(1 r1 )(1 r2 )(1 r3 )...(1 rn ) 1
Then annualize the time-weighted return. BDY = Bank Discount Yield =
rBD
( FV P0 ) 360 FV t
365/t -1
EAY = Effective annual yield = (1+HRY) Money market yield = HPY × (360/t)
Ly (n 1)
y 100
Arithmetic mean: sum of all observation values in sample/population,divided by number of observations. Geometric mean: used when calculating investment returns over multiple periods or to measure compound growth rates.
Coefficient of Variation(CV):express how much dispersion exists relative to mean of a distribution.
Geometric mean:
G N X1 X 2 X 3 ... X N ( X i )1/ N
Normal Distribution: 1. Completely described by mean and variance (μ, σ2) 2. It is symmetric with skewness measure of 0, i.e., mean = mode = median 3. Kurtosis = 3 4. Linear combinations of normal random variables are normally distributed. Z-score:
FV Ct (1 r )T t
t 1
T
Present Value of Uneven Cash Flows =
PV
t 1
T
Ct (1 r )t
Discounted Cash Flow Applications
NPV = Net present value

t 0 N
2 2
2 2
P( X 1 ) x1 E ( X ) P( X 2 ) x2 E ( X ) L P( X n ) xn E ( X )
Covariance:
2
0, x a xa F ( x) P( X x) ,a x b b a 1, x b

X

Safety First Ratio:
SFR
E ( RP ) RL
P
Multinominal labelling:

n! n1 ! n2 ! ... nk !
If Normal distr., SFRmax
Cov( X , Y ) E[ X E( X )][Y E(Y )]
Correlation coefficient: X ,Y

Cov( X , Y )
XY
Portfolio expected value:
E ( RP ) wi E ( Ri ) w1E ( R1 ) w2 E ( R2 ) ... wn E ( Rn )
PMT [(1 r )n 1] r
PVAo=Present value of an annuity=
Money market yield = BDY / (1- BDY×t/360)
Statistical Concepts and Market Returns
Position of the observation at a given percentile, y;
(X
i 1
N
i
)2
B)
N
Population standard
deviation=
B)
(Xi 1Ni )2
P(R)=P(R│S1)P(S1)+…+P(R│SN)P(SN)
N

2
S1, S2,…, SN are mutually exclusive and exhaustive Expected value = E ( X )
1
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Population mean:
x
Xi
i 1
N
N
Sample variance =
s2
(X
i 1
n
i
X )2
n 1
Sample mean:
X
Xi
i 1
σ > MAD that holds in general
X P( X )
i 1 i i
n
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CFA Level I Easy Sheet
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Probabilistic variance:
( X ) P( X i ) xi E ( X )
FV PV n （ 1 I / Y）
Annuities:series of equal cash flows that occur at evenly spaced intervals over time. Ordinary annuity:cash folw at end-of-time period. Annuity due:cash flow at beginning-of-time period. Perpetuities:annuities with infinite lives. FVAo=Future value of an annuity=
金程教育
CFA Level I Easy Sheet
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QUANTITATIVE METHODS
The Time Value of Money
Interest rate = Nominal risk-free rate + Default risk premium + Liquidity risk premium + Maturity risk premium Nominal risk-free rate = Real risk-free rate +expected inflation rate Required Rate of Return
PMT 1 1 r (1 r )n
FVAD=Future value of annuity due = FVAo×(1+r) PVAD=Present value of annuity due = PVAo×(1+r) Present Value of Perpetuity = PMT / r Future Value of Uneven Cash Flows =
th
MAD =Mean absolute deviation =
X
i 1
N
i

Sample kurtosis = K P
(X 1
i 1
n
i
X )4
n
4
N
Variance and Standard Deviation Variance:average of squared deviations from mean. Standard deviation:square root of variance. Population variance =
2
Excess kurtosis = sample kurtosis – 3
Probability Concepts
Joint probability = P( AB) P( B) P( A Addition rule of probability = P( A U B) P( A) P( B) P( A I Total Probability Rule =
n
n
n
Sample standard deviation= s Chebyshev’s inequality:
(X
i 1
n
i
X )2
n 1
Weighted mean:
X ( wi X i )
i 1
P( x k ) 1
1 k2
where
wi are weights that sum to 1.
i 1 i
N
( X i )3 1 i 1 SK = Sample skewness n 3
Positive skewness: Mode < Median < Mean Negative skewness: Mode > Median > Mean
y Y percentile = LY (n 1) 100
i 1
N
CV = Coefficient of variance=
s X
Geometric mean return:
RG N (1 R1)(1 R2)…(1 Rn) 1
Harmonic mean:
Sharp ratio
RP R f
P
N
XH