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CFA Level 1 Study Notes – Quantitative Methods

CFA Level 1 Study Notes – Quantitative Methods

2022 Syllabus

Study Session 1

R01 2022 – 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 2022 – 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 2022 – 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 2022 – 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 2022 – 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 2022 – 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 2022 – 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

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