Quant Flashcards
When liquidity is low, what is the impact to the interest rate?
The interest rate increases, to represent the liquidity premium
Since the investor is not easily able to get their cash, there is a premium, increasing the interest rate.
When default risk is high, what happens to the interest rate?
The interest rate increases
(default premium)
The EAR equals the stated rate when?
Compounding periods equals 1 (annual)
Represents the annual rate of return actually being earned after adjustments for compounding periods have been made
EAR
The EAR considers the effects of compounding on:
return on investment (ROI)
An investors increase in purchasing power is their:
real rate of return
Interest rate adjusted to remove the effects of inflation:
real rate of return
Compensates investors for the increased price sensitivity to changes in interest rates, as maturity is extended
Maturity Premium
An investors equilibrium rate of return is calculated as:
required rate of return =
+ Risk-free rate
+ Inflation Premium
+ Risk premium
Equilibrium rate of return= required rate of return
Risk premium includes: liquidity, default, maturity
Investors require interest on an investment that is calculated as:
required interest rate =
nominal rate
+liquidity premium
+default premium
+maturity premium
(Interest rate formula)
Rate that contains inflation premium
Nominal interest rate
US T-bills are an example of?
Nominal risk-free interest rates
Stream of equal CF that occurs at equal intervals, over a given period
annuity
Pays fixed amount of money at set intervals, over an infinite period of time
perpetuity
CF additivity principle:
PV of any stream of CF =
sum of PV of the CFs
Real risk-free interest rate is a _ rate, that includes:
theoretical rate
includes no expectation of inflation
Interest rates have many different names that include:
discount rates
opportunity cost
required rate of return
cost of capital
The required rate of return on an investment
Equilibrium rate
(nominal required return)
the market rate of return that investors & savers require to get them to willingly lend their funds
Equilibrium rate
Preferred stock is an example of?
Perpetuity
When the compounding periods increase, the EAR _ at a _rate.
Increases;
at a decreasing rate
Real risk free rate
+ Inflation premium
=
Nominal risk-free rate
T/F: On monthly compounded loans, the effective annual rate (EAR) will exceed the annual percentage rate (APR)
EAR > Stated rate (APR)
when compounding increases
The harmonic mean is used to calculate:
- average share cost purchased over time
- average price/unit
The geometric mean is used to calculate:
- investment returns over multiple periods
- compound growth rates
Used to visualize a data set based on quantiles
Box and whisker plot
The arithemetic mean is used to calculate:
the average returns over a one-period time horizon
Panel data is a combination of:
cross-sectional (columns)
time-series (rows)
displays the cumulative relative or absolute frequency distribution in columns (bars) or lines
Cumulative (relative or absolute) frequency distribution chart
Published ratings on stocks ranging from 1 (strong sell) to 5 (strong buy) are examples of which measurement scale?
ordinal, sorts data into categories that are ordered with respect to some characteristic, but numbers cannot be used to perform calculations
Categorical data that can be logically ordered or ranked
ordinal data
Assigning the value 1 for “Value” stocks & 2 for “Growth” stock is an example of:
Nominal data
No logical order
Categorical values that are not amenable to being organized in a logical order
Nominal data
Price change of a stock is an example of:
Continuous data
data that can be measured and can take on any numerical value in a specified range of values
continuous data
Example of data organization:
Studying the GDP of three different countries, from the periods 2020-2022
Panel Data:
- Cross-sectional: three different countries GDP (multiple observational units)
- GDP for each country
- Time series: period of 2 years
Panel Data
Consist of observations through time on one or more variables for multiple observational units
panel data
a list of the observations of a specific variable from multiple observational units at a given point in time
cross-sectional data
Mutliple observation units: US, UK, Canada
Time: 2022
GDP: specific variable
sequence of observations of a specific variable collected over time and at discrete and typically equally spaced intervals of time
time-series data
Specific variable: stock prices
Time: 2000-2022
Fatter tails in a distribution means there’s a higher probability of:
Outliers:
more data in the tails shows more risk of expected value being further from the mean
The sum of joint frequencies for a row or column for the attribute
Marginal frequency
Bar chart that orders categories by frequency in descending order and includes a line displaying cumulative relative frequency
Pareto Chart
Line charts are used to display the change in a:
Used to display the change in a data series over time and underlying trends
Used to visualize the joint variation in two numerical values
scatter plot
graphical tool used to display and compare categorical data
tree-map
Used to visualize the degree of correlation between different variables
heat map
Used to make comparisons of three or more variables over time
Bubble line chart
A set of scatter plots that is useful for visualizing correlations among multiple pairs of variables:
scatter plot matrix
The interquartile range on the box & whisker plot is represented by:
The box represents the 25th to 75th percentile (interquartile range)
Given this, what can it be interpretted as?
P(Ei)= 0
The probability that the event will occur is never
P(Ei)= 1:
The event is certain to occur, and the event is not random
What are the two conditions of probabilities?
- The probability of occurrence of any event is between 0 and 1: 0 ≤ P(Ei) ≤ 1
- The sum of probabilities of all possible mutually exclusive, exhaustive events is 1
Two events are independent if the probability of occurrence of event A:
does not affect the probability of occurence of event B
The expected value of a random variable, given an event or scenario:
Conditional expected value
the probability weighted average of the possible outcomes of the random variable:
expected value
(not a probability)
Days of rainfall
discrete (there are countable whole numbers- 30 days in a month)
amount of rainfall in a month
continuous (there are infinite numbers of possible fractional outcomes)
The probability of a specific outcome in a continuous distribution=
0; there are infinite numbers of possible fractional outcomes
The feature that distinguishes a multivaraite distribution from a univariate distribution
correlation
Correlation is only meaningful when the behavior of each variable is :
Dependent on the behavior of others
specifies the probabilities for a group of related random variables:
Multivariate distribution
Indicates the strength of a linear relationship between a pair of random variables:
Correlation
The probability of correctly rejecting the null hypothesis
Power of the test
Rejecting the null hypothesis when it is false
The power of a test=
= 1- P(Type II error)
Rejecting the null hypothesis when it is true
Type I error
Failing to reject the null hypothesis when it is false
Type II error
The probability of making a Type I error:
The significance level (Alpha)
Significance level of 5% means:
There is a 5% chance of rejecting a true null hypothesis
The null hypothesis is most appropriately rejected when the p-value is:
Close to Zero
The smaller the p-value the stronger the evidence against the null hypothesis, suggesting that it should be rejected
The smallest level of significance at which the hypothesis can be rejected:
P-value:
A p-value of 0.02% means that the smallest significance level at which the hypothesis can be rejected is 0.0002
Test statistic to test that a population variance is equal to a chosen value:
Chi-square statistic
- Test of a single variance
- Bound by zero
Test statistic to test that two variances are equal:
F-statistic
Variance B/ Variance A
Which test statistic & defining properties?
To test that the means of two normally distributed populations are equal, when variance is assumed to be equal:
T-statistic
df= n1 + n2 - 2
Difference in means
Reviews the correlations of a firm’s rank in one period and it’s rank in the next period, across many periods:
Rank Correlation
Non-parameter test
A test of whether a mutual fund’s performance rank in one period provides information about the fund’s performance rank in a subsequent period:
Rank Correlation
Nonparametric test
A parametric tests is one that involves:
Parameters
One that has to make assumptions about the parameters of the distribution for it to be valid
According to the Central Limit Theorem, the distribution of the sample means is approximately normal if:
sample size n > 30, even if the population is not normal
What is the null hypothesis in a paired comparisons test?
Mean of the population of paired differences = hypothesized mean of paired differences (commonly 0)
t-test
df= n-1
Testing whether the difference of the two, dependent sample’s means = 0
The difference between a paired comparison & difference in means test is:
Paired comparison tests dependent samples
samples for both are normally distributed
Concerned with the mean of differences between two dependent, normally distributed samples:
Paired comparison test (mean differences)
t-statistic, df= n-1
Used to test the difference between means of two, normal, independent populations
Difference in Means
T-stat, Df= n1 + n2 -2
To determine whether the mean returns on two stocks over the last year were the same or not; what test should be used:
Paired comparison (mean differences)
The samples are not independent, since they both contain some systematic risk. In this test we will take the difference between the two over some time, and then determine if they are statistically different from zero
Determining the number of ways n tasks can be done in order:
Factorial function
Which probability rule determines the probability that two events will both occur?
Multiplication Rule
used to determine the joint probability of two events
Which probability rule can be used to determine the unconditional probability of an event?
Total probability rule
The number of successes in n Bernoulli Trials:
Binomial random variable
Bernoulli Trial: produces one of two outcomes (success/failure)
A binomial distribution is symmetric when:
Symmetric when probability on a trial is 50%
asymmetric otherwise
50% chance for event A
50% chance for event B
- Assumes a variable can take one of two values; stock up/down movements
- Used to compute expected value over several periods
Binomial Distribution
The value of the cumulative distribution function lies between:
0 and 1
Any descriptive measure of a population characteristic is best described as a:
Parameter
Used to determine all potential outcomes of mutually exclusive & exhaustive events:
Total probability rule
A confidence interval is contructed by:
= point estimate
+/- reliability factor * standard error
Reliability factor = Z-statistic
Lognormal distributions can never be:
Negative
Lognormal distributions are more suitable, than a normal distribution, for a probability model of:
Asset prices
Asset prices can never be negative
Asset returns can be negative, and normal distributions are more appropriate
Mimics the simple random sampling process, by repeatedly drawing samples from the original sample, and each resample is of the same size as the original sample & used to construct the distribution
Bootstrapping
Resampling method
A computer simulation is used to repeatedly draw random samples from the original sample. The resamples are then used to construct a sampling distribution.
The degree of confidence:
Reliability factor
Data organization example:
Daily closing price of a stock recorded over a period spanning 13 weeks
Time-series data
Data organization:
Microsoft, Apple, Google shareholders earnings in the year ended, 31st December 2021
Cross-sectional
Resampling Method:
Samples are selected by taking the original observed data sample and leaving out one observation at a time.
Jacknife
Samples are drawn without replacement
For regression lines, it is preferred to have the coefficient of determination & F-statistic to be:
Coefficient of determination (R2) & F-statistic:
High value is better
For nonlinear relationships, how do we transform the data into linear regression:
Log-Lin
Lin-Log
Log-Log
Dependent (Y) - Independent (X)
Lin=Linear
Log= logarithmic
We will take the natural log (ln) of which ever variable is logarimathic
Log-Lin:
Y= :og
X= Lin
Scatter plots can also be used to identify nonlinear information like:
Correlation
the strength of the linear relationship between 2 variables
Sampling error is the difference between:
sample statistic (estimate) & population paramter (actual)
- Regression analysis (linear regression) makes no assumptions about:
- Instead it is the analysis of:
- Makes no assumptions about causation (X does not cause Y)
- Analysis of of the linear association between the two variables
Assumes:
Variance is constant (homeskedacity)
residual terms are independently distributed (uncorrelated)
The regression line from a simple linear regression is the line that minimizes the sum of squared differences between:
the values of the dependent variable
&
the predicted values of the dependent variable
A lower coefficient of variation would be desired by a risk-averse investor because:
CV= risk / unit of return
Lower CV= lower risk
Monte carlo simulations provide answers to:
What if questions
Limitations:
* statistical, rather than analytical method
* results are no better than the assumptions used to generate it
Frequency polygons represent frequency lines linking their:
Midpoints
In a histogram, the vertical bar heights represent:
Frequencies
