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• Present Value (PV): PV = FV/(1+I/Y)Ncurrent value of some future cash fl ow
• Annuities: series of equal cash fl ows thatoccur at evenly spaced intervals over time.
• Ordinary annuity: cash fl ow at end of period.
• Perpetuities: annuities with infi nite lives.PVperpetuity = PMT/(discount rate)
Required Rate of Return Components1. Real risk-free rate (RFR).
2. Expected infl ation rate premium (IP).
3. Risk premium.Approximation formula for nominal requiredrate:
MeansArithmetic mean: sum of all observationvalues in sample/population, divided by # ofobservations.Geometric mean: used when calculatinginvestment returns over multiple periods or tomeasure compound growth rates.Geometric mean return:
Variance and Standard DeviationVariance: average of squared deviations frommean.
Standard Deviation: square root of variance.
Holding Period Return (HPR)
Coeffi cient of VariationCoeffi cient of variation (CV): expresses howmuch variation exists relative to mean of adistribution; allows for direct comparison ofdispersion across different data sets. CV iscalculated by dividing the SD of a distribution bythe mean (or expected value) of the distribution:
Sharpe RatioSharpe ratio: measures excess return per unitof risk.
For both ratios, large is better.
Expected Return/Standard Deviation
Probabilistic variance:
Standard Deviation: take square root ofvariance.
Correlation and CovarianceCorrelation: covariance divided by the productof the two standard deviations.
Expected return, variance of 2-stock portfolio:
Normal DistributionsNormal distribution is completely described byits mean and variance.68% of observations fall within90% fall within95% fall within
Computing Z-scoresZ-score: “standardizes” observation from normaldistribution; represents # of standard deviationsa given observation is from population mean.
Binomial Models
Sampling Distribution
Central Limit Theorem
Standard ErrorStandard error of the sample mean is thestandard deviation of the distribution of thesample means.
Confi dence IntervalsConfi dence interval: gives range of valuesthe mean value will be between, with a givenprobability (say 90% or 95%). With a knownvariance, formula for a confi dence interval is:
(signifi cance level 10%, 5% in each tail)
(signifi cance level 5%, 2.5% in each tail)
Null Hypothesis (H0)(signifi cance level 1%,0.5% in each tail)Alternative Hypotheses: hypothesis theresearcher wants to reject; the Alternativehypothesis (Ha) is actually tested; the basis forthe selection of the tests statistics. Alternativehypothesis (Ha): concluded if there is suffi cientevidence to reject the null hypothesis.
One-tailed test: tests whether value is greaterthan or less than a given number.Two-tailed test: tests whether value is equal toa given number.One-tailed test:Two-tailed test:
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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 AnalysisReversal patterns: head and shoulders, inverseH&S, double/trip top or bottom.Continuation patterns: triangles, rectangles,pennants, fl ags.Price-based indicators: moving averages,Bollinger bands, momentum oscillators (rate ofchange, RSI, stochastic, MACD).Sentiment indicators: opinion polls, put/callratio, VIX, margin debt, short interest ratio.Flow of funds indicators: TRIN, margin debt,mutual fund cash position, new equity issuance,secondary offerings.
ECONOMICSInfl ationInfl ation rate: rate of change in Consumer PriceIndex over given period of time. Unexpectedinfl ation leads to uncertainty in the market andthus less economic growth
Unemployment
• Structural: unemployed workers do nothave the skills to match newly created jobs.
• Cyclical: recession phase of business cycle,economy producing at less than capacity.
Labor Demand and Supply• A fi rm’s demand for labor is increased by:Increase in price of the fi rm’s output.
• Increase in price of a productive input thatthat is a substitute to labor.
• Decrease in price of a products that is acomplement to labor.
• The supply of labor is infl uenced by:• Substitution effect: increase in wage rate
causes workers to substitute labor hours forleisure hours.
• Income effect: increases in income increaseworker’s demand for leisure.
Schools of Macroeconomic Thought• Classical: shifts in AD and AS driven by
technology changes; money changes adjustrapidly to restore equilibrium.
• Keynesian: shifts in AD caused by changesin expectations; wages are “downwardsticky”, use fi scal and monetary policy toincrease AD and restore equilibrium.
• Monetarist: monetary policy is the mainfactor leading to business cycles; centralbank should increase money supply atpredictable rate.
Timing of Fiscal PolicyTime Lags:(1) Recognition. (2) Administrative.(3) Impact.
• Reserve requirements.• Open market operations—most used.• Discount rate.
Elasticity of DemandIf absolute value > 1, demand is elastic; ifabsolute value < 1, demand is inelastic; ifabsolute value = 1, demand is unit elastic. Priceelasticity has two main determinants:• Availability of substitutes.• Share of budget spent on product.Elasticity of demand and supply is greater in thelong run.On a straight-line demand curve, demand ismore elastic at high prices/low quantities, andless 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 CostsAccounting costs include fi rm’s explicit costs;economic costs include both explicit/implicitcosts (opportunity cost of equity capital)Short run vs. long run: in short run, size of plant/equipment cannot be changed. In a long run, allresources (costs) are available.
Competitive ModelsPrice taker accepts market price to sell product.Price searcher seeks price that maximizesprofi t.Pure competition:• Large number of independent fi rms.• All fi rms produce a homogenous product.• Each seller is small, relative to the market.• No barriers to entry.
Monopolistic Competition:• Large number of independent fi rms.
• Each fi rm produces a differentiated product.• Low barriers to entry.
• Demand is highly elastic.
Monopoly is a market where one fi rm sells a well-defi ned product that has no good substitutesand high entry barriers. Oligopoly is a similarstructure but has a small number of fi rms.
Any fi rm will maximize profi ts by expandingoutput until marginal revenue = marginal cost.
Marginal Revenue ProductIf a fi rm uses an additional of an input, increasein output is marginal product (MP) of last unitof resource employed. Increase in revenuefrom producing/selling marginal product isthe marginal revenue product (MRP). Profi tmaximizing fi rms will increase use of eachresource until MRP = price of the resource.
Unusual or Infrequent Items• Gains/losses from disposal of a business
segment.• Gains/losses from sale of assets or
investments in subsidiaries.
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FINANCIAL REPORTING AND ANALYSIScontinued...• 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 fromexpropriation of assets). IFRS does not allowextraordinary items.
Discontinued OperationsTo be accounted for as a discontinued operation,a business—assets, operations, investing,fi nancing activities—must be physically/operationally distinct from rest of fi rm. Income/losses are reported net of tax after net incomefrom continuing operations.
Compute Cash Flows From OperationsDirect method: start with cash collections(cash equivalent of sales); cash inputs (cashequivalent of cost of goods sold); cash operatingexpenses; cash interest expense; cash taxes.Indirect method: start with net income,subtracting back gains and adding backlosses resulting from fi nancing or investmentcash fl ows, adding back all noncash charges,and adding and subtracting asset and liabilityaccounts that result from operations.
Free Cash FlowFree cash fl ow (FCF) measures cash availablefor discretionary purposes. It is equal to operatingcash fl ow less net capital expenditures.
Critical RatiosCommon-size fi nancial statement analysis:
• Common-size cash fl ow statementexpresses each line item as a percentageof total cash infl ows (outfl ows), or as apercentage of net revenue.
Horizontal common-size fi nancial statementanalysis:Expresses each line item relative to its value ina common base period.Liquidity ratios:
Receivables, inventory, payables turnover, anddays’ supply ratios—all of which are used in thecash conversion cycle:
Total asset, fi xed asset, and working capitalturnover ratios:
Gross, operating, and net profi t margins:
Return of assets, [return on total capital(ROTC)]:
Debt to equity ratio and total debt ratio:
Interest coverage and fi xed charge coverage:
Liquidity ratios indicate company’s ability to payits short-term liabilities.Operating performance ratios indicate how wellmanagement operates the business.
DuPont AnalysisTraditional DuPont equation:
You may also see it presented as:
Extended DuPont equation further decomposesnet profi t margin:
You may also see it presented as:
Inventory AccountingIn periods of rising prices and stable orincreasing inventory quantities.
Higher COGS Lower COGSLower gross profi t Higher gross profi tLower inventory Higher inventory
Basic and Diluted EPSBasic EPS calculation does not consider effectsof any dilutive securities in computation of EPS:
Therefore, diluted EPS is:
Expensing: opposite effect
Depreciation
Double declining balance:
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CFA L1 Exam Formula & Concepts Sheet (2013)FINANCE REPORTING AND ANALYSIScontinued...Units of Production:
Revaluation of Long-Lived AssetsIFRS: revaluation gain recognized in netincome only to the extent it reverses previouslyrecognized impairment loss; further gainsrecognized in equity as revaluation surplus.U.S. GAAP: revaluation is not permitted.
Deferred Taxes• Created when taxable income (on tax return)
≠ pretax income (on fi nancial statements)due to temporary differences.
• Deferred tax liabilities are created whentaxable income < pretax income. Treat DTLas equity if not expected to reverse.
• Deferred tax assets are created whentaxable income > pretax income. Mustrecognize valuation allowance if more likelythan not that DTA will not be realized.
at issuance.• Discount bond: coupon rate < market rate at
issuance.• Interest expense equals book value at
the beginning of the year multiplied by themarket rate of interest at the time the bondswere issued.
LeasesFinancial statement/ratio impact of leaseaccounting from the lessee perspective: capitalleases results in:• Higher: assets, liabilities, CFO, debt/equity.
Same: total cash fl ow.
Cost of Equity Capital
Cost of Equity using CAPM:
Capital Budgeting
Pure-Play Method Project BetaDelivered asset beta for comparable company:
Relevered project beta for subject fi rm:
Measures of LeverageTotal leverage: percent change in net incomefrom a given percent change in sales.Financial leverage: percent change in netincome from a given percent change in EBIT.
Dividends and Shares RepurchasesCash dividend and share repurchase havesame effect on shareholder wealth.Share repurchase with borrowed funds willincrease EPS if cost of debt < earnings yield,decrease EPS if cost of debt > earnings yield.Share repurchase will increase book value pershare if stock price < BVPS, decrease bookvalue per share if stock price > BVPS.
Combining Preferences with the OptimalSet of PortfoliosMarkowitz effi cient frontier is the set of portfoliosthat have highest return for given level of risk.
Security Market Line (SML)Investors should only be compensated forrisk relative to market. Unsystematic risk isdiversifi ed away; investors are compensatedfor systematic risk. The equation of the SMLis the CAPM, which is a return/systematic riskequilibrium relationship.
The SML and EquilibriumIdentifying 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.
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PensionsDefi ned contribution: employer contributionexpensed in period incurred.Defi ned benefi t: overfunded plan recognized asasset, underfunded plan recognized as liability.Balance sheet value equals funded status ofplan under U.S. GAAP but not under IFRS.
Marketable Security Classifi cationsHeld-for-trading: fair value on balance sheet;dividends, interest, realized and unrealized G/Lis other comprehensive income.Available-for-sale: fair value on balance sheet;dividends, interest, realized G/L recognizedon income statement; unrealized G/L is othercomprehensive income.Held-to-maturity: amortized cost on balancesheet; interest, realized G/L recognized onincome statement.
Incorporate Investments• 20% ownership: no signifi cant infl uence;
• Joint control: proportionate consolidationpermitted under IFRS only, equity methodusually required under U.S. GAAP.
• 50% ownership: control of investee; useconsolidation method.
CORPORATE FINANCE
Weighted Average Cost of Capital
Cost of Preferred Stock
CFA L1 Exam Formula & Concepts Sheet (2013)Risk Adjusted ReturnsSharpe ratio and M-squared measure excessreturn per unit of total risk.Treynor measure and Jensen’s alpha measureexcess return per unit of systematic risk.
EQUITY INVESTMENTSWell-Functioning Security Markets• Operational effi ciency (lowest possible
Types of OrdersExecution instructions: how to trade; e.g.,market orders, limit orders.Validity instructions: when to execute; e.g., stoporders, day orders, fi ll-or-kill orders.Clearing instructions: how to clear and settle;for sell orders, specify short sale or long sale.
Five Competitive Forces1. 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.Infi nite Period Dividend Discount ModelSupernormal 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 andgc 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 termsunder which money is borrowed.
• Term to Maturity. Length of time until loancontract or agreement expires.
• Par value. Amount borrower promises topay on or before maturity date of the issue.
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Market StructuresQuote-driven markets: investors trade withdealers.Order-driven markets: buyers and sellersmatched by rules.Brokered markets: brokers fi nd counterparties.
Forms of EMH• Weak form. Current stock prices fully refl ect
available security market info. Volumeinformation/ past price do not relate to futuredirection of security prices. Investor cannotachieve excess returns using tech analysis.
• Semi-strong form. Security prices instantlyadjust to new public information. Investorcannot achieve excess returns usingfundamental analysis.
• Strong form. Stock prices fully refl ect allinformation from public and private sources.Assumes perfect markets in which allinformation is cost free and available toeveryone at the same time. Even with insideinfo, investor cannot achieve excess returns.
Industry Life Cycle StagesEmbryonic: slow growth, high prices, largeinvestment needed, high risk of failure.Growth: rapid growth, falling prices, limitedcompetition, increasing profi tability.Shakeout: slower growth, intense competition,declining profi tability, cost cutting, weaker fi rmsfail or merge.Mature: slow growth, consolidation, stableprices, high barriers to entry.Decline: negative growth, declining prices,consolidation.
%marginemaintenanc-
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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 predefi ned principalpayments over life of the issue.
• Call provisions. Issuer has right (but notobligation) to retire all or part of issue priorto maturity. Issuer owns option to call thebonds away from investor.
• Refunding provisions. Nonrefundablebonds prohibit premature retirement of anissue from proceeds of a lower couponbond. Bonds that carry these provisions canbe freely callable but nonrefundable.
Basics of Floating Rate Bonds• These securities pay variable rate of
interest.• Common procedure for setting coupon rates
on fl oating-rate bonds starts with referencerate; then adds/subtracts a stated margin.
Interest Rate RiskKey point: there is an inverse relationshipbetween interest rates and bond prices.How bond’s feature affect interest rate risk:• Longer maturity bonds. Higher interest rate
• Discount at constant rate applied to all cashfl ows (YTM) to fi nd all future cash fl ows’ PV.
• Treat each cash fl ows as a single zero-coupon bond and fi nd PV of each “zero”using appropriate spot rates for each cashfl ow.
Price must be the same to prevent arbitrage.
Accrued Interest and Clean PricesBond price without accrued interest is cleanprice. Full price includes accrued interest.
Yield Calculations
Annual Equivalent Yield
Converting a bond-equivalent yield (BEY) to anequivalent annual yield (EAY) or vice versa:
Spot RatesTo derive a bond’s value using spot rates,discount the individual cash fl ows at appropriatefor each fl ow’s time horizon; sum PV of the cashfl ows to get bond’s current value. This value isthe arbitrage-free value.Duration and ConvexityDuration is the slope of a bond’s price yieldfunction. It is steeper at low interest rates, fl atterat high interest rates. So, duration (interest rate
•Convexity is a measure of degree of curvatureor convexity in the price/yield relationship.Convexity accounts for amount of error inestimated price (based on duration).
• Expectations analysis. Yield curve shaperefl ects investor expectations about futurebehavior of short-term interest rates.Forward rates computed using today’s spotrates are best guess of future interest rates.
• Liquidity preference theory. Investors prefergreater liquidity; will demand premium(higher yields to invest in longer-termissues).
• Market segmentation theory. Market for debtsecurities is segmented on basis of investormaturity preferences. Each segment’sinterest rate level is determined by supply/demand.
• Credit rating of the issue is different from thecredit rating of the corporate
• Ratings from rating agencies are updatedless frequently that makes them less reliable
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• If market interest rates are high, pricevolatility will be lower than if market interestrates are low.
Floating rate securities have very low levelsof price volatility in relation to interest ratechanges.
Reinvestment RiskIf interest rates decline, investors are forced toreinvest 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 interestrate 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 elseequal, the riskier the bond, the higher thespread.
• Downgrade risk. Bond may be reclassifi edas riskier security by a major rating agency.
Basic Bond PricingTo value a semi-annual pay bond using a
fi nancial calculator:
There are two equivalent ways to price a bond:
CFA L1 Exam Formula & Concepts Sheet (2013)DERIVATIVES
Futures vs. Forwards
Arbitrage• Law of one price: two assets with identical
cash fl ows in the future, regardless of futureevents, should have the same price. If Aand B have identical future payoffs, and A ispriced lower than B, buy A and sell B.
• Second type of arbitrage: two assets withuncertain returns can be combined in aportfolio that have a certain payoff. If aportfolio of A and B has a certain payoff, theportfolio should yield the risk-free rate.
Forward Contracts• Long must pay a certain amount at specifi c
future date to short, who will deliver theunderlying asset.
• A cash settlement forward does not requireactual delivery of the underlying asset, but acash payment to the party disadvantaged bythe difference between market price of theasset and contract price at settlement date.
• Early termination can be achieved by enteringinto a new forward contract with the oppositeposition, at the then-current expected futureprice. This will fi x the amount of payment tobe made/received at settlement date.
Each security in the put-call parity relationshipcan 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 INVESTMENTSFeatures of Alternative investments
Signifi cance for Portfolio Management
Risk Management
• Valuation methods: cost method, salescomparison method, and income method.
• Income method uses a discounted cash fl owmodel similar to that of a perpetuity:
• Net operating income (NOI) equals grossoperating income less estimated vacancy,collections, and other operating expenses,(including property taxes, but excludingincome taxes. NOI does not includedepreciation or fi nancing costs.
• Illiquidity.• Potential for mispricing. Investments
in esoteric, infrequently traded securities maylead to diffi culty determining true value.• Counterparty credit risk.
• Short covering. Risk that managers whoshort sell as a strategy will have to cover theirshorts and repurchase securities at pricehigher than where they original sold.
• Margin calls. Can result in forced selling ofassets, possibly at a loss, on an alreadyhighly leveraged position.
• Price return: due to change in futures price.• Roll yield: positive for backwardation,
negative for contango.
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Forward Rate Agreements (FRA)Can be viewed as a forward contract to borrow/lend money at a certain rate at some futuredate. Formula for payment to the long atsettlement is:
Futures vs. ForwardsForwardsPrivate contractsUnique contractsDefault riskFuturesExchange –tradedStandardized contractsGuaranteed by clearinghouseAmerican vs. European OptionsAmerican options let the owner exercisethe option any time before or at expiration.European options can be exercised only atexpiration. Value of the American option willequal/exceed value of the European option.Lower and Upper Bounds for Options
Note: t=time to expiration.Put-Call ParityPut-call parity holds that portfolios with identicalpayoffs must sell for the same price to preventarbitrage. The put-call parity relationship:
