# Quantitative Methods Flashcards

## Acquire knowledge of time value of money, data organization and visualization, probability concepts, common probability distributions, sampling and estimation, hypothesis testing, and linear regression.

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*A priori* probability

Probability **based on logical analysis** rather than on observation/experience or personal judgment.

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Absolute dispersion

The **amount of variability**, without comparison to any reference point or benchmark.

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Absolute frequency

**The number of times an observation occurs** for a particular variable or interval.

(for grouped data)

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Addition rule

for probabilities

The probability that A **or** B occurs equals the probability that A occurs, plus the probability that B occurs, minus the probability that both A and B occur.

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Annuity

A finite set of **level sequential cash flows**.

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Annuity due

An annuity where the **first cash flow is paid immediately**.

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Bernoulli random variable

A random variable with outcomes of either 0 or 1.

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Bernoulli trial

An experiment which produces one of two outcomes.

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Binomial model

An options pricing model where the underlying price can move to one of **two possible new prices**.

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Binomial random variable

The number of successes in *n* Bernoulli trials

probability of success is constant for all, and trials are independent.

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Binomial tree

Model of asset price dynamics where the asset moves up with probability p or down with probability (1 – p).

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Coefficient of variation

(CV) The relationship between the standard deviation of a set of observations and their mean value.

Makes it easier to compare “risk/reward” across datasets.

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Combination

Ways to choose *r* objects from *n* total objects. **Order does not matter**.

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Conditional probability

The probability of an event occurring, given another event has occurred.

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Continuous random variable

A random variable whose range of possible outcomes is the real line (all real numbers between −∞ and +∞) or some subset of the real line.

uncountable

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Continuously compounded return

ln(1+HPR)

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Correlation

A measure of the comovement (**linear relationship**) between two random variables.

A number between −1 and +1

A standardized version of covariance, demonstrating direction and strength of linear relationship.

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Correlation coefficient

A number between −1 and +1 measuring the linear relationship between two variables.

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Covariance

A measure of the co-movement (linear association) between two random variables.

Measure of how the variation in two variables changes together. Covariability of the two variables around their respective means.

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Covariance matrix

A matrix whose entries are covariances.

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Cross-sectional analysis

Analysis that involves comparisons across individuals in a group *at a point in time*.

Differs from time-series analysis, which analyzes over time.

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Cross-sectional data

Observations over individual units *at a point in time.*

Differs from time-series data.

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Cumulative distribution function

A function giving the probability that a random variable is **less than or equal to** a specified value.

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Cumulative relative frequency

The fraction of total observations less than the upper limit of a stated interval.

For data grouped into intervals.

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Data mining

Determining a model by repeatedly searching through a dataset for statistically significant patterns.

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Degree of confidence

The probability that a confidence interval includes the unknown population parameter.

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Degrees of freedom (df)

The number of independent observations used.

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Dependent Events

When one event occurring depends on the occurrence of another event.

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Descriptive statistics

Summarizing and communicating the characteristics of the dataset.

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Discount

1)Reducing value of a future payment for how far away it is in time (calculating present value of a future amount).

2) the amount an instrument is priced below its face (par) value.

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Discount rates

The interest rate used to calculate a present value.

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Discounted cash flow models

Valuation models that *estimate the intrinsic value* of a security as the **present value of the future benefits** expected to be received (dividends).

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Discrete random variable

A random variable which can be a **countable** number of possible values.

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Dispersion

Variability around the central tendency.

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Effective annual rate

EAR

The actual rate of return in a year, when interest throughout the year is compounded.

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Effective annual yield

EAY

An annualized return that accounts for the effect of compounding interest.

aka EAR

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Empirical probability

The probability of an event, estimated as a relative frequency of occurrence, **based on experimentation or historical data.**

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Estimate

The value calculated, using an estimator, from sample observations.

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Estimator

An estimation formula

Formula to calculate sample mean is an example of an estimator

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Estimation

Estimating the value of a population parameter.

Statistical Inference

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Event

An *outcome*, or set of outcomes, of a random variable.

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Excess kurtosis

Degree to which the peakedness exceeds that of the normal distribution.

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Exhaustive

Covering all possible outcomes.

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Expected value

The probability-weighted average of all possible outcomes for a random variable.

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Frequency distribution

Display of data summarized into a small number of intervals.

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Future value (FV)

The amount a payment, or series of payments, will grow to by a future date.

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Geometric mean

A measure of central tendency computed by taking the *nth* root of the product of *n* values.

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Harmonic mean

A type of weighted mean computed by averaging the reciprocals of the observations, then taking the reciprocal of that average.

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Histogram

A bar chart of data grouped into a frequency distribution.

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Holding period return

The return earned during a specified holding period.

aka total return for the period

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Hypothesis testing

The testing of hypotheses about one or more populations.

Major part of inferential statistics. Using a sample to better understand the population.

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Independent

When the occurrence of one event **does not change the probability** of another event.

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Internal rate of return

The **discount rate that results in NPV = 0**; said differently, the discount rate where PV( investment’s costs)= PV(investment’s benefits).

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Interest rate

A *rate of return* that reflects the **relationship between cashflows** at *different points in time*; a discount rate.

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IRR rule

Investment decision rule, accept a project or investment if **IRR > opportunity cost** of capital.

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Joint probability

The probability that **both stated events occur**.

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Kurtosis

The statistical measure of **peakedness of a distribution.**

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Leptokurtic

When a distribution is **more peaked** than a normal distribution.

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Level of significance

The **probability of a Type I error** in testing a hypothesis.

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Linear interpolation

Estimating an unknown value by using two known values which fall on either side of it.

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Logarithmic scale

A scale in which equal distances represent equal **proportional changes** in the underlying quantity.

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Linear scale

A scale in which equal distances correspond to equal **absolute amounts**.

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Mean absolute deviation

The mean of the **absolute values** of deviations from the sample mean.

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Measure of central tendency

A quantitative measure of where data are centered.

Mean, median, mode

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Median

The value of **the middle item** when sorted into ascending or descending order.

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Mesokurtic

When a distribution has the **same kurtosis as the normal distribution.**

meso- means middle or moderate

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Mode

The **most frequently occurring** value in a set of observations.

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Money-weighted return

The IRR of a portfolio, considering all cash flows. It measures the rate of return over time while considering the impact of withdrawals, deposits, and transfers.

The money weighted return = IRR

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Monte Carlo simulation

A simulation with repeated random sampling, given a set of variable inputs, which is used **to estimate a probability distribution of outcomes**.

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Multivariate distribution

A probability distribution for a **group of related random variables**.

multivariate = multiple variables

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**Multiplication rule** for probabilities

The **joint probability** of events A and B equals the probability of A given B multiplied by the probability of B.

P(A and B) = P(A|B) x P(B)

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Multivariate normal distribution

A **probability distribution for a group of random variables**; completely defined by the means, variances, and correlations of the variables.

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Mutually exclusive projects

When the projects or choices compete directly with each other. It is **not possible to choose/complete both**, it is a binary decision.

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n Factorial

n!

For a positive integer n, the product of the first n positive integers

0 factorial equals 1 by definition.

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Nash equilibrium

When two or more participants in a *non-cooperative game* have **no incentive to deviate from their own equilibrium strategies** given their opponent’s strategies.

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Net present value

NPV

The present value of an investment’s cash inflows (benefits) minus the present value of its cash outflows (costs).

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Nonconventional cash flow

A cashflow pattern where the **initial outflow is not followed by inflows only**. Cash flows can flip multiple times from positive (inflows) to negative (outflows) and back to positive again.