2018 CFA一级公式大全
CFAL1一级公式汇总
CFAL1一级公式汇总CFA一级考试包含许多公式和概念，这些公式和概念涉及财务报表分析、投资组合管理、估值模型、公司财务等方面。
以下是一级考试中常见的一些公式的汇总：1.资本预算公式：净现值(Net Present Value, NPV) = 初始投资 + 现金流量的现值2.资本预算指标：报酬率(Return on Investment, ROI) = (净利润/投资额) × 100%财务杠杆(Financial Leverage) = 总资产/股东权益盈利杠杆(Earnings Leverage) = 净利润/营业利润财务杠杆乘以盈利杠杆(Financial Leverage × Earnings Leverage) = 杠杆系数(Leverage Factor)3.财务报表分析公式：流动比率(Current Ratio) = 流动资产/流动负债速动比率(Quick Ratio) = (流动资产 - 存货)/流动负债现金比率(Cash Ratio) = 现金/流动负债利息保障倍数(Interest Coverage Ratio) = 息税前利润/利息开支股东权益比率(Equity Ratio) = 股东权益/总资产股东权益报酬率(Return on Equity, ROE) = 净利润/股东权益4.会计公式：利润总额=营业收入-营业成本-营业税金-利润分享给优先股东-利润分享给普通股东净利润=利润总额-所得税总资产=股东权益+负债股东权益=资产-负债5.宏观经济指标公式：国内生产总值(Gross Domestic Product, GDP) = 消费者支出 + 投资 + 净出口通货膨胀率(Inflation Rate) = (物价指数现值 - 物价指数上期值)/物价指数上期值×100%6.估值模型公式：股票估值=(股票股利/折现率)+终值折现债券估值=公允价值-未来现金流量的现值现金流估值(Cash Flow Valuation) = 现金流量/折现率7.风险管理公式：标准差(Standard Deviation) = [(X1 - μ)^2 + (X2 - μ)^2 + (X3 - μ)^2 + ... + (Xn - μ)^2/(n-1)]^(1/2)协方差(Covariance) = [(X1 - μx)(Y1 - μy) + (X2 - μx)(Y2 - μy) + (X3 - μx)(Y3 - μy) + ... + (Xn - μx)(Yn - μy)]/(n-1)以上是CFA一级考试中一些常见的公式。
2018 CFA level 1 知识点——Portfolio Management
Portfolio ManagementPortfolio Management: An OverviewDescribe the portfolio approach to investing1.The portfolio perspective refers to evaluating individual investments by theircontribution on the risk and return of an investor’s portfolio.投资组合视角指的是通过投资组合对风险和回报的贡献来评估个人投资。
2.把所有钱用于买一只股票并不是一种portfolio perspective，把钱分散在多只证券中才能降低风险，增加收益。
3.One measure of the benefits of diversification is the diversification ratio. It iscalculated as the ratio of the risk of an equally weighted portfolio of n securities to the risk of a single security selected at random from the n securities.衡量多样化的好处之一是多样化比率。
它计算的是n证券等加权组合的风险与随机从n证券中选择的单一证券的风险之比。
4.If the average standard deviation of returns for the n stocks is 25%, and thestandard deviation of returns for an equally weighted portfolio of the n stocks is 18%, the diversification ratio is 18/25=0.72.Describe types of investors and distinctive characteristics and needs of each1.Individual investor个人投资者就是个人为了满足生活目标而进行理财的投资者，是牺牲当前消费以期获得未来更高水平消费的个人。
2018CFAlevel1知识点——QuantitativeMethods
2018CFAlevel1知识点——QuantitativeMethodsThe time value of moneyTime value of money concepts and applications/doc/bd1209418.html,pound interest (interest on interest)复利2.Future value3.Present valueUsing financial calculator1.Set up P/Y to”1”Time lines1.It is often a good idea to draw a time line before you start to solve a TVMproblem.2.Discounting贴现/doc/bd1209418.html,pounding4.Equilibrium interest rates均衡利率are the required rate of return for aparticular investment.5.Interest rates are also referred to as discount rates贴现率.6.We can also view interest rates as the opportunity cost of current consumption.7.Real risk-free rate真正的无风险利率: It is a theoretical rate on a single-periodloan that has no expectation of inflation in it.8.Nominal risk-free rate名义无风险利率= real risk-free rate+ expected inflationrate9.Default risk违约风险: The risk that a borrower will not make the promisedpayments in a timely manner.10.Liquidity risk流动性风险: The risk of receiving less than fair value for aninvestment if it must be sold for cash quickly.11.Maturity risk到期风险: The prices of longer-term bonds are more volatile不稳定的than those of shorter-term bonds. Longer maturity bonds have more maturity risk than shorter-term bonds and require a maturity risk premium.12.Required interest rate on a security= nominal risk-free rate+ default riskpremium+ liquidity premium+ maturity risk premium13.Effective annual rate (EAR) 实际年利率represents the annual rate of returnactually being earned after adjustments have been made for different compounding periods.14.EAR=(1+periodic rate)m-1Future value of a single sum1.Future value factor: (1+r)n2.FV=PV(1+r)nPresent value of a single sum1.Present value factor: 1/(1+r)n2.Annuities1.An annuity is a stream of equal cash flow that occurs at equal intervals over agiven period.2.Ordinary annuities普通年金: Cash flow occurs at the end of each period.3.Annuities due期初应付年金：Cash flow occurs at thebeginning of each period.Future value of an annuity due1.Future value of annuity due= future value of ordinary annuity*(1+n)2.做和annuity due相关的题目的时候都可以用两种方法，第一种是用计算器的BGN模式，另一种是用上面那条公式（用计算器的普通模式计算出结果，然后乘以“1+n”）。
2018年CFA一级衍生品科目复习攻略
2018年CFA一级衍生品科目复习攻略今天CFA小编为大家奉上衍生品(Derivatives)这门课，在CFA考试中占比5%，比重较小，但内容不是很难，算是可以答满分的科目，所以大家一定要好好把握哦。
CFA一级衍生品包括3个reading,比较重要的是Reading 58:Basics of Derivative Pricing and Valuation.CFA小编总结了各个reading的重要考点：Reading 57:Derivative Markets and Instruments（金融衍生品市场及工具）金融衍生品的定义；金融衍生品市场的分类及区别；金融衍生品的分类；金融衍生品的优缺点；Reading 58:Basics of Derivative Pricing and Valuation（金融衍生品基本定价和估值原理）金融衍生品定价的基本原理；区别远期和期货合约的定价以及估值；合约期初、期中、期末如何计算远期的价值，以及理解影响远期价值的因素；解释期货和远期定价的异同；解释互换和远期定价的不同；欧式期权价值的计算以及影响因素；欧式期权的平价公式、远期平价公式以及二叉树模型的理解；美式期权与欧式期权定价的差异。
Reading 59:Risk Management Applications of Option Strategies（风险管理应用：期权策略）看涨期权和看跌期权的到期价值、利润、最大/小盈亏、盈亏平衡点的计算；Covered call和protective put的到期价值、利润、最大/小盈亏、盈亏平衡点的计算；好啦，小编来拎拎衍生品里的干干货啦！敲黑板啦！必考！：衍生品的基本分类，交易所市场和OTC市场之间的区别，了解Forward, Futures, Option, Swap的特征，辨析远期和期货的异同，远期利率协议（FRA），期权定价的影响因素，期权平价公式（Put –Call Parity），一期二叉树模型，期权的风险管理策略（Covered Call & Protective Put）。
吐血整理,超全CFA考试公式大汇总
吐血整理，超全CFA考试公式大汇总一、经营状况指标部分CFA公式1、流动比率＝流动资产÷流动负债×l00％；流动资产是指可以在一年内或者超过一年的一个营业周期内变现或者耗用的资产，包括现金及各银行在中央银行和专业银行的各种存款、短期贷款、短期投资、应收及预付款项等。
流动负债是指将在一年内或者超过一年的一个营业周期内偿还的债务，包括短期借款、活期存款、活期储蓄存款、应付票据、应付账款、应付工资、应交税金、应付利润、其他应付款、预提费用等。
2、速动比率=速动资产÷流动负债×100%；速动资产是指现金、短期投资和应收款项等项目的合计数，它们具有直接快速变现的能力，因此称为速动资产。
3、资本风险比率＝不良贷款÷资本金×100％；4、固定资产比率＝(固定资产净值＋在建工程)÷所有者权益（不含未分配利润）×100％；二、经营成果指标部分CFA公式1、利润率＝利润总额÷营业收入×100％；2、资本金利润率＝利润总额÷资本金×100％；3、成本率＝总成本÷营业收入×100％；4、综合费用率＝营业费用÷(营业收入＋投资收益)×100%。
三、资产负债比例管理指标部分CFA公式1、备付金比例＝备付金余额÷各项存款余额×100％——法定存款准备金比例；（标准：不得低于3％）备付金包括：现金、业务周转金、缴存存款准备金、存农业银行款项、存放其他同业款项、存放联社款项。
2、资产流动性比例＝流动性资产期末余额÷流动性负债期末余额×100％；（标准：不得低于25％）流动性资产是指资产负债表上的流动资产；流动性负债是指资产负债表上的流动负债。
3、存贷比例＝各项贷款余额÷各项存款余额×100％；（标准：年末不得高于80％）4、对流动负债依存率＝流动负债净额÷长期资产×100％；（标准：不得高于30％）流动负债净额＝流动负债——流动资产；长期资产是指资产负债表上的长期资产。
CFA一级常用公式和学习笔记总结可以直接打印
CFA一级常用公式和学习笔记总结从第一次考CFA一级到今天，四年过去了，持证也已经是前年的事情了。
感谢，FRM，CFA，让我见识了更多不一样的人生。
记录自己考试前的公式总结，很怀念那些用word公式编辑器逐个编辑公式的日子，现在也在从事与CFA考试相关的工作，所以决定把它们重新发上来，希望可以帮助到更多的有志于此道的同路人。
Statistic (5)1.1 Standard error of the sample mean： (5)1.2Measure of performance (5)1.3远期利率公式： (6)1.4 Leptokurtotic: (6)1.5 Positive skewed (6)1.6 Holding period return(HPR) (7)1.7 arithmetic or mean return (7)1.8 Geometric Mean return (7)1.9 Money-weighted return or time-weighted return (8)1.10 quartiles/quintiles/deciles/percentiles (8)1.11 probability (9)1.12 ratio/ordinal/interval/nominal (9)1.13 Chebyshev’s Inequality (9)1.14 distribution (10)1.15 desirable properties of an estimator (10)1.16 Bayes’ formula (10)1.17 type I and type II error (10)1.18 hypothesis testing (11)1.19 technical analysis (13)derivatives (16)2.1 option portfolio (16)2.2 Put-call parity (16)2.3 backwardation \contango (16)Corporate finance (16)3.1 NPV (16)3.2 IRR(internal rate of return) (17)3.3 PBP（backed period） (17)3.4DPB(discounted backed period) (17)3.5 Profitable index(PI) (17)3.6 WACC (17)3.7 cost of debt (18)3.8 Cost of preferred stock (18)3.9 Cost of equity (18)3.10 Break point (20)3.11 Floatation cost (20)3.12 Degree of operating leverage (21)3.13 Degree of financial leverage(DFL) (21)3.14 Degree of total leverage(DTL) (21)3.15 Breakeven Analysis (22)3.16 working capital management (22)3.17 Liquidity ratios and turnover ratios (22)portfolio (23)4.1 nominal 与real之间的转换 (23)4.2 portfolio’s deviation (24)4.3 Many risk assets (24)4.4 MPT理论 (24)4.5 Capital allocating line(CAL) (25)4.6 beta : a measure of systematic risk (26)FINANCIAL REPORTING (27)5.1 应收应付/预收预付 (27)5.2 audit report (27)5.3 Footnotes/MD&A/proxy statement (28)5.4 美国准则和国际准则 (30)5.5 IFRS对sales of goods销售商品收入确认的方法 (31)5.6 IFRS对rendering of service？收入确认的方法 (32)5.7 Financial statement Elements (32)5.8 steps in the financial statement analysis framework (33)5.9 Revenue recognition criteria (33)5.10 Revenue recognition (34)5.11 installment sales and cost recovery method (35)5.12 accounting equation 有计算 (36)5.13 income statement其它处理 (37)5.14 income statement线下项目 (38)5.15 EPS计算 (39)5.16 comprehensive income (40)5.17 金融资产与负债的计量有计算 (40)5.18 bad debt计算坏账 (41)5.19 CFO直接法与间接法有计算 (41)5.20 CFI和CFF的计算 (42)5.21 FCFE和FCFF的计算 (43)5.22 CF中的其它知识点 (44)5.23 financial analysis techniques (44)5.24 inventory 理解 (47)5.25 depreciation 理解 (50)5.26 impairment 理解 (51)5.27 capitalized and expense 的理解 (52)5.28 investment property (new) (54)5.29 early repayment of bond (55)5.30 issuance cost of bond (56)5.31 debt security 理解 (57)5.32 defer tax 理解 (59)5.33 承租人和出租人理解 (64)5.34 off-balance sheet (66)5.35 ratio (68)5.37 cash management manipulation (68)Economics (70)6.1 Utility Theory and indifference Curves (70)6.2 Economic profit and accounting profit (70)6.3 elasticity (70)6.4 Cross elasticity of demand, (71)6.5 盈亏平衡点 (71)6.6 GDP的定义： (71)6.7 nation income (72)6.8 GDP deflator: GDP平减指数 (73)6.9 IS-LM model (74)6.10 LM曲线是指货币市场的均衡。
CFA一级知识点概要总结
CFA一级知识点概要总结============Quantitative Methods============#05 Time Value of Money1) EAR在离散复利（Monthly，Quarterly，Semi-annually）和连续复利时的计算2) 分期付款下利率、每期支付金额、FV、PV和支付次数的关系#06 Discounted Cash Flow Applications1) 如何计算Time-Weighted Rate of Return2) 如何计算Money-Weighted Rate of Return3) 如何用计算器计算NPV4) 如何用计算器计算IRR#07 Statistical Concepts and Market Return1) 4种Measurement Scle：Norminal Scale，Ordinal Scale，Interval Scale，Ratio Scale2) 车比雪夫不等式（Chebyshev's Inequality）的含义3) Sharp Ratio的定义4) 偏度（Skewness）的定义以及正偏（Positively Skewness）、负偏（Negatively Skewness）的判断5) Sample Skewness (样本偏度)的计算6) 什么是峰度（Kurtosis）以及尖峰的（Leptokurtic）和平峰的（Platykurtic）7) 如何计算样本偏度（Sample Skewness）和样本峰度（Sample Kurtosis）8) 正态分布(Standard Distribution)的几点属性：比如Sample Kurtosis等于3,mean/middle/mode三者相等#08 Probability Concepts1) 两个事件的联合概率（P(AB)），条件概率（P(A|B)）以及概率加法法则和乘法法则#09 Common Probability Distribution1) 什么是置信区间（Confidence Interval），并且记住90%，95%和99%的置信区间幅度2) 如何计算Safty-First Ratio3) 蒙特卡洛模拟（Monte Carlo Simulation）的思路4) 历史模拟（Historical Simulation）的思路5) 蒙特卡洛模拟（Monte Carlo Simulation）与历史模拟（Historical Simulation）的不同6) 正态分布（Normal Distribution）的三点主要特征#10 Sampling and Estimation1) Standard Error of Sample Mean的计算公式以及它的含义2) 什么是t分布（Student's t-distribution）以及其中自由度（Degrees of Freedom，df）的概念3) t分布的特点以及与正态分布的区别#11 Hypothesis Testing1) Hypothesis Testing的7个步骤（顺序）2) 什么是无效假设（Null Hypothesis）和备择假设（Altanative Hypothesis）3) 什么是单尾检验（One-Tailed Test）和双尾检验（Two-Tailed Test）4) 检验统计量（Test Statistic）的定义5) 如何得到Standard Error of Sample Statistic6) 什么是第一类错误（Type I Error）和第二类错误（Type II Error）============Economics============#13 Elasticity1) Price Elasticity of Demand的定义2) 影响Price Elasticity of Demand的三个方面3) Elastic，Inelastic，Perfectly Elastic和Perfectly Inelastic的图形表示4) Cross Elasticity of Demand的定义5) Income Elasticity的定义以及三个不同等级的商品与它的对应关系6) Price Elasticity of Supply的定义7) 影响Price Elasticity of Supply的两种因素8) 理解在直线需求曲线（Straight-Ling Demand Curve）时，High Elasticity，Unitary Elasticity 以及Low Elasticity的位置（Notes V2 P16）9) Demand Curve在价格越高时弹性越大#14 Efficiency & Equity1) MC(Marginal Cost)和MB(Marginal Benefits)的定义以及关系2) 如何计算消费者剩余（Consumer Surplus）以及它在MC-MB图中的位置3) 什么是生产者剩余（Producer Surplus）以及它在MC-MB图中的位置4) 什么是Equilibrium Quantity5) 阻碍资源分配有效性的几个因素6) 什么是Deadweight Loss，以及它在MC-MB图上的表示7) 有关资源分配公平性/有效性的两种学派：Utilitarianism（功利主义）和Symmetry Principle （对称原则）的中心思想#16 Organizing Production1) 机会成本（Opportunity Cost）的含义2) 两种不同的机会成本：Explicit Cost和Implicit Cost3) 两种不同的隐性成本（Implicit Cost）4) 什么是Implicit Rental Rate，并且知道它是Economic Depreciation和Foregone Interest的和5) Economic Profit的定义以及它与Total Revenue，Total Cost（含Opportunity Cost）的关系6) 理解什么是Economic Profit，并且理解为什么Economic Profit小于Accounting Profit7) 理解在Normal情况下，Economic Profit等于08) 对Maximum Profit的三种类型的限制：技术限制、信息限制和市场限制9) 理解什么是技术有效性（Technological Efficiency），什么是经济有效性（Economic Efficiency），并结合例子（Notes V4 P52）10) 公司组织生产的两种形式：Command System和Incentive System，以及它们的不同11) 什么是Principal-Agent Problem，以及减少Principal Agent Problem的三种常用方法：Ownership，Incentive Pay和Long Term Contract12) 商务组织的三种形式的优缺点：Proprietorships，Partnerships，Corporations13) 四种市场类型：Perfect Competition, Monopllistic Competition, Oligopoly和Monoploy等含义和特点14) Her Findahl-Hirschman Index (HHI)指数的定义是什么15) 四公司集中度（Four Firm Concentration Ratio）的定义是什么16) Concentration Measurement的局限性：地理因素、壁垒因素、市场-行业的差异17) 企业比市场更有效的四个原因：Transaction Cost，Economies of Scale，Economies of Scope，Economies of Team Production#17 Output and Costs1) Short Run Decision和Long Run Decision有什么本质区别：Short Run Decision时，投入的资源固定；Long Run Decision时，可以调节投入的资源2) 什么是Total Product，Marginal Product，Average Product（Notes V4 P65）3) 什么是Total Cost（Total Fixed Cost和Total Variable Cost），Marginal Cost，4) 什么是Average Cost（Average Fixed Cost，Average Variable Cost），并熟悉它们的图形关系（Notes V4 P69）5) 什么是一个公司的生产函数（Production Function）以及为什么会产生Diminishing Returns6) Law of Diminishing Returns的中心思想是什么7) 什么是Marginal Product of Capital以及为什么会产生Diminishing Marginal Product of Capital8) LRATC曲线（Long Run Average Total Cost）是什么形状的9) Economies of Scale和Diseconomies of Scale的区别以及在LRATC曲线上的位置10) LRATC曲线上面的三个阶段Economies of Scale, Constant Returns to Scale，Diseconomies of Scale11) A TC = AFC + A VC等式的含义以及图形表示#18 Perfect Competition1) 在完全竞争市场（Perfect Competition Market）中，Price Taker的概念：价格合适可以卖出任意多；价格高出，可以卖出02) Perfect Competition的若干假定3) Perfect Competition的主要特点#19 Monopoly1) Monopoly市场的特点：没有竞争者；没有替代品；高壁垒2) Monopoly市场的两种壁垒形式：Leagal Barriers和Natural Barries3) Monopoly市场的两种价格方式：Single-Price和Price Discrimination4) 理解Price Discrimination的三个前提：Demand Curve右下斜；至少两个具有不同价格需求弹性的消费群体；消费者不能转卖5) 理解Price Discrimination的目的是为了将消费者剩余（Consumer Surplus）转变成经济收益（Economic Profit）6) Price Discrimination对Economic Profit和Consumer Surplus的影响7) 理解为什么在MC=MR时垄断者的产量最佳8) 理解为什么在垄断市场（Monopoly Market）会产生Deadeight Loss：Monoploy Market没有将Consumer Surplus+Producer Surplus最大化#20 Monopoly Competition & Oligopoly1) Monopoly Competition的特征2) 理解Monopoly Competition下，Price Demand Elasticity大3) 理解Kinked Demand Curve Model产生的原因4) 囚徒困境（Prisoners' Dilemma）是什么道理#21 Markets for Factors of Production1) 什么是Derived Demand2) Marginal Product，Marginal Revenue与Marginal Revenue Product的定义和相互关系3) 在完全竞争（Perfect Competition）环境下，MRP（Marginal Revenue Product）曲线的形状和含义4) 理解什么是Wage Rate5) 理解一个公司产出的商品的价格和它雇佣的Labor量成正比6) 理解影响Demand for Labor的几个因素：商品价格、其他生产因素（是否替代品）、技术进步水平7) 影响Labor Supply的两个因素：Substitution Effect，Income Effect是如何相互作用的：Substitution Effect导致工人用休闲时间换更多工资；Income Effect导致工人更多的用Income去休闲8) 工会（Labor Union）设法增加工人Wage Rate和保证工人就业的主要办法：Collective Bargaining，Traing to Increase MP，Restrick for importing，Increasesubstitution price9) Physical Capital和Financial Capital分别是什么10) 理解为什么Non-Renewable Resource的供应曲线是完全弹性的；为什么Renewable Resource的供应曲线是完全非弹性的11) 理解Economic Rent的经济学意义，以及它的供应曲线图形意义：Supply Curve完全弹性时，Economic Rent等于零；Supply Curve完全非弹性时，Economic Rent最大#22 Monitoring Jobs and the Price Level1) 失业率（Unemployment Rate）的计算公式，主要是其中Labor Force的意义（所有已经工作和有意工作的人群）2) 劳动力参加率（Labor-Force Participation Rate）的计算公式3) 就业人口比率（Employment-to-Population Ratio）的计算公式4) 什么是Aggregate Hours5) 什么是Real Wage Rate（一小时劳动可以换回多少商品和劳务，扣除价格水平变化），以及它和Wage Rate比较6) 失业的三种类型（Frictional Unemployment，Structural Unemployment，Cyclical Unemployment），注意区分Frictional Unemployment和Structual Unemployment的区别7) 什么是充分就业（Full Employment）：没有Cyclical Unemployment8) 什么是自然失业率（Natual Rate of Unemployment）：Frictional Unemployment和Structual Unemployment导致的失业率9) 什么是Potential GDP：当失业率维持在自然失业率的时候可以产生的GDP10) CPI（Consumer Price Index）的定义以及如何计算11) 哪个单位负责报告CPI，报告频率（Bureau of Labor Statistics BLS，Monthly）12) 通货膨胀率（Inflation Rate）如何计算13) CPI偏差（CPI Bias）的主要因素：New Goods，Quality Change，Commodity Substitution，Outlet Substitution#23 Aggregate Supply and Aggregate Demand1) 什么是总供给（Aggregate Supply）2) 短期总供给（Short Run Aggregate Supply SAS），长期总供给（Long Run Aggregate Supply LAS）的曲线图是什么样的3) 理解为什么LAS不受价格变化的影响，它反映了potential real output of the economy4) 什么是Potential Output（Full Employment下产生的Output）5) Potential Output正相关的几个因素：Quantity of Labor，Quantity of Capital，Technology6) 影响Money Wage Rate的两个因素：Unemployment（负相关）；Inflation Expectation（正相关）7) Aggregate Demand的四个构成成分（Comsumption，Investment，Government Spending，Net Export）8) 影响Aggregate Demand曲线的三个因素（Expectation About Future Income/Inflation/Profits，Fiscal/Monetory Policies，World Economy）1) Classical Macroeconomics，Keynesian Macroeconomics和Monetarist Macroeconomics三种经济学观点的异同比较#24 Money, the Price Level, and Inflation1) Money的三种职能：Means of Payment；Unit of Account；Store of V alue2) 什么是M1，什么是M23) 理解为什么Checks Outstanding和Credit Card都不属于Money4) 三种主要的储蓄机构：Commercial Banks，Thrift Institution5) 存款机构（Depository Institution）的四种主要功能：提供流动性；金融中介；监控风险；分散贷款风险6) Fed的三种政策工具：贴现率；Bank Reserve Requirement；Open Market Operations7) 银行允许贷款量与Required Reserved Ratio之间的关系（Notes V2 P156）8) 什么是Monetary Base，它由什么构成9) 什么是现金漏损（Currency Drain）10) 货币乘数（Money Multiplier）的计算公式，以及它在Quantity of Money公式中的作用11) 理解Demand for Money与Interest Rate负相关的原理12) 什么是Money Velocity，并理解M*V=P*Y=GDP的含义#25 US Inflation, Unemployment, and Business Cycle1) Cost-Push Inflation是如何产生的：Aggregate Supply减少所致2) Demand-Pull Inflation是如何产生的：Aggregate Demand增加所导致3) 飞利浦线（Phillips Curve）是用来表达什么关系的（Inflation与失业率的关系）4) Short-Run Phillips Curve是什么形态；Long-Run Phillips Curve是什么形态5) 什么是期望通胀（Expected Inflation）：在Full Employment下的通胀6) Natural Rate变化对Long-Run Phillip Curve的影响：Natural Rate增大，Long-Run Phillip Curve向右移动#26 Fiscal Policy1) 什么是Supply-Side Effects（Fiscal Policy对Supply的影响，尤其通过税收）2) 理解Laffer Curve描述的是什么原理（Notes V2 P184）3) Financing for Investment的来源主要包括哪些（National Savings，Government Savings，Borrowing from Foreigners）4) 挤出效应（Crowding Out Effect）：政府扩张财政，挤出私人投资/支出机会#27 Monetary Policy1) Fed的货币政策的三个目标：扩大就业；稳定价格；稳定利率2) 理解Fed的主要货币手段是联邦基金利率（Federal Fund Rate）3) Open Market Operations是如何实现的：买入、卖出Treasury Securities#28 An Overview of Central Bank1) 中央银行实施货币政策（Monetary Policy）的工具有哪些2) Inflation Targeting指什么：将通胀率控制在一个区间内为目标的货币政策============FSA============#29 Financial Statement Analysis: Introduction1) 审计的三种结果的含义：Unqualified，Qualified，Adversed Opinion的分别的含义2) MD&A（Management's Discussion and Analysis）记录的内容是什么：一些Disclosure，Discussion3) Footnotes记录什么东西：Accounting Methods，4) Proxy Statement主要记录什么东西：有关Shareholder的信息5) Standard Auditor's Opinion的三部分内容（Notes V3 P14）6) FSA Framework的六步：State Objective and Context；Gather Data；Process Data；Analyze Date；Report Conclusion；Update#30 Financial Reporting Mechanics1) 什么是Contra Account2) 什么是Asset3) 什么是Liability4) 什么是Owners' Equity5) 什么是Income6) 什么是Expense7) 基本会计等式8) 什么是Double-Entry Accounting原则9) 什么是Accrual Basis Accounting，并解释什么是Unearned Revenue，Accrued Revenue，Prepaid Expense，Accrued Expense10) 什么是Cash Basis Accounting11) 什么是Prepaid Expenses12) 什么是Accrued Expenses13) 会用Balance Sheet、Income Statement和Cash Statement之间的金额互算14) Revenue和Unearned Revenue（Liabilities）的区别15) 知道Ending Retained Earning和Beginning Retained Earning的差等于Net Income减去Dividend Declared#31 Financial Reporting Standards1) 国际会计准则(IFSR)和美国会计准则(GAAP)的大略异同2) 国际会计准则No.1对哪些财务报表是必须的3) 什么是Proxy Statements4) 什么是MD&A5) 报表的质量：Understandability，Comparability，Relevance，Reliability6) 制作报表的两个Assumption：Accrual Basis，Going Concern Assumption分别是什么意思6) 一个完好的报表架构需要满足的几点要求：透明性（Transparency），可理解（Comprehensiveness）和一致性（Consistency）#32 Understanding The Income Statement1) Net Income与Revenue和Expense的关系：Revenue - Expense = Net Income2) 明白GnL（Gain and Loss）是Incidental Transaction产生的3) 什么是COGS：Cost of Goods Sold4) Gross Profit与Revenue的关系：Revenue - COGS = Gross Profit5) 什么是Operating Profit（Operating Profit（EBIT）= Gross Profit - Operating Expense - Depreciation Expense）以及它与Gross Profit的不同6) 明白为什么Unearned Revenue是一种负债7) GAAP下的FASB确认Revenue的四项原则是什么：Evidence of Arrangement；Product Delivered；Price Determined；Seller Sure Collecting Money8) Long-Term Contract下确认Revenue的方法：Percentage of Completion；Completed Contract9) 什么是Installment Sale，并且明白Profit根据收到的Cash确认；更有Cost Recovery Method 要求收到的Cash超过Cost时才确认Profit10) 什么是Barter Transaction以及它在GAAP和IFSR下得到Fair Value的不同方法11) Revenue的两种计量方法：Gross Reporting和Net Reporting的区别是什么（Gross Reporting 分别记Revenue和COGS；Net Reporting只记它们的差值）12) Expense确认的原则之一：Matching Principle是什么含义（Expense确认的时间要与Revenue确认的时间一致）13) Expense中的Period Cost是怎么回事，以及它的确认方式14) Straight-line Depreciation的计算方法（Notes V3 P58）15) Double-Declining Balance Depreciation的计算方法16) 关于Inventory的三种会计记录方法：FIFO、LIFO和Average Cost的原理是什么17) 无形资产（Intangible Assets）如何摊销（Amortization）：分有固定使用期限（如Franchise Agreement）和没有固定使用期限（如Goodwill）两种情况18) 被停止的经营项目（Discontinued Operations）的记账原则：与其他项目分开报；对持续经营项目无影响19) 什么样的事情是Unusual Items（比如：Gain n Loss for Sale Assets）；什么样的事情是Infrequent Items（比如：Impairement，Write Down，Write Off）20) 什么样的事情是Extraordinary Items21) 什么是Basic EPS以及公式，尤其清楚如何计算Weighted Average Shares22) 什么是简单资本结构（Simple Capital Structure）；什么是复杂资本结构（Complex Capital Structure）23) 什么是Antidilutive Securities以及与Dilutive Securities的区别24) 什么是Diluted EPS以及公式25) 什么是Common-Size Income Statement，分母是什么26) Gross Profit Margin和Net Profit Margin的公式分别是什么，并且知道Net Sale就是Revenue27) 列举哪些收入不记入Income Statements：Issuing Stock；Reacquiring Stock；Dividend Paid；Other Comprehensive Income（FX，Pension Liability，HedgingDerivative，Available for Sale Securities）28) 什么是Available for Sale Securities29) 理解Comprehensive Income是Net Income和Other Comprehensive Income之和30) 计量Income的方法：Sale Basis Method，Percentage-of-Completion Method，Completed Contract Method，Installment Methods，Cost Recovery Method#33 Understanding Balance Sheet1) Balance Sheet的几种主要格式：Account Format；Report Format和Classified Balance Sheet2)1) 什么是Working Capital2) Current Asset包括哪些3) Long-Term Asset包括哪些4) Current Liability包括哪些5) Stakeholder Equity包括哪些6) Current Ratio如何计算7) Quick Ratio的计算#34 Understanding the Cash Flow Statement1) 呈现CFO的两种方法：Direct Method和Indirect Method分别是什么原理以及它们的异同2) Direct Method是将Cash-Basis Accounting的Income Statement直接转变成CFO的方法3) 针对CFO的Indirect Method的4个步骤以及其中涉及到的加减（Notes V3，第117页和第119页）4) 什么是Free Cash Flow以及它的计算方法5) 什么是Free Cash Flow to the Firm （FCFF）以及它分别用Net Income和CFO两种方法表示的公式6) 什么是Free Cash Flow to Equity（FCFE）以及它用CFO表示的公式7) 罗列所有Cash Flow Ratios，包括Performance Ratios和Coverage Ratios#35 Inventories1) 什么是LIFO Reserve，以及它的公式2) LIFO Reserve的重要衍生公式：FIFO COGS = LIFO COGS - (Ending LIFO Reserve - Beginning LIFO Reserve)#36 Long-Lived Asset1) 什么是ARO（Asset Retirement Obligation）2) 明白为什么每一年的ARO Expense由Depreciation Expense和Accretion Expense组成#37) Income Taxes1) Tax Payable与Income Tax Paid的不同含义2) Taxable Income的含义以及与Tax Base的不同3) Tax Loss Carryforward的含义4) 什么是Income Tax Expense并且理解它的公式（对于Tax Payable, DTL, DTA）5) 什么是Valuation Allowance并且明白它的作用6) Temporary Difference和Permanant Difference的不同含义7) 可以罗列出四种Permanant Difference的情况#38 Long-Term Liabilities & Leases1) Bond的一些名词定义：face value（maturity value, par value）、coupon rate、coupon payments、market rate、balance sheet liability（bond book value，carryingvalue）、interest expense、par bond、discount bond、premium bond2) Finance Lease和Operating Lease的异同3) Direct Financing Lease和Operating Lease对现金流分别不同的影响4) Market Rate与Bond Rate之间大小关系的比较决定Bond是Premium还是Discount的关系5) 什么是Sale Type Lease#39 Financial Analysis Techniques1) Dividend Declared的概念2) Sustainable Growth Rate的计算方法3) DSO（Days Sales Outstanding）的几种计算方法4) Inventory Turnover的计算方法5) Cash Conversion Cycle的计算方法6) Total Asset Turnover的公式7) Financial Leverage Multiplier的公式#41 Accounting Shenanigans on The Cash Flow Statement1) Stretching Out Payable是如何实现舞弊的2) Financing Of Payable是如何实现舞弊的3) Securitization of Receivable是如何实现舞弊的4) Using Stock Buybacks to Offset Dilution of Earning是如何实现舞弊的5) 如何计算Days' Sales in Accounts Payable（应付账款天数）#42 Financial Statement Analysis: Application1) 如何利用common-sized的报表预测下年的一些财务指标#43 International Standards Convergence1) Marketable Investment Securities的几种类型以及它们对Balance Sheet和Income Statement 的影响================ Corporate Finance ==================#44 Capital Budgeting1) Capital Budgeting的几个基本原则2) 什么是沉没成本（Sunk Cost）3) 什么是外部性（Externalities）4) 什么是同型装配（Cannibalization），以及它对现金流的影响5) Conventional Cash Flow Pattern与Unconventional Cash Flow Pattern的区别6) 什么是机会成本（Opportunity Cost），并且明白Capital Budgeting的现金流基于机会成本考虑7) 评估资本项目的方法之一：NVP法的原理是什么8) 评估资本项目的方法之二：IRR法的原理是什么9) 评估资本项目的方法之三：PBP法的原理是什么10) 评估资本项目的方法之四：Discounted PBP法的原理是什么11) 评估资本项目的方法之五：AAR法的原理和公式12) 罗列为什么NPV方法和IRR方法可能产生不同的衡量结果#45 Cost of Capital1) Marginal Cost of Capital的定义是什么2) 加权资本成本（Weighted Average Cost of Capital）的公式3) 清楚投资机会曲线（Investment Opportunity Schedule）和MCC Curve（Marginal Cost of Capital Curve）的形状、关系。
CFA level 1 level II 公式表
CFA公式表-Level IEthical and Professional Standards1.Professionalisma)Knowledge of the Lawb)Independence and objectivityc)Misrepresentationd)Misconduct2.Integrity of Capital Marketsa)Material Nonpublic Informationb)Market Manipulation3.Duties to Clientsa)Loyalty, Prudence, and Careb)Fair Dealingc)Suitabilityd)Performance Presentatione)Preservation of Confidentiality4.Duties to Employersa)Loyaltyb)Additional Compensation Arrangementsc)Responsibilities of Supervisors5.Investment Analysis, Recommendations, and Actiona)Diligence and Reasonable Basisb)Communication with Clients and Prospective Clients.c)Record Retention6.Conflicts of Interesta)Disclosure of Conflictsb)Priority of Transactionsc)Referral Fees.7.Responsibilities as a CFA Institute Member or CFA Candidatea)Conduct as Members and Candidates in the CFA Programb)Reference to CFA Institute, the CFA designation, and the CFA Program.Global Investment Performance Standards (GIPS)pliance Statement:” [Insert name of firm] has prepared and presented this report incompliance with the Global Investment Performance Standards (GIPS).”Compliance must be applied on a firm-wide basis.2.Eight sections:a)Fundamentals of complianceb)Input datac)Calculation methodologyd)Composite constructione)Disclosuresf)Presentation and reportingg)Real estateh) Private equityQUANTITATIVE METHODS 1. Time Value of Money Basicsa) Future Value (FV): amount to which investment grows after one or more compoundingperiods.b)N Y I PV )/1(FV +=c) Present Value (PV): current value of some future cash flow d) N Y I FV PV )/1/(+=e) Annuities: series of equal cash flows that occur at evenly spaced intervals over time. f) Ordinary annuity: cash flow at end-of-time period. g) Annuities due: cash flow at beginning-of-time period. h) Perpetuities: annuities with an infinite lifei))//(Y I PMT PV perpetuity =2. Meansa) Arithmetic mean: sum of all observation values in sample/population, divided by # ofobservations.b) Geometric mean: used when calculating investment returns over multiple periods or tomeasure compound growth rates. c) Geometric mean return:1)]1(......)1[(/11-+⨯⨯+=N N G R R RHarmonic mean =∑=⎥⎦⎤⎢⎣⎡Ni i X N113. Variance and Standard Deviationa) Variance: average of squared deviations from mean.b) Population variance = N X Ni i212)∑=-=μσ（c) Sample variance = 1)(122--=∑=n X Xs Ni id) Standard deviation: square root of variance.4. Holding Period Return (HRP) 1111-+=+-=---t tt t t t t t P D P P D P P R5. Coefficient of Variationa) Coefficient of variation (CV): express how much dispersion exists relative to mean of adistribution; allows for direct comparison of dispersion across different data sets. CV is calculated by dividing standard deviation of a distribution by the mean or expected value of the distribution.b)XS CV =6. Sharpe Ratioa) Sharpe Ratio: measures excess return per unit of risk.b) Sharpe Ratio =pfp r r σ-c) Roy ’s safety – first ratio:pett p r r σarg -7. Expected Return/Standard Deviationa) Expected return: ∑=iixx P X E )()(n n x x P x x P x x P X E )()()()(2211+++=b) Probabilistic variance:[][][][]222221122)()()()()()()()()X E x x P X E x x P X E x x P X E x x P X n n i i -++-+-=-=∑ （σc) Standard deviation: take square root of variance.8. Correlation and Covariancea) Correlation = covariance divided by product of the two standard deviations.)()(),(),(j i j i j i R R R R COV R R corr σσ=b) Expected return, variance of 2-stock portfolio:)()()(B B A A p R E w R E w R E +=),()()(2)()()var(2222B A B A B A B B A A p R R R R w w R w R w R ρσσσσ++=9. Normal Distributionsa) Normal distribution is completely described by its mean and variance.68% of observations fall within σ1± 90% fall within σ65.1± 95% fall within σ96.1± 99% fall within σ58.2±10. Computing Z-scoresa) Z-score: “standardizes ” observation from normal distribution; represents # of standarddeviations a given observation is from population mean.σμ-=-=x i o n d a r d d e v i a t s m e a n p o p u l a t i o n n o b s e r v a t i o z t a n11. Binomial Modelsa) Binomial distribution: assumes a variable can have one of two values (success/failure)or, in the case of a stock, movements (up/down). A Binomial Model can describe changes in the value of an asset or portfolio; it can be used to compute its expected value over several periods.12. Sampling Distributiona) Sampling distribution: probability distribution of all possible sample statistics computedfrom a set of equal-size samples randomly drawn from the same population. The sampling distribution of the mean is the distribution of estimates of the mean.13. Central Limit Theorema) Central limit theorem: when selecting simple random samples of size n from populationwith mean μand finite variance σ2, the sampling distribution of sample meanapproaches normal probability distribution with mean μand variance equal to σ2、/n as the sample size becomes large.14. Standard Errora) Standard error of the sample mean is the standard deviation of distribution of the samplemeans.Known population variance: n x σσ=Unknown population variance: nss x =15. Confidence Intervalsa) Confidence interval: gives range of values the mean value will be between, with a givenprobability (say 90% or 95%). With known variance, formula for a confidence interval is:nz x aσ2±2a z =1.645 for 90% confidence intervals (significance level 10%, 5% in each tail)2a z =1.960 for 95% confidence intervals (significance level 5%, 2.5% in each tail)2a z =2.575 for 99% confidence intervals (significance level 1%, 0.5% in each tail)17. Null and Alternative Hypothesesa) Null hypothesis (0H ): hypothesis the researcher wants to reject; the hypothesis that isactually tested; the basis for selection of the test statistics.b) Alternative hypothesis (1H ): concluded if there is sufficient evidence to reject the null hypothesis.18. Difference between One & Two-Tailed Testsa) One-tailed test: tests whether value is greater than or less than a given number. b) Two-tailed test: tests whether value is equal to a given number.E.g. One-tailed test: 0:0≤μH versus 0:0 μH E.g. Two-tailed test: 0:0=μH versus 0:0H μ≠19. Type I And Type II Errorsa) When hypothesis testing, two possible errors: i. Type I error: rejection of null hypothesis when it is actually true. ii. Type II error: failure to reject null hypothesis when it is actually false.20. Regression Equationa) General form of linear regression model:i i i X b b Y ε++=10●i Y And i X are the th i observation of the dependent and independent variables,respectively.● 0b = intercept term (represents the value of Y if X is zero).● 1b = slope coefficient (measures the change in Y for a one unit change in X ).●i ε= residual error of the th i observation.SSTSSRiation total iation lained R ==var var exp 22-=n SSESSETest of r=0: 212rn r t --=MACROECONOMICS 1. Inflationa) Inflation rate: rate of change in price index over given period of timei c e I n d e xL a s t P e r i o d i c e I n d e xL a s t P e r i o d i c e I n d e x C u r r e n t i Pr Pr Pr -=2. Labor market indicatorsa) Unemployment rate:×100NumberOfUnemployedLaborForceb) Labor force participation rate:100LaborForceWorking agePopulation ⨯-c) Employment-to-population ratio:100NumberOfEmployedWorking agePopulation⨯-3. Unemploymenta) Frictional: economic changes prevent matching qualified workers with job openings. b) Structural: the unemployment works do not currently have the skills needed to performthe newly created jobs.c) Cyclical: caused by changes in the general level of economic output. 4. Schools of Macroeconomic Thoughta) Classical: shifts in AD and AS driven by technology changes; money wages adjustrapidly to restore equilibrium.b) Keynesian: shifts in AD caused by changes in expectations; wages are “downwardsticky;” use fiscal and monetary policy to increase AD and restore equilibrium.c) Monetarist: monetary policy is the main factor leading to business cycles; central bankshould increase money supply at predictable rate.5. Timing of Fiscal policya) Time lags: i. Recognition ii. Administrative iii. Impactb) Automatic stabilizers: i. Induced taxes ii. Needs-tested spending6. Monetary Policya) Deposit expansion Multiplier=quirementserve Re Re 1b) Fed controls money supply three ways: i. Reserve requirements ii. Open market operations-most usediii. Discount rate. MICROECONOMICS 1. Elasticity of Demanda) Price elasticity of demand=icemandQuantityDe Pr %%∆∆If absolute value > 1, demand is elastic; if absolute value < 1, demand is inelastic. Price elasticity has two main determinants: ● Availability of substitutes● Share of budget spent on productb) Elasticity of demand and supply is greater in the long run. 2.Accounting Costs vs. Economic Costsa) Accounting costs include firm ’s explicit costs;b) Economic costs include both explicit/implicit costs (opportunity cost of equity capital). 3. Short run vs. long run: in short run, size of plant/equipment cannot be changed. In long run, all resources (costs) are variable.4. Law of diminishing returns: as more resources are devoted to production process, they increase output but at ever-decreasing rate.5.Competitive Modelsa) Price taker accepts market price to sell product. b) Price searcher seeks price that maximizes profit. c) Pure competition:● Large number of independent firms.● All firms produce a homogeneous product. ● Each seller is small relative to the market. ● No barriers to entry. d) Monopolistic competition:● Large number of independent firms.● Each firm produces a differentiated product. ● Low barriers to entry ● Demand is highly elastic.e) Monopoly is a market where one firm sells a well-defined product that has no goodsubstitutes and high entry barriers. Oligopoly is a similar structure but has a small number of firms.f) Any firm will maximize profits by expanding output until marginal revenues=marginalcost.6.Marginal Revenue Producta) If a firm uses an additional unit of an input, increase in output is marginal product (MP)of last unit of resource employed. Increase in revenue from producing/selling marginal product is the marginal revenue product (MRP). Profit- maximizing firms will increase use of each resource until MRP= price of the resource.INTERNATIONAL ECONOMICS 1. Foreign Exchangea) Direct quotes: domestic currency (DC) per foreign currency (DC/FC).b) Bid-ask spread stated as percent of asking price:% spread =100Pr Pr Pr ⨯-iceAsk iceBid ice Askc) Foreign currency is at forward discount (premium) if forward rate is blow (above) spotrate, using direct quotes:Forward Prem or Disct = ⎪⎪⎭⎫ ⎝⎛⎪⎭⎫⎝⎛-s ontractDay ofForwardC S S F #360 d) Currency appreciates/depreciate due to:i. Relative income growth rates. ii. Relative rates of inflation. iii. Changes in real interest rates. 2. Interest Rate Parity (IRP)a) If you can borrow in low interest rate country, and lend those borrowed funds at a higherrate in another country, the forward exchange rate must adjust to offset interest difference.fdr r S F IRP ++=11:(Note: S and F are DC/FC) IRP must hold due to arbitrage opportunities.3. Purchasing Power Parity (PPP)a) The law of one price: identical goods should have same price in all locations. AbsolutePPP asks if law of one price is correct on average. Relative PPP requires that exchange rate changes be proportion to price level changes (i.e. differences in inflation).Formula for relative PPP: ()()tFC tDC t i i e e E ++⨯=11)(0FINANCIAL STATEMENT ANALYSIS 1. Revenue Recognitiona) Two requirements: i. Completion of earnings process ii. Assurance of payment b) Revenue recognition methods: i. Sales basis method ii. Percentage-of-completion method iii. Completed contract method iv. Installment sales. v. Cost recovery method2. Unusual or Infrequent Itemsa) Gains/losses from disposal of a business segmentb) Gains/losses from sale of assets or investments in subsidiaries c) Provisions for environmental remediation.d) Impairments, write-offs, write-downs, and restructuring costs.e) Integration expenses associated with businesses recently acquired. 3.Extraordinary Itemsa) Similar to unusual/infrequent items, except extraordinary items are both unusual andinfrequent in occurrence, and material in nature. (e.g., losses from expropriation of assets).4.Discontinued Operationsa) To be accounted for as discontinued operation, a business – assets, operations, investing,financing activities – must be physically/operationally distinct from rest of firm. Income/losses are reported net of tax after net income from continuing operations. 5.Compute Cash Flow From Operations (CFO)a) Direct method: start with cash collections (cash equivalent of sales); cash inputs (cashequivalent of cost of goods sold); cash operating expenses; cash interest expense; cash taxes.b) Indirect method: start with net income, subtracting back gains and adding back lossesresulting from financing or investment cash flows, adding back all non-cash charges, and adding and subtracting asset and liability accounts that result from operations. 6.Free Cash Flowa) Free cash flow measures cash available for discretionary purposes. It is equal tooperating cash flow less net capital expenditures. i. Free cash flow to the forms:[(1)][(1)]FCFF NI NCC INT TaxRate FCinv WCinvFCFF CFO INT TaxRate FCinv=++⨯---=+⨯--ii.Free cash flow to equityFCFE CFO FCinv NetBorrowing =-+7. Critical ratiosa) Common-size balance sheets/income statements: i. Common-size balance sheet expresses all balance sheet accounts as a percentage oftotal assets. ii. Common-size income statement expresses all income statement items as apercentage of sales.b) Current ratio and quick ratio: i. Current ratio: current assets/current liabilities ii. Quick ratio: (cash + marketable securities + receivables)/current liabilitiesc) Receivables, inventory, payables turnover, and days ’ supply ratios-all of which are usedin the cash conversion cycle. i. Receivable turnover = net annual sales/average receivables ii. Inventory turnover = cost of goods sold/average inventory iii. Payables turnover ratio = cost of goods sold/average trade payables iv. Average receivables collection period = 365/receivables turnover v. Average inventory processing period = 365/inventory turnover vi. Payables payment period = 365/ payables turnover ratio vii. Cash conversion cycle = average receivables collection period + averageinventory processing period –payables payment periodd) Total asset, fixed asset, and equity turnover ratios: i. Total asset turnover = net sales/average total net assets ii. Fixed asset turnover = net sales/ average net fixed assets iii. Equity turnover = net sales/average equity e) Gross, operating, and net profit margins: i. Gross profit margin = gross profit/net sales ii. Operating profit margin = operating profit/net sales=EBIT/ net sales iii. Net profit margin = net income / net sales f) Return on assets: (return on total capital: “ROTC ”) i. Return on assets (total capital) = (net income + interest exp.)/average total capital g) Debt to equity ratio and total debt ratio: i. Debt to equity ratio = total long term debt / total equity ii. Total debt ratio = (current liabilities + total long term debt) / (total debt + totalequity)h) Interest coverage and the CF to LTD ratio: i. Interest coverage = EBIT / interest ii. Cash flow to LTD = CFO / (BV of LTD + PV of operation leases) i) Growth rate (g): g = RR × ROEj) Retention rate = 1- dividends declared / operating income after taxesk) Liquidity ratios indicate company ’s ability to pay its short-term liabilities.l) Operating performance ratios indicate how well management operates the business. 8. DuPont analysisa) Traditional DuPont equation:⎪⎪⎭⎫⎝⎛⎪⎭⎫ ⎝⎛⎪⎭⎫ ⎝⎛=Equity Assets Assets Sales Sales NetIncome ty turnOnEqui Re Return on equity = (net profit margin) × (asset turnover) × (equity Multiplier) b) Extended DuPont equation further breaks down net profit margin:()t Equity Assets Assets Interests Assets Sales Sales EBIT ROE -⎪⎪⎭⎫⎝⎛⎥⎦⎤⎢⎣⎡⎪⎭⎫ ⎝⎛-⎪⎭⎫ ⎝⎛⎪⎭⎫ ⎝⎛=1 ROE = [(operating profit margin) × (total asset turnover)-(interest expense rate)] × (financial leverage multiplier) × (tax retention rate)9. Inventory Accountinga) Relationship between FIFO and LIFO i. FIFO Inventory = LIFO Inventory + LIFO reserve ii. FIFO COGS = LIFO COGS – △LIFO reserve iii. When converse FIFO COGS to LIFO COGS:LIFO COGS = FIFO COGS + (Beginning Inventory FIFO ×Inflation Rate)10.Basic and Diluted EPSa)Basic EPS calculation does not consider effects of any dilutive securities in computationof EPS:Basic EPS = (net income –preferred dividends) / wtd. Avg. no. of common shs.OutstandingDiluted EPS = (adj income avail for common shares) / wtd. mon shares pluspotential common shares outstandingTherefore, diluted EPS is:[(net income – preferred dividend) + convertible preferred dividends + (convertible debtinterest) ×(1-t)] /[(wtd.avg.sh’s)+(shares from conversion of Conv.pfd.sh’s) + (sh’s from conversion conv.debt) + (shares issuable from stock options)]11.Financial statement Impacts:a)Capitalizing vs. Expensingi.Capitalizing: lowers income variability and increases near-term profits. Increase TA,equity.b)Depreciation and Impairmenti.Calculation: straight line and SYD methods subtract salvage value; the double –declining balance method does not.ii.Assuming continued investment in new assets,relative to a firm that usesc)Impairmenti.Recognized when the carrying value of an asset is higher than the sum of the futurecash flows (undiscounted) from their use and disposal. This makes impairmentssubject to management manipulation.ii.Loss measured as the carrying value of the asset minus the fair value of the assets. iii.Financial statement impact: write-down will immediately cause income, asset value, deferred taxes, and equity to decline, and as a result, future net income will rise.d)Deferred Taxesi.Created when taxable income (on tax return) differs from pretax income (financialstatement).ii.Deferred tax liabilities (DLT) are created by the use of accelerated depreciation methods for tax purposes (resulting in lower taxable income) and straight line forfinancial reporting (lower depreciation expense results in higher net income).iii.If DLT are not expected to reverse, treat as equity for analysis.iv.Income tax expense = taxes payable + △DTL-△DTAe)Financing Liabilitiesi.Premium bond: coupon rate > market rate at issuance.ii.Discount bond: coupon rate < market rate at issuance.iii.Interest expense equals book value at the beginning of the year multiplied by the market rate of interest at the time the bonds were issuediv.Analystic cash flow perspective: for premium bonds, CFF is overstated and CFO is understated relative to par bonds.f)Leasesi.Financial statement/ratio impact of lease accounting from the lessee perspective:capital lease result in:1.Higher: assets, liabilities, CFO, Debt/equity2.Lower: Net income (early years), asset turnover, ROA, ROECORPORATE FINANCE1. Weighted Average Cost of Capital()()[]()()()()s ce ps ps d d k w k w t k w W ACC ++-=12. Cost of retained earnings using CAPM ()RFR R RFR k mkt s -+=β3. Cost of Preferred Stock PD K ps p =4. Cost of Equity Capital g p D k e +=15. Capital Budgeting ()()()nnk CF k CF k CF CF NPV +++++++=11122116. IRR: discount rate that sets NPV equal to zero.7. Operating Leverage: variable/fixed cost tradeoff.SalesEBITDOL ∆∆=%%()()FV P Q V P Q DOL Qty ---=FVC S VCS DOL Sales ---=8. Financial Leverage: refers to use of fixed-income securities (debt and preferred stock).INTERESTEBIT EBITEBIT EPS DFL -=∆∆=%%()()EBIT DFL EPS B∆=∆%%9. Total Leverage: degree of total leverage (DTL) combines degree of operating leverageand financial leverage. Measures effect on EPS of given change in sales. ()()D F L D O L D T L = 10. EPS After a Share RepurchaseuyBackdingAfterB SharesOuts stOfFundsAfterTaxCo ngs TotalEarni EPS tan -=If after-tax cost of debt is less then earnings yield, a share repurchase will increase EPS,if After-tax cost of debt is greater than earnings yield, a share repurchase will decrease EPS.11. BV per Share After a Share RepurchaseIf the share price is greater than the original BVPS, a share repurchase will decrease BVPS. If the share price is less than the original BVPS, a share repurchase will increase BVPS.12. Effective Tax Rate on Dividendsa) Double taxation or split rate systems:Eff.rate = corp rate + (1-corp rate) (indiv rate)b) Imputation system: effective tax rate is the shareholder ’s individual tax rate. 13. Signaling Effect of Dividend Changesa) Initiation: ambiguous signal. b) Increase: positive signal.c) Decrease: negative signal unless management sees many profitable investmentopportunities.PORTFOLIO MANAGEMENT1. Investment Policy Statementa) Investment objective i. Return objectives ii. Risk tolerance b) Constrains i. Liquidity needs ii. Time horizon iii. Tax concerns iv. Legal and regulatory factors v. Unique needs and preferences2. Required Rate of Returna) Components:i. Real risk-free rate ii. Expected inflation rate premium (IP) iii. Risk premiumb) Formula for nominal RFR()()111m i n -++=IP RFR RFR real al no 3. Risk Premiuma) Investors demand risk premium for the uncertainty associated with investment;addresses factors such as business, financial, liquidity. Exchange rate and country risk.()()()()1111-+++=RP IP RFR R E realApproximation formula for nominal required rate:()RP IP RFR R E ++≅4. Combining Preferences with the Optimal set of PortfoliosMarkowitz efficient frontier is the set of portfolios that have highest return for given level of risk.5. Security Market Line (SML)a) Investors should only be compensated for risk relative to market. Unsystematic riskis diversified away; investors are compensated for systematic risk. The equation of the SML is the CAPM, which is a return/systematic risk equilibrium relationship. Total risk = systematic + unsystematic risk6. The SML and Equilibriuma) Identifying mispriced stocksConsider three stocks (A, B, C) and SML: Estimated stock returns should plot on SML! ● A return plot over the line is underpriced. ● A return plot under the line is overpriced.SECURITIES MARKETS & EQUITY INVESTMENTS1. Well-Functioning Security Marketsa) Timely, accurate information b) Liquidityc) Internal efficiency (lowest possible transactions costs)d) Informational (external) efficiency (prices rapidly adjust to new information) 2. Margin Purchasea) For margin transactions:Leverage factor = 1/margin percentage. Levered return = HPR * leverage factor.3. Margin Callsa) Margin Call Trigger PricesMargin purchase: P 0（1- initial margin %）/ (1-maintainence margin %) Short sale: P 0（1+ initial margin %）/ (1+ maintenances margin %)4. Computing Index PricesPrice – weighted Index =visorAdjustedDi ices Stock ∑PrValue-weighted Index =()()()()BaseValue ares BaseYearShices BaseYear shares ice Current ⨯∑∑#Pr #Pr5. Forms of EMHa) Weak form. Current stock prices fully reflect available security market information.Volume information/past price do not relate to future direction of security prices. Investor cannot achieve excess returns using tech analysis.b) Semi-strong form. Security prices instantly adjust to new public information.Investor cannot achieve excess returns using fundamental analysis.c) Strong form. Stock prices fully reflect all information from public and privatesources. Assumes perfect markets in which all information is cost free and available to everyone at the same time. Even with inside information, investor cannot achieve excess returns.EQUITY INVESTMENTS1. One-period valuation model()ee k P k D V +++=111110 Be sure to use expected dividend D 1in calculation. 2. Infinite period dividend discount modelsa) Supernormal growth model (Multi-stage) DDM()()ne n n e n e k P k D k D V ++++++=11110 Where: ()c e n n g k D P -=+1b) Constant growth model()ce c e c g k D k k g D V -=-+=1001 c) Critical relationship between k and g:i. As difference between k and g widens, value of stock falls ii. As difference narrows, value of stock rises iii. Small changes in difference between k and g cause large changes in stock ’svalue.d) Critical assumptions of infinite period DDM: i. Stock pays dividends; constant growth rate.ii. Constant growth rate, g, never changes. iii. k must be greater than g (or math will not work) 3. Price Indexes and Biasa) Price weighted: average of prices of index stocks, divisor adjusted for splits, biaseddownward due to splits of good performers.b) Value weighted: base period value increased by percentage increase in total marketvalue of index firms ’ stock, large cap stocks have disproportionately large influence.c) Equal weighted: either arithmetic or geometric mean of individual index stockreturns, geometric mean has downward bias.4. Earnings Multiplier Modelgk o P a y o u t R a t i g k E D E P -=-=1110 5. Estimating EPSEPS 1=[sales × (EBITDA%) – interest – depreciation](1-t) Where sales, interest and depreciation are all per share amounts. 6. Concentration ratiosN-firm concentration ratio is sum of the market shares of the N largest firms.Herfindahl index (N – firm or industry) is sum of the squared market shares. Herfindahl < 0.1 is competitive industry, > 0.18 is concentrated. 1/ Herfindahl is equivalent number of equal –size firms.7. Assumptions of technical analysisa) Supply/demand determine values (prices)b) Supply/demand is driven by both rational and irrational behavior. c) Security prices move in trends that persist for long period of time.d) While causes of supply/demand changes are hard to determined, we can see theactual shifts in supply/demand in market price behavior.Technicians tend to take one of two views when analyzing general market rules:a) Contrarian. Thinks majority is wrong, so does the opposite of what investors aredoing.b) Follow the smart money. Thinks smart investors know best, so wants to “jump onthe bandwagon ” while there ’s still time.DEBT INVESTMENT1. Basic Features of Bond Structuresa) Indenture. Agreement containing the terms under which money is borrowed. b) Term to maturity. Length of time until loan contract or agreement expires.c) Par value. Amount borrower promises to pay on or before maturity date of theissue.d) Coupon rate. When multiplied by par value, gives amount of interest to be paid perperiod.e) Zero-coupon bonds. No interest bond; are sold at a deep discount from their parvalue.。
cfa一级 数量 公式
cfa一级数量公式CFA一级考试中的数量公式CFA一级考试是金融领域的国际专业资格认证考试，数量部分是考试的一个重要内容。
在数量部分中，掌握一些常用的公式是非常重要的。
下面我将介绍一些在CFA一级考试中常见的数量公式。
1. 资本资产定价模型（CAPM）：CAPM公式用于计算资产的预期回报率。
该公式如下：r = rf + β × (rm - rf)其中，r为资产的预期回报率，rf为无风险利率，β为资产的贝塔值，rm为市场回报率。
通过这个公式，我们可以计算出一个资产在给定市场条件下的预期回报率。
2. 现值（Present Value）：现值是指未来现金流的现在价值，计算现值的公式如下：PV = CF / (1 + r)^n其中，PV为现值，CF为未来的现金流，r为贴现率，n为未来现金流发生的期数。
通过计算现值，我们可以将未来的现金流折算到当前时点。
3. 持有期收益率（Holding Period Return）：持有期收益率用于衡量一个投资的收益率。
计算持有期收益率的公式如下：HPR = (Ending Price - Beginning Price + Dividends) / Beginning Price其中，HPR为持有期收益率，Ending Price为持有期结束时的价格，Beginning Price为持有期开始时的价格，Dividends为持有期内获得的股息。
通过计算持有期收益率，我们可以评估一个投资的盈利能力。
以上是CFA一级考试中常见的一些数量公式。
熟练掌握这些公式将有助于提高我们在考试中的表现，同时也对实际的金融分析和投资决策有一定的指导作用。
希望以上内容能对您有所帮助。
cfa1级公式表
cfa1级公式表CFA1级公式表是CFA（注册金融分析师）中级认证考试的一个重要部分。
CFA是一个非常具有挑战性的考试，并且需要通过三个级别的考试才能获得CFA认证。
CFA1级公式表是CFA1级考试的一部分，包括各种金融和投资领域的重要公式和概念。
CFA1级公式表的内容非常广泛，涵盖了财务报表分析、投资组合管理、公司财务管理等方面的公式和定义。
接下来我们将介绍CFA1级公式表的重要性和内容，以及如何使用它来更好地准备考试。
CFA1级公式表的重要性CFA1级公式表的重要性在于它将所有的公式和概念集中在一起，并提供了一个易于使用和理解的格式。
考生可以将公式表视为一个参考指南，在考试前和考试期间使用。
他们可以使用公式表查找和记忆所有的必要公式和定义，帮助他们更好地理解和记忆CFA1级考试中的各种概念和知识点。
CFA1级公式表还可以帮助考生加深对概念和实践之间关系的理解。
CFA1级公式表的内容在CFA1级公式表中，有一些概念和公式非常重要，考生应该花时间深入理解和记忆它们。
以下是一些重要的主题和公式要点：1. 财务报表分析- 会计方程：A=L+E - 资产负债表: A=L+E - 损益表: 收入成本=净收益 - 现金流量表: 操作活动+投资活动+融资活动=变更量2. 股票和债券投资- 股票估值: DDM方法和价格/收益率比较法 - 债券估值：现值法和久期法 - 投资回报率: 计算公式是（期间投资回报/期间初始投资）-1.3. 企业财务分析- WACC (加权平均资本成本) = E/(E+D) X Re +D/(E+D) X Rd X (1-T) - NPV(净现值) = 当前净现值-投资 - IRR(内部收益率) = 投资的内部回报率以上列出了重要的主题和公式，但并不是全部。
考生需要认真研读所有的公式和概念，并练习使用它们，以确保能够在考试中顺流而下。
如何使用CFA1级公式表使用CFA1级公式表的关键是熟悉它并将它反复使用。
cfa一级公式
Quantitative1010365/:D 360360:==360:1360A :(1)1Continuously 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 tr Money Market Yield r HPY t t r Effective nnual Yield EAY HPY -+ =- ⨯⨯ =⨯=-⨯ =+-()12turn: r ln ln 1cc s HPR s ⎛⎫==+ ⎪⎝⎭23653651111(1)(1)21;;);1t tTime weighted Money weighted nini Arithmetic Weighted i i Geometric Geometric Arithmetic Harmonic ni i iy BEY HPY EAY R R IRR Xn X X W X X X X X n X L ⨯--===+=+=+=====<==∑∑∑(1)100y n +⨯2222111[()]2Excess kurtosis = Sample kurtosis - 3()();:;:;111nnniiii i i x X ks Range MaxValue MinValue XXXX MAD PopulationVariance SampleVariance s MAD n nn P k Coefficient of Variat μμσσ===-≤= ----===<-≥- ∑∑∑切比雪夫不等式：:;xp fpsion CV XR 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 xn P A B P B P x C P P P A -⨯=⋅⋅-=;贝努力实验：2221,2121,21111222212221122121,21;()[()()][()()]()[()()][()()]()();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 Returnp LL pX sx X N Z F z F z E R R R μμσσσ±-=-=--=/2/20000000000Confidence 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 < -=-=-22221121222212121/222212121(1) :~(1);:(S S )~(1,1)Test for equality of means: t-statistic=(Sample Variances assumed unequal);t-statistic=PPs 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：1/222(equal)n ⎛⎫ ⎪⎝⎭Portfolio Management22221,21212221122121,2,,2()()():()[()]pM f p f pM i mkti i i mkt mktmkti f i M f p fpCov w w w w Cov E R R CML E R R Total Risk systematic Risk unsystematic RiskCov SML CAPM E R R E R R R R Sharpe Ratio ρσσσσσσσσβρσσβσ==++-⎡⎤:=+⎢⎥⎣⎦= + ==⨯=+-- =;()();'()()Mp f M f pp fp p f p M f pM 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 QOwn price elasticity e elastic e inelasticice QIncome elasticity e e e IncomeQCross elasticity ∆- =><∆∆ =><∆∆ =∆;0,;0,oodbreakeven 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/QTC=TFC+TVC;MC=TC/QAccounting profit = total revenue - total accounting costsEconomic profit = Accounting profit-implicit opportunity costs=total revenue-explicit costs-implicit costs Normal p ∆∆∆1110rofit = accounting profit - economic profit=;x y x nyNominal GDPGDP deflator=Real GDP ()()()();Fiscal budget deficit=Excess over dome xy yMRS n xQ P Base BaseQ P GDP C I G X M C S TG T S I X M ∆=-∆⨯⨯=⨯⨯=+++-=++-=---用替代，用1替代currentBase PeriodRe [stic investment+trade balance Price CPI=100Price 1Money multiplier =Reserve MV=PY;Real money supply Velocity of money=Price level Real GDP :Nom al Inflati requirementFisher Effect R R E ⨯ ⨯⨯ =+]1Fiscal multiplier =;Marginal propensity to consume1(1)Real Exchange Rate(d/f)=nominal forex rate 1domestic interst (d/f):(d/f)on MPC MPC t foreign CPIdomestic CPIForward No Arbitrage Forex Rate Spot =-- ⨯+- =rate 3601foreign interest rate 360tt ⨯+⨯Equity001111Trigger Price();Trigger ()11Pr ice Weighted Index=number of stocksPrice-changeEqual Weighted Index =(1+) Equal Weighted In ni i nii Arithmetic IM IMLong P price Short P MM MMPinitial index valuen==-+=⨯=⨯-+⨯∑∑1110dex current total market valueMarket capitalization-weighted index=base year index valuebase year total market valueOne-year DDM:;Multiple-y 11Geometric n ps pss s X initial index valueD P k D P P k k ⨯⨯==+++12020ear 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 ns s s s ns D P D D P k k k k FCFE k =++++++++==+0110100000111) :;(1);(1);:[()](1)///;/nni s s f i M f D DGordon Growth Model P D D g g RR ROE payout ratio ROE payout ratio k g EPSCAPM 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 equityRatio g k g P B Ratio MV ⨯+- ==erred stockAlternativeNAV Per Share Assets - Per Share LiabilitiesProb (1)Appraisal price NOI /Market cap rate;NOI=Income-Operating Expense Market cap rate Benchmark NOI /Benchmark trans nSuccess nCF 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 ( )360Option v days FRA FRA days daysNet 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 )Tfc X R S pp p p =+++=+=---=++-+－cFixed Income112n tt=1t 0Full Price Clean PriceAccrued Interest Accrued interestt PVCF Macaulay duration=PVCF ()Macaulay duration Modified duration=1+periodic market yield Effective Duration=T CouponT T P P P P y+0/2Δy 21absolute yield spread Absolute yield spread =high yield-low yield;Relative yield spread=benchmark bond yieldsubject Yield ratioOptionbondoptionfree bondPut Call OptionP V V V STRIPS Maturity 10111(1)1 bond yield benchmark bond yieldTax Free YieldTax equivalent yield1tax rateOAS Z-spread - Option cost(Z-spread > Nominal Spread, if spot Yield is upward sloping)(1)(1)(1)(1);TT T S f f ff 00n 2N MRT 2Face valueZero coupon bond value=(interest rate risk )(1+)2Reinvestment Income=PV (1+r )-FV-Coupon Total percentage price change=duration effect + convexity effect [MD ()][Conv ()S i Py y P最大]Dollar duration duration bond price 1%(100)PVBPduration bond price 0.01%(1) [Duration PV ]bp bp 不求，算出两个相减也可计算FSAA=L+E; E=CC+R/E; R/E R/E +NI-Div; A=L+CC+R/E +Revenue-Expense-Div current assets Current ratio =current liabilitiescash + marketable securities + A/RQuick ratio =current liabilitiescash Cash ratio =E B B =+ marketable securitiescurrent liabilitiescash + marketable securities + A/RDefensive interval=Average daily expend annual salesReceivables turnover =A/R Inventory turnover =Payables turn COGSInventory over =A/P365Average receivables collection period =receivable turnover365Average inventory processing period =inventory turnover 365Average payment period =payable Cash conversion c turn yc overPurchasePretax margin =total debt total debtD/E ratio=;D/A le = collection period + inve ratio=Equtiy AssetRevenueWorking Capital turno ntory period - payme ver=;Working Ca Average Working Capital nt period EBT Sales pital=Current Asset-Current LiabilityInterest Coverage EBIT+Lease PaymentFixed Charge Coverage=Interest+Leasr Payment Return on assets (ROA) =Return on equity(ROE) Net =ROE=EBITInterestNIAsset NIEquity=Profit Margin Asset Turnover Financial Leverage Tax burden Interest burden EBIT Margin Asset Turnover Financial Leverage =ROE=EBT NI Sales AssetSales Asset EquityNI EBIT Sales Asset EBT EBIT Sales Asset Equit ⨯⨯⨯⨯⨯⨯⨯⨯=⨯⨯⨯⨯LIFO Reserve COGS LIFO Reserve taxable income tax rate=tax payableIncome tax expense=tax payable+DTL-DTAReported effec END BGN FIFO LIFO FIFO LIFO yInventory Inventory Purchase COGS Inventory Inventory COGS =+-=+=-∆⨯∆∆income tax expensetive tax rate=pretax incometax payableeffective tax rate=pretax incomeCorporate Finance120120101100...(1)(1)(1)(1)1(1):();;(1);nnniii d d ps ps c spsps s f m f s s Asse CF CF CF NPV CF k k k CF CF IRR NPVPI CF WACC W k t W k W k D k PCAPM k R R R D D D k g P g RR ROE payout ratio ROE payout ratio P k g EPSββ==+++++++=+=+=⨯-+⨯+⨯==+-=+==⨯=- ⨯ =-∑Pr ;[1(1)]1(1)cost of capital change :Break Point=weight of capital structure()();()()(Equityt oject Asset D t EDt EMCC Q P V S TVC EBIT Q P V FDOL DFL Q P V F S TVC F EBIT Interest Q P V F IQ P DTL DOL DFL βββ==⨯+-⋅+-⋅----====--------=⨯=)();365365365;//Net working capital=Current Asset-Current Liabilitie Breakeven OperatingBE V S TVCQ P V F I S TVC F IF I FQ Q P V P VCash Conversion Cycle Purchase Inv COGSCOGS Sales Purchase Inventory A R A PC --=------+==-- =+-=∆+365/()(1)11tdiscount ost of trade credit EAR discount=+--史上最全的CFA复习笔记，爱不释手T-bill rates是nominal risk-free ratesnominal risk-free rate= real risk-free rate + expected inflation ra te风险种类：default risk违约风险liquidity risk 流动性风险maturity risk 久期风险（利率风险）EAR=e^t-1贴现率=opportunity cost，required rate of return，cost of capital ordinary annuity在期末产生现金流annuity due在期初产生现金流永续年金perpetuity PV=PMT/(I/Y)对于同一个项目IRR和NPV结论相同：IRR大于必要收益率则NPV为正，否则NPV为负如果公司目标是权益所有人财富最大化，那么始终选择NPV（通常都是这样）HPR(持有期回报）=（期末值-期初值）/期末值或者（期末值-期初值+现金）/期末值Time-weighted rate of return时间的加权平均值，（1+HPR1)(1+HPR2)…即几何平均数如果组合处于高上涨期，时间加权平均会比金钱加权平均小，反之则大。
常见的CFA考试公式表
一、经营成果指标部分CFA公式1、利润率＝利润总额÷营业收入×100％；2、资本金利润率＝利润总额÷资本金×100％；3、成本率＝总成本÷营业收入×100％；4、综合费用率＝营业费用÷(营业收入＋投资收益)×100%。
二、经营状况指标部分CFA公式1、流动比率＝流动资产÷流动负债×l00％；流动资产是指可以在一年内或者超过一年的一个营业周期内变现或者耗用的资产，包括现金及各银行在中央银行和专业银行的各种存款、短期贷款、短期投资、应收及预付款项等。
流动负债是指将在一年内或者超过一年的一个营业周期内偿还的债务，包括短期借款、活期存款、活期储蓄存款、应付票据、应付账款、应付工资、应交税金、应付利润、其他应付款、预提费用等。
2、速动比率=速动资产÷流动负债×100%；速动资产是指现金、短期投资和应收款项等项目的合计数，它们具有直接快速变现的能力，因此称为速动资产。
3、资本风险比率＝不良贷款÷资本金×100％；4、固定资产比率＝(固定资产净值＋在建工程)÷所有者权益（不含未分配利润）×100％；三、会计分析部分CFA公式1、负债比率＝负债总额÷资产总额×100%；2、权益比率（产权比率）＝所有者权益总额÷资产总额×100%；3、负债对所有者权益比率＝负债总额÷所有者权益×100%；4、流动资产比率＝流动资产÷资产总额×100%；5、贷款收息率＝贷款利息收入÷贷款年平均余额×100%；6、应收利息比率＝应收未收利息÷利息收入总额×100%；7、存款平均付息率＝存款利息支出总额÷各项存款年均余额×100%；8、拆入资金平均利率＝拆入资金利息支出额÷拆入资金年平均余额×100%；9、利润完成率＝当年实现利润总额÷本年计划利润×100%；10、利润增减率＝(本年实际利润——本年计划利润)÷本年计划利润总额×100%；11、资产利润率＝净利润÷资产平均余额×100%；12、资本(权益)收益率＝净利润÷资本总额×100%。
CFAlevel1公式总结考点中文总结
定量分析类财务：资金的时间价值。
投资：是对未来事件进行评估。
储蓄：是延迟的消费。
也即用现在的消费换取将来的消费。
一、单一现金流的计算：(1)(1)p pnp np FVFV PV i PV i =+⇒=+ sp i i m=p n m n =⨯ 利率（i ），收益率（r 或y ），增长率（g ），FV 未来现金值，PV 当前现金值， 票面利率（s i ）又称年度回报率（APR i ）：s APR p i i mi ==实际年利率（EAR ）(1)1EARp m i i =+-二、连续复利求FV/PV ： ininFVFV PVe PV e =⇒=三、连续复利求有效年利率：1i EAR e =- [1]i APR Ln EAR ==+四、年金——相等的连续现金流 终身年金的现值：10P PPMT PV I =普通年金的FV ：(1)1[]pn p p pi FV PMT i +-=五、年百分率：s p i APR m i ==⨯有效年利率：(1)1mpEAR i =+- 六、持有期收益率 ： 1V HPR V =-期末期初七、货币加权收益率=内部收益率(IRR)八、时间加权收益率=几何平均数九、银行贴现基准：十、实际年收益率：十一、货币市场收益率： =绝对频数相对频数样本总数十二、算术平均数： 总体：-⎛⎫= ⎪⎝⎭0BD F P 360r F t =+-365/tEAY (1HPY)1⎛⎫= ⎪⎝⎭MM 360r HPY t 12NX X X Nμ++=1nii XX n==∑样本：几何平均数：加权平均数：投资组合的平均年回报率：十三、方差和标准差 总体：样本：变异系数： 或夏普比率：或十四、概率P(X)：事件X 发生的可能性 特点： 其中Xi 为一组互斥集体无遗漏事件 概率分布的数字特征：期望/预期： 方差、标准差——风险衡量()112NN X X X μ=1G r =112233123..................N NNw X w X w X w X w w w w μ+++=+++11tt t V R V -=-221()Nix i x xu N σ=-=∑x σ=221()1nii x xXS n =-=-∑x S =x xσμ=xS X =p Fp R R S -=p FpR R σ-=-=夏普比率P FXR R σ=XXσCV μ0P(X)1≤≤1()1Nii P X==∑()1()Ni i i E X X P X ==∑[]()()()2222221()()x Ni i i E X E X E X E X E XXP X σ==-=-⎡⎤⎣⎦=∑其中x σ=(){}1[[]][[]][,][][()]Nii i XY XE X Y E Y Cov X Y NE X E X Y E Y σ=--===--∑总体协方差：=XY XY X Y COV r σσ协方差和联合概率=XY XYX YCOV r σσ相关系数： 投资组合的预期回报和方差 =++=++22222P 1122121,222221122121,212σw σw σ2w w COV w σw σ2w w r σσZ 值分布：Roy 安全第一条件——最佳投资是安全第一比率SFR 最大的组合总体均值的置信区间称为显著程度称为显著水平 可以以总体平均值的样本估计值为中心构建置信区间α是显著性水平，等于1 -用%表示的置信水平。
CFA一级学习重点记录
CFA一级学习重点记录Q uantitative methodP99、P253Continuous compounding: EAR=eRcc-1Continuous compounding of return (Rcc) = ln(1+EAR)P141:Time-weighted rate of return（分期计算收益率，然后相乘再开根，与投入资金的时间无关）Money-weighted rate of return（IRR）P143:Bank discount yield = D/F * 360/t 即把折扣率单利年化HPY holding period yieldEAY effective annual yield = (1+HPY)365/t – 1 即把HPY按照复利年化（365）MMY money market yield（CD equivalent yield ）= HPY * 360/t 即把HPY单利年化(360)BEY bond-equivalent yield = HPY * 365 / t 即把HPY按照单利年化（365）: (1 + BEY/2)2 = 1 + EAY切比雪夫不等式：在k standard deviation 以内的概率至少有1-1/k2 (k>1)夏普比率Sharpe ratio = ( portfolio return – risk-free return )／standard deviation of portfolio returns条件概率P(I|O) = P(O|I)*P(I) / P(O)置信区间：Two-tailed : 90% ? 1.65 , 95% ? 1.96 , 99% ? 2.58 .One-tailed : 90% ? 1.28 , 95% ? 1.65 , 99% ? 2.33 .SFR ratio SFR比率越大，越不可能小于threshold level ? P250 中央极限定理：Standard error of the sample mean isReliability factor is 置信区间的上界如90% （a=10%）? Z=1.65 , 95% (a=5%)? Z=1.96 , 99% ? 2.58 .假设检验：Type I error: H0 is true but reject it. = significance levelType II error: H0 is false but fail to reject it. Power of the test = 1 – P (Type II error)差异假设检验：正态分布、两变量有关联，用paired comparisons test （difference 的均值检验）正态分布、方差未知、方差可相等可不相等，两变量相互独立时，用t检验。
CFA一级笔记-第二部分 数量分析报告方法
CFA一级考试知识点第二部分数量分析方法名义利率等于实际利率加上预期通货膨胀率，而不是当期的实际通货膨胀率。
Holding period return,HPR持有期收益率Bank discount yield,BDY银行贴现利率，本金为F，价格为P，公式： *Money market yield,MMY货币市场收益率 *Effective yield,EAY有效年利率（1+HPY）^365/t-1Money-weighted rate of return,MWR货币加权收益率（内部收益率）Time-weighted rate of return,TWR时间加权收益率（几个收益期间的几何平均）Bond equivalent yield,BEY债券等价收益率（irr的年化）货币加权受现金流入流出影响，因此时间加权更加广泛四种度量衡：名义尺度nominal scale（分类不排序）、排序尺度ordinal scale（排序进行比较，不能够加减，有优先次级，不成比例）、区间尺度interval scale（温度、评分，零不具备数学意义）、比例尺度ratio scale（常用最高级、身高、收入、资产收益率）算术平均arithmetic mean：相加后除以数据几何平均geometric mean：可以排除算术平均的极端值，相乘后开次方。
计算多期平均价收益率调和平均harmonic mean：用于计算定投平均成本N/，3期1元定投价格X1、X2、X3，总共3元买入了份股票，调和平均成本即为3/调和平均≤几何平均≤算术平均，等号成立只有X1=X2=X3时加权平均weighted mean：加入资产比重计算分位数L =(N+1)Y/100，N是样本数、Y是分位数位置数：四分位、五分位。
总体方差variance：开根号后即为总体标准差standard deviation。
样本方差：开根号后即为样本标准差。
以上公式用于衡量收入偏离均值的平均距离值。
CFA一级常用公式和学习笔记总结
CFA一级常用公式和学习笔记总结从第一次考CFA一级到今天，四年过去了，持证也已经是前年的事情了。
感谢，FRM，CFA，让我见识了更多不一样的人生。
记录自己考试前的公式总结，很怀念那些用word 公式编辑器逐个编辑公式的日子，现在也在从事与CFA考试相关的工作，所以决定把它们重新发上来，希望可以帮助到更多的有志于此道的同路人。
Statistic (6)1.1 Standard error of the sample mean： (6)1.2Measure of performance (6)1.3远期利率公式： (7)1.4 Leptokurtotic: (7)1.5 Positive skewed (7)1.6 Holding period return(HPR) (8)1.7 arithmetic or mean return (8)1.8 Geometric Mean return (8)1.9 Money-weighted return or time-weighted return (9)1.10 quartiles/quintiles/deciles/percentiles (9)1.11 probability (10)1.12 ratio/ordinal/interval/nominal (10)1.13 Chebyshev’s Inequality (10)1.14 distribution (11)1.15 desirable properties of an estimator (11)1.16 Bayes’ formula (11)1.17 type I and type II error (11)1.18 hypothesis testing (12)1.19 technical analysis (14)derivatives (17)2.1 option portfolio (17)2.2 Put-call parity (17)2.3 backwardation \contango (17)Corporate finance (17)3.1 NPV (17)3.2 IRR(internal rate of return) (18)3.3 PBP（backed period） (18)3.4DPB(discounted backed period) (18)3.5 Profitable index(PI) (18)3.6 WACC (18)3.7 cost of debt (19)3.8 Cost of preferred stock (19)3.9 Cost of equity (19)3.10 Break point (21)3.11 Floatation cost (21)3.12 Degree of operating leverage (22)3.13 Degree of financial leverage(DFL) (22)3.14 Degree of total leverage(DTL) (22)3.15 Breakeven Analysis (23)3.16 working capital management (23)3.17 Liquidity ratios and turnover ratios (23)portfolio (24)4.1 nominal 与real之间的转换 (24)4.2 portfolio’s deviation (25)4.3 Many risk assets (25)4.4 MPT理论 (25)4.5 Capital allocating line(CAL) (26)4.6 beta : a measure of systematic risk (27)FINANCIAL REPORTING (28)5.1 应收应付/预收预付 (28)5.2 audit report (28)5.3 Footnotes/MD&A/proxy statement (29)5.4 美国准则和国际准则 (31)5.5 IFRS对sales of goods销售商品收入确认的方法 (32)5.6 IFRS对rendering of service？收入确认的方法 (33)5.7 Financial statement Elements (33)5.8 steps in the financial statement analysis framework (34)5.9 Revenue recognition criteria (34)5.10 Revenue recognition (35)5.11 installment sales and cost recovery method (36)5.12 accounting equation 有计算 (37)5.13 income statement其它处理 (38)5.14 income statement线下项目 (39)5.15 EPS计算 (40)5.16 comprehensive income (41)5.17 金融资产与负债的计量有计算 (41)5.18 bad debt计算坏账 (42)5.19 CFO直接法与间接法有计算 (42)5.20 CFI和CFF的计算 (43)5.21 FCFE和FCFF的计算 (44)5.22 CF中的其它知识点 (45)5.23 financial analysis techniques (45)5.24 inventory 理解 (48)5.25 depreciation 理解 (51)5.26 impairment 理解 (52)5.27 capitalized and expense 的理解 (53)5.28 investment property (new) (56)5.29 early repayment of bond (57)5.30 issuance cost of bond (57)5.31 debt security 理解. (58)5.32 defer tax 理解 (60)5.33 承租人和出租人理解 (65)5.34 off-balance sheet (67)5.35 ratio (69)5.37 cash management manipulation (69)Economics (71)6.1 Utility Theory and indifference Curves (71)6.2 Economic profit and accounting profit (71)6.3 elasticity (71)6.4 Cross elasticity of demand, (72)6.5 盈亏平衡点 (72)6.6 GDP的定义： (72)6.7 nation income (73)6.8 GDP deflator: GDP平减指数 (74)6.9 IS-LM model. (75)6.10 LM曲线是指货币市场的均衡。
fcff fcfe cfa一级
fcff fcfe cfa一级FCFF, FCFE, CFA一级金融领域有许多指标和模型，用于衡量公司的价值和财务状况。
在这些指标和模型中，FCFF（自由现金流）、FCFE（股东自由现金流）和CFA一级（特许金融分析师一级）是非常重要且常用的。
本文将分别介绍并解释这些概念，以便更好地理解它们的意义和应用。
一、FCFF（自由现金流）FCFF是能够自由流动给所有的债权人和股东的现金流量。
它表示了企业在经营活动过程中所产生的现金净流入，可以用来支付利息、偿还债务以及分配给股东的股息。
计算FCFF的公式如下：FCFF = 税后营业利润 + 非现金费用 - 税息 - 资本支出 + 净债务增加其中，税后营业利润是指企业在税后的净利润加上非现金费用，非现金费用主要包括折旧和摊销等。
税息是指支付给债权人的利息和税金。
资本支出是指企业进行设备购买、基础设施建设等方面的支出。
净债务增加是指企业债务净增加的数量。
通过计算FCFF，我们可以评估企业的经营活动所产生的现金流量情况，并判断其财务状况的健康程度。
二、FCFE（股东自由现金流）FCFE代表了归属于股东的自由现金流。
它是在满足企业所需资本支出后，可分配给股东的剩余现金流量。
计算FCFE的公式如下：FCFE = FCFF - 净债务增加 - (净债务增加 x (1 - 税率))其中，净债务增加是指企业债务净增加的数量，税率则是企业所在地的适用税率。
FCFE对于股东来说是一个重要的指标，它直接反映了股东在企业经营活动中能够享受到的现金流量。
三、CFA一级（特许金融分析师一级）CFA一级是全球最具权威性的金融资格认证之一，由国际特许金融分析师协会（CFA Institute）颁发。
CFA一级考试涵盖了金融和投资领域的广泛知识和技能要求，考察考生对金融市场、投资工具、股权和固定收益证券等方面知识的掌握程度。
CFA一级考试的主要内容包括估值和资产定价、投资组合管理、金融报表分析、道德与职业规范等。
(完整版)cfa一级公式
Quantitative1010365/:D 360360:==360:1360A :(1)1Continuously 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 tr Money Market Yield r HPY t t r Effective nnual Yield EAY HPY -+ =- ⨯⨯ =⨯=-⨯ =+-()12turn: r ln ln 1cc s HPR s ⎛⎫==+ ⎪⎝⎭23653651111(1)(1)21;;);1t tTime weighted Money weighted nini Arithmetic Weighted i i Geometric Geometric Arithmetic Harmonic ni i iy BEY HPY EAY R R IRR Xn X X W X X X X X n X L ⨯--===+=+=+=====<==∑∑∑(1)100y n +⨯2222111[()]2Excess kurtosis = Sample kurtosis - 3()();:;:;111nnniiii i i x X ks Range MaxValue MinValue XXXX MAD PopulationVariance SampleVariance s MAD n nn P k Coefficient of Variat μμσσ===-≤= ----===<-≥- ∑∑∑切比雪夫不等式：:;xp fpsion CV XR 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 xn P A B P B P x C P P P A -⨯=⋅⋅-=;贝努力实验：2221,2121,21111222212221122121,21;()[()()][()()]()[()()][()()]()();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 Returnp LL pX sx X N Z F z F z E R R R μμσσσ±-=-=--=/2/20000000000Confidence 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 < -=-=-22221121222212121/222212121(1) :~(1);:(S S )~(1,1)Test for equality of means: t-statistic=(Sample Variances assumed unequal);t-statistic=PPs 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：1/222(equal)n ⎛⎫ ⎪⎝⎭Portfolio Management22221,21212221122121,2,,2()()():()[()]pM f p f pM i mkti i i mkt mktmkti f i M f p fpCov w w w w Cov E R R CML E R R Total Risk systematic Risk unsystematic RiskCov SML CAPM E R R E R R R R Sharpe Ratio ρσσσσσσσσβρσσβσ==++-⎡⎤:=+⎢⎥⎣⎦= + ==⨯=+-- =;()();'()()Mp f M f pp fp p f p M f pM 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 QOwn price elasticity e elastic e inelasticice QIncome elasticity e e e IncomeQCross elasticity ∆- =><∆∆ =><∆∆ =∆;0,;0,oodbreakeven 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/QTC=TFC+TVC;MC=TC/QAccounting profit = total revenue - total accounting costsEconomic profit = Accounting profit-implicit opportunity costs=total revenue-explicit costs-implicit costs Normal p ∆∆∆1110rofit = accounting profit - economic profit=;x y x nyNominal GDPGDP deflator=Real GDP ()()()();Fiscal budget deficit=Excess over dome xy yMRS n xQ P Base BaseQ P GDP C I G X M C S TG T S I X M ∆=-∆⨯⨯=⨯⨯=+++-=++-=---用替代，用1替代currentBase PeriodRe [stic investment+trade balance Price CPI=100Price 1Money multiplier =Reserve MV=PY;Real money supply Velocity of money=Price level Real GDP :Nom al Inflati requirementFisher Effect R R E ⨯ ⨯⨯ =+]1Fiscal multiplier =;Marginal propensity to consume1(1)Real Exchange Rate(d/f)=nominal forex rate 1domestic interst (d/f):(d/f)on MPC MPC t foreign CPIdomestic CPIForward No Arbitrage Forex Rate Spot =-- ⨯+- =rate 3601foreign interest rate 360tt ⨯+⨯Equity001111Trigger Price();Trigger ()11Pr ice Weighted Index=number of stocksPrice-changeEqual Weighted Index =(1+) Equal Weighted In ni i nii Arithmetic IM IMLong P price Short P MM MMPinitial index valuen==-+=⨯=⨯-+⨯∑∑1110dex current total market valueMarket capitalization-weighted index=base year index valuebase year total market valueOne-year DDM:;Multiple-y 11Geometric n ps pss s X initial index valueD P k D P P k k ⨯⨯==+++12020ear 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 ns s s s ns D P D D P k k k k FCFE k =++++++++==+0110100000111) :;(1);(1);:[()](1)///;/nni s s f i M f D DGordon Growth Model P D D g g RR ROE payout ratio ROE payout ratio k g EPSCAPM 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 equityRatio g k g P B Ratio MV ⨯+- ==erred stockAlternativeNAV Per Share Assets - Per Share LiabilitiesProb (1)Appraisal price NOI /Market cap rate;NOI=Income-Operating Expense Market cap rate Benchmark NOI /Benchmark trans nSuccess nCF 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 ( )360Option v days FRA FRA days daysNet 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 )Tfc X R S pp p p =+++=+=---=++-+－cFixed Income112n tt=1t 0Full Price Clean PriceAccrued Interest Accrued interestt PVCF Macaulay duration=PVCF ()Macaulay duration Modified duration=1+periodic market yield Effective Duration=T CouponT T P P P P y+0/2Δy 21absolute yield spread Absolute yield spread =high yield-low yield;Relative yield spread=benchmark bond yieldsubject Yield ratioOptionbondoptionfree bondPut Call OptionP V V V STRIPS Maturity 10111(1)1 bond yield benchmark bond yieldTax Free YieldTax equivalent yield1tax rateOAS Z-spread - Option cost(Z-spread > Nominal Spread, if spot Yield is upward sloping)(1)(1)(1)(1);TT T S f f ff 00n 2N MRT 2Face valueZero coupon bond value=(interest rate risk )(1+)2Reinvestment Income=PV (1+r )-FV-Coupon Total percentage price change=duration effect + convexity effect [MD ()][Conv ()S i Py y P最大]Dollar duration duration bond price 1%(100)PVBPduration bond price 0.01%(1) [Duration PV ]bp bp 不求，算出两个相减也可计算FSAA=L+E; E=CC+R/E; R/E R/E +NI-Div; A=L+CC+R/E +Revenue-Expense-Div current assets Current ratio =current liabilitiescash + marketable securities + A/RQuick ratio =current liabilitiescash Cash ratio =E B B =+ marketable securitiescurrent liabilitiescash + marketable securities + A/RDefensive interval=Average daily expend annual salesReceivables turnover =A/R Inventory turnover =Payables turn COGSInventory over =A/P365Average receivables collection period =receivable turnover365Average inventory processing period =inventory turnover 365Average payment period =payable Cash conversion c turn yc overPurchasePretax margin =total debt total debtD/E ratio=;D/A le = collection period + inve ratio=Equtiy AssetRevenueWorking Capital turno ntory period - payme ver=;Working Ca Average Working Capital nt period EBT Sales pital=Current Asset-Current LiabilityInterest Coverage EBIT+Lease PaymentFixed Charge Coverage=Interest+Leasr Payment Return on assets (ROA) =Return on equity(ROE) Net =ROE=EBITInterestNIAsset NIEquity=Profit Margin Asset Turnover Financial Leverage Tax burden Interest burden EBIT Margin Asset Turnover Financial Leverage =ROE=EBT NI Sales AssetSales Asset EquityNI EBIT Sales Asset EBT EBIT Sales Asset Equit ⨯⨯⨯⨯⨯⨯⨯⨯=⨯⨯⨯⨯LIFO Reserve COGS LIFO Reserve taxable income tax rate=tax payableIncome tax expense=tax payable+DTL-DTAReported effec END BGN FIFO LIFO FIFO LIFO yInventory Inventory Purchase COGS Inventory Inventory COGS =+-=+=-∆⨯∆∆income tax expensetive tax rate=pretax incometax payableeffective tax rate=pretax incomeCorporate Finance120120101100...(1)(1)(1)(1)1(1):();;(1);nnniii d d ps ps c spsps s f m f s s Asse CF CF CF NPV CF k k k CF CF IRR NPVPI CF WACC W k t W k W k D k PCAPM k R R R D D D k g P g RR ROE payout ratio ROE payout ratio P k g EPSββ==+++++++=+=+=⨯-+⨯+⨯==+-=+==⨯=- ⨯ =-∑Pr ;[1(1)]1(1)cost of capital change :Break Point=weight of capital structure()();()()(Equityt oject Asset D t EDt EMCC Q P V S TVC EBIT Q P V FDOL DFL Q P V F S TVC F EBIT Interest Q P V F IQ P DTL DOL DFL βββ==⨯+-⋅+-⋅----====--------=⨯=)();365365365;//Net working capital=Current Asset-Current Liabilitie Breakeven OperatingBE V S TVCQ P V F I S TVC F IF I FQ Q P V P VCash Conversion Cycle Purchase Inv COGSCOGS Sales Purchase Inventory A R A PC --=------+==-- =+-=∆+365/()(1)11tdiscount ost of trade credit EAR discount=+--史上最全的CFA复习笔记，爱不释手T-bill rates是nominal risk-free ratesnominal risk-free rate= real risk-free rate + expected inflation ra te风险种类：default risk违约风险liquidity risk 流动性风险maturity risk 久期风险（利率风险）EAR=e^t-1贴现率=opportunity cost，required rate of return，cost of capital ordinary annuity在期末产生现金流annuity due在期初产生现金流永续年金perpetuity PV=PMT/(I/Y)对于同一个项目IRR和NPV结论相同：IRR大于必要收益率则NPV为正，否则NPV为负如果公司目标是权益所有人财富最大化，那么始终选择NPV（通常都是这样）HPR(持有期回报）=（期末值-期初值）/期末值或者（期末值-期初值+现金）/期末值Time-weighted rate of return时间的加权平均值，（1+HPR1)(1+HPR2)…即几何平均数如果组合处于高上涨期，时间加权平均会比金钱加权平均小，反之则大。
CFA分析师公式
CFA 定量分析类财务：资金的时间价值。
投资：是对未来事件进行评估。
储蓄：是延迟的消费。
也即用现在的消费换取将来的消费。
一、单一现金流的计算：(1)(1)ppn p n p FV FV PV i PV i =+⇒=+ s p i i m=p n m n =⨯利率（i ），收益率（r 或y ），增长率（g ），FV 未来现金值，PV 当前现金值， 票面利率（s i ）又称年度回报率（A P R i ）：sA P R pi i m i ==实际年利率（EAR ）(1)1EARp mi i =+-二、连续复利求FV/PV ： ininF V F V P V eP V e=⇒=三、连续复利求有效年利率： 1iEAR e =- [1]i A P R L n E A R==+四、年金——相等的连续现金流 终身年金的现值：1P PP M T P V I =普通年金的FV ： (1)1[]pn pp pi F V P M T i +-=五、年百分率： s p i A P R m i ==⨯有效年利率：(1)1mp EAR i =+-六、持有期收益率 ： 1V H P R V =-期末期初七、货币加权收益率=内部收益率(IRR)八、时间加权收益率=几何平均数九、银行贴现基准：十、实际年收益率：十一、货币市场收益率： =绝对频数相对频数样本总数十二、算术平均数： 总体：-⎛⎫= ⎪⎝⎭0B D F P 360r Ft=+-365/tEAY (1HPY )1⎛⎫= ⎪⎝⎭M M 360r H P Y t 12NX XXNμ++=1nii X Xn==∑样本：几何平均数：加权平均数：投资组合的平均年回报率：十三、方差和标准差总体： 样本：变异系数： 或夏普比率：或十四、概率P(X)：事件X 发生的可能性特点： 其中Xi 为一组互斥集体无遗漏事件 概率分布的数字特征： 期望/预期：方差、标准差——风险衡量()112NNX X X μ=1G r =-112233123..................N NNw X w X w X w X w w w w μ+++=+++11t t t V R V -=-221()Ni x i x x u Nσ=-=∑x σ=221()1ni i x x X S n =-=-∑x S =x xσμ=xS X =p Fp R R S -=p FpR R σ-=-=夏普比率P FXR R σ=X XσC V μ0P(X )1≤≤1()1Ni i P X ==∑()1()Ni i i EX X P X ==∑[]()()()2222221()()xNii i EXE X EX EXEX XP X σ==-=-⎡⎤⎣⎦=∑其中xσ=(){}1[[]][[]][,][][()]Nii i X YXE X Y E Y C o v X Y NEXEX Y E Y σ=--===--∑总体协方差：=XY XY X YCOV r σσ协方差和联合概率=X Y X Y X YC O V r σσ相关系数： 投资组合的预期回报和方差=++=++22222P 1122121,222221122121,212σw σw σ2w w C O V w σwσ2w w r σσZ 值分布：Roy 安全第一条件——最佳投资是安全第一比率SFR 最大的组合总体均值的置信区间称为显著程度称为显著水平 可以以总体平均值的样本估计值为中心构建置信区间α是显著性水平，等于1 -用%表示的置信水平。
2018-CFA-level-1-知识点——Portfolio-Management
Portfolio ManagementPortfolio Management: An OverviewDescribe the portfolio approach to investing1.The portfolio perspective refers to evaluating individual investments by theircontribution on the risk and return of an investor’s portfolio.投资组合视角指的是通过投资组合对风险和回报的贡献来评估个人投资。
2.把所有钱用于买一只股票并不是一种portfolio perspective，把钱分散在多只证券中才能降低风险，增加收益。
3.One measure of the benefits of diversification is the diversification ratio. It iscalculated as the ratio of the risk of an equally weighted portfolio of n securities to the risk of a single security selected at random from the n securities.衡量多样化的好处之一是多样化比率。
它计算的是n证券等加权组合的风险与随机从n证券中选择的单一证券的风险之比。
4.If the average standard deviation of returns for the n stocks is 25%, and thestandard deviation of returns for an equally weighted portfolio of the n stocks is 18%, the diversification ratio is 18/25=0.72.Describe types of investors and distinctive characteristics and needs of each1.Individual investor个人投资者就是个人为了满足生活目标而进行理财的投资者，是牺牲当前消费以期获得未来更高水平消费的个人。
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Normal Distributions Normal distribution is completely described by its mean and variance. 68% of observations fall within ± la . 90% fall within ± 1.65a. 95% fall within ± 1.96a. 99% fall within ± 2.58a. Computing Z-Scores Z-score: “standardizes” observation from normal distribution; represents # of standard deviations a given observation is from population mean. z= observation —population mean standard deviation x —/x < 7
x)2 n —1
Standard deviation: square root of variance. H olding Period Return (HPR) P , - P ^ + D,omial Models Binomial distribution: assumes a variable can take one of two values (success/failure) or, in the case of a stock, movements (up/down). A binomial model can describe changes in the value of an asset or portfolio; it can be used to compute its expected value over several periods. Sampling Distribution Sampling distribution: probability distribution of all possible sample statistics computed from a set of equal-size samples randomly drawn from the same population. The sampling distribution o f the mean is the distribution of estimates of the mean. Central Limit Theorem Central lim it theorem: when selecting simple random samples of size n from population with mean p, and finite variance a 2, the sampling distribution of sample mean approaches normal probability distribution with mean |i and variance equal to o2ln as the sample size becomes large. Standard Error Standard error o f the sample mean is the standard deviation of distribution of the sample means. known population variance: cr- = a ■r*
Coefficient o f Variation Coefficient o f variation (CV): expresses how much dispersion exists relative to mean of a distribution; allows for direct comparison of dispersion across different data sets. CV is calculated by dividing standard deviation of a distribution by the mean or expected value of the distribution:
Global Investment Performance Standards (GIPS®) • Compliance statement: “ [Insert name of firm] has prepared and presented this report in compliance with the Global Investment Performance Standards (GIPS).” Compliance must be applied on a firm-wide basis. • Nine sections: fundamentals of compliance, input data, calculation methodology, composite construction, disclosures, presentation and reporting, real estate, private equity, and wrap fee/separately managed account portfolios.
cv = 4
X
Sharpe Ratio Sharpe ratio: measures excess return per unit of risk. Sharpe ratio =
rP ~ rf
QUANTITATIVE METHODS
Time Value o f M oney Basics • Future value (FV): amount to which investment grows after one or more compounding periods. • Future value: FV = PV(1 + I/Y)N. • Present value (PV): current value of some future cash flow PV = FV/(1 + I/Y)N. • Annuities: series of equal cash flows that occur at evenly spaced intervals over time. • Ordinary annuity: cash flow at ^W-of-time period. • Annuity due: cash flow at beginning-of-time period. • Perpetuities: annuities with infinite lives. PVperpetuity . = PMT/(discount rate). v ' Required Rate o f Return Components: 1. Real risk-free rate (RFR). 2. Expected inflation rate premium (IP). 3. Risk premium.
Var( R p) = WAa 2 (R a ) + W2 B<72 ( R b )
+ 2w a w b< t (R a ) ^ ( R b ) p ( r
a -r b )
Rc= (1 + R,)x...x(l + RN) P - 1
harmonic mean = N N Jl^
E i=i .5 c ,
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Approximation formula for nominal required rate: E(R) = RFR + IP + RP Means Arithmetic mean: sum of all observation values in sample/population, divided by # of observations. Geometric mean: used when calculating investment returns over multiple periods or to measure compound growth rates. Geometric mean return:
C r i t i c a l C o n c e pt
d
s for t he
2018 CFA® E x a m
Expected return, variance o f 2-stock portfolio:
E ( R P) =
w a
ETHICAL AND PROFESSIONAL STANDARDS
Variance and Standard Deviation Variance: average of squared deviations from mean.
2
population variance = cr = — -----N
n
!>.— u
N
P)'
sample variance - s2- i=i
E(R a ) +
w b E(Rb)
^
I 1(A) 1(B) 1(C) 1(D) II 11(A) 11(B) III III (A) III(B) III(C) III(D) III(E) IV IV(A) IV(B) IV(C) V V(A) V(B) V(C) VI VI (A) VI(B) VI (C) VII VII(A) VII(B)