CFA Level I Facts and Formula Sheet 2024

2024 Level I Fact Sheet Quantitative Methods Key Facts & Formulas for the CFA® where m = number of compounding periods per year, Rs = quoted Exam Three interpretations of interest rates: (1) required rate of return (2) discount rate (3) opportunity cost Components of Interest Rates r = real risk-free interest rate + inflation premium + default risk premium + liquidity premium + maturity premium Nominal risk-free rate = real risk-free rate + inflation premium Holding Period Return (R): total return for holding an investment over a given time period (P −P )+I R= 1 0 1 P0 Holding period return can be computed for a period longer than a year. E.g., holding period return over a 3-year period using three annual returns: R = [(1 + R1) × (1 + R2) × (1 + R3)] - 1 Arithmetic mean: sum of all the observations divided by the total number of observations. µ = ∑N i=1 Xi N Geometric mean: used to calculate compound growth rate. ̅ Gi = [(1 + R1 ) (1 + R 2 ) … … . (1 + R T )]1/T − 1 R Harmonic mean: used to find average purchase price for equal periodic investments. 1 ̅ XH = n / ∑ni=1 ( ) Xi Harmonic mean ≤ Geometric mean ≤ Arithmetic mean Arithmetic mean × Harmonic mean = (Geometric mean)2 Internal rate of return (IRR): the discount rate at which the sum of present values of cash flows will equal zero. Money weighted rate of return (MWRR): the IRR of a project. It reflects the actual return earned on an investment after accounting for the value and timing of cash flows relating to the investment. Time weighted rate of return (TWRR): compound growth rate at which $1 invested in a portfolio grows over a given measurement period. The geometric mean formula is used. The TWRR is not impacted by timing and amount of cashflows and is therefore preferred as a performance measure if the portfolio manager does not control the timing and amount of the investment. Gross return: the return earned by an asset manager prior to deducting management fees and taxes. It measures investment skill. Net return: accounts for all managerial and administrative expenses. It is what the investor is concerned with. Pre-tax nominal return: the return before accounting for inflation and taxes; this is the default, unless otherwise stated. After-tax nominal return: the return after accounting for taxes. Real return: the return after accounting for taxes and inflation. Future value: value to which an investment will grow after one or more compounding periods. FVt = PV(1 + r)t If t→: FVt = PVe r t Present value: current value of some future cash flow. 1 PV = FVt [(1+𝑟)𝑡] If t→: PVt = FVe- r t Non-annual compounding: FV = PV / (1 + Rs/m)mN annual interest rate, and N = number of years Annualized Return: Rannual = (1 + Rperiod)c – 1 where c = number of periods in a year Continuously compounded return: r0,T = ln(PT/P0) Return on a leveraged portfolio: 𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑅𝑒𝑡𝑢𝑟𝑛 V RL = = RP + B (RP – rD) 𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝐸𝑞𝑢𝑖𝑡𝑦 VE Perpetuity: never ending series of equal cash flows at regular intervals: PV = PMT / r Annuity: series of equal cash flows at regular intervals: A= 𝑟(𝑃𝑉) 1−(1+𝑟)−𝑡 Cash flow additivity principle: only cash flows occurring at the same point in time can be added. This principle ensures that market prices reflect the condition of no arbitrage. Measures of Central Tendency Sample mean: the arithmetic mean of a sample, where n is the number of observations in the sample: ∑n X ̅ = i=1 i X 𝑛 Mode: Most frequently occurring value in a distribution. Median: Midpoint of a data set that has been sorted into ascending or descending order. Position of a percentile in a data set: Ly = (n+1) y /100 Box and whiskers plot: used to visualize the dispersion of data across quartiles. Measures of Dispersion Range = maximum value – minimum value Mean absolute deviation (MAD): average of the absolute values of deviations from the mean. ̅|]/n MAD = [∑ni=1|Xi − X Variance: mean of the squared deviations from the arithmetic mean 2 Population variance σ2 = ∑N i=0(X i − μ) / N Standard deviation: square root of variance Target downside deviation (target semideviation): A measure of the risk of being below a given target. n STarget = √ ∑ for all Xi ≤B (Xi − B)2 n−1 Coefficient of variation: measures the risk per unit of return; lower 𝑠 value is better. CV = ̅ 𝑋 Skewness Symmetrical distribution: mean = median = mode Positively skewed (long tail on right side): mean > median > mode Negatively skewed (long tail on left side): mean < median < mode Kurtosis Excess kurtosis = kurtosis - 3. Leptokurtic distribution: Fatter tails than a normal distribution and an excess kurtosis > 0. Platykurtic distribution: Thinner tails than a normal distribution and an excess kurtosis < 0. Mesokurtic distribution: identical to a normal distribution and has an excess kurtosis = 0. 1 Covariance: measure of how two variables move together. ∑𝑛 (𝑋 −𝑋̅ )(𝑌 −𝑌̅) 𝑖 Sample Covariance: 𝑠𝑋𝑌 = 𝑖=1 𝑖 𝑛−1 Correlation: standardized measure of the linear relationship between two variables; covariance divided by product of two standard deviations. 𝑠 Sample Correlation: rXY = 𝑋𝑌 𝑠𝑋 𝑠𝑌 Correlation ranges from -1 and +1. A correlation of +1 indicates a perfect positive relationship. A correlation of -1 indicates a perfect negative relationship. Expected value (probability-weighted average): E(X) = X1P(X1) + X2P(X2) + ... + XnP(Xn) Variance of a random variable: σ2 (X) = E[X − E(X)]2 Cov (X,Y) = E[X - E(X)] [Y - E(Y)] Corr (X,Y) = Cov (X,Y) / σ (X) σ (Y) Multiplication rule: used to determine the joint probability of two events. P (AB) = P (A│B) P (B), P(B) ≠ 0 Addition rule: used to determine the probability that at least one of the events will occur. P (A or B) = P(A) + P(B) − P(AB) Multiplication rule for independent events: P(AB) = P(A) P(B) Conditional expected value: the expected value of a random variable X given an event or scenario S: E(X|S) = P(X1|S)X1 + P(X2|S)X2 + ... + P(Xn|S)Xn Total probability rule: used to calculate the unconditional probability of an event, given conditional probabilities. P(A) = P(A|S1)P(S1) + P(A|S2)P(S2) + ... + P(A|Sn)P(Sn) Bayes’ formula: used to update the probability of an event based on new information. P(Information|Event) P(Event|Information) = × P(Event) P(Information) Portfolio expected return: E(Rp) = w1E(R1) + w2E(R2) + … + wnE(Rn) Portfolio variance: Variance of a 2-asset portfolio: σ2 (R P ) = w12 σ12 (R1 ) + w22 σ22 (R 2 ) + 2w1 w2 Cov (R1 R 2 ) Variance of a 3-asset portfolio: σ2 (R P ) = w12 σ12 (R1 ) + w22 σ22 (R 2 ) + w32 σ23 (R 3 ) + 2w1 w2 Cov (R1 R 2 ) + 2w1 w3 Cov (R1 R 3 ) + 2w2 w3 Cov (R 2 R 3 ) Covariance between random variables Ri and R: Cov (R i , R j ) = E ([R i – ER i ][ R j – ER j ]) Correlation: ρ(Ri,Rj) = Cov(Ri,Rj)/[σ(Ri)σ(Rj)] Safety first ratio: used to measure shortfall risk; higher number is E(RP )−RL preferred. SFratio = Judgmental sampling: the researcher uses his knowledge and professional judgment to selectively handpick members from the population. Central limit theorem: if we draw a sample from a population with mean µ and variance σ2, the sampling distribution of the sample mean will: ▪ be normally distributed. ▪ have a mean of µ. ▪ have a variance of σ2/n. Standard error of the sample mean: standard deviation of the distribution of the sample means.  ▪ If population variance () is known:  𝑋̅ = √𝑛 𝑠 ▪ If population variance is not known: 𝑠 𝑋̅ = √𝑛 ̅ ) 2 / (n − 1) Sample variance: s2 = ∑ni=0(Xi − X Sampling distribution: If we draw samples of the same size several times and calculate the sample statistic. The sample statistic will be different each time. The distribution of values of the sample statistic is called a sampling distribution. Bootstrap: Resampling method that uses computer simulation for statistical inference by repeatedly drawing samples with replacement. Jackknife: Samples are selected by leaving out one observation at a time from the set (and not replacing it). Hypothesis testing steps 1. State the hypothesis. 2. Identify the appropriate test statistic and its probability distribution. 3. Specify the level of significance. 4. State a decision rule to accept or reject the hypothesis. 5. Collect sample data and calculate the test statistic. 6. Decide if the hypothesis can be accepted/rejected. Null hypothesis (H0): hypothesis that the researcher wants to reject. It should always include the ‘equal to’ condition. Alternative hypothesis (Ha): hypothesis that the researcher wants to prove. One-tailed tests: used to assess if the value of a population parameter is greater than or less than a hypothesized value. Two-tailed tests: used to assess if the value of a population parameter is different from a hypothesized value. Test statistic calculated from sample data and is compared to a critical value to decide whether or not we can reject the null hypothesis. σP Monte Carlo simulation: a computer simulation that produces a distribution of possible security prices using randomly generated values for risk factors, based on their assumed distributions. It is also used as a tool for valuing complex securities with embedded options where no analytic pricing formula is available. Stratified random sampling: the population is divided into subgroups based on one or more distinguishing characteristics. Samples are then drawn from each subgroup, with sample size proportional to the size of the subgroup relative to the population. Finally, samples from each subgroup are pooled together to form a stratified random sample. Cluster sampling: requires the population to be divided into subpopulation groups, called clusters. Each cluster is essentially a mini-representation of the entire population. Then some random clusters are chosen as a whole for sampling. Convenience sampling: the researcher selects members from a population based on how easy it is to access the member i.e., data is collected from a conveniently available pool of respondents. Ver 1.0 Type I error: reject a true null hypothesis. Type II error: fail to reject a false null hypothesis. Level of significance (α) = (1 – level of confidence) = P(Type I error) Power of a test = 1 – P(Type II error) p-value: the smallest level of significance at which the null hypothesis can be rejected. ▪ If p-value < α → reject null hypothesis ▪ If p-value > α → do not reject null hypothesis 2 Parametric tests are based on specific assumptions about the distribution of the population from which samples are drawn. Examples: t-test, F-test or chi-square test. Nonparametric tests are either not concerned with a parameter or make minimal assumptions about the population from which the sample comes. Nonparametric test: The Spearman rank correlation coefficient is equivalent to the usual correlation coefficient but is calculated on the ranks of two variables within their respective samples. For a sample size n, the spearman rank correlation is: 6 ∑ni=1 d2i rs = 1 − n(n2 − 1) Regression equation: Yi = b0 + b1 Xi + εi Linear regression model: computes the best fit line through the scatter plot. Dependent variable (Yi): the variable whose variation we want to explain. Independent variable (Xi): the explanatory variable. Intercept (b0): the value of the dependent variable when the independent variable is zero. Slope (b1): measures the change in the dependent variable for a one-unit change in the independent variable. Simple linear regression model assumptions: 1. Linearity: The relationship between the dependent variable, Y, and the independent variable, X, is linear. 2. Homoskedasticity: The variance of the regression residuals is the same for all observations. 3. Independence: The observations, pairs of Ys and Xs, are independent of one another. This implies the regression residuals are uncorrelated across observations. 4. Normality: The regression residuals are normally distributed. Estimated variance of the prediction error: 1 (X − ̅ X)2 sf2 = s2 ∗ [1 + + ] n (n − 1)sx2 Creating a prediction interval around the predicted dependent variable: 1. Make the prediction. 2. Compute the variance of the prediction error. 3. Determine tc at the chosen significance level α. 4. Compute the (1-α) prediction interval using the formula below: ̂ ± t c ∗ sf Y Functional forms: ▪ Log-lin model: The dependent variable is logarithmic but the independent variable is linear. ▪ Lin-log model: The dependent variable is linear but the independent variable is logarithmic. ▪ Log-log model: Both the dependent and independent variables are in logarithmic form. Fintech: the technological innovation in the design and delivery of financial products and services. Big Data: vast amounts of data generated by industry, governments, individuals, and electronic devices. Characteristics of Big Data (Four Vs): volume, velocity, variety, veracity Artificial intelligence (AI): computer systems perform tasks that have traditionally required human intelligence. They exhibit cognitive and decision-making ability comparable or superior to that of human beings. Machine learning (ML): computer-based techniques that “extract knowledge from large amounts of data by “learning” from known examples and then generating structure or predictions” without relying on any help from a human. Aim: find the pattern, apply the pattern. Main types: supervised learning, unsupervised learning, and deep learning. Text analytics: the use of computer programs to derive meaning from large, unstructured text- or voice-based data. Natural language processing (NLP) is an application of text analytics whereby computers analyze and interpret human language. Economics Standard error of estimate (SEE)= √MSE A low SEE implies that the the linear regression model does a good job of capturing the relationship between dependent and independent variables. Coefficienct of determination: Explained variation Regression sum of squares (RSS) R2 = = Total variation Sum of squares total (SST) Interpretation of F-test statistic: ▪ The higher the F-statistic, the better. ▪ A high F-statistic implies that the regression model does a good job of explaining the variation in the dependent variable and vice versa. ▪ An F-statistic of 0 indicates that the independent variable does not explain variation in the dependent variable. Test statistic to test whether an estimated slope coefficient is statistically significant: ̂1 − B1 Estimated value − Hypothesized value b t= = sb̂1 standard error where sb̂1 = Ver 1.0 SEE Perfect competition: Price = MR, horizontal demand curve at market price Imperfect competition: Price > MR, negatively sloped demand curve and MR curve Total Revenue (TR) = Price x Quantity Maximum economic profit: MR = MC and MC does not fall with output Minimum efficient scale = minimum point on LR ATC curve Breakeven point: TR = TC, ATC = Price Situation Price > ATC Price = ATC AVC < Price < ATC Price < AVC Short Run Economic Profit Operate Breakeven Operate Long Run Economic Profit Operate Breakeven Operate Operate Shutdown Shutdown Shutdown Economies of scale: as output increases, the long-run cost per unit decreases ̅ 2 √∑n i=1(Xi −X) 3 Perfect Competition Monopolistic Competition Many firms Oligopoly Monopoly Number of Many firms Few firms Single firm Sellers Barriers to Very low Low High Very high Entry and Exit Product Homogeneous Substitutes Close Unique Differentiation but substitutes or product differentiat differentiated ed Non-price None Advertising Advertising Advertising Competition and product and product differentiati differentiation on Pricing Power None. Price Some Some to Considerable taker. significant Example Oranges; Milk; Toothpaste Prices of Electricity Wheat commercial provider/any airlines for a utility given route company (water, cooking gas) as they are typically controlled by a government authority Supply and demand relationships Monopolistic competition ▪ Since the products are unique, a monopolistic firm has a downward sloping demand curve. MR is steeper and lies below the demand curve. ▪ Profit maximization output is based on MR = MC. ▪ Price is determined based on the demand curve. ▪ The supply function is not well-defined in monopolistic competition. Dominant firm oligopoly ▪ As in monopolistic competition, the supply function is not well defined. ▪ We cannot determine equilibrium output and price without considering the demand function and competitive strategies. ▪ Profit-maximizing condition: MR = MC. ▪ The equilibrium price is based on the demand curve Concentration measures N-firm: sum of percentage market shares of industry’s N largest firms. HHI: sum of squared market shares of industry’s N largest firms. ▪ Ranges from 0 to 1 – where 0 indicates perfect competition and 1 indicates a perfect monopoly. Business cycle phases: recovery, expansion, slowdown, contraction Credit cycles: describe the changing availability and pricing of credit Economic indicators: leading indicators, coincident indicators, lagging indicators Fiscal policy: government’s decisions about taxation and spending Monetary policy: central bank activities that are directed toward influencing the quantity of money and credit in an economy Fiscal multiplier = Ver 1.0 Crowding-out effect: may occur as government borrowing increases demand for loanable funds, thus leading to increased interest rates and decreased private sector investments. Ricardian equivalence may prevail: private savings rise in anticipation of the need to repay principal on government debt. At below full employment levels, deficits do not necessarily crowd out private investment. Fiscal policy is subject to recognition, action, and impact lags. Fiscal policy can be contractionary or expansionary. Roles of central bank: supply currency, banker to government and other banks, regulate risk and supervise payment system, lender of last resort, repository of gold and foreign exchange reserves, conductor of monetary policy Objectives of central bank: control inflation (primary objective), secondary objectives: maintain full employment and output, maintain confidence in the financial system, promote understanding of the financial sector Tools of central bank to control the money supply: policy rates, open market operations, reserve requirements Expansionary or contractionary monetary policy Neutral interest rate = real trend rate of economic growth + inflation target If policy rate > neutral interest rate → contractionary monetary policy. If policy rate < neutral interest rate → expansionary monetary policy. Interaction of monetary and fiscal policy Easy/Expansionary Fiscal Tight Fiscal Policy Policy AD up. AD down. Low rates → private sector Low rates→ private demand up. sector stimulated. Growing private and public The public sector will sector. become a smaller percentage of the economy. Tight Monetary Easy/Expansionary Policy Monetary Policy Diseconomies of scale: as output increases, the long-run cost per unit increases Characteristics of economic market structures AD up. High interest rates → private sector down. Public spending will become a higher percentage of GDP. AD down. High interest rates → private sector demand down. Shrinking private and public sectors. Quantitative easing: an unconventional approach adopted by the U.S. and U.K. governments during the recent recession of 2008-09 to print money. Cooperative country: A country that engages/reciprocates in rule standardization; tariff harmonization; international agreements on trade, immigration, or regulation; and allows free flow of information. Non-cooperative country: A country with inconsistent and even arbitrary rules; restricted movement of goods, services, people, and capital across borders; retaliation; and limited technology exchange. Geopolitical actors can be classified into four categories based on two axes – ‘political cooperation versus non-cooperation’ and ‘globalization versus nationalism’. The four categories are: autarky, hegemony, multilateralism, and bilateralism. International Monetary Fund: Assists in international monetary cooperation and exchange rate stability. 1 1−MPC(1−tax rate) 4 World Bank: Provides resources and knowledge and helps form private/public partnerships with the overall aim of fighting poverty. World Trade Organization: Ensures that trade flows freely and works smoothly. Types of geopolitical risk: event risk, exogenous risk, thematic risk Geopolitical tools: National security tools, economic tools, financial tools To assess geopolitical threats, an investor considers geopolitical risk in terms of: likelihood it will occur, velocity (speed) of its impact, size and nature of impact. Benefits of international trade: lower-cost goods (importing country), better prices (exporting country), greater product variety, efficient allocation of resources, lower costs due to economies of scale, increased employment opportunities Costs of international trade: short-term loss of employment in importing countries, less efficient firms will go out of business Types of trade restrictions ▪ Tariffs: taxes imposed on imported goods by the government ▪ Quotas: restrictions on the absolute amount of imports allowed in a country over some period ▪ Export subsidies: government incentives to exporting firms which artificially reduce cost of production ▪ Voluntary Export Restraint: agreements by exporting countries to voluntarily restrict exported amount to avoid tariffs or quotas imposed by trading partners Types of trading blocs and regional trading agreements ▪ Free-Trade Area: All barriers to import and export goods and services among member countries are removed. E.g., North American Free Trade Agreement (NAFTA). ▪ Customs Union: Free-trade area + all member countries adopt a common set of trade restrictions with non-members. ▪ Common Market: Customs union + all barriers to the movement of labor and capital goods among member countries are removed. ▪ Economic Union: Common market + member countries establish common institutions and economic policy. E.g., European Union (EU). ▪ Monetary Union: Economic union + member countries adopt a single currency. E.g., European Zone. Net welfare effect of tariffs: consumer surplus + producer surplus + government tax revenue Exchange rates Real exchange rate P/B = nominal exchange rate P/B x (base currency CPI / price currency CPI). Real exchange rate (d/f) = Sd/f x (Pf/Pd) Foreign price level in domestic currency = Sd/f x Pf Forward rate: Ff/d = Sf/d ( 1+𝑟𝑓 1+𝑟𝑑 ) Forward discount or premium: ▪ If forward rate > spot rate, the base currency is trading at a forward premium. ▪ If forward rate < spot rate, the base currency is trading at a forward discount. ▪ Interest rate differential = iP − iB ▪ Percentage change in spot rates is proportional to the interest rate differential. Ver 1.0 Corporate Issuers Forms of business structures ▪ Sole proprietorship: The owner personally funds the capital required to operate the business and retains full control over the business’s operations. ▪ General partnership: Similar to a sole proprietorship with the important distinction that they have two or more owners called ‘partners’. ▪ Limited partnership: A special type of partnership that has at least one ‘general partner’ (GP) with unlimited liability, who is responsible for managing the business. The remaining partners are ‘limited partners’ (LPs) with limited liability. ▪ Corporation: It is an evolved model of the limited partnership, also called a limited liability company (LLC) or limited company in many countries. A private company can go public through IPO, direct listing or acquisition. Special purpose acquisition company (SPAC): A a shell company, often called a “blank check” company; it exists for the purpose of acquiring an unspecified private company. Corporate issuer financing: • Debt: finite length, interest and principal payments promised on pre-specified future dates, debtholders have a priority claim to an issuer’s cash flows and assets • Equity: permanent financing, no promises of repayments, residual claim on an issuer’s cashflows and assets Issuer perspective: debt is riskier than equity Investor perspective: equity is riskier than debt Examples of ESG Factors Environmental Issues ▪ Climate change ▪ Air and water pollution ▪ Biodiversity ▪ Deforestation ▪ Energy efficiency ▪ Waste management ▪ Water scarcity Social Issues Governance Issues ▪ Customer satisfaction ▪ Data protection and privacy ▪ Gender and diversity ▪ Employee engagement ▪ Community relations ▪ Human rights ▪ Labor standards ▪ Board composition ▪ Audit committee structure ▪ Bribery and corruption ▪ Executive compensation ▪ Lobbying ▪ Political contributions ▪ Whistleblower schemes Principal-agent relationship: owner (principal) hires agents to perform a particular task or service on their behalf. The agent is meant to act in the best interest of the principal. Conflict arises when the interests of the principal and agent diverge. Corporate governance: the arrangement of checks, balances, and incentives that exists to manage conflicting interests among a company’s management, board, shareholders, creditors, and other stakeholders. Risks of poor corporate governance: weak control systems, ineffective decision making, legal risk, regulatory risk, reputational risk, default and bankruptcy risk Benefits of effective corporate governance: higher operational efficiency, control, operating and financial performance; lower default risk, lower cost of capital 5 Cash conversion cycle (CCC): length of time from paying suppliers to collecting cash from customers, how quickly an issuer converts inventory investments into cash CCC = Days of inventory on hand + Days sales outstanding – Days payable outstanding Effective annual rate of supplier financing: ((1 + Discount % ) Days in Year Payment period−Discount period 100%−Discount % )−1 Total working capital = Current assets – current liabilities Net working capital = current assets (excluding cash and marketable securities) – current liabilities (excluding short-term and current debt) Primary sources: Cash sources used in day-to-day operations (e.g., cash balances, trade credit, lines of credit from bank). Secondary sources: Impacts the day-to-day operations, alter the financial structure, and may indicate deteriorating financial condition (e.g., liquidating assets, filing for bankruptcy, negotiating debt agreements). Drags on liquidity reduce cash inflows, ex: uncollectible receivables, obsolete inventory Pulls on liquidity are accelerations in cash outflows or interruptions in credit Working capital management: conservative, moderate or aggressive approach Types of capital investment: going concern projects, regulatory/compliance projects, expansion projects, other projects Net present value (NPV): expected impact to shareholder wealth if the project is undertaken. NPV = 𝐶𝐹0 + 𝐶𝐹1 (1+𝑟)1 + 𝐶𝐹2 (1+𝑟)2 +⋯ + 𝐶𝐹𝑇 (1+𝑟)𝑇 ▪ If NPV > 0, invest. ▪ If NPV < 0, do not invest. ▪ For mutually exclusive projects, invest in the project with higher and positive NPV. Internal rate of return (IRR): CF1 CF2 ▪ If IRR  r, invest. ▪ If IRR < r, do not invest. Return on invested capital (ROIC): reflects how effectively a company’s management is able to convert capital into after-tax operating profits. After−tax operating profit𝑡 Average invested capital = (1−Tax rate) x Operating profit𝑡 Average total LT liabilities and equity𝑡−1,𝑡 Types of real options include: 1. Timing options 2. Sizing options - abandonment options or growth options 3. Flexibility options - price-setting options or productionflexibility options 4. Fundamental options If NPV is positive without considering options, go ahead and make the investment. If NPV is negative without considering options, calculate NPV (based on DCF alone) – Cost of options + Value of options. Weighted average cost of capital (WACC): overall cost of sources of capital; required return or opportunity costs for the firm as a whole; appropriate discount rate for cash flows of projects having similar risk profile as the firm WACC = wd rd (1 − t) + wp rp + we re Ver 1.0 Without Taxes Proposition I VL = VU With Taxes VL = VU + tD Proposition re = r0 + (r0 − rd ) D⁄E re = r0 + (r0 − rd )(1 II − t) D⁄E Value of a leveraged company: VL = VU + tD – PV(Costs of financial distress) Static trade-off theory: while selecting a capital structure, a company balances the value of the tax benefit on interest payments with the present value of the costs of financial distress. Pecking order theory (in order of most preferred to least preferred): internal financing (retained earnings), debt financing, equity financing Business model: It describes how a business is organized to deliver value to its customers. It should have a value proposition and a value chain. Value proposition: The product or service attributes valued by a firm’s target customers that lead them to prefer its offering over those of its competitors, given relative pricing. Value chain: How the firm is structured to deliver value, encompassing the systems and processes within a firm that create value for its customers. Omnichannel strategy: using both digital and physical channels to complete a sale. Financial Statement Analysis Financial statement analysis framework 1. Define the purpose and context of the analysis. 2. Collect data. 3. Process the data. 4. Analyze and interpret the data. 5. Develop and communicate conclusions. 6. Follow up. CFt IRR: [(1+IRR)1] + [(1+IRR)2] + ⋯ + [(1+IRR)t] = 0 ROIC = Modigliani–Miller propositions regarding capital structure: Role of financial statement analysis: form expectations about a company’s future performance, financial position, and risk factors for making investment, credit, and other economic decisions. Revenue recognition: Revenue is recognized in the period it is earned. Expense recognition: expenses are matched to the period in which revenue is recognized (matching principle), to the period in which the expense occurs, or to the period of expected benefits of the expenditures. Non-recurring items Discontinued operations: An operation that the company has disposed in the current period or is planning to dispose in future. Unusual or infrequent items: either unusual in nature or infrequent in occurrence, but not both. 𝐁𝐚𝐬𝐢𝐜 𝐄𝐏𝐒 = net income − preferred dividends weighted average number of shares outstanding 𝐃𝐢𝐥𝐮𝐭𝐞𝐝 𝐄𝐏𝐒 NI + Conv debt int (1 − t) − Pref div + Conv pref div = Weighted average shares + New shares issued Diluted EPS (Treasury Stock method): [NI – Pref div] ÷ [Weighted average shares + (New shares that would have been issued at option exercise – Shares that could have 6 been purchased with cash received upon exercise) x (Proportion of year during which the financial instruments were outstanding)] Financial assets Measured at Fair value through profit or loss (FVTPL) under IFRS or Held-for-Trading under US GAAP: measured at fair value; unrealized gains shown on Income Statement. Measured at Fair value through other comprehensive income (FVTOCI) under IFRS or available-for-sale under US GAAP: measured at fair value; unrealized gains/losses shown in OCI. Measured at Cost or Amortized Cost: measured at cost or amortized cost; unrealized gains not recorded anywhere. Common size analysis ▪ Common-size balance sheet expresses each balance sheet account as a percentage of total assets. ▪ Common-size income statement expresses each item as a percentage of sales. ▪ Common size cash flow statement expresses each item as a percentage of total cash inflows/outflows or as a percentage of sales. Cash flow from operations (CFO): Direct method of computing CFO: take each item from the income statement and convert to cash equivalent by removing the impact of accrual accounting. The rules to adjust are: ▪ Increase in assets is use of cash (-ve adjustment). ▪ Decrease in asset is source of cash (+ve adjustment). ▪ Increase in liability is source of cash (+ve adjustment). ▪ Decrease in liability is use of cash (-ve adjustment). Indirect method of computing CFO: CFO is obtained from reported net income through a series of adjustments. ▪ Begin with net income. ▪ Add back all noncash charges to income and subtract all noncash components of revenue. ▪ Subtract any gains that resulted from financing or investing cashflows. ▪ Add or subtract changes to related balance sheet operating accounts. Cash flow from investing (CFI): change in gross asset account that results from the purchase or sale of equipment. Cash from sale of equipment = Historical cost of equipment sold Accumulated depreciation on equipment sold + Gain on sale of equipment where: Historical cost of equipment sold = beginning balance + equipment purchased - ending balance equipment Accumulated depreciation on equipment sold = beginning value of depreciation + depreciation expense – ending value of depreciation Cash flow from financing (CFF): the sum of net cash flows from creditors and net cash flows from shareholders. It can be calculated using the following formulae: (1) CFF = net cash flow from creditors + net cash flow from shareholders (2) Net cash flow from creditors = new borrowings – principal repaid (3) Net cash flow from shareholders = new equity issued – shares repurchased – cash dividends Ver 1.0 Classification of Cash Flows Interest received Interest paid Dividends received Dividends paid IFRS Operating or investing Operating or financing Operating or investing Operating or financing US GAAP Operating Operating Operating Financing Retained Earnings: REbeg + NI – Dividends = REend Free cash flow to the firm (FCFF) FCFF = NI + NCC + Int (1 - Tax rate) – FCInv – WCInv FCFF = CFO + Int (1 - Tax rate) – FCInv Free cash flow to equity (FCFE) FCFE = CFO – FCInv + Net borrowing Activity ratios: measure the efficiency of a company’s operations Inventory turnover = COGS / average inventory Receivables turnover = revenue / average receivables Payables turnover = purchases / average trade payables Days of inventory on hand = 365 / inventory turnover Days of sales outstanding = 365 / receivables turnover Number of days of payable = 365 / payables turnover Total asset turnover= Revenue/ Average total assets Cash conversion cycle = days of inventory on hand + days of sales outstanding – number of days of payables Liquidity ratios: measure a company’s ability to meet short-term obligations. Current ratio = current assets / current liabilities Quick ratio = (cash + short term marketable investments + receivables) / current liabilities Cash ratio = (cash + short term marketable investments) / current liabilities Defensive interval ratio = (cash + short term marketable investments + receivables) / daily cash expenditures Solvency ratios: measure a company’s ability to meet long term obligations. Debt to assets ratio = total debt / total assets Debt to equity ratio = total debt / total shareholder’s equity Financial leverage ratio = average total assets / average total equity Debt coverage = CFO / Total debt Interest coverage = (CFO + Interest paid + Taxes paid) / Interest paid Fixed charge coverage = (EBIT + Lease payments) / (Interest payments + Lease payments) Profitability ratios: measure the ability of a company to generate profits. Gross profit margin = gross profit / revenue Operating profit margin = operating profit / revenue Net profit margin = net profit / revenue Return on assets (ROA) = net income / average total assets Return on equity (ROE) = net income / average total equity Return on total capital = EBIT/(Average short term and long term debt Debt + equity) 7 DuPont analysis decomposes a firm’s ROE to better analyze a firm’s performance. ROE = Net income × EBT EBT EBIT Average total assets × EBIT Revenue × Revenue Average total assets × Average shareholders′ equity net income sales assets )( )( ) sales assets equity ROE = ROA x Leverage ROE = ( Inventory methods First in first out (FIFO) assumes that the earliest items purchased are sold first. Last in first out (LIFO) assumes that the most recent items purchased are sold first. Weighted average cost averages total cost over total units available. Specific identification identifies each item in the inventory and uses its historical cost for calculating COGS, when the item is sold. LIFO v/s FIFO: When prices are rising, and inventory levels are stable or increasing, as compared to FIFO, LIFO results in higher COGS, lower taxes, lower net income, lower ending inventory, lower working capital, higher cash flow (after tax). LIFO reserve = FIFO inventory value – LIFO inventory value LIFO liquidation occurs when the number of units in ending inventory is less than the number of units in the beginning inventory. Conversion from LIFO to FIFO FIFO inventory = LIFO inventory + LIFO reserve FIFO COGS = LIFO COGS – (ending LIFO reserve – beginning LIFO reserve) FIFO NI = LIFO NI + change in LIFO reserve (1 - T) FIFO retained earnings = LIFO retained earnings + LIFO reserve (1 – T) Net realizable value = estimated sales price – estimated selling costs Market value limits = (NRV – normal profit margin, NRV) IFRS: inventories are valued at the lower of cost or net realizable value. Inventory write-ups are allowed but only to the extent to which a previous write-down to net realizable value was recorded. US GAAP: inventories are valued at lower of cost or market. If cost exceeds market, inventory is written down. No subsequent writeups are allowed. Capitalizing v/s expensing an asset As compared to expensing, capitalizing an asset results in higher total assets, higher equity, lower income variability, higher CFO, lower CFI, lower debt/equity. Treatment of research and development costs: IFRS: research costs must be expensed, development costs (not only software development costs) may be capitalized if technical feasibility and intent to sell the asset are established. US GAAP: both research and development costs must be expensed, certain development costs related to software can be capitalized. Accounting for software for sale and software for internal use differs. are reviewed for impairment when a change of circumstances indicate the carrying amount may not be recoverable. Intangibles with indefinite useful lives are tested annually for impairment. IFRS: an asset is impaired when carrying value > recoverable amount. Recoverable amount is the greater of (fair value – selling costs) and (PV of expected CFs from the asset, i.e. value in use). If impaired, the asset is written down to recoverable amount. Subsequent loss recoveries are allowed, but they cannot exceed the historical cost. US GAAP: an asset is impaired when carrying value > asset’s undiscounted future cash flows. If impaired, written down to fair value. Subsequent loss recoveries are not allowed. Fixed asset ratios and relationships: Average age of a company's assets = (Accumulated depreciation)/(Depreciation expense) Average remaining life of a company's assets = (Net PPE)/(Depreciation expense) Assuming straight-line depreciation and no salvage value, we can state the following relationships: Estimated total useful life = Time elapsed since purchase (Age) + Estimated remaining life Estimated total useful life = Historical cost ÷ annual depreciation expense Historical cost = Accumulated depreciation + Net PPE Financial reporting of leases from a lessee’s (entity using the asset) perspective: Under IFRS: Single accounting model for both finance and operating leases for lessees. ▪ Recognize a lease liability and corresponding right-of-use asset on the balance sheet, both equal to the present value of lease payments. ▪ The liability is subsequently reduced using the effective interest method ▪ The right-of-use asset is amortized, often on a straight-line basis over the lease term. ▪ Interest and amortization expenses are shown separately on the income statement. ▪ The principal repayment component is reported as cash outflow under financing activities. The interest expense can be reported under either operating or financing activities. Under US GAAP: Two accounting models for lessees: one for finance leases and another for operating leases. The finance lease accounting model is the same as the lease accounting model for IFRS. The operating lease accounting model is different: ▪ Recognize a lease liability and corresponding right-of-use asset on the balance sheet, both equal to the present value of lease payments. ▪ The liability is subsequently reduced using the effective interest method ▪ But the amortization of the right-of-use asset is the lease payment less the interest expense. ▪ Interest expense and amortization expense are shown together as a single operating expense on the income statement. ▪ The entire lease payment is reported as cash outflow under operating activities. Depreciation, amortization, impairment: Long-lived tangible assets with finite useful lives are depreciated and intangible assets with finite useful lives are amortized. Both Ver 1.0 8 Financial reporting of leases from a lessor’s perspective. Finance lease lessors (IFRS and US GAAP) ▪ Recognize a lease receivable asset equal to the present value of future lease payments and de-recognize the leased asset, simultaneously recognizing any difference as a gain or loss. ▪ The lease receivable is subsequently reduced by each lease payment using the effective interest method. ▪ Interest income is reported on the income statement, typically as revenue. ▪ The entire cash receipt is reported under operating activities on the statement of cash flows. Operating lease lessors (IFRS and US GAAP) ▪ The balance sheet is not affected: the lessor continues to recognize the underlying asset and depreciate it. ▪ Lease revenue is recognized on a straight-line basis on the income statement. ▪ The entire cash receipt is reported under operating activities on the statement of cash flows. Defined Contribution (DC) Plan: cash payment made into plan is recognized as pension expense. Defined Benefit (DB) Plan: net pension asset (liability) is reported on the balance sheet. For each period, the change in net pension asset (liability) is recognized either on the income statement or in OCI. Stock-based compensation and stock options: measured using fair value at the grant date and recognized as compensation expense over the service/vesting period. Deferred tax assets are created when income tax payable is greater than income tax expense. Deferred tax liabilities are created when income tax expense is greater than income tax payable. If DTL is not expected to reverse, treat it as equity. Deferred tax liability = (Carrying amount – Tax Base) x Tax Rate Income tax expense = Income tax payable + + ΔDTL - ΔDTA Reported effective tax rate = Income tax expense / pretax income Reporting quality: refers to the information disclosed in the firm’s financial statements. High-quality reporting means that the financial statements are decision useful and represent the economic reality of the company. Results quality: refers to the earnings and cash generated by the company’s actual economic activities. High-quality earnings mean that the earnings are sustainable. Steps while building a financial statement model: 1. Perform an industry overview using the Porter’s five forces model. 2. Perform a company overview to account for company specific factors. 3. Construct a pro-forma income statement. 4. Construct a pro-forma balance sheet. 5. Construct a pro-forma cash flow statement using the income statement and the balance sheet. 6. Determine the intrinsic value of the company using an appropriate valuation model. Equity Types of financial intermediaries 1. Brokers, exchanges, and alternative trading systems 2. Securitizers 3. Depository institutions 4. Insurance companies 5. Clearinghouse 6. Depositories or custodians 7. Arbitrageurs 𝐋𝐞𝐯𝐞𝐫𝐚𝐠𝐞 𝐫𝐚𝐭𝐢𝐨 = value of position value of equity investment in that position 𝐌𝐚𝐫𝐠𝐢𝐧 𝐜𝐚𝐥𝐥 𝐩𝐫𝐢𝐜𝐞 = initial purchase price × (1 − initial margin) (1 − maintenance margin) Execution instruction: specifies how the order will be filled. Types are: market orders, limit orders, all or nothing orders, hidden orders, iceberg orders. Validity instruction: specifies when the orders may be filled. Types are: day orders, good-till-cancelled orders, immediate or cancel orders, good-on-close orders, stop-loss orders. Clearing instructions convey who is responsible for clearing and settling the trade. Types of markets Quote driven markets: trade takes place at the price quoted by dealers who maintain an inventory of the security. Order driven markets: trading rules match buyers to sellers, thus making them supply liquidity to each other. Brokered markets: brokers arrange trades between counterparties. Characteristics of a well-functioning financial system Operationally efficient markets where trading costs like commissions, bid-ask spreads and price impacts are low, increases market pricing efficiencies. Informationally efficient markets allow for absorption of timely financial disclosures making the prices a close reflection of the fundamental values. Allocationally efficient markets allow for better utilization of capital by allocating it to the most productive use. A security market index serves as a benchmark that investors can use to track, measure and compare performance. Index returns can be calculated using two methods: Price return = (index end value – index start value)/ index start value Total return = (index end value – index start value + income earned over the holding period)/ index start value Different weighting methods used in index construction Price weighting: weights are the arithmetic averages of the prices of constituent securities. Price weighted index = Sum of Stock Prices No.of stocks in index adjusted for splits Equal weighted index: weights are the arithmetic averages of the returns of constituent securities. Market capitalization weighted index: weight of each security is determined by dividing its market capitalization with total market capitalization. Fundamental weighing: weights are based on fundamental parameters such as earnings, book value, cash flow, revenue, and dividends. Forms of market efficiency Weak form: prices reflect only past market data. Ver 1.0 9 Semi-strong form: prices reflect past market data + public information. Strong form: prices reflect past market data + public information + private information. Market share = Revenue / Market size Degree of operating leverage (DOL) measures operating risk. %  Operating Profit DOL = %  Sales Degree of financial leverage (DFL) measures financial risk. %  Net Income DFL = %  Operating Income Porter’s five forces: the profitability of companies in an industry is determined by: (1) threat of new entrants, (2) bargaining power of suppliers, (3) bargaining power of buyers, (4) threat of substitutes, (5) intensity of rivalry among existing competitors. PESTLE analysis: political, economic, social, technological, legal, and environmental influences on an industry. This type of analysis focuses on an industry’s growth rate and market share dynamics. Forecast approaches: four approaches including historical results, historical base rates and convergence, management guidance and analyst discretion. Revenue can be forecasted using a top-down or bottom-up approach. Dividend discount models: value is estimated as the present value of expected future dividends plus the present value of a terminal value. V0 = Dt ∑.nt=1 (1+r)t + Pn (1+r)n Free cash flow to equity models: value is estimated as the present value of expected future free cash flow to equity. FCFE = CFO – FCInv + net borrowing ∞ FCFEt V0 = ∑.t=1 ∗ ((1+r)t ) Gordon growth model: assumes that dividends will grow indefinitely at a constant growth rate. V0 = D1 r−g Multi-stage dividend discount model: used for companies with high growth rate over an initial few number of periods followed by a constant growth rate of dividends forever. n V0 = ∑.t=1 Vn = D0 (1+gs )t (1+r)t V n + (1+r) n Dn+1 r−g Multiples based on fundamentals: tell us what a multiple should be based on some valuation models. Forward P/E = P0 /E1 = D1 E1 r−g = dividend payout ratio r−g Multiples based on comparables: compares the stock’s price multiple to a benchmark value based on an index or with a peer group. Commonly used price multiples are P/E, P/CF, P/S, P/BV. Enterprise value = market value of debt +market value of equity – cash and short-term investments. Ver 1.0 Fixed Income Basic features of a fixed-income security Issuer: Entity issuing the bond. Bonds can be issued by supranational organizations, sovereign governments, nonsovereign governments, quasi-government entities, corporate issuers. Maturity date: Date when issuer will pay back principal (redeem bond) ▪ Money market securities: original maturity is one year or less. ▪ Capital market securities: original maturity is more than a year. Par value: Principal amount that is repaid to bond holders at maturity. ▪ Premium bond: market price > par value ▪ Discount bond: market price < par value ▪ Par bond: market price = par value Coupon rate and frequency: Coupon rate is the interest rate paid on a bond every year by the issuer until its maturity date. Bonds that have only one payment at maturity are called zero-coupon bonds. Seniority: Seniority ranking determines who gets paid first, or who has the first claim on the cash flows of the issuer, in the event of default/bankruptcy/restructuring. Contingency provisions: Some bonds may be issued with embedded call/put/conversion options. Bond indenture: legal agreement between the bond issuer and the investor. Bond covenants: legally enforceable rules that borrowers and lenders agree on at the time of a new bond issue. They can be affirmative (positive) or negative (restrictive). Cash flows of fixed-income securities Bullet structure: pays coupon periodically and entire payment of principal occurs at maturity. Fully amortized bond: regular payments include both interest and principal; outstanding principal amount is reduced to zero by the maturity date. Partially amortizing bond: regular payments include both interest and principal; balloon payment is required at maturity to repay the remaining principal as a lump sum. Sinking fund agreements: issuer is required to retire a portion of the bond issue at specified times during the bond’s life. Floating rate notes (FRN): coupon is set based on some reference rate plus a spread. Contingency provisions Callable bond: gives the issuer the right to redeem the bond prior to maturity at a specified call price; call provision lowers price. Putable bond: gives the bondholder the right to sell bonds back to the issuer prior to maturity at a specified put price; put provision increases price. Convertible bond: gives the bondholder the right to convert the bond into common shares of the issuing company; increases price. Warrant: gives the bondholder the right to buy the underlying common shares at a fixed price any time before the expiration date. Contingent Convertible Bonds: bonds with contingent write-down provisions; can be converted into equity contingent to a specific condition. Mechanisms available for issuing bonds Underwritten offerings: investment bank buys the entire issue and takes the risk of reselling it to investors or dealers. Best effort offerings: investment bank serves only as a broker and sells the bond issue only if it is able to do so. 10 Shelf registrations: issuer files a single document with regulators that allows for additional future issuances. Auction: price discovery through bidding. Private placement: entire issue is sold to a qualified investor or to a group of investors. Repurchase agreement (repo): sale of a security with a simultaneous agreement by the seller to buy the same (or similar) security back from the purchaser at an agreed-on repurchase price and future date (repurchase date). Initial margin = Security Price0 / Purchase Price0 Haircut = (Security Price0 - Purchase Price0) / Security Price0 Variation margin = (Initial margin x Purchase Pricet) – Security Pricer The factors that affect the repo rate include: ▪ The risk of the collateral ▪ Term of the repurchase agreement ▪ Delivery requirement ▪ Supply and demand ▪ Interest rates of alternative financing Sovereign debt: issued by national governments primarily for fiscal reasons. Non-sovereign governments: may issue general obligation or revenue bonds. Government agencies: quasi-government entities that issue debt to fund specific public goods or services. Supranational organizations: created and supported by sovereign governments in pursuit of a common objective. Bond pricing Using market discount rate: bond’s price is the present value of its future cash flows, discounted at the bond’s market discount rate, also called YTM. Using spot rates: PMT 1 1) PV = (1+Z PMT 2 2) + (1+Z PMT+FV N N) + ⋯ + (1+Z ; where ZN are the spot rates. Full price or dirty price = flat price + accrued interest t Accrued interest = ∗ PMT T Full price = PV x (1 + r)t/T Matrix pricing: method used to value illiquid bonds by using prices and yields on comparable securities. Relationships among a bond’s price, coupon rate, maturity, and discount rate (yield-to-maturity) Inverse effect Bond price is inversely related to discount rate (YTM). Convexity effect For the same coupon/maturity bond: the percentage price change is more when discount rate goes down than when it goes up. Coupon effect For the same time to maturity and same change in discount rate: prices of lowcoupon bonds change more than a highcoupon bond. Maturity effect For the same coupon rate and same change in discount rate: prices of longterm bonds change more than short-term bonds. Note: Low-coupon and Long-term bonds are more sensitive to discount rates. Ver 1.0 Stated Annual Rate: The formula for conversion based on periodicity is APR m m APR n n (1 + ) = (1 + ) m n Yield measures: Street convention yield: assumes payments are made on scheduled dates, neglecting weekends and holidays for simplicity. True yield: is the yield-to-maturity calculated using an actual calendar. Here we consider weekends and holidays. Current yield is the annual coupon payment divided by the flat price. Simple yield: adjusts the current yield by using straight-line amortization of the discount or premium. Yield to call: assumes bond will be called. PMT PMT PV = (1+r)1 + (1+r)2 + ⋯ + PMT+Call price (1+r)N Yield to worst: lower of YTM and YTC. Price of a money market instrument quoted on a discount basis: PV = FV x (1- days to maturity year x DR) Money market discount rate: DR = ( Year )∗ FV−PV days to maturity FV Present value or price of a money market instrument quoted on an add-on basis: PV = FV 1+ Days to maturity x AOR Year Add-on rate: AOR = ( Year )∗ Days FV−PV PV Relationship between AOR and DR: DR AOR = Days to maturity 1 − ∗ DR Year Yield spread: the difference in yield between a fixed-income security and a benchmark. G-spread: benchmark is yield-to-maturity on government bonds. I-spread: benchmark is a swap rate. Z-spread (zero-volatility spread): the constant spread that is added to each spot rate to make the present value of the bond equal to its price. Option-adjusted spread (OAS): adjusts Z-spread by the value of the embedded option. FRN pricing model: PMT = (𝑀𝑅𝑅+𝑄𝑀)×𝐹𝑉 𝑚 Spot rates: yields to maturity on zero-coupon bonds maturing at the date of each cash flow. Forward rate: an interest rate in the future. The one-year interest rate after one year is an example of a forward rate. The implied forward rate can be calculated using spot rates. Relationships among spot curve, par curve, and forward curve 11 Total return on a bond = reinvested coupon interest payments + sale/redemption of principal at maturity Price risk: bond price decreases when the interest rate goes up. Reinvestment risk: value of reinvested coupons increases when the interest rate goes up. For short term horizon, market price risk dominates. For long term horizon, coupon reinvestment risk dominates. If an investor’s investment horizon equals the Macaulay duration of a bond, the risks equally offset each other. Macaulay duration: Time horizon at which market price risk exactly offsets coupon reinvestment risk. Also interpreted as the weighted average of the time to receipt of coupon interest and principal payments. Duration gap = Macaulay duration – Investment horizon Modified duration: linear estimate of the percentage price change in a bond for a 100 basis points change in its yield-to-maturity. Modified duration = macaulay duration / (1 + r) Approximate modified duration = (PV− ) − (PV+ ) 2 ∗ ∆ yield ∗ PV0 Price value of a basis point (PVBP) is an estimate of the change in the price of a bond given a 1 basis point change in the yield-tomaturity. PVBP = PV− − PV+ 2 Cs of traditional credit analysis: Bottom-up factors: capacity, capital, collateral, covenants, and character Top-down factors: country, conditions, and currency Financial Ratios in Corporate Credit Analysis EBIT Margin: Operating Income/Revenue EBIT to Interest Expense: Operating Income/Interest Expense Debt to EBIDTA: Total Debt/EBIDTA Retained cash flow (RCF) to Net Debt: Retained Cash Flow/(Debt – Cash and Marketable Securities) Measures of economic growth and stability: Average real GDP growth: (Real GDPt-1 – Real GDPt) / Real GDPt Real GDP growth volatility: standard deviation of real GDP Size of economy: GDP in PPP terms Per capita GDP: GDP / population Measures of external stability: External debt burden: LT external debt / GDP External debt due: External debt due in 12 months / GDP Reserve ratio: FX reserves / external debt FX reserves / GDP Convexity refers to the curvature of a bond’s price-yield relationship. 𝐴pproximate convexity = PV− + PV+ − 2∗PV0 (Δyield)2 ∗PV0 Duration + convexity effect: 1 % Δ PV FULL = (−AnnModDur ∗ Δyield) + [ ∗ AnnConvexity ∗ 2 (Δyield)2 ] Effective duration: linear estimate of the percentage change in a bond’s price that would result from a 100 basis points change in the benchmark yield curve. Used for bonds with embedded options. Effective duration = (PV− ) − (PV+ ) 2∗∆curve∗PV0 Key rate duration is a measure of the price sensitivity of a bond to a change in the spot rate for a specific maturity. Effective convexity, like effective duration, is useful for bonds with embedded options. Effective convexity = PV− + PV+ − 2∗PV0 (Δcurve)2 ∗PV0 1 % Δ PV FULL = (−EffDur ∗ Δyield) + [ ∗ EffConvexity ∗ (Δyield)2 ] 2 Money Duration: measure of the price change in currency units. MoneyDur = AnnModDur × PVFull MoneyCon = AnnConvexity × PVFull ΔPVFull ≈ - (MoneyDur × ΔYield) + [(1/2) × MoneyCon × (ΔYield)2] Analytical duration approach: uses mathematical formulas to estimate duration and convexity. It assumes that benchmark yields and credit spreads are uncorrelated with one another. Empirical duration approach: uses statistical methods and historical bond prices to derive the price-yield relationship for specific bonds or bond portfolios. Credit risk has two components: Probability of default, loss given default Probability of default (POD): probability that the borrower will default. Loss given default (LGD): investor’s loss conditional on an issuer event of default, LGD = EE x (1 – RR) Recovery rate (RR): percentage of outstanding debt Loss severity: if the borrower does default, how severe is the loss. Loss severity = (1 – RR) Expected exposure (EE): size of investor’s claim at the time of default. Expected loss (EL) = POD x LGD Ver 1.0 Securitization refers to a process in which financial assets such as mortgages, loans or receivables are pooled together. Securities are issued that are backed by this pool, called ABS. Parties involved in the securitization process ▪ SPV (Special Purpose Vehicle): also called the trust or the issuer. ▪ Seller of pool of securities: also known as the originator or depositor. ▪ Servicer: Servicing involves collecting payments from borrowers, notifying borrowers who may be delinquent, and if necessary, seizing equipment from borrowers who default. ▪ Other parties: Independent accountants, underwriters, trustees, rating agencies, and guarantors. Types of ABS Auto loan ABS: backed by auto loans. Solar ABS: backed by solar loans. Credit card ABS: backed by credit card receivables. CDO: backed by a diversified pool of one or more debt obligations. Agency RMBS: backed by home mortgages; guaranteed by the government or a quasi-government entity Non-agency RMBS: backed by home mortgages; issued by private entities that are not guaranteed by a federal agency or a government sponsored enterprise CMO: backed by RMBS, has multiple tranches. CMBS: backed by commercial mortgages; two important characteristics of a CMBS structure are call protection and balloon risk. Covered bonds: have lower credit risks and offer lower yields than otherwise similar ABS. They differ from ABS because of their: dual recourse nature, balance sheet impact, dynamic cover pool, and redemption regimes in the event of sponsor default. Credit tranching: focus is on redistribution of credit risk. Time tranching: focus is on redistribution of prepayment risk. Prepayment risk has two components: Contraction risk: faster prepayments. Extension risk: slower prepayments. 12 LTV = Loan amount / House price Operational Advantages Reduced cash outlay, lower transaction costs versus the underlying, increased liquidity and ability to “short” Less costly to exploit arbitrage opportunities or mispricing Market Efficiency Derivative Risks Risk Greater Potential for Speculative Use Lack of Transparency Derivatives Exchange-traded derivatives: standardized, highly regulated, transparent and free of default. Over-the-counter derivatives: customized, flexible, less regulated than exchange-traded derivatives, but are not free of default risk. ▪ Firm commitments: Both parties have an obligation to complete the transaction. Example: forwards, futures, swaps. ▪ Contingent claims: Seller has the obligation. The buyer has a right but no obligation to complete the transaction. Example: Options, credit derivatives. Call option: It gives the buyer the right to buy the underlying at a given price on a specified expiration date. The seller has an obligation to sell the underlying. Put option: It gives the buyer the right to sell the underlying asset at a given price on a specified expiration date. The seller has an obligation to buy the underlying. Credit derivative: Credit protection seller provides protection against a specific credit loss to the credit protection seller. Call option payoff, profit at expiration ▪ Call buyer payoff: cT = Max(0, ST – X) ▪ Call seller payoff: –cT = –Max(0, ST – X) ▪ Call buyer profit: Max(0, ST – X) – c0 ▪ Call seller profit: Π = –Max(0, ST – X) + c0 Put option payoff, profit at expiration ▪ Put buyer payoff: pT = Max(0, X – ST) ▪ Put seller payoff: –pT = –Max(0, X – ST) ▪ Put buyer profit: Π = Max(0, X – ST) – p0 ▪ Put seller profit: Π = –Max(0, X – ST) + p0 Arbitrage-free pricing: a derivative must be priced such that no arbitrage opportunities exist, and there can only be one price for the derivative that earns the risk-free return. Derivative Benefits Purpose Description Risk Allocation, Allocate, trade, and/or manage underlying Transfer, and exposure without trading the underlying Management Create exposures unavailable in cash markets Information Deliver expected price in the future as well Discovery as expected risk of underlying Ver 1.0 Basis Risk Liquidity Risk Counterparty Credit Risk Destabilization/ Systemic Risk Description High degree of implicit leverage for some strategies may increase the likelihood of financial distress. Derivatives add portfolio complexity and may create an exposure profile that is not well understood by stakeholders. Potential divergence between the expected value of a derivative instrument versus an underlying or hedged transaction Potential divergence between the cash flow timing of a derivative instrument versus an underlying or hedged transaction Derivatives often give rise to counterparty credit exposure, resulting from differences in the current price versus the expected future settlement price. Excessive risk taking and use of leverage in derivative markets may contribute to market stress. Hedge types ▪ Cash flow hedge: A derivative designated as absorbing the variable cash flow of a floating-rate asset or liability. ▪ Fair value hedge: A derivative used to offset the fluctuation in fair value of an asset or liability. ▪ Net investment hedge: A net investment hedge occurs when either a foreign currency bond or a derivative such as an FX swap or forward is used to offset the exchange rate risk of the equity of a foreign operation. Price v/s Value of Forward Contracts Cost of carry = Cost – Benefits. The price of a forward or futures contract is the forward price that is specified in the contract. Forward or futures price using discrete compounding for individual underlying assets (e.g. a stock): F0(T) = [S0 – PV0(I) + PV0(C)](1 + r)T. Forward or futures price using continuous compounding for underlying assets that represent a portfolio (e.g. an equity index): F0(T) = S0e(r+c–i)T Price for FX forward contract: F0 (T) = S0 e(rf −rd )T The value of a forward or futures contract is zero at initiation. The value of a forward contract may increase or decrease during its life according to changes in the spot price. Value of a forward contract during its life Vt (T) = (S𝑡 – PV𝑡 (I) + F (T) 0 PV𝑡 (C)) − (1+r) T−t MTM value of the FX forward at any given time t is calculated as: Vt (T) = St − F0 (T) e(rf −rd)(T−t) 13 Relationship between Interest Rate Futures and FRAs Contract Type Gains from Rising Gains from MRR Falling MRR Interest rate Short futures Long futures futures contract contract FRA Long FRA: FRA Short FRA: FRA fixed-rate payer floating-rate payer Forward and futures price differences ▪ If futures prices are positively correlated with interest rates, long futures contracts are more desirable than long forward contracts. ▪ If future prices are negatively correlated with interest rates, then long forward positions are more desirable than long future positions. Similarities between FRAs and Swaps ▪ Both allow users to lock-in a fixed rate for future. The net difference between a fixed rate agreed upon at inception and a future MRR is used to determine cash settlement. ▪ Both have a symmetric payoff profile. ▪ No cash is exchanged upfront. Both have a value of zero at initiation. ▪ Both involve counterparty credit exposure. Differences between FRAs and Swaps ▪ An FRA has a single settlement, which occurs at the beginning of an interest period, while a swap has periodic settlements, which occur at the end of each respective period. ▪ A swap contract is like a series of FRAs, where each FRA has a different time to maturity. While a swap has a constant fixed rate over its life, the series of FRAs will have different fixed rates for different times to maturity. Par swap rate: the fixed rate that equates the present value of all future expected floating cash flows to the present value of fixed cash flows. Σ PV(Floating payments) = Σ PV(Fixed payments), or N ∑ i=1 N IFR si =∑ i (1 + zi ) (1 + zi )i i=1 Moneyness refers to whether an option is in the money or out of the money. In the money At the money Out of the money Call Option S>X S=X SX Exercise value of an option is the maximum of zero and the amount that the option is in the money. X Call Option Exercise Value = max (0, St – ) (1 + r)(T−t) X Put Option Exercise Value = max (0, − St ) (1 + r)(T−t) Time value of an option is the amount by which the option premium exceeds the exercise value. Factors that determine the value of an option Increase in Value of call Value of put Value of Increase Decrease underlying Exercise price Decrease Increase Risk-free rate Increase Decrease Ver 1.0 Time to expiration Volatility Holding costs Holding benefits Increase Increase Increase Decrease Increase (except for deep in the money European options) Increase Decrease Increase Call option lower bound = max (0, St – Call option upper bound = St Put Option Lower Bound = max (0, X ) (1 + r)(T−t) X − St ) (1 + r)(T−t) Put Option Upper Bound = X Put–call parity for European options fiduciary call = protective put c0 + (1 X + r)T = p0 + S0 Put–Call Forward Parity Fo (T) (1+r)T X + p0 = c0 + (1+r)T Option Put–Call Parity Applications: Firm Value V0 = c0 + PV(D) - p0 Valuing a derivative using a one-period binomial model Hedge Ratio for a Call Option 𝑐1𝑢 − 𝑐1𝑑 ℎ= 𝑢 𝑆1 − 𝑆1𝑑 𝑉0 = ℎ𝑆0 − 𝑐0 𝑉1𝑢 = ℎ𝑆1𝑢 − 𝑐1𝑢 𝑉1𝑑 = ℎ𝑆1𝑑 − 𝑐1𝑑 𝑉1 𝑉0 = 1+𝑟 𝑉 Or ℎ𝑆0 − 𝑐0 = 1 1+𝑟 Valuing a call option using risk neutral probability (𝜋𝑐1𝑢 + (1 − 𝜋)𝑐1𝑑 ) 𝑐0 = (1 + 𝑟)𝑇 Risk-Neutral Probability 1 + 𝑟 − 𝑅𝑑 𝜋= 𝑢 𝑅 − 𝑅𝑑 Alternative Investments The three methods of investing in alternative investments are: ▪ Fund investing: The investor contributes capital to a fund, and the fund makes investments on the investors’ behalf, e.g., investments in a PE fund. ▪ Co-investing: The investor can make investments alongside a fund, e.g., investments in a portfolio company of a fund. ▪ Direct investing: The investor makes a direct investment in a company or project without the use of an intermediary, e.g., direct investments in infrastructure or real estate assets. Compensation structures The GP receives a management fee based on assets under management (commonly used for hedge funds) or committed capital (commonly used for private equity). The GP also receives a performance fee (also called incentive fee or carried interest) based on realized profits. Generally, the performance fee is paid only if the returns exceed a hurdle rate. 14 Common fee structure is 2 and 20 which means 2% management fee and 20% incentive fee. Catch-up clause: It allows the GP to receive 100% of the distributions above the hurdle rate until he receives 20% of the profits generated, and then every excess dollar is split 80/20 between the LPs and GP. High water mark: In some cases, the incentive fee is paid only if the fund has crossed the high-water mark. A high-water mark is the highest value net of fees reported by the fund. Waterfall: It defines the way in which cash distributions will be allocated between the GP and the LPs. There are two types of waterfalls: ▪ Whole-of-fund (or European) waterfalls: As deals are exited, all distributions go to the LPs first. The GP does not participate in any profits until the LPs receive their initial investment and the hurdle rate has been met. ▪ Deal-by-deal (or American) waterfalls: Performance fees are collected on a per-deal basis. Clawback: A clawback provision allows LPs to reclaim a part of the GP’s performance fee. Performance appraisal of alternative investments IRR and MOIC calculations: frequently used to evaluate private equity investments. MOIC = (Realized value of investment + Unrealized value of investment)/(Total amount of invested capital) Cap rate: frequently used to evaluate real estate investments; calculated as the annual rent actually being earned divided by the price originally paid for the property. Hedge fund index returns can be overstated due to survivorship, and backfill biases. Private equity categories include leveraged buyouts, venture capital and growth capital. Leveraged buyouts (LBOs) include: ▪ Management buyouts: existing management team is involved in the purchase. ▪ Management buy-ins: external management team replaces the current management. Stages in venture capital include: ▪ Formative stage: Company is still being formed; consists of angel investing, seed and early stages. ▪ Later stage: company is in expansion phase; after commercial production and sales but before IPO. ▪ Mezzanine stage: company is preparing for an IPO. Exit strategies include: ▪ Trade sale: company is sold to a competitor or another strategic buyer. ▪ IPO: company is sold to the public. ▪ Special purpose acquisition company (SPAC): a shell company, often called a “blank check” company, because it exists solely for the purpose of acquiring an unspecified private company in the future. ▪ Recapitalization: Increases leverage or introduces it to the company. Re-leverages itself when interests are low and pays itself a dividend. ▪ Secondary sale: company is sold to another private equity firm. ▪ Write off/ liquidation: worst case scenario, VC firm sells the assets or writes it off to focus on other projects. Private Debt Private debt refers to various forms of debt provided to private entities including: ▪ Direct lending: Debt capital provided directly to entities that are unable to get capital from traditional bank lenders. ▪ Mezzanine debt: Refers to private credit that is subordinated to senior secured debt but is senior to equity in the borrower’s capital structure. Ver 1.0 ▪ Venture debt: Debt provided to start-up/early-stage companies that may be generating little or negative cash flow. ▪ Distressed debt: Refers to buying debt of mature companies with financial difficulty. Real estate Investment characteristics of real estate are as follows: ▪ Indivisibility – requires large capital investments ▪ Unique characteristics (no two properties are identical). ▪ It can be difficult to diversify ▪ Indexes replicating the performance of real estate are not directly investable. ▪ Local markets can be very different from national or global markets. Basic forms of real estate investments and examples Debt Equity Private ▪ Mortgages Direct ownership ▪ Construction ▪ Sole ownership lending ▪ Joint ventures ▪ Mezzanine debt ▪ Limited partnerships Indirect ownership ▪ Real estate funds ▪ Private REITs Public ▪ MBS/CMBS/CMOs Publicly traded shares ▪ Covered Bonds ▪ Construction ▪ Mortgage REITs ▪ Operating ▪ Mortgage ETFs ▪ Development ▪ Public REITs ▪ Mutual funds/ETFs Infrastructure ▪ Economic infrastructure assets: Include transportation, communication, and social utility assets that are needed to support economic activity. ▪ Social infrastructure assets: Required for the benefit of the society such as educational and healthcare facilities. ▪ Brownfield investments: Investments in existing investable infrastructure assets. ▪ Greenfield investments: Investments in yet-to-be-constructed infrastructure assets. ▪ Secondary-stage investments; invest in existing infrastructure facilities or fully operational assets. Natural Resources Natural resources include commodities, farmland, and timberland. Commodity investments take place through derivatives. Their return is based mainly on price changes rather than an income stream such as dividends. Timberland provides an income stream through the sale of trees, wood, and other timber products. It is considered a sustainable investment that mitigates climaterelated risks. Farmland also provides an income component related to harvest quantities and agricultural commodity prices. It does not provide production flexibility. ESG investors looking for responsible and sustainable investing can include timberland and farmland in their portfolios. Hedge funds Types Event-driven: includes merger arbitrage, distressed/restructuring, activist shareholder and special situations. 15 Relative value: includes fixed-income convertible arbitrage, fixedincome asset backed, fixed-income general, volatility and multistrategy. Opportunistic: includes macro strategies and managed futures. Equity hedge: includes fundamental long/short, market neutral, fundamental growth, fundamental value and short bias. Hedge fund index returns can be overstated due to self-reporting, survivorship, and backfill biases. Digital Assets Distributed ledger: a database which can be shared across computer entities (or nodes) in a network. Consensus protocol: a set of rules that govern how blocks in a blockchain network are cryptographically chained together for the verification of the complete and immutable history of transaction records. They are classified into two types: "proof of work" (PoW) and "proof of stake" (PoS). Digital assets: differ from traditional assets in terms of inherent value, transaction validation approach, uses as a legal medium of exchange, and legal and regulatory protection. Investment in digital assets: can be in the form of direct investment on the blockchain or indirect investments through exchange-traded products and hedge funds. Direct ownership: of Bitcoin and other cryptocurrencies is accomplished through the use of a cryptocurrency wallet. Cryptocurrency exchanges: can be classified into centralized exchanges and decentralized exchanges. Asset-backed tokens: are digital claims on physical assets, financial assets, or financial instruments and are collateralized by these underlying assets. Performance of Bitcoin: characterized by high return, high volatility, and low correlations with traditional asset classes. Portfolio Management Portfolio management process has three phases: 1. Planning 2. Execution 3. Feedback Asset managers are usually referred to as a buy-side firm since it uses (buys) the services of sell-side firms. The three key trends in the asset management industry include growth of passive investing, “Big Data” in the investment process, and robo-advisers (use of automation and investment algorithms) in the wealth management industry. The portfolio having the least risk (variance) among all the portfolios of risky assets is called the global minimum-variance portfolio. The part of minimum-variance frontier above the global minimumvariance portfolio is called the efficient frontier. Drawing a line tangent from the risk free asset to the efficient frontier will give the capital allocation line (CAL). The point where this line intersects the efficient frontier is called the optimal risky portfolio. The optimal investor portfolio is the point at which the investor’s indifference curve is tangential to the CAL line. Ver 1.0 Under homogeneity of expectations, all investors have the same efficient frontier. Thus, all investors have the same optimal risky portfolio and CAL. This optimal CAL, using homogenous expectations, is the capital market line (CML). The optimal risky portfolio is called the market portfolio. Total risk (standard deviation) = systematic risk (nondiversifiable) + unsystematic risk (diversifiable) Beta is a standardized measure of covariance of an asset’s return with the market returns. βi = Cov(i,M) σ2M = ρiM ∗σi ∗ σM σ2M = ρiM ∗σi σM SML plots returns versus systematic risk i.e. beta on the x-axis. The equation of the line is given by CAPM. ▪ Securities on the SML line (CAPM) → fairly valued. ▪ Securities above the SML line → undervalued. ▪ Securities below the SML line → overvalued. CML: Rp = Rf Rm −Rf σm +( )* 𝜎p re = Rf + β[E(Rmkt ) − Rf ] Slope of the CML is the Sharpe ratio Slope of the SML is the market risk premium The four measures commonly used in performance evaluation are: Sharpe ratio = M2 = (Rp −Rf )σm σp portfolio excess returns portfolio total risk = Rp −Rf σp − (R m − R f ) Treynor measure = Portfolio risk premium beta risk (systematic risk) = Rp −Rf βp Jenson′ s alpha = Actual portfolio return − SML expected return = R p − [R f + β(R m − R f )] Investment policy statement (IPS) Investment objectives ▪ Return objectives ▪ Risk tolerance Investment constraints (LLTTU) ▪ Liquidity requirements ▪ Legal and regulatory ▪ Time horizon ▪ Tax ▪ Unique circumstances 16 IPS may also include policy regarding sustainable investing which takes into account environmental, social, and governance (ESG) factors. The ESG implementation approaches may have a negative impact on expected risk and return of a portfolio as it may limit the manager’s investment universe and the manner in which investment management firms operate. Risk management is the process by which an organization or individual defines the level of risk to be taken (i.e. risk tolerance), measures the level of risk being taken (i.e. risk exposure), and modifies the risk exposure to match the risk tolerance. Methods to estimate target capital structure weights. 1. Assume the current capital structure at market value weights for the components. 2. Examine trends in the capital structure or statements by management regarding capital structure policy. 3. Use averages of comparable companies’ capital structures. Factors affecting capital structure Internal External ▪ ▪ ▪ ▪ ▪ Business model characteristics ▪ Market conditions/Business Existing leverage cycle Corporate tax rate ▪ Regulatory constraints Capital structure policies, guidelines ▪ Industry/Peer firm leverage Company life cycle stage Modigliani–Miller propositions regarding capital structure. Without Taxes With Taxes Proposition VL = VU VL = VU + tD I Proposition re = r0 + (r0 − rd ) D⁄E re = r0 + (r0 − rd )(1 − t) D⁄E II Technical Analysis Charts: line, bar, candlestick, volume. Reversal patterns: head & shoulders, inverse head & shoulders, double/triple tops & bottoms. Continuation patterns: triangles, rectangles, flags, pennants. Price based indicators: moving averages, Bollinger bands. Momentum oscillators: ROC, RSI, Stochastic, MACD. Sentiment indicators: put/call ratio, VIX, margin debt, short interest. Head and shoulders pattern: price target = neckline – (head – neckline) 𝐒𝐡𝐨𝐫𝐭 𝐢𝐧𝐭𝐞𝐫𝐞𝐬𝐭 𝐫𝐚𝐭𝐢𝐨 = short interest average daily trading volume Uptrend: If prices are reaching higher highs and higher lows. An upward trendline can be drawn by connecting the increasing low points with a straight line. Downtrend: If prices are reaching lower highs and lower lows. A downward trendline can be drawn by connecting the decreasing high points with a straight line. Support: Price level at which there is sufficient buying pressure to stop a further price decline. Resistance: Price level at which there is sufficient selling pressure to stop the further price hike. Major fintech applications include: ▪ Text analytics and natural language processing ▪ Robo-advisory services ▪ Risk analysis ▪ Algorithmic trading Ver 1.0 Major DLT applications include: ▪ Cryptocurrencies ▪ Tokenization ▪ Post-trade clearing and settlement ▪ Compliance Ethical and Professional Standards I(A) Knowledge of the law: comply with the strictest law; disassociate from violations. I(B) Independence and objectivity: do not offer, solicit or accept gifts; but small token gifts are ok. I(C) Misrepresentation: do not guarantee performance; avoid plagiarism. I(D) Misconduct: do not behave in a manner that affects your professional reputation or integrity. II(A) Material nonpublic information: do not act or help others to act on this information; but mosaic theory is not a violation. II(B) Market manipulation: do not manipulate prices/trading volumes to mislead others; do not spread false rumors. III(A) Loyalty, prudence, and care: place client’s interest before employer’s or your interests. III(B) Fair dealing: treat all client’s fairly; disseminate investment recommendations and changes simultaneously. III(C) Suitability: in advisory relationships, understand client’s risk profile, develop and update an IPS periodically; in fund/index management, ensure investments are consistent with stated mandate. III(D) Performance presentation: do not misstate performance; make detailed information available on request. III(E) Preservation of confidentiality: maintain confidentiality of clients; unless disclosure is required by law, information concerns illegal activities, client permits the disclosure. IV(A) Loyalty: do not harm your employer; obtain written consent before starting an independent practice; do not take confidential information when leaving. IV(B) Additional compensation arrangements: do not accept compensation arrangements that will create a conflict of interest with your employer; but you may accept if written consent is obtained from all parties involved. IV(C) Responsibilities of supervisors: prevent employees under your supervision from violating laws. V(A) Diligence and reasonable basis: have a reasonable and adequate basis for any analysis, recommendation or action. V(B) Communication with clients and prospective clients: distinguish between fact and opinion; make appropriate disclosures. V(C) Record retention: maintain records to support your analysis. 17 VI(A) Disclosure of conflicts: disclose conflict of interest in plain language. VI(B) Priority of transactions: client transactions come before employer transactions which come before personal transactions. VI(C) Referral fees: disclose referral arrangements to clients and employers. VII(A) Conduct as participants in CFA Institute programs: don’t cheat on the exams; keep exam information confidential. VII(B) Reference to CFA Institute, the CFA designation, and the CFA program: don’t brag, references to partial designation not allowed. GIPS ▪ The GIPS standards were created to avoid misrepresentation of performance. ▪ A composite is an aggregation of one or more portfolios managed according to a similar investment mandate, objective, or strategy. ▪ Verification is performed by an independent third party with respect to an entire firm. It is not done on composites, or individual departments. Ver 1.0 18