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.
Define:
A priori probability
Probability based on logical analysis rather than on observation/experience or personal judgment.
Define:
Absolute dispersion
The amount of variability, without comparison to any reference point or benchmark.
Define:
Absolute frequency
The number of times an observation occurs for a particular variable or interval.
(for grouped data)
Define:
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.
Define:
Annuity
A finite set of level sequential cash flows.
Define:
Annuity due
An annuity where the first cash flow is paid immediately.
Define:
Bernoulli random variable
A random variable with outcomes of either 0 or 1.
Define:
Bernoulli trial
An experiment which produces one of two outcomes.
Define:
Binomial model
An options pricing model where the underlying price can move to one of two possible new prices.
Define:
Binomial random variable
The number of successes in n Bernoulli trials
probability of success is constant for all, and trials are independent.
Define:
Binomial tree
Model of asset price dynamics where the asset moves up with probability p or down with probability (1 – p).
Define:
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.
Define:
Combination
Ways to choose r objects from n total objects. Order does not matter.
Define:
Conditional probability
The probability of an event occurring, given another event has occurred.
Define:
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
Define:
Continuously compounded return
ln(1+HPR)
Define:
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.
Define:
Correlation coefficient
A number between −1 and +1 measuring the linear relationship between two variables.
Define:
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.
Define:
Covariance matrix
A matrix whose entries are covariances.
Define:
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.
Define:
Cross-sectional data
Observations over individual units at a point in time.
Differs from time-series data.
Define:
Cumulative distribution function
A function giving the probability that a random variable is less than or equal to a specified value.
Define:
Cumulative relative frequency
The fraction of total observations less than the upper limit of a stated interval.
For data grouped into intervals.
Define:
Data mining
Determining a model by repeatedly searching through a dataset for statistically significant patterns.
Define:
Degree of confidence
The probability that a confidence interval includes the unknown population parameter.
Define:
Degrees of freedom (df)
The number of independent observations used.
Define:
Dependent Events
When one event occurring depends on the occurrence of another event.
Define:
Descriptive statistics
Summarizing and communicating the characteristics of the dataset.
Define:
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.
Define:
Discount rates
The interest rate used to calculate a present value.
Define:
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).
Define:
Discrete random variable
A random variable which can be a countable number of possible values.
Define:
Dispersion
Variability around the central tendency.
Define:
Effective annual rate
EAR
The actual rate of return in a year, when interest throughout the year is compounded.
Define:
Effective annual yield
EAY
An annualized return that accounts for the effect of compounding interest.
aka EAR
Define:
Empirical probability
The probability of an event, estimated as a relative frequency of occurrence, based on experimentation or historical data.
Define:
Estimate
The value calculated, using an estimator, from sample observations.
Define:
Estimator
An estimation formula
Formula to calculate sample mean is an example of an estimator
Define:
Estimation
Estimating the value of a population parameter.
Statistical Inference
Define:
Event
An outcome, or set of outcomes, of a random variable.
Define:
Excess kurtosis
Degree to which the peakedness exceeds that of the normal distribution.
Define:
Exhaustive
Covering all possible outcomes.
Define:
Expected value
The probability-weighted average of all possible outcomes for a random variable.
Define:
Frequency distribution
Display of data summarized into a small number of intervals.
Define:
Future value (FV)
The amount a payment, or series of payments, will grow to by a future date.
Define:
Geometric mean
A measure of central tendency computed by taking the nth root of the product of n values.
Define:
Harmonic mean
A type of weighted mean computed by averaging the reciprocals of the observations, then taking the reciprocal of that average.
Define:
Histogram
A bar chart of data grouped into a frequency distribution.
Define:
Holding period return
The return earned during a specified holding period.
aka total return for the period
Define:
Hypothesis testing
The testing of hypotheses about one or more populations.
Major part of inferential statistics. Using a sample to better understand the population.
Define:
Independent
When the occurrence of one event does not change the probability of another event.
Define:
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).
Define:
Interest rate
A rate of return that reflects the relationship between cashflows at different points in time; a discount rate.
IDefine:
IRR rule
Investment decision rule, accept a project or investment if IRR > opportunity cost of capital.
Define:
Joint probability
The probability that both stated events occur.
Define:
Kurtosis
The statistical measure of peakedness of a distribution.
Define:
Leptokurtic
When a distribution is more peaked than a normal distribution.
Define:
Level of significance
The probability of a Type I error in testing a hypothesis.
Define:
Linear interpolation
Estimating an unknown value by using two known values which fall on either side of it.
Define:
Logarithmic scale
A scale in which equal distances represent equal proportional changes in the underlying quantity.
Define:
Linear scale
A scale in which equal distances correspond to equal absolute amounts.
Define:
Mean absolute deviation
The mean of the absolute values of deviations from the sample mean.
Define:
Measure of central tendency
A quantitative measure of where data are centered.
Mean, median, mode
Define:
Median
The value of the middle item when sorted into ascending or descending order.
Define:
Mesokurtic
When a distribution has the same kurtosis as the normal distribution.
meso- means middle or moderate
Define:
Mode
The most frequently occurring value in a set of observations.
Define:
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
Define:
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.
Define:
Multivariate distribution
A probability distribution for a group of related random variables.
multivariate = multiple variables
Define:
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)
Define:
Multivariate normal distribution
A probability distribution for a group of random variables; completely defined by the means, variances, and correlations of the variables.
Define:
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.
Define:
n Factorial
n!
For a positive integer n, the product of the first n positive integers
0 factorial equals 1 by definition.
Define:
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.
Define:
Net present value
NPV
The present value of an investment’s cash inflows (benefits) minus the present value of its cash outflows (costs).
Define:
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.
Define:
Normal distribution
A continuous, symmetric (no skew) probability distribution that is completely described by its mean and variance.
Define:
NPV rule
An investment decision rule: An investment should be undertaken if its NPV is positive.
Define:
One-tailed hypothesis test
Unlike a two-tailed test, where the null is rejeted if the evidence indicates the parameter is either greater than or less than the hypothesized value, the null hypothesis of a one-tailed test is only rejected if the evidence indicates that the population parameter falls on one side of the hypothesized value (either greater, or less, depending on the test.
The alternative hypothesis only has one side.
Define:
Opportunity cost
The value that investors forgo by choosing a particular course of action.
Define:
Ordinary annuity
An annuity with a first cash flow that is paid one period from the present.
Define:
Parameter
A descriptive measure computed from or used to describe a population of data.
Define:
Perpetuity
A set of never-ending level sequential cash flows, with the first cash flow occurring one period from now.
A perpetual annuity
Define:
Parametric test
Any test concerned with parameters, or whose validity depends on the assumption that the population is normally distributed.
Define:
Platykurtic
Less peaked than the normal distribution.
Define:
Population
All members of a specified group.
Define:
Population mean
The arithmetic mean value of a population
Define:
Population variance
A measure of dispersion relating to a population, calculated as the mean of the squared deviations around the population mean.
Define:
Population standard deviation
A measure of a population’s dispersion, in the same unit of measurement as the observations.
the positive square root of the population variance.
Define:
Power of a test
The probability of correctly rejecting the null (rejecting the null hypothesis when it is false).
1-𝛽
Define:
Present value (PV)
The current value of future cash flows. This requires discounting the future cash flows back through time.
Can be used to determine current value of cash inflows from assets, or outflows from liabilities.
Define:
Probability
The chance that an event will occur, represented by a number between 0 and 1.
Define:
Probability distribution
A distribution which specifies the probabilities of a random variable’s possible outcomes.
Define:
Probability density function
A function with non-negative values such that probability can be described by area under the curve.
Define:
Probability function
A function that specifies the probability that the random variable takes on a specific value.
Define:
Quantile
A value at which a stated fraction of the data lies below.
aka fractile
Define:
Random variable
A quantity whose future outcomes are uncertain.
Define:
Range
The difference between the maximum and minimum values in a dataset.
Define:
Risk
The chance of a loss or adverse outcome.
Exposure to uncertainty
Define:
Risk premium
Extra return required for bearing a specified risk.
Define:
Sample
A subset of a population.
Define:
Sample Statistic
A quantity computed from or used to describe a sample.
Define:
Sample selection bias
Bias introduced by systematically excluding some of the population according to a particular attribute
Define:
Sampling error
The difference between the observed value of a statistic and the quantity it is intended to estimate.
Define:
Scenario analysis
Analysis that shows the changes in key financial quantities which would result from specific events. It is a risk management technique considering what the performance of a portfolio would be under specified situations.
Define:
Sensitivity analysis
Analysis of the range of possible outcomes as specific variables are changed.
Define:
Sharpe ratio
The average return in excess of the risk-free rate divided by the standard deviation of returns.
average excess return earned per unit of standard deviation
Define:
Skewness
A quantitative measure of skew (lack of symmetry).
Define:
Spearman rank correlation coefficient
A measure of correlation applied to ranked data.
Define:
Standard deviation
Measure of dispersion, in the same units as the original data.
The positive square root of the variance
Define:
Standardizing
Transforming a set of data by subtracting the mean and dividing the result by the standard deviation. This is done to make the different data comparable.
Define:
Standard normal distribution
The normal density with mean (μ) equal to 0 and standard deviation (σ) equal to 1.
Define:
Statistic
A quantity computed from or used to describe a sample of data.
Define:
Statistically significant
A result indicating that the null hypothesis can be rejected.
Define:
Systematic sampling
A procedure of selecting every nth member from the population until reaching desired sample size.
Resulting sample should be random
Define:
Time-series data
Observations of a variable at multiple points in time.
This differs from cross sectional data, which is at a given point in time.
Define:
t-Test
A hypothesis test using a t-statistic, which follows a t-distribution.
Define:
Time-weighted rate of return
A measure of investment performance (compounded return) which is not sensitive to the timing or size of cashflows (in or out).
In contrast with money weighted rate of return.
Define:
Time value of money
The principles which determine the relationships between cashflows at different points in time.
Define:
Total probability rule
A rule explaining the unconditional probability of an event in terms of probabilities of the event conditional on mutually exclusive and exhaustive scenarios.
Define:
Two-tailed hypothesis test
A test in which the null hypothesis (that the hypothesized value = a specific value) is rejected if indication is that the population parameter is either smaller or larger than a hypothesized value.
This differs from a one tailed test which only considers one direction, not both.
Define:
Type I error
Rejecting a true null hypothesis.
Define:
Type II error
Not rejecting a false null hypothesis.
Define:
Unconditional probability
The probability of an event not affected by another event.
Define:
Variance
Squared deviations from a random variable’s mean (expected value).
Define:
Weighted mean
An average in which each observation is weighted by its relative importance.
Define:
Alternative hypothesis
The hypothesis that is accepted if the null hypothesis is rejected.
Define:
Analysis of variance
ANOVA
Analysis of the sources of variation in a dataset.
Define:
Bayes’ formula
Formula used to update the probability of an event, when new information has been received.
Define:
Bimodal
Distribution with two modes (frequently occuring data)
Define:
Bootstrap
Resampling method which repeatedly draws samples and then replaces them into the original population.
Define:
Box and whisker plot
Graph representing the dispersion of data across quartiles.
Define:
Bubble line chart
Line chart which uses different sized bubbles to represent a third feature of the data.
Define:
categorical data
Values which describe a group of observations and therefore can be used to divide dataset into groups.
Define:
Central limit theorem
The sampling distribution of a variable’s mean approaches a normal distribution as the sample size grows.
Define:
Chi-square test
Test for potential association between categorical variables.
Define:
Confidence level
The degree of confidence that the sample distribution represents the population distribution
Confidence that the population parameter would occur within the confidence interval.
Define:
Continuous data
Data which is measureable and can take on any numerical value within a range of values.
Can be measured, not counted.
Define:
Critical values
The specific test statistic value where the decision changes from fail to reject to reject the null hypothesis.
Define:
Cumulative frequency distribution chart
Either cumulative relative or cumulative absolute frequency plotted on y axis against the upper limit of the interval.
Easy to visualize what percent of observations is below a certain value.
Data
Information
Can be many formats: words, numbers, images, audio
Define:
Dependent variable
Variable whose variation is explained by the regression.
Variation results from variation in the independent variable.
Define:
Error term
Difference between an observation and the expected value.
Define:
Estimated parameters
In regression analysis, estimated values of the population intercept and slope.
Define:
False discovery rate
Rate of type 1 errors when testing a null hypothesis repeatedly for a specific level of significance.
Define:
False discovery approach
Adjustment to p-values when test is performed multiple times.
Define:
Fat tailed
When a distribution has a higher probability of extreme outcomes (fatter tails) than a normal distribution.
leptokurtic
Define:
Grouped bar chart
Bar chart showing joint frequencies for two categorical variables.
Define:
Heteroscedasticity
When variance of the error term differs across observations.
When the variance varies
Define:
Independent variable
The explanatory variable. (Explains the dependent variable in a regression),
Define:
Indicator Variable
Variable with value of either 0 or 1, based on a binary condition.
“Dummy Variable”
Define:
Intercept
Expected value of the dependent variable in a simple linear regression if the independent is zero.
Where the regression line intercepts the y axis, as the x-axis is 0.
Define:
Inverse transformation method
Using randomly generated numbers from a continuous uniform distribution in order to generate random observations from any distributions.
Define:
Jackknife
Resampling method which takes from original observed data sample and leaves out one observation at a time (without replacement).
Define:
Judgmental sampling
Selecting from a population based on own knowledge and judgement.
Define:
Lin-log model
Regression model with independent variable in logarithmic form.
Define:
Linear regression
regression modeling the straight line relationship between the dependent and independent variables.
Define:
Log-log model
Regression model where both dependent and independent variables are in logarithmic form.
Define:
Log-lin model
Regression model where dependent variable is in logarithmic form.
Define:
Mean square error (MSE)
Sum of squares error divided by the degrees of freedom
df =(n - k - 1)
Define:
Mean square regression (MSR)
Sum of squares regression divided by the number of independent variables, k
Define:
Multiplication rule for independent events
When two events are independent, the joint probability of the two is the product of the individual probabilities of each.
Define:
Multiple testing problem
Risk of getting statistically significant result when performing test multiple times.
Define:
Non-probability sampling
Sampling based on factors other than probability, like judgement or convenience.
Define:
Null hypothesis
The hypothesis being tested.
Either reject, or fail to reject (result is not statistically significant).
Define:
Observation
Value of a specific variable
Can becollected at a point in time or over a period.
Define:
Overfitting
When too many independent variables are used to try and explain the dependent. This results in the coefficients being noise rather than a true relationship.
Can cause false sense of predictive power.
Define:
p-value
Smallest level of significance at which the null can be rejected.
Define:
Pearson correlation
Measure of the relationship between two variables.
Correlation
differs from spearman’s rank correlation
Define:
Probability sampling
Sampling method where every member of a population has an equal chance of being selected.
Define:
Probability tree diagram
Diagram where branches, with the probabilities, stem from nodes, representing events.
The branches are mutually exclusive
Define:
Regression analysis
Used to examine if a variable is useful in explaining another variable.
Define:
Regression coefficients
Intercept and slope coefficients of a regression.
Define:
Resampling
Repeatedly drawing samples from original data sample in order to statistically infer population parameters.
Define:
Residual
Difference between the observation and the predicted value.
Define:
Sample correlation coefficient
Standardized measure of how two variables move together.
standardizing the covariance
done by dividing the covariance by the product of the two variables’ standard deviation
Define:
Scatter plot
When two variables are plotted along the axis and points represent pairs of the two variables.
Define:
Slope coefficient
Coefficient of an independent variable.
Average change in the dependent variable per one-unit change in the independent.
Define:
Spurious correlation
When a correlation between variables is not a causal relationship. It may actually be due to chance or a relationship with a third variable.
Define:
Stacked bar chart
Bars represent sub-groups and are placed on top of each other to form a single bar. Each sub section is a different color to represent its contribution, and overall height represents the marginal frequency for the category.
Define:
Standard error of the estimate
Measure of the fit of a regression line.
Square root of the Mean Squared Error
Define:
Standard error of the forecast
Measure of the uncertainty associated with a forecasted value of the dependent variable.
Define:
Standard error of the slope coefficient
The ratio of the SEE:square root of the variation of the independent variable.
Define:
Stratified random sampling
Sampling method in which the population is divided into subpopulations (strata) based on criteria, then random samples are drawn from each.
Sample proportional to size of stratum relative to overall population.
Define:
Structured data
Data that are highly organized in a pre-defined manner.
Define:
Sum of squares error
SSE
Sum of the squared deviations of the observed dependent variable and the estimated value (based on the estimated regression line).
Aka the residual sum of squares.
Define:
Sum of squares regression
SSR
Sum of the squared deviations of the estimated value of the dependent variable (based on the regression line), and the mean of the dependent variable.
Define:
Sum of squares total
SST
Sum of the squared deviations of the observed dependent variable from its mean.
SST=SSR+SSE
Define:
Thin tailed
A distribution with a lower number of extreme outcomes than the normal distribution.
platykurtic
Define:
Tree map
Set of colored rectangles representing groups, the area of each is proportional to the value of the group.
Define:
Two dimensional rectangular array
A data table. Columns and rows hold multiple variables and observations.
Define:
Unimodal
Distribution with one mode (most fequent value).
Define:
Variable
Quantity or characteristic which can be measured, counted, or categorized and is subject to change.
