical prowess with hypothesis testing for slope coefficients, confidence intervals, t-tests, p-values, and the F-test in linear regression analysis.
• Functional Forms for Simple Linear Regression: Unravel the complexities of functional forms for simple linear regression, covering time-series, log-lin, lin-log, and log-log models, and sharpen your model selection skills.

11. Introduction to Big Data

Step into the world of Fintech where finance meets cutting-edge technology. Learn how Big Data, AI, and distributed ledger technology like blockchain are revolutionizing investment management. Get ready to understand their applications and challenges in the rapidly evolving field of finance.

• Big Data and Artificial Intelligence: Dive into the realm of Fintech, focusing on Big Data, Data Science, and AI, and their transformative effect on investment management.