Quantitative methods Flashcards
1
Q
What does interest rates measure?
A
Time value of money
2
Q
What is the equilibrium rate of interest rates?
A
Required rate of return
3
Q
What does interest rate represents?
A
Opportunity cost of current consumption
4
Q
What is real risk free interest rate?
A
Theoretical term with no inflation and zero probability of default
5
Q
What is time preference?
A
Degree to which current consumption is preferred to euqal future consumption
6
Q
T-bills are example of which interest rate?
A
Nominal risk free rates
7
Q
Is inflation premium included in t-bills?
A
Yes
8
Q
What is the formula for real risk-free interest rate?
A
=nominal rate-inflation rate
9
Q
What are the types of securities risks? (4)
A
Inflation, default, liquidity, maturity
10
Q
What is default risk?
A
Risk that borrower will fail to make payments
11
Q
What is liquidity risk?
A
Risks of receiving less than fair value if sold quickly for liquidity
12
Q
What is maturity risk?
A
Risk that long-term maturity risks possesses as prices are more volatile
13
Q
What is holding period return (HPR)
A
% increase in the investment value over time
14
Q
HPR formula
A
HPR=(end period value-beg.period value+Dividends)/beg.value-1
15
Q
HPR formula over multiple periods
A
HPR=(1+HPR1)(1+HPR2)…-1
16
Q
What is arithmetic mean return?
A
Simple mean average
17
Q
What is geometric mean return?
A
compound rate -> sqrt(n)(1+R1)(1+R2)…-1
18
Q
Which is bigger - geometric or arithmetic?
A
Arithmetic
19
Q
What is harmonic mean?
A
N/sum(1/X)
20
Q
Relationship between 3 means
A
arithmetic*harmonic =geometric^2
21
Q
What is IRR?
A
Rate of return for which NPV=0
22
Q
Which content is money-weighted applies?
A
IRR
23
Q
What is money-weighted rate of return?
A
IRR of portfolio taking into account all inflows and outflows.
24
Q
What is time-weighted rate of return?
A
Compound growth, rate of which $1 compounds over time.
25
If manager can control inflows and outflows which return to use?
Money-weighted rate of return
26
Annualized return formula
(1+HPR)^(365/days)-1
27
What happens to PV and FV with more frequent compounding?
FV goes up, PV goes down
28
PV of annualized return formula
FV*(1+(r/m)^-mN, where N is number of years and m is number of periods within the year
29
Continuesly compounding return formula
ln(1+HPR)=ln(ending value/beg.value)
30
What is gross return?
Total return of a portfolio before deducting management and admin fees
31
What is net returns?
Total portfolio return after taxes have been deducted
32
What is pre-tax nominal return?
Total portfolio return before paying taxes
33
What is after-tax nominal return?
Total portfolio return after tax liability.
34
What is real return?
Nominal return adjusted for inflation
35
Real returns formula
(1+real returns)=(1+nominal risk-free rate)(1+risk premium)/(1+inflation premium)
36
What is leveraged returns?
Return that is a multiple of a return on the underlying asset
37
Leveraged return formula
(r(V0+Vb)-rbVb)/Vo
38
FV formula (compounding)
PVe^(r*t)
39
PV formula (compounding)
FVe^(-r*t)
40
Zero coupon bonds pays..
less than face value to buy the investment and receives the face value at maturity
41
On what the price investor pays for the investment depends on?
YTM and time until maturity
42
Zero coupon is bond is prices at
discount
43
Fixed coupon bond
investor receives a cash interest payment (coupon)
44
Perpetuity
has no maturity date
45
PV(perpetuity) formula
PV=payment/r
46
Example of amortized bond
annuity
47
Amortized bond
Similar to fixed coupon bond, but each payment includes some portion of its principle.
48
Preffered stock
Stock that pays dividend as a % of its par value
49
Annuity payment formula
r*PV/(1-(1+r)^-t)
50
What is discount rate of preffered stock?
Required rate of return
51
Preffered stock value formula
Dp/kp
52
Common stock
residual claim to company's assets after it satisfies all other claims, dividends based on management decision
53
Value of the stock based on DDM model
D1/(k-g)
54
Dividend yield formula
D1/V0
55
Required rate of return formula
(D1/V0)+gc
56
Cash flow additivity principle
PV of any stream of cashflows equals the sum of the PVs of the cash flows
57
No arbitrage principle
Two identical cash flow series will have the same price today
58
Forward interest rate
Interest rate for a loan to be made at some future date
59
2y1y annotation
1 year loan, 2 years from today
60
Forward interest rate formula
(1+S3)^3=(1+S1)(A+1y1y)(1+2y1y)
61
USD/EUR interpretation
EUR base currency, USD price currency
62
Forward/spot relationship
(1+interest rate_price)/(1+interest rate_base)
63
What is an option?
Right, but not the obligation to buy or sell an asset on a future date for a specific price
64
When option is in the money and when out of money?
If its worth it exercise it -> in the money, if it's worth to leave it expire -> out of money
65
What is measures of central tendency
center or average of a dataset (mean, median, mode)
66
What is median?
Middle point, not affected by outliers
67
What is mode?
Most frequent value
68
What is trimmed mean?
A mean to deal with outliers, excluding point above or below certain percentage
69
What is winsorized mean?
A mean to deal with outliers, where values are substituted based on percentiles, with the percentiles values.
70
What is quantile?
Value at or below stated proportion of a dataset
71
What is quartile?
1/4
72
What is quintile?
1/5
73
What is decile?
1/10
74
What is percentile?
1/100
75
What is interquartile range?
3rd quartile - 1st quartile
76
What is dispersion?
Variability around the central tendency
77
What does dispersion measure in finance?
Risk
78
What does central tendency measure in finance?
Reward
79
What is range and how it is calculated?
Max value-min value
80
What is mean absolute deviation (MAD)?
Average of the absolute values of the deviation of individual observations from arithmetic mean
81
MAD formula
sumIXi-XI/n
82
Sample variance formula
sum(Xi-X)^2/(n-1)
83
Sample standard deviation formula
sqrt(sample variance)
84
What is relative dispersion?
Amount of variability in a distribution around a reference point or benchmark
85
Coefficient of variation formula
CV=Sx/X(mean)
86
Target downside deviation formula
sqrt((Xi-B)^2/(n-1))
87
What is skeweness?
how symmetrical the distribution is
88
Positive skew (outliers vs mean)
Outliers>mean
89
Negative skew (outliers vs mean)
Outliers
90
Symmetrical skew (MMM)
mean=median=mode
91
Positive skew (MMM)
mean>median>mode
92
Negative skew (MMM)
mode>median>mean
93
What is kurtosis?
Measure of how peaked the distribution is
94
What kurtosis are there?
Leptokurtic, playtikurtic, mesokurtic
95
What covariance measures?
How two variables move together around their means
96
What does correlation measures?
Strenght of linear relationship between two variables
97
Correlation formula
COV(x,y)/sdx*sdy
98
What is spurious correlation?
Result of chance or present due to changes in both variables as a result cause by a third variable
99
What is expected value?
Weighted average of the possible outcomes for the variable
100
What is Bayers theorem?
Update set given set of information based on arrival of new information
101
Expected return of a portfolio formula
Sum of w1*E(R1)
102
Sample covariance formula
sum of (Ri-Rmean)*(R2-R2mean)/(n-1)
103
How many unique covariance terms there are?
n(n-1)/2
104
Portfolio covariance formula
w^2_a*variance^2_a+w^2_b*variance^2_b+2w_a*w_b*Cov(a,b)
105
What is shortfall risk?
Probability that a return will fall below a particular threshold
106
What is Ray's safety first criterion?
Optimal portfolio will minimize the probability that the return of the portfolio falls below some acceptable minimal level
107
Safety-first ratio formula
E(Rp)-Rl/s.d.(p)
108
Lognormal asset prices formula
P0e^rt
109
What is CFA assumption about returns?
They are independently and identically dsiributed
110
What does it mean for returns to be independently distributed?
Past returns cannot be used to model future
111
What does it mean for returns to be identically distributed?
Mean and variance does not change over time
112
What is monte carlo simulation?
Repeated generation of one or more risk factors that affect securities values to generate a distribution of those values
113
What is resampling?
Generation of data inputs to use in simulation
114
What is bootstrap resampling?
Drawing repeated samples of sizen, replacing so they could be redrawn.
115
What is probability sampling?
Selection of sample when we know probability of each sample member
116
What is random sampling?
Each is assumed to have the same probability of being selected
117
What is systematic sample?
Selecting every nth member
118
What is stratified random sampling?
Seperating population into smaller groups and using whole group as a sample
119
What is cluster sampling?
Seperating population into smaller groups and mixing members from each group as a sample
120
What is convenience sampling?
Selecting sample based on ease
121
What is judgemental sampling?
Sample selected by researchers based on his judgement
122
What is central limit theory?
As sample size increases, it approches normal distribution
123
What is considered as large sample?
N=>30
124
Standard error of a sample formula
s.d./sqrt(n)
125
What is jackknife resampling?
Calculating sample means with one observation removed
126
What is bootstrap resampling?
Redraw repeated samples a lot.
127
What is hypothesis?
Statement about testing the theory
128
What is null hypothesis?
Hypothesis that a researcher wants to reject
129
What is alternative hypothesis?
What is concluded when there is sufficient evidence to reject H0
130
What is type I error?
H0 is true, but we rejected it
131
What is type II error?
H0 is false, but we failed to reject it.
132
What is significance level?
Probability of making type I error
133
What is power of a test?
Making a right decision and rejecting H0 when it is false
134
What is relationship between significance level and type II error?
Inverse
135
What is p-value?
Probability obtaining test statistic that would lead to a rejection of H0.
136
Which test is used for value of population mean?
T-test or z-test
137
Which test is used for equality of two population means?
T-test
138
Which test is used for value of population variance?
Chi-squared
139
Which test is used for equality of two population variance?
F-test
140
What is paired comparison test?
Two samples depend on some other factor.
141
What is parametric test?
Test with assumptions regarding distribution of the population
142
What is non parametric tests?
Test when particular population parameters are not considered
143
What is Pearson's correlation test?
It is used to assess the strenght of the relationship between two variables
144
What is formula for Pearson's and Spearman's test statistic?
r*sqrt(n-2)/sqrt(1-r^2)
145
What is Spearman rank correlation test?
A test to determine whether two sets of data are correlated(strenght and direction)
146
What is contingency or two-way table?
It is number of observations from a sample that have a combination of two characteristics.
147
What is simple linear regression?
A regression line that explains variation in dependent variable in terms of variability in the independent variable
148
What is simple regression line formula?
Y=b0+b1X+e
149
What is sum of squared error?
It is sum of sqaured vertical differences between estimated and actual values
150
What is formula of the slope coefficient?
COV(x,y)/variance(x)
151
What is homoskedasticity?
It says that variance of the residual term is constant
152
What are assumptions of OLS?
1. Independent and dependent variables have linear relationship
2. Homoskedasticity
3. Residula term is normally and independently distributed.
153
What is analysis of variance (ANOVA?
It analyses total variability of the dependent variable
154
What is total of sum squared (SST)?
Total variation of the dependent variable (actual-mean)
155
What is sum of square regression (SSR)?
Measures variation explained by the independent variable (predicted-mean)
156
What is sum of squared error (SSE)?
It measures unexplained variation (actual- predicted)
157
Mean squared error formula
SSE/(n-2)
158
What is coefficient of determination (R^2)?
% of variation in the dependent variable explained by the independent variable
159
What is R^2 formula?
SSR/SST
160
What does F-test measures?
How well the set of independent variables explains variation
161
What is formula for F?
MSR/MSE=SSR/k/(SSE/n-k-1)
162
What does T-test measure?
Whether true slope coefficient is equal to hypothesized value.
163
What is t-test statistic value?
Tb1=b1hat-b1/Sb1hat
164
What are predicted values?
Dependent variables based on linear regression
165
What is confidence level?
Values within true statistic should lie
166
What is formula of confidence level?
Y+-(tc*SE)
167
How to interpret log and linear results?
Linear-> absolute change, log -> relative change
168
What is fintech?
Development in the technology that can be applied to financial services industry
169
What is big data?
All potential useful information that is generated in the economy
170
What are characteristics of big data?
Volume, velocity, variety
171
What does volume represent?
Orders of magnitude
172
What does velocity represent?
How quickly data is communicated
173
What does variety represent?
Degree of structure
174
What does AI aim for?
Stimulate human cognition
175
What does machine learning learn?
Associations between inputs and outputs
176
What is supervised learning?
When inputs and outputs are labelled
177
What is unsupervised learning?
When machine learns how to structure the data
178
What is deep learning?
It uses layers of network to identify patterns
179
What is algorithmic trading?
Securities trading based on set of rules
180
What is high frequency trading?
It takes advantage of intraday securities mispricings.
