Quantitative Methods Flashcards
Three ways of interpreting interest rates?
opportunity cost, required rate of return, discount rate
Two factors that complicate interest rates in an uncertain world
Inflation: The nominal cost of money consists of the real rate (a pure rate of interest) and an inflation premium.
Risk: The return that borrowers pay thus comprises the nominal risk-free rate (real rate + an inflation premium) and a default risk premium.
What is discounting?
Discounting is the calculation of the present value of some known future value. Discount rate is the rate used to calculate the present value of some future cash flow. Discounted cash flow is the present value of some future cash flow.
Annuity
Annuity is a finite set of sequential cash flows, all with the same value.
Difference between annuity & ordinary annuity
Ordinary annuity has a first cash flow that occurs one period from now (indexed at t = 1). In other words, the payments occur at the end of each period.
An annuity due is an annuity with payment due or made at the beginning of the payment interval. In contrast, an ordinary annuity generates payments at the end of the period.
Future value of an annuity due
This consists of two parts: the future value of one annuity payment now, and the future value of a regular annuity of (N -1) period.
Present value of an annuity due
This consists of two parts: an annuity payment now and the present value of a regular annuity of (N - 1) period. Use the above formula to calculate the second part and add the two parts together.
Perpetuity
A perpetuity is a perpetual annuity: an ordinary annuity that extends indefinitely. In other words, it is an infinite set of sequential cash flows that have the same value, with the first cash flow occurring one period from now.o
Additivity principle
Dollar amounts indexed at the same point in time are additive.
Periodic interest rate
rate of interest earned over a single compounding period. For example, a bank may state that a particular CD pays a periodic quarterly interest rate of 3% that compounds 4 times a year.
Effective annual rate (EAR)
is the annual rate of interest that takes full account of compounding within the year. The periodic interest rate is the stated annual interest rate divided by m, where m is the number of compounding periods in one year: EAR = (1 + periodic interest rate)m - 1. Note that the higher the compounding frequency, the higher the EAC.
For example, a $1 investment earning 8% compounded semi-annually actually earns 8.16%: (1 + 0.08/2)2 - 1 = 8.16. The annual interest rate is 8%, and the effective annual rate is 8.16%.
Effective annual rate (EAR)
is the annual rate of interest that takes full account of compounding within the year. The periodic interest rate is the stated annual interest rate divided by m, where m is the number of compounding periods in one year: EAR = (1 + periodic interest rate)m - 1. Note that the higher the compounding frequency, the higher the EAC.
For example, a $1 investment earning 8% compounded semi-annually actually earns 8.16%: (1 + 0.08/2)2 - 1 = 8.16. The annual interest rate is 8%, and the effective annual rate is 8.16%.
Target Semi-Deviation
Downside risk assumes security distributions are non-normal and non-symmetrical. This is in contrast to what the capital asset pricing model (CAPM) assumes: that security distributions are symmetrical, and thus that downside and upside betas for an asset are the same.
Downside deviation
modification of the standard deviation such that only variation below a minimum acceptable return is considered. It is a method of measuring the below-mean fluctuations in the returns on investment.
Relative dispersion
amount of variability present in comparison to a reference point or benchmark
coefficient of variation
standardize the measure of absolute dispersion cv = s / x where cv = coefficient of variation, s = standard deviation, x = mean
platykurtic.
Distributions with small tails (that is, less peaked than normal) are called “platykurtic.” If a return distribution has more returns with large deviations from the mean, it is platykurtic.
leptokurtic
Distributions with relatively large tails (that is, more peaked than normal) are called “leptokurtic.” If a return distribution has more returns clustered closely around the mean, it is leptokurtic.
mesokurtic
A distribution with the same kurtosis as the normal distribution is called “mesokurtic.”
skewness formula
kurtosis formula
Absolute dispersion
amount of variability without comparison to any benchmark. Measures of absolute dispersion include range, mean absolute deviation, variance, and standard deviation.
Relative dispersion
amount of variability in comparison to a benchmark. Measures of relative dispersion include the coefficient of variance.
Dutch Book Theorem
one of the most important probability results theories for investments, inconsistent probabilities create profit opportunities. Investors should eliminate the profit opportunity and inconsistency through buy and sell decisions exploiting inconsistent probabilities.
variance of return on portfolio
σ2(RP) = wA2σ2(RA) + wB2σ2(RB) + 2wAwBCov(RA, RB)
how do you calculate variance of return given a covariance matrix
covariance formula
sum((x-mean(x))(y-mean(y)))/n-1
bayes formula
Updated probability = (probability of the new information given event / unconditional probability of the new information) x prior probability of event.
combination
listing in which the order of listing does not matter.
nCr = N!/(N-R)!R!
permutation
ordered listing
test statistic =
(sample statistic - parameter value under Ho) / standard error of sample statistic
correct action
reject false null hypothesis / don’t reject true null hypothesis
type 1 error
reject null hypothesis when it is false
type 2 error
reject null hypothesis when it is true
