# 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.

*Question of the Week*.

## 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.

**Exam weight**

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.

### 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.

## 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%.

2018 | 2019 | 2020 | 2021 | 2022 |
---|---|---|---|---|

12% | 10% | 10% | 10% | 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.

## What is CFA Level 2 Quantitative Methods Topic?

CFA Level 2 Quantitative Methods builds on the material covered in Level 1 while emphasizing hypothesis testing. At 5-10%, Quantitative Methods is one of the less heavily weighted topics on the exam.

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, meaning that approximately **6-8** of the **88** CFA Level 2 exam questions focus on this topic.

Topic Weight | No. of Readings | No. of Formulas | No. of Questions |
---|---|---|---|

8-12% | 5 | ca. 50 | ca. 7 |

## Syllabus & Readings Overview

The CFA Level 2 Quantitative Methods syllabus spans 5 readings and contains 50 LOS. It is divided into the following two study sessions:

Study Session | No. of Readings | No. of LOS | Summary |
---|---|---|---|

1 | 3 | 38 | Covers how to use linear regression and time-series analysis as tools in financial analysis for identifying relationships among variables. The session also explores multiple regression. |

2 | 2 | 12 | Covers fundamental techniques related to fintech and its influence on the investment industry. Techniques in machine learning (ML) and an examination of sentiment analysis are also explored. |

The CFA Level 2 exam includes 47 total readings for 2022. Five of these readings (1-5) center on Quantitative Methods (10.6% of the total curriculum).

### Introduction to Linear Regression

Introduction to Linear Regression is the final reading for CFA Level 1 Quantitative Methods. For 2022, it is repeated in the Level 2 curriculum. The learning outcome statements and readings are the same at Level 2.

For a description of this reading, please refer to “Introduction to Linear Regression” in this article’s Level 1 reading section.

### 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.

- 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.

### 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.

## Exam Weight and Topic Changes in Quantitative Methods Level 2

The weight of the Quantitative Methods section has consistently remained at 5-10% since 2018. Other changes include:

2018 | 2019 | 2020 | 2021 | 2022 |
---|---|---|---|---|

5-10% | 5-10% | 5-10% | 5-10% | 5-10% |

**Updated**: Introduction to Linear Regression, and Multiple Regression, 2 LOS**Removed**: Excerpt from “Probabilistic Approaches”

## Study Tips for Quantitative Methods L2

- Level 2 is more conceptual than Level 1, but you’ll still have to do the math
- Put the time in
- Understand and practice your vignette exam technique
- Be sure to master calculator functions

## What is CFA Level 3 Quantitative Methods Topic?

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 Level 3. Visit our **CFA level 3 study guide** for more information about these topics.

## FAQs

### Is the Quantitative Method topic hard?

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.

### How can I study Quantitative Methods for the CFA exam?

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.

### How do I practice for the CFA Quantitative Methods topic?

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).