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CFA L1 Matheus > 3. Quantitative Methods > Flashcards

3. Quantitative Methods Flashcards

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1
Q

Nominal scale

A

Names are discretionary

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2
Q

Ordinal scale

A

Scale order with specific criteria

e.g.: lower to higher

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3
Q

Interval Scale

A

Scale order based in ranges

0-10 % vol / 11-20 % vol / 21-30% vol

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4
Q

Ratio Scale

A

Scale order based in ratios
e.g.: debt-to-equity
2 x / 3x / 4x

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5
Q

Absolute Frequency

A

Example: #1 case (even if out of 20 or 30)

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6
Q

Relative Frequency

A

Example:
1 out of 10 = 10%
1 out of 20 = 5%

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7
Q

Histogram

A

Graphic based in two axis:
X: interval / specific values
Y: frequency

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8
Q

Population Average (formula)

A

Sum of Observations / #Number of Observations

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9
Q

Median

A
  1. Ordenate observations
  2. Choose the one that divides the # of observations in two
  3. If there are 4 observations, take the measure between numbers #2 and #3
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10
Q

Mode

A

The most frequent observation

- Distributions may be unimodal, bimodal, trimodal etc

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11
Q

Geometric Mean

A

1 + Rg = Raiz cúbica de (1+R1)(1+R2)(1+R3)

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12
Q

Harmonic Mean

A
  1. Calculate the average price of a stock, given:
  • total budget waste
  • average price for each tranche
  • # number of tranches
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13
Q

Quantile

A 
Quartile = divided by 4
Quintile = divided by 5
Decile = divided by 10
Percentile = divided by 100
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14
Q

Measure of Location

“What is the 3rd. quartile for the following distribution?”

A

Location where y% of the observations lie below, in a given distribution

L (y) = (n+1) * y / 100, where

Given:
Ascending order
y = Position below which y% of observations lie

Instructions:

  • Count the numbers
  • If L(y) = 8.5, interpolate 50% of the difference between observations #8 and #10
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15
Q

Mean Absolut Deviation (formula)

A

Average of all absolute deviations from the mean

  1. Pega todos os desvios
  2. Tira a média deles
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16
Q

Population Variance (formula)

A

Var = [(Deviation - Avg)^2 + (Deviation - Avg)^2] / 2

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17
Q

Standard Deviation (formula)

A

StDev = Raiz da Variância

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18
Q

Sample Variance (difference in comparison to Population Var)

A

Instead of using N, divide by (n-1)

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19
Q

Skewness

A

Measure of symmetry

Positive: outliers on the right; outliers on higher values

Negative: outliers on the left; outliers on lower values

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20
Q

Kurtosis

A

Kurtosis = 3 (for normal distribution)

↑ Kurtosis = ↑ Mode

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21
Q

Coefficient of Variation (formula)

A

CV = StDev x / Avg Value of X

CV = Vol / X (it should be the benchmark)

↑ CV = ↑ Risk

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22
Q

Order of Average, Mode, Median given skewness

A

Positive (+) Skewness: Avg > Median > Mode
Due to high outliers

Negative (-) Skewness: Mode > Median > Avg
Due to low outliers

  1. Median always in the middle
  2. Average is push to where outliers are (lower numbers / higher numbers)
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23
Q

Correlation range

A

Between (-1) and (1)

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24
Q

Variance range

A

Unbounded

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25
Q

Correlation (formula)

A

Correl = Cov(A,B) / StDevA * StDevB

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26
Q

Odds (concept)

A

Odds: 1 to 7 means one win to 7 loses.

Probability of wins: 1/8

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27
Q

Portfolio Variance (formula)

A

Var (Rp) = ∑ Wi r Wj Cov (Ri, Rj)

Var (Rp) = W1²Var(R1) + W2²Var(R2) + 2W1W2Cov(R1,R2)

Std Dev = Raiz disso

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28
Q

Labeling (concept)

A

Labeling = ways to order

  • Different ways of labeling
  • You DO DISCOUNT redundant orders
29
Q

Combination (concept and formula)

A
  • Special case where labeling has two subgroups

C = n! / (n-r)! r!

Ex.: Divide 8 stocks between 4 buy and 2 sell
Combination: 8! / 4! 2!

30
Q

Permutation (concept and formula)

A
  • Case where ORDER MATTER, so you do NOT remove redundant orders

P = n! / (n-r)!

Ex.: How many ways to order the sell of 3 stocks out of 8 if the order matters

31
Q

Expected value of X for a binomial distribution (formula)

A

For a binomial distribution

E (X) = n * p, where

p = probability of success of each trial
n = n trials
32
Q

Variance of X for a binomial distribution (formula)

A

Variance of (X) = np (1-p), where

p = probability of success of each trial
n = n trials
33
Q

Probability of X successes in n trials (binomial distribution formula)

A

P (x) = [ n! / (n-x)! x! ] * pˆx * (1-p)^n-x

34
Q

Confidence of Interval @ 90% (Normal Distribution)

A

1.65 σ

35
Q

Confidence of Interval @ 95% (Normal Distribution)

A

1.96 σ

36
Q

Confidence of Interval @ 99% (Normal Distribution)

A

2.58 σ

37
Q

Z (standardized) for a Normal Distribution (formula)

A

z = (Obs - μ) / σ

38
Q

Roy’s Safety First Ratio (formula and concept)

A

Minimizes probability of the portfolio obtaining a return below target

SFR = [ E (Rp) - Rthreshold ] / σ P

↑ SFR = ↑ Better = Choose the largest

39
Q

Lognormal distribution properties

A
  • Positive skewness (outliers to the right)

- Used to price derivatives

40
Q

Lognormal distribution formulas

A

a. S1 / Szero = 1 + HPR
b. ln (S1/Szero) = ln (1 + HPR) = Rcc, where

S1 = Price @ t = 1
S0 = Initial Price
HPR = Return, disregarding time-period
Rcc = Continuously Compounded Return
41
Q

Find HPR, given Rcc

HP12C - Lognormal

A

Formula: Rcc = (e^HPR - 1)

a. Press Rcc (given)
b. Press G
c. Press e^x
d. Subtract 1

42
Q

Find Rcc, given HPR

A
  1. Press HPR
  2. Add +1
  3. Press LN
  4. You will find Rcc
43
Q

Monte Carlo Simulation

A
  1. Assume probabilities for random variables, given historical data
  2. Generate multiple random results
  3. Uses these results to calculate a distribution of possible values
44
Q

Minimum Sample Size (#)

A

30 observations

45
Q

Central Limit Theory

A

Randomly generated samples will tend to a normal distribution where:

a. x̄ ~ Pop. μ
b. Standard error (from mean) = σ / √N
c. Large Sample!!

46
Q

Estimator Properties

A

CEU

  1. Consistent: lower standard error
  2. Efficient: lowest variance of all samples
  3. Unbiased: Expected Value Sample ~ EV Estimator
47
Q

T-student Parameters

A

a. Only one parameter: Degrees of Freedom
b. Fatter tails (less observations around the mean)
c. ↑ DF = ↑ Sample = ↑ Obs. around x̄ = Approaches Normal

48
Q

Effects from T-Student Fatter Tails

↑ DF = ↑ # Sample

A

The hypothesis test is more strict, as it is more difficult to reject H0

49
Q

Survivorship Bias

A

Surviving funds’ returns are naturally higher, so the historical returns database is overrated

50
Q

Look Ahead Bias

A

Price to Book Ratio shoould consider Today’s Price, even though Book Value is known for FY2019 only

51
Q

Sample Selection Bias

A

It refers to the bias where theinformation is not totally tested/considered only because part of it is unavailable

52
Q

Time Period Bias

A

Too short = not enough observations to find causality

Too long = there is causality, but it is dilluted so you can’t find it

53
Q

Hypothesis testing steps

A
  1. State the Hypothesys
  2. Select the test (t or z)
  3. State the decision rule
  4. Sample
  5. Decide
54
Q

Error Type #1

A

Reject H0 when H0 is true

55
Q

Error Type #2

A

Not to reject H0 when H0 is false

56
Q

Power of Test (formula)

A

Power of Test = 1 - (P Error Type II)

Probability of rejecting H0 when it is false

57
Q

P-value (concept)

A

Lowest level of significance that allows me rejecting H0

If you expand the level of significance, the test will not work

58
Q

Difference of Means Test (distribution to be used)

A

a. Two t-student (depends on whether variances are assumed to be equal/different)

59
Q

Difference of Variances Test (distributions to be used)

A

Chi-squared

60
Q

Equal Variances (distribution to be used)

A

F-distribution

61
Q

Two-tailed test

A

H0 = 0

H1 ≠ 0

62
Q

One-tailed test

A

H0 ≤ 0

H1 > 0

63
Q

H0

A

H0 = 0
H0 ≤ 0
H0 ≥ 0

It always include “=”, even though it is an one-tailed test

64
Q

Multivariate Distribution

A

A multivariate distribution is best defined as describing the behavior of:

2 or more DEPENDENT random variables

65
Q

Sample Efficiency (Concept)

A

Variance of its sampling distribution is smaller than that of all other unbiased estimators of the parameter

66
Q

According to the Central Limit Theorem, the distribution of the sample means is approximately normal if:

A

If the sample size is sufficiently large (i.e. greater than 30) the sampling distribution of the sample means will be approximately normal.

67
Q

Unusual requirement in the U.S. (regarding the securities trading in the country)

A

The United States requires a signed management statement about the effectiveness of the firm’s internal controls is required by U.S. regulators for securities that trade in the U.S., but not elsewhere.

68
Q

Estimate Pro Forma Earnings (Do / Don’ts)

A

There may be changes in KG, despesa de capital, novos ativos fixos, repagamento de dívida e recompra de stocks.

Fixed Ratios: Non-Cash Items as % of Sales

CFA L1 Matheus (5 decks)

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