Module 1-3 Pre-Requisite Quantitative Methods

A comprehensive set of vocabulary flashcards covering basic financial math, data classification, descriptive statistics, and fundamental probability rules from Modules 1 through 3.

Default Risk

Risk that issuer of bond or credit will go bankrupt or not be able to pay

Equilibrium Interest Rate

Required rate of return for a particular investment

Real Risk Free Rate

Rate in absence of inflation

Liquidity Risk

Risk that you’ll need to accept a lower than fair value price to convert into cash

Risk Premium

Default risk premium + liquidity risk premium + maturity risk premium

Stated Rate

Rate that does not account for interest earned on interest (Stated rate and EAR only equal when compounding annually)

Periodic Rate

Stated rate / $m$

Perpetuity

Infinite series of equal payments ($PV = \frac{\text{pmt}}{I/Y}$), calculated one period before the first payment

Ordinary Annuity

Equal cash flows at the end of each period

Annuity Due

Equal cash flows at the beginning of each period

Present Value (Single Sum)

$$PV = \frac{FC}{(1+I/Y)^N}$$

Future Value (Single Sum)

$$FV = PV(1+I/Y)^N$$

Amortization

Process of spreading out a loan into a series of fixed equal payments over time

Effective Annual Rate (EAR)

True cost or yield for an investment or loan ($EAR = (1+\text{Periodic Rate})^M - 1$)

Nominal Risk Free Rate

Real risk free rate + Expected inflation

T Bills

Short term, low risk debt securities issued by the government

Maturity Risk

The risk that the longer time to maturity the higher the sensitivity to interest rate changes

Annuity

Receiving or paying equal cash flows spaced evenly over a period of time

Determining Quantiles

$$L_y = (n+1) \times \frac{y}{100}$$

Numerical Data

Can be counted or measured

Discrete Data

Data in countable units

Continuous Data

Can take on any fractional value

Nominal Data

Labels with no logical ordering (e.g., energy companies)

Categorical Data

Labels for grouping or classifying data

Ordinal Data

Labels that can be ordered or ranked (e.g., Small Cap Firms)

Frequency Distribution

Summarizes large data sets by assigning the observation to intervals

Time Series Data

Data collected at equal time intervals (e.g., Monthly stock returns for a company)

Cross Sectional Data

Data collected at a single point in time (e.g., 2023 Returns for a sample of utility companies)

Panel Data

Combination of cross sectional and time series data (e.g., Monthly returns for utility companies during 2023)

Structured Data

Organized in a defined way such as time series or cross sectional

Unstructured Data

Information in forms with no defined structure (typically needs to be transformed into structured data for analysis)

One-Dimensional Array

Represents a single variable (e.g., time series)

Two-Dimensional Array (or Data table)

Represents two variables (e.g., panel data)

Absolute Frequency

$\#$ of observations

Relative Frequency

$\%$ of all observations ($\frac{\# \text{ of observations}}{\text{Total observations}}$)

Cumulative Absolute Frequency

Sum of values less than the upper bound of each interval

Cumulative Relative Frequency

Total percentage of observations less than the upper bound of each interval

Contingency Tables

Two dimensional array that displays joint frequencies of two variables

Marginal Frequency

Total of a specific row or column

Confusion Matrix

Contingency table that displays predicted and actual occurrences of an event

Frequency Polygon

Use midpoints of each interval and connect with line

Measures of central tendency

Center of a data set or average of data set

Sample Mean

Mean of a subset of a population

Population Mean

Mean of an entire population

Trimmed Mean

Exclude the most extreme observations (e.g., $1\%$ trimmed mean excludes $0.5\%$ greatest and $0.5\%$ smallest observations)

Winsorized Mean

Substitute values for the most extreme observations (e.g., $90\%$ winsorized mean substitutes $95\text{th}$ percentile value for greatest $5\%$ and the $5\text{th}$ percentile value for smallest $5\%$)

Arithmetic Mean

Sum of observations / $\#$ of observations; good for estimating a single future observation from a distribution

Median

Midpoint of data set or average of two middle observations

Mode

Most frequently occurring value in the data set (there can be multiple modes)

Geometric Mean

Used for compound rate of return over multiple periods; arithmetic exceeds geometric more as variability of returns increases

Harmonic Mean

Used to find average cost per share of a stock purchased over time if each purchase is a constant dollar amount

Inter quartile range

$3\text{rd}$ quartile minus $1\text{st}$ quartile (Middle $50\%$)

Range

Difference between the largest and smallest values in a data set

Mean absolute deviation (MAD)

Average of the absolute values of deviation from the mean

Coefficient of variation (CV)

Measure of risk per unit of return

Target Downside Deviation (Target Semi Deviation)

Measures investment risk by calculating volatility of returns that fall below a specific threshold

Random Variable

Uncertain Value

Outcome

Realization of a random variable

Event

Set of one or more outcomes

Mutually exclusive

Events that cannot happen simultaneously; Joint probability is always $0$

Exhaustive

Set of events that includes all possible outcomes

Empirical Probability

Based on analysis of data (objective)

A Priori Probability

Based on reasoning, not experience (objective)

Odds for A

$$\frac{P(A)}{1 - P(A)}$$

Odds against A

$$\frac{1 - P(A)}{P(A)}$$

Unconditional probability (marginal probability)

The probability of an event regardless of the outcomes of other events

Conditional probability

The probability of $A$ given that $B$ has occurred ($P(A|B)$)

Addition Probability Rule

$$P(A \text{ or } B) = P(A) + P(B) - P(AB)$$

Multiplication Probability Rule

$P(AB) = P(A|B) \times P(B)$ (Joint probability)

Total Probability Rule

$$P(A) = P(A|B) \times P(B) + P(A|B^c) \times P(B^c)$$

Independent events

Knowing the outcome of one does not change the probability of occurrence of the other

Combination Formula

Calculates the number of ways to select a subset of items where the order of selection does not matter

Permutation Formula

Number of ways to arrange items in a specific sequence where order matters