Formulas Flashcards
Return on money market Instrument
E.g. Treasury or commercial bill
Gain/loss at maturity
Sharp ratio
Sharpe ratio = (Rp - Rf)/standard deviation
Percentage above (or below if negative) an investment has performed in relation to a risk free investment by each unit of risk taken.
Information Ratio formula
IR= (Rp-Rb)/Te
IR Information Ratio
Rp Return of Portfolio
Rb Return of Benchmark
Te Tracking Error (Standard deviation of the difference between the investment’s returns and the benchmark’s returns)
Standard deviation formula
σ = √[∑(x-x̄)²/n]
σ = population standard deviation
n = the size of the population
x = each value from the population
x̄ = the population mean
Σ = Sum each (x-x̄)
e.g. 2%, 5%, 6%, 8% 9%
Step 1 Calculate the mean
x̄ = (2+5+6+8+9)/5 = 6%
Step 2 Obtain the set of deviations from the mean
(2-6)²+(5-6)²+(6-6)²+(8-6)²+(9-6)²
Step 3 Square each deviation & then add together
16+1+0+4+9 = 30
Step 4 Divide by n to obtain the variance
30/5 = 6
Step 5 Square root
√6
Simple annual interest
Fv=Pv(1 + r)^n
AER/APR formula
Fv= Pv(1 + r/n)^n
Annuity Formula (monthly withdrawals)
Fv = Pmt x [1-(1+r)^-n )/r]
PV = present value
FV = future value
PMT = payment per period
r = interest rate in percent per period
n = number of periods
Accumulation of regular savings formula
Fv = Pmt x [(1+r)^n -1 )]/r
If the interest is paid at the start of the year 1 needs to be added to the power n.
Fv = Pmt x [(1+r)^(n+1) -1 )]/r
TWR
TWR = (V1/V0) x (V2/[V1+C])-1
V0 = Value at the start
V1 = Value at the end of 1st sub period
V2 = Value at the end of 2nd sub period
C = Contribution made
(The above can be extended further if there are more than 2 periods to calculate)
MWR
MWR = [D+V1-V0-C] / [V0+(C x n/12)]
V0 = Value at the start
V1 = Value at the end of 1st sub period
D = Income such as dividends
C = Contribution made
