Quantitative Methods provides the mathematical foundation for investment analysis. It covers the time value of money, statistical concepts, probability theory, hypothesis testing, and regression analysis. These tools are used throughout the CFA curriculum.
The time value of money (TVM) is the concept that a dollar today is worth more than a dollar in the future due to its earning potential. Key calculations include present value (PV), future value (FV), annuities (ordinary and annuity due), and perpetuities. Understanding TVM is fundamental to bond valuation, equity valuation, and capital budgeting.
Descriptive statistics summarize data through measures of central tendency (mean, median, mode), dispersion (range, variance, standard deviation), and shape (skewness, kurtosis). The arithmetic mean is used for single-period returns, the geometric mean for multi-period returns, and the harmonic mean for dollar-cost averaging scenarios.
Probability theory underpins risk analysis. Key concepts include conditional probability, Bayes' theorem, expected value, variance of random variables, and covariance/correlation between variables. The multiplication rule, addition rule, and total probability rule are essential tools for calculating joint and conditional probabilities.
The normal distribution is the most important continuous distribution in finance, characterized by its bell shape and defined by mean and standard deviation. The standard normal distribution (z-distribution) has mean 0 and standard deviation 1. Other key distributions include the t-distribution (used with small samples), chi-square, and F-distribution. The lognormal distribution is used to model asset prices.
Hypothesis testing is a statistical method for making decisions about population parameters based on sample data. The process involves stating null and alternative hypotheses, selecting a significance level, calculating a test statistic, and making a decision. Key tests include z-tests, t-tests, chi-square tests, and F-tests. Type I error (rejecting a true null) and Type II error (failing to reject a false null) are critical concepts.
Calculates the future value of a lump sum invested at rate r for n periods.
Discounts a future cash flow back to its present value.
Present value of a series of equal payments at the end of each period.
Future value of a series of equal payments at the end of each period.
Present value of an infinite series of equal payments.
Measures the dispersion of sample data around the mean.
Standardized measure of dispersion relative to the mean; useful for comparing risk across investments with different expected returns.
Updates the probability of event A given new information B.
Number of standard deviations an observation is from the population mean.
A structured approach to statistical inference used throughout quantitative analysis.
The foundational principle that money available now is worth more than the same amount in the future.