CFA Level 1 Study Notes – Quantitative Methods

CFA Level 1 Study Notes – Quantitative Methods

2023 Syllabus >>>>

2024/2025 Syllabus

Learning Module 1 – Rates and Returns

LOS

LOS a: interpret interest rates as required rates of return, discount rates, or opportunity costs and explain an interest rate as the sum of a real risk-free rate and premiums that compensate investors for bearing distinct types of risk

LOS b: calculate and interpret different approaches to return measurement over time and describe their appropriate uses

LOS c: compare the money-weighted and time-weighted rates of return and evaluate the performance of portfolios based on these measures

LOS d: calculate and interpret annualized return measures and continuously compounded returns and describe their appropriate uses

LOS e: calculate and interpret major return measures and describe their appropriate uses

Learning Module 2 – Time Value of Money in Finance

LOS a: calculate and interpret the present value (PV) of fixed-income and equity instruments based on expected future cash flows

LOS b: calculate and interpret the implied return of fixed-income instruments and required return and implied growth of equity instruments given the present value (PV) and cash flows

LOS c: explain the cash flow additivity principle, its importance for the no-arbitrage condition, and its use in calculating implied forward interest rates, forward exchange rates, and option values

Learning Module 3 – Statistical Measures of Asset Returns

LOS a: calculate, interpret, and evaluate measures of central tendency and location to address an investment problem

LOS b: calculate, interpret, and evaluate measures of dispersion to address an investment problem

LOS c: interpret and evaluate measures of skewness and kurtosis to address an investment problem

LOS d: interpret the correlation between two variables to address an investment problem

Learning Module 4 – Probability Trees and Conditional Expectations

LOS a: calculate expected values, variances, and standard deviations and demonstrate their application to investment problems

LOS b: formulate an investment problem as a probability tree and explain the use of conditional expectations in investment application

LOS c: calculate and interpret an updated probability in an investment setting using Bayes’ formula

Learning Module 5 – Portfolio Mathematics

LOS a: calculate and interpret the expected value, variance, standard deviation, covariances, and correlations of portfolio returns

LOS b: calculate and interpret the covariance and correlation of portfolio returns using a joint probability function for returns

LOS c: define shortfall risk, calculate the safety-first ratio, and identify an optimal portfolio using Roy’s safety-first criterion

Learning Module 6 – Simulation Methods

LOS a: explain the relationship between normal and lognormal distributions and why the lognormal distribution is used to model asset prices when using continuously compounded asset returns

LOS b: describe Monte Carlo simulation and explain how it can be used in investment applications

LOS c: describe the use of bootstrap resampling in conducting a simulation based on observed data in investment applications

Learning Module 7 – Estimation and Inference

LOS a: compare and contrast simple random, stratified random, cluster, convenience, and judgmental sampling and their implications for sampling error in an investment problem

LOS b: explain the central limit theorem and its importance for the distribution and standard error of the sample mean

LOS c: describe the use of resampling (bootstrap, jackknife) to estimate the sampling distribution of a statistic

Learning Module 8 – Hypothesis Testing

LOS a: explain hypothesis testing and its components, including statistical significance, Type I and Type II errors, and the power of a test

LOS b: construct hypothesis tests and determine their statistical significance, the associated Type I and Type II errors, and the power of the test given a significance level

LOS c: compare and contrast parametric and nonparametric tests, and describe situations where each is the more appropriate type of test

Learning Module 9 – Parametric and Non-Parametric

LOS a: explain parametric and non-parametric tests of the hypothesis that the population correlation coefficient equals zero and determine whether the hypothesis is rejected at a given level of significance

LOS b: explain tests of independence based on contingency table data

Learning Module 10 – Introduction to Linear Regression

LOS a: describe a simple linear regression model, how the least squares criterion is used to estimate regression coefficients, and the interpretation of these coefficients

LOS b: explain the assumptions underlying the simple linear regression model, and describe how residuals and residual plots indicate if these assumptions may have been violated

LOS c: calculate and interpret measures of fit and formulate and evaluate tests of fit and of regression coefficients in a simple linear regression

LOS d: describe the use of analysis of variance (ANOVA) in regression analysis, interpret ANOVA results, and calculate and interpret the standard error of estimate in a simple linear regression

LOS e: calculate and interpret the predicted value for the dependent variable, and a prediction interval for it, given an estimated linear regression model and a value for the independent variable

LOS f: describe different functional forms of simple linear regressions

Learning Module 11 Introduction to Big Data Techniques

LOS a: describe aspects of “fintech” that are directly relevant for the gathering and analyzing of financial data.

LOS b: describe Big Data, artificial intelligence, and machine learning

LOS c: describe applications of Big Data and Data Science to investment management

 

2026/2027 Syllabus

Learning Module 1: Returns of Financial Assets and Instruments

LOS a: Describe, compare, and interpret returns

LOS b: describe, compare, and interpret required rates of return, risk-free rates, risk premia, and inflation

Learning Module 2: Types of Financial Returns

LOS a: Calculate, compare, and interpret different types of returns for financial assets, instruments, and indicators

Learning Module 3: Benchmarking Returns

LOS a: Calculate and compare money-weighted and time-weighted rates of return

LOS b: Describe the choices and the implications of the different weighting methods used in index construction and management, and calculate, interpret, and explain the value and the returns of an index

Learning Module 4: Time Value of Money in Finance

LOS a: Calculate and interpret the present value (PV) of fixed-income and equity instruments based on expected future cash flows

LOS b: Calculate and interpret the implied return of fixed-income instruments and required return and implied growth of equity instruments given the present value (PV) and cash flows

LOS c: Explain the cash flow additivity principle, its importance for the no-arbitrage condition, and its use in calculating implied forward interest rates, forward exchange rates, and option values

Learning Module 5: Statistical Characteristics of Asset Returns

LOS a: Calculate, interpret, and evaluate various measures of (1) central tendency and location and (2) dispersion

LOS b: Describe, interpret, and evaluate measures of skewness and kurtosis

LOS c: Calculate, interpret, and evaluate covariance and correlation

LOS d: Calculate, interpret, and evaluate semi-deviation and coefficient of variation

Learning Module 6: Statistical Distributions for Financial Asset Prices and Returns

LOS a: Calculate, interpret, and evaluate unconditional expected values for mean, variance, and covariance

LOS b: Calculate, interpret, and evaluate the principal moments of key statistical distributions used in finance

LOS c: Calculate, interpret, and evaluate conditional expectations, variances, and covariances

LOS d: Formulate investment problems through Bayesian updating

Learning Module 7: Estimation and Hypothesis Testing

LOS a: Explain the central limit theorem and the application of confidence intervals and sampling methodologies

LOS b: Explain hypothesis testing and its components, including statistical significance, Type I and Type II errors, and the power of a test; construct appropriate hypothesis tests; and interpret the results

LOS c: Compare and contrast parametric and non-parametric tests, describe situations in which each is the more appropriate type of test, construct appropriate hypothesis tests, and interpret the results

Learning Module 8: The Return and Risk of a Financial Portfolio

LOS a: Calculate, interpret, and evaluate the expected return, variance, standard deviation, covariance, and correlation of portfolio returns

LOS b: Describe, calculate, and interpret the minimum-variance portfolio and portfolios that lie on the efficient frontier

LOS c: Explain the selection of an optimal portfolio, given an investor’s risk aversion and the capital allocation line, and how this extends to the market portfolio and the capital market line

Learning Module 9: Simulation of Financial Asset Prices and Returns

LOS a: Describe historical simulation and explain how it can be used in investment applications

LOS b: Describe bootstrap resampling, and explain how it can be used in investment applications

LOS c: Describe Monte Carlo simulation and explain how it can be used in investment applications

Learning Module 10: Applications of Simple Linear Regression in Finance

LOS a: Describe, interpret, and explain simple linear regression, including coefficient estimation using the least squares criterion

LOS b: Describe and compare the assumptions of simple linear regression, identify violations through analyzing residuals, evaluate the estimated model’s goodness-of-fit and regression coefficients, and results of ANOVA estimates

LOS c: Calculate and interpret predicted values, the standard error of the estimate, and prediction intervals for the dependent variable in a simple linear regression model and describe different functional forms

LOS d: Calculate and interpret the variable estimates of the capital asset pricing model (CAPM)

Learning Module 11: Introduction to Financial Data Science

LOS a: Describe how big data, machine learning, and artificial intelligence are used in financial data science, fintech, and investment management

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