CFA一级公式表168.docx
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CFA一级公式表168.docx
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CFA一级公式表168
金程教育WWW.GFEDU.NETCFALevelIEasySheet版权所有不得翻印
QUANTITATIVEMETHODS
TheTimeValueofMoney
Interestrate=Nominalrisk-freerate
T
FVCr
t
(1)
Tt
t1
PresentValueofUnevenCashFlows=
+Defaultriskpremium
+Liquidityriskpremium
+Maturityriskpremium
PV
TC
t
1(1r)
t
t
Nominalrisk-freerateDiscountedCashFlowApplications
=Realrisk-freerate+expectedinflationrate
RequiredRateofReturn
E(R)(1r)(1IP)(1RP)1
freal
NPV=Netpresentvalue
T
CF
t
0(1r)
t
t
rIPRP
f
SAR=Statedannualrate=rp×m
TheIRRrule:
NPV
N
CF
t
(1IRR)
t
t0
0
rp=periodrate;IfIRR≥costofcapital,acceptit;
m=numberofcompoundingperiodsperpearIfIRR EAR=Effectiveannualrate(1rp)m1 HoldingPeriodReturn=holdingperiodyield=HPYt= Thefuturevalueofcashflow FutureValue(FV): amounttowhichinvestmentgrows afteroneormorecompoundingperiods. HPR t PPDPD 11 ttttt PP t1t1 FVPV(1r)n MoneyWeightedReturnisanIRRcalculation. TimeWeightedReturnmeasurescompoundgrowth FV PV () 1I/Yn Annuities: seriesofequalcashflowsthatoccurat andpast-periodreturnfornperiods TWR=n(1r1)(1r2)(1r3)...(1rn)1 evenlyspacedintervalsovertime. Ordinaryannuity: cashfolwatend-of-timeperiod. Annuitydue: cashflowatbeginning-of-timeperiod. Thenannualizethetime-weightedreturn. ()360 FVP BDY=BankDiscountYield=r0 BD FVt Perpetuities: annuitieswithinfinitelives. FVAo=Futurevalueofanannuity= EAY=Effectiveannualyield=(1+HRY)365/t-1 Moneymarketyield=HPY×(360/t) PMT r [(1r)n1] Moneymarketyield=BDY/(1-BDY×t/360) StatisticalConceptsandMarketReturnsPVAo=Presentvalueofanannuity= PMT1 1 r(1r)n FVAD=Futurevalueofannuitydue=FVAo×(1+r) Positionoftheobservationatagivenpercentile,y; y L(n1) y 100 Arithmeticmean: sumofallobservationvaluesin PVAD=Presentvalueofannuitydue=PVAo×(1+r)sample/population,dividedbynumberofobservations. PresentValueofPerpetuity=PMT/rGeometricmean: usedwhencalculatinginvestment FutureValueofUnevenCashFlows=returnsovermultipleperiodsortomeasurecompound growthrates. 专业来自百分百的投入1 金程教育WWW.GFEDU.NETCFALevelIEasySheet版权所有不得翻印 N X i Populationmean: 1 i x N Samplevariance= n (XX) 2 i s 2i1 n1 n X i Samplemean: X1 i n Samplestandarddeviation= s n (XX)2 i i1 n1 n X(wX) ii i1 Chebyshev’sinequality: P(xk)1 Weightedmean: 1 k 2 where wareweightsthatsumto1. i CoefficientofVariation(CV): expresshowmuch Geometricmean: dispersionexistsrelativetomeanofadistribution. N GXXX...X(X) 1/N N 123Ni i1 CV=Coefficientofvariance=s X Geometricmeanreturn: RRR…R G12nN (1) (1) (1)1 N (1) (1) (1)1 Sharpratio RR Pf P Harmonicmean: N X HN (1/X) i i1 SK=Sampleskewness 1 n N (X)3 i i1 3 y Ythpercentile= (1) Ln Y 100 MAD=Meanabsolutedeviation= N i1 X i N Positiveskewness: Mode Negativeskewness: Mode>Median>Mean Samplekurtosis=K P n (XX) 4 1 i i1 n 4 Excesskurtosis=samplekurtosis–3 VarianceandStandardDeviation Variance: averageofsquareddeviationsfrommean. Standarddeviation: squarerootofvariance.ProbabilityConcepts Populationvariance= N (X) 2 i 21 i N Jointprobability=P(AB)P(B)P(AB) Additionruleofprobability Populationstandarddeviation= =P(AUB)P(A)P(B)P(AIB) N (X) 2 i i1 N σ>MADthatholdsingeneral 2 TotalProbabilityRule= P(R)=P(R│S1)P(S1)+…+P(R│SN)P(SN) S1,S2,…,SNaremutuallyexclusiveandexhaustive n Expectedvalue= E(X)XP(X) ii i1 专业来自百分百的投入2 金程教育WWW.GFEDU.NETCFALevelIEasySheet版权所有不得翻印 Probabilisticvariance: (X)P(X)xE(X) 2 2 ii P(X)xE(X)P(X)xE(X) 22 1122 LP(X)xE(X) 2 nn 0,xa xa F(x)P(Xx),axb ba xb 1, NormalDistribution: Covariance: Cov(X,Y)E[XE(X)][YE(Y)] 1.Completelydescribedbyme
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