Quantitaive Methods Formula

Question 1

Rate of Return

Answer 1

Dividend / Price

Question 2

Effective Annual Rate

Answer 2

( 1 + periodic rate) ^m - 1

Question 3

Compound Annual Growth Rate

Answer 3

(Year Y / Year X) ^ (1/y-x)

Question 4

NPV

Answer 4

SUM( CFt / (1+r)^t)

Question 5

Holding Period Return

Answer 5

(Ending Value / Beginning Value) - 1

Question 6

Total Return

Answer 6

([Ending Value + CF received] / Beginning Value) -1

Question 7

Money Weighted Rate of Return

Answer 7

PV in = PV out

x1 + x2/(1+r) = x3/ (1+r)^2 – > Solve for r

Question 8

Time Weighted Rate of Return

Answer 8

= ( HPR1 * HPR2 * … * HPRn)^ (1/n) - 1

Question 9

Bank Discount Yield

Answer 9

BDY = (Dollar Discount / Face Value) * (360/t)

Question 10

Effective Annual Yield

Answer 10

EAY = ( 1 + HPR)^(365/t) - 1

The annual value based on a 365-day year that accounts for compounded interest.

Question 11

Money Market Yield

Answer 11

= 360 /t * HPR
Annualized HPR based on 360-day year.

OR

= (360BDY) / (360 - (tBDY))

Question 12

Geometric Mean

Geometric Mean Return

Answer 12

=(X1X2…*Xn)^(1/n)

= [(1+R1)(1+R2)…*(1+Rn)]^(1/n)

Question 13

Harmonic mean

Answer 13

N / SUM( 1/xi)

Question 14

Quartile Calculation

Answer 14

= (n+1)*(y/100)

Question 15

Population Variance

Answer 15

sigma^2 = [SUM( xi - mean)^2] / N

Question 16

Population Standard Deviation

Answer 16

sigma = ([SUM( xi - mean)^2] / N]^1/2

Question 17

Chebyshev’s Inequality

Answer 17

1 - 1/k^2

Question 18

Coefficient of Variation

Answer 18

Std. Dev of X / Avg. value of X

Question 19

Sharpe Ratio

Answer 19

Rp - Rf / Sigmap

Question 20

Correlation Coefficient

Answer 20

= Covariance (Ri, Rj) / ( sigma (Ri) * sigma(Rj))

Question 21

Covariance

Answer 21

= E{[Ri-E(Ri)]*[Rj-E(rj)]}

Question 22

Bayes Theorem

Answer 22

P(A I B) = [P(B I A)/P(A)] * P(B)

Question 23

Probability of x successes in n trials

Answer 23

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

Question 24

Standard Error

Answer 24

std. dev / n^(1/2)

Question 25

Confidence Interval Calculation

Answer 25

Xbar +/- z * (sigma/[n^1/2])

Question 26

Safety First Ratio

Answer 26

(Expected Return - Threshold Return) / Std. Dev.