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CFA level I > Quantitative methods > Flashcards

Quantitative methods Flashcards

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CFA flashcards
1
Q

What does interest rates measure?

A

Time value of money

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2
Q

What is the equilibrium rate of interest rates?

A

Required rate of return

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3
Q

What does interest rate represents?

A

Opportunity cost of current consumption

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4
Q

What is real risk free interest rate?

A

Theoretical term with no inflation and zero probability of default

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5
Q

What is time preference?

A

Degree to which current consumption is preferred to euqal future consumption

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6
Q

T-bills are example of which interest rate?

A

Nominal risk free rates

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7
Q

Is inflation premium included in t-bills?

A

Yes

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8
Q

What is the formula for real risk-free interest rate?

A

=nominal rate-inflation rate

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9
Q

What are the types of securities risks? (4)

A

Inflation, default, liquidity, maturity

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10
Q

What is default risk?

A

Risk that borrower will fail to make payments

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11
Q

What is liquidity risk?

A

Risks of receiving less than fair value if sold quickly for liquidity

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12
Q

What is maturity risk?

A

Risk that long-term maturity risks possesses as prices are more volatile

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13
Q

What is holding period return (HPR)

A

% increase in the investment value over time

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14
Q

HPR formula

A

HPR=(end period value-beg.period value+Dividends)/beg.value-1

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15
Q

HPR formula over multiple periods

A

HPR=(1+HPR1)(1+HPR2)…-1

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16
Q

What is arithmetic mean return?

A

Simple mean average

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17
Q

What is geometric mean return?

A

compound rate -> sqrt(n)(1+R1)(1+R2)…-1

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18
Q

Which is bigger - geometric or arithmetic?

A

Arithmetic

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19
Q

What is harmonic mean?

A

N/sum(1/X)

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20
Q

Relationship between 3 means

A

arithmetic*harmonic =geometric^2

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21
Q

What is IRR?

A

Rate of return for which NPV=0

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22
Q

Which content is money-weighted applies?

A

IRR

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23
Q

What is money-weighted rate of return?

A

IRR of portfolio taking into account all inflows and outflows.

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24
Q

What is time-weighted rate of return?

A

Compound growth, rate of which $1 compounds over time.

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25
Q

If manager can control inflows and outflows which return to use?

A

Money-weighted rate of return

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26
Q

Annualized return formula

A

(1+HPR)^(365/days)-1

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27
Q

What happens to PV and FV with more frequent compounding?

A

FV goes up, PV goes down

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28
Q

PV of annualized return formula

A

FV*(1+(r/m)^-mN, where N is number of years and m is number of periods within the year

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29
Q

Continuesly compounding return formula

A

ln(1+HPR)=ln(ending value/beg.value)

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30
Q

What is gross return?

A

Total return of a portfolio before deducting management and admin fees

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31
Q

What is net returns?

A

Total portfolio return after taxes have been deducted

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32
Q

What is pre-tax nominal return?

A

Total portfolio return before paying taxes

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33
Q

What is after-tax nominal return?

A

Total portfolio return after tax liability.

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34
Q

What is real return?

A

Nominal return adjusted for inflation

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35
Q

Real returns formula

A

(1+real returns)=(1+nominal risk-free rate)(1+risk premium)/(1+inflation premium)

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36
Q

What is leveraged returns?

A

Return that is a multiple of a return on the underlying asset

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37
Q

Leveraged return formula

A

(r(V0+Vb)-rbVb)/Vo

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38
Q

FV formula (compounding)

A

PVe^(r*t)

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39
Q

PV formula (compounding)

A

FVe^(-r*t)

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40
Q

Zero coupon bonds pays..

A

less than face value to buy the investment and receives the face value at maturity

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41
Q

On what the price investor pays for the investment depends on?

A

YTM and time until maturity

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42
Q

Zero coupon is bond is prices at

A

discount

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43
Q

Fixed coupon bond

A

investor receives a cash interest payment (coupon)

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44
Q

Perpetuity

A

has no maturity date

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45
Q

PV(perpetuity) formula

A

PV=payment/r

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46
Q

Example of amortized bond

A

annuity

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47
Q

Amortized bond

A

Similar to fixed coupon bond, but each payment includes some portion of its principle.

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48
Q

Preffered stock

A

Stock that pays dividend as a % of its par value

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49
Q

Annuity payment formula

A

r*PV/(1-(1+r)^-t)

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50
Q

What is discount rate of preffered stock?

A

Required rate of return

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51
Q

Preffered stock value formula

A

Dp/kp

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52
Q

Common stock

A

residual claim to company’s assets after it satisfies all other claims, dividends based on management decision

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53
Q

Value of the stock based on DDM model

A

D1/(k-g)

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54
Q

Dividend yield formula

A

D1/V0

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55
Q

Required rate of return formula

A

(D1/V0)+gc

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56
Q

Cash flow additivity principle

A

PV of any stream of cashflows equals the sum of the PVs of the cash flows

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57
Q

No arbitrage principle

A

Two identical cash flow series will have the same price today

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58
Q

Forward interest rate

A

Interest rate for a loan to be made at some future date

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59
Q

2y1y annotation

A

1 year loan, 2 years from today

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60
Q

Forward interest rate formula

A

(1+S3)^3=(1+S1)(A+1y1y)(1+2y1y)

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61
Q

USD/EUR interpretation

A

EUR base currency, USD price currency

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62
Q

Forward/spot relationship

A

(1+interest rate_price)/(1+interest rate_base)

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63
Q

What is an option?

A

Right, but not the obligation to buy or sell an asset on a future date for a specific price

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64
Q

When option is in the money and when out of money?

A

If its worth it exercise it -> in the money, if it’s worth to leave it expire -> out of money

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65
Q

What is measures of central tendency

A

center or average of a dataset (mean, median, mode)

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66
Q

What is median?

A

Middle point, not affected by outliers

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67
Q

What is mode?

A

Most frequent value

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68
Q

What is trimmed mean?

A

A mean to deal with outliers, excluding point above or below certain percentage

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69
Q

What is winsorized mean?

A

A mean to deal with outliers, where values are substituted based on percentiles, with the percentiles values.

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70
Q

What is quantile?

A

Value at or below stated proportion of a dataset

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71
Q

What is quartile?

A

1/4

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72
Q

What is quintile?

A

1/5

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73
Q

What is decile?

A

1/10

74
Q

What is percentile?

A

1/100

75
Q

What is interquartile range?

A

3rd quartile - 1st quartile

76
Q

What is dispersion?

A

Variability around the central tendency

77
Q

What does dispersion measure in finance?

A

Risk

78
Q

What does central tendency measure in finance?

A

Reward

79
Q

What is range and how it is calculated?

A

Max value-min value

80
Q

What is mean absolute deviation (MAD)?

A

Average of the absolute values of the deviation of individual observations from arithmetic mean

81
Q

MAD formula

A

sumIXi-XI/n

82
Q

Sample variance formula

A

sum(Xi-X)^2/(n-1)

83
Q

Sample standard deviation formula

A

sqrt(sample variance)

84
Q

What is relative dispersion?

A

Amount of variability in a distribution around a reference point or benchmark

85
Q

Coefficient of variation formula

A

CV=Sx/X(mean)

86
Q

Target downside deviation formula

A

sqrt((Xi-B)^2/(n-1))

87
Q

What is skeweness?

A

how symmetrical the distribution is

88
Q

Positive skew (outliers vs mean)

A

Outliers>mean

89
Q

Negative skew (outliers vs mean)

A

Outliers<mean

90
Q

Symmetrical skew (MMM)

A

mean=median=mode

91
Q

Positive skew (MMM)

A

mean>median>mode

92
Q

Negative skew (MMM)

A

mode>median>mean

93
Q

What is kurtosis?

A

Measure of how peaked the distribution is

94
Q

What kurtosis are there?

A

Leptokurtic, playtikurtic, mesokurtic

95
Q

What covariance measures?

A

How two variables move together around their means

96
Q

What does correlation measures?

A

Strenght of linear relationship between two variables

97
Q

Correlation formula

A

COV(x,y)/sdx*sdy

98
Q

What is spurious correlation?

A

Result of chance or present due to changes in both variables as a result cause by a third variable

99
Q

What is expected value?

A

Weighted average of the possible outcomes for the variable

100
Q

What is Bayers theorem?

A

Update set given set of information based on arrival of new information

101
Q

Expected return of a portfolio formula

A

Sum of w1*E(R1)

102
Q

Sample covariance formula

A

sum of (Ri-Rmean)*(R2-R2mean)/(n-1)

103
Q

How many unique covariance terms there are?

A

n(n-1)/2

104
Q

Portfolio covariance formula

A

w^2_avariance^2_a+w^2_bvariance^2_b+2w_aw_bCov(a,b)

105
Q

What is shortfall risk?

A

Probability that a return will fall below a particular threshold

106
Q

What is Ray’s safety first criterion?

A

Optimal portfolio will minimize the probability that the return of the portfolio falls below some acceptable minimal level

107
Q

Safety-first ratio formula

A

E(Rp)-Rl/s.d.(p)

108
Q

Lognormal asset prices formula

A

P0e^rt

109
Q

What is CFA assumption about returns?

A

They are independently and identically dsiributed

110
Q

What does it mean for returns to be independently distributed?

A

Past returns cannot be used to model future

111
Q

What does it mean for returns to be identically distributed?

A

Mean and variance does not change over time

112
Q

What is monte carlo simulation?

A

Repeated generation of one or more risk factors that affect securities values to generate a distribution of those values

113
Q

What is resampling?

A

Generation of data inputs to use in simulation

114
Q

What is bootstrap resampling?

A

Drawing repeated samples of sizen, replacing so they could be redrawn.

115
Q

What is probability sampling?

A

Selection of sample when we know probability of each sample member

116
Q

What is random sampling?

A

Each is assumed to have the same probability of being selected

117
Q

What is systematic sample?

A

Selecting every nth member

118
Q

What is stratified random sampling?

A

Seperating population into smaller groups and using whole group as a sample

119
Q

What is cluster sampling?

A

Seperating population into smaller groups and mixing members from each group as a sample

120
Q

What is convenience sampling?

A

Selecting sample based on ease

121
Q

What is judgemental sampling?

A

Sample selected by researchers based on his judgement

122
Q

What is central limit theory?

A

As sample size increases, it approches normal distribution

123
Q

What is considered as large sample?

A

N=>30

124
Q

Standard error of a sample formula

A

s.d./sqrt(n)

125
Q

What is jackknife resampling?

A

Calculating sample means with one observation removed

126
Q

What is bootstrap resampling?

A

Redraw repeated samples a lot.

127
Q

What is hypothesis?

A

Statement about testing the theory

128
Q

What is null hypothesis?

A

Hypothesis that a researcher wants to reject

129
Q

What is alternative hypothesis?

A

What is concluded when there is sufficient evidence to reject H0

130
Q

What is type I error?

A

H0 is true, but we rejected it

131
Q

What is type II error?

A

H0 is false, but we failed to reject it.

132
Q

What is significance level?

A

Probability of making type I error

133
Q

What is power of a test?

A

Making a right decision and rejecting H0 when it is false

134
Q

What is relationship between significance level and type II error?

A

Inverse

135
Q

What is p-value?

A

Probability obtaining test statistic that would lead to a rejection of H0.

136
Q

Which test is used for value of population mean?

A

T-test or z-test

137
Q

Which test is used for equality of two population means?

A

T-test

138
Q

Which test is used for value of population variance?

A

Chi-squared

139
Q

Which test is used for equality of two population variance?

A

F-test

140
Q

What is paired comparison test?

A

Two samples depend on some other factor.

141
Q

What is parametric test?

A

Test with assumptions regarding distribution of the population

142
Q

What is non parametric tests?

A

Test when particular population parameters are not considered

143
Q

What is Pearson’s correlation test?

A

It is used to assess the strenght of the relationship between two variables

144
Q

What is formula for Pearson’s and Spearman’s test statistic?

A

r*sqrt(n-2)/sqrt(1-r^2)

145
Q

What is Spearman rank correlation test?

A

A test to determine whether two sets of data are correlated(strenght and direction)

146
Q

What is contingency or two-way table?

A

It is number of observations from a sample that have a combination of two characteristics.

147
Q

What is simple linear regression?

A

A regression line that explains variation in dependent variable in terms of variability in the independent variable

148
Q

What is simple regression line formula?

A

Y=b0+b1X+e

149
Q

What is sum of squared error?

A

It is sum of sqaured vertical differences between estimated and actual values

150
Q

What is formula of the slope coefficient?

A

COV(x,y)/variance(x)

151
Q

What is homoskedasticity?

A

It says that variance of the residual term is constant

152
Q

What are assumptions of OLS?

A
  1. Independent and dependent variables have linear relationship
  2. Homoskedasticity
  3. Residula term is normally and independently distributed.
153
Q

What is analysis of variance (ANOVA?

A

It analyses total variability of the dependent variable

154
Q

What is total of sum squared (SST)?

A

Total variation of the dependent variable (actual-mean)

155
Q

What is sum of square regression (SSR)?

A

Measures variation explained by the independent variable (predicted-mean)

156
Q

What is sum of squared error (SSE)?

A

It measures unexplained variation (actual- predicted)

157
Q

Mean squared error formula

A

SSE/(n-2)

158
Q

What is coefficient of determination (R^2)?

A

% of variation in the dependent variable explained by the independent variable

159
Q

What is R^2 formula?

A

SSR/SST

160
Q

What does F-test measures?

A

How well the set of independent variables explains variation

161
Q

What is formula for F?

A

MSR/MSE=SSR/k/(SSE/n-k-1)

162
Q

What does T-test measure?

A

Whether true slope coefficient is equal to hypothesized value.

163
Q

What is t-test statistic value?

A

Tb1=b1hat-b1/Sb1hat

164
Q

What are predicted values?

A

Dependent variables based on linear regression

165
Q

What is confidence level?

A

Values within true statistic should lie

166
Q

What is formula of confidence level?

A

Y+-(tc*SE)

167
Q

How to interpret log and linear results?

A

Linear-> absolute change, log -> relative change

168
Q

What is fintech?

A

Development in the technology that can be applied to financial services industry

169
Q

What is big data?

A

All potential useful information that is generated in the economy

170
Q

What are characteristics of big data?

A

Volume, velocity, variety

171
Q

What does volume represent?

A

Orders of magnitude

172
Q

What does velocity represent?

A

How quickly data is communicated

173
Q

What does variety represent?

A

Degree of structure

174
Q

What does AI aim for?

A

Stimulate human cognition

175
Q

What does machine learning learn?

A

Associations between inputs and outputs

176
Q

What is supervised learning?

A

When inputs and outputs are labelled

177
Q

What is unsupervised learning?

A

When machine learns how to structure the data

178
Q

What is deep learning?

A

It uses layers of network to identify patterns

179
Q

What is algorithmic trading?

A

Securities trading based on set of rules

180
Q

What is high frequency trading?

A

It takes advantage of intraday securities mispricings.

CFA level I (12 decks)

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