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Access detailed syllabus, curriculum changes, and essential formulas for CFA and FRM programs.

Quantitative Methods

Learning outcomes and topics for Quantitative Methods

Course

Session

1. Returns of Financial Assets and Instruments

  • a. describe, compare, and interpret returns
  • b. describe, compare, and interpret required rates of return, risk-free rates, risk premia, and inflation

2. Types of Financial Returns

  • a. calculate, compare, and interpret different types of returns for financial assets, instruments, and indicators

3. Benchmarking Returns

  • a. calculate and compare money-weighted and time-weighted rates of return
  • b. describe the choices and the implications of the different weighting methods used in index construction and management, and calculate, interpret, and explain the value and the returns of an index

4. The Time Value of Money in Finance

  • a. calculate and interpret the present value of fixed-income and equity instruments based on expected future cash flows
  • b. calculate and interpret the implied return of fixed-income instruments and required return and implied growth of equity instruments given their present value and cash flows
  • c. explain the cash flow additivity principle and its importance for the condition of no arbitrage, and explain its use in calculating implied forward interest rates, forward exchange rates, and option values

5. Statistical Characteristics of Asset Returns

  • a. calculate, interpret, and evaluate various measures of (1) central tendency and location and (2) dispersion
  • b. describe, interpret, and evaluate measures of skewness and kurtosis
  • c. calculate, interpret, and evaluate covariance and correlation
  • d. calculate, interpret, and evaluate semi-deviation and coefficient of variation

6. Statistical Distributions for Financial Asset Prices and Returns

  • a. calculate, interpret, and evaluate unconditional expected values for mean, variance, and covariance
  • b. calculate, interpret, and evaluate the principal moments of key statistical distributions used in finance
  • c. calculate, interpret, and evaluate conditional expectations, variances, and covariances
  • d. formulate investment problems through Bayesian updating

7. Estimation and Hypothesis Testing

  • a. explain the central limit theorem and the application of confidence intervals and sampling methodologies
  • b. explain hypothesis testing and its components, including statistical significance, Type I and Type II errors, and the power of a test; construct appropriate hypothesis tests; and interpret the results
  • c. compare and contrast parametric and non-parametric tests, describe situations in which each is the more appropriate type of test, construct appropriate hypothesis tests, and interpret the results

8. The Return and Risk of a Financial Portfolio

  • a. calculate, interpret, and evaluate the expected return, variance, standard deviation, covariance, and correlation of portfolio returns
  • b. describe, calculate, and interpret the minimum-variance portfolio and portfolios that lie on the efficient frontier
  • c. explain the selection of an optimal portfolio, given an investor�s risk aversion and the capital allocation line, and how this extends to the market portfolio and the capital market line

9. Simulation of Financial Asset Prices and Returns

  • a. describe historical simulation and explain how it can be used in investment applications
  • b. describe bootstrap resampling, and explain how it can be used in investment applications
  • c. describe Monte Carlo simulation and explain how it can be used in investment applications

10. Applications of Simple Linear Regression in Finance

  • a. describe, interpret, and explain simple linear regression, including coefficient estimation using the least squares criterion
  • b. describe and compare the assumptions of simple linear regression, identify violations through analyzing residuals, evaluate the estimated model�s goodness-of-fit and regression coefficients, and results of ANOVA estimates
  • c. calculate and interpret predicted values, the standard error of the estimate, and prediction intervals for the dependent variable in a simple linear regression model and describe different functional forms
  • d. calculate and interpret the variable estimates of the capital asset pricing model (CAPM)

11. Introduction to Financial Data Science

  • a. describe how big data, machine learning, and artificial intelligence are used in financial data science, fintech, and investment management