Quantitative Methods

Question 1

Three ways of interpreting interest rates?

Answer 1

opportunity cost, required rate of return, discount rate

Question 2

Two factors that complicate interest rates in an uncertain world

Answer 2

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.

Question 3

What is discounting?

Answer 3

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.

Question 4

Annuity

Answer 4

Annuity is a finite set of sequential cash flows, all with the same value.

Question 5

Difference between annuity & ordinary annuity

Answer 5

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.

Question 6

Future value of an annuity due

Answer 6

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.

Question 7

Present value of an annuity due

Answer 7

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.

Question 8

Perpetuity

Answer 8

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

Question 9

Additivity principle

Answer 9

Dollar amounts indexed at the same point in time are additive.

Question 10

Periodic interest rate

Answer 10

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.

Question 11

Effective annual rate (EAR)

Answer 11

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%.

Question 12

Effective annual rate (EAR)

Answer 12

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%.

Question 13

Target Semi-Deviation

Answer 13

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.

Question 14

Downside deviation

Answer 14

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.

Question 15

Relative dispersion

Answer 15

amount of variability present in comparison to a reference point or benchmark

Question 16

coefficient of variation

Answer 16

standardize the measure of absolute dispersion cv = s / x where cv = coefficient of variation, s = standard deviation, x = mean

Question 17

platykurtic.

Answer 17

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.

Question 18

leptokurtic

Answer 18

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.

Question 19

mesokurtic

Answer 19

A distribution with the same kurtosis as the normal distribution is called “mesokurtic.”

Question 20

skewness formula

Question 21

kurtosis formula

Question 22

Absolute dispersion

Answer 22

amount of variability without comparison to any benchmark. Measures of absolute dispersion include range, mean absolute deviation, variance, and standard deviation.

Question 23

Relative dispersion

Answer 23

amount of variability in comparison to a benchmark. Measures of relative dispersion include the coefficient of variance.

Question 24

Dutch Book Theorem

Answer 24

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.

Question 25

variance of return on portfolio

Answer 25

σ2(RP) = wA2σ2(RA) + wB2σ2(RB) + 2wAwBCov(RA, RB)

Question 26

how do you calculate variance of return given a covariance matrix

Question 27

covariance formula

Answer 27

sum((x-mean(x))(y-mean(y)))/n-1

Question 28

bayes formula

Answer 28

Updated probability = (probability of the new information given event / unconditional probability of the new information) x prior probability of event.

Question 29

combination

Answer 29

listing in which the order of listing does not matter.

nCr = N!/(N-R)!R!

Question 30

permutation

Answer 30

ordered listing

Question 31

test statistic =

Answer 31

(sample statistic - parameter value under Ho) / standard error of sample statistic

Question 32

correct action

Answer 32

reject false null hypothesis / don’t reject true null hypothesis

Question 33

type 1 error

Answer 33

reject null hypothesis when it is false

Question 34

type 2 error

Answer 34

reject null hypothesis when it is true