CFA Level I Formula Sheet & Key Concepts - 2023 Exam Preparation
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CFA cheat sheet - CFA
CFA Program Curriculum (CFA Université Et Sports) QUANTITATIVE METHODS
Mean Absolute Deviation Sample Covariance MAD = 1 ∑n |X − XE| n i=1 i
∑n 1(Xi − Xb)(𝑌𝑖 − 𝑌b)
THE TIME VALUE OF MONEY n − 1
Variance and Standard Deviation
Required Rate of Return n
Sample Correlation Coefficient 1
interest rate = real risk-free rate Sample variance, s2 = F(Xi − XE)2 r + inflation premium n − 1 i=1 + default risk premium
Standard deviation is square root of variance PROBABILITY CONCEPTS + liquidity premium
Target Downside Deviation + maturity premium Odds
Sample target semideviation, s = X∑Xi≤B(Xi–B)2 P(E)
Future Value (FV) and Present Value (PV) Target n–1 Odds of E = 1 − P(E) FV = PV(1 + r)N
Coefficient of Variation Probabilities Effective Annual Rates
CV = s⁄EX; measures dispersion relative to mean r m
Unconditional: P(A), probability of A EAR = >1 + stated − 1 Skewness
Conditional: P(A|B), probability of A given B
Joint: P(AB), probability of A and B Probability Rules
Annuity: Finite set of level sequential cash flows,
Conditional: P(A|B) = P(AB)/P(B)
valued using calculator’s TVM function
Multiplication: P(AB) = P(A|B) × P(B)
Ordinary Annuity: 1st cash flow received in one year
Addition: P(A or B) = P(A) + P(B) − P(AB)
Annuity Due: 1st cash flow received immediately
Perpetuity: Ordinary annuity with payments that
Total: P(A) = P(A|S1)P(S1) + ⋯ + P(A|Sn)P(Sn) where S O c RG ont A i N nuIZ e I f N orG e , v V e I r S , UA PV LIZING, AND D ESCRIBING
1, S2,… Sn is an exhaustive set of mutually DATA exclusive probabilities Independence AND DESCRIBING DATA
If A and B are independent events, Data Visualization P(AB) = P(A) × P(B)
Histogram and frequency polygon Expected Value Bar chart (and Pareto chart) Tree-map Word cloud/tag cloud
Line chart (and bubble line chart)
E(X) = E(X|S1)P(S1) + ⋯ + E(X|Sn)P(Sn)
Scatter plot (and scatter plot matrix) Variance Heat map 1 ∑n (X − EX)3 Arithmetic Mean Return Skewness ≈ \ ] i=1 i n s3 1
Sample mean, EX = F X ; n = sample size Covariance n
Kurtosis (Excess Kurtosis = Kurtosis – 3) Distribution 𝑇𝑎𝑖𝑙𝑠 Peaked Kurtosis Geometric Mean Return Leptokurtic Fatter More >3
An asset’s covariance with itself is its variance Mesokurtic Normal Normal 3
Harmonic Mean Return (Cost Averaging) Platykurtic Thinner Less <3 n
Expected Value & Variance of Portfolio Return E X =
, where X > 0 for i = 1, 2, … , n If returns are volatile, XE
Arith. > XEGeo. > EXHar. Quantiles y Location of y percentile, L = (n + 1) 100 Market value of investment i w = If L
y is not an integer, use linear interpolation. Market value of portfolio
Distributions may be divided into quarters
(Quartiles), fifths (Quintiles), or tenths (Deciles)
E.g., 50th percentile = 2nd quartile = 5th decile www.saltsolutions.com 1 1 ∑n (X − EX)4
Excess kurtosis, KE ≈ \ ] i=1 i − 3 n s4 www.saltsolutions.com 2
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For portfolio with 2 investments: Lognormal Distribution SAMPLING AND E STIMATION EmRpn = wARA + wBRB
- eX where X is normally distributed Sampling - Used to model asset prices
Simple random sampling: Subset of population is
Cov(RA, RB) = σ(RA)σ(RB)ρ(RA, RB) - Positively skewed chosen at random σ2mR
Continuously compounded return from t to t + 1: pn = w2σ2(R ) + w2σ2(R )
Systematic sampling: Every kth observation is St+1 + 2w = ln \ ] = lnm1 + R
chosen until desired sample size is achieved AwBCov(RA, RB) rt,t+1 S t,t+1n t
Stratified sampling: Simple random samples are Correlation
where Rt,t+1 is the effective annual rate
drawn from each subpopulation (strata) ρ
Cluster sampling: Sample set is divided into mini- = CorrmR , R n = ; min −1, max 1
Student’s t-Distribution σ(R σ mR n
representations of the population (cluster)
Parameters: degrees of freedom (df) Bayes’ Formula
Convenience sampling: Samples are selected based
The ratio below is t-distributed with df = n − 1: P(Info|Event) × P(Event) on accessibility XE − µ P(Event|Info) = t = P(Info)
Judgmental sampling: Samples are selected based s/√n
Updates prior probabilities to give posterior
on researchers’ knowledge and expertise
probabilities based on new information
Sampling error = Sample mean – Population mean Counting Rules
Central Limit Theorem (CLT)
Factorial: n! = n(n − 1)(n − 2) … 1
For a sample of size n ≥ 30 from a population with
mean µ and variance σ2, the sample mean XE Multinomial:
approximately follows a normal distribution with
Counts ways to label n items with k labels mean µ and variance σ2⁄n n
Standard Error of Sample Mean Combination: C = (r) =
Chi-Square Distribution
Population variance is known: σx̅ = σ⁄√n
Definition: Sum of squares of independent normal
Counts ways to choose r items from n if order does
Population variance is not known: sx̅ = s⁄√n
random variables. It cannot be negative. NOT matter
Properties of Estimators Permutation: nPr = A point estimator is:
Counts ways to choose r items from n if
Unbiased if its value matches the value of the order does matter parameter it estimates
Efficient if it has the lowest variance of all unbiased estimators COMMON P ROBABILITY D ISTRIBUTIONS
Consistent if its value approaches the parameter
Discrete Uniform Distribution as the sample size increases 1 p(x) = , x = x , x , F-Distribution … , x n Confidence Interval
Definition: A ratio of two chi-square random
Continuous Uniform Distribution
Point estimate ± Reliability factor × Std error
variables (two df’s). It cannot be negative. 1
Point estimate: Estimate of population parameter f(x) = ; a ≤ x ≤ b b − a
Reliability factor: Value from distribution of point x − a F(x) = ; a ≤ x ≤ b
estimate, such as normal or t-distribution b − a
E.g., XE ± z𝝰⁄2 × σ⁄√n Binomial Distribution
Reliability factors for normal distributions Significance Confidence 𝑧𝛼⁄2
n = number of Bernoulli trials level interval p = probability of success 10% 90% 1.645 E(X) = np Simulation Techniques 5% 95% 1.960 σ
Monte Carlo simulation: Generate many random 2(X) = np(1 − p)
samples to produce a distribution of outcomes 1% 99% 2.575
Normal Distribution (µ = mean, σ = SD)
Historical simulation: Sample from a historical
If the population is not normally distributed
~50% of observations are within ± 2 𝜎 of µ
record of returns to simulate a process
and/or variance is unknown, the t- or z-
~68% of observations are within ±𝜎 of µ
distributions may be used to get reliability factors.
~95% of observations are within ±2𝜎 of µ Normally Variance Small Large
~99% of observations are within ±3𝜎 of µ Distributed? known? Sample Sample Yes Yes z z
Observed value − Population mean X − µ Yes No t t or z Z = = Standard deviation σ No Yes n/a z No No n/a t or z EmRpn − shortfall level Shortfall Ratio = σ Resampling P
Bootstrap: Replace each drawn sample with an
identical element for the next draw
Jackknife: Draw each sample by leaving out one
observation at a time without replacement www.saltsolutions.com 3 Biases
Tests Concerning Differences between Means
Assumptions of Simple Linear Regression
Data snooping bias: “Drilling” data to find any
Normal populations with unknown variances that Model
statistically significant relationship are assumed equal:
- Linear relationship between X and Y
Sample selection bias: Excluding unavailable data (XE
- Homoscedasticity (i.e., constant variance of t-statistic = 1 − EX2) − (µ1 − µ2)
Survivorship bias: Excluding the impact of failed s2 s2 1⁄2 residuals)
funds or companies that no longer exist
- Independence between X and Y
Look-ahead bias: Information needed is not known (n - Normality of the residuals 1 − 1)s2 + (n − 1)s2
on the date the observation was recorded Analysis of Variance
Time-period bias: Using data from an era that df = n1 + n2 − 2
Sum of squares error (SSE): Unexplained variation
makes the results time-period specific in Y
Tests Concerning Mean Differences SSE = ∑n mY − YÖ n2 HYPOTHESIS T ES TE TIN STIG NG
Normal populations with unknown variances: i=1 i i db − µ
Sum of squares regression (SSR): Explained
Steps in Hypothesis Testing t-statistic = dO , df = n − 1 variation in Y
State hypotheses (null and alternative) Identify test statistic
Tests Concerning a Single Variance SSR = ∑n mÖY − EYn2 i=1 i Specify significance level
Normal population (df = n – 1):
Sum of squares total (SST): Total variation in Y State decision rule SST = SSE + SSR = ∑n (Y (n − 1)s i − EY)2 2 1 i=1
Collect data; calculate test statistic , σ2 O
Coefficient of determination:
Make decision regarding hypothesis SSR
Tests Concerning Two Variances R2 =
Test Statistic (General) SST Normal populations:
= r2 (if there is only one independent variable)
Sample statistic − Hypothesized value F-statistic:
Standard error of sample statistic s2 1 s2 = − xb n2 for j = 1, 2 MSR s2 SSR/k F = =
Hypothesis Test Results MSE SSE/(n − [k + 1])
Reject H0 if test
Standard error of regression: Type Hypotheses statistic is Nonparametric Tests ∑n mY − YÖ n2 One-tailed H0: µ ≤ µ0
Test that is not concerned with parameter and is s = √MSE = Ü i=1 i i e > critical value n − 2 (upper) Ha: µ > µ0
implemented in situations such as: One-tailed H0: µ ≥ µ0
Data do not meet distributional assumptions
Hypothesis Testing of Linear Regression < critical value (lower) Ha: µ < µ0 Data are subject to outliers Coefficients Data are given in ranks
To test a hypothesis about the slope: < lower critical Two- H0: µ = µ0
Hypothesis does not concern a parameter bÑ value or > upper t = 1 − b1 tailed Ha: µ ≠ µ0 s critical value
Tests Concerning Correlation b^1 s s e ^ = 𝑟√n − 2
Hypothesis Testing Decision Errors t-statistic = b1 , df = n − 2 I∑ n i=1 (Xi − XE)2 √1 − r2 Decision 𝐻O is True 𝐻O is False
To test a hypothesis about the intercept:
To use the Spearman rank correlation coefficient, Do not reject H bÑ O Correct Type II ()
substitute the following value into the t-statistic t = O − bO s Reject HO Type I () Correct calculation: b^0 1 (XE)2 s = ÜMSE á + )
Power of a test = 1 − P(Type II error) = 1 – b^ n(n2 − 1) 0 n n ∑ ( i=1 Xi − EX)2
p-value: smallest value of at which 𝐻O is rejected
INTRODUCTION TO LINEAR REGRESSION
Tests Concerning a Single Mean
Estimated variance of the prediction error for Y: 1 (
Population is normal with known variance:
Simple Linear Regression X − EX)2 s2 = s2 â1 + + ä XE − µ
Y: Dependent variable/explained variable f e n (n − 1)s2x z-statistic = O σ⁄√n
X: Independent variable/explanatory variable
Large sample from any population with unknown Y = bO + b1X + ϵ, variance (2 choices):
where bO is the intercept, b1 is the slope coefficient, XE − µ t-statistic = O , df = n − 1 and ϵ is the error term s⁄√n XE − µ
The parameters can be estimated by: z-statistic = O σ⁄√n Cov[Y, X] ∑n (Y − EY)(X − EX) =
Small sample from normal population with Var[X]
unknown population variance: bÑ E O = EY − bÑ1 X XE − µ t-statistic = O , df = n − 1 s⁄ √n www.saltsolutions.com 3 ECONOMICS Breakeven Analysis
Monopolistic Competition
Economic breakeven occurs if a firm’s accounting - Firms: Many TOPICS IN DEMAND A ND SUPPLY A NALYSIS
profit is enough to cover its implicit opportunity
- Products: Differentiated (via advertising)
costs (i.e., normal profit). In the long run, firms
Own-Price Elasticity of Demand - Barriers to entry: Low
cannot earn positive economic profits.
- Pricing power of firms: Some
Shutdown Decision (Short-term vs. Long-term)
Profit maximization: MR = MC Short-Term Long-Term
Qd = quantity demanded, P = price per unit TR ≥ TC Stay in Stay in éEd é > 1: elastic TVC < TR < TC Stay in Exit market éEd é < 1: inelastic TR < TVC Shut down Exit market
éEd é = ∞: perfectly elastic Economies of Scale Ed = 0: perfectly inelastic
Each stage of expansion has its own short-run ATC Ed = −1: unit elastic
curve. Minimum efficient scale is the low point on
the long-run average total cost curve.
Income Elasticity of Demand I %ΔI ΔI where I = consumers’ income
Ed > 0: normal good; Ed < 0: inferior good Oligopoly - Firms: Few
Cross-Price Elasticity of Demand
- Products: Similar (close substitutes) - Barriers to entry: High
- Pricing power: Some or considerable
where Py is the price per unit of another good Y
Profit maximization: MR = MC
Ed > 0: substitutes; Ed < 0: complements
Income and Substitution Effects THE FIRM A ND MAR
KET STRUCTURES
Impacts of a reduction in a good’s price: Perfect Competition Substitution Type of good Income effect Firms: Many effect Products: Identical Normal Buy more Buy more Barriers to entry: Very low Inferior Buy less Buy more Pricing power of firms: None
Goods with positively sloped demand curves: Profit maximization:
Giffen goods: Negative income effect is greater P = MR = MC
than positive substitution effect if good’s price
P > ATC economic profit, P < ATC economic loss falls
Veblen goods: Demand for a status symbol good
Kinked demand curve: A price increase will impact falls if its price is reduced
sales more than an equivalent price decrease Revenue Terms
Cournot assumption: Competitors will maintain
current output levels if one firm changes its price
Total revenue (TR): Price times quantity; P × Q
Game theory: If one firm changes its prices,
Average revenue (AR): TR⁄Q
competitors will adjust to maximize their profits,
Marginal revenue (MR): ΔTR⁄ΔQ
resulting in a Nash equilibrium Cost Terms
Price collusion is more likely to happen if:
- Few firms or one dominant firm
Total fixed cost (TFC): Sum of fixed costs
- Products are relatively similar
Total variable cost (TVC): Sum of variable costs
- Firms have similar cost structures
Total costs (TC): TFC + TVC
- Orders are frequent and relatively small
Average fixed cost (AFC): TFC⁄Q
- Credible threat of retaliation for breaking pact
Average variable cost (AVC): TVC⁄Q
- The threat of external competition is high
Average total cost (ATC): AFC + AFV or TC⁄Q
Marginal cost (MC): ΔTC⁄ΔQ Profit Measures
Accounting profit = Revenue − Accounting costs
Economic costs = Accounting costs + Implicit costs
Economic profit = Revenue – Economic costs
= Accounting profit−Implicit costs
Normal profit = Zero economic profit
Profits maximized if MR = MC and MC isn’t falling Monopoly
Relationship among Saving, Investment, the
Shifts in Aggregate Supply (SRAS and LRAS) Firm: One
Fiscal Balance, and the Trade Balance SRAS LRAS Increase in
Products: Unique (no close substitutes)
(G − T) = (S − I) − (X − M) Shift Shift Barriers to entry: Very high G − T = fiscal balance Labor supply Right Right
Pricing power of firm: Considerable (price
S − I = savings minus domestic investment Natural resources Right Right discrimination possible) X − M = trade balance Human capital Right Right
Profit maximization: MR = MC Aggregate Demand (AD) Physical capital Right Right
The downward slope of the AD curve results from: Productivity/Tech Right Right
- Wealth effect: Price level ↑, real wealth ↓, quantity Nominal wages Left None demanded ↓ Input prices Left None
- Interest rate effect: Price level ↑, interest rate ↑, Price expectations Right None
investment and consumption expenditures ↓ Business taxes Left None
- Real exchange rate effect: Price level ↑, real Business subsidies Right None
exchange rate ↑, exports ↓ and imports ↑ Foreign currency Right None Aggregate Supply (AS) values Inflationary Gap
Price discrimination by monopolists:
1st degree: Different price for each customer
2nd degree: Quantity-based menu options
3rd degree: Pricing for demographic groups Market Power Measures
N-firm concentration ratio: Sum of market share
of the N largest firms in the industry
Herfindahl-Hirschman Index (HHI): Sum of squared
market share of the N largest firms
AGGREGATE OUTPUT, PRICES, AND ECONOMIC
Full employment level of output: Long-run GR A OW ND T E H C ONOMIC GROWTH equilibrium level of output
Gross Domestic Product (GDP)
Factors Increasing Aggregate Demand (AD)
Nominal GDP: GDP in terms of current prices - Higher household wealth
Effect of Combined Changes in AS and AD
Real GDP: GDP in terms of base-year prices
- Higher business and consumer confidence
GDP deflator: (Nominal GDP⁄Real GDP) × 100 Changes in Real GDP Prices - Higher capacity utilization GDP = C + I + G + (X − M) AS and AD
- Expansionary monetary and fiscal policies C = consumption AS ↑, AD ↑ Increase Unclear
- Depreciating domestic currency value I = investment AS ↓, AD ↓ Decrease Unclear
- Faster global economic growth G = government spending AS ↑, AD ↓ Unclear Decrease X = exports; M = imports AS ↓, AD ↑ Unclear Increase GDI = Net domestic income UNDERSTANDING B
USINESS C YCLES
+ Consumption of fixed capital Business Cycle Phases + Statistical discrepancy Recovery
Economy: Going through a trough GDI
Activity level: Below potential but start to increase = Compensation of employees
Employment: Layoffs slow, but firms prefer
+ Gross operating surplus + Gross mixed income
extending overtime to rehiring full-time
+ Taxes (net of subsidies) on production Inflation: Moderate
+ Taxes (net of subsidies) on products and imports
Capital spending: Low but increasing, with a focus Personal household income
on efficiency rather than capacity = Compensation of employees Expansion + Net mixed income from
Economy: Enjoying an upswing unincorporated businesses
Activity level: Above-average growth rates +Net property income
Employment: Full-time rehiring, more overtime
Inflation: Moderate, but increasing
Capital spending: Focused on capacity expansion www.saltsolutions.com 5 Slowdown
MONETARY AND FISCAL P OLICY INTRODUCTION TO G EOPOLITICS
- Economy: Going through a peak Monetary Policy
National Governments and Political
- Activity level: Decelerating Required reserves Cooperation Required reserve ratio =
- Employment: Hiring slows
State actors possesses the authority to deploy a
- Inflation: Accelerating
Money multiplier = 1⁄Reserve requirement
country’s national security resources
- Capital spending: Strong capital spending, but
Non-State Actors and the Forces of
inventory starts building up as sales growth Globalization Central Bank Roles slows
Non-state actors participate in global political, Sole currency supplier Contraction
economic, or financial affairs but do not control a Lender of last resort
- Economy: Weakens and may go into a recession
country's national security resources
Bank for commercial banks and government
- Activity levels: Below potential
Regulate and supervise payments system
Assessing Geopolitical Actors and Risk
- Employment: Hiring freezes, then layoffs
Gold and foreign exchange reserves holder
- Inflation: Decelerating, but with a lag Oversee monetary policy
- Capital spending: New orders halted and existing Monetary Policy Tools
orders canceled, scale back on maintenance
Expansionary monetary policy measures:
Business Cycle Theories
Policy rate: Set policy rate below neutral level
- Neoclassical: “Invisible hand” lets markets reach a
Reserve requirement: Reduce reserves for
The Tools of Geopolitics
natural equilibrium; government should not commercial banks
National security tool: Military force, espionage intervene
Open market operations: Buy bonds from
Economic tools: Currency union, nationalization
- Austrian: Like Neoclassical, focus on loose commercial banks
Financial tools: Currency markets, sanctions,
monetary policy causing credit-fueled booms capital controls
Fiscal Policy: Spending Tools
- Keynesian: Countercyclical fiscal policy should be
Transfer payments: Redistribution of wealth (e.g.,
Incorporating Geopolitical Risk into the
used to support aggregate demand Investment Process unemployment benefits)
- Monetarist: Oppose Keynesian fiscal focus, call for Types of geopolitical risk:
Current spending: Spending on goods and services steady growth of money Event risk
Capital spending: Spending on infrastructure Unemployment Exogenous risk
- Unemployed: Jobless people who are seeking jobs
Fiscal Policy: Revenue Tools Thematic risk -
Direct taxes: Tax on income (e.g., income taxes,
Labor force: People with a job or unemployed
Assessing Geopolitical Threats
- Unemployment rate: Unemployed⁄Labor force
corporate taxes, capital gains taxes)
To assess geopolitical risk, consider:
Indirect taxes: Tax on goods and services Type Result of The likelihood of occurrence Frictional Temporary transitions Fiscal Multiplier
The velocity (speed) of impact Structural Long-run changes in economy 1 The size and nature of impact = , where MPC = marginal Cyclical Changes in economic activity 1 − MPC(1 − t)
propensity to consume; t = tax rate
INTERNATIONAL TRADE AND CAPITAL FLOW S Inflation
Difficulties Executing Fiscal Policy
Basics of International Trade
Deflation: Negative inflation rate
Recognition lag: Government must see need
Terms of trade: Price of exports/Price of imports
Disinflation: Declining inflation rate
Action lag: Time needed to choose policy
Autarky: No trade with other countries
Hyperinflation: Extremely high inflation rate
Impact lag: Policies do not have immediate impact
Absolute advantage: Lower total cost of production
Cost-push: From decrease in aggregate supply
Comparative advantage: Lower opportunity cost
Demand-pull: From increase in aggregate demand
Laspeyres index: Use base consumption basket International Trade Models
Ricardian: Labor is the only factor of production,
Paasche index: Use current consumption basket
comparative advantage due to labor productivity
Fisher index: ILaspeyres × Paasche
Hecksher-Ohlin: Both labor and capital are factors, Economic Indicators
income redistribution is possible through trade
Leading: Stock indexes, building permits Trade Restrictions
Coincident: Real income, industrial production
Tariffs: Taxes on imported goods
Lagging: Unemployment rate, prime lending rate
Quotas: Limits on quantity of imported goods
Export subsidies: Payments to exporters
Minimum domestic content requirements
Voluntary export restraints: Self-imposed
limitations by foreign producers
Impact of Trade Restrictions Exchange Rate Regimes
Income Statement Line Items
Dollarization: Adopt another country’s currency Revenue
Monetary union: Adopt a common currency − Cost of goods sold (COGS)
Currency board: Commitment to exchange Gross Profit
domestic currency at fixed exchange rate
− Selling, General & Admin. (SG&A)
Fixed peg: Currency is pegged to foreign currency EBITDA
(or basket of currencies) within ±1% margin
Target zone: Fixed peg with wider margin
− Depreciation and Amortization
Crawling peg: Peg rate is periodically adjusted EBIT (Operating profit)
Crawling bands: Margin increases over time, − Interest
usually to transition from fixed peg to floating EBT (Earnings before taxes)
Managed floating: Monetary authority intervenes, − Taxes
but no official target exchange rate Net Income (NI)
Price increases from P∗ to Pt
Independently floating: Market sets exchange rate
Separately Reported Items
Domestic production increases from Q1 to Q2
Marshall-Lerner Condition Discontinued operations
Domestic consumption falls from Q4 to Q3
Currency devaluation can improve a country’s
Unusual or infrequent items (US GAAP only)
Imports fall from (Q4 − Q1)to (Q3 − Q2)
trade balance if demand elasticities cause export Non-operating items
Loss of consumer surplus = (A + B + C + D)
receipts to increase more than import
National welfare loss = (B + D) expenditures
Basic Earnings per Share
Increase in producer surplus = A
Net income − Preferred dividends Tariff revenue/Quota rent = C
Weighted average of shares outstanding Regional Trading Blocs
FINANCIAL STATE MENT ANALY SIS
Diluted Earnings per Share
Free trade area (FTA): Free trade among members Convertible Convertible
Net − Preferred + preferred + debt (1 − 𝑡)
Customs union (CU): FTA + common trade policy FINANCIAL R EPORTING S TANDARDS income dividends dividends interest
Common market (CM): CU + free movement of FASB, IASB, and IOSCO
Weighted Shares from Shares from Shares issuable
factors of production within bloc
average + preferred + convertible + from stock
FASB: Sets forth US GAAP shares shares debt options
Economic union (EU): CM + common economic IASB: Establishes IFRS
institutions and coordination of economic policies
Must be equal to or less than basic EPS
IOSCO: International body of regulatory authorities
Monetary union (MU): EU + common currency
SEC: US capital markets regulator UNDERSTANDING B
ALANCE S HEETS
Balance of Payments Components
Fundamental Qualities of Financial Reports
Current account: Merchandise and services, income
1. Relevance 2. Faithful Representation
Classified Balance Sheet
receipts, unilateral transfers
Enhancing Characteristics
Current Assets: To be used within one year
Capital account: Capital transfers, non-financial
1. Comparability 2. Verifiability Cash and equivalents assets sales/purchases
Timeliness 4. Understandability Marketable securities
Financial account: Government-owned assets
Accounts receivable, net of bad debt expense
abroad, foreign-owned assets in the country UNDERSTANDING I
NCOME S TATEMENTS Inventories
Other (e.g., prepaid expenses) CURRENCY E XCHANGE R ATES Revenue Recognition Non-Current Assets
Revenue must not be recognized unless:
Exchange Rate Calculations
Property, Plant, and Equipment (PP&E)
Risks of ownership have been transferred CPIf Investment property
Real ex. rate = Nominal ex. rate × \ ]
Amount of revenue can be reliably measured Intangible assets Customer is likely to pay
Forward exchange rated⁄f 1 + id Goodwill =
Transaction is unlikely to be reversed Spot exchange rated⁄f 1 + if Financial assets
Service revenue may be recognized as earned
Cross rate: SA⁄B = SA⁄C × SC⁄B
Current Liabilities: To be settled within one year
Allowance for doubtful accounts: Contra-asset
Forward exchange rates in points: Accounts payable
account, estimated based on historical experience
- Unit of points is last decimal place in the rate Notes payable
quote (e.g., 1.5301 to 1.5302 is a 1-point increase) Expense Recognition Accrued expenses
Matching principle: Expenses must be recognized Ideal Currency Regime
Deferred income (Unearned revenue)
in the same period as associated revenue
Exchange rates are credibly fixed Long-term Liabilities
Fully convertible currencies, free capital flows Long-term debt
Countries pursue independent monetary policies Deferred tax liabilities
Such an ideal currency regime is NOT possible Equity Contributed capital Preferred shares Treasury shares Retained earnings
Accumulated other comprehensive income (OCI)
Non-controlling (minority) interest www.saltsolutions.com 7 UNDERSTANDING C
ASH F LOW S TATEMENTS
FINANCIAL ANALYSIS TECHNIQUES Solvency Ratios Total debt
Cash Flow Statement Classifications Common-Size Analysis Debt-to-equity =
CFO: Cash flows from regular operations Vertical: Total shareholders' equity
CFI: Cash flows for buying/selling long-term assets
State income statement items as % of revenue Total debt
CFF: Financial transactions with capital providers
State balance sheet items as a % of total assets
Debt-to-capital = Total debt + Total shareholders' Item US GAAP IFRS
State each cash flow statement item as a % of equity Dividends paid CFF CFO/CFF total cash inflows/outflows Total debt
Horizontal (Trend) Analysis: Interest paid CFO CFO/CFF Debt-to-assets = Total assets
State each item relative to its base-year value Dividends received CFO CFO/CFI Average total assets Financial leverage = Interest received CFO CFO/CFI Activity Ratios Average total equity Tax expenses CFO CFO* Annual sales
Receivables turnover = Average receivables EBIT
*I FRS treat tax expenses for investing or financing
Interest coverage = Interest payments transactions as CFI or CFF Fixed Days of sales = 365 EBIT + Lease payments CFO Direct Method outstanding Receivables turnover
charge = Interest payments + Lease pmts
Convert each accrual-based item in the income coverage Cost of goods sold Inventory turnover =
statement to cash inflow/outflow Average inventory Profitability Ratios
CFO is net of cash inflows and outflows Net income Days of inventory 365 Net profit margin = = Revenue CFO Indirect Method on hand Inventory turnover Gross profit Start with net income Gross profit margin = Purchases
Add noncash expenses (e.g., Depreciation) Payables turnover = Revenue Average trade payables Subtract gains/add losses EBIT Operating profit margin =
Add increases in current liabilities Number of days 365 = Revenue of payables Payables turnover
Subtract increases in (non-cash) current assets EBT Revenue Pretax margin = Beginning accounts receivable Total asset turnover = Revenue Average total assets + Revenue Net income Return on assets (ROA) = Revenue
− Ending accounts receivable Average total assets Fixed asset turnover = Average net fixed assets
Cash collected from customers EBIT Working capital = Revenue Return on total capital = Cost of goods sold turnover Average working capital Average total capital + Increase in inventory Net income Liquidity Ratios Return on equity (ROE) = Purchases from suppliers Average total equity Current assets Current ratio =
− Increase in accounts payable Current liabilities Valuation Ratios Cash paid to suppliers Dividends declared
Cash + Marketable + Receivables Dividend payout ratio = Free Cash Flow (FCF) Quick ratio = securities NI available to common Current liabilities
Free cash flow to the firm (FCFF): Cash available to
Retention rate (RR) = 1 − Dividend payout ratio Cash + Marketable securities
equity owners and debt holders. ( ) Cash ratio = Current liabilities
Sustainable growth rate g = RR × ROE
FCFF = NI + NCC + I × (1 − t) − FCI − WCI
= CFO + I × (1 − t) − FCI Price per share
Cash + Marketable + Receivables P/E Ratio = Defensive securities = Earnings per share
Free cash flow to equity (FCFE): Cash flow available interval Average daily expenditures to common shareholders DuPont Analysis Cash Days of Days of Number ] \ Assets
FCFE = CFO − FCI + Net Borrowing ROE = \ Net income Assets conversion = sales + inventory − of days ] Book Value of Equity cycle outstanding on hand payables = (ROA) >Leverage) ratio NI Revenue Assets ] \ ] \ ] = \ Revenue Assets Equity
= \Net profit] > Asset ) >Leverage) margin turnover ratio NI EBT EBIT Revenue Assets = / 5 / 5 / 5 / 5 / 5 EBT EBIT Revenue Assets Equity = ( Tax ) (I nterest ) ( EBIT ) ( burden margin ) ( Asset Financial leverage ) burden turnover IN I VE NV N E TO NT R O IE R S I ES Depreciation Methods INCOME TAX TA ES XE S
Inventory Valuation Requirements
Straight-line: = Cost–Salvage value
Temporary Taxable Differences Depreciable life
IFRS: Lower of cost or net realizable value
Deferred tax assets (DTA): Created when taxes
US GAAP: Lower of cost or market value
Double-declining balance (DDB):
payable exceeds income tax expense
Reversals of inventory write-downs are allowed Book valuet Depreciation = \ ] × 2
Deferred tax liabilities (DTL): Created when taxes t
under IFRS, but not under US GAAP Depreciable life
payable is less than income tax expense Units-of-production:
Tax base of assets: Amount that will be deducted on
Inventory Valuation Methods and Systems Cost − Salvage Depreciation = × Output units
the tax return as asset’s benefits are realized US GAAP IFRS t Total output t
Tax base of liabilities: Carrying value of liability FIFO Allowed Allowed Intangible Assets
minus amount that will be deductible LIFO Allowed N/A
Purchased: Record at fair value (purchase price) Weighted Allowed Allowed
Asset carrying amount > Tax base DTL Developed internally: average
Asset carrying amount < Tax base DTA IFRS Specific Allowed Allowed
Liability carrying amount > Tax base DTA
- Research expenditures are expensed Identification
Liability carrying amount < Tax base DTL
- Development expenditures are capitalized
Impact of Inventory Valuation Method US GAAP
Impact of tax rate changes If prices are rising FIFO LIFO
- Generally, both R&D costs are expensed
If tax rate increases, DTA and DTL will increase Ending Inventory Higher Lower
Acquired in business combination:
If tax rate decreases, DTA and DTL will decrease COGS Lower Higher
Purchase price is allocated to each asset on fair
Income tax exp. = Taxes payable + ΔDTL − ΔDTA Net income Higher Lower
value basis; excess recorded as goodwill Valuation Allowance Income Tax Expense Higher Lower
Capitalizing vs. Expensing
Contra account used if it is unlikely that future Operating cash flow Lower Higher
- Capitalizing increases assets on the balance sheet
profits will be sufficient to use DTAs and credits and investing cash outflows
Deferred Tax Charges Directly to Equity
Perpetual vs. periodic inventory system:
- Expensing reduces net income by the after-tax
Periodic system matches total units sold for the
Revaluation of PP&E (IFRS only)
expenditure amount in the period it is incurred
Impact of changes in accounting policies
period with total purchases for the same period
Perpetual system updates after each transaction
Impairment of PP&E and Intangible Assets
Impact of exchange rate fluctuations
Under FIFO, ending inventory and COGS are the US GAAP
Changes in fair value of certain investments
same for periodic or perpetual
- Asset tested for impairment only when firm may
Weighted average and LIFO will show differences
NON-CURRENT (LONG-TERM) LIABILITIES
not recover carrying value through future use
- Asset is impaired when carrying value exceeds Long-Term Liabilities LIFO Reserve
asset’s future undiscounted cash flows
Premium bond: Coupon rate > yield at issuance
Used to adjust LIFO COGS and ending inventory
- Impaired asset’s value is written down to fair
Discount bond: Coupon rate < yield at issuance
(EI) to FIFO-equivalent values
value and a loss is recognized and cannot be Issuance costs: subsequently reversed
US GAAP – capitalized as an asset IFRS
IFRS – reduces initial bond liability
- Assets are tested annually for impairment
Derecognition of debt: If an issuer redeems a bond LIFO Liquidations
- Impaired if carrying value > recoverable amount
before maturity, a gain/loss (book value minus
Happen when units sold exceed units purchased
- Impaired asset’s value is written down to
redemption price) is recognized
May result in higher gross profit than otherwise
recoverable amount and a loss is recognized
Debt covenants: Affirmative – borrower promises
- Loss can be reversed if asset value recovers, but
to do certain things; negative – borrower promises LONG-LIVED A SSETS
only up to pre-impairment carrying value
to refrain from certain things Long-Term Assets Lessee Accounting
Property, plant, and equipment (PP&E): US GAAP IFRS Finance lease:
Both cost model and revaluation model allowed
Lessee purchases the asset, financed by the lessor
Recoverable amount is greater of:
Lessee's periodic lease payments have separate
fair value less selling costs, and
value in use (PV of asset’s future cash flows)
depreciation and interest components - Loss recoveries are allowed
Operating lease (like a rental agreement):
Single lease expense, not separated into different US GAAP
components for depreciation and interest Only cost model is allowed
The value of an operating lease payment is Loss recoveries not allowed
calculated as a straight-line allocation of total
payments over the term of the lease www.saltsolutions.com 9
Conditions requiring a lease to be a finance lease: Limited Partnership
Principal-Agent and Other Relationships
- Ownership of the leased asset is transferred to Set by partnership agreement
Shareholder vs. manager/director the lessee Operated by GP
- Entrenchment: Managers avoid justifiable risks to
- Lessee has the option to purchase the asset and
Business liability is limited by LPs and unlimited avoid losing their positions will likely do so for GP
- Empire building: Making unjustified acquisitions
- Lease term covers most of asset's useful life
Business profits are shared by partners and taxed
to increase company size and compensation
- The present value of lease payments at inception as personal income
- Excessive risk taking: Taking unjustifiable risks to
is close to the asset’s fair value
Partners are the main source of income
maximize returns on stock-based compensation
- The leased asset is so specialized that only the
Partners’ resources, risk appetite, and GP’s
- Agency costs reduce the potential for exploitation
lessee can use it without modification
competence/integrity limit business growth in an agency relationship
IFRS require all leases to be treated in the manner
Corporations (Limited Companies)
Controlling shareholder vs. minority shareholder
that is prescribed by US GAAP for finance leases.
Legal identity is separated from owners
- Dispersed ownership: Controlled by many
Operated by management team voted by Lessor Accounting minority shareholders shareholders -
- Concentrated ownership: Controlled by a single
For operating leases (under both IFRS and US
Limited business liability for shareholders shareholder
GAAP), the lessor retains the leased asset on its Financed by equity and debt
- Multiple-class share structures: Disproportionate
balance sheet and incurs the associated
Profits are taxed directly; double taxation occurs
voting power to certain shareholder classes
depreciation expense. Lease income from the
when shareholders are taxed on their dividend
lessor is recorded as revenue. Shareholder vs. creditor income
- For finance leases (under both IFRS and US
- Equity owners prefer growth and have a higher
GAAP), the lessor removes the leased asset from
Public and Private Corporations risk tolerance
its balance sheet and creates an asset with a
Market capitalization: Product of the current share
- Creditors prefer stability and limited downside
value equal to the lease receivable and any
price and the number of outstanding shares risk residual value.
Enterprise value = MVShares + MVDebt – Cash
Corporate governance can be described as:
- Lease payments are recognized as an operating
Private placement memorandum (PPM) is used by
- A system of internal controls and procedures for
inflow on the lessor’s cash flow statement (for
private companies to raise capital in primary
managing organizational business
both operating leases and finance leases) market
- A framework for defining the rights and
Private companies can go public by: Pensions
responsibilities of individuals and groups within Initial public offering (IPO)
Defined benefit (DB): Firm makes periodic the organization Direct listing (DL)
payments to employee after retirement.
- An arrangement of checks, balances, and Acquisition
Overfunded (underfunded) plan is recognized as
incentives to minimize and manage conflicts an asset (liability).
Public companies can go private by:
between the interests of insiders and external Leveraged buyout (LBO) stakeholders Management buyout (MBO) Stakeholder Mechanisms CORPORATE ISSUERS Lenders and Owners Shareholder:
Risk vs return characteristics of equity and debt: - CORPORATE S
TRUCTURES A ND O WNERSHIP
Corporate reporting and transparency Equity Debt
- Shareholder meetings (cumulative voting, proxy Sole Proprietorship Upside Limited to voting) Extension of owner Unlimited potential payments - Shareholder activism Operated by owner Maximum Cannot be more than the - Derivative lawsuits
Business liability is retained by owner loss investment value
- Corporate takeovers (proxy contests, tender
Business profits are owned by owner and taxed offers, hostile takeovers) as personal income Investment Higher Lower
Owner is the main source of capital risk Creditor:
Owner’s capital and risk appetite limit business Investment Maximize Timely
- Bond indentures, collateral, and trustees growth interest company repayment - Corporate reporting value - Creditor committees General Partnership Set by partnership agreement
INTRODUCTION TO CORPORATE GOVERNANCE
Board of director and management: Operated by partner A AND ND O T O HE TH R E E R SEG C SG O N C S O IDE
NSI RDAETRIO A NS TI ONS - Audit committee
Business liability is retained and shared by - Governance committee Stakeholder Groups partners
- Remuneration/Compensation committee
Business profits are shared by partners and taxed - Nomination committee as personal income - Risk committee
Partners are the main source of capital - Investment committee
Partners’ resources and risk appetite limit business growth Employee: BUSINESS MO DELS & R ISKS
Business Models: Financial Implications - Labor laws Value Proposition External factors:
- Code of ethics and compliance department Target customers Economic conditions - Whistleblower protections Product/service offering Demographics - Employee contracts Channel strategy Sector demand Pricing strategy Customer and supplier: Industry cost characteristics - Commercial contracts Channel strategy: Social and political trends
- Public reputation and social media Traditional channel Firm-specific factors: Direct sales Government: Firm maturity Drop shipping - Laws and regulations Competitive position Omnichannel strategy - Corporate governance codes Business model
- Common law and civil law systems Pricing model: Business Models: Risks Cost-based Macro risk:
Risks and Benefits of Corporate Governance Value-based Exchange rates
and Stakeholder Management Interest rates
Operational risks of poor stakeholder governance: Price discrimination: Political instability
- Weak control systems that do not treat all Tiered pricing Legal and regulatory changes stakeholders fairly Dynamic pricing Country-level risks
- Ineffective decision-making process
Auction/reverse auction models - Inadequate board scrutiny Business risk:
Pricing for multiple products:
- Diminished operating performance Industry risks Bundling Company-specific risks
Financial risks of poor stakeholder governance: Razors-and-blades pricing
- Higher default and bankruptcy risks Optional product pricing Financial risk: - Higher borrowing costs
Total leverage = Operating leverage Pricing for rapid growth: - Poor equity returns × Financial leverage Penetration pricing Contribution margin EBIT
Factors Relevant to Corporate Governance and Freemium pricing = × EBIT EBT
Stakeholder Management Analysis Hidden revenue business model Contribution margin
- Economic ownership and voting control = EBT Alternatives to ownership:
- Board of directors representation Subscription pricing
- Remuneration and company performance CAPITAL INVE NV S E TM ST E M N E TS NT S Fractionalization - Investors in the company
Types of Capital Investments Leasing
- Strength of shareholders’ rights Business maintenance: Licensing
- Management of long-term risks Going concern projects Franchising
Regulatory/compliance projects
ESG Considerations for Investors and Analysts Value Chain ESG investment approaches: Business growth:
Value chain: Systems and functions within the firm - Responsible investing Expansion projects
that create value for its customers - Sustainable investing
Pet projects/high-risk investments
Supply chain: Series of steps and processes needed
- Socially responsible investing (SRI)
to prepare a product to be sold to the consumer
Principles of Capital Budgeting
- Value-based and values-based approaches
Key assumptions of capital allocation:
Profitability and Unit Economics ESG investment styles:
Decisions are based on cash flows instead of
Unit economics: The quantitative analysis of a - Negative screening accounting concepts
company's revenues and costs on a per unit basis - Positive screening
Cash flows are not equivalent to accounting Fixed costs - ESG integration Breakeven point = income or economic income Contribution margin - Thematic investing
Cash flows must account for opportunity costs Fixed costs - Engagement/active ownership =
Analysis is done on an after-tax basis
Unit price − Variable cost per unit - Impact investing
Timing of cash flows is important Business Model Types Financing costs are ignored
Green finance: Use financial instruments to Private label manufacturers
support economic growth while minimizing
Other important considerations: Licensing arrangements environmental impact Sunk costs are ignored Value added resellers
Opportunity cost is the value of a resource’s next- Franchises best use Network effects
Incremental cash flows reflect the cash flows Crowdsourcing realized from a decision Hybrid business models
Externalities (e.g., cannibalization) may have E-commerce business models:
unexpected negative impact the company Affiliate marketing
Conventional cash flow pattern only has Marketplace businesses one sign change Aggregators www.saltsolutions.com 11
Net Present Value (NPV)
External Financing: Capital Markets
COST OF CAPITAL – FOUNDATIONAL TOPIC
Sum of present values of expected future cash - Short-term commercial paper
Weighted Average Cost of Capital (WACC)
inflows, net of initial cash outlay - Long-term debt
WACC = wdrd(1 − t) + wprp + were - Common equity w
d = percentage of debt in capital structure (1 + r)t
wp = percentage of preferred stock
Conservative Working Capital Management
Accept a project if NPV > 0 Advantages:
we = percentage of common stock - Low rollover risk t = tax rate
Internal Rate of Return (IRR) - Greater cash flow certainty rd = cost of debt IRR is r such that NPV = 0
- Low risk of inventory shortages
rp = cost of preferred stock = Dp⁄P
Accept a project if its IRR > required return
- Flexibility to adapt to adverse market conditions re = cost of common stock
BA II Plus NPV Worksheet Function Disadvantages:
Cash inflows are positive; outflows are negative (CAPM) - High borrowing costs
F01, F02, etc. refer to cash flow frequencies = rd + Risk Premium
- High cost of equity and shareholder dilution
CPT + NPV to compute NPV; CPT + IRR for IRR
(Bond Yield plus Risk Premium)
- Less flexibility to borrow on an as-needed basis
Common Capital Budgeting Pitfalls - Longer lead times
Costs of the Various Sources of Capital Inertia - More covenants Cost of debt: Source of capital bias
- High risk of obsolete inventory - Yield-to-maturity approach
Failing to consider alternatives
Aggressive Working Capital Management P = â∑ + Pet projects Advantages:
Basing decisions on earnings metrics
Debt rating approach (e.g., matrix pricing)
- Low financing costs under an upward-sloping Internal forecasting errors yield curve Cost of preferred stock:
Corporate Usage of Capital Allocation Methods
- Great flexibility to borrow only as needed
Return on invested capital (ROIC):
- Short-term borrowing involves less rigorous After-Tax Net Profit Cost of common stock: credit analysis
ROIC = Average BV of Invested Capital Yield-to-maturity approach Disadvantages: Real Options
- Risk of having to refinance at higher Multifactor model
Timing option: Option to delay the investment short-term rates
Sizing option: Option to expand, grow, or abandon
- Potential difficulty rolling over short-term debt + ⋯ + βjmFactorjn
Flexibility option: Option to alter operations, with market turmoil
Bond yield plus risk premium approach
such as changing prices or substituting inputs
- Possible need to rely on expensive trade credit re = rd + Risk Premium
Fundamental option: Option to alter decisions - Tight customer credit terms
based on future events (e.g., drill based on price Estimating Beta
Liquidity and Short-Term Funding Needs
of oil, continue R&D depending on initial results)
Blume’s beta adjustment formula:
Primary sources of liquidity: 2 1
Analyzing Projects with Real Options
Adjusted β = \ ] (Unadjusted β) + \ ] (1.0) - Free cash flows 3 3
Use the discounted cash flow (DCF) analysis
- Ready cash balances (bank accounts)
Asset beta/unlevered beta for comparable
without considering real options
- Short-term funds (lines of credit) company:
Adjust the stand-alone DCF analysis by including
- Cash flow management (centralized collection)
the present value of the expected costs and
Secondary sources of liquidity: 1 β = β û benefits options - Negotiating debt contracts (1 − t) D + 1 E Use option pricing models - Liquidating assets
Levered project beta for subject firm: Use decision trees - Filing for bankruptcy
Drag on liquidity: Delayed cash inflows, such as = β †(1 − t) + 1°
WORKING CAPITAL & LIQUIDITY
uncollected receivables and obsolete inventory Internal Financing Flotation Costs
Pull on liquidity: Accelerated cash outflows, such as
Increasing after-tax operating cash flows r settling payables earlier
e adjusted for flotation costs (amount):
Improving working capital efficiency D
Net operating cycle (a.k.a. cash conversion cycle) = r = + g
Converting liquid assets to cash P0 − F
# days of inventory + # days of receivable – # days
re adjusted for flotation costs (percentage): of payable
External Financing: Financial Intermediaries D r = + g Uncommitted lines of credit
Evaluating Short-Term Financing Choices P0[1 − f] Committed lines of credit
Factors influencing a company’s short-term Revolving credit agreements borrowing strategy: Secured (asset-based) loans - Size and creditworthiness Factoring
- Legal and regulatory considerations Others (web-based lenders and - Sufficient access non-bank lenders)
- Flexibility of borrowing options CAPITAL S TRU STR C U T C U T R U E R E Breakeven
Internal Factors Affecting Capital Structure F + C
Breakeven: QBE = P − V
Business model characteristics: F
Revenue, earnings, and cash flow sensitivity
Operating breakeven: Q OBE = P − V Asset type
Q = quantity; P = price; V = variable cost/unit Asset ownership
F = fixed operating cost; C = fixed financial cost Existing leverage: Liquidity Profitability EQUITY Interest coverage Leverage
To estimate a company’s target capital structure:
MARKET ORGANIZATION AND STRUCTURE
Corporate tax rate: The higher the tax rate, the
Assume the company will main its current capital
Functions of the Financial System more benefit of using debt structure Saving
Capital structure policies/guidelines: Firm-specific
Infer target weights the company is moving Borrowing policies and debt covenants toward Raising Equity Capital Company life stage: Use the industrial average
Pecking order theory: Since managers have an Managing Risks
asymmetric information advantage, they prefer Exchanging Assets
capital sources that reveal the least amount of Information-Motivated Trading information: Securities Markets
Internally generated earnings (best option)
Spot vs. Forward Markets: Spot market trades are New debt settled within 3 days.
New equity (least attractive for managers)
Primary vs. Secondary Markets: Primary market Stakeholder Interests
transactions are done directly with the issuer,
Agency costs arise from conflicts between
while secondary market trades take place on
managers and owners. The interests of managers, organized exchanges.
External Factors Affecting Capital Structure
shareholders, and bondholders are not always
Capital vs. Money Markets: Money markets are
Market conditions/business cycles aligned.
used for securities with maturities of less than Regulatory constraints
one year, while longer-dated securities are traded Industry/peer firm leverage MEASURES OF L EVERAGE in capital markets.
Modigliani and Miller Propositions Leverage Positions
MM Proposition I: A firm's capital structure would
Long positions: Benefit from price appreciation
have no effect on its value, assuming:
Short positions: Benefit from price depreciation
Investors have homogeneous expectations Leveraged Positions
No market frictions (e.g., transaction costs, taxes, Position
or costs of financial distress) Leverage ratio = Equity No agency costs 1
Investors can borrow and lend at risk-free rate
Maximum initial leverage ratio = Intial margin
Investing/financing decisions are independent
Maintenance margin: minimum amount of equity
MM Proposition II: Cost of equity increases with the required debt-to-equity ratio.
Margin call is triggered if the equity falls below the Business Risk Without Taxes
maintenance margin. Additional equity will be
Two components of business risk are:
requested to bring the account balance back to the Firm value VL = VU
Sales risk: determined by the elasticity of demand D initial margin. ] for products and services Cost of Equity r = r + (r − r ) e 0 0 d \E
Operating risk: determined by the share of fixed
Execution Instructions (How to fill) With Taxes
costs as a share of total operating costs
Market: Fill immediately at market price
Limit: Buy below maximum price or sell above Firm value VL = VU + tD Measures of Leverage D
minimum price specified in order Cost of Equity
Degree of operating leverage (DOL):
re = r0 + (r0 − rd)(1 − t) / 5 E
All-or-nothing: Cancel order if not fully filled %Δ Operating income Q(P − V) DOL = =
Hidden: Visible to brokers and exchanges, but
r0 = cost of capital for a firm financed only by equity %Δ Units sold Q(P − V) − F invisible to other traders
Optimal and Target Capital Structure
Degree of financial leverage (DFL):
Iceberg: Only a fraction of order amount is visible
Static trade-off theory balances costs of financial %Δ Net income Q(P − V) − F DFL = =
Validity Instructions (When to fill)
distress with tax shield benefits from using debt: %Δ Operating income Q(P − V) − F − C
Day orders: Cancelled if unfilled at end of day
VL = VU + tD − PV(costs of financial distress)
Degree of total leverage (DTL):
Good-till-cancelled: No set expiry date %Δ Net income Q(P − V) DTL = =
Good-on-close: Filled at end of day %Δ Units sold Q(P − V) − F − C
Stop-loss: Sell if prices fall below specified level DTL = DOL × DFL www.saltsolutions.com 13 Clearing Instructions Price-Weighted Indexes Implications of EMH
Settlement/clearing typically done by brokers for P
If weak form holds, investors will not earn w =
retail trades; brokers or custodians for
abnormal profits from technical analysis institutional trades
Like buying one share of each stock
If markets are semi-strong efficient, investors Advantage is simplicity
must have a comparative advantage to earn
Primary Market Transactions
Disadvantage is arbitrary weights
abnormal profits from fundamental analysis
Initial Public Offerings (IPOs)
A stock’s weight is halved due to a stock split, Private placements Market Anomalies
requiring an adjustment to the divisor
Shelf registrations: Part of issue is held back to be
Changes in a security’s price that are not
sold directly to secondary market investors later
Equally Weighted Indexes
attributable to known information
Dividend reinvestment plans (DRIPs): Investors 1 w =
can roll over dividend payments to purchase new
Selected Behavioral Biases N
shares, possibly at a discount
Like investing the same amount in each stock
Loss aversion: Disliking losses more than liking
Rights offerings: Current shareholders gain right Advantage is simplicity equivalent gains
to purchase additional shares at below-market
Disadvantages are that the impact of large
Information Cascades: Those who act first will
price; dilutes value of existing shares
companies is underrepresented and frequent
convey information that influences others rebalancing is required
Representativeness: Rely too much on current Market Structure
state when assessing probabilities
Quote-driven: Investors trade with dealers
Capitalization-Weighted Indexes
Mental accounting: Keep track of gains and losses
Order-driven: Exchanges use order matching rules Q P w =
separately for different investments/goals
Brokered: Trades arranged by brokers
Conservatism: Failing to incorporate new
Call markets: Conduct periodic single price
Like holding all stocks in proportion to their
information in a timely manner
auctions, otherwise completely illiquid market values
Narrow framing: Focusing on certain issues in
Continuous Trading markets: Allow trades
Float adjustment may be used to reflect the isolation
whenever market is open, may use call market
number of shares that may be actively traded
auction at beginning and/or end of each day
Advantage is that the asset classes’ performance
OVERVIEW OF EQUITY SECURITIES is well-represented
Common Share Voting Methods Trade Pricing Rules
Disadvantage is that returns are heavily driven by
Uniform pricing rules: Used by call markets, all
Statutory: One vote per share
large-cap (possibly overvalued) firms
trades executed at the price that maximizes total
Cumulative: Votes can be bundled quantity traded
Fundamentally Weighted Indexes Example: 10 board positions
Discriminatory pricing rules: Used by continuous
Built like price-weighted indexes, but using a
Statutory: 1 share votes for 10 different candidates
markets, fills most aggressively priced orders first
fundamental measure such as sales or cash flows
Cumulative: 10 votes may go to 1 candidate
Derivative pricing rules: Used by crossing networks
Contrarian effect of rebalancing by selling off top
Cumulative method advantages small shareholder
to trade at midpoint of quotes from other markets
performers and buying underperforming stocks Preference Shares produces a value tilt Complete Markets
Cumulative: Accrue dividends if payments missed Facilitate savings/investment
Types of Equity Market Indexes
Non-cumulative: Missed dividends do not accrue,
Facilitate lending to creditworthy borrowers
Broad market indexes: Covers one equity market
but no common dividends allowed if preferred
Allow risk exposures to be hedged
Multi-market indexes: Covers equity markets in
shareholders do not receive their dividend
Facilitate exchange of currencies/commodities multiple countries
Participating: May receive additional dividend if
An ideal financial system is complete (see above),
Sector indexes: Important for assessing a
firm is profitable or in the event of liquidation
operationally efficient (low transaction costs), and
manager’s performance (selection vs. allocation)
Non-participating: No compensation beyond
informationally efficient (prices reflect all info.)
Style indexes: Large/small cap; Value/growth
dividends and face value in a liquidation
Private Equity Securities SECURITY MAR KET I NDEXES MARKET E EFFFI F C I I CEIN E C NYC Y
Venture capital (VC): Start-up, early-state, or
Price Return over Single Period
Forms of Efficient Market Hypothesis (EMH)
mezzanine financing with IPO as exit strategy P − P Market Prices Reflect: PR
Leveraged buyouts (LBO): Debt-financed deals to = P iO Past
take undervalued listed companies private Public Private Form market
Private investment in public equity (PIPE):
Total Return over Single Period info info data
Companies can raise new capital quickly, P − P + Inc Weak TR
investors can negotiate discounts = ✔ P iO Semi- ✔ ✔
Price Return Index over Multiple Periods strong Strong ✔ ✔ ✔
Total Return Index over Multiple Periods
Depository Receipts (DRs) Multistage DDM: Credit Enhancements n D P
Sponsored DRs: Issued directly by foreign
Internal: Subordination, over-collateralization, V0 = F t + n
company; Investors receive same voting rights and (1 + r)t (1 + r)n reserve accounts t=1
dividends as other common shareholders D
External: Surety bonds, letters of credit, guarantees P = n+1 n r − g from financial institutions L
Unsponsored DRs: Foreign company not involved; Dn+1 = D0(1 + gS)n(1 + gL)
Depository bank purchases shares, issues DRs, and
Bonds with Contingency Provisions retains voting rights Price Multiples Callable Bonds P
May be recalled by issuer if rates fal 0 D
Global DRs: Issued outside company’s home = 1/E1 E1 r − g
country to avoid limits on capital flows; May be
P⁄B = Price per share⁄Book value per share
denominated in any currency, but USD is common; Putable Bonds
P⁄CF = Price per share⁄Cash flow per share
Cannot be listed on US exchanges, but US investors
May be sold back to issuer if rates rise
P⁄S = Price per share⁄Sales per share
can purchase them via private placements
Asset-Based Valuation Models
American DRs: USD-denominated GDRs that can be
Useful for companies with natural resource or a Convertible Bonds
traded on US exchanges; Underlying securities,
large share of current assets/liabilities; Not useful
Conversion price: Price per share at which bond
American depository shares, trade in issuer’s
if company has a large share of PP&E/intangibles can be converted into shares domestic market Enterprise Value (EV)
Conversion ratio: Number of common shares
= MV(Common equity) + MV(Preferred stock)
each bond can be converted into
Global Registered Shares: Traded on multiple
+ MV(Debt) − (Cash + Short term investments) Conversion value:
exchanges, including issuer’s domestic market;
Current share price × Conversion ratio
Denominated in multiple local currencies; Unlike Conversion premium:
DRs, GRS represent an actual ownership interest FIXED INCOME
Convertible bond’s price − Conversion value
Warrants: Options to buy equity, lowers debt costs
INTRODUCTION TO INDUSTRY & COMPANY
FIXED-INCOME SECURITIES: DEFINING AN C A O L MYPSI A S NY ANALYSIS
Convertible Contingent Bonds (CoCos) EL D E E M FI EN NI TS NG ELEMENTS
Porter’s Five Forces Framework
Automatically convert to equity if a condition is Types of Bonds Threat of substitute products
met (e.g., capitalization ratio falls)
Collateral Trust Bonds: Backed by financial assets Bargaining power of customers
Lender does not control if option is exercised
Equipment Trust Bonds: Backed by physical assets Bargaining power of suppliers
Primarily issued by financial institutions
Covered Bonds: Backed by a segregated pool of Threat of new entrants
loans that are replaced if they stop performing Intensity of rivalry
FIXED-INCOME MARKETS: ISSUANCE, TRADING, AN TRD A F D U I NDI NG, N AG
Principal Repayment Structures ND FUNDING
Industry Life Cycle Stages
Bullet Bonds: Full principal repaid at maturity Bond Markets
Embryonic: Slow growth, high prices, high failure
Fully Amortizing: Equal annuity-like payments
Primary bond markets: Markets in which issuers
risk, significant investment required
contain a mix of interest and principal
initially sell bonds to investors to raise capital
Growth: Rapidly increasing demand, improving
Partially Amortizing: Some principal is amortized,
Secondary bond markets: Markets in which bonds
profitability, falling prices, low competition
remainder repaid as a lump sum at maturity
are subsequently traded among investors; Most
Shakeout: Slowing growth, intense competition,
Sinking Funds: Certain percentage of principal
trading is OTC rather than on organized declining profitability retired each year exchanges
Mature: Little or no growth, industry
Grey market: Informal forward market to gauge
consolidation, high entry barriers Coupon Structures
interest in upcoming bond issues and set prices
Decline: Negative growth, excess capacity,
Fixed-rate bonds: Set percentage of principal for the primary market high competition
Floating-rate (FRNs): Reference rate + spread
Step-up: Coupon rate increases on schedule Sovereign Debt
Key Competitive Strategies
Credit-Linked: Coupon rate is increased if issuer is
Issued by national governments, zero default risk
Low-cost leadership: To hold/gain market share
downgraded, reduced if upgraded
Bills mature < 1 year; Bonds mature > 1 year
Product differentiation: To charge premium prices
Payment-in-kind: Coupons may be paid with more
On-the-run: Most recent issues of a given bonds rather than cash
maturity; more liquid than off-the-run issues
EQUITY VALUATION: CONCEPTS AND BASIC
Deferred (Split) Coupon: No coupons in early TO B O A L SIS C TOOLS Non-Sovereign Debt
years, high coupons in later years
Dividend Discount Model (DDM)
Municipal bonds (sub-national issuers)
Inflation-Indexed Bonds
Quasi-government bonds (gov’t-backed agencies) D D P ( +
Zero-coupon: Principal amount is adjusted
Supranational bonds (i.e., IMF, World Bank) 1 + r)t (1 + r)t (1 + r)n
Interest-indexed: Coupons are adjusted
Perpetual preferred stock; constant dividend: Corporate Debt
Capital-indexed: Fixed rate, adjusted principal D
Commercial paper (CP) used for < 1 year, but V =
Indexed-annuity: Amortizing bonds with annuity r carries rollover risk
payments adjusted for inflation
Gordon constant growth model (GGM): Long-term bonds ~12+ years
Bilateral/syndicated bank loans are also used D (1 + g)t D 0(1 + g) D1 ( = 1 + r)t r − g r − g
g = (Retention rate) × ROE = (1 − D⁄E) × ROE www.saltsolutions.com 15
Medium-Term Notes (MTNs) Yield Measures Securitization Example
- Used to bridge gap between CP and L/T bonds Annual cash coupon payment Current yield =
- Firm sells equipment on credit
- Offered to investors through an agent in a range Flat price
- Firm creates bankruptcy-remote SPV of maturities Annual cash + Amortized
- SPV issues debt to purchase loans from firm - coupon payment gain/loss
Lower registration/underwriting costs than Simple yield = - Flat price
SPV creates securities backed by loans
bonds, but relatively illiquid
Yield-to-call (YTC) = IRR assuming bond is called
- Investors purchase securities from SPV -
USCP vs. Eurocommercial Paper
Yield-to-worse = min[YTC, YTM]
SPV collects loan payments from firm’s customers
- SPV distributes cash flows to investors USCP ECP
Yield Measures for FRNs
Residential Mortgage Loans Currency US dollar Any currency
Quoted margin (QM): Spread paid by FRN
- Interest: fixed, adjustable, convertible Maturity Overnight Overnight to
Discount margin (DM): Spread required by market
- Amortization: full, partial, interest-only to 270 days 364 days
If QM > DM, FRN will trade above par
- Prepayment: penalty, no penalty Interest Discount Interest- FRN pricing formula:
- Foreclosure: non-recourse, recourse calculation basis bearing or (Ref + QM)(FV) (Ref + QM)(FV) + FV discount = m
Residential Mortgage-Backed Securities 1 … + m basis \1 + (Ref + DM) N
- Agency RMBS: Issued by government agencies; m ] \1 + (Ref + DM) m ] Settlement T + 0 T + 2 must have conforming loans Negotiable Can be sold Can be sold
Yield Measures for Money Market Instrument
- Non-agency RMBS: Issued by private companies
and may have non-conforming loans
Structured Financial Instruments
Discount Rate (DR) Basis Days
- Guarantee certificate: Zero-coupon bond with a PV = FV × \1 − × DR]
- Pass-through rate: MBS coupon rate
call option on the issuer’s equity Year
- Prepayment risk: Contraction (faster-than-
- Credit-linked note: Seller earns a premium for
Add-on Rate (AOR) Basis
expected); extension (slower-than-expected)
providing credit protection on underlying bond Days
- Prepayment rates are relative to PSA benchmark PV = FV£\1 + × AOR]
- Participation Instruments: Coupon payments Year
Collateralized Mortgage Obligations (CMO)
based on underlying rate (e.g., FRNs)
- Unlike pass-through securities, CMOs have
Implied Forward Rate (IFR)
- Leveraged Instruments: Modify returns
tranches to redistribute cash flows and risks (1 + zA )A × m1 + IFR A ,B–A nB–A = (1 + zB )B
Leveraged floater: 2 × (Reference rate)
- Sequential-pay CMOs have principal and
Deleveraged floater: 0.5 × (Reference rate)
prepayments paid to the tranches sequentially
Leveraged inverse floater: Max coupon − 2 × (RR)
- Planned amortization class (PAC) CMOs have
support tranches to absorb prepayment risk
Factors Increasing Repurchase (Repo) Rates - Higher Collateral risk
Yield Spreads over Benchmark Yield Curve Non-Mortgage ABS
- Amortizing: E.g., auto loan ABS - Longer term
G-spread= YTM − Government bond yield
- Non-amortizing: E.g., credit card receivable ABS - Delivery requirement I-spread= YTM − Swap rate - Low quality collateral
Collateralized Debt Obligations (CDO) Z-spread
- Higher rates for alternative sources of funds PMT PMT PMT + FV
Securities backed by pool of debt obligations, such PV = + + ⋯ + (1 + z
as corporate bonds, leveraged bank loans, or credit 1 + Z)1 (1 + z2 + Z)2 (1 + zN + Z)N IN I T N R T O R D O U D CTIO I N O N TO TOFI F X I E X D E - D I-N I COME
NCOM EV A V L A U L A U T A I T O I N O N
(Can only be calculated by trial-and-error) default swap on securities
Bond Pricing with Spot Rates
Option-adjusted spread (OAS) Covered Bonds PMT PMT PMT + FV PV = + + ⋯ +
OAS = Z-spread − Option value (in basis points)
- Dual recourse against the issuing financial (1 + z1)1 (1 + z2)2 (1 + zN)N
institution and the cover pool
CR: Coupon Rate; MDR: Market Discount Rate INTRODUCTION TO
- One bond class per cover pool
INTRODUCTION TO ASSET-BACKED CR = MDR Price = Par Value Par SE A C S U
SERTI-TBIE A S C KED SECURITIES
- Issuer must replace non-performing asset with CR < MDR Price < Par Value Discount performing asset
Parties to a Securitization CR > MDR Price > Par Value Premium
- Seller/Depositor: Originates loans (assets) -
Bond Pricing Relationships
Issuer: Special purpose vehicle (SPV) established
to create asset-backed securities (ABS)
- Inverse effect: Price moves opposite to yield
- Servicer: Collects payments on underlying loans
- Convexity effect: Falling yield has greater price
impact than equivalent increase in yield ABS Tranching
- Coupon effect: Yield changes have greater impact
- Credit tranching: Certain tranches absorb credit on lower coupon bonds losses before others
- Maturity effect: Yield changes have greater impact
- Absolute priority rule: Senior claims outrank
on longer-term bonds (may not apply to low-
subordinated claims in the event of a liquidation
coupon bonds trading at very deep discounts)
- Time tranching: Certain tranches are exposed to prepayment risk
Flat Price, Accrued Interest, and Full Price
PVFull = PVFlat + AI = (PV)(1 + r)t⁄T AI = (t⁄T) × PMT
UNDERSTANDING FIXED-INCOME RISK AND Convexity DERIVATIVES RE RITU SKR N A S ND RETURNS (PV ApproxCon = –) + (PV+) − [2 × (PVO)]
Constant Yield Price Trajectory (ΔYield)2(PVO)
DERIVATIVE INSTRUMENT AND DERIVATIVE 1 MAR MA K RKET E T F E F A E T A UR TU E R SE S %ΔPVFull = −D × ΔYTM + (Conv)(ΔYTM)2 2 Derivative Underlyings (PV–) + (PV+) − 2(PVO) EffConv = Equities (ΔCurve)2(PVO)
Fixed-income instruments and interest rates Currencies Commodities Credit
Other (e.g., weather, crypto, longevity risk) Derivatives Markets OTC ETD Market Market Liquidity Lower Higher
Yield Duration vs. Curve Duration Trading costs Higher Lower
Yield duration: Sensitivity to YTM Transparency Less Greater
Measures: Macaulay duration, modified duration,
money duration, price value of basis point (PVBP) Standardization Lower Higher Duration Gap
Curve duration: Sensitivity to benchmark yields Flexibility/ Higher Lower
Duration gap = DMac − Investment horizon
(e.g., effective duration); for bonds with options customization
If positive: Price risk > Reinvestment risk Counterparty Macaulay Duration Higher Lower
If negative: Reinvestment risk > Price risk credit risk 1 + r 1 + r + N(c − r) t D − − c[(1 + r)N − 1] + r T
FUNDAMENTALS OF C REDIT A NALYSIS
FORWARD COMMITMENT AND CONTINGENT r: YTM CL C AI LA M I MF E F A E T A UR TU E R SE A S N AD IN ND S I TRUM NSTR E U N MTES NTS Credit Risk c: Coupon rate Types of Derivatives
Default risk: Probability of default
N: Number of periods to maturity
Forward commitments: Obligation to trade on a
Loss severity: Loss given default
t: Number of days since last coupon payment
specified date at a previously agreed price
E[Loss] = Pr(Default) × Loss severity
T: Number of days in each coupon period
Contingent claims: Trade may or may not occur
Loss severity = 1 − Recovery rate
depending on market conditions Spread Risk
Credit migration risk: Possibility of downgrade Forward
Market liquidity risk: Need to sell at a discount Contingent Claims Commitments Seniority Ranking Forward contract Options
First Lien Loan – Senior Secured Futures contracts Credit derivatives Second Lien Loan – Secured Swaps Senior Unsecured
DERIVATIVE BENEFITS, RISKS, AND ISSUER Senior Subordinated A AND ND I N I VE NV S ETO ST R O U R S E U S SES Subordinated Modified Duration
Derivative Benefits and Risks D Junior Subordinated ModDur = Mac Benefits:
Pari passu: All creditors in the same ranking, 1 + r
Risk allocation, transfer, and management
%ΔPVFull = −AnnModDur × ΔYield
regardless of maturity, have the same priority Information discovery Credit Ratings ApproxModDur = Operational advantages 2(ΔYield)(PVO)
Investment grade: Baa3/BBB- and above Market efficiency
Money Duration and PVBP
Non-investment grade: Ba1/BB+ and below Risks:
MoneyDur = AnnModDur × PVFull
Four C’s of Credit Analysis Potential for speculative use
ΔPVFull ≈ −MoneyDur × ΔYield Capacity Lack of transparency Collateral
Price value of a basis point = Basis risk 2 Covenants Liquidity risk
Basis point value = DMod × 0.0001 Character Counterparty credit risk Effective Duration
Destabilization and systemic risk
Corporate Bond Yield Components EffDur = Real risk-free interest rate
Derivative Benefits and Risks 2(ΔCurve)(PVO) Expected inflation rate
Issuers use derivatives to perform: Maturity premium Cash flow hedge Liquidity premium Yield spread Fair value hedge Credit spread Net investment hedge www.saltsolutions.com 17
