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 (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
Macaulay Duration (Duration) & Modified Duration
What’s the difference?
Modified duration is frequently used type of duration for bonds. Different from Macaulay duration, which measures the average time to receive the present value of cash flows equivalent to the current bond price in years.
Modified duration identifies the sensitivity of the bond price to the change in interest rate. It is thus measured in percentage change in price. It moves in opposite direction to interest times the modified duration
Macaulay Duration (Duration) - Calc
∑(Net present value of the bond cash flows x time to cash flow being received) / ∑ Net present value of the cash flows to be received.
e.g
Coupon 4% paid annually
Exactly 3 years to maturity
GRY 5%
Step 1
Cashflow Formula Pv
1yr - Int 4 4/1.05 3.81
2yr - Int 4 4/(1.05)² 3.63
3yr - Int 4 4/(1.05)³ 3.46
3yr - Redemp 100/(1.05)³ 86.38
Total 112 97.28
Next multiply the NPV cash flows by the time being received
Pv No. of Yrs Pv x No.Yrs
1yr - 3.81 1 3.81
2yr - 3.63 2 7.26
3yr - 3.46 3 10.38
3yr - 86.38 3 259.14
Total 97.28 280.59
Then use the formula
280.59/97.28 = 2.88Yrs
Modified Duration (calc)
= Duration/ (1 + GRY)
PEG ratio (Price/Earnings to growth)
PEG = P/E ratio / Annual EPS growth
P = Stock Price
E = Stock earnings
MAD (Mean Absolute Deviation)
- Calculate Arithmetic Mean
- Work out the deviation for each result (removing minuses)
- Add the results together
- Divide by number of results
e.g 3%, 6%, 8%, 9% & 10%
1. Mean (3+6+8+9+10)/5 = 7.2%
2.
3 - 7.2 = -4.2
6 - 7.2 = -1.2
8 - 7.2 = 0.8
9 - 7.2 = 1.8
10 - 7.2 = 2.8
- 4.2 + 1.2 + 0.8 + 1.8 + 2.8 = 10.8
- 10.8/5 = 2.16
