《2017年cfa一级公式表资料》由会员分享，可在线阅读，更多相关《2017年cfa一级公式表资料（10页珍藏版）》请在金锄头文库上搜索。
1、金程教育 WWW.GFEDU.NET CFA Level I Easy Sheet 版权所有 不得翻印 专业来自百分百的投入 1 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
2、Rate of Return ( )(1r)(1)(1)1 freal f E RIPRP rIPRP SAR=Stated annual rate= rpm rp = period rate; m=number of compounding periods per pear EAR=Effective annual rate 11()mpr The future value of cash flow Future Value(FV):amount to which investment grows after one or more compounding periods. (1)nFVPV
3、r 1/ n FV PV 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= (1)1 n PMT r r P
4、VAo=Present value of an annuity= 1 1 (1)n PMT rr 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 = 1 (1) T T t t t FVCr Present Value of Uneven Cash Flows = 1(1 ) T t t t C PV r Discoun
5、ted Cash Flow Applications NPV = Net present value 0(1 ) T t t t CF r The IRR rule: 0 0 (1) N t t t CF NPV IRR If IRR cost of capital, accept it; If IRR MAD that holds in general Sample variance = 2 2 1 () 1 n i i XX s n Sample standard deviation= 2 1 () 1 n i i XX s n Chebyshevs inequality: 2 1 ()1
6、P xk k Coefficient of Variation(CV):express how much dispersion exists relative to mean of a distribution. CV = Coefficient of variance= s X Sharp ratio Pf P RR SK = Sample skewness 3 1 3 () 1 N i i X n Positive skewness: Mode Mean Sample kurtosis = 4 1 4 () 1 n i i P XX K n Excess kurtosis = sample
7、 kurtosis 3 Probability Concepts Joint probability =()( ) ()P ABP B P A B Addition rule of probability =()( )( )()P ABP AP BP ABUI Total Probability Rule = P(R)=P(RS1)P(S1)+P(RSN)P(SN) S1, S2, SN are mutually exclusive and exhaustive Expected value = 1 ()() n ii i E XX P X 金程教育 WWW.GFEDU.NET CFA Lev
8、el I Easy Sheet 版权所有 不得翻印 专业来自百分百的投入 3 Probabilistic variance: 2 2 22 1122 2 ()()() ()()()() ()() ii nn XP XxE X P XxE XP XxE X P XxE X L Covariance: (, )()( )Cov X YE XE XYE Y Correlation coefficient: , (, ) X Y XY Cov X Y Portfolio expected value: 1122 1 ()()()().() n Piinn i E RwE RwE Rw E Rw E R
9、 Portfolio variance: 11 ()(,) nn ijj Pi ij Var RwwCov R R Bayes Formula: Updated probability = Probability of new information for a given event / Unconditional probability of new information Prior probability of event =P(A1|B) =P(B |A1|)/ P(B)*P(A1) Multinominal labelling: 12 12 ! ! .! . k k n nnn n
10、nnn Combination (binominal labelling): ! !()! nr n C r nr Permutation: ! ()! nr n P nr Common Probability Distributions Binomial Probability: ( )(1) xxn x n p xC pp E(X) = np 2 = np(1-p) Continuous Uniform Distribution: 0, ( )(), 1, xa xa F xP Xxaxb ba xb Normal Distribution: 1. Completely described
11、 by mean and variance (, 2) 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: x z 68% of observations fall within 1 90% fall within 1.65 95% fall within 1.96 99% fall within 2
12、.58 Confidence Interval for Sample Mean: c z Standardized Normal Variate: X z Safety First Ratio: () PL P E RR SFR If Normal distr., SFRmax P(Rp 1, demand is elastic. If absolute value 0 Income effect0 (normal) Substitution effect 0 Income effect0 (inferior) if negative effect exceeds substitution,
13、Giffen Veblen goods: P increases, demand increases, no consistent with utility theory. Shift in Demand for resources: (1) Demand for final product (2) Productivity of resource (3) Price of related products. Marginal revenue product (MRP) = Marginal Revenue (MR) x Marginal Product (MP) Profit Maximiz
14、ing Condition: MRP = Price (of additional resource unit), for all resource types Cost Minimizing Condition: MP1 / P1 = MP1 / P1 1 2 3 4 5 6 7 8 10 20 30 40 50 60 70 80 (a) high elasticity (b) unitary elasticity (c)unitary elasticity Price ($) Quantity Quantity D tax DWL E Tax revenue from buyers Tax
15、 revenue from buyers Tax on producers Ptax PE PS Stax S P 金程教育 WWW.GFEDU.NET CFA Level I Easy Sheet 版权所有 不得翻印 专业来自百分百的投入 7 Profit maximizing Condition: MRP1=P1 Revenues and Costs Total revenue=price*quantity,summed across all units sold. Average revenue=total revenue/quantity sold. Marginal revenue=total revenue/quantity sold.quantity sold. Total fixed costs are costs that do not vary with output in the
