Quantitative Methods Flashcards
Annuity
A stream of equal cash flows that occur at equal intervals
Annuity Due
With an annuity due, there is one less discounting period since the first cash flow occurs at t=0 and thus is already PV. All else equal, PV of an annuity due is always greater than the PV of an ordinary annuity
Loan Amortization
Process of paying off a loan with a series of periodic loan payments whereby a portion of the outstanding loan amount is paid off, or amortized, with each payment
Cash Flow Additivity Principle
PV of any stream of cash flows equals the sum of the present values of the cash flows
NPV
Assumes the reinvestment of a poroject’s cash flows at the opportunity cost of capital while the IRR method assumes the reinvestment rate is the IRR
Holding Period Return
(Ending value / beginning value) - 1 This is also known as the actual return an investor will receive if the money market instrument is held until maturity
Money Weighted Return
Applies the concept of IRR to investment portfolios. Defined as the IRR of the return on a portfolio, taking into account all cash inflows and outflows.
Bank Discount Yield
Expresses the dollar discount from the face (par) value as a fraction of the face value, not the market price of the instrument. Assumes simple interest
A yield quoted on a bank discount basis is not representative of the return earned by an investor for the following reasons
- Bank discount yield annualizes using simple interest and ignores the effect of compounding
- Bank discount yield is based on the face value of the bond, not its purchase price - investment returns should be evaluated relative to the amount invested
- Bank discount yield is annualized based on a 360 day year rather than 365
EAY
The annualized HPY on the basis of a 365-day year and incorporates the effects of compounding
Money Market Yield
The annualized yield that is based on price and a 360 day year and does not account for the effects of compounding, it assumes simple interest
Bond Equivalent Yield
2 x the semiannual discount rate. Yields on bonds are quoted as twice the semiannual rate because the coupon interest is paid in two semiannual payments
When to use time-weighted return vs. money weighted return
Time-weighted return is the preferred measure of a manager’s ability to select investments. If the manager controls the inflow and outflows, the money weighted return is preferred
Statistics
data and the methods used to analyze data
Descriptive Statistics
summarize the important characteristics of large data
Inferential Statistics
pertain to procedures used to make forecasts, estimates, or judgements about a large set of data
Population
the set of all possible members of a stated group
Sample
Subset of the population of interest
Four major measurement scales
- Nominal Scales - contain the least information
- Ordinal Scales - every observation is assigned to one of several categories
- Interval Scales - provide relative ranking plus the assurance that differences between scale values are equal
- Ratio Scales - represent the most refined level of measurement. Provides ranking and equal differences between scale values, and they also have a true zero point as the origin
Parameter
a measure used to describe a characteristic of a population
Frequency Distribution
a tabular presentation of statistical data that aids the analysis of large data sets. Summarizes statistical data by assigning it to specified groups, or intervals
How to construct frequency distribution
Define the intervals, tally the observations, count the observations
Relative Frequency
The percentage of total observations falling within each interval
Cumulative and Absolute Frequency
Sums the absolute or relative frequencies starting at the lowest interval to the desired interval (usually the highest)
Histogram
Graphical presentation of the absolute frequency distribution
Frequency Polygon
The midpoint of each interval is plotted on the horizontal axis and absolute frequency for that interval is plotted on the vertical axis
Measures of Central Tendency
Identify the center, or average, of a data set. This central point can then be used to represent the typical, or expected, value in a data set
Arithmetic mean
Only measure of central tendency for which the sum of the deviations from the mean is zero. This can be affected by outliers which skew the mean
The return for a portfolio is the..
weighted average of the returns of the individual assets in the portfolio
Median
midpoint of a data set when the data is arranged in ascending or descending order (half of the observations lie above the mean and the other half below the mean)
Unimodal, Bimodal, and trimodal
When a distribution has one value / two value / or three values that occur most frequently
Harmonic Mean
For all values that are not all equal - harmonic mean
Quantile
Examples include quartiles, quintile, decile, and percentile. A quantile is the general term for a value at or below which a stated proportoin of the data in a distribution lies
Formula for the position of the observation at a given percentile
(n + 1) y/100 where y is the given percentile and n is the number of datapoints
Mean Absolute Deviation
aka (MAD) the average of the absolute values of the deviations of individual observations from the arithmetic mean
Problem with Variance
The computed variance, unlike the mean, is in terms of squared units of measurement
Difference between formula for population variance and sample variance (or population variance and sample variance)
n-1 in the denominator vs. just n. Using n-1 improves the statistica properties of s squared as an estimator of variance
Chebyshev Inequality
For any set of observations, whether sample or population data and regardless of the shape of the distribution, the percentage of the observations tha tlie within k standard deviations of the mean is at least 1 - 1/ksquared for all value of k>1
Coefficient of Variation
Measures the amount of dispersion in a distribution relative to the distribution’s mean. Enables us to make direct comparisons of dispersion across different sets of data
Sharpe Ratio
Measures excess return per unit of risk
Limitations of the sharpe ratio
- If two portfolios have negative Sharpe ratios, it is not necessarily true that the higher sharep ratio implies superior risk adjusted performance.
- The sharpe ratio is useful when standard deviation is an appropriate measure of risk
Skewness
The extent to which a distributionis not symmetrical
Leptokurtic
Peaked distribution (high mountain)
Platykurtic (platypus flat)
flatter distribution (hills)
How to interpret kurtosis
Always relative to the kurtosis of a normal distribution which is three
Random Variable
An uncertain quantity/number
Outcome
an observed value of a random variable
Event
a single outcome or a set of outcomes
Mutually exclusive events
events that cannot both happen at the same time
Exhaustive Events
Include all possible outcomes
Two defining properties of probability
The probability of occurrence of any event is between 0 and 1
If a set of events E1 E2 En is mutually exclusive and exhaustive, the probabilities of those events sum to 1
Empirical Probability
Established by analyzing past data (OBJECTIVE)
Priori Probability
Determined using a formal reasoning and inspection process (OBJECTIVE)
Subjective Probability
Involves the use of personal judgement
Unconditional Probability
Refers to the probability of an event regardless of the past or futures occurrence of other events
Conditional Probability
One where the occurrence of one event affects the probability of the occurrence of another event
Multiplication Rule of Probability
Used to determine the joint probability of two events
P(AB) = P(A [ B) X P(B)
Can be rearranged to find the conditional probability of A given B
P (A [ B) = P(AB) / P(B)
Addition Rule of Probability
Used to determine the probability that at least one of two events will occur
P (A or B) = P(A) + P(B) - P(AB)
Total Probability Rule
Used to determine the unconditional probability of an event, given conditional probabilities
When dealing with two events
the word AND indicates multiplication and the word OR indicate addition
Tree Diagram
Used to show probability of various outcomes
Covariance
Measure of how two assets move together. It is a general representation of the same concept as the variance. Covariance may range from negative infinity to positive infinity
Difficult to interpret
Correlation
Measures the strength of the linear relationship between two random variables. It ranges from -1 to +1
Bayes Formula
Used to update a given set of prior probabilities for a given event in response to the arrival of new information
Labeling
refers to the situation where there are n items that can each receive one of k different labels
Factorial
Given n items, there are n! ways of arranging them
Combination Formula
Applies to only two groups of predetermined size. Look for the word choose or combination
Permutation Formula
Applies to only two groups of predetermined size. Look for a specific reference to order being important
Labeling Formula
Applies to three or more sub-groups of predetermined size. Each element of the entire group must be assigned a place, or label, in one of the three or more sub-groups
Multipliation Rule of Counting
“If there are k steps required to complete a task and each step can be done in n ways, the number of different ways to complete the task is n1! x n2! x nk!”k
