Quantitative Methods

Question 1

Future Value of a Single Cash Flow

Answer 1

FV = PV(1+r)^N

Question 2

Continuous Compounding Lump Sum

Answer 2

FV = PV * e^(r.s * N)

Question 3

Effective Annual Rate

Answer 3

EAR = ((1 + Periodic Rate)^m) - 1

Question 4

Future Value Ordinary Annuity

Answer 4

FV = A * [(((1 + r)^N) - 1)/r]

Question 5

Future Value of Annuity Factor

Answer 5

[(((1 + r)^N) - 1)/r]

Question 6

Present Value Single Cash Flow

Answer 6

PV = FV * (1 + r)^-N

Question 7

Present Value Factor

Answer 7

(1 + r)^-N

Reciprocal of future value factor

Question 8

Present Value Ordinary Annuity

Answer 8

PV = A * [(1-(1/((1+r)^N)))/r]

Question 9

Present Value of a Perpetuity

Answer 9

PV = A/r

Question 10

Solving for interest rate/growth rate

Answer 10

G = (FV/PV)^(1/N) - 1

Question 11

Solving for number of periods

Answer 11

N = [ln(FV/PV)/ln(1+r)]

Question 12

Solving for annuity Payments

Answer 12

A = PV/PF Annuity Factor

= PV/ [(1-(1/(1+r)^N))/r]

Question 13

Numerical Data

Answer 13

Can be continuous or Discrete (meaning finite number of values

Question 14

Categorical Data

Answer 14

Values that describe a quality or characteristic (dividend vs. No dividend)

Question 15

Nominal vs. Ordinal Data

Answer 15

Nominal cannot be logically ordered or ranked, while ordinal can

Question 16

Cross Sectional vs. Time Series vs. Panel Data

Answer 16

Cross sectional: List of observations for time period (January inflation rates for each country)

Time Series: List of observations of a specific variable (Daily closing prices)

Panel Data: Mix of the two (Table is with columns time series and rows cross section)

Question 17

Structured vs. Unstructured Data

Answer 17

Structured is highly organized (Financial Statements for example)

Unstructured does not follow conventional organization (financial news for example)

Question 18

1 Dimensional Array and 2 Dimensional Rectangular Array

Answer 18

1 Dimensional has only 1 variable and has a date and the observation

2 is a fancy way of saying a fucking table

Question 19

Geometric Mean and Geometric Mean Return Formulas

Answer 19

Geometric Mean: multiply each number then take the root (root number is amount of numbers)

Geometric Mean Return: multiply each return (1+whatever) then take the root and subtract 1

Question 20

Variance and Standard Deviation

Answer 20

s^2 = SUM[(observation-mean)^2]/(n-1)

Standard Deviation is the square root of this

Question 21

Downside deviation/target semideviation

Answer 21

Using all values below the chosen target

Square root of SUM[((Observation - target)^2)/(n-1)]

n is the total, not just the values you use

Question 22

Coefficient of Variation

Answer 22

CV = standard dev/mean

Question 23

Sample Covariance

Answer 23

SUM[(obs x - mean x)*(obs y - mean y)]

All divided by (n-1)

Question 24

Correlation Coefficient

Answer 24

= Covariance/(standard dev x * standard dev y)

Question 25

Conditional and Joint Probability

Answer 25

P(A|B) = P(AB)/P(B)

Joint probability is P(AB) = P(A|B)*P(B)

Question 26

Probability that A happens or B happens (not both)

Answer 26

P(A or B) = P(A) + P(B) - P(AB)

Question 27

Expected Value Variance

Answer 27

= SUM OF:

probability* [(X-Expected value)^2]

Question 28

Expected Value Conditional Probabilites

Answer 28

= probability (X1|S)X1 + p(X2|S)X2 etc

Adding up the conditional probabilities for all scenarios (S1, S2 etc) gives you the total expected value E(X)

Question 29

Covariance with expected values

Answer 29

Covariance between X and Y: (population Covariance)

Cov(x,y) = E[(X-EX)*(Y-EY)]

Sample Covariance:

Cov(x,y) = SUM OF {[(X-X mean)* (Y-Y mean)]/(n-1)}

Question 30

Correlation

Answer 30

= covariance/(standard dev X * standard dev y)

Question 31

Portfolio variance

Answer 31

= (weight^2)(variance) + (weight2^2)(variance2) + 2(weight1weight2Covariance)

Question 32

Bayes Formula

Answer 32

= (prob of new information given event/unconditional prob of new information)* prior probability

P(Event|Info) = [P(Info|Event)/P(Info)]*P(Event)

Question 33

Number of combinations binomial distribution

Answer 33

= (n!)/[(n-x)! * x!]

Question 34

Binomial probability function

Answer 34

= (n!)/[(n-x)! * x!] * [p^x * (1-p)^n-x]

Question 35

Z Score

Answer 35

Z = (X - mean)/standard dev

Question 36

Central Limit Theorem

Answer 36

With a large enough sample size, the distribution of sample means will be normal distribution

Variance/Sample size, as sample gets bigger the fraction gets smaller

Question 37

Standard error

Answer 37

Standard deviation/root of sample size

= standard dev/sqrt(n)

Measured how much inaccuracy comes from sampling

Question 38

Confidence interval z scores 90%, 95%, 99%

Answer 38

90%: z = 1.65

95%: z = 1.96

99%: z = 2.58

Question 39

Confidence intervals

Answer 39

Mean +/- Z*(standard dev/sqrt(n))

*Z for probability/2