Quantitaive Methods Formula Flashcards
Rate of Return
Dividend / Price
Effective Annual Rate
( 1 + periodic rate) ^m - 1
Compound Annual Growth Rate
(Year Y / Year X) ^ (1/y-x)
NPV
SUM( CFt / (1+r)^t)
Holding Period Return
(Ending Value / Beginning Value) - 1
Total Return
([Ending Value + CF received] / Beginning Value) -1
Money Weighted Rate of Return
PV in = PV out
x1 + x2/(1+r) = x3/ (1+r)^2 – > Solve for r
Time Weighted Rate of Return
= ( HPR1 * HPR2 * … * HPRn)^ (1/n) - 1
Bank Discount Yield
BDY = (Dollar Discount / Face Value) * (360/t)
Effective Annual Yield
EAY = ( 1 + HPR)^(365/t) - 1
The annual value based on a 365-day year that accounts for compounded interest.
Money Market Yield
= 360 /t * HPR
Annualized HPR based on 360-day year.
OR
= (360BDY) / (360 - (tBDY))
Geometric Mean
Geometric Mean Return
=(X1X2…*Xn)^(1/n)
= [(1+R1)(1+R2)…*(1+Rn)]^(1/n)
Harmonic mean
N / SUM( 1/xi)
Quartile Calculation
= (n+1)*(y/100)
Population Variance
sigma^2 = [SUM( xi - mean)^2] / N
Population Standard Deviation
sigma = ([SUM( xi - mean)^2] / N]^1/2
Chebyshev’s Inequality
1 - 1/k^2
Coefficient of Variation
Std. Dev of X / Avg. value of X
Sharpe Ratio
Rp - Rf / Sigmap
Correlation Coefficient
= Covariance (Ri, Rj) / ( sigma (Ri) * sigma(Rj))
Covariance
= E{[Ri-E(Ri)]*[Rj-E(rj)]}
Bayes Theorem
P(A I B) = [P(B I A)/P(A)] * P(B)
Probability of x successes in n trials
p(x) = [n! / (n-x)!x!] * [p^x(1-p)^n-x]
Standard Error
std. dev / n^(1/2)
Confidence Interval Calculation
Xbar +/- z * (sigma/[n^1/2])
Safety First Ratio
(Expected Return - Threshold Return) / Std. Dev.
