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CFA - QM Flashcards

1
Q

Nominal Risk free Rate =

A

Real Risk free rate + expected inflation

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2
Q

EAR =

A

Effective Annual Rate - (1 + I)^T - 1

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3
Q

Nominal rate of interest =

A

Nominal risk free rate + risk premium

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4
Q

Annuity due

A

Beginning of each period

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5
Q

Ordinary annuities

A

end of each compounding period

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6
Q

PV perpetuity =

A

PMT / r

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7
Q

Numerical data

A

values that can be counted or measured

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8
Q

Dentro de Numerical data, temos discrete data que seria

A

countable (days, months, etc)

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9
Q

Dento de Numerical data, temos Contiunous data que seria

A

can take any fractional value

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10
Q

Categorical data

A

Labels that can be used to classify a set of data into grupos

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11
Q

Dento de Categorical Data, temos Nominal data que seria

A

cannot be placed in order logically

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12
Q

Dento de Categorical Data, temos Ordinary data que seria

A

can be ranked in a logical order

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13
Q

Time series

A

set of observations taken periodically

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14
Q

Cross-sectional data

A

set of comparable observations all taken at one specific point in time

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15
Q

Structural data

A

organized in a defined way

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16
Q

Unstructured data

A

no defined structured

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17
Q

Marginal Frequency

A

total of frenquecies for a row ou colum

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18
Q

Joint frequencies

A

displays of two variables

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19
Q

Confusion Matrix

A

is a contigency table that displays predicted and actual occurences of an event

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20
Q

Arithmetic mean =

A

( x1 + x2 + x3 + xn) / n

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20
Q

Geometric Mean =

A

=[(1+R 1 )(1+R 2)…(1+R n)] 1/n −1

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21
Q

Weighted Mean =

A

W1 x R1 + W2 x R2 + W3 X R3 + Wn x Rn

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22
Q

Weighted Mean often used to calculate …

A

Portfolio return

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23
Q

Harmonic Mean =

A

N / (1/xi) -> Sendo N=numero total e Xi=valores

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24
Q

Trimmed Mean

A

exclude a stated percentage of most extreme observations

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25
Q

Winsorized mean

A

substitute values for the most extreme observations

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26
Q

Median

A

midpoint of a data set

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27
Q

Mode

A

value occruing most frequently in a data set

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28
Q

Quantile =

A

(n+1) x Y/100

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29
Q

Mean Absolute Deviation (MAD) =

A

MAD= ∑∣x i​ − xˉ ∣ / n

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30
Q

Sample Variance =

A

s^2 = ∑ (x i​ − xˉ)^2 / n − 1

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31
Q

Sample Standard Deviation =

A

s = raiz quadrada de: ∑ (x i​ − xˉ)^2 / n − 1

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32
Q

Sample Variance nos mostra…

A

a variação dos dados em relação ao ponto central

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33
Q

Sample Standard Deviation nos mostra

A

a variação média

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34
Q

Coefficient of Variation (CV) =

A

Standard Deviation (s) / average value of x

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35
Q

Coefficient of Variation nos mostra…

A

quantas unidades de risco por quantas unidades de retorno - (Measures the amount of dispersion in a distribution relative to the distributions mean

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36
Q

Coefficient of Varition é melhor: um coeficiente alto ou baixo?

A

Baixo, pq indica pouca variação

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37
Q

Target Downside Deviation =

A

s = raiz quadrada de: ∑ (x i​ − Bˉ)^2 / n − 1

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38
Q

Target Downside Deviation calulate…

A

risk based on outcomes both above and below the mean

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39
Q

Skew measures…

A

the dregree to wich a distribuiton lacks symmetry

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40
Q

Skew = 0; Median, Mode and mean is

A

Mean = Median = Mode

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40
Q

Skew positiva

A

Mean > Median > Mode

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41
Q

Kurtosis measures

A

the degree to which a distribution is more or less peaked than a normal distribution (concentação nas caldas)

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42
Q

Skew negativa

A

Mean < Median < Mode

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43
Q

Kurtosis é igual a qual número se a distribuição for simétrica

A

igual 3

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44
Q

Sample Covariance =

A

Cov(X,Y)=∑(Xi−¯X)(Yi−¯Y) / n−1

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45
Q

Sample Covariance measure…

A

of how two variables move together

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46
Q

Correlation is

A

a standardized measure of the linear relationship between two variables

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47
Q

Correlation =

A

Corr(X,Y) = Cov[X,Y] / ( StdDev(X) ∙ StdDev(Y) )

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48
Q

Spurious Correlation refers

A

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 third variable. Exemplo: morte de pinguim e queimada na amazonia.

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49
Q

Random Variable is

A

an uncertain quantity/number

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50
Q

Probability of an event, a probabilidade é de xx até xx

A

de 0 até 1

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51
Q

Mutually exclusive events are

A

events that cannot both happen at the same time

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52
Q

Exhaustive events are

A

those tha include all possible outcomes

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52
Q

Probability Empirical is based…

A

on analysis of data

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53
Q

Probability of a priori is based

A

on reasing, not experience

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54
Q

Probability Subjective is based on…

A

personal perception

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55
Q

Probability Unconditional is …..

A

probabilidade de um evento acontecer, sem ter nenhuma condição de outro evento P(A)

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56
Q

Probability Conditional is ….

A

probabilidade de um evento acontecer, por conta de outro evento P(A | B)

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57
Q

Joint probability is …

A

de dois eventos acontecerem ao mesmo tempo P(AB)

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58
Q

Rules of Probability, Quando usar + e - e quando usar X. Sobre and e or

A

Para and -> P (AB) = P (A|B) X P (B) / Para or -> P (A or B) = P(A) + P(B) - P(AB)

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59
Q

Bayer´s Formula =

A

Prob (HG | DI) = P (DI | HG) X P(HG) / P (DI)

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60
Q

Portifolio expected return =

A

E(rp) = W1xE(R1) + W2xE(R2) + WnxE(Rn) -> W = peso do ativo e E(R) = retorno esperado

61
Q

Variance =

A

σ^2 = P(xi) x [xi - E(x)]^2 -> E(x) seria o valor esperado com base no peso e retorno esperado de todos ativos

62
Q

Standard Deviation =

A

σ = raiz de (P(xi) x [xi - E(x)]^2 )

63
Q

Covariance (Ra,Rb) =

A

{[Ra - E(Ra)] x [Rb - E(Rb)]} x P

64
Q

Portifolio Standard Deviation or Portfolio Variance =

A

Portfolio variance = w1^2σ1^2 + w2^2σ2^2 + 2w1w2Cov1,2

65
Q

Labeling, qual é a fórmula e qunado usar?

A

= n! / (n1!) x (n2!) x …. -> “there are n items that can each receive one K different labels, seria omo quero classificar. Ex: quantas classificações consigo fazer para ações de diferentes segmentos

66
Q

Combination Fórmula, qual é a fórmula e qunado usar?

A

= n! / ((n-r) x r! ) -> neste caso a ordem importa (dica memorização, “combination = combinações, ou seja, quantas combinações consigo fazer considerando que a ordem não importa). Ex: número de possiblidade de venda das ações.

67
Q

Permutation Fórmula, qual é a fórmula e qunado usar?

A

= n! / (n-r)! -> neste caso a ordem importa. Ex: ordem de venda de ações diferentes

68
Q

Probability Distribution gives …

A

the probabilities of all possible outcomes for a random variable.

69
Q

Discrete Distribution is ….

A

a countable number of possibles outcomes

70
Q

Continuous Distribution is …

A

an infinite number of possible outcomes

71
Q

Probability fuction gives the probability that a discrete random variable will take ….

A

on the value x

72
Q

Continuous Uniform Distribution defined ….

A

over a range that spans between some lower limit a, and some upper limit b.

72
Q

Cumulative distribution fuction gives the probability that a random variable will be ….

A

less than or equal to a given value

73
Q

Binomial Random Variable da a probabilidade de … e formula?

A

sucesso ou falhar em n tentativa (dica memorização, bi pode dar duas coisas). Formula = (n! / ((n-x)! x!) . p^x . (1-p)^n-x (dica memorização da formula, primeira parte é a combination formula)

74
Q

Binominal tree, qual é a formula para calcular o Down factor?

A

D = 1 / up

75
Q

Para o confidence Interval (Normal Distribution), qual valor para 68%, 90%, 95% e 99%

A

68% = 1,00 ; 90% = 1,65; 95% = 1,96 ; 99% = 2,58

76
Q

Para normal distribution, no intervalo de confiança de 68%, quantos desvios padrões tem?

A

1

77
Q

Para normal distribution, no intervalo de confiança de 95%, quantos desvios padrões tem?

A

2

78
Q

Standard Normal Distribution, a formula é ….

A

z = x - u / σ

79
Q

Shortfall risk is the probability that a …..

A

portfolio return or value will be below a target return or value

80
Q

Sobre target return ou treshhold, usar a formula?

A

Sf Ratio = [ E(Rp) - RL ] / σp -> E(Rp) = valor esperado; RL = minimo acieto; σp = desvio padrão

81
Q

Em uma Lognormal Distribution the skewed será? (Positiva ou negativa / Para direita ou esquerda?

A

Será positiva e para direita, sempre.

82
Q

Continuous Compounding Rate =

A

ln (1 + HPR)

83
Q

Quando falamos de continuous compounding ratem com EAY with continuous compounding a formula é?

A

=e^i - 1

84
Q

T-students, principais caracteristicas

A

small samples (n<30), unkonwn variance, symmetrical (bell shaped), fatter tails than a normal distribution.

85
Q

Para T-students degrees of fredoom é

A

df = n -1

86
Q

Chi-Square Distribution princiapis caracteristicas

A

asymetric

87
Q

F-Distribution is quotient of two

A

chi-squared distributions with m and n degrees of freedom.

88
Q

F-Distribution is symmetric ou asymmetric?

A

asymetric

89
Q

T-students nos da o resultado de

A

population mean, difference between means of two populations, difference between paired observations, population correlation

90
Q

Chi-square nos da o resultado de

A

value of variance of normal population

91
Q

F-Distribution nos da o resultado de

A

equality of variances for two normal population

92
Q

Monte Carlo Simulation can be used to estimate a

A

distribution of derivatives prices or of NPVs

93
Q

Passo a Passo de Monte Carlo

A

1) Specify the parameters of the distribution; 2) Use computer random generation of variables; 3) Value the derivative using those values; 4)Repeat steps 2 and 3, 1000s of times; 4) Calculate mean/variance of all values

94
Q

Sampling Error is the difference between

A

a sample statistic and true population parameter.

95
Q

Sampling Distribution is the distribution of all …

A

possible values of a statistic for samples of size n

96
Q

Simple random sampling, every population member has an equal or different probability of being select?

A

equal

97
Q

Nonprobability sampling, use judment of researcher and it is

A

low cost/readily available data, to select sample items

98
Q

Stratified Random Sampling you need to create..

A

subgrupos da população com base nas caracteristicas principais

99
Q

Cluster Sampling create …

A

subsets, each of which is representative of an aoveral population.

100
Q

Convenience sampling you use…

A

readily available low cost dat for prelimary investigation

101
Q

Judmental sampling you use..

A

select observations from population based on analyst judment

102
Q

Central limit Theorem, a teoria é sobre?

A

quanto maior a amostra (sample), mais próximo de uma distribuição normal fica.

103
Q

Standard Error of the sample mean, as duas formulas usadas são:

A

σxi = σ / raiz n ; sxi = s / raiz n

104
Q

About Desirable Estimator Properties, there is Unbiased, Efficient and Consistent. Explicar os 3

A

Unbiased = expected value equal to parameter; Efficient = sampling distribution has smallest variance of all unbiased estimators; Consistent = a larger sample

105
Q

Normal Distribution and you Known variance. Qual tabela usa para Small Sample e para Large Sample

A

Para Small Sample = Z-statistic; Para Large = Z-Statistic

106
Q

Normal Distribution and you Unknown variance. Qual tabela usa para Small Sample e para Large Sample

A

Para Small Sample = t-statistic; Para Large = t-Statistic

107
Q

NonNormal Distribution and you Unknown variance. Qual tabela usa para Small Sample e para Large Sample

A

Para Small Sample = N.a ; Para Large = t-Statistic

108
Q

NonNormal Distribution and you known variance. Qual tabela usa para Small Sample e para Large Sample

A

Para Small Sample = N.a; Para Large = Z-Statistic

109
Q

Two alternative methods to estimate the standard error of the sample mean is Jacknife and BootStrap. Explicar os dois

A

Jacknife: calculate multiple sample mean, each with one observation;
BootStrap: take many samples of size n, calculate their sample mean

110
Q

Data-Snooping bias:

A

from repeatedly doing tests on same data sample

111
Q

Sample Selection bias:

A

sample not really random

112
Q

Survivership bias:

A

sampling only surviving firms

113
Q

Look=ahead bias:

A

using information not available at the time to construct sample

114
Q

Time-period bias:

A

relatioship existis only during the time period of sample data

115
Q

Self-selection bias:

A

backfill bias

116
Q

Para que serve Alternative Hypothesis (Ha)?

A

supported if the researcher rejects the null hypothesis

117
Q

Para hypothesis testing, o passo a passo é (1 até 7):

A

1) State the hypothesis-relation to be tested; 2) Select a test statistic; 3) Specify the level of Significance; 4) State the decision rule for the hypothesis; 5) Collect the sample and calculate statistics; 6) Make a decision about the hypothesis; 7) Make a decision based on the test results

118
Q

Para que serve Rull Hypothesis (Ho)?

A

é para ver se a hipotese nula é verdadeira ou falsa

119
Q

Em hypothesis testing, the test statistic is calculated from sample data and compared to

A

critical values to test Ho

120
Q

Em hypothesis testing, the test statistic if exceeds the critical value or is outside the range of critical values, the researcher rejects or accept the Ho?

A

Rejects.

121
Q

Em hypothesis testing, type I Error is

A

rejecting Ho when it is actually true

122
Q

Em hypothesis testing, type II Error is

A

failing to reject when Ho it is false

123
Q

Em hypothesis testing, significance leve is probability of Type I Error or II Error?

A

Type I Error

123
Q

Em hypothesis testing, two independent normal populations. Assume population variance are equal and use prob. estimate of variance using both sample. Use t-test, f-test or Chi-square?

A

T-test and reject if test statistic is outside critical values.

123
Q

Power test is 1 - prob. of type I Error or II Error?

A

Type Error II

124
Q

Em hypothesis testing, p-value is the smallest level of significance at the null can be rejected or accepeted?

A

Rejected.

125
Q

Em hypothesis testing test of weather the variance of a normal population equals σ^2.Use t-test, f-test or Chi-square?

A

Uses Chi-square, two tailed test, reject if outside the critical values

125
Q

Em hypothesis testing, two dependent normal populations. Numerator is avarage difference between paired observations and denominator is standard deviation of the differences.Use t-test, f-test or Chi-square?

A

T-test and reject if test statistic is outside critical values.

126
Q

Em hypothesis testing test of weather the variance of two normal population are equal.Use t-test, f-test or Chi-square?

A

Uses F-test, VarA / VarB, put larger variance in numerator for one tail test

127
Q

Em hypothesis testing test of weather the population correlation coefficient equals zero.Use t-test, f-test or Chi-square?

A

Uses t-test, two tailed, with n-2 degres of fredom

128
Q

Em hypothesis testing, parametric tests are based on assumptions about …

A

population distributions and population parametres (t-test, z-test, f-test)

129
Q

Em hypothesis testing, nonparametric tests are based on assumptions about …

A

population distributions and test things other than parameter values.

130
Q

Formula de parametric test of correlation =

A

t-stat = (r . raiz de n-2) / raiz de 1 - r^2

131
Q

formula de test of independence from contingency table =

A

expected if independent = (total for row i x total for colum j) / total for all colums and rows ; Ou pode usar (o - E)^2 / E

132
Q

Steps in hypothesis testing (1 até 7)

A

1 Stating the hypotheses.
2 Identifying the test statistic and its probability distribution.
3 Specifying the significance level.
4 Stating the decision rule.
5 Collecting the data and performing the calculations.
6 Making the statistical decision.
7 Making the economic or investment decision.

133
Q

Null Hypothesis (Ho)

A

sempre inclui =< ou =>. É para ver se é V ou F

134
Q

Alternative Hipothesis (Ha)

A

supported if the researcher rejects the null hipothesis

135
Q

Em hypothesis testing. O test statistic é comparado com o critical value do test Ho. If the test statistic exceeds the critical value . The researcher should reject Ho or not?

A

Yes, because is outside the range of critical values.

136
Q

P-Value

A

Is the smallest level of significance a which the null can be rejected. Ex: if the p-valeu is given as 0.0213 -> You can reject the null at 5% significance but not at 1%

137
Q

Em hypothesis testing. When do you use two-tailed test?

A

Use when testing to see if a population parameter is different from a specified value. (Ex: Ho: u = 0 ; Ha: u <> 0 )

138
Q

Em hypothesis testing. When do you use one-tailed test?

A

Use when testing to see if a parameter is above or below a specified value. (Ex: Ho: u <= 0 ; Ha: u > 0 )

139
Q

Em hypothesis testing. Type I Error

A

rejecting Ho when it is true

140
Q

Em hypothesis testing. Type I Error Type II Error

A

Failing to reject Ho when it is false

141
Q

Em hypothesis testing. Significa Level is ?

A

Probability of Type I Error

142
Q

Em hypothesis testing. Power test is

A

1 - Probability of Type II Error

143
Q

Em hypothesis testing. Difference in means test. Two INDEPENDENT NORMAL populations, variances are equal. What Type of test should you use?

A

T-test, reject if test statistic is outside of the critical value

144
Q

Em hypothesis testing. Difference in means test. Two DEPENDENT NORMAL populations, numerator is avarage difference between paired observations and denominator is standard deviation of the differences. What Type of test should you use?

A

T-test, reject if test statistic is outside of the critical value

145
Q
A
146
Q
A
147
Q
A
148
Q
A
149
Q
A
150
Q
A

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