1、2021 CFA 一级一级考试考试 公式表公式表速速 记记1PART 1 Quantitative AnalysisReading 6 The Time Value of Money利率的组成无风险利率 Nominal Risk-free Interest Rate=Real Risk-free Interest Rate+Inflation Premium风险资产收益率Return of Risky Asset=Nominal Risk-free Interest Rate+Risk PremiumRisk Premium=Default premium+Liquidity premium+
2、Maturity premium计息方式报价利率 有效年利率(EAR)=1+1 ：报价利率；：一年内的计息次数。连续复利=1现值与终值的转换终值(FV)=1+：年数年金永续年金(Perpetuity Annuity)=：每期年金Reading 7 Discounted Cash Flow ApplicationsNPV=0净现值(Net Present Value,NPV)0=+1+(1+)1(1+)2+12(1+)NPV=0=0内部回报率(Internal Rate of Return,IRR)1+0=+12(1+)1(1+)2+(1+)资产组合收益率（Portfolio Return）持有
3、期收益率(Holding Period Return,HPR)(1 0+1)=00：期初投资1：期末价值1：期末投资带来的现金收益货币加权收益率(Money-weighted Rate of Return，MWR)120+(1+)1+(1+)2+1+=0时间加权收益率(Time-weighted Rate of Return，TWR)1 TWR=1+1 1+2 1+1Reading 7 Discounted Cash Flow Applications货币市场收益率（Money market yield）名称名称公式公式持有期收益率(Holding Period Return,HPR)=(1
4、0+1)0有效年利率(Effective annual yield,EAY)=1+365 1复利，365天银行贴现利率(Bank discount yield,BDY)360=贴现率，单利，360天货币市场收益率(Money market yield,MMY)360=附加率，单利，360天债券等价收益率(Bond equivalent yield,BEY)365=附加率，单利，365天Reading 8 Statistical Concepts and Market Returns均值(Mean)名称名称公式公式算术平均(Arithmetic Mean)=1 =1几何平均(Geometric
5、Mean)=123 Periodic Return=1+1+1+1compound12调和平均(Harmonic Mean)=Harmonic 1=1加权平均(Weighted Mean)W =1中位数(Median)n为奇数 中位数=(n+1)/2位置的数n为偶数 中位数=n/2与(n+2)/2两个位置上的数的平均值。Reading 8 Statistical Concepts and Market Returns绝对离散程度(Absolute Dispersion)名称名称公式公式分位数(Quantiles)=+1 100：数据个数；：百分位点；：分位数的位置。几何平均(Geometric
6、 Mean)=123 Periodic Return=1+1+1+1compound12调和平均(Harmonic Mean)=Harmonic 1=1加权平均(Weighted Mean)W =1中位数(Median)n为奇数 中位数=(n+1)/2位置的数n为偶数 中位数=n/2与(n+2)/2两个位置上的数的平均值。2PART 2 EconomicsReading 14 The Topics in Demand and Supply Analysis需求弹性(Elasticity of demand)价格弹性 The sensitivity of the quantity demande
7、d to a change in price.收入弹性 The sensitivity of the quantity demanded to a change in income.交叉价格弹性 the responsiveness of the quantity demanded to a change in price of substitutes or complements.计算公式价格弹性（Own-price elasticity of demand）%=%：商品X的价格交叉弹性（Cross-price elasticity of demand）%=%：商品Y的价格收入弹性（Inco
8、me elasticity of demand）%=%：消费者收入Reading 14 The Topics in Demand and Supply Analysis收入（Revenue）总收入(Total Revenue,TR)=平均收入(Average Revenue,AR)=边际收入（Marginal Revenue,MR)=1 1:需求价格弹性成本（Cost）总成本（Total Cost,TC)=+平均固定成本(Average Fixed Cost,AFC)=平均可变成本(Average Variable Cost,AVC)=边际成本(Marginal Cost,MC)=Readin
9、g 16 Aggregate Output,Prices,and Economic GrowthGDP平减指数(GDP deflator)=100GDP的核算方法（GDP calculation）支出法(Expenditure approach)=+：私人部门消费：国内私人部门投资：政府部门支出 ：净出口收入法(Income approach)=+：私人部门储蓄：政府税收货币数量论（Quantity theory of money）=：名义货币供给：货币流通速度：平均价格水平：实际收入/支出Reading 16 Aggregate Output,Prices,and Economic Grow
10、th生产函数（The production function）生产函数(Production function)=(,):技术水平/全要素生产率Growth in potential GDP=Growth in technology+WL(Growth in labor)+WC(Growth in capital)Growth in potential GDP=long-term growth rate of labor force+long-term labor productivity growth rate人均潜在GDP增长率（Growth in per capita potential
11、 GDP）Growth in per capita potential GDP=Growth in technology+WC(Growth in capital-to-labor ratio)潜在GDP增长率（Growth in potential GDP）Reading 17 Understanding Business Cycles失业率（Unemployment rate）Unemployment rate=()劳动率参与率（Participation ratio）Participation ratio=()货币乘数（Money multiplier）Money multiplier=
12、1/reserve requirementReading 20 Currency Exchange Rates实际汇率(Real exchange rate)利率平价(Interest rate parity)/=/:/:实际汇率名义汇率外国物价水平 本国物价水平()1+=()1+():():远期汇率即期汇率本国无风险利率外国无风险利率3PART 3 Financial Reporting and AnalysisReading 21 Financial Statement Analysis:An introduction财务报表等式（Financial statement equation）
13、名称名称公式公式资产负债表恒等式(Balance sheet equation)Assets=Liabilities+OwnersEquity利润表等式(Income statement equation)Income Expenses=Net Income综合收益表等式(Comprehensive income statement equation)Comprehensive Income=Net Income+OCIReading 23 Understanding the I/S特殊收入确认方法-长期合同(Special Cases of Revenue Recognition Long
14、Term Contracts)完工百分比(Percentage-of-completion)total cost incurred todatePOC=The latest estimation of the total cost for the project某年应确认收入(Recognized revenue)Revenue=Contract Price POC Total Revenue Recognized in Prior Periods某年应确认利润(Recognized net income)Net Income=Revenue Cost Incurred For the Yea
15、每股收益-基本每股收益(Earnings Per Share Basic EPS)Basic EPS=NI Divpreferred stockweighted average number of shares outstanding每股收益-稀释每股收益(Earnings Per Share Diluted EPS)Diluted EPS=NI Divpreferred stock+分子weighted average number of shares outstanding+分母Reading 23 Understanding the I/S复杂结构证券-可转换优先股分子 可转换优先股股数
16、 每股股利分母 可转换优先股股数 转换比率复杂结构证券-可转债复杂结构证券-期权/权证分子 可转债税后利息费用分母 债券张数(可转债总面值 1,000)转换比率分子 0分母 债行权认购股份数 公开市场回购股份数公开市场回购股份数 行权认购股份数 执行价格 公开市场回购价格Reading 23 Understanding the I/S比较结果处理原则分子Basic EPS 分母反稀释作用，此时Diluted EPS=Basic EPS分子Basic EPS分母稀释作用，代入公式计算出Diluted EPSBasic EPS每股收益-检验反稀释作用Reading 24 Understanding
17、 the B/S合并商誉(Consolidated Goodwill)合并商誉(Consolidated Goodwill)Consolidated Goodwill=Consideration Fair Value of Acquirees Net Identifiable Assets可辨认净资产公允价值 (Fair Value of Net Identifiable Assets)Fair Value of Net Identifiable Asset=Fair Value of Acquirees Identifiable Assets Fair Value of Liabilitie
18、s and Contingent liabilitiesReading 25 Understanding the C/FCFO Calculation by Direct MethodCash received from customers A/RBeg+Net Sales Cash received=A/REndCash paid to suppliersInvBeg+Purchase COGS=InvEnd A/PBeg+Purchase Cash paid=A/PEndCash paid to employeesWage PayableBeg+Wage Expense Cash paid
19、=Wage PaybleEndInterest paidInterest PaybleBeg+Interest Expense Cash paid=Interest PaybleEndTaxes paidTax PaybleBeg+Tax Expense Cash paid=Tax PaybleEnd经营活动现金流(CFO)-间接法(Direct Method)Reading 25 Understanding the C/FCFO Calculation by Indirect MethodStart pointNIStep one:Adj.income statementitems+Depr
20、eciationAmortizationStep two:Adj.balance sheetitems+IncreaseDecrease in non cash current asset accounts(eg:A/R,Inventory.)+DecreaseIncrease in current liability accounts(eg:A/P,Tax payble.)=CFO经营活动现金流(CFO)-间接法(Direct Method)Reading 25 Understanding the C/FCalculation of BV of DisposalBVBeg+Purchase
21、Depreciation BVDisposal=BVEndCalculation of Cash proceeds from disposalGainLoss from disposal=Cash proceeds BVDisposal投资活动现金流(CFI)-处置长期资产自由现金流(FCFF/FCFE)FCFF(1)FCFF=NI+NCC WC Inv.FC Inv.+Interest exp.(1 Tax rate)FCFF(2)FCFF=CFO FC Inv.+Interest exp.(1 Tax rate)CFO NI+NCC WC Inv.FCFE(1)FCFE=FCFF Inte
22、rest exp.1 Tax rate+Net debt borrowingFCFE(2)FCFE=CFO FC Inv.+Net debt borrowingReading 26 Financial Analysis TechniquesTurnover Ratios Number of Days=365/turnoverAR turnover=RevenueAve.A/R Days of Sales outstanding(DSO)Inventory turnover=COGSAve.Inventory Days of Inventory on hands(DOH)AP turnover=
23、PurchaseAve.AP Number of Days of PayableTotal Asset turnover=RevenueAve.Total Asset 略营运能力比率(Activity Ratios)短期偿债能力比率(Liquidity Ratios)流动比率(Liquidity Ratio)Current AssetsCurrent Liabilities速动比率(Quick Ratio)Cash+Marketbale securities+ARCurrent Liabilities现金比率(Cash Ratio)Cash+Marketbale securitiesCurre
24、nt Liabilities经营周期(Operating Cycle)DOH+DSO现金循环周期(Cash Conversion Cycle)DOH+DSO Number of Days of PaybaleReading 26 Financial Analysis Techniques长期偿债能力比率(Solvency Ratios)杠杆(Leverage)Debt/Equity,Debt/(Debt+Equity),Debt/Assets.Assets/Equity利息保障倍数 Interest Coverage=EBITInterest保障倍数(Coverage)固定成本保障倍数 Fix
25、ed charge Coverage=EBIT+Lease paymentInterest+Lease payment盈利能力比率(Profitability Ratios)资本回报率(Return on Capital)ROA=NI/Average total assetsROE=NI/Average total equity利润率(Profit/Sales)Gross profit margin=Gross profit/Revenue Operating profit margin=Operating profit/Revenue Net profit margin=Net Income
26、/RevenueReading 26 Financial Analysis Techniques杜邦财务分析(DuPont Analysis)初始比率NIROE=Ave.Equity二分法NIAve.AssetsROE=ROA Financial leverageAve.AssetsAve.Equity三分法ROENIRevenue=Net Profit Margin Total Asset TurnoverRevenueAve.AssetsAve.Assets Financial leverageAve.Equity五分法ROENIEBTEBT=Tax Burden Int.Burden E
27、BIT MarginEBTEBITRevenueRevenueAve.Assets Total Asset Turnover Financial leverageAve.AssetsAve.EquityReading 26 Financial Analysis Techniques每股经营活动现金流(CFO per share)CFOWeighted average number of shares outstanding每股股利(Dividend per share)/DPSCommon dividends declaredWeighted average number of shares
28、outstanding股利支付率(Dividend payout Ratio)Common dividends declaredDPSorNet income attributable to common sharesEPS留存收益率(Retention Ratio)1 Dividend payout Ratio可持续增长率(Sustainable grow rate)ROE Retention rate or ROE (1 Dividend payout ratio)市价比率(Valuation Ratios)I/S(From LIFO to LIFO)COGSFIFO=COGSLIFO L
29、IFO ReserveLIFO Reserve=LIFO ReserveEnd LIFO ReserveBegB/S(From LIFO to LIFO)InventoryFIFO=InventoryLIFO+LIFO ReserveReading 27 Inventories减值计提(Loss recognized)Loss recognized=BV of Inventory NRV可变现净值(NRV)NRV=Selling price Selling costs存货减值(Loss Measurement)-IFRS存货减值(Loss Measurement)-US GAAP减值计提(Lo
30、ss recognized)Loss recognized=BV of Inventory Market条件市场(Market)取值Replacement cost (NRV Profit,NRV)Replacement cost市场(Market)Replacement cost NRV ProfitNRV-ProfitReplacement cost NRVNRV存货分析(Inventory Analysis)-LIFO ReserveReading 28 Long-Lived Assets折旧方法当期折旧(Depreciation cost/expense)直线折旧法(Straight
31、line Method)Cost Residual ValueDepreciation Expense=Useful life加速折旧法(DDB)2Depreciation Expense=(Cost Accumulated Depreciation)Useful life产量法(Units of production Method)Cost Residual ValueDepreciation Expense=Actual output in current period Total Capacity长期资产折旧(Depreciation)Reading 28 Long-Lived Asse
32、ts减值计提(Impairment recognized)Impairment loss=BV of Assets Recoverable Amount可收回金额(Recoverable Amount)The higher of NRV or Vaue in use(PV of CFi)可变现净值(NRV)NRV=Fair value of Assets Selling Costs长期资产减值(Impairment)-IFRS长期资产减值(Impairment)-US GAAP减值测试(Impairment test)有减值：BV of AssetsUndiscounted future ca
33、sh flows generated by assets无减值：BV of AssetsUndiscounted future cash flows generated by assets减值计提(Impairment recognized)Impairment loss=BV of Assets Fair Value of Assets(or PV of CFi)Reading 29 Income Taxes所得税费用(Income Tax expense)Income Tax Expense=Current Tax Payable+DTL DTA应交所得税(Tax payable)Curr
34、ent Tax Payable=Taxable Income Current tax rate递延所得税资产/负债(DTA or DTL)Temporary Difference Accounting Base Tax Base Future Tax rate所得税(Income Taxes)-基本公式所得税(Income Taxes)-税率变更调整税率调整后新递延所得税资产/负债(DTA or DTL)old DTA or DTLTemporary Difference()New Tax Rateold Tax rate税率调整带来的变化(DTA or DTL)DTA or DTL=New
35、DTA or DTL Old DTA or DTLReading 30 Non-current(Long-term)Liabilities长期负债初始确认金额(PV)FV=Par value,PMT=Coupon payments,IY=Effective market rate,N=N PV长期负债(Long-Term Liabilities)-初始确认长期负债(Long-Term Liabilities)-后续计量某年末长期负债金额(BVt)FV=Par value,PMT=Coupon payments,IY=Effective market rate,N=N t PVt(BVt)BVt
36、1+Interest expenset Coupon payments=BVt某年利息费用(Interest expenset)BVt1 Effective market rate某年支付利息(Coupon payments)Par value Coupon rate某年利息摊销(Bond amortization)Interest expense Coupon payments长期负债(Long-Term Liabilities)-终止确认提前赎回债券/提前还债提前赎回债券/提前还债损益Cash Paid BVt=GainLossCash PaidBVt Loss Cash PaidBVt
37、LossReading 30 Non-current(Long-term)Liabilities初始确认 Leased asset=Lease liability=the lower of FV of the leased asset or PV of lease payments后续计量Lease payableBeg+Interest expense lease payment=Lease payableEnd Interest expense=Lease payableBeg implicit interest rate承租人租赁(Lessee)-融资租赁(Finance Lease)承
38、租人租赁(Lessor)-融资租赁(Finance Lease)销售型融资租赁(Sale-type lease)直接融资租赁(Direct-financing type)初始确认Gross profit=Sales COGSI/SSales=PV of Lease payments COGS=Cost of assetNo revenue recognized后续计量I/SB/SLease Receivable=PV of lease paymentsLease Receivable=PV of lease paymentsInterest income=implicit interest r
39、ate Lease ReceivableBeg4PART 4 Corporate FinanceReading 34 Capital Budgeting作为投资决策标准的变量净现值（Net present value，NPV)=(1+)=1=after-tax cash flow at time t=required rate of return of the project=cash investment at time zeroDecision criterion:If NPV 0,then investIf NPV .Reading 35 Cost of capital纯玩法（The P
40、ure Play method）计算步骤Step 1:Select a comparable company(Company C).Step 2:Estimate Company Cs beta:L,.,Step 3:Unlever Company Cs beta:,=D.1+(1)Step 4:Lever the beta for target company(Company T)s financial risk:L,=,1+(1 )国家风险溢价（Country risk premium,CRP）=Reading 35 Cost of capital与资本成本估计相关的其他概念和公式资本结构
41、的边际成本（Marginal cost of capitalschedule）=%发行费用（Flotation costs）11=+=1 +00=flotation costs in monetary terms on a per share basis=the flotation cost as percentage of theissue priceReading 36 Measures of leverage经营杠杆水平（Degree of operating leverage,DOL）基本形式：%()DOL=%其中：=()P=unit price of a product=unit v
42、ariable cost of a product=quantity of a product=fixed costs of production,irrelevant to quantity produced对DOL基本形式作变形：DOL=(P)Reading 36 Measures of leverage财务杠杆水平（Degree of financial leverage,DFL）基本形式：%DFL=%对DFL基本形式作变形：Q (1 )Q DFL=(1 )=fixed financial costs(interest expense)总杠杆水平（Degree of total leve
43、rage，DTL）基本形式：%DTL=%DTL is the product of DOL and DFL.对DTL基本形式作变形：()DTL=Reading 37 Working capital management流动性测量指标汇总流动比率（Current ratio）速动比率+（Quick ratio）应收账款周转率（Accounts receivable(AR)turnover）Number of days in receivables=365 存货周转率（Inventory turnover）()Number of days of inventory=365 应付账款周转率（Acco
44、unts payable(AP)turnover）Number of days of payables=365 经营净周期 +（Net operating cycle）Reading 37 Working capital management短期投资品种收益率（Yield）公式汇总货币市场收益率（Money market yield）360债券等价收益率（Bond equivalent yield，BEY）365=face value=purchase price=number of days to maturity贴现基准收益率（Discount-basis yield）360短期借款成本（
45、Costs of borrowing）借款成本（Costs of borrowing）+应付账款管理（Management of accounts payable）贸易信贷成本（Costs of trade credit）365%1+11%5PART 5 Portfolio ManagementReading 39 Portfolio Risk and Return:Part 收益率的衡量(Measurements of Return)效用理论(Utility Theory)效用函数(Utility Function)=1 22:投资者的效用:风险厌恶系数持有期收益率(Holding Peri
46、od Return)+=100：资产期初价格：资产期末价格：股息（或者其他收入）算数平均收益率(Arithmetic Return)=1+2+3+1,2：每期的持有期收益率几何平均收益率 (Geometric Return,Time-weighted return)=1+1+1+-112货币加权收益率(Money-weighted Return,MWR,IRR)+1+2+=00(1+)1(1+)21+两个风险资产组合的收益(Return of portfolio with two risky assets)=11+1 1 21：资产1的权重1：资产1的收益率2：资产2的收益率两个风险资产组合的
47、风险(Risk of portfolio with two risky assets)1 12 2 =22+2 2+212 1,21 12 2=22+2 2+212121,2 1,2：资产1和2收益率的协方差1,2：资产1和2收益率的相关系数总体 ,=1 ,=;样本 ,=1 1，,=,.Reading 39 Portfolio Risk and Return:Part 无风险资产和单个风险资产组合的收益(Return of portfolio with risk-free asset and one risky asset)=+：风险资产的权重：风险资产的收益率：无风险资产的收益率无风险资产和
48、单个风险资产组合的风险(Risk of portfolio with risk-free asset and one risky asset)=：风险资产收益率的标准差=+资本配置线(Capital Allocation Line,CAL)Reading 39 Portfolio Risk and Return:Part 资本市场线(Capital Market Line,CML)=+：无风险收益率 ：市场的预期收益率：市场收益率的标准差贝塔值(Beta,)=,=2,2=,i,m：和的相关系数=,2=22：市场的贝塔值：投资组合的贝塔值：资产的市值占组合市值的比率,且=1=11Reading
49、40 Portfolio Risk and Return:Part 多因子模型(Multi-factor Model)=,1 1+,2 2+,：资产的超额收益率相对于某个因子的敏感性单因子模型(Single-index Model)=：市场的预期收益率市场模型(Market Model)=+：截距项：残差项Reading 40 Portfolio Risk and Return:Part 资本资产定价模型(Capital Asset Pricing Model)=+：资产的系统性风险夏普比率(Sharpe Ratio)=：投资组合的夏普比率、CAL的斜率：投资组合的总风险M-Squared(2
50、)2 =：市场组合的夏普比率Reading 40 Portfolio Risk and Return:Part 特雷诺指数(Treynor Ratio)=：投资组合的系统性风险詹森指数,(Jensens Alpha)=+6PART 6 Equity InvestmentReading 44 Market Organization and Structure杠杆头寸(Leveraged Position)名称名称公式公式杠杆比率（Leverage Ratio）Value of the PositionLeverage Ratio=Value of Equity Investment追加保证金价格
