CFA® Quantitative Methods
CFA® Institute’s Quantitative Methods curriculum introduces 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. For example, if you invest $100 today into a bank account that pays 5% effective annual interest, you will have $105 in a year. The 5% rate of return and the duration of one year are the factors that relate the present value of $100 to the future value of $105.
Of course, actual exam questions are more complex and may involve discounting or compounding a series of cash flows over many periods. Such questions may ask you to determine present value, future value, the discount rate, the size of the intermittent cash flows, or the length of time involved.
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 is included 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%, 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.
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 Readings||No. of Formulas||No. of Questions|
|8-12%||7||ca. 100||ca. 18|
Syllabus & Readings Overview
The CFA Level 1 Quantitative Methods syllabus spans 7 readings and contains 73 LOS. It is divided into the following two study sessions:
|Study Session||No. of Readings||No. of LOS||Summary|
|1||3||34||Introduces quantitative techniques and concepts such as the time value of money (TVM) and discounted cash flow analysis. Methods for visualizing and organizing data are introduced. Additionally, probability theory and its application are covered.|
|2||4||39||Introduces common probability distributions used to describe random variable behavior (asset prices/returns). Provides a framework for hypothesis testing. Ends with coverage of simple linear regression as a method for understanding the relationship between two variables to facilitate forecasting.|
The CFA Level 1 exam includes 60 total readings for 2022. The first seven readings (1-7) center on Quantitative Methods (11.6% of the total curriculum).
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 equivalent value at a future date of 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.
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.
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.
Exam weight and Topic Changes in Quantitative Methods Level 1
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%.
Other changes include:
- Added: Organizing, Visualizing, and Describing Data, and Introduction to Linear Regression
- Updated: Probability Concepts, Common Probability Distributions, Sampling & Estimate, and Hypothesis Testing, 2 LOS
- Removed: 1 LOS
Study Tips for Quantitative Methods L1
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.
Lots of Practice and Repetition
CFA Institute suggests the importance of practice, particularly the CFA quant section. UWorld’s Qbank provides over 350 individual questions and explanations 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 format.
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.
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.
Quantitative Methods is one of the more difficult topics in the CFA Level 1 and Level 2 curriculum, since it is often the least familiar. Candidates who have not had much exposure to quantitative techniques and concepts may have a harder time with this topic.
The CFA Quant section is the most formula-driven and mathematical. It is also significant in the CFA exam at the first two levels, accounting for 12%of the exam at Level 1 and 5-10% of the Level 2 exam. But the knowledge really carries over into all sections of the curriculum, so candidates must understand the fundamentals of Quantitative Methods at Level 1. People learn quantitative ideas differently, but it’s always best to practice, practice, practice.
The best method, after reviewing the CFA Institute curriculum, is to adopt an active learning approach. But don’t just take our word for it. Give us a try and discover for yourself what it’s like to experience active learning with UWorld’s extensive Level 1 Qbank and with our Level 2 Qbank (expected September 2022).