cfa一级公式分析和总结.docx
Quantitative
HoldingPeriodYield:HPY?
P?P
1 0
P
CF
1
0
D 360 FV?P
360
BankDiscountYield:r = ? = 0?
BD F t FV t
BDMoneyMarketYield:r ?HPY?360? r
BD
MM t 1?r ? t
BD 360
EffectiveAnnualYield:EAY?(1?HPY)365/t?1
???s? ? ?
?
?
Continuouslycompoundedrateofreturn:r ?ln? 1??ln
1?HPR
1?HPY?(1?
BEY)2?
t
365
?(1?EAY)
cc s
2
t
365
R
Time?weighted
2n
2
n(1?r)(1?r)...(1?r)
1 2 n
? ?1
?IRR
Money?weighted
?n X
nx?x???x1 2 ni ?n
nx?x???x
1 2 n
X ?
Arithmetic
i?1
n
;X ?
Weighted
i?1
WX;X
i i
?
Geometric
(X
Geometric
?X
Arithmetic
);X
Harmonic
?
?n 1
X
i?1 i
L ?(n?1)?
y
y
100
Range?MaxValue?MinValue
Excesskurtosis=Samplekurtosis-3
MAD?
?n X
i
i?1
??
;PopulationVariance:?2?
?n(X
i
i?1
??)2
;SampleVariance:s2?
?n(X
i
i?1
?X)2
;MAD??
n n n?1
切比雪夫不等式：P ?1?1
s[(x?X)?ks] k2
s
CoefficientofVariation:CV? x
X
SharpRatio?
R;越大越好
Rfp?
R
f
p
p
ExcessKurtosis=SampleKurtosis?3
Oddsofevent= P(E) ;Oddsagainstofevent=1?P(E)
1?P(E) P(E)
一般条件：P(AB)?P(A|B)?P(B)?P(B|A)?P(A);P(AorB)?P(A)?P(B)?P(AB)
互斥事件：P(AB)=0；P(AorB)?P(A)?P(B)
P(AB) P(A|B)
贝叶斯公式：P(B|A)? = ?P(B);贝努力实验：P(x)?Cx?Px?(1?P)n?x
P(A) P(A) n
??? ?Cov1,2;Cov
?
?
?P(AB)?[P(A)?E(r
)]?[P(B)?E(r
)]?P(AB
)?[P(A
)?E(r
)]?[P(B
)?E(r)]
12
1 2
1,2 11 1 A 1 B
2 2 2 A 2 B
E(R
)??nw?E(R);?
?w2? ?w2?
2wwCov
p i
p1122i?1
p
1
1
2
2
2 2 2
i
1 2 1,2
90%ConfidenceintervalforXisX?1.65s;95%forX?1.96s;95%forX?2.58s
x??
X~N(?,?2),Z? ? ;F(?z)?1?F(z)
RoysSafety-firstRatio=
E(R
p
p)
R
L;R
L
p
?MinimumAcceptableReturn
中心极限定理：Z?
X??
? /
? /
x
n
Confidenceinterval:X?Z
?
n?/2
n
;XpointEstimate;Z
?/2
reliabilityfactor;?
StandardError
nOnetail:H
n
0
??,H
0 ?
??;H
0 0
??,H
0 ?
??;Twotail:H
0 0
??,H ??
0 ? 0
Re