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CFA Level 1 > Quantitave Methods > Flashcards

Quantitave Methods Flashcards

1
Q

What is the formula of Bank Discount Yield?

A

(Discount / Face) x (360/Days to Maturity)

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2
Q

What is the formula of Holding Period Yield?

A

(Ending Value / Beginning Value) - 1

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3
Q

What is the formula of Effective annual yield?

A

(1+HPY) ^ (365/Days) -1

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4
Q

What is the Formula of Money Market Yield?

A

HPY * (360/Days to maturity)

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5
Q

a. What is Numerical Data?

b. What are the sub categories?

A

a. Numerical or quantitative data can be counted or measured.

b. - Discrete : Countable units
- Countinuous : Data can take on any fractional value.

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6
Q

a. What is Categorical Data?

b. What are the sub categories?

A

a. Categorical or qualitative data are labels for grouping or classifying data.
b. - Nominal : Data are labels with no logical ordering
- Ordinal : Data are labels that can be ordered or ranked.

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7
Q

Compare Time-Series and Cross-sectional data

A

Time-Series : At equal time intervals

Cross-Sectional : At single point in time

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8
Q

Compare Structured and Unstructured Data

A

Structured data : Organized in a defined way, such as time-series or cross-sectional data

Unstructured data : Information in forms with no defined structure; typically my be transforms into data for analysis.

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9
Q

What is a one-dimensional array?

A

It represents a single variable.

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10
Q

What is a two-dimensional array or data table?

A

It represents two variables.

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11
Q

What are the best graphs to represent relationship?

A

Scatter plots

Heat maps

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12
Q

What are the best graphs to represent comparisons among categories?

A

Bar charts
Tree maps
Heat maps

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13
Q

What are the best graphs to represent comparaison over time?

A

Line Charts
Bubble Line Charts
Dual-Scale Line Charts

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14
Q

What are the best graphs to represent distributions of numerical data?

A

Histograms
Frequency polygons
Cumulative distributions charts

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15
Q

What are the best graphs to represent distributions of categorical data?

A

Bar charts
Tree maps
Heat maps

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16
Q

What are the best graphs to represent a distribution of text?

A

Word clouds

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17
Q

In which order the mean, median, mode are when the skew = 0? (Smallest to largest value)

A

Mean = Median = Mode

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18
Q

In which order the mean, median, mode are when the skew > 0 ? (Smallest to largest value)

A

Mode < Median < Mean

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19
Q

In which order the mean, median, mode are when the skew < 0? (Smallest to largest value)

A

Mean < Median < Mode

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20
Q

What is the characteristics of a Leptokurtic (Kurtosis >3) distribution?

A
  • More peaked

- Fatter tails –> Higher probability in tails

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21
Q

Which order are the means (i.e Harmonic, Geometric, Arithmetic) for the same data? (Smallest to largest)

A

Harmonic < Geometric < arithmetic

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22
Q

Definition of Random Variable

A

Uncertain Number

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23
Q

Definition of outcome

A

Realization of random variable

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24
Q

Definition of Event

A

Set of one or more outcomes

25
Q

Definition of Mutually exclusive

A

Cannot both happen

26
Q

Definition of Exhaustive

A

Set of events includes all possible outcomes

27
Q

What is the difference between empirical, subjective, a priori types of probability?

A

Empirical : Based on analysis of data
Subjective : Based on personal percetion
A priori : Based on reasoning, not experience (logical reasoning –> forecast, tendency, anticipation)

28
Q

What is the condition of using combination formula?

A

When order does not matter

29
Q

What is the condition of using permutation formula?

A

When order does matter

30
Q

Definition of multivariate normal

A

More than one random variable, need means, variances, and correlation coefficients.

31
Q

What are the formule for a 90%, 95%, 99% confidence of interval?

A 
90% = x barre +- 1.645s
95% = x barre +- 1.96s
99% = x barre +- 2.58s
32
Q

Define shortfall risk and Roy’s Safety-Fist Ratio.

A

Shortfall risk : Probability that a portfolio return or value will be below a target return or value.

Roy’s Safety-First Ratio : Number of std. dev. tarer is below the expected return/valye.

33
Q

What is the advantage and disadvantage of a Historical Simulation?

A

Advantage : Don’t have to estimate distribution of risk factors.

Disadvantage : Future outcomes for risk factors may be outside the historical range.

34
Q

What is a simple random sample?

A

Where every population member has an equal change of being selected.

35
Q

What is a sampling distribution?

A

The distribution of sample statistics for repeated samples of size n.

36
Q

Definition of sampling error

A

The difference between a sample statistic and true population parameter.

37
Q

Define Stratified Random Sampling.

A
  1. Create subgroups from population based on important characteristics
  2. Select samples from each subgroup in proportion for the size of the subgroup.
38
Q

What are the estimator properties and define then?

A
  1. Unbiased : Expected value equal to parameter
  2. Efficient : Sampling distribution has smallest variance of all unbiased estimators.
  3. Consistent : Large sample –> better estimator
39
Q

Define data-mining bias

A

From repeatedly doing tests on same data sample

40
Q

Define sample selection bias

A

Sample not really random

41
Q

Define survivorship bias

A

Sampling only surviving firms, mutual funds, hedge funds

42
Q

Define Look-ahed bias

A

Using information not available at the time to construct sample

43
Q

Define Time-Period Bias

A

Relationship exists only during the time period of sample data

44
Q

Define Type I Error.

A

Rejecting true null hypothesis (H0).

Significance level is Probability of Type I Error

45
Q

a. Define Type II Error

b. What we can calculate with Type II Error?

A

Failing to reject false null hypothesis (H0)

Power of a test = 1 - Probability of Type II Error

46
Q

Why Statistical significance does not necessarily imply economic significance?

A
  • Transactions costs
  • Taxes
  • Risk
47
Q

What is the formula of b^1?

A

Cov (X,Y) / variance x

48
Q

What is the formula of b^0?

A

Y barre - b^1 * x barre

49
Q

What is the Assumptions of Linear Regression?

A
  1. Linear relation between dependent and independent variables
  2. Variances of the error terms is constant (homoskedasticity)
  3. Error Terms are independently distributed, i.e. uncorrelated with each other
  4. Error Terms are normally distributed
50
Q

Anova table

A
51
Q

Hypothesis testing with different components

A
52
Q

Compare

a. Frequency Distribution
b. Relative Frequency
c. Cumulative absolute frequency

A

a. Frequency distributions summarize statistical data by assigning them to specified groups, or intervals.
b. The relative frequency is calculated by dividing the absolute frequency of each return interval by the total number of observations.
c. Summing the absolute or relative frequencies starting at the lowest interval and progressing through the highest.

53
Q

Compare

a. Trimmed mean
b. Winterized mean

A

a. A trimmed mean excludes a stated percentage of the most extreme observations.
b. Instead of discarding the highest and lowest observations, we substitute a value for them

54
Q

Forumla of Mean absolute deviation (MAD)

A

MAD = Somme |xi-x| / n

55
Q

Define spurious correlation

A

It refers to correlation that is either the result of chance or present due to changes in both variables over time that is caused by their association with a third variable.

Example : we can find instances where two variables that are both related to the inflation rate exhibit significant correlation but for which causation in either direction is not present.

56
Q

What is Bayes’ formula?

A

P(Event | Information) = [ P(information | Event) / P(Information) ] * P(Event)

57
Q

What are the probability function and the cumulative distribution function for a uniform random variable?

A

f(x ) = 1 / (b-a) for a <= x <= b ; 0 otherwise

F(x) = 0 for x

58
Q

What is the probability formula for binomial random variable?

A

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CFA Level 1 (4 decks)

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