Quant 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?
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
premium
42
Fixed coupon bond
investor receives a cash interest payment (coupon)
42
Perpetuity
has no maturity date
42
PV(perpetuity) formula
PV=payment/r
42
Example of amortized bond
annuity
42
Amortized bond
Similar to fixed coupon bond, but each payment includes some portion of its principle.
42
Preffered stock
Stock that pays dividend as a % of its par value
43
Annuity payment formula
r*PV/(1-(1+r)^-t)
44
What is discount rate of preffered stock?
Required rate of return
45
Preffered stock value formula
Dp/kp
46
Common stock
residual claim to company's assets after it satisfies all other claims, dividends based on management decision
47
Value of the stock based on DDM model
D1/(k-g)
48
Dividend yield formula
D1/V0
48
Required rate of return formula
(D1/V0)+gc
49
Cash flow additivity principle
PV of any stream of cashflows equals the sum of the PVs of the cash flows
50
No arbitrage principle
Two identical cash flow series will have the same price today
51
Forward interest rate
Interest rate for a loan to be made at some future date
52
2y1y annotation
1 year loan, 2 years from today
53
Forward interest rate formula
(1+S3)^3=(1+S1)(A+1y1y)(1+2y1y)
54
USD/EUR interpretation
EUR base currency, USD price currency
55
Forward/spot relationship
(1+interest rate_price)/(1+interest rate_base)
56
What is an option?
Right, but not the obligation to buy or sell an asset on a future date for a specific price
57
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
58
What is measures of central tendency
center or average of a dataset (mean, median, mode)
59
What is median?
Middle point, not affected by outliers
60
What is mode?
Most frequent value
61
What is trimmed mean?
A mean to deal with outliers, excluding point above or below certain percentage
62
What is winsorized mean?
A mean to deal with outliers, where values are substituted based on percentiles, with the percentiles values.
63
What is quantile?
Value at or below stated proportion of a dataset
64
What is quartile?
1/4
65
What is quintile?
1/5
66
What is decile?
1/10
67
What is percentile?
1/100
68
What is interquartile range?
3rd quartile - 1st quartile
69
What is dispersion?
Variability around the central tendency
70
What does dispersion measure in finance?
Risk
71
What does central tendency measure in finance?
Reward
72
What is range and how it is calculated?
Max value-min value
73
What is mean absolute deviation (MAD)?
Average of the absolute values of the deviation of individual observations from arithmetic mean
74
MAD formula
sumIXi-XI/n
75
Sample variance formula
sum(Xi-X)^2/(n-1)
76
Sample standard deviation formula
sqrt(sample variance)
77
What is relative dispersion?
Amount of variability in a distribution around a reference point or benchmark
78
Coefficient of variation formula
CV=Sx/X(mean)
79
Target downside deviation formula
sqrt((Xi-B)^2/(n-1))
80
What is skeweness?
how symmetrical the distribution is
81
Positive skew (outliers vs mean)
Outliers>mean
82
Negative skew (outliers vs mean)
Outliers
83
Symmetrical skew (MMM)
mean=median=mode
84
Positive skew (MMM)
mean>median>mode
85
Negative skew (MMM)
mode>median>mean
86
What is kurtosis?
Measure of how peaked the distribution is
87
What kurtosis are there?
Leptokurtic, playtikurtic, mesokurtic
88
What covariance measures?
How two variables move together around their means
89
What does correlation measures?
Strenght of linear relationship between two variables
90
Correlation formula
COV(x,y)/sdx*sdy
91
What is spurious correlation?
Result of chance or present due to changes in both variables as a result cause by a third variable
92
What is expected value?
Weighted average of the possible outcomes for the variable
93
What is Bayers theorem?
Update set given set of information based on arrival of new information
94
Expected return of a portfolio formula
Sum of w1*E(R1)
95
Sample covariance formula
sum of (Ri-Rmean)*(R2-R2mean)/(n-1)
96
How many unique covariance terms there are?
n(n-1)/2
97
Portfolio covariance formula
w^2_a*variance^2_a+w^2_b*variance^2_b+2w_a*w_b*Cov(a,b)
98
What is shortfall risk?
Probability that a return will fall below a particular threshold
99
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
100
Safety-first ratio formula
E(Rp)-Rl/s.d.(p)
101
Lognormal asset prices formula
P0e^rt
102
What is CFA assumption about returns?
They are independently and identically dsiributed
103
What does it mean for returns to be independently distributed?
Past returns cannot be used to model future
104
What does it mean for returns to be identically distributed?
Mean and variance does not change over time
105
What is monte carlo simulation?
Repeated generation of one or more risk factors that affect securities values to generate a distribution of those values
106
What is resampling?
Generation of data inputs to use in simulation
107
What is bootstrap resampling?
Drawing repeated samples of sizen, replacing so they could be redrawn.
108
What is probability sampling?
Selection of sample when we know probability of each sample member
109
What is random sampling?
Each is assumed to have the same probability of being selected
110
What is systematic sample?
Selecting every nth member
111
What is stratified random sampling?
Seperating population into smaller groups and using whole group as a sample
112
What is cluster sampling?
Seperating population into smaller groups and mixing members from each group as a sample
113
What is convenience sampling?
Selecting sample based on ease
114
What is judgemental sampling?
Sample selected by researchers based on his judgement
115
What is central limit theory?
As sample size increases, it approches normal distribution
116
What is considered as large sample?
N=>30
117
Standard error of a sample formula
s.d./sqrt(n)
118
What is jackknife resampling?
Calculating sample means with one observation removed
119
What is bootstrap resampling?
Redraw repeated samples a lot.
120
What is hypothesis?
Statement about testing the theory
121
What is null hypothesis?
Hypothesis that a researcher wants to reject
122
What is alternative hypothesis?
What is concluded when there is sufficient evidence to reject H0
123
What is type I error?
H0 is true, but we rejected it
124
What is type II error?
H0 is false, but we failed to reject it.
125
What is significance level?
Probability of making type I error
126
What is power of a test?
Making a right decision and rejecting H0 when it is false
127
What is relationship between significance level and type II error?
Inverse
128
What is p-value?
Probability obtaining test statistic that would lead to a rejection of H0.
129
Which test is used for value of population mean?
T-test or z-test
130
Which test is used for equality of two population means?
T-test
131
Which test is used for value of population variance?
Chi-squared
132
Which test is used for equality of two population variance?
F-test
133
What is paired comparison test?
Two samples depend on some other factor.
134
What is parametric test?
Test with assumptions regarding distribution of the population
135
What is non parametric tests?
Test when particular population parameters are not considered
136
What is Pearson's correlation test?
It is used to assess the strenght of the relationship between two variables
137
What is formula for Pearson's and Spearman's test statistic?
r*sqrt(n-2)/sqrt(1-r^2)
138
What is Spearman rank correlation test?
A test to determine whether two sets of data are correlated(strenght and direction)
139
What is contingency or two-way table?
It is number of observations from a sample that have a combination of two characteristics.
140
What is simple linear regression?
A regression line that explains variation in dependent variable in terms of variability in the independent variable
141
What is simple regression line formula?
Y=b0+b1X+e
142
What is sum of squared error?
It is sum of sqaured vertical differences between estimated and actual values
143
What is formula of the slope coefficient?
COV(x,y)/variance(x)
144
What is homoskedasticity?
It says that variance of the residual term is constant
145
What are assumptions of OLS?
1. Independent and dependent variables have linear relationship
2. Homoskedasticity
3. Residula term is normally and independently distributed.
146
What is analysis of variance (ANOVA?
It analyses total variability of the dependent variable
147
What is total of sum squared (SST)?
Total variation of the dependent variable (actual-mean)
148
What is sum of square regression (SSR)?
Measures variation explained by the independent variable (predicted-mean)
149
What is sum of squared error (SSE)?
It measures unexplained variation (actual- predicted)
150
Mean squared error formula
SSE/(n-2)
151
What is coefficient of determination (R^2)?
% of variation in the dependent variable explained by the independent variable
152
What is R^2 formula?
SSR/SST
153
What does F-test measures?
How well the set of independent variables explains variation
154
What is formula for F?
MSR/MSE=SSR/k/(SSE/n-k-1)
155
What does T-test measure?
Whether true slope coefficient is equal to hypothesized value.
156
What is t-test statistic value?
Tb1=b1hat-b1/Sb1hat
157
What are predicted values?
Dependent variables based on linear regression
158
What is confidence level?
Values within true statistic should lie
159
What is formula of confidence level?
Y+-(tc*SE)
160
How to interpret log and linear results?
Linear-> absolute change, log -> relative change
161
What is fintech?
Development in the technology that can be applied to financial services industry
162
What is big data?
All potential useful information that is generated in the economy
163
What are characteristics of big data?
Volume, velocity, variety
164
What does volume represent?
Orders of magnitude
165
What does velocity represent?
How quickly data is communicated
166
What does variety represent?
Degree of structure
167
What does AI aim for?
Stimulate human cognition
168
What does machine learning learn?
Associations between inputs and outputs
169
What is supervised learning?
When inputs and outputs are labelled
170
What is unsupervised learning?
When machine learns how to structure the data
171
What is deep learning?
It uses layers of network to identify patterns
172
What is algorithmic trading?
Securities trading based on set of rules
173
What is high frequency trading?
It takes advantage of intraday securities mispricings.
