(完整版)cfa一级公式

Quantitative

101

0365/:D 360360:=

=360

:1360

A :(1)1

Continuously compounded rate of re BD BD MM BD t P P CF Holding Period Yield HPY P FV P Bank Discount Yield r F t FV t

r Money Market Yield r HPY t t r Effective nnual Yield EAY HPY -+ =- ⨯⨯ =⨯=

-⨯ =+-()

12turn: r ln ln 1cc s HPR s ⎛⎫

==+ ⎪⎝⎭

2365

365

1

1

11(1)(1)2

1

;;);1t t

Time weighted Money weighted n

i

n

i Arithmetic Weighted i i Geometric Geometric Arithmetic Harmonic n

i i i

y BEY HPY EAY R R IRR X

n X X W X X X X X n X L ⨯--===+=+=+===

==<=

=∑∑∑(1)100

y n +⨯

2

2

221

1

1

[()]

2Excess kurtosis = Sample kurtosis - 3()

();:;:;1

1

1n

n

n

i

i

i

i i i x X ks Range MaxValue MinValue X

X

X

X MAD PopulationVariance SampleVariance s MAD n n

n P k Coefficient of Variat μ

μσσ

===-≤= -

---=

=

=

<-≥- ∑∑∑切比雪夫不等式：:;x

p f

p

s

ion CV X

R R Sharp Ratio σ=- =越大越好

Excess Kurtosis=Sample Kurtosis 3

()1()

Odds of event=

;Odds against of event=

1()()

()(|)()(|)();()()()()()=0()()()()(|)()P E P E P E P E P AB P A B P B P B A P A P AorB P A P B P AB P AB P AorB P A P B P AB P B A P A ---=⨯=⨯=+-=+=

一般条件：互斥事件：；贝叶斯公式：(|)

()()(1)()

x x n x

n P A B P B P x C P P P A -⨯=⋅⋅-=;贝努力实验：

2221,2

121,21111222212

221122121,2

1

;()[()()][()()]()[()()][()()]

()();290% Confidence interval for X is 1.65 ; 95% for 1.96A B A B n p p i i i Cov Cov P A B P A E r P B E r P A B P A E r P B E r E R w E R w w w w Cov X s X s ρσσσσσ==

=⋅-⋅-+⋅-⋅-=⋅=++±±∑2) ; 95% for 2.58~(,),;()1()

(Roy's Safety-first Ratio=

;Minimum Acceptable Return

p L

L p

X s

x X N Z F z F z E R R R μ

μσσ

σ±-=-=--=

/2/2000000000

0Confidence interval: point Estimate;One tail:,;,;Two tail:,Reject :;F X Z X Z X Z H H H H H H H test statistic critical value αααααμμμμμμ=

±≥<≤>== >

中心极限定理：0ail to reject ::~(0,1);:~(1)

H test statistic critical value X X Z test Z N t test t t n < -=

-=-

2

2

2

2

112122

22

12121/2

2221

2

121(1) :~(1);:(S S )~(1,1)

Test for equality of means: t-statistic=

(Sample Variances assumed unequal);t-statistic=

P

P

s n s chi Square test x x n F test F F n n s x x x x s s s s n n n σ--=

--=>----⎛⎫++ ⎪⎝⎭

条件：1/2

22(equal)

n ⎛⎫ ⎪⎝⎭

Portfolio Management

2

2

2

2

1,2

1212

221122121,2

,,2()()():()[()]p

M f p f p

M i mkt

i i i mkt mkt

mkt

i f i M f p f

p

Cov w w w w Cov E R R CML E R R Total Risk systematic Risk unsystematic Risk

Cov SML CAPM E R R E R R R R Sharpe Ratio ρσσσσσσσσβρσσβσ==++-⎡⎤

:=+⎢⎥⎣⎦

= + =

=⨯=+-- =

;()

();'()()

M

p f M f p

p f

p p f p M f p

M Squared R R R R R R Treynor Measure Jensen s R CAPM R R R R σσαββ-=---- =

=-=---