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 -+  =-  ⨯⨯  =⨯=
odds
-⨯  =+-()
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-=---- =
=-=---
Economics
%;1,;1,%Pr %;0,normal good(0<<1,necessity good;>1,Luxury);e 0,inferior good
%%%Price of related g p p i i i i Q
Own price elasticity e elastic e inelastic
ice Q
Income elasticity e e e Income
Q
Cross elasticity ∆- =
><∆∆  =><∆∆ =∆;0,;0,ood
breakeven point if AR=ATC(Perfect competition);TR=TC(imperfect competition)shutdown point if AR<AVC(Perfect competition);TR<TVC(imperfect competition)TR=P Q;AR=TR/Q;c c e substitute e complement
><⨯MR=TR/Q
TC=TFC+TVC;MC=TC/Q
Accounting profit = total revenue - total accounting costs
Economic profit = Accounting profit-implicit opportunity costs=total revenue-explicit costs-implicit costs Normal p ∆∆∆1110
rofit = accounting profit - economic profit
=;x y x ny
Nominal GDP
GDP deflator=Real GDP ()()()();Fiscal budget deficit=Excess over dome xy y
MRS n x
Q P Base Base
Q P GDP C I G X M C S T
G T S I X M ∆=-∆⨯⨯=⨯⨯=+++-=++-=---用替代，用1替代current
Base Period
Re [stic investment+trade balance Price CPI=
100
Price 1
Money multiplier =
Reserve MV=PY;Real money supply Velocity of money=Price level Real GDP :Nom al Inflati requirement
Fisher Effect R R E ⨯ ⨯⨯ =+]
1
Fiscal multiplier =
;Marginal propensity to consume
1(1)
Real Exchange Rate(d/f)=nominal forex rate 1domestic interst (d/f):(d/f)on MPC MPC t foreign CPI
domestic CPI
Forward No Arbitrage Forex Rate Spot =-- ⨯
+-  =
rate 3601foreign interest rate 360t
t ⨯
+⨯
Equity
001
1
11Trigger Price();Trigger ()11Pr ice Weighted Index=
number of stocks
Price-change
Equal Weighted Index =(1+
)  Equal Weighted In n
i i n
i
i Arithmetic IM IM
Long P price Short P MM MM
P
initial index value
n
==-+=⨯
=⨯
-+⨯∑∑1110dex  current total market value
Market capitalization-weighted index=base year index value
base year total market value
One-year DDM:;Multiple-y 11Geometric n ps ps
s s X initial index value
D P k D P P k k ⨯⨯=
=
+++12
020ear DDM:...1(1)(1)(1)FCFE=CFO-FCInv+net borrowing;FCFF=CFO-FCInv+Int(1-t)
CFO=NI+Dep-Increase in working capital;net borrowing -debt principal+new debt issues P (1n n n n
s s s s n
s D P D D P k k k k FCFE k =++++++++==+0110100000111)  :;(1);(1);:[()](1)///;/n
n
i s s f i M f D D
Gordon Growth Model P D D g g RR ROE payout ratio ROE payout ratio k g EPS
CAPM k R E R R P P D g E D E Payout Ratio Payout Leading P E Trailing P E E k g k g E k g β==
=⨯+=⨯=- ⨯ =-=+-+  === ===
---∑
(1)
Enterprise Value=MV of common stock+MV of Pre-stock+MV of Debt-Cash and Investment Market Value of equity
/;Common equity=total asset-total liabilities-pref Book Value of equity
Ratio g k g P B Ratio MV ⨯+- =
=erred stock
Alternative
NAV  Per Share Assets - Per Share Liabilities
Prob (1)Appraisal price NOI /Market cap rate;NOI=Income-Operating Expense Market cap rate Benchmark NOI /Benchmark trans n
Success n
CF Venture Capital NPV CF i =  =⨯-+==()()
()()
action price After Tax Net Income NOI D INT *1t After Tax Cash Flow ATNI D PRN principal repayment NOI TAX PRN INT =---=+-=--+
Derivative
()()floating rate at settlement forward rate 360notional principal  39361+floating rate at settlement 360  rincipal ( )360
Option v days FRA FRA days days
Net Fixed Rate Payment P Fixed rate LIBOR ⎡
⎤-⨯⎢⎥=⨯=⎢⎥⎢⎥⨯
⎣⎦=⨯-⨯
；期前，期后()
0000alue intrinsic value  time value /1covered call S ;Breakeven=S c;Maximum Gain= X (S c)protective put S ;Breakeven=S ;Maximum Loss= X (S )
T
f
c X R S p
p p p =+++=+=---=++-+－c
Fixed Income
1
12
n t
t=1
t 0Full Price  Clean Price
Accrued Interest Accrued interest
t PVCF Macaulay duration=PVCF ()
Macaulay duration Modified duration=1+periodic market yield Effective Duration=T Coupon
T T P P P P y
+0/2Δy 21
absolute yield spread Absolute yield spread =high yield-low yield;Relative yield spread=benchmark bond yield
subject Yield ratio
Option
bond
option
free bond
Put Call Option
P V V V STRIPS Maturity  10
11
1(1)
1 bond yield benchmark bond yield
Tax Free Yield
Tax equivalent yield
1tax rate
OAS Z-spread - Option cost(Z-spread > Nominal Spread, if spot Yield is upward sloping)(1)(1
)(1
)
(1
);T
T T S f f f
f 00
n 2N MRT 2Face value
Zero coupon bond value=
(interest rate risk )(1+)
2
Reinvestment Income=PV (1+r )-FV-Coupon Total percentage price change=duration effect + convexity effect [MD ()][Conv ()S i P
y y P
最大]Dollar duration duration bond price 1%(100)PVBP
duration bond price 0.01%(1) [Duration PV ]
bp bp 不求，算出两个相减也可计算

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