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CFA Material > Quantitative Methods > Flashcards

Quantitative Methods Flashcards

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1
Q

Annuity

A

A stream of equal cash flows that occur at equal intervals

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2
Q

Annuity Due

A

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

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3
Q

Loan Amortization

A

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

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4
Q

Cash Flow Additivity Principle

A

PV of any stream of cash flows equals the sum of the present values of the cash flows

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5
Q

NPV

A

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

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6
Q

Holding Period Return

A

(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

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7
Q

Money Weighted Return

A

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.

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8
Q

Bank Discount Yield

A

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

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9
Q

A yield quoted on a bank discount basis is not representative of the return earned by an investor for the following reasons

A
  1. Bank discount yield annualizes using simple interest and ignores the effect of compounding
  2. 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
  3. Bank discount yield is annualized based on a 360 day year rather than 365
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10
Q

EAY

A

The annualized HPY on the basis of a 365-day year and incorporates the effects of compounding

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11
Q

Money Market Yield

A

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

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12
Q

Bond Equivalent Yield

A

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

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13
Q

When to use time-weighted return vs. money weighted return

A

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

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14
Q

Statistics

A

data and the methods used to analyze data

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15
Q

Descriptive Statistics

A

summarize the important characteristics of large data

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16
Q

Inferential Statistics

A

pertain to procedures used to make forecasts, estimates, or judgements about a large set of data

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17
Q

Population

A

the set of all possible members of a stated group

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18
Q

Sample

A

Subset of the population of interest

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19
Q

Four major measurement scales

A
  1. Nominal Scales - contain the least information
  2. Ordinal Scales - every observation is assigned to one of several categories
  3. Interval Scales - provide relative ranking plus the assurance that differences between scale values are equal
  4. 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
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20
Q

Parameter

A

a measure used to describe a characteristic of a population

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21
Q

Frequency Distribution

A

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

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22
Q

How to construct frequency distribution

A

Define the intervals, tally the observations, count the observations

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23
Q

Relative Frequency

A

The percentage of total observations falling within each interval

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24
Q

Cumulative and Absolute Frequency

A

Sums the absolute or relative frequencies starting at the lowest interval to the desired interval (usually the highest)

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25
Q

Histogram

A

Graphical presentation of the absolute frequency distribution

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26
Q

Frequency Polygon

A

The midpoint of each interval is plotted on the horizontal axis and absolute frequency for that interval is plotted on the vertical axis

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27
Q

Measures of Central Tendency

A

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

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28
Q

Arithmetic mean

A

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

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29
Q

The return for a portfolio is the..

A

weighted average of the returns of the individual assets in the portfolio

30
Q

Median

A

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)

31
Q

Unimodal, Bimodal, and trimodal

A

When a distribution has one value / two value / or three values that occur most frequently

32
Q

Harmonic Mean

A

For all values that are not all equal - harmonic mean

33
Q

Quantile

A

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

34
Q

Formula for the position of the observation at a given percentile

A

(n + 1) y/100 where y is the given percentile and n is the number of datapoints

35
Q

Mean Absolute Deviation

A

aka (MAD) the average of the absolute values of the deviations of individual observations from the arithmetic mean

36
Q

Problem with Variance

A

The computed variance, unlike the mean, is in terms of squared units of measurement

37
Q

Difference between formula for population variance and sample variance (or population variance and sample variance)

A

n-1 in the denominator vs. just n. Using n-1 improves the statistica properties of s squared as an estimator of variance

38
Q

Chebyshev Inequality

A

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

39
Q

Coefficient of Variation

A

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

40
Q

Sharpe Ratio

A

Measures excess return per unit of risk

41
Q

Limitations of the sharpe ratio

A
  1. If two portfolios have negative Sharpe ratios, it is not necessarily true that the higher sharep ratio implies superior risk adjusted performance.
  2. The sharpe ratio is useful when standard deviation is an appropriate measure of risk
42
Q

Skewness

A

The extent to which a distributionis not symmetrical

43
Q

Leptokurtic

A

Peaked distribution (high mountain)

44
Q

Platykurtic (platypus flat)

A

flatter distribution (hills)

45
Q

How to interpret kurtosis

A

Always relative to the kurtosis of a normal distribution which is three

46
Q

Random Variable

A

An uncertain quantity/number

47
Q

Outcome

A

an observed value of a random variable

48
Q

Event

A

a single outcome or a set of outcomes

49
Q

Mutually exclusive events

A

events that cannot both happen at the same time

50
Q

Exhaustive Events

A

Include all possible outcomes

51
Q

Two defining properties of probability

A

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

52
Q

Empirical Probability

A

Established by analyzing past data (OBJECTIVE)

53
Q

Priori Probability

A

Determined using a formal reasoning and inspection process (OBJECTIVE)

54
Q

Subjective Probability

A

Involves the use of personal judgement

55
Q

Unconditional Probability

A

Refers to the probability of an event regardless of the past or futures occurrence of other events

56
Q

Conditional Probability

A

One where the occurrence of one event affects the probability of the occurrence of another event

57
Q

Multiplication Rule of Probability

A

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)

58
Q

Addition Rule of Probability

A

Used to determine the probability that at least one of two events will occur

P (A or B) = P(A) + P(B) - P(AB)

59
Q

Total Probability Rule

A

Used to determine the unconditional probability of an event, given conditional probabilities

60
Q

When dealing with two events

A

the word AND indicates multiplication and the word OR indicate addition

61
Q

Tree Diagram

A

Used to show probability of various outcomes

62
Q

Covariance

A

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

63
Q

Correlation

A

Measures the strength of the linear relationship between two random variables. It ranges from -1 to +1

64
Q

Bayes Formula

A

Used to update a given set of prior probabilities for a given event in response to the arrival of new information

65
Q

Labeling

A

refers to the situation where there are n items that can each receive one of k different labels

66
Q

Factorial

A

Given n items, there are n! ways of arranging them

67
Q

Combination Formula

A

Applies to only two groups of predetermined size. Look for the word choose or combination

68
Q

Permutation Formula

A

Applies to only two groups of predetermined size. Look for a specific reference to order being important

69
Q

Labeling Formula

A

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

70
Q

Multipliation Rule of Counting

A

“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

CFA Material (6 decks)

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