Learning Module 2: The Time Value of Money in Finance

• Calculate and interpret the present value (PV) of fixed-income and equity instruments based on expected future cash flows.

• 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.

• 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

• Calculate, interpret, and evaluate measures of central tendency and location to address an investment problem.

• Calculate, interpret, and evaluate measures of dispersion to address an investment problem.

• Interpret and evaluate measures of skewness and kurtosis to address an investment problem.

• Interpret the correlation between two variables to address an investment problem.

Learning Module 4: Probability Trees and Conditional Expectations

• Calculate expected values, variances, and standard deviations and demonstrate their application to investment problems.

• Formulate an investment problem as a probability tree and explain the use of conditional expectations in investment application.

• Calculate and interpret an updated probability in an investment setting using Bayes’ formula.

Learning Module 5: Portfolio Mathematics

• Calculate and interpret the expected value, variance, standard deviation, covariances, and correlations of portfolio returns.

• Calculate and interpret the covariance and correlation of portfolio returns using a joint probability function for returns.

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

Learning Module 6: Simulation Methods

• 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.

• Describe Monte Carlo simulation and explain how it can be used in investment applications.

• Describe the use of bootstrap resampling in conducting a simulation based on observed data in investment applications.

Module 7: Estimation and Inference

• Compare and contrast simple random, stratified random, cluster, convenience, and judgmental sampling and their implications for sampling error in an investment problem.

• Explain the central limit theorem and its importance for the distribution and standard error of the sample mean.

• Describe the use of resampling (bootstrap, jackknife) to estimate the sampling distribution of a statistic.

Learning Module 8: Hypothesis Testing

• Explain hypothesis testing and its components, including statistical significance, Type I and Type II errors, and the power of a test.

• Construct hypothesis tests and determine their statistical significance, the associated Type I and Type II errors, and power of the test given a significance level.

• 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 Tests of Independence

• 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.

• Explain tests of independence based on contingency table data.

Learning Module 10: Simple Linear Regression

• Describe a simple linear regression model, how the least squares criterion is used to estimate regression coefficients, and the interpretation of these coefficients.

• Explain the assumptions underlying the simple linear regression model, and describe how residuals and residual plots indicate if these assumptions may have been violated.

• Calculate and interpret measures of fit and formulate and evaluate tests of fit and of regression coefficients in a simple linear regression.

• 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.

• 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.