Handbook for Formulas List of formulas for Level 1 CFA® Program Bond equivalent yield= {(1+ effective annual yield)1/2-1} * 2 13 Geometric Mean=
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Handbook for
Formulas
List of formulas for
Level 1
CFAProgram
TIME VALUE OF MONEY
1 Nominal interest rate= real risk-free rate + expected inflation rate 2 Required interest rate on security= nominal risk-free rate + default risk premium+ liquidity premium + maturity risk premium 3 Effective Annual Return (EAR)= EAR=(1+periodic rate) m -1Periodic rate= stated annual rate/m
M= number of compounding periods per year
FV= future value
PV= Present value
I/Y=Rate of return per compounding period
N=Number of compounding periods
CF= Expected cash flow
r =Discount rateIRR= Internal rate of return.
HPR= Holding period return
RBD= D/F*360/t
RBD= Annualised yield on a bank discount basis
D=Dollar discount= purchase price - face value
F=Face value
t=Number of days until maturity360=Bank convention of number of days in a year4
FV= PV(1+ I/Y)
N5PV perpetuity = PMT (I/Y)
6 PV= N Y 1+IFVPMT= Fixed periodic cash flow
DISCOUNTED CASH FLOW APPLICATION
CF (1+r) t 7IRR 8 9Effective Annual Yield (EAY)= (1+HPY)
365/t-1
HPY= Holding period yield10HPR=
CF1 (1+IRR)CF2 (1+IRR) 2 (Ending Value-Beginning Value) (Beginning Value) CF3 (1+IRR) 30=CF+++
Centre for Financial Learning
11RMM= 360/days*HPY
RMM=Money market yield
12 Bond equivalent yield= {(1+ effective annual yield) 1/2 -1} * 213Geometric Mean= [(1+R1)(1+R2).... (1+Rn)]
1/n -1 Geometric mean return is also known as compound annual rate of return14 Harmonic Mean=
N n15 Position of observation at a given percentile16 Range= Maximum Value- Minimum Value
18 Population Variance
19 Standard Deviation
= square root of variance20 Sample Variance
Coefficient of Variation17 Mean Absolute Deviation (MAD)=N(∑(Xi-μ)
2 2N-1(∑(Xi-μ)
2 2 (standard deviation of x) (average value of x)CV= (Rp-RFR) p 3 S 3Sharpe Ratio=
s =sample standard deviationLy=(n+1)
y 10021
Chebyshev's Inequality
Percentage of observations that lie within k standard deviations of the m ean is at least= 1-1/k 2Rp= Portfolio Return
RFR= Risk Free Rate
p= standard deviation of portfolio return22Excess Kurtosis= Sample Kurtosis - 3
2623Sample Skewness (Sk) =
244 S 4
Sample Skewness (Sk) = 25
Centre for Financial Learning
PROBABILITY CONCEPTS
COMMON PROBABILITY DISTRIBUTIONS27
Multiplication Rule Of Probability,
P(AB)=P(A/B)*P(B)
28Addition Rule Of Probability,
P(A or B)= P(A)+P(B)-P(AB)
29Total Probability Rule (Used to determine unconditional probability of an even
30Expected value of random variable= weighted average of possible outcomes
, Weights = probabilities that the outcome will occur 31Covariance
Cov(Ri, Rj)= E{[Ri-E(Ri)][(Rj-E(Rj)]}
Cov(Ri, Rj)= Corr(Ri, Rj) σ(Ri)σ(Rj)
32Correlation Cofficient
33Weight of asset in portfolio,
w= market value of investment in asset i/market value of the portfolio 34Portfolio Expected Value
E(Rp)=w1E(R1) + w2E(R2)+...... wnE(Rn)
35Variance of 2 Asset Portfolio
36Variance of 3 asset Portfolio
37Bayes Formula,
Updated Probability=( Probability of new information for a given event / unconditional probability of new event )*(prior probability of event) 38Factorial
n! = n*(n-1)*(n-2)*(n-3)...... *1 0!=139Labelling,n! / (n1!)*(n2!)*.... ( nn!)
40Combination,n Cr=n! /(n-r)!r!
41Permutation,
n! /(n-r)! 42To standardize a normal variable,Corr(Ri,Rj)=
(Cov(Ri,Rj)) (Ri) (Rj)) z= (Observation - Population Mean) (Standard Deviation)Centre for Financial Learning
43Roy's safety first criteria,
44Continuously compounded rate of return,
Rcc=ln(1+HPR)
45Standard Error of sample Mean,
x= = Standard deviation of population n=Size of the sample 46t-distribution to construct a confidence interval,
When variance is unknown,
x=t /2When variance is known,
x=t /2 x= Point estimate of population mean t /2 =The t-reliability factor 48t-statistic
When population variance is unknown,
49When population variance is known,47**Choose the portfolio with largest SFR SFR= ([E(Rp)-Rl]) p)