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.
1
Q
Define:
A priori probability
A
Probability based on logical analysis rather than on observation/experience or personal judgment.
2
Q
Define:
Absolute dispersion
A
The amount of variability, without comparison to any reference point or benchmark.
3
Q
Define:
Absolute frequency
A
The number of times an observation occurs for a particular variable or interval.
For grouped data.
4
Q
Define:
Addition rule
for probabilities
A
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.
5
Q
Define:
Annuity
A
A finite set of level sequential cash flows.
6
Q
Define:
Annuity due
A
An annuity where the first cash flow is paid immediately.
7
Q
Define:
Bernoulli random variable
A
A random variable with outcomes of either 0 or 1.
8
Q
Define:
Bernoulli trial
A
An experiment which produces one of two outcomes.
9
Q
Define:
Binomial model
A
An options pricing model where the underlying price can move to one of two possible new prices.
10
Q
Define:
Binomial random variable
A
The number of successes in n Bernoulli trials.
Probability of success is constant for all, and trials are independent.
11
Q
Define:
Binomial tree
A
Model of asset price dynamics where the asset moves up with probability p or down with probability (1 – p).
12
Q
Define:
Coefficient of variation
A
The relationship between the standard deviation of a set of observations and their mean value.
Makes it easier to compare “risk/reward” across datasets.
13
Q
Define:
Combination
A
Ways to choose r objects from n total objects. Order does not matter.
14
Q
Define:
Conditional probability
A
The probability of an event occurring, given another event has occurred.
15
Q
Define:
Continuous random variable
A
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
16
Q
Define:
Continuously compounded return
A
ln(1+HPR)
17
Q
Define:
Correlation
A
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.
18
Q
Define:
Correlation coefficient
A
A number between −1 and +1 measuring the linear relationship between two variables.
19
Q
Define:
Covariance
A
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.
20
Q
Define:
Covariance matrix
A
A matrix whose entries are covariances.
21
Q
Define:
Cross-sectional analysis
A
Analysis that involves comparisons across individuals in a group at a point in time.
Differs from time-series analysis, which analyzes over time.
22
Q
Define:
Cross-sectional data
A
Observations over individual units at a point in time.
Differs from time-series data.
23
Q
Define:
Cumulative distribution function
A
A function giving the probability that a random variable is less than or equal to a specified value.
24
Q
Define:
Cumulative relative frequency
A
The fraction of total observations less than the upper limit of a stated interval.
For data grouped into intervals.
25
# Define:
Data mining
Determining a model by repeatedly searching through a dataset for statistically significant patterns.
26
# Define:
Degree of confidence
The probability that a confidence interval includes the unknown population parameter.
27
# Define:
Degrees of freedom
| (DF)
The number of independent observations used.
28
# Define:
Dependent Events
When one event occurring depends on the occurrence of another event.
29
# Define:
Descriptive statistics
Summarizing and communicating the characteristics of the dataset.
30
# 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.
31
# Define:
Discount rates
The interest rate used to calculate a present value.
32
# 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).
33
# Define:
Discrete random variable
A random variable which can be a **countable** number of possible values.
34
# Define:
Dispersion
Variability around the central tendency.
35
# Define:
Effective annual rate
| (EAR)
The actual rate of return in a year, when interest throughout the year is compounded.
36
# Define:
Effective annual yield
| (EAY)
An annualized return that accounts for the effect of compounding interest.
## Footnote
aka EAR
37
# Define:
Empirical probability
The probability of an event, estimated as a relative frequency of occurrence, **based on experimentation or historical data.**
38
# Define:
Estimate
The value calculated, using an estimator, from sample observations.
39
# Define:
Estimator
An estimation formula.
## Footnote
Formula to calculate sample mean is an example of an estimator.
40
# Define:
Estimation
Estimating the value of a population parameter.
## Footnote
Statistical Inference.
41
# Define:
Event
An *outcome*, or set of outcomes, of a random variable.
42
# Define:
Excess kurtosis
Degree to which the peakedness exceeds that of the normal distribution.
43
# Define:
Exhaustive
Covering all possible outcomes.
44
# Define:
Expected value
The probability-weighted average of all possible outcomes for a random variable.
45
# Define:
Frequency distribution
Display of data summarized into a small number of intervals.
46
# Define:
Future value
| (FV)
The amount a payment, or series of payments, will grow to by a future date.
47
# Define:
Geometric mean
A measure of central tendency computed by taking the *nth* root of the product of *n* values.
48
# Define:
Harmonic mean
A type of weighted mean computed by averaging the reciprocals of the observations, then taking the reciprocal of that average.
49
# Define:
Histogram
A bar chart of data grouped into a frequency distribution.
50
# Define:
Holding period return
The return earned during a specified holding period.
## Footnote
aka total return for the period
51
# Define:
Hypothesis testing
The testing of hypotheses about one or more populations.
## Footnote
Major part of inferential statistics. Using a sample to better understand the population.
52
# Define:
Independent
When the occurrence of one event **does not change the probability** of another event.
53
# 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).
54
# Define:
Interest rate
A *rate of return* that reflects the **relationship between cashflows** at *different points in time*; a discount rate.
55
# Define:
IRR rule
Investment decision rule, accept a project or investment if **IRR > opportunity cost** of capital.
56
# Define:
Joint probability
The probability that **both stated events occur**.
57
# Define:
Kurtosis
The statistical measure of **peakedness of a distribution.**
58
# Define:
Leptokurtic
When a distribution is **more peaked** than a normal distribution.
59
# Define:
Level of significance
The **probability of a Type I error** in testing a hypothesis.
60
# Define:
Linear interpolation
Estimating an unknown value by using two known values which fall on either side of it.
61
# Define:
Logarithmic scale
A scale in which equal distances represent equal **proportional changes** in the underlying quantity.
62
# Define:
Linear scale
A scale in which equal distances correspond to equal **absolute amounts**.
63
# Define:
Mean absolute deviation
The mean of the **absolute values** of deviations from the sample mean.
64
# Define:
Measure of central tendency
A quantitative measure of where data are centered.
## Footnote
Mean, median, mode
65
# Define:
Median
The value of **the middle item** when sorted into ascending or descending order.
66
# Define:
Mesokurtic
When a distribution has the **same kurtosis as the normal distribution.**
## Footnote
meso - means middle or moderate
67
# Define:
Mode
The **most frequently occurring** value in a set of observations.
68
# 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.
## Footnote
The money weighted return = IRR
69
# 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**.
70
# Define:
Multivariate distribution
A probability distribution for a **group of related random variables**.
## Footnote
multivariate = multiple variables
71
# 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.
## Footnote
P(A and B) = P(A|B) x P(B)
72
# Define:
Multivariate normal distribution
A **probability distribution for a group of random variables**; completely defined by the means, variances, and correlations of the variables.
73
# 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.
74
# Define:
n Factorial
| n!
For a positive integer n, the product of the first n positive integers.
## Footnote
0 factorial equals 1 by definition.
75
# 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.
76
# Define:
Net present value
| (NPV)
The present value of an investment’s cash inflows (benefits) minus the present value of its cash outflows (costs).
77
# 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.
78
# Define:
Normal distribution
A continuous, symmetric (no skew) probability distribution that is **completely described by its mean and variance**.
79
# Define:
NPV rule
An investment decision rule: An investment should be undertaken if its NPV is positive.
80
# 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.
## Footnote
The alternative hypothesis only has one side.
81
# Define:
Opportunity cost
The value that investors forgo by choosing a particular course of action.
82
# Define:
Ordinary annuity
An annuity with a first cash flow that is paid *one period from the present.*
83
# Define:
Parameter
A **descriptive measure** computed from or used to **describe** **a population of data**.
84
# Define:
Perpetuity
A set of **never-ending level sequential cash flows**, with the first cash flow occurring one period from now.
## Footnote
A perpetual annuity.
85
# Define:
Parametric test
Any test concerned with parameters, or whose validity depends on the assumption that the population is normally distributed.
86
# Define:
Platykurtic
Less peaked than the normal distribution.
87
# Define:
Population
All members of a specified group.
88
# Define:
Population mean
The arithmetic mean value of a population.
89
# Define:
Population variance
A measure of dispersion relating to a population, calculated as the mean of the squared deviations around the population mean.
90
# Define:
Population standard deviation
A measure of a population's dispersion, in the same unit of measurement as the observations.
## Footnote
the positive square root of the population variance.
91
# Define:
Power of a test
The probability of correctly rejecting the null (rejecting the null hypothesis when it is false).
## Footnote
1-𝛽
92
# Define:
Present value
| (PV)
The current value of future cash flows. This requires discounting the future cash flows back through time.
## Footnote
Can be used to determine current value of cash inflows from assets, or outflows from liabilities.
93
# Define:
Probability
The chance that an event will occur, represented by a number between 0 and 1.
94
# Define:
Probability distribution
A distribution which specifies the probabilities of a random variable’s possible outcomes.
95
# Define:
Probability density function
| (PDF)
A function with non-negative values such that probability can be described by area under the curve.
96
# Define:
Probability function
A function that specifies the **probability that the random variable takes on a specific value.**
97
# Define:
Quantile
A value at which a stated fraction of the data lies below.
## Footnote
aka fractile
98
# Define:
Random variable
A quantity whose future outcomes are uncertain.
99
# Define:
Range
The difference between the maximum and minimum values in a dataset.
100
# Define:
Risk
The chance of a loss or adverse outcome.
## Footnote
Exposure to uncertainty.
101
# Define:
Risk premium
Extra return required for bearing a specified risk.
102
# Define:
Sample
A subset of a population.
103
# Define:
Sample Statistic
A quantity computed from or used to describe a sample.
104
# Define:
Sample selection bias
Bias introduced by systematically *excluding* some of the population according to a particular attribute.
105
# Define:
Sampling error
The **difference** between the *observed value* of a statistic and the *quantity it is intended to estimate*.
106
# 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.
107
# Define:
Sensitivity analysis
Analysis of the **range of possible outcomes** as specific variables are changed.
108
# Define:
Sharpe ratio
The average return in excess of the risk-free rate divided by the standard deviation of returns.
## Footnote
Average excess return earned per unit of standard deviation.
109
# Define:
Skewness
A quantitative measure of skew (lack of symmetry).
110
# Define:
Spearman rank correlation coefficient
A measure of correlation **applied to ranked data**.
111
# Define:
Standard deviation
Measure of dispersion, in the same units as the original data.
## Footnote
The positive square root of the variance.
112
# 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.
113
# Define:
Standard normal distribution
The normal density with mean (μ) equal to 0 and standard deviation (σ) equal to 1.
114
# Define:
Statistic
A quantity computed from or used to describe a sample of data.
115
# Define:
Statistically significant
A result indicating that the **null hypothesis can be rejected**.
116
# Define:
Systematic sampling
A procedure of selecting every nth member from the population until reaching desired sample size.
## Footnote
Resulting sample should be random.
117
# Define:
Time-series data
Observations of a variable **at multiple points in time.**
## Footnote
This differs from cross sectional data, which is at a given point in time.
118
# Define:
t-Test
A hypothesis test using a t-statistic, which follows a t-distribution.
119
# 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).
## Footnote
In contrast with money weighted rate of return.
120
# Define:
Time value of money
The principles which determine the relationships between cashflows at different points in time.
121
# 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.
122
# 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.*
## Footnote
This differs from a one tailed test which only considers one direction, not both.
123
# Define:
Type I error
Rejecting a true null hypothesis.
124
# Define:
Type II error
Not rejecting a false null hypothesis.
125
# Define:
Unconditional probability
The probability of an event **not affected** by another event.
126
# Define:
Variance
**Squared deviations** from a random variable’s mean (expected value).
127
# Define:
Weighted mean
An average in which each observation is weighted by its relative importance.
128
# Define:
Alternative hypothesis
The hypothesis that is accepted **if the null hypothesis is rejected.**
129
# Define:
Analysis of variance
| (ANOVA)
Analysis of the **sources of variation** in a dataset.
130
# Define:
Bayes' formula
Formula used to update the probability of an event, when new information has been received.
131
# Define:
Bimodal
Distribution with two modes (frequently occuring data).
132
# Define:
Bootstrap
*Resampling method* which repeatedly draws samples and then **replaces** them into the original population.
133
# Define:
Box and whisker plot
Graph representing the dispersion of data across quartiles.
134
# Define:
Bubble line chart
Line chart which uses different sized bubbles to represent a third feature of the data.
135
# Define:
categorical data
Values which **describe a group** of observations and therefore can be used to divide dataset into groups.
136
# Define:
Central limit theorem
The sampling distribution of a variable's mean approaches a normal distribution as the sample size grows.
137
# Define:
Chi-square test
Test for potential association between **categorical variables**.
138
# Define:
Confidence level
The degree of confidence that the sample distribution **represents** the population distribution.
## Footnote
Confidence that the population parameter would occur within the confidence interval.
139
# Define:
Continuous data
Data which is measureable and can take on any numerical value within a range of values.
## Footnote
Can be measured, not counted.
140
# Define:
Critical values
The specific test statistic value where the decision changes from fail to reject to reject the null hypothesis.
141
# Define:
Cumulative frequency distribution chart
Either cumulative relative or cumulative absolute frequency plotted on y axis against the upper limit of the interval.
## Footnote
Easy to visualize what percent of observations is below a certain value.
142
# Define:
Data
Information
## Footnote
Can be many formats: words, numbers, images, audio.
143
# Define:
Dependent variable
Variable whose variation is explained by the regression.
## Footnote
Variation results from variation in the independent variable.
144
# Define:
Error term
Difference between an observation and the expected value.
145
# Define:
Estimated parameters
In regression analysis, estimated values of the population intercept and slope.
146
# Define:
False discovery rate
Rate of type 1 errors when testing a null hypothesis repeatedly for a specific level of significance.
147
# Define:
False discovery approach
Adjustment to p-values when test is performed multiple times.
148
# Define:
Fat tailed
When a distribution has a higher probability of extreme outcomes (fatter tails) than a normal distribution.
## Footnote
leptokurtic
149
# Define:
Grouped bar chart
Bar chart showing joint frequencies for two categorical variables.
150
# Define:
Heteroscedasticity
When variance of the error term differs across observations.
## Footnote
When the variance varies.
151
# Define:
Independent variable
The explanatory variable.
## Footnote
Explains the dependent variable in a regression.
152
# Define:
Indicator Variable
Variable with value of either 0 or 1, based on a binary condition.
| "Dummy Variable"
153
# Define:
Intercept
Expected value of the dependent variable in a simple linear regression *if the independent is zero*.
## Footnote
Where the regression line intercepts the y axis, as the x-axis is 0.
154
# Define:
Inverse transformation method
Using randomly generated numbers from a continuous uniform distribution in order to generate random observations from any distributions.
155
# Define:
Jackknife
Resampling method which takes from original observed data sample and leaves out one observation at a time (without replacement).
156
# Define:
Judgmental sampling
Selecting from a population **based on own knowledge and judgement.**
157
# Define:
Lin-log model
Regression model with **independent variable in logarithmic form**.
158
# Define:
Linear regression
Regression modeling the straight line relationship between the dependent and independent variables.
159
# Define:
Log-log model
Regression model where both dependent and independent variables are in logarithmic form.
160
# Define:
Log-lin model
Regression model where dependent variable is in logarithmic form.
161
# Define:
Mean square error
| (MSE)
Sum of squares error divided by the degrees of freedom.
## Footnote
*df* =(n - k - 1)
162
# Define:
Mean square regression
| (MSR)
Sum of squares regression divided by the number of independent variables, k.
163
# 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.
164
# Define:
Multiple testing problem
Risk of getting statistically significant result when performing test multiple times.
165
# Define:
Non-probability sampling
Sampling based on factors other than probability, like judgement or convenience.
166
# Define:
Null hypothesis
The hypothesis being tested.
## Footnote
Either reject, or fail to reject (result is not statistically significant).
167
# Define:
Observation
Value of a specific variable.
## Footnote
Can be collected at a point in time or over a period.
168
# 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.
## Footnote
Can cause false sense of predictive power.
169
# Define:
p-value
**Smallest level of significance** at which the null can be rejected.
170
# Define:
Pearson correlation
Measure of the relationship between two variables.
| Correlation
## Footnote
Differs from spearman's rank correlation.
171
# Define:
Probability sampling
Sampling method where every member of a population has an equal chance of being selected.
172
# Define:
Probability tree diagram
Diagram where branches, with the probabilities, stem from nodes, representing events.
## Footnote
The branches are mutually exclusive.
173
# Define:
Regression analysis
Used to examine if a variable is useful in explaining another variable.
174
# Define:
Regression coefficients
Intercept and slope coefficients of a regression.
175
# Define:
Resampling
Repeatedly drawing samples from original data sample in order *to statistically infer population parameters*.
176
# Define:
Residual
Difference between the observation and the predicted value.
177
# Define:
Sample correlation coefficient
Standardized measure of how two variables move together.
## Footnote
Standardizing the covariance.
Done by dividing the covariance by the product of the two variables' standard deviation
178
# Define:
Scatter plot
When two variables are plotted along the axis and points represent pairs of the two variables.
179
# Define:
Slope coefficient
Coefficient of an independent variable.
## Footnote
Average change in the dependent variable per one-unit change in the independent.
180
# 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.
181
# 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.
182
# Define:
Standard error of the estimate
Measure of the fit of a regression line.
## Footnote
Square root of the Mean Squared Error.
183
# Define:
Standard error of the forecast
Measure of the uncertainty associated with a forecasted value of the dependent variable.
184
# Define:
Standard error of the slope coefficient
The ratio of the SEE:square root of the variation of the independent variable.
185
# 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.
## Footnote
Sample proportional to size of stratum relative to overall population.
186
# Define:
Structured data
Data that are highly organized in a pre-defined manner.
187
# 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).
## Footnote
Aka the residual sum of squares.
188
# 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**.
189
# Define:
Sum of squares total
| (SST)
Sum of the squared deviations of the **observed dependent variable from its mean.**
## Footnote
*SST=SSR+SSE*
190
# Define:
Thin tailed
A distribution with a lower number of extreme outcomes than the normal distribution.
## Footnote
Often referred to as platykurtic.
191
# Define:
Tree map
Set of colored rectangles representing groups, the area of each is proportional to the value of the group.
192
# Define:
Two dimensional rectangular array
A data table. Columns and rows hold multiple variables and observations.
193
# Define:
Unimodal
Distribution with **one mode** (most fequent value).
194
# Define:
Variable
Quantity or characteristic which can be measured, counted, or categorized and **is subject to change**.
