Quantitative methods Flashcards
What does interest rates measure?
Time value of money
What is the equilibrium rate of interest rates?
Required rate of return
What does interest rate represents?
Opportunity cost of current consumption
What is real risk free interest rate?
Theoretical term with no inflation and zero probability of default
What is time preference?
Degree to which current consumption is preferred to euqal future consumption
T-bills are example of which interest rate?
Nominal risk free rates
Is inflation premium included in t-bills?
Yes
What is the formula for real risk-free interest rate?
=nominal rate-inflation rate
What are the types of securities risks? (4)
Inflation, default, liquidity, maturity
What is default risk?
Risk that borrower will fail to make payments
What is liquidity risk?
Risks of receiving less than fair value if sold quickly for liquidity
What is maturity risk?
Risk that long-term maturity risks possesses as prices are more volatile
What is holding period return (HPR)
% increase in the investment value over time
HPR formula
HPR=(end period value-beg.period value+Dividends)/beg.value-1
HPR formula over multiple periods
HPR=(1+HPR1)(1+HPR2)…-1
What is arithmetic mean return?
Simple mean average
What is geometric mean return?
compound rate -> sqrt(n)(1+R1)(1+R2)…-1
Which is bigger - geometric or arithmetic?
Arithmetic
What is harmonic mean?
N/sum(1/X)
Relationship between 3 means
arithmetic*harmonic =geometric^2
What is IRR?
Rate of return for which NPV=0
Which content is money-weighted applies?
IRR
What is money-weighted rate of return?
IRR of portfolio taking into account all inflows and outflows.
What is time-weighted rate of return?
Compound growth, rate of which $1 compounds over time.
If manager can control inflows and outflows which return to use?
Money-weighted rate of return
Annualized return formula
(1+HPR)^(365/days)-1
What happens to PV and FV with more frequent compounding?
FV goes up, PV goes down
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
Continuesly compounding return formula
ln(1+HPR)=ln(ending value/beg.value)
What is gross return?
Total return of a portfolio before deducting management and admin fees
What is net returns?
Total portfolio return after taxes have been deducted
What is pre-tax nominal return?
Total portfolio return before paying taxes
What is after-tax nominal return?
Total portfolio return after tax liability.
What is real return?
Nominal return adjusted for inflation
Real returns formula
(1+real returns)=(1+nominal risk-free rate)(1+risk premium)/(1+inflation premium)
What is leveraged returns?
Return that is a multiple of a return on the underlying asset
Leveraged return formula
(r(V0+Vb)-rbVb)/Vo
FV formula (compounding)
PVe^(r*t)
PV formula (compounding)
FVe^(-r*t)
Zero coupon bonds pays..
less than face value to buy the investment and receives the face value at maturity
On what the price investor pays for the investment depends on?
YTM and time until maturity
Zero coupon is bond is prices at
discount
Fixed coupon bond
investor receives a cash interest payment (coupon)
Perpetuity
has no maturity date
PV(perpetuity) formula
PV=payment/r
Example of amortized bond
annuity
Amortized bond
Similar to fixed coupon bond, but each payment includes some portion of its principle.
Preffered stock
Stock that pays dividend as a % of its par value
Annuity payment formula
r*PV/(1-(1+r)^-t)
What is discount rate of preffered stock?
Required rate of return
Preffered stock value formula
Dp/kp
Common stock
residual claim to company’s assets after it satisfies all other claims, dividends based on management decision
Value of the stock based on DDM model
D1/(k-g)
Dividend yield formula
D1/V0
Required rate of return formula
(D1/V0)+gc
Cash flow additivity principle
PV of any stream of cashflows equals the sum of the PVs of the cash flows
No arbitrage principle
Two identical cash flow series will have the same price today
Forward interest rate
Interest rate for a loan to be made at some future date
2y1y annotation
1 year loan, 2 years from today
Forward interest rate formula
(1+S3)^3=(1+S1)(A+1y1y)(1+2y1y)
USD/EUR interpretation
EUR base currency, USD price currency
Forward/spot relationship
(1+interest rate_price)/(1+interest rate_base)
What is an option?
Right, but not the obligation to buy or sell an asset on a future date for a specific price
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
What is measures of central tendency
center or average of a dataset (mean, median, mode)
What is median?
Middle point, not affected by outliers
What is mode?
Most frequent value
What is trimmed mean?
A mean to deal with outliers, excluding point above or below certain percentage
What is winsorized mean?
A mean to deal with outliers, where values are substituted based on percentiles, with the percentiles values.
What is quantile?
Value at or below stated proportion of a dataset
What is quartile?
1/4
What is quintile?
1/5
What is decile?
1/10
What is percentile?
1/100
What is interquartile range?
3rd quartile - 1st quartile
What is dispersion?
Variability around the central tendency
What does dispersion measure in finance?
Risk
What does central tendency measure in finance?
Reward
What is range and how it is calculated?
Max value-min value
What is mean absolute deviation (MAD)?
Average of the absolute values of the deviation of individual observations from arithmetic mean
MAD formula
sumIXi-XI/n
Sample variance formula
sum(Xi-X)^2/(n-1)
Sample standard deviation formula
sqrt(sample variance)
What is relative dispersion?
Amount of variability in a distribution around a reference point or benchmark
Coefficient of variation formula
CV=Sx/X(mean)
Target downside deviation formula
sqrt((Xi-B)^2/(n-1))
What is skeweness?
how symmetrical the distribution is
Positive skew (outliers vs mean)
Outliers>mean
Negative skew (outliers vs mean)
Outliers<mean
Symmetrical skew (MMM)
mean=median=mode
Positive skew (MMM)
mean>median>mode
Negative skew (MMM)
mode>median>mean
What is kurtosis?
Measure of how peaked the distribution is
What kurtosis are there?
Leptokurtic, playtikurtic, mesokurtic
What covariance measures?
How two variables move together around their means
What does correlation measures?
Strenght of linear relationship between two variables
Correlation formula
COV(x,y)/sdx*sdy
What is spurious correlation?
Result of chance or present due to changes in both variables as a result cause by a third variable
What is expected value?
Weighted average of the possible outcomes for the variable
What is Bayers theorem?
Update set given set of information based on arrival of new information
Expected return of a portfolio formula
Sum of w1*E(R1)
Sample covariance formula
sum of (Ri-Rmean)*(R2-R2mean)/(n-1)
How many unique covariance terms there are?
n(n-1)/2
Portfolio covariance formula
w^2_avariance^2_a+w^2_bvariance^2_b+2w_aw_bCov(a,b)
What is shortfall risk?
Probability that a return will fall below a particular threshold
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
Safety-first ratio formula
E(Rp)-Rl/s.d.(p)
Lognormal asset prices formula
P0e^rt
What is CFA assumption about returns?
They are independently and identically dsiributed
What does it mean for returns to be independently distributed?
Past returns cannot be used to model future
What does it mean for returns to be identically distributed?
Mean and variance does not change over time
What is monte carlo simulation?
Repeated generation of one or more risk factors that affect securities values to generate a distribution of those values
What is resampling?
Generation of data inputs to use in simulation
What is bootstrap resampling?
Drawing repeated samples of sizen, replacing so they could be redrawn.
What is probability sampling?
Selection of sample when we know probability of each sample member
What is random sampling?
Each is assumed to have the same probability of being selected
What is systematic sample?
Selecting every nth member
What is stratified random sampling?
Seperating population into smaller groups and using whole group as a sample
What is cluster sampling?
Seperating population into smaller groups and mixing members from each group as a sample
What is convenience sampling?
Selecting sample based on ease
What is judgemental sampling?
Sample selected by researchers based on his judgement
What is central limit theory?
As sample size increases, it approches normal distribution
What is considered as large sample?
N=>30
Standard error of a sample formula
s.d./sqrt(n)
What is jackknife resampling?
Calculating sample means with one observation removed
What is bootstrap resampling?
Redraw repeated samples a lot.
What is hypothesis?
Statement about testing the theory
What is null hypothesis?
Hypothesis that a researcher wants to reject
What is alternative hypothesis?
What is concluded when there is sufficient evidence to reject H0
What is type I error?
H0 is true, but we rejected it
What is type II error?
H0 is false, but we failed to reject it.
What is significance level?
Probability of making type I error
What is power of a test?
Making a right decision and rejecting H0 when it is false
What is relationship between significance level and type II error?
Inverse
What is p-value?
Probability obtaining test statistic that would lead to a rejection of H0.
Which test is used for value of population mean?
T-test or z-test
Which test is used for equality of two population means?
T-test
Which test is used for value of population variance?
Chi-squared
Which test is used for equality of two population variance?
F-test
What is paired comparison test?
Two samples depend on some other factor.
What is parametric test?
Test with assumptions regarding distribution of the population
What is non parametric tests?
Test when particular population parameters are not considered
What is Pearson’s correlation test?
It is used to assess the strenght of the relationship between two variables
What is formula for Pearson’s and Spearman’s test statistic?
r*sqrt(n-2)/sqrt(1-r^2)
What is Spearman rank correlation test?
A test to determine whether two sets of data are correlated(strenght and direction)
What is contingency or two-way table?
It is number of observations from a sample that have a combination of two characteristics.
What is simple linear regression?
A regression line that explains variation in dependent variable in terms of variability in the independent variable
What is simple regression line formula?
Y=b0+b1X+e
What is sum of squared error?
It is sum of sqaured vertical differences between estimated and actual values
What is formula of the slope coefficient?
COV(x,y)/variance(x)
What is homoskedasticity?
It says that variance of the residual term is constant
What are assumptions of OLS?
- Independent and dependent variables have linear relationship
- Homoskedasticity
- Residula term is normally and independently distributed.
What is analysis of variance (ANOVA?
It analyses total variability of the dependent variable
What is total of sum squared (SST)?
Total variation of the dependent variable (actual-mean)
What is sum of square regression (SSR)?
Measures variation explained by the independent variable (predicted-mean)
What is sum of squared error (SSE)?
It measures unexplained variation (actual- predicted)
Mean squared error formula
SSE/(n-2)
What is coefficient of determination (R^2)?
% of variation in the dependent variable explained by the independent variable
What is R^2 formula?
SSR/SST
What does F-test measures?
How well the set of independent variables explains variation
What is formula for F?
MSR/MSE=SSR/k/(SSE/n-k-1)
What does T-test measure?
Whether true slope coefficient is equal to hypothesized value.
What is t-test statistic value?
Tb1=b1hat-b1/Sb1hat
What are predicted values?
Dependent variables based on linear regression
What is confidence level?
Values within true statistic should lie
What is formula of confidence level?
Y+-(tc*SE)
How to interpret log and linear results?
Linear-> absolute change, log -> relative change
What is fintech?
Development in the technology that can be applied to financial services industry
What is big data?
All potential useful information that is generated in the economy
What are characteristics of big data?
Volume, velocity, variety
What does volume represent?
Orders of magnitude
What does velocity represent?
How quickly data is communicated
What does variety represent?
Degree of structure
What does AI aim for?
Stimulate human cognition
What does machine learning learn?
Associations between inputs and outputs
What is supervised learning?
When inputs and outputs are labelled
What is unsupervised learning?
When machine learns how to structure the data
What is deep learning?
It uses layers of network to identify patterns
What is algorithmic trading?
Securities trading based on set of rules
What is high frequency trading?
It takes advantage of intraday securities mispricings.
