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Cfa l1 exam formula & concepts sheet 2013
1.
AnalystBuddy is an
online CFA exam preparation provider, which will save you time and money. Access comprehensive StudyNotes, 1000’s of Practice Questions, Flash Cards, Mock Exams and more for just $69 per exam. Or try it now free.... Visit www.AnalystBuddy.com ©AnalystBuddy Pty Ltd All Rights Reserved. QUANTITATIVE METHODS Time Value of Money Basics • Future Value: FV = PV(1+I/Y)N • Present Value (PV): PV = FV/(1+I/Y)N current value of some future cash flow • Annuities: series of equal cash flows that occur at evenly spaced intervals over time. • Ordinary annuity: cash flow at end of period. • Perpetuities: annuities with infinite lives. PVperpetuity = PMT/(discount rate) Required Rate of Return Components 1. Real risk-free rate (RFR). 2. Expected inflation rate premium (IP). 3. Risk premium. Approximation formula for nominal required rate: 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: Variance and Standard Deviation Variance: average of squared deviations from mean. Standard Deviation: square root of variance. Holding Period Return (HPR) Coefficient of Variation Coefficient of variation (CV): expresses how much variation exists relative to mean of a distribution; allows for direct comparison of dispersion across different data sets. CV is calculated by dividing the SD of a distribution by the mean (or expected value) of the distribution: Sharpe Ratio Sharpe ratio: measures excess return per unit of risk. For both ratios, large is better. Expected Return/Standard Deviation Probabilistic variance: Standard Deviation: take square root of variance. Correlation and Covariance Correlation: covariance divided by the product of the two standard deviations. Expected return, variance of 2-stock portfolio: Normal Distributions Normal distribution is completely described by its mean and variance. 68% of observations fall within 90% fall within 95% fall within Computing Z-scores Z-score:“standardizes”observationfromnormal distribution; represents # of standard deviations a given observation is from population mean. Binomial Models Sampling Distribution Central Limit Theorem Standard Error Standard error of the sample mean is the standard deviation of the distribution of the sample means. Confidence Intervals Confidence interval: gives range of values the mean value will be between, with a given probability (say 90% or 95%). With a known variance, formula for a confidence interval is: (significance level 10%, 5% in each tail) (significance level 5%, 2.5% in each tail) Null Hypothesis (H0)(significance level 1%, 0.5% in each tail) Alternative Hypotheses: hypothesis the researcher wants to reject; the Alternative hypothesis (Ha) is actually tested; the basis for the selection of the tests statistics. Alternative hypothesis (Ha): concluded if there is sufficient evidence to reject the null hypothesis. One-tailed test: tests whether value is greater than or less than a given number. Two-tailed test: tests whether value is equal to a given number. One-tailed test: Two-tailed test: ettp rr ratiofirstsafetyRoy arg :' 0:0:0 aHversusH 0:0:0 aHversusH
2.
CFA L1 Exam
Formula & Concepts Sheet (2013) QUANTITATIVE METHODS continued… Type I and Type II Errors • Type I error: rejection of null hypothesis when it is actually true. • Type II error: failure to reject null. Technical Analysis Reversal patterns: head and shoulders, inverse H&S, double/trip top or bottom. Continuation patterns: triangles, rectangles, pennants, flags. Price-based indicators: moving averages, Bollinger bands, momentum oscillators (rate of change, RSI, stochastic, MACD). Sentiment indicators: opinion polls, put/call ratio, VIX, margin debt, short interest ratio. Flow of funds indicators: TRIN, margin debt, mutual fund cash position, new equity issuance, secondary offerings. ECONOMICS Inflation Inflation rate: rate of change in Consumer Price Index over given period of time. Unexpected inflation leads to uncertainty in the market and thus less economic growth Unemployment • Structural: unemployed workers do not have the skills to match newly created jobs. • Cyclical: recession phase of business cycle, economy producing at less than capacity. Labor Demand and Supply • A firm’s demand for labor is increased by: Increase in price of the firm’s output. • Increase in price of a productive input that that is a substitute to labor. • Decrease in price of a products that is a complement to labor. • The supply of labor is influenced by: • Substitution effect: increase in wage rate causes workers to substitute labor hours for leisure hours. • Income effect: increases in income increase worker’s demand for leisure. Schools of Macroeconomic Thought • Classical: shifts in AD and AS driven by technology changes; money changes adjust rapidly to restore equilibrium. • Keynesian: shifts in AD caused by changes in expectations; wages are “downward sticky”, use fiscal and monetary policy to increase AD and restore equilibrium. • Monetarist: monetary policy is the main factor leading to business cycles; central bank should increase money supply at predictable rate. Timing of Fiscal Policy Time Lags: (1) Recognition. (2) Administrative. (3) Impact. Automatic Stabilizers: Induced taxes. (2) Needs-tested spending Monetary Policy • Reserve requirements. • Open market operations—most used. • Discount rate. Elasticity of Demand If absolute value > 1, demand is elastic; if absolute value < 1, demand is inelastic; if absolute value = 1, demand is unit elastic. Price elasticity has two main determinants: • Availability of substitutes. • Share of budget spent on product. Elasticity of demand and supply is greater in the long run. On a straight-line demand curve, demand is more elastic at high prices/low quantities, and less elastic at low prices/high quantities. • Elastic range: price increase will decrease total revenues. • Inelastic range: price increase will increase total revenues. Accounting Costs vs. Economic Costs Accounting costs include firm’s explicit costs; economic costs include both explicit/implicit costs (opportunity cost of equity capital) Short run vs. long run: in short run, size of plant/ equipment cannot be changed. In a long run, all resources (costs) are available. Competitive Models Price taker accepts market price to sell product. Price searcher seeks price that maximizes profit. Pure competition: • Large number of independent firms. • All firms produce a homogenous product. • Each seller is small, relative to the market. • No barriers to entry. Monopolistic Competition: • Large number of independent firms. • Each firm produces a differentiated product. • Low barriers to entry. • Demand is highly elastic. Monopoly is a market where one firm sells a well- defined product that has no good substitutes and high entry barriers. Oligopoly is a similar structure but has a small number of firms. Any firm will maximize profits by expanding output until marginal revenue = marginal cost. Marginal Revenue Product If a firm uses an additional 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. FINANCIAL REPORTING AND ANALYSIS Revenue and Recognition Revenue Recognition Methods • Percentage-of-completion method. • Completed contract method. • Installment sales. • Cost recovery method. Unusual or Infrequent Items • Gains/losses from disposal of a business segment. • Gains/losses from sale of assets or investments in subsidiaries. AnalystBuddy is an online CFA exam preparation provider, which will save you time and money. Access comprehensive StudyNotes, 1000’s of Practice Questions, Flash Cards, Mock Exams and more for just $69 per exam. Or try it now free.... Visit www.AnalystBuddy.com ©AnalystBuddy Pty Ltd All Rights Reserved.
3.
FINANCIAL REPORTING AND
ANALYSIS continued... • Provisions for environmental remediation. • Impairments, write-offs, write-downs, and restructuring costs. • Integration expenses associated with businesses recently acquired. Extraordinary Items (U.S. GAAP only) Both unusual and infrequent (e.g., losses from expropriation of assets). IFRS does not allow extraordinary items. Discontinued Operations To be accounted for as a 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. Compute Cash Flows From Operations Direct method: start with cash collections (cash equivalent of sales); cash inputs (cash equivalent of cost of goods sold); cash operating expenses; cash interest expense; cash taxes. Indirect method: start with net income, subtracting back gains and adding back losses resulting from financing or investment cash flows, adding back all noncash charges, and adding and subtracting asset and liability accounts that result from operations. Free Cash Flow Free cash flow (FCF) measures cash available fordiscretionarypurposes.Itisequaltooperating cash flow less net capital expenditures. Critical Ratios Common-size financial statement analysis: • Common-size cash flow statement expresses each line item as a percentage of total cash inflows (outflows), or as a percentage of net revenue. Horizontal common-size financial statement analysis: Expresses each line item relative to its value in a common base period. Liquidity ratios: Receivables, inventory, payables turnover, and days’ supply ratios—all of which are used in the cash conversion cycle: Total asset, fixed asset, and working capital turnover ratios: Gross, operating, and net profit margins: Return of assets, [return on total capital (ROTC)]: Debt to equity ratio and total debt ratio: Interest coverage and fixed charge coverage: Liquidity ratios indicate company’s ability to pay its short-term liabilities. Operating performance ratios indicate how well management operates the business. DuPont Analysis Traditional DuPont equation: You may also see it presented as: Extended DuPont equation further decomposes net profit margin: You may also see it presented as: Inventory Accounting In periods of rising prices and stable or increasing inventory quantities. Higher COGS Lower COGS Lower gross profit Higher gross profit Lower inventory Higher inventory Basic and Diluted EPS Basic EPS calculation does not consider effects of any dilutive securities in computation of EPS: Therefore, diluted EPS is: Expensing: opposite effect Depreciation Double declining balance: AnalystBuddy is an online CFA exam preparation provider, which will save you time and money. Access comprehensive StudyNotes, 1000’s of Practice Questions, Flash Cards, Mock Exams and more for just $69 per exam. Or try it now free.... Visit www.AnalystBuddy.com ©AnalystBuddy Pty Ltd All Rights Reserved. RatioTurnoverPayables payablesofdaysofNumber 365 CapitalWorkingAverage venue TurnoverCapitalWorking Re venue IncomeNet inMofitNet Re argPr goutstandinsharescommon potentialplussharescommonavg.wtd. sharescommonforavail.incomeadj. EPSdiluted optionsstockfromissuableshares debtconv.conversionssh' ssh'pfdconv.ofconversionfromsharesssh'avgwtd interestdebteconvertibl dividendspfdeconvertibldivpfd-incomenet t1
4.
CFA L1 Exam
Formula & Concepts Sheet (2013) FINANCE REPORTING AND ANALYSIS continued... Units of Production: Revaluation of Long-Lived Assets IFRS: revaluation gain recognized in net income only to the extent it reverses previously recognized impairment loss; further gains recognized in equity as revaluation surplus. U.S. GAAP: revaluation is not permitted. Deferred Taxes • Created when taxable income (on tax return) ≠ pretax income (on financial statements) due to temporary differences. • Deferred tax liabilities are created when taxable income < pretax income. Treat DTL as equity if not expected to reverse. • Deferred tax assets are created when taxable income > pretax income. Must recognize valuation allowance if more likely than not that DTA will not be realized. Long-Term Liabilities • Premium bond: coupon rate > market rate at issuance. • Discount bond: coupon rate < market rate at issuance. • Interest expense equals book value at the beginning of the year multiplied by the market rate of interest at the time the bonds were issued. Leases Financial statement/ratio impact of lease accounting from the lessee perspective: capital leases results in: • Higher: assets, liabilities, CFO, debt/equity. Same: total cash flow. Cost of Equity Capital Cost of Equity using CAPM: Capital Budgeting Pure-Play Method Project Beta Delivered asset beta for comparable company: Relevered project beta for subject firm: Measures of Leverage Total leverage: percent change in net income from a given percent change in sales. Financial leverage: percent change in net income from a given percent change in EBIT. Dividends and Shares Repurchases Cash dividend and share repurchase have same effect on shareholder wealth. Share repurchase with borrowed funds will increase EPS if cost of debt < earnings yield, decrease EPS if cost of debt > earnings yield. Share repurchase will increase book value per share if stock price < BVPS, decrease book value per share if stock price > BVPS. Working Capital Management Primary sources of liquidity: cash balances Corporate Governance Favor shareholder interests: independent board, strong code of ethics, confidential voting. Harm shareholder interests: management- aligned board, voting restrictions, takeover defenses. PORTFOLIO MANAGEMENT Combining Preferences with the Optimal Set of Portfolios Markowitz efficient frontier is the set of portfolios that have highest return for given level of risk. Security Market Line (SML) Investors should only be compensated for risk relative to market. Unsystematic risk is diversified away; investors are compensated for systematic risk. The equation of the SML is the CAPM, which is a return/systematic risk equilibrium relationship. The SML and Equilibrium Identifying mispriced stocks: Consider 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. AnalystBuddy is an online CFA exam preparation provider, which will save you time and money. Access comprehensive StudyNotes, 1000’s of Practice Questions, Flash Cards, Mock Exams and more for just $69 per exam. Or try it now free.... Visit www.AnalystBuddy.com ©AnalystBuddy Pty Ltd All Rights Reserved. Pensions Defined contribution: employer contribution expensed in period incurred. Defined benefit: overfunded plan recognized as asset, underfunded plan recognized as liability. Balance sheet value equals funded status of plan under U.S. GAAP but not under IFRS. Marketable Security Classifications Held-for-trading: fair value on balance sheet; dividends, interest, realized and unrealized G/L is other comprehensive income. Available-for-sale: fair value on balance sheet; dividends, interest, realized G/L recognized on income statement; unrealized G/L is other comprehensive income. Held-to-maturity: amortized cost on balance sheet; interest, realized G/L recognized on income statement. Incorporate Investments • 20% ownership: no significant influence; use accounting methods for passive investments. • 20% to 50% ownership: significant influence; use equity method. • Joint control: proportionate consolidation permitted under IFRS only, equity method usually required under U.S. GAAP. • 50% ownership: control of investee; use consolidation method. CORPORATE FINANCE Weighted Average Cost of Capital Cost of Preferred Stock
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CFA L1 Exam
Formula & Concepts Sheet (2013) Risk Adjusted Returns Sharpe ratio and M-squared measure excess return per unit of total risk. Treynor measure and Jensen’s alpha measure excess return per unit of systematic risk. EQUITY INVESTMENTS Well-Functioning Security Markets • Operational efficiency (lowest possible transaction costs). • Informational efficiency (prices rapidly adjust to new information). Margin Purchases For margin transactions: • Leverage factor = 1/margin percentage. • Levered return = HPR x leverage factor. Margin Call Price Computing Index Prices Value weighted-Index Types of Orders Execution instructions: how to trade; e.g., market orders, limit orders. Validity instructions: when to execute; e.g., stop orders, day orders, fill-or-kill orders. Clearing instructions: how to clear and settle; for sell orders, specify short sale or long sale. Five Competitive Forces 1. Rivalry among existing competitors. 2. Threat of new entrants. 3. Threat of substitute products. 4. Bargaining power of buyers. 5. Bargaining power of suppliers. One-Period Valuation Model Be sure to use expected dividend in calculation. Infinite Period Dividend Discount Model Supernormal growth model (multi-stage) DDM: Constant growth model: Critical relationship • As difference between and widens, value of stock falls. • As difference between and narrows, value of stock rises. • Small changes in difference between ke and gc cause large changes in stock’s value. • Stock pays dividends; constant growth rate. • Constant growth rate, gc never changes. • ke must be greater than gc (or math will not work). Earnings Multiplier Model • Indenture. Agreement containing the terms under which money is borrowed. • Term to Maturity. Length of time until loan contract or agreement expires. • Par value. Amount borrower promises to pay on or before maturity date of the issue. AnalystBuddy is an online CFA exam preparation provider, which will save you time and money. Access comprehensive StudyNotes, 1000’s of Practice Questions, Flash Cards, Mock Exams and more for just $69 per exam. Or try it now free.... Visit www.AnalystBuddy.com ©AnalystBuddy Pty Ltd All Rights Reserved. Market Structures Quote-driven markets: investors trade with dealers. Order-driven markets: buyers and sellers matched by rules. Brokered markets: brokers find counterparties. Forms of EMH • Weak form. Current stock prices fully reflect available security market info. Volume information/ past price do not relate to future direction of security prices. Investor cannot achieve excess returns using tech analysis. • Semi-strong form. Security prices instantly adjust to new public information. Investor cannot achieve excess returns using fundamental analysis. • Strong form. Stock prices fully reflect all information from public and private sources. Assumes perfect markets in which all information is cost free and available to everyone at the same time. Even with inside info, investor cannot achieve excess returns. Industry Life Cycle Stages Embryonic: slow growth, high prices, large investment needed, high risk of failure. Growth: rapid growth, falling prices, limited competition, increasing profitability. Shakeout: slower growth, intense competition, declining profitability, cost cutting, weaker firms fail or merge. Mature: slow growth, consolidation, stable prices, high barriers to entry. Decline: negative growth, declining prices, consolidation. %marginemaintenanc- %margininitial- 1 1Po
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CFA L1 Exam
Formula & Concepts Sheet (2013) Repayment/Prepayment Provisions • Bullet bonds. Lump sum at maturity pays entire principal. • Serial bonds. Pay off principal through series of payments over time. • Amortizing securities. Periodic principal and interest payments. • Sinking fund provisions. Provide for bond retirement through predefined principal payments over life of the issue. • Call provisions. Issuer has right (but not obligation) to retire all or part of issue prior to maturity. Issuer owns option to call the bonds away from investor. • Refunding provisions. Nonrefundable bonds prohibit premature retirement of an issue from proceeds of a lower coupon bond. Bonds that carry these provisions can be freely callable but nonrefundable. Basics of Floating Rate Bonds • These securities pay variable rate of interest. • Common procedure for setting coupon rates on floating-rate bonds starts with reference rate; then adds/subtracts a stated margin. Interest Rate Risk Key point: there is an inverse relationship between interest rates and bond prices. How bond’s feature affect interest rate risk: • Longer maturity bonds. Higher interest rate risk (all else same) • Smaller coupon bonds. Higher interest rate risk (all else same). • Discount at constant rate applied to all cash flows (YTM) to find all future cash flows’ PV. • Treat each cash flows as a single zero- coupon bond and find PV of each “zero” using appropriate spot rates for each cash flow. Price must be the same to prevent arbitrage. Accrued Interest and Clean Prices Bond price without accrued interest is clean price. Full price includes accrued interest. Yield Calculations Annual Equivalent Yield Converting a bond-equivalent yield (BEY) to an equivalent annual yield (EAY) or vice versa: Spot Rates To derive a bond’s value using spot rates, discount the individual cash flows at appropriate for each flow’s time horizon; sum PV of the cash flows to get bond’s current value. This value is the arbitrage-free value. Duration and Convexity Duration is the slope of a bond’s price yield function. It is steeper at low interest rates, flatter at high interest rates. So, duration (interest rate • Convexity is a measure of degree of curvature or convexity in the price/yield relationship. Convexity accounts for amount of error in estimated price (based on duration). • Expectations analysis. Yield curve shape reflects investor expectations about future behavior of short-term interest rates. Forward rates computed using today’s spot rates are best guess of future interest rates. • Liquidity preference theory. Investors prefer greater liquidity; will demand premium (higher yields to invest in longer-term issues). • Market segmentation theory. Market for debt securities is segmented on basis of investor maturity preferences. Each segment’s interest rate level is determined by supply/ demand. • Credit rating of the issue is different from the credit rating of the corporate • Ratings from rating agencies are updated less frequently that makes them less reliable • Charater, Collateral, Capacity or Covenants • Economic factors & Stock Fundamentals affects spread volatility AnalystBuddy is an online CFA exam preparation provider, which will save you time and money. Access comprehensive StudyNotes, 1000’s of Practice Questions, Flash Cards, Mock Exams and more for just $69 per exam. Or try it now free.... Visit www.AnalystBuddy.com ©AnalystBuddy Pty Ltd All Rights Reserved. • If market interest rates are high, price volatility will be lower than if market interest rates are low. Floating rate securities have very low levels of price volatility in relation to interest rate changes. Reinvestment Risk If interest rates decline, investors are forced to reinvest at lower yields. Bonds with high coupons have greater risk. Greatest risk is with callable bonds, where all/ part of principal can be repaid in low interest rate environment. Credit Risk • Default risk. Issuer may not take payments. • Credit spread risk. Difference in bond’s yield from yield on risk-free security. All else equal, the riskier the bond, the higher the spread. • Downgrade risk. Bond may be reclassified as riskier security by a major rating agency. Basic Bond Pricing To value a semi-annual pay bond using a financial calculator: There are two equivalent ways to price a bond:
7.
CFA L1 Exam
Formula & Concepts Sheet (2013) DERIVATIVES Futures vs. Forwards Arbitrage • Law of one price: two assets with identical cash flows in the future, regardless of future events, should have the same price. If A and B have identical future payoffs, and A is priced lower than B, buy A and sell B. • Second type of arbitrage: two assets with uncertain returns can be combined in a portfolio that have a certain payoff. If a portfolio of A and B has a certain payoff, the portfolio should yield the risk-free rate. Forward Contracts • Long must pay a certain amount at specific future date to short, who will deliver the underlying asset. • A cash settlement forward does not require actual delivery of the underlying asset, but a cash payment to the party disadvantaged by the difference between market price of the asset and contract price at settlement date. • Early termination can be achieved by entering into a new forward contract with the opposite position, at the then-current expected future price. This will fix the amount of payment to be made/received at settlement date. Each security in the put-call parity relationship can be expressed as: • Buyer of a call option—long position. • Writer (seller) of a call option—short position. • Buyer of a put option—long position. • Writer (seller) of a call option—short position. intrinsic value of a call option = Max[0,S-X] intrinsic value of a put option = Max[0,X-S] ALTERNATIVE INVESTMENTS Features of Alternative investments Significance for Portfolio Management Risk Management • Valuation methods: cost method, sales comparison method, and income method. • Income method uses a discounted cash flow model similar to that of a perpetuity: • Net operating income (NOI) equals gross operating income less estimated vacancy, collections, and other operating expenses, (including property taxes, but excluding income taxes. NOI does not include depreciation or financing costs. • Illiquidity. • Potential for mispricing. Investments in esoteric, infrequently traded securities may lead to difficulty determining true value. • Counterparty credit risk. • Short covering. Risk that managers who short sell as a strategy will have to cover their shorts and repurchase securities at price higher than where they original sold. • Margin calls. Can result in forced selling of assets, possibly at a loss, on an already highly leveraged position. • Price return: due to change in futures price. • Roll yield: positive for backwardation, negative for contango. AnalystBuddy is an online CFA exam preparation provider, which will save you time and money. Access comprehensive StudyNotes, 1000’s of Practice Questions, Flash Cards, Mock Exams and more for just $69 per exam. Or try it now free.... Visit www.AnalystBuddy.com ©AnalystBuddy Pty Ltd All Rights Reserved. Forward Rate Agreements (FRA) Can be viewed as a forward contract to borrow/ lend money at a certain rate at some future date. Formula for payment to the long at settlement is: Futures vs. Forwards Forwards Private contracts Unique contracts Default risk Futures Exchange –traded Standardized contracts Guaranteed by clearinghouse American vs. European Options American options let the owner exercise the option any time before or at expiration. European options can be exercised only at expiration. Value of the American option will equal/exceed value of the European option. Lower and Upper Bounds for Options Note: t=time to expiration. Put-Call Parity Put-call parity holds that portfolios with identical payoffs must sell for the same price to prevent arbitrage. The put-call parity relationship: European call (c) American call (C) European put (p) American put (P) Option Minimum Maximum Value Value
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