CFA® Quantitative Methods
Summary, Syllabus, Topics, and Sample Questions (L1, L2, L3)
CFA Institute’s Quantitative Methods 2023 curriculum introduces analytical tools and concepts such as the Time Value of Money (TVM), and probability concepts. TVM is a foundational principle in the quantitative part of the CFA exam that cascades into many other areas of the curriculum, such as equity investments, fixed income valuation, and corporate issuers. TVM explores the relationship between time and value and how that relationship affects valuing assets or determining rates of return.
CFA Quantitative Methods has a significant role in the Level 1 exam and a slightly smaller role in the Level 2 exam. On the Level 3 exam, these foundational concepts are not tested directly. However, the material has a significant overlap with other topics in the curriculum.
What to Expect in CFA Level 1 Quantitative Methods?
CFA Level 1 Quantitative Methods curriculum covers the understanding and interpretation of a normal distribution and how it relates to quantifying risk. At 8-12% of the exam, Quantitative Methods is given less weight than Ethics and Financial Statement analysis but is weighted more heavily than most topics. Candidates will also become familiar with data visualization, probability distributions, sampling and estimation, hypothesis testing, and regression analysis.
Exam Weighting
The CFA Quantitative Methods topic has a weight of 8-12%, meaning that approximately 15-21 (ca. 10%) of the 180 CFA Level 1 exam questions focus on this topic.
| Topic Weight | No. of Learning Modules | No. of Formulas | No. of Questions |
|---|---|---|---|
| 8-12% | 7 | ca. 100 | ca. 18 |
Level 1 Quantitative Methods 2023 Syllabus, Readings, and Changes
The CFA Level 1 Quantitative Methods syllabus spans 7 learning modules and contains 81 LOS. The CFA Level 1 curriculum includes 73 total learning modules for 2023. The first seven readings (1-7) center on Quantitative Methods (9.6% of the total curriculum).
The weight of the Quantitative Methods section was 12% in 2018 but dropped to 10% in 2020 through 2021. Since 2022, weight has fluctuated between 8-12%. There are no changes in CFA Level 1 curriculum for Quantitative methods.
| 2018 | 2019 | 2020 | 2021 | 2022 | 2023 |
|---|---|---|---|---|---|
| 12% | 10% | 10% | 10% | 8-12% | 8-12% |
Time Value of Money
We can express one of the core concepts of the time value of money through an age-old proverb—a bird in the hand is worth two in the bush. How does this relate to finance? Money now is worth more than money later: time imposes risk, which has a cost that detracts from value. Therefore, financial analysts must understand how to factor time into valuation.
This reading covers how to calculate
- the future value of a cash flow or a series of cash flows or
- the present value of a cash flow or series of cash flows happening in the future
Candidates are introduced to terminology and concepts that will curate a sense of economic intuition for material covered in later readings.
Organizing, Visualizing, and Describing Data
Never have financial analysts had such an abundance of data and data analysis tools as they have today. The analyst must learn to separate the wheat from the chaff to take advantage of this abundance rather than be smothered by it.
- This reading provides the foundation for understanding the more sophisticated Quantitative Methods concepts confronted later in the CFA curriculum.
- Candidates will learn core data types and how to organize, summarize, and visualize them.
- Candidates will also become familiar with the tools that allow analysts to transform raw data into useful information.
Probability Concepts
Financial analysts use tools based on probability concepts that allow them to evaluate data used to make decisions consistently and logically.
- The reading will discuss fundamental probability concepts and tools and apply them to a broad range of investment problems.
- Candidates will learn about independence, expectation, and variability, and acquire tools that will help them navigate a financial environment.
Common Probability Distributions
Decisions are made about the future, which is inevitably uncertain. Analysts must understand concepts of probability. Probability distributions provide the means to assess the possible outcomes of a random variable.
- The reading introduces seven probability distributions used extensively in investment analysis (the uniform, binomial, normal, lognormal, Student’s t-, chi-square, and F-distributions).
- Candidates will also learn about the Monte Carlo simulation; a model used to estimate possible outcomes that are influenced by random variables.
Sampling and Estimation
Samples are clues to the truth about a population. Financial analysts use sample data to assess past performance and forecast future performance.
- The reading introduces the process of obtaining samples and how to employ the mean as a measure of core tendencies of random variables.
- Candidates will learn the proper applications of the Central Limit Theorem and the implications of probability distributions.
Hypothesis Testing
Analysts have to sift through an avalanche of data to assess the investment environment and develop hypotheses. To test these hypotheses, analysts will employ statistical inference, allowing them to make judgments about populations based on smaller sample sizes.
- The reading discusses the three quantities commonly used in investments (mean, variance, and correlation) via a hypothesis-testing framework.
Introduction to Linear Regression
The process of determining relationships between variables is an important tool in the analyst’s toolkit. One of these tools is regression analysis.
- The reading explains the assumptions underlying the simple linear regression model and the roles of independent variables within that model.
- Candidates will also learn to formulate various hypotheses using this tool.
CFA Quantitative Methods Level 1 Sample Questions and Answers
The sample questions are typical of the probing multiple-choice questions on the L1 exam. During the exam, you have about 90 seconds to read and answer each question, carefully designed to test knowledge from the CFA Curriculum. UWorld’s question bank is built to expose you to exam-like questions and illustrate and explain the concepts tested thoroughly.
An analyst determines that the probabilities of two events are as follows:
| Event | Description | Probability |
|---|---|---|
| A | Price of oil increases | 0.33 |
| B | S&P 500 Index increases | 0.49 |
Assuming the events are independent but not mutually exclusive, the probability that at least one of the two events will occur is closest to:
- 0.16
- 0.66
- 0.82
A researcher formulates a null hypothesis stating that a country’s average inflation is 2%. After testing a sample, the researcher fails to reject the null hypothesis when the actual average inflation is not 2%. This most likely results in a:
- Type I error.
- Type II error.
- correct decision.
If a cumulative distribution function of a random variable indicates that P(X < a) is equal to P(X ≤ a), then the distribution is most likely :
- normal.
- discrete.
- binomial.
What to Expect in CFA Level 2 Quantitative Methods?
CFA Level 2 Quantitative Methods builds on the material covered in Level 1 while emphasizing hypothesis testing. At 5-10% of the exam, Quantitative Methods is one of the less heavily weighted topics.
Candidates will become familiar with tools used to identify relationships among variables and examine fintech, machine learning, and sentiment analysis as they relate to developing an investment hypothesis.
Exam Weighting
The CFA Quantitative Methods topic has a weight of 5-10% of the total exam content, so that approximately 4-8 of the 88 CFA Level 2 exam questions, or 1-2 of the 22 item sets focus on this topic.
| Topic Weight | No. of Learning modules | No. of Formulas | No. of Questions |
|---|---|---|---|
| 5-10% | 7 | ca. 50 | ca. 4-8 |
Level 2 Quantitative Methods 2023 Syllabus, Readings, and Changes
The CFA Level 2 Quantitative Methods syllabus spans 5 learning modules and contains 50 LOS. The CFA Level 2 curriculum includes 49 total learning modules for 2023. Quantitative Methods holds 14.3% of the total curriculum. The weight of the Quantitative Methods section has consistently remained at 5-10% since 2018.
| 2018 | 2019 | 2020 | 2021 | 2022 |
|---|---|---|---|---|
| 5-10% | 5-10% | 5-10% | 5-10% | 5-10% |
Reading-related updates for 2023 include:
- Updated: Basics of Multiple Regression and Underlying Assumptions, Evaluating Regression Model Fit and Interpreting Results, Model Misspecification, Extensions of Multiple Regression
- Removed: Introduction to Linear Regression
Basics of Multiple Regression and Underlying Assumptions
Financial analysts typically work with sophisticated statistical models that involve more than one independent variable. For example, analysts may want to assess particular macroeconomic variables behind the demand for an individual company’s products or services. To make such assessments, analysts employ multiple linear regression (linear regression with more than one independent variable) to make such assessments.
- The reading introduces the core principles and models of multiple regression models and the foundational assumptions applied to and adjusted for real-world situations.
- Candidates will learn to diagnose an assumption violation and to adjust to these violations.
- The reading also dives into the role of logistic regression in machine learning for Big Data analysis.
Evaluating Regression Model Fit and Interpreting Results
The reading helps understanding:
- How well a multiple regression model explains the dependent variable by analyzing ANOVA table results and measures of goodness of fit
- The hypotheses on the significance of two or more coefficients in a multiple regression model and interpret the results of the joint hypothesis tests
- The Calculation and interpretation of a predicted value for the dependent variable, given the estimated regression model and assumed values for the independent variable
Model Misspecification
The reading helps understanding:
- How model misspecification affects the results of a regression analysis and how to avoid common forms of misspecification
- The types of heteroskedasticity and how it affects statistical inference
- Serial correlation and how it affects statistical inference
- Multicollinearity and how it affects regression analysis
Extensions of Multiple Regression
Financial analysts typically work with sophisticated statistical models that involve more than one independent variable. For example, analysts may want to assess particular macroeconomic variables behind the demand for an individual company’s products or services. To make such assessments, analysts employ multiple linear regression (linear regression with more than one independent variable) to make such assessments. Four learning modules delve into the complexities of multiple regression, including:
- The core principles and models of multiple regression models and the foundational assumptions applied to and adjusted for real-world situations.
- The diagnosis of an assumption violation and relevant adjustments.
- The role of logistic regression in machine learning for Big Data analysis.
Time-Series Analysis
A set of these progressive observations is known as a time series, for example, a company’s quarterly sales over three years.
- The reading explores the two fundamental uses of time-series models: understanding the past and forecasting the future of a time series.
- Candidates will learn to estimate time-series models and how these models explain the changes in a time series over time.
Machine Learning
Since their introduction in the 1990s, machine learning techniques have become an integral tool in the tool kits of investment firms. Machine learning (ML) aids analysts in discovering new sources of value and efficiently executing trades.
- The reading provides an overview of machine learning and essential machine learning algorithms applied to investing.
- Candidates will learn about unsupervised machine learning algorithms, neural networks, deep learning nets, and how to choose an appropriate ML algorithm for the task.
Big Data Projects
Big data is an umbrella term that refers to data generated by organizations (business, financial markets, governments), individuals (credit cards, social media), sensors, and the Internet of Things. The true impact of big data on financial analysis is yet to be fully understood, but it has already become an integral part of analysts’ toolkits. Data can aid analysts in developing their hypotheses, forecasting trends in asset prices, detecting anomalies, etc.
- Candidates will learn about the concepts that allow analysts to make predictions using structured and unstructured data.
- The reading provides a real-world ‘big data’ project case study that uses sentiment analysis to assess stock movements.
CFA Quantitative Methods Level 2 Sample Questions and Answers
The sample questions here are typical of the L2 exam’s complexity and depth: formatted as item sets, with a vignette to deliver a scenario that tests the CFA L2 Curriculum. (On the actual exam, each vignette applies to four questions; we’ve thrown in a couple extra to get a bit more learning in). And be sure to review the illustrated explanations we’ve provided for each question: UWorld’s question bank is designed to expose you to exam-like questions and explain the concepts tested thoroughly.
Passage
Jae Park, CFA, is a manager of a hedge fund that bases its security selection on advanced quantitative analysis. For several open job positions with the fund, Park is looking to hire people with scientific and research backgrounds. Using multiple regression, she would like to evaluate the relationship between the expected salary of the candidates based on their years of experience (EXP), number of published research papers (PRP), and amount of grant funding received in their career (GF). The results of that regression are shown below, along with sample critical values. Park wishes to test the results at a 5% significance level (α = 0.05).
Park also notices that each candidate attended one of five universities. She is considering how to add a variable for university attended to the regression model and believes dummy variables are the best way to capture this.
Finally, Park suspects that her regression in its current form may violate regression assumptions. Her concern is that her model might have an artificially large R2 and t-statistics that are understated.
Based on the data in Exhibit 1, the regression is most likely a good predictor of projected salary since:
- it has a high R 2
- the F – statistic has a low p – value.
- most coefficients are statistically significant.
According to Exhibit 1, the most appropriate interpretation of the coefficients is that a higher expected salary will result from:
- more published papers and less grant funding.
- more published papers and more grant funding.
- fewer published papers and more grant funding.
Based on Exhibits 1 and 2, which slope coefficient is most likely to be statistically significant?
- GF
- EXP
- PRP
What to Expect in CFA Level 3 Quantitative Methods?
The CFA Institute does not provide a stand-alone Level 3 Quantitative Methods curriculum. However, the foundational knowledge in the Level 1 and Level 2 curriculum is implicit at CFA Level 3.
Study Tips for CFA Quantitative Methods
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Create a Solid Foundation
Because they will come up regularly as you move through the curriculum, Quantitative Methods subjects are fundamental knowledge you need to study closely. Candidates can expect to refer back to these readings for refreshers throughout the exam process.
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Lots of Practice and Repetition
CFA Institute suggests the importance of practice, particularly the CFA quant section. UWorld’s Qbank provides over 425 individual questions and explanations (from Level 1 and Level 2) to help you gain fluency with quantitative concepts and practice. Answering as many questions as possible can significantly aid in your grasp of the concepts and the exam's testing formats.
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Start your studies (early) with Quantitative Methods
The order of topics is a common question with most candidates. It is a good idea to start with Quantitative Methods, or at least learn it early in your preparation. These readings introduce fundamental concepts that make up the Level 1 syllabus and that you must grasp to do well on exam day. Additionally, as you go toward your CFA charter, this content will recur throughout the program at every level.
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Prioritize the rationale over memorization of the formula
You would do well to become very familiar with a number of the equations; you'll probably use your calculator a lot when responding to questions on this subject. However, mastering this content involves more than just crunching numbers. While it is important to apply the concepts, it’ll be easier to recall how to do that if you understand the context as well. In some cases, if you really understand the concepts, you won’t have to rely on your calculator at all.
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Level 2 is more conceptual than Level 1, but you’ll still have to do the math
Level 2 Quantitative Methods is more: more complex models, more variables, more formulae, but also more theory and understanding of why the math works. But you will still have to crunch the numbers.
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Put the time in understanding and practicing your itemset/vignette exam technique
Quant is a great place to misread and misuse numbers, so be sure you have a plan for reading through the vignette and then doubling back to find the necessary data—and to ignore the unnecessary data—as you answer specific questions. Always be aware of what the vignette does and doesn’t give you.
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Be sure to master calculator functions
During the exam, you don’t want to be wishing that you had paid more attention to learning the calculator functions. They can be a huge time saver, keeping you from fumbling and wasting time. And anyways, these are skills that will always come in handy.
For more information, visit our CFA Level 1 Study Guide and Level 2 Study Guide
