2018 CFA Level 1 Quicksheet.pdf

C r i t i c a l C o n c e pt s for t he 2018 CFA® E x a md ETHICAL AND PROFESSIONAL Approximation formula for nominal required rate: Expected return, variance o f 2-stock portfolio: ^ STANDARDS ___________________________________________________________________________________________________________ E(R) = RFR + IP + RP E ( R P) = w a E(R a ) + w b E(Rb) Means I Professionalism Arithmetic mean: sum of all observation values in 1(A) Knowledge of the Law. Var( R p) = WAa 2 (R a ) + W2B<72 ( R b ) sample/population, divided by # of observations. 1(B) Independence and Objectivity. + 2 w a w b <t (R a ) ^ ( R b ) p ( r a -r b ) 1(C) Misrepresentation. Geometric mean: used when calculating investment 1(D) Misconduct. returns over multiple periods or to measure Normal Distributions II Integrity of Capital Markets compound growth rates. Normal distribution is completely described by its 11(A) Material Nonpublic Information. Geometric mean return: mean and variance. 11(B) Market Manipulation. 68% of observations fall within ± la . Rc= (1 + R,)x...x(l + RN) P - 1 III Duties to Clients 90% fall within ± 1.65a. III (A) Loyalty, Prudence, and Care. N 95% fall within ± 1.96a. III(B) Fair Dealing. harmonic mean = N Jl^ 99% fall within ± 2.58a. III(C) III(D) Suitability. Performance Presentation. E i=i .5 c , V 1 Computing Z-Scores III(E) Preservation of Confidentiality. Z-score: “standardizes” observation from normal IV Duties to Employers Variance and Standard Deviation distribution; represents # of standard deviations a IV(A) Loyalty. Variance: average of squared deviations from mean. given observation is from population mean. IV(B) Additional Compensation Arrangements. !>.—u N IV(C) Responsibilities of Supervisors. observation —population mean x —/x P)' z= V Investment Analysis, Recommendations, 2 standard deviation <7 and Actions population variance = cr = — ------ N Binomial Models V(A) Diligence and Reasonable Basis. V(B) Communication with Clients and n Binomial distribution: assumes a variable can take Prospective Clients. one of two values (success/failure) or, in the case of x)2 V(C) Record Retention. a stock, movements (up/down). A binomial model VI Conflicts of Interest sample variance - s2- i=i n —1 can describe changes in the value of an asset or VI (A) Disclosure of Conflicts. portfolio; it can be used to compute its expected VI(B) Priority of Trans actio ns. Standard deviation: square root of variance. value over several periods. VI (C) Referral Fees. H olding Period Return (HPR) VII Responsibilities as a CFA Institute Sampling Distribution P , - P ^ + D, + Sampling distribution: probability distribution of Member or CFA Candidate VII(A) Conduct as Participants in CFA Institute P.-i P«-i all possible sample statistics computed from a set of Programs. equal-size samples randomly drawn from the same Coefficient o f Variation VII(B) Reference to CFA Institute, the CFA population. The sampling distribution o f the mean is Designation, and the CFA Program. Coefficient o f variation (CV): expresses how much the distribution of estimates of the mean. dispersion exists relative to mean of a distribution; Global Investment Performance Standards Central Limit Theorem allows for direct comparison of dispersion across (GIPS®) Central lim it theorem: when selecting simple different data sets. CV is calculated by dividing • Compliance statement: “ [Insert name of firm] has standard deviation of a distribution by the mean or random samples of size n from population with prepared and presented this report in compliance expected value of the distribution: mean p, and finite variance a 2, the sampling with the Global Investment Performance distribution of sample mean approaches normal Standards (GIPS).” Compliance must be applied cv = 4 probability distribution with mean |i and variance on a firm-wide basis. X equal to o2ln as the sample size becomes large. • Nine sections: fundamentals of compliance, Sharpe Ratio input data, calculation methodology, composite Standard Error construction, disclosures, presentation and Sharpe ratio: measures excess return per unit of risk. Standard error o f the sample mean is the standard reporting, real estate, private equity, and wrap rP ~ rf deviation of distribution of the sample means. fee/separately managed account portfolios. Sharpe ratio = a known population variance: cr- = ■r* QUANTITATIVE METHODS Roy’s safety-first ratio: rp fiarget CT„ unknown population variance: s? = Time Value o f M oney Basics For both ratios, larger is better. Confidence Intervals • Future value (FV): amount to which investment grows after one or more compounding periods. Expected Return/Standard Deviation Confidence interval: gives range of values the mean • Future value: FV = PV(1 + I/Y)N. Expected return: E(X ) = ^ ^ P ( x j) xn value will be between, with a given probability (say • Present value (PV): current value of some future 90% or 95%). With known variance, formula for a E(X ) = P (x1)x 1+ P ( x 2)x 2 + . . . + P (xn)x n cash flow PV = FV/(1 + I/Y)N. confidence interval is: • Annuities: series of equal cash flows that occur at Probabilistic variance'. a x ± za l l evenly spaced intervals over time. a 2( X ) = y > ( x i ) [ x i - E ( X ) f • Ordinary annuity: cash flow at ^W-of-time period. = P(x1)[x1-E (X )f + P(x2)[x2 -E(X )]: 1.645 for 90% confidence intervals • Annuity due: cash flow at beginning-of-time period. Za/2 (significance level 10%, 5% in each tail) • Perpetuities: annuities with infinite lives. + ... + P(xn)[x„—E(X)f Z\x!2 ,= 1.960 for 95% confidence intervals PVperpetuity . = PMT/(discount rate). v ' Standard deviation: take square root of variance. (significance level 5%, 2.5% in each tail) Required Rate o f Return Z = 2.575 for 99% confidence intervals Components: Correlation and Covariance a/2 (significance level 1%, 0.5% in each tail) 1. Real risk-free rate (RFR). Correlation: covariance divided by product of the 2. Expected inflation rate premium (IP). two standard deviations. 3. Risk premium. COV (Rj, Rj corrlR ^R : = E(R) = (l + RFRreal)(l + IP)(l + RP) —1 <T(R i)<T(R i N ull and Alternative Hypotheses Oligopoly: Few firms that may have significant Balance o f Payments N ull hypothesis (HQ): hypothesis that contains the pricing power; high barriers to entry; products may Current account: merchandise and services; income equal sign (=, <, >); the hypothesis that is actually be homogeneous or differentiated. receipts; unilateral transfers. tested; the basis for selection of the test statistics. Monopoly: Single firm with significant pricing Capital account: capital transfers; sales/purchases of Alternative hypothesis (Ha): concluded if there is power; high barriers to entry; advertising used to nonfinancial assets. sufficient evidence to reject the null hypothesis. compete with substitute products. Financial account: government-owned assets Difference Between One- and Two-Tailed Tests In all market structures, profit is maximized at abroad; foreign-owned assets in the country. One-tailed test: tests whether value is greater than or the output quantity for which marginal revenue = Regional Trading Agreements less than a given number. marginal cost. Free trade area: Removes barriers to goods and Two-tailed test: tests whether value is equal to a Gross D om estic Product services trade among members. given number. Real GDP = consumption spending + investment + Customs union: Members also adopt common trade • One-tailed test: Ho: p < 0 versus H a: p > 0. government spending + net exports. policies with non-members. • Two-tailed test: Ho: p = 0 versus H a: p * 0. Savings, Investment, Fiscal Balance, and Trade Common market: Members also remove barriers to Type I and Type II Errors Balance labor and capital movements among members. • Type I error: rejection of null hypothesis when it is Fiscal budget deficit (G —T) = excess of saving over Economic union: Members also establish common actually true. domestic investment (S —I) —trade balance (X —M) institutions and economic policy. • Type II error: failure to reject null hypothesis when Monetary union: Members also adopt a common Equation o f Exchange it is actually false. currency. MV = PY, where M = real money supply, V = Types o f Hypothesis Tests velocity of money in transactions, P = price level, Foreign Exchange Rates Use t-statistic for tests involving the population and Y = real GDP. For the exam, FX rates are expressed as price mean (location of mean, difference in means, currency / base currency and interpreted as the Business Cycle Phases paired comparisons). number of units of the price currency for each unit Expansion; peak; contraction; trough. Use chi-square statistic for tests of a single of the base currency. Economic Indicators population variance. Real Exchange Rate Leading: Turning points occur ahead of peaks and Use F-statistic for tests comparing two population base currency CPI troughs (stock prices, initial unemployment claims, = nominal FX ra te X variances. manufacturing new orders) Vprice currency CPI y Technical Analysis Coincident: Turning points coincide with peaks Reversal patterns: head and shoulders, inverse H&S, No-Arbitrage Forward Exchange Rate and troughs (nonfarm payrolls, personal income, double/triple top or bottom. manufacturing sales) forward 1 + price currency interest rate Continuation patterns: triangles, rectangles, Lagging: Turning points follow peaks and troughs spot 1 + base currency interest rate pennants, flags. (average duration of unemployment, inventory/ Price-based indicators: moving averages, Bollinger sales ratio, prime rate) Exchange Rate Regimes bands, momentum oscillators (rate of change, RSI, Formal dollarization: country adopts foreign Factors Affecting Aggregate Demand stochastic, MACD). currency. Consumers’ wealth; business expectations; Monetary union: members adopt common currency. Sentiment indicators: opinion polls, put/call ratio, consumers’ income expectations; capacity VIX, margin debt, short interest ratio. Fixed peg: ± 1% margin versus foreign currency or utilization; monetary and fiscal policy; exchange Flow o f funds indicators: TRIN, margin debt, basket of currencies. rates; global economic growth. Target zone: Wider margin than fixed peg. mutual fund cash position, new equity issuance, secondary offerings. Factors Affecting SR Aggregate Supply Crawling peg: Pegged exchange rate adjusted Input prices; labor productivity; expectations for periodically. output prices; taxes and subsidies; exchange rates; Crawling bands: W idth of margin increases over all factors that affect LR aggregate supply. ECONOMICS Factors Affecting LR Aggregate Supply time. Managedfloating: Monetary authority acts to Elasticity Size of labor force; human capital; supply of influence exchange rate but does not set a target. _ . . . . %A quantity demanded natural resources; stock of physical capital; level of Independently floating: Exchange rate is market- Own price elasticity = ------- -------- — ------------ determined. %A price technology. If absolute value > 1, demand is elastic. Types o f Unemployment If absolute value < 1, demand is inelastic. Frictional: time lag in matching qualified workers O n a straight line demand curve, total revenue is with job openings. F in a n c ia l r ep o r t in g a n d Structural: unemployed workers do not have the maximized where price elasticity = —1. skills to match newly created jobs. .ANALYSIS T , . . %A q uantity demanded income elasticity = ------ -------- -J-------------- Cyclical: economy producing at less than capacity %A income Revenue Recognition during contraction phase of business cycle. Two requirements: (1) completion of earnings If positive, the good is a normal good. Policy Multipliers process and (2) reasonable assurance of payment. If negative, the good is an inferior good. _ . . . . %A quantity demanded money multiplier = --------------- ---------- Revenue Recognition Methods Cross price elasticity = ------- — m------ --------------- • Percentage-of-completion method. %A price of related good reserve requirement • Completed contract method. If positive, related good is a substitute. fiscal multiplier = -------- — -------- • Installment sales. If negative, related good is a complement. l-M P C (l-t) • Cost recovery method. Breakeven and Shutdown where M PC = marginal propensity to consume, Converged Standards Issued May 2014 Breakeven: total revenue = total cost. t = tax rate. Five-step revenue recognition model: Operate in short run if total revenue is greater than Expansionary and Contractionary Policy 1. Identify contracts total variable cost but less than total cost. Monetary policy is expansionary when the policy 2. Identify performance obligations Shut down in short run if total revenue is less than rate is less than the neutral interest rate (real trend 3. Determine transaction price total variable cost. rate of economic growth + inflation target) and 4. Allocate price to obligations Market Structures 5. Recognize when (as) obligations are satisfied contractionary when the policy rate is greater than Perfect competition: Many firms with no pricing the neutral interest rate. Unusual or Infrequent Items power; very low or no barriers to entry; Fiscal policy is expansionary when a budget • Gains/losses from disposal of a business segment. homogeneous product. deficit is increasing or surplus is decreasing, and • Gains/losses from sale of assets or investments in Monopolistic competition: Many firms; some contractionary when a budget deficit is decreasing subsidiaries. pricing power; low barriers to entry; differentiated or surplus is increasing. • Provisions for environmental remediation. products; large advertising expense.  Impairments, write-offs, write-downs, and Total asset, fixed-asset, and working capital turnover Held-to-maturity: amortized cost on balance restructuring costs. ratios: sheet; interest, realized G/L recognized on income • Integration expenses associated with businesses revenue statement. recendy acquired. total asset turnover = average total assets Inventory Accounting Discontinued Operations In periods of rising prices and stable or increasing To be accounted for as a discontinued operation, a revenue inventory quantities: fixed asset turnover = business— assets, operations, investing, financing average fixed assets LIFO results in: FIFO results in: activities— must be physically/operationally distinct Higher COGS Lower COGS revenue from rest of firm. Income/losses are reported net of working capital turnover = Lower gross profit Higher gross profit tax after net income from continuing operations. average working capital Lower inventory Higher inventory Compute Cash Flows From Operations (CFO) Gross, operating, and net profit margins: balances balances Direct method: start with cash collections (cash Basic and D iluted EPS ~ . gross profit equivalent of sales); cash inputs (cash equivalent of gross profit margin = —----- i------ Basic EPS calculation does not consider effects of cost of goods sold); cash operating expenses; cash revenue any dilutive securities in computation of EPS: interest expense; cash taxes. ^ . operating profit EBIT net income —preferred dividends Indirect method: start with net income, subtracting operating profit margin = —--------—------ — basic EPS = revenue net sales wtd. avg. no. of common shs. outstanding back gains and adding back losses resulting from financing or investment cash flows, adding back all net mcome adj. income avail, for common shares net profit margin = diluted EPS = noncash charges, and adding and subtracting asset revenue wtd. avg. common shares plus potential and liability accounts that result from operations. Return on assets [return on total capital (ROTC)]: common shares outstanding Free Cash Flow return on assets _ EBIT Therefore, diluted EPS i s : < fJi convertible convertible Free cash flow (FCF) measures cash available for (total capital) average total capital net _ prd + preferred + debt (1- t ) discretionary purposes. It is equal to operating cash income div dividends interest flow less net capital expenditures. Debt to equity ratio and total debt ratio: wtd shares from sh ’s from shares Critical Ratios total debt avp + conversion of + conversion + issuable from debt-to-equity ratio = sh s conv. pfd. sh ’s ^conv. debt / stock options Common-size financial statement analysis: total equity • Common-size balance sheet expresses all balance sheet accounts as a percentage of total assets. total debt total-debt-ratio = Long-Lived Assets Capitalizing vs. Expensing • Common-size income statement expresses all total assets Capitalizing: lowers income variability and income statement items as a percentage of sales. Interest coverage andfixed charge coverage: increases near-term profits. Increase assets, equity. • Common-size cash flow statement expresses each EBIT Expensing: opposite effect. line item as a percentage of total cash inflows interest coverage = 7 (outflows), or as a percentage of net revenue. interest Depreciation Horizontal common-sizefinancial statement analysis: EBIT + lease payments cost —residual value fixed charge coverage = - Straight-line: expresses each line item relative to its value in a interest + lease payments useful life common base period. Growth rate (g): g = RR x ROE Double declining balance: Liquidity ratios: current assets dividends declared 2 current ratio = ---------- ;—77-7— retention rate = 1— (cost —accum. depreciation) current liabilities operating income after taxes , useful life, cash + marketable securities + receivables Units o f production: quick ratio = Liquidity ratios indicate company’s ability to pay its current liabilities cost —salvage value short-term liabilities. -------------------------- X output units cash + marketable securities Operating performance ratios indicate how well useful life in units cash ratio = current liabilities management operates the business. Revaluation o f Long-Lived Assets cash + mkt. sec. -j- receivables DuPont Analysis IFRS: revaluation gain recognized in net income defensive interval = Traditional DuPont equation: daily cash expenditures only to the extent it reverses previously recognized \ net income sales assets impairment loss; further gains recognized in equity Receivables, inventory, payables turnover, and days’ return on equity = as revaluation surplus. (For investment property, supply ratios— all o f which are used in the cash k sales kassets, , equity / all gains and losses from marking to fair value are conversion cycle: You may also see it presented as: recognized as income.) . .. annual sales receivables turnover = ---------------;------- U S. GAAP: revaluation is not permitted. average receivables net profit asset equity return on equity = Deferred Taxes margin turnover multiplier cost of goods sold • Created when taxable income (on tax return) ^ inventory turnover = --------- ------------- Extended DuPont equation further decomposes net average inventory pretax income (on financial statements) due to profit margin: temporary differences. purchases • Deferred tax liabilities are created when taxable payables turnover ratio = net income v E B T ) v ' EBIT average trade payables ROE = A A income < pretax income. Treat DTL as equity if EBT EBIT revenue / 2 not expected to reverse. 365 revenue vA avg. total assets • Deferred tax assets are created when taxable income days of sales outstanding = x receivables turnover avg. total assets avg. equity > pretax income. Must recognize valuation 365 allowance if more likely than not that DTA will days of inventory on hand = 7 You may also see it presented as: not be realized. inventory turnover ROE = tax burden x interest burden x Long-Term Liabilities ________365________ EBIT margin x asset turnover x leverage number of days of payables = • Premium bond: coupon rate > market rate at payables turnover ratio Marketable Security Classifications issuance. Held-for-trading: fair value on balance sheet; • Discount bond: coupon rate < market rate at days of inventory dividends, interest, realized and unrealized G/L cash conversion cycle = issuance. on hand recognized on income statement. • Interest expense equals book value at the beginning days of sales number of days Available-for-sale: fair value on balance sheet; of the year multiplied by the market rate of interest + dividends, interest, realized G/L recognized outstanding of payables at the time the bonds were issued. on income statement; unrealized G/L is other comprehensive income. Leases Cost of trade credit: CAPM : E(Rj) = RFR + j3- [E(Rmkt) - RFR 365 Financial statement!ratio impact of lease % discount days past discount accounting from the lessee perspective: capital E(Ri) 1—% discount leases result in: • Higher: assets, liabilities, CFO, debt/equity. Corporate Governance • Lower: net income (early years), CFF, current One-tier board: Includes internal and external ratio, working capital, asset turnover, ROA, directors ROE. Two-tier board: Supervisory board of external • Same: total cash flow. directors, management board of internal directors Pensions Board committees: Defined contribution: employer contribution Audit: Financial reporting expensed in period incurred. Governance: Legal and ethics compliance Defined benefit: overfunded plan recognized as Nominations: Find Board candidates asset, underfunded plan recognized as liability. Remuneration: Compensation for senior managers Risk: Firm risk tolerance and risk management Investment: Review large capital projects, asset The SML and Equilibrium purchases, asset sales Identifying mispriced stocks: CORPORATE FINANCE Consider three stocks (A, B, C) and SML. Estimated stock returns should plot on SML. W eighted Average Cost o f Capital • A return plot over the line is underpriced. WACC = (wd) [kd (1-t)] + (wps )(kps) + (wce)(ks) • A return plot under the line is overpriced. Cost o f Preferred Stock PORTFOLIO MANAGEMENT E(R) kP = ^K- Investment Policy Statement P Investment objectives: Cost o f Equity Capital • Return objectives. • Risk tolerance. k. = a +g Constraints: o • Liquidity needs. Cost o f Equity Using CAPM • Time horizon. k e = RFR + ^ ( R mtt - RFR) • Tax concerns. • Legal and regulatory factors. RFR Capital Budgeting • Unique needs and preferences. 0 risk Com bining Preferences with the Optimal Set o f 1 NPV - CF0 + CFl . + CFz CF" (1 + k )1 (l + k); (1 + k)n Portfolios Risk-Adjusted Returns Markowitz efficient frontier is the set of portfolios Sharpe ratio and M-squared measure excess return IRR: discount rate that makes NPV equal to that have highest return for given level of risk. per unit of total risk. zero. Treynor measure and Jensens alpha measure excess E(Rp) Pure-Play M ethod Project Beta return per unit of systematic risk. Delevered asset beta for comparable company: 1 E(R) P aasset sse t P ^ e q u ity X i+ (i-0 - v ' e Relevered project beta for subject firm: D 0project . r-'nroiecr = 0 asset X 1 + ( i - t ) r^ ' Measures o f Leverage Total leverage: percent change in net income Security Market Line (SML) from a given percent change in sales. Investors should only be compensated for risk Operating leverage: percent change in EBIT from relative to market. Unsystematic risk is diversified a given percent change in sales. away; investors are compensated for systematic risk. Financial leverage: percent change in net income The equation of the SML is the CAPM, which is a from a given percent change in EBIT. return/systematic risk equilibrium relationship. breakeven quantity of sales = total risk = systematic + unsystematic risk Fixed operating & financing costs price —variable costs per unit SECURITIES MARKETS operating breakeven quantity of sales = & EQUITY INVESTMENTS fixed operating costs W ell-Functioning Security Markets price —variable costs per unit • Operational efficiency (lowest possible transactions costs). Working Capital Management • Informational efficiency (prices rapidly adjust to Primary sources ofiliquidity, cash balances, new information). short-term funding, cash flow management of RFR Margin Purchases collections and payment. For margin transactions: Secondary sources ofiliquidity, liquidating assets, • Leverage factor = 1/margin percentage. negotiating debt agreements, bankruptcy • Levered return = PIPR x leverage factor. protection. Margin Call Price P0(l —initial margin %) 1 —maintenance margin %  Com puting Index Prices Critical relationship between k and g : full price = PV at last coupon date x (1 + YTM)r/I • As difference between ke and gc widens, value of accrued interest = coupon payment x (t/T) „ . •i it j S stock prices Price-weighted Index = —---------— stock falls. where: adjusted divisor • As difference narrows, value of stock rises. t = days from most recent coupon payment to Value-weigh ted Index • Small changes in difference between ke and gc trade settlement cause large changes in stock’s value. T = days in coupon payment period XXcurrent prices) (# shares) . . = --------------------- 4-------------------------- x base value Critical assumptions of infinite period DDM: Matrix pricing: For illiquid bonds, use yields of bonds XXbase year prices)(#base year shares) • Stock pays dividends; constant growth rate. with same credit quality to estimate yield; adjust for • Constant growth rate, g , never changes. maturity differences with linear interpolation. Types o f Orders • k must be greater than g (or math will not work) Execution instructions: how to trade; e.g., market Bond Markets orders, limit orders. Earnings Multiplier Model National bond market includes domestic bonds and Validity instructions: when to execute; e.g., stop D foreign bonds. orders, day orders, fill-or-kill orders. o_ i _ payout ratio • Domestic bonds. Domestic issuer and currency. Clearing instructions: how to clear and settle; for sell k -g k -g • Foreign bonds. Foreign issuer, domestic currency. orders, specify short sale or sale of owned security. Eurobond market is outside any one country, with Market Structures Price Multiples bonds denominated in currencies other than those Quote-driven markets: investors trade with dealers. price per share of countries in which bonds are sold. leading P/E = Order-driven markets: buyers and sellers matched forecast EPS next 12 mo. Global bonds trade in both a national bond market by rules. and the eurobond market. price per share Brokered markets: brokers find counterparties. trailing P/E = Bond Issuance EPS previous 12 mo. Forms o f EM H Underwritten offering: Investment banks buy entire • Weakform. Current stock prices fully reflect price per share issue, sell to public. P/B = Best efforts offering: Investment banks act as brokers. available security market info. Volume book value per share information/past price do not relate to future Shelfregistration: Register entire issue with direction of security prices. Investor cannot price per share regulators but sell over a period of time. P/S = achieve excess returns using tech analysis. sales per share Embedded Options • Semi-strongform. Security prices instantly adjust Callable: Issuer may repay principal early. Increases price per share to new public information. Investor cannot achieve P/CF = yield and decreases duration. excess returns using fundamental analysis. cash flow per share Putable: Bondholder may sell bond back to issuer. • Strongform. Stock prices fully rfleet all Decreases yield and duration. information from public and private sources. Convertible: Bondholder may exchange bond for Assumes p efect markets in which all information V FIXED INCOME — —‘ -- / issuer’s common stock. is cost free and available to everyone at the same Embedded warrants: Bondholder may buy issuer’s time. Even with inside info, investor cannot Basic Features o f Bonds common stock at exercise price. achieve excess returns. Issuer. Sovereign, non-sovereign, quasi-government, Yield Measures supranational, corporate, SPE. Effective yield depends on periodicity. YTM = Maturity. Money market (one year or less); capital effective yield for annual-pay bonds. l EQUITY INVESTMENTS market (greater than one year). Par value. Bond’s principal value (face value). Semiannual bond basis: YTM = 2 x semiannual discount rate. Industry Life Cycle Stages Coupon. Annual percent of par; fixed or floating. Current yield = annual coupon / price. Embryonic: slow growth, high prices, large Divide by periodicity to get periodic rate. Simple yield = current yield ± amortization. investment needed, high risk of failure. Currency. Single, dual, currency option. Yield to call is based on call date and call price. Growth: rapid growth, falling prices, limited Indenture. Affirmative and negative covenants. Yield to worst is lowest of a bond’s YTCs or YTM. competition, increasing profitability. Price, Yield, Coupon Relationships Money market yields may be on a discount or add- Shakeout: slower growth, intense competition, Bond prices and yields are inversely related. on basis and may use a 360- or 365-day year. declining profitability, cost cutting, weaker firms Increase in yield decreases price; decrease in yield Bond-equivalent yield is an annualized add-on yield fail or merge. increases price. based on a 365-day year. Mature: slow growth, consolidation, stable prices, Coupon < yield: Discount to par value. high barriers to entry. Forward and Spot Rates Coupon > yield: Premium to par value. Decline: negative growth, declining prices, Forward rate is a rate for a loan that begins at a Constant-yield price trajectory: Price approaches consolidation. future date. “Iy3y” = 3-year forward rate 1 year par as bond nears maturity from amortization of from today. Five Competitive Forces discounts and premiums. Capital gains and losses Example of spot-forward relationship: 1. Rivalry among existing competitors. are calculated relative to this trajectory. (1 + S2)2 = (1 + S,)(l + lyly) 2. Threat of entry. Cash Flow Structures 3. Threat of substitutes. Yield Spreads Bullet: All principal repaid at maturity. 4. Power of buyers. G-spread: Basis points above government yield. Fully amortizing: Equal periodic payments include 5. Power of suppliers. I-spread: Basis points above swap rate. both interest and principal. Z-spread: Accounts for shape of yield curve. One-Period Valuation Model Partially amortizing: Periodic payments include Option-adjusted spread: Adjusts Z-spread for effects D, interest and principal, balloon payment at maturity + of embedded options. repays remaining principal. (l + k„) (l + k_) Interest Rate Risk Sinking fund: Schedule for early redemption. Be sure to use expected dividend in calculation. Floating-rate: Coupon payments based on reference Interest rate risk has two components: reinvestment risk rate plus margin. and market price risk from YTM changes. These risks Infinite Period Dividend D iscount Models have opposing effects on an investor’s horizon yield. Supernormal growth model (multi-stage) DDM: Bond Pricing • Bond investors with short horizons are more Dn There are two equivalent ways to price a bond: p , n concerned with market price risk. V0 = + + + • Constant discount rate applied to all cash flows (1 + k„) (i + k e)n d + k e)n • Bond investors with long horizons are more (YTM) to find PV. This is a bond’s fla t price (does D n+1 concerned with reinvestment risk. where: Pn = not include accrued interest). • The horizon at which market price risk and (k e Sc) • Discount each cash flow using appropriate spot reinvestment risk just offset is a bond’s Macaulay rate for each. This is a bond’s no-arbitrage price. Constant growth model: duration. This is the weighted average of times Full price includes accrued interest. Government until a bond’s cash flows are scheduled to be paid. v _ P pfl + gc) _ bonds use actual day counts; corporate bonds use 0 1 ke - g c 30/360 method. Modified duration is the approximate change in a Forward Contract Value bond’s price given a 1% change in its YTM: At time t. Fq (T) Macaulay duration (V -)-(V .) Vt (T) = St + PVt (cost) - PVt (benefit) rs~/ r (1 + Rf)T -t 0 + r) 2V0 (Ay) A t expiration (time t = T): payoff to long = S.r - FQ(T) Effective duration is required if a bond has embedded options: Futures vs. Forwards Forwards Futures (V -)-(V + ) Private contracts Exchange-traded 2V q (Acurve) Unique contracts Standardized contracts Price change estimates based on duration only are Default risk Guaranteed by clearinghouse improved by adjusting for convexity: Little or no regulation Regulated 1 Forward Rate Agreements (FRA) %Aprice = —duration (Ay) H— convexity (Ay)' Can be viewed as a forward contract to borrow/ Asset-Backed Securities lend money at a certain rate at some future date. ALTERNATIVE INVESTMENTS Residential M BS: home mortgages are collateral. Interest Rate Swaps Hedge Funds Agency RMBS include only conforming loans; May be replicated by a series of off-market FRAs Event-driven strategies: merger arbitrage; distressed/ nonagencv RMBS may include nonconforming with present values at swap initiation that sum to restructuring; activist shareholder; special loans and need credit enhancement. zero. situations. Prepayment risk: contraction risk from faster Options Relative value strategies: convertible arbitrage; prepayments; extension risk from slower • Buyer of a call option— long asset exposure. asset-backed fixed income; general fixed income; prepayments. • Writer (seller) of a call option— short asset volatility; multi-strategy. CMOs: pass-through MBS are collateral. May have exposure. Equity strategies: market neutral; fundamental sequential-pay or PAC/support structure. • Buyer of a put option— short asset exposure. growth; fundamental value; quantitative Commercial MBS: non-recourse mortgages on • Writer (seller) of a put option— long asset directional; short bias. commercial properties are collateral. exposure. Macro strategies: based on global economic trends. Auto ABS: auto loans are collateral. intrinsic value of a call option = Max[0, S —X] Hedge fund fees: Credit card ABS: credit card receivables are intrinsic value of a put option = Max[0, X —S] • “2 and 20”: 2% management fee plus 20% collateral. American vs. European Options incentive fee. CDOs: Bonds, bank loans, MBS, ABS, or other American options allow the owner to exercise the • Hard hurdle rate: incentive fee only on return CDOs are collateral. option any time before or at expiration. European above hurdle rate. Collateral and Credit Enhancement options can be exercised only at expiration. Value • Soft hurdle rate: incentive fee on whole return, Secured bonds are backed by specific collateral and of American option will equal or exceed value of but only paid if return is greater than hurdle rate. senior to unsecured bonds. European option. They will have identical values • High water mark: no incentive fee until value Unsecured bonds are general claims to issuer’s cash except for: (1) call options on dividend paying exceeds previous high. flows and assets. stocks and (2) in-the-money put options. Private Equity Internal credit enhancement: Excess spread, Factors that Affect O ption Values Leveraged buyouts: management buyouts (existing overcollateralization, waterfall structure. managers), management buy-ins (new managers) Increase in: Calk Puts External credit enhancement: Surety bonds, letters of Venture capital stages of development: credit, bank guarantees. Asset price Increase Decrease • Formative stage: angel investing, seed stage, early Credit Analysis Exercise price Decrease Increase stage. Investment grade: Baa3/BBB—or above • Later stage: finance product development, Risk-free rate Increase Decrease Non-investment grade: Bal/BB+ or below marketing, market research. Corporate family rating (CFR): issuer rating. Volatility Increase Increase • Mezzanine stage: prepare for IPO. Corporate credit rating (CCR): security rating. Time to Increase Increase* Portfolio company valuation methods: market/ “Four Cs”: capacity, collateral, covenants, character, expiration comparables; discounted cash flow; asset-based. default risk = probability of default Exit strategies: trade sale; IPO; recapitalization; Holding costs Increase Decrease loss severity = percent of value lost if borrower secondary sale; write-off. defaults Holding Decrease Increase Real Estate expected loss = default risk x loss severity benefits Includes residential property; commercial property; recovery rate = 1 —expected loss percentage *Except some deep-in-the-money European puts. real estate investment trusts (REITs); farmland/ Put-Call Parity timberland; whole loans; construction loans. The put-call parity relationship for European Property valuation methods: comparable sales; options at time tr. income approach; cost approach. DERIVATIVES ct + 7 X ~7f"— St + pt Commodities Contango: futures price > spot price. Arbitrage and Replication (l + R f)T Backwardation: futures price < spot price. • Law o f one price: two assets with identical cash Sources of investment return: flows in the future, regardless of future events, • Collateralyield: return on T-bills posted as margin. should have the same price. • Price return: due to change in spot price. • Two assets with uncertain returns can be combined ISBN: • Rollyield: positive for backwardation, negative for in a portfolio that will have a certain payoff. If a contango. portfolio has a certain payoff, the portfolio should futures price « spot price (1 + Rf) + storage costs yield the risk-free rate. For this reason, derivatives —convenience yield values are based on risk-neutral pricing. Infrastructure Derivatives Values vs. Prices Long-lived assets for public use, including The price of a forward, futures, or swap contract transportation, utility, communications, social is the forward price stated in the contract and is Brownfield: Existing infrastructure set such that the contract has a value of zero at Greenfield: Infrastructure to be built initiation. Value may change during the contract’s life with opposite gains/losses to the long and short. U.S. $29.00 © 2017 Kaplan, Inc. All Rights Reserved.