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
