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CFA Level 1 Study Notes – Quantitative Methods

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CFA Level 1 Study Notes – Quantitative Methods

07 Aug 2019

2023 Syllabus

Study Session 1

R01 2023 – Time Value of Money

-LOS a: interpret interest rates as required rates of return, discount rates, or opportunity costs

-LOS b: 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 c: calculate and interpret the effective annual rate, given the stated annual interest rate and the frequency of compounding

-LOS d: calculate the solution for time value of money problems with different frequencies of compounding

-LOS e. calculate and interpret the future value (FV) and present value (PV) of a single sum of money, an ordinary annuity, an annuity due, a perpetuity (PV only), and a series of unequal cash flows

-LOS f. demonstrate the use of a time line in modeling and solving time value of money problems

R02 2023 – Organizing, Visualizing, and Describing Data

-LOS a: identify and compare data types

-LOS b: describe how data are organized for quantitative analysis

-LOS c: interpret frequency and related distributions

-LOS d: interpret a contingency table

-LOS e: describe ways that data may be visualized and evaluate the uses of specific visualizations.

-LOS f: describe how to select among visualization types.

-LOS g: calculate and interpret measures of central tendency

–LOS h: evaluate alternative definitions of mean to address an investment problem

-LOS i: calculate quantiles and interpret related visualizations

-LOS j: calculate and interpret measures of dispersion

-LOS k: calculate and interpret target downside deviation

-LOS l: interpret skewness

-LOS m: interpret kurtosis

-LOS n: interpret correlation between two variables

R03 2023 – Probability Concepts

–LOS a: define a random variable, an outcome, and an event

– LOS b: identify the two defining properties of probability, including mutually exclusive and exhaustive events, and compare and contrast empirical, subjective, and a priori probabilities

– LOS c: describe the probability of an event in terms of odds for and against the event

– LOS d: calculate and interpret conditional probabilities

– LOS e: demonstrate the application of the multiplication and addition rules for probability

– LOS f: compare and contrast dependent and independent events

– LOS g: calculate and interpret an unconditional probability using the total probability rule

– LOS h: calculate and interpret the expected value, variance, and standard deviation of random variables

– LOS i: explain the use of conditional expectation in investment applications

– LOS j: interpret a probability tree and demonstrate its application to investment problems

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

– LOS l: calculate and interpret the covariances of portfolio returns using the joint probability function

– LOS m: calculate and interpret an updated probability using Bayes’ formula

– LOS n: identify the most appropriate method to solve a particular counting problem and analyze counting problems using factorial, combination, and permutation concepts

Study Session 2

R04 2023 – Common Probability Distributions

-LOS a. define a probability distribution and compare and contrast discrete and continuous random variables and their probability functions

-LOS b. calculate and interpret probabilities for a random variable given its cumulative distribution function

-LOS c. describe the properties of a discrete uniform random variable, and calculate and interpret probabilities given the discrete uniform distribution function

-LOS d. describe the properties of the continuous uniform distribution, and calculate and interpret probabilities given a continuous uniform distribution

-LOS e. describe the properties of a Bernoulli random variable and a binomial random variable, and calculate and interpret probabilities given the binomial distribution function

-LOS f. explain the key properties of the normal distribution

-LOS g. contrast a multivariate distribution and a univariate distribution, and explain the role of correlation in the multivariate normal distribution

-LOS h. calculate the probability that a normally distributed random variable lies inside a given interval

-LOS i. explain how to standardize a random variable

-LOS j. calculate and interpret probabilities using the standard normal distribution

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

-LOS l. explain the relationship between normal and lognormal distributions and why the lognormal distribution is used to model asset prices

-LOS m. calculate and interpret a continuously compounded rate of return, given a specific holding period return

-LOS n. describe the properties of the Student’s t-distribution, and calculate and interpret its degrees of freedom

-LOS o. describe the properties of the chi-square distribution and the F-distribution, and calculate and interpret their degrees of freedom

-LOS p. describe Monte Carlo simulation

R05 2023 – Sampling and Estimation

-LOS a: compare and contrast probability samples with non-probability samples and discuss applications of each to an investment problem

-LOS b: explain sampling error

-LOS c: compare and contrast simple random, stratified random, cluster, convenience, and judgmental sampling

-LOS 5d: explain the central limit theorem and its importance

-LOS e: calculate and interpret the standard error of the sample mean

-LOS f: identify and describe desirable properties of an estimator

-LOS 5g: contrast a point estimate and a confidence interval estimate of a population parameter

-LOS h: calculate and interpret a conidence interval for a population mean, given a normal distribution
with 1) a known population variance, 2) an unknown population variance, or 3) an unknown population variance and a large sample size

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

-LOS j: describe the issues regarding selection of the appropriate sample size, data snooping bias, sample selection bias, survivorship bias, look-ahead bias, and time-period bias

R06 2023 – Hypothesis Testing

– LOS a: define a hypothesis, describe the steps of hypothesis testing, and describe and interpret the choice of the null and alternative hypotheses

– LOS b: distinguish between one-tailed and two-tailed tests of hypotheses

-LOS c: explain a test statistic, Type I and Type II errors, a significance level, how significance levels are used in hypothesis testing,and the power of a test

-LOS d: explain a decision rule and the relation between confidence intervals and hypothesis tests, and determine whether a statistically significant result is also economically meaningful

-LOS e: explain and interpret the p-value as it relates to hypothesis testing

-LOS f: describe how to interpret the significance of a test in the context of multiple tests

– LOS g: identify the appropriate test statistic and interpret the results for a hypothesis test concerning the population mean of both large and small samples when the population is normally or approximately normally distributed and the variance is 1) known or 2) unknown

-LOS h: identify the appropriate test statistic and interpret the results for a hypothesis test concerning the equality of the population means of two at least approximately normally distributed populations based on independent random samples with equal assumed variances

– LOS i: identify the appropriate test statistic and interpret the results for a hypothesis test concerning the mean difference of two normally distributed populations

– LOS j: identify the appropriate test statistic and interpret the results for a hypothesis test concerning 1) the variance of a normally distributed population, and 2) the equality of the variances of two normally distributed populations based on two independent random samples

LOS k: distinguish between parametric and nonparametric tests and describe situations in which the use of nonparametric tests may be appropriate

-LOS l: explain parametric and nonparametric 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 m: explain tests of independence based on contingency table data

R07 2023 – Introduction to Linear Regression

-LOS 7a: describe a simple linear regression model and the roles of the dependent and independent variables in the model

-LOS 7b: describe the least squares criterion, how it is used to estimate regression coefficients, and their interpretation

-LOS 7c: 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 7d: calculate and interpret the coefficient of determination and the F- statistic in a simple linea regression

-LOS 7e: 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 7f: formulate a null and an alternative hypothesis about a population value of a regression coefficient, and determine whether the null hypothesis is rejected at a given level of significance

-LOS 7g: 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 7h: describe different functional forms of simple linear regressions

2024 Syllabus

Learning Module 1 – Rates and Returns

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

Sergio Torrico

2021-07-23

Excelente para el FRM 2 Escribo esta revisión en español para los hispanohablantes, soy de Bolivia, y utilicé AnalystPrep para dudas y consultas sobre mi preparación para el FRM nivel 2 (lo tomé una sola vez y aprobé muy bien), siempre tuve un soporte claro, directo y rápido, el material sale rápido cuando hay cambios en el temario de GARP, y los ejercicios y exámenes son muy útiles para practicar.

diana

2021-07-17

So helpful. I have been using the videos to prepare for the CFA Level II exam. The videos signpost the reading contents, explain the concepts and provide additional context for specific concepts. The fun light-hearted analogies are also a welcome break to some very dry content. I usually watch the videos before going into more in-depth reading and they are a good way to avoid being overwhelmed by the sheer volume of content when you look at the readings.

Kriti Dhawan

2021-07-16

A great curriculum provider. James sir explains the concept so well that rather than memorising it, you tend to intuitively understand and absorb them. Thank you ! Grateful I saw this at the right time for my CFA prep.

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2021-06-28

Very well explained and gives a great insight about topics in a very short time. Glad to have found Professor Forjan's lectures.

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2021-06-22

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2021-05-10

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2021-03-24

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2021-03-18

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