CFA LEVEL I SMARTSHEET 2018 - FUNDAMENTALS FOR CFA EXAM SUCCESS - Wiley Efficient Learning
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2018
CFA® EXAM REVIEW
CRITICAL
CONCEPTS
FOR THE
CFA EXAM
CFA LEVEL I ®
SMARTSHEET
FUNDAMENTALS FOR CFA® EXAM SUCCESS
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ETHICAL AND QUANTITATIVE METHODS • Standard deviation: positive square root of the variance
• Coefficient of variation: used to compare relative
PROFESSIONAL STANDARDS TIME VALUE OF MONEY dispersions of data sets (lower is better)
ETHICS IN THE INVESTMENT PROFESSION • Present value (PV) and future value (FV) of a single cash s
Coefficient of variatio
ar
ariation=
flow X
• Challenges to ethical behavior: overconfidence bias,
situational influences, focusing on the immediate rather PV =
FV
• Sharpe ratio: used to measure excess return per unit of
than long-term outcomes/consequences. (1 + r) N
risk (higher is better)
• General ethical decision-making framework: identify, • PV and FV of ordinary annuity and annuity due
consider, decide and act, reflect.
rp − rf
• CFA Institute Professional Conduct Program sanctions: PVAnnuity Duee = PVOrdinary Annuity × (1 + r)
inary ar ratio =
Sharpe
arpe
sp
FVAnnuity Duee = FVOrdinary Annuity × (1 + r)
public censure, suspension of membership and use of inary
the CFA designation, and revocation of the CFA charter • Positive skew: mode < median < mean
(but no monetary fine). • PV of a perpetuity
• Kurtosis: leptokurtic (positive excess kurtosis),
PMT
STANDARDS OF PROFESSIONAL CONDUCT PVPerpetuity = platykurtic (negative excess kurtosis), mesokurtic (same
I/Y
kurtosis as normal distribution; i.e. zero excess kurtosis)
I. Professionalism DISCOUNTED CASH FLOW APPLICATIONS
A. Knowledge of the Law
PROBABILITY CONCEPTS
B. Independence and Objectivity • Positive net present value (NPV) projects increase • Expected value and variance of a random variable (X)
shareholder wealth. using probabilities
C. Misrepresentation
D. Misconduct
• For mutually exclusive projects, choose the project with
the highest positive NPV.
II. Integrity of Capital Markets E(X) = P( X1 ) X1 + P(X 2 )X 2 + … P(X
X n )X
)X n
• Projects for which the IRR exceeds the required rate of
A. Material Nonpublic Information return will have positive NPV.
B. Market Manipulation • For mutually exclusive projects, use the NPV rule if the n
III. Duties to Clients NPV and IRR rules conflict. σ 2 (X) = ∑ P(X i ) [X
[ X i − E (X)]2
i =1
A. Loyalty, Prudence and Care
B. Fair Dealing
YIELDS FOR US TREASURY BILLS • Covariance and correlation of returns
C. Suitability • Bank discount yield
D. Performance Presentation Corr(R A ,R B ) = ρ(R A ,R
,RB) =
Cov(R ,RB)
R A ,R
D 360 (σ A )(σ B )
E. Preservation of Confidentiality rBD = ×
F t
IV. Duties to Employers
• Holding period yield • Expected return on a portfolio
A. Loyalty
B. Additional Compensation Arrangements P − P + D1 P1 + D1 N
HPY = 1 0 = −1
C. Responsibilities of Supervisors P0 P0 R p ) = ∑ wi E
E(R (R i ) = w1E(R
E(R R1 ) + w 2 E (R 2 ) + + w N E(R
E(R RN )
i =1
V. Investment Analysis, Recommendations and Actions • Money market yield
A. Diligence and Reasonable Basis • Variance of a 2-asset portfolio
B. Communication with Clients and Prospective 3600 × rBD
R MM =
Clients 360 − (t × rBD ) Va R p ) = w2A σ 2 ((R
Var( R A ) + w2B σ 2 ((R
R B ) + 2w A w Bρ((R R B )σ (R A )σ ((R
R A ,,R RB)
C. Record Retention
R MM = HPY × (360/t)
VI. Conflicts of Interest DiscounTeD cash floW applicaTions
BINOMIAL DISTRIBUTION
A. Disclosure of Conflicts
• Effective annual yield
B. Priority of Transactions Effective Annual Yield • Probability of x successes in n trials (where the
C. Referral Fees EAY = (1 + HPY)365/ t − 1
probability of success, p, is equal for all trials) is given by:
VII. Responsibilities as a CFA Institute Member or CFA x) = nCx (p))x ((1 – p)n – x
X = x)
P(X
Candidate where:
HPY =STATISTICAL
holding period yield CONCEPTS
A. Conduct as Participants in CFA Institute Programs t = numbers of days remaining till maturity • Expected value and variance of a binomial random
B. Reference to CFA Institute, the CFA Designation, • Data scales: Nominal (lowest), Ordinal, Interval, Ratio variable
and the CFA Program (highest)
HPY = (1 + EAY) t /365 − 1
E(x) = n × p
•
Money Market Yield mean: simple average
Arithmetic
GLOBAL INVESTMENT PERFORMANCE • Geometric mean return: used to average rates of change σ 2 = n × p × (l-p)
STANDARDS (GIPS®) (or
R
360 × rBD
MMgrowth)
= over time
360 − (t × rBD ) NORMAL DISTRIBUTION
• Compliance by investment management firms with GIPS R G = n (1 + R1 ) × (1 + R 2 ) ×…×
×… × (1 + R n ) − 1
is voluntary. R MM = HPY × (360/t) • 50% of all observations lie in the interval µ ± (2/3)σ
• Comply with all requirements of GIPS on a firm-wide • 68% of all observations lie in the interval µ ± 1σ
• Harmonic
Bond Equivalent Yieldmean: used to determine the average cost of
basis in order to claim compliance.
shares purchased over time • 90% of all observations lie in the interval µ ± 1.65σ
• Third-party verification of GIPS compliance is optional. 0.5
BEY = [(1 + EAY) − 1] × 2 • 95% of all observations lie in the interval µ ± 1.96σ
• Present a minimum of five years of GIPS-compliant N
Harmonic mean: X H = N • 99% of all observations lie in the interval µ ± 2.58σ
historical performance when first claiming compliance, 1
∑x • A z-score is used to standardize a given observation of a
then add one year of compliant performance each i =1 i
normally distributed random variable
subsequent year so that the firm eventually presents a
• Variance: average of the squared deviations around the
(minimum) performance record for 10 years. z = (observed value − population mean)/standard
erve nda deviationn = (x − µ) /σ
ndard
mean
• Nine major sections: Fundamentals of Compliance; Input
data; Calculation Methodology; Composite Construction; n • Roy’s safety-first criterion: used to compare shortfall risk
Disclosures; Presentation and Reporting; Real Estate; ∑ (X i − µ)2 of portfolios (higher SF ratio indicates lower shortfall
Private Equity; and Wrap Fee/Separately Managed σ =2 i =1 risk)
n
Account (SMA) Portfolios.
E (RP ) − RT
tfall ratio (SF Ratio) =
Shortf
hortfal
hortf
n σP
∑ (X i − X) 2
i =1
s2 =
n −1
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SAMPLING THEORY TECHNICAL ANALYSIS MARKET STRUCTURES
• Central limit theorem: Given a population with any • Reversal patterns: head and shoulders, inverse head • Perfect competition
probability distribution, with mean, µ, and variance, and shoulders, double top and bottom, triple top and • Minimal barriers to entry, sellers have no pricing power.
σ2, the sampling distribution of the sample mean x, bottom. • Demand curve faced by an individual firm is perfectly
computed from sample size n will approximately be • Continuation patterns: triangles (ascending/descending/ elastic (horizontal).
normal with mean, µ (the population mean), and symmetrical), rectangles, flags and pennants. • Average revenue (AR) = Price (P) = MR.
variance, σ2/n, when the sample size is greater than or
• Price-based indicators: moving averages, Bollinger • In the long run, all firms in perfect competition will
equal to 30.
bands, momentum oscillators (rate of change, relative make normal profits.
• The standard deviation of the distribution of sample strength index, stochastic, moving average convergence/
means is known as the standard error of sample mean. • Monopoly
divergence).
• High barriers to entry, single seller has considerable
• When the population variance is known, the standard • Sentiment indicators: opinion polls, put-call ratio, VIX, pricing power.
error of sample mean is calculated as margin debt levels, short interest ratio. • Product is differentiated through non-price strategies.
σx = σ
n
• Flow of funds indicators: Arms index, margin debt, • Demand curve faced by the monopoly is the industry
mutual fund cash positions, new equity issuance, demand curve (downward sloping).
• When the population variance is not known, the standard secondary offerings.
error of sample mean is calculated as
• An unregulated monopoly can earn economic profits
• Cycles: Kondratieff (54-year economic cycle), 18-year in the long run.
(real estate, equities), decennial (best DJIA performance
sx =
s • Monopolistic competition
n in years that end with a 5), presidential (third year has
the best stock market performance). • Low barriers to entry, sellers have some degree of
pricing power.
• Confidence interval for unknown population parameter
based on z-statistic • Product is differentiated through advertising and other
σ
ECONOMICS non-price strategies.
• Demand curve faced by each firm is downward sloping.
x ± z α /2
n
DEMAND ELASTICITIES • In the long run all will make normal profits.
• Confidence interval for unknown population parameter • Oligopoly
• Own-price elasticity of demand is calculated as: • High costs of entry, sellers enjoy substantial pricing
based on t-statistic
%∆Q
QDx power.
s EDPx = … (Equation 6)
x ± tα
n
%∆Px • Product is differentiated on quality, features,
2
marketing and other non-price strategies.
• If the absolute value of price elasticity of demand • Pricing strategies: pricing interdependence (kinked
• When to use z-statistic or t-statistic equals 1, demand is said to be unit elastic. demand curve), Cournot assumption, game theory
When Sampling from a:
Small Sample Large Sample
n < 30 n > 30
• If the absolute value of price elasticity of demand (Nash equilibrium), Stackelberg model (dominant
lies between 0 and 1, demand is said to be relatively firm).
Normal distribution with known variance z‐statistic z‐statistic
inelastic. • Firms always maximize profits at the output level where
Normal distribution with unknown variance t‐statistic t‐statistic*
• If the absolute value of price elasticity of demand is MR = MC
Non-normal distribution with known variance not available z‐statistic greater than 1, demand is said to be relatively elastic. • Identification of market structure
Non-normal distribution with unknown variance not available t‐statistic* • Income elasticity of demand is calculated as: • N-firm concentration ratio.
* Use of z‐statistic is also acceptable % change in quantity demanded • HHI (add up the squares of the market shares of each
EI =
% change in income of the largest N companies in the market).
HYPOTHESIS TESTING
• Positive for a normal good. AGGREGATE SUPPLY AND DEMAND
• One-tailed versus two-tailed tests • Negative for an inferior good. • Components of GDP
Type of test
Null
hypothesis
Alternate
hypothesis Reject null if
Fail to reject
null if P‐value represents • Cross-price elasticity of demand is calculated as: • Expenditure approach
One tailed H0 : μ ≤ μ0 Ha : μ > μ0 Test statistic > Test statistic ≤ Probability that lies
(upper tail) critical value critical value above the computed test % change in quantity demanded
test statistic. EC = GDP = C + I + G + (X
(X − M
M)
% change in price of substitute or complement
One tailed H0 : μ ≥ μ0 Ha : μ < μ0 Test statistic < Test statistic ≥ Probability that lies
(lower tail) critical value critical value below the computed test
• Income approach
test statistic.
• Positive for substitutes.
Two‐tailed H0 : μ = μ0 Ha : μ ≠ μ0 Test statistic < Lower critical Probability that lies
GDP = National income + Capital consumption allowance
lower critical value ≤ test above the positive • Negative for complements. + Statistical discrepancy
value statistic ≤ value of the computed … (Equation 1)
Test statistic >
upper critical
upper critical
value
test statistic plus the
probability that lies
• Normal good: substitution and income effects reinforce
value below the negative one another. • Equality of Expenditure and Income
value of the computed
test statistic. • Inferior good: income effect partially mitigates the
substitution effect. S = I + (G − T) + ( X − M) … (Equation 7)
• Type I versus Type II errors • Giffen good: inferior good where the income effect • To finance a fiscal deficit (G – T > 0), the private sector
Decision H0 is True H0 is False outweighs the substitution effect, making the demand must save more than it invests (S > I) and/or imports
Do not reject H0 Correct decision Incorrect decision curve upward sloping. must exceed exports (M > X).
Type II error • Veblen good: status good with upward sloping demand • Factors causing a shift in aggregate demand (AD)
Reject H0 Incorrect decision Correct decision curve.
Type I error Power of the test
Significance level = = 1 − P(Type II error) An Increase in the
P(Type I error) PROFIT MAXIMIZATION, BREAKEVEN AND Following Factors Shifts the AD Curve Reason
SHUTDOWN ANALYSIS Stock prices Rightward: Increase in AD Higher consumption
• Hypothesis test concerning the mean of a single
population • Profits are maximized when the difference between total
Housing prices Rightward: Increase in AD Higher consumption
Consumer confidence Rightward: Increase in AD Higher consumption
x − µ0 revenue (TR) and total cost (TC) is at its highest. The level
t-stat =
s n of output at which this occurs is the point where: Business confidence Rightward: Increase in AD Higher investment
• Marginal revenue (MR) equals marginal cost (MC); and Capacity utilization Rightward: Increase in AD Higher investment
• Hypothesis test concerning the variance of a normally • MC is not falling Government spending Rightward: Increase in AD Government spending a component
distributed population of AD
• Breakeven occurs when TR = TC, and price (or average
( n − 1) s 2
revenue) equals average total cost (ATC) at the breakeven Taxes Leftward: Decrease in AD Lower consumption and investment
χ2 =
σ 20 quantity of production. The firm is earning normal profit. Bank reserves Rightward: Increase in AD Lower interest rate, higher
investment and possibly higher
• Short-run and long-run operating decisions consumption
• Hypothesis test related to the equality of the variance of
Exchange rate (foreign Leftward: Decrease in AD Lower exports and higher imports
two populations Revenue/ Cost Relationship Short-run Decision Long-run Decision
currency per unit
TR = TC Continue operating Continue operating domestic currency)
s12
F= TR > TVC, but < TC Continue operating Exit market Global growth Rightward: Increase in AD Higher exports
s22
TR < TVC Shut down production Exit market
• Factors causing a shift in aggregate supply (AS)
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An Increase in Shifts SRAS Shifts LRAS Reason
expansion. Expansionary fiscal policy (increase spending
and/or reduce taxes) is used to raise employment and FINANCIAL REPORTING
AND ANALYSIS
Supply of labor Rightward Rightward Increases resource base
output in a recession
Supply of natural resources Rightward Rightward Increases resource base
Supply of human capital Rightward Rightward Increases resource base
• Fiscal multiplier
Supply of physical capital Rightward Rightward Increases resource base 1
FINANCIAL REPORTING BASICS
Productivity and technology Rightward Rightward Improves efficiency of inputs [1 − MPC(1 − t )]
Nominal wages Leftward No impact Increases labor cost
• Types of audit opinions: unqualified, qualified, adverse,
• Limitations fiscal policy: recognition, action and disclaimer.
Input prices (e.g., energy) Leftward No impact Increases cost of production
Expectation of future prices Rightward No impact Anticipation of higher costs and/or impact lags • Accruals: unearned or deferred revenue (liability),
perception of improved pricing
• Relationships between monetary and fiscal policy unbilled or accrued revenue (asset), prepaid expenses
power
(asset), accrued expenses (liability).
Business taxes Leftward No impact Increases cost of production • Easy fiscal policy/tight monetary policy – results in
Subsidy Rightward No impact Lowers cost of production higher output and higher interest rates (government • Qualitative characteristics of financial information:
expenditure would form a larger component of relevance, faithful representation, comparability,
Exchange rate Rightward No impact Lowers cost of production
national income). verifiability, timeliness, understandability (first two are
• Impact of changes in AD and AS fundamental qualitative characteristics).
• Tight fiscal policy/easy monetary policy – private
sector’s share of overall GDP would rise (as a result • General features of financial statements: fair
Unemployment Aggregate Level presentation, going concern, accrual basis, materiality
Real GDP Rate of Prices of low interest rates), while the public sector’s share
would fall. and aggregation, no offsetting, frequency of reporting,
An increase in AD Increases Falls Increases comparative information, consistency.
A decrease in AD Falls Increases Falls
• Easy fiscal policy/easy monetary policy – this would
An increase in AS Increases Falls Falls lead to a sharp increase in aggregate demand, lowering INCOME STATEMENTS
A decrease in AS Falls Increases Increases interest rates and growing private and public sectors.
• Tight fiscal policy/tight monetary policy – this would • Revenue recognition methods: percentage of
• Effect of combined changes in AD and AS lead to a sharp decrease in aggregate demand, higher completion, completed contract, installment method,
Effect on Real Effect on Aggregate
interest rates and a decrease in demand from both cost recovery method.
Change in AS Change in AD GDP Price Level private and public sectors. • Discontinued operations: reported net of tax as a
Increase Increase Increase Uncertain separate line item after income from continuing
Decrease Decrease Decrease Uncertain INTERNATIONAL TRADE operations.
Increase Decrease Uncertain Decrease
Decrease Increase Uncertain Increase
• Comparative advantage: a country’s ability to produce • Unusual or infrequent items: listed as separate line
a good at a lower opportunity cost than its trading items, included in income from continuing operations,
reported before-tax.
BUSINESS CYCLES partners
• Ricardian model: labor is the only variable factor of • Accounting changes
• Phases: trough, expansion, peak, contraction (or production and differences in technology are the key • Change in accounting principle (applied
recession) source of comparative advantage. retrospectively).
• Theories • Heckscher-Ohlin model: capital and labor are variable • Change in an accounting estimate (applied
• Neoclassical (Say’s Law). factors of production and differences in factor prospectively).
• Austrian (misguided government intervention). endowments are the primary source of comparative • Correction of prior-period errors (restate all prior-
advantage. period financial statements).
• Keynesian (advocates government intervention during
a recession). • Effect of tariffs, import quotas, export subsidies and • Basic EPS
voluntary export restraints
• Monetarist (steady growth rate of money supply). Net incomee − Preferred dividends
• Price, domestic production and producer surplus Basic EPS =
• New Classical (business cycles have real causes, no increase.
Weighted average number of share
ha s outstanding
hare
government intervention).
• Domestic consumption and consumer surplus
• Neo-Keynesian (prices and wages are downward
sticky, government intervention is useful in eliminating
decrease. • Diluted EPS (taking into account all dilutive securities)
unemployment and restoring macroeconomic • Balance of payments components
Conver
Convertible Convertible
Conver
equilibrium). • Current account (merchandise trade, services, income Net income − Preferred +
dividends
prefe
pref rred +
eferred debt × (1 − t)
dividends interest
• Unemployment: natural rate vs frictional vs structural receipts and unilateral transfers). Diluted EPS =
Shares from
Weighted Shares from Shares
vs cyclical. • Capital account (capital transfers and sales/purchases average +
conversion
conve
convers
rsio
ionn of
convertible
convertible
of
+ conversion of + issuable from
conver
convertible stock options
• Prices indices: using a fixed basket of goods and of non-produced, non-financial assets). shares prefe
ef rred shares
efe debt
services to measure the cost of living results in an • Financial account (financial assets abroad and foreign-
upward bias in the computed inflation rate due to owned financial assets in the reporting country). BALANCE SHEETS
substitution bias, quality bias and new product bias. • Current account surplus or deficit.
• Economic indicators • Accounting for gains and losses on marketable securities
• Leading (used to predict economy’s future state). CA = X – M = Y – (C + I + G)
• Coincident (used to identify current state of the
Held‐to‐Maturity
Securities Available‐for‐Sale Securities Trading Securities
economy). CURRENCY EXCHANGE RATES Balance Sheet Reported at cost or
amortized cost.
Reported at fair value. Reported at fair value.
• Lagging (used to identify the economy’s past Unrealized gains or losses due
condition). • Exchange rates are expressed using the convention to changes in market values are
reported in other comprehensive
A/B; i.e. number of units of currency A (price currency) Items recognized Interest income.
income within owners’ equity.
Dividend income. Dividend income.
MONETARY AND FISCAL POLICY required to purchase one unit of currency B (base on the income
Realized gains and Interest income. Interest income.
statement
currency). USD/GBP = 1.5125 means that it will take losses.
Realized gains and losses. Realized gains and losses.
• Quantity theory of money 1.5125 USD to purchase 1 GBP.
Unrealized gains and losses
• Real exchange rate due to changes in market
values.
MV = PY
Real exchange rate DC/FCC = SDC/FC × ((P
PFC //P
PDC ) • Common-size balance sheet: expresses each balance
• Contractionary monetary policy (reduce money supply C/FC
sheet as a % of total assets to allow analysts to compare
and increase interest rates) is meant to rein in an firms of different sizes
overheating economy. Expansionary monetary policy • Forward exchange rate (arbitrage-free)
(increase money supply and reduce interest rates) is CASH FLOW
meant to stimulate a receding economy 1 (1 + rDC ) (1 + rDC )
FDC/FC = × or FDC/FC = SDC/FC
C/FC ×
• Limitations of monetary policy: SFC/DC (1 + rFC ) (1 + rFC ) • CFO (direct method)
• Central bank cannot control amount of savings. • Step 1: Start with sales on the income statement.
• Central bank cannot control willingness of banks to • Exchange rate regimes: dollarization, monetary union, • Step 2: Go through each income statement account
extend loans. fixed parity, target zone, crawling pegs, fixed parity with and adjust it for changes in all relevant working capital
crawling bands, managed float, independently floating accounts on the balance sheet.
• Central bank may lack credibility. rates.
• Contractionary fiscal policy (reduce spending and/ • Step 3: Check whether changes in these working
or increase taxes) is used to control inflation in an capital accounts indicate a source or use of cash.
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• Step 4: Ignore all non-operating items and non-cash • Profitability ratios • COGS under FIFO = COGS under LIFO – Change in LIFO
charges. Gross profit reserve
Gross profit margin =
• CFO (indirect method) Revenue • Net income under FIFO = Net income under LIFO +
• Step 1: Start with net income. Change in LIFO reserve × (1 – tax rate)
• Step 2: Go up the income statement account and of margin =
Operating profit
ofit
Operating profit • Equity under FIFO = Equity under LIFO + LIFO reserve ×
Revenue
remove the effect of all non-cash expenses and gains (1 – tax rate)
from net income. EBT (earnings
ear
earnings before tax, but afte
af r interes
nter t)
nteres
• Liabilities under FIFO = Liabilities under FIFO + LIFO
• Step 3: Remove the effect of all non-operating activities Pretax margin =
Revenue
reserve × tax rate
from net income.
• Step 4: Make adjustments for changes in all working Net profit
LONG-LIVED ASSETS
Net profit margin =
capital accounts. Revenue
• Capitalizing vs expensing
• Free cash flow to the firm (FCFF)
Net income
ROA = Capitalizing Expensing
FCFF = NI + NCC
C + [In
Intt * (1 − tax rate)]] − FCI
[[Int nv − WCInv
FCInv
FCInv Average total assets Net income (first year) Higher Lower
Net income (future years) Lower Higher
FCFF = CFO
CFO + [[Int * (1 − tax
tax rat e)]] − F
rrate)]
ate) FCInv Net incomee + Interest expense (1 − Tax rate)
nteres Total assets Higher Lower
Adjusted ROA = Shareholders’ equity Higher Lower
Average total assets
• Free cash flow to equity (FCFE) Cash flow from operations Higher Lower
Cash flow from investing Lower Higher
FCFE = CFO − FCInv + Net borrowing Operating income or EBIT Income variability Lower Higher
Operating ROA =
Average total assets Debt-to-equity Lower Higher
FINANCIAL ANALYSIS TECHNIQUES • Depreciation expense
• Activity ratios Return on total capital =
EBIT • Straight line
hor term debt + Long-term debt + Equity
Short-
hort-
Original cost − Salvage value
Cost of goods sold Depreciation expense =
y tturnover =
Inventory Depreciable life
lif
Average inventory
nventor
nventory Net income
Return on equity =
Average total equity
365 • Double declining balance (DDB)
invent y on hand (DOH) =
Days of inventor
Inventory
nventory turnove
nventor ur r
2
Net incomee − Preferred dividends DDB depreciatio
depr n in Year X = × Book value att tthe beginning of Year X
Return on common equity = Depreciable life
lif
Revenue Average common equity
Receivabless tturnover =
Average receivables
• Depreciation components
Depreciation Components
365 • DuPont decomposition of ROE
Days of sales outstanding (DSO) = Gross investment in fixed assets
Receivables turnove
tur r Estimated useful lif =
ef life
eful
Annual depreciation expense
Net income Average total assets
ROE = ×
Purchases Average total assets Average share
ha holders’ equity
hare
Payabless tturnover =
Averagee ttrade payables
↓ ↓ Accumulated depreciation
Average age of asset =
ROA Leverage Annual depreciation expense
365
Number of days of payables =
Payables turnove
tur r
Net income Revenue Average total assets Net investment in fixed assets
ROE = × × lif =
Remaining useful life
Revenue Revenue Average total assets Average share
ha holders’ equity
hare Annual depreciation expense
Working capital turnover =
Average working
or
orking capital ↓ ↓ ↓
Net profit margin Assett ttur
urnover
urnove Leverage
Fixed assett tturnover =
Revenue • Revaluation of long-lived assets
Averagee ffixed assets
Interest burden Assett ttur
urnover
urnove • IFRS allows revaluation model or cost model (only cost
Revenue ↓ ↓ model under US GAAP).
Total assett tturnover =
Average total assets ROE =
Net income EBT
× ×
EBIT
×
Revenue
×
Average total assets • If revaluation initially decreases the asset’s carrying
EBT EBIT Revenue Average total assets Avg. shareholders
eholde ’ equity
eholders
amount, the decrease is recognized as a loss on the
↓ ↓ ↓
• Liquidity ratios income statement.
Tax burden EBIT margin Leverage
• If revaluation initially increases the asset’s carrying
Current assets
at =
Current ratio
atio amount, the increase goes directly to equity.
Current liabilities • Dividend-related measures
• Impairment of property, plant and equipment
Cash + Short-term marketable investments + Receivables
ort- at =
Dividend payout ratio
atio
Common share
ha dividends
hare • IFRS: asset is impaired when its carrying amount
at =
Quick ratio
atio Net income attributable
ttr
ttributable to common share
ha s
hare
Current liabilities exceeds its recoverable amount (impairment loss is the
difference between these two amounts).
Cash ratio =
Cash + Short-
hor term mark
hort- ma etable investments
Retention Rate =
Net income attributable
ttr
ttributable ha s − C
to common share
hare Common share
ha dividends
hare • US GAAP: asset is impaired when its carrying value
Current liabilities Net income attributable
ttr
ttributable to common share
ha s
hare exceeds the total value of its undiscounted expected
future cash flows (impairment loss is the difference
Cash + Short-term marketable investments + Receivables
hort-
Defensive interval ratio = Sustainable growth rate = Retention rate × ROE between the asset’s carrying value and its fair value).
Daily cash expenditures
DEFERRED TAXES
Cash conversion cycle = DSO + DOH − Number of days of payables INVENTORIES (DUE TO TEMPORARY DIFFERENCES)
• Solvency ratios • LIFO vs FIFO with rising prices and stable inventory levels • A deferred tax liability (asset) arises when:
Debt -to-assets
- ratio =
Total debt • Taxable income is lower (higher) than pretax
Total assets accounting profit.
Total debt
• Taxes payable is lower (higher) than income tax
Debt -to-capital
- at =
ratio
atio expense.
Total debtt + S
Share
ha holders’ equity
hare
• If a company has a DTL, a reduction (increase) in tax rates
Total debt would reduce (increase) liabilities, reduce (increase)
Debt -to-equity
- ratio =
Shareholders
eholde ’ equity
eholders income tax expense, and increase (reduce) equity
• If a company has a DTA, a reduction (increase) in tax rates
Financial leverage ratio =
Average total assets would reduce (increase) assets, increase (reduce) income
Average total equity • LIFO to FIFO conversion with rising prices and stable or tax expense, and reduce (increase) equity
rising inventory quantities • DTA carrying value should be reduced to the expected
EBIT
Interest coverage ratio = • Inventory under FIFO = Inventory under LIFO + LIFO recoverable amount using a valuation allowance
Interest payments
reserve
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ACCOUNTING FOR BONDS • Dividend discount model RISK MANAGEMENT
D
• Effective interest method required under IFRS and re = 1 + g
P0
• Financial risks: market, credit (default or counterparty
preferred under US GAAP risks), liquidity (or transaction cost risk)
• Interest expense for a given period is calculated as • Bond yield plus risk premium • Non-financial risks: settlement, legal, compliance
the book value of the liability at the beginning of the (including regulatory, accounting and tax risks), model,
period multiplied by market interest rate at bond re = rd + risk premium operational, solvency
issuance. • Methods of risk modification: risk prevention/avoidance,
• Project beta
• Coupon payments are classified as cash outflows. risk acceptance (self-insurance and diversification), risk
• unleveraged beta for a comparable asset transfer, risk shifting/modification
• Book value of the bond liability at any point in time is
the PV of the bond’s remaining cash flows (discounted
at the market interest rate at issuance). β ASSET
ASSET = β E
EQUITY
1
PORTFOLIO RISK AND RETURN
1 + (1 − t ) D
E
LEASES • Utility function
• Beta for a project using a comparable asset releveraged 1
• Lease accounting from lessee’s perspective: treating a for target company (R)) − Aσ 2
U = E(R
E(R)
E
2
lease as a finance lease (compared to an operating lease) D
results in: β PROJEC ASSET 1 + (1 − t )
T = β ASSET
PROJECT
PROJECT
E • The higher the correlation between the individual assets,
• Higher assets, current liabilities, long-term liabilities, the higher the portfolio’s standard deviation and the
EBIT, CFO, leverage ratios. MEASURES OF LEVERAGE lower the diversification benefits (no diversification
• Lower net income (early years), CFF, asset turnover, benefits with a correlation coefficient of +1)
current ratio, ROA (early years), ROE (early years). • Degree of operating leverage (DOL) • The Markowitz efficient frontier contains all the possible
• Same total cash flow. portfolios in which rational, risk-averse investors will
Percentage change in operating income
DOL = consider investing
Percentage change in units sold
FINANCIAL REPORTING QUALITY • Optimal capital allocation line: line drawn from the risk-
• Degree of financial leverage (DFL) free asset to a portfolio on the efficient frontier, where
• Conditions conducive to issuing low quality financial the portfolio is at the point of tangency. The optimal CAL
reports: opportunity, motivation, rationalization DFL =
Percentage change in net income offers the best risk-return tradeoff to an investor
Percentage change in operating income
• Mechanisms that discipline financial reporting • The point where an investor’s indifference (utility) curve
quality: markets, regulatory authorities, registration • Degree of total leverage (DTL) is tangent to the optimal CAL indicates the investor’s
requirements, auditors, private contracting optimal portfolio
DTL =
Percentage change in net income • With homogenous expectations, the capital market line
Percentage change in the number of units sold
CORPORATE FINANCE (CML) becomes a special case of the optimal CAL, where
the tangent portfolio is the market portfolio
DTL = DOL × DFL • CML equation (slope of line is called the market price
CORPORATE GOVERNANCE of risk)
• Breakeven quantity of sales = (Fixed operating costs + Equation of CML
• Key areas of interest: economic ownership and voting Fixed financial costs) ÷ Contribution margin per unit Rm ) − Rf
E(R
control, board of directors representation, remuneration Rp ) = Rf +
E(R × σp
• Operating breakeven quantity of sales = Fixed operating σm
and company performance, investors in the company, costs ÷ Contribution margin per unit
strength of shareholders’ rights, managing long-term
risks WORKING CAPITAL MANAGEMENT • Complete diversification of a portfolio eliminates
unsystematic risk. A well-diversified investor expects to
CAPITAL BUDGETING • Sources of liquidity: primary (e.g. cash balances and be compensated for taking on systematic risk
short-term funds) and secondary (e.g. negotiating • Beta captures an asset’s systematic risk (relative to the
• Consider incremental after-tax cash flows, externalities debt contracts, liquidating assets, filing for bankruptcy risk of the market)
and opportunity costs. Ignore sunk costs and financing protection).
costs from calculations of operating cash flows Cov(R , R m ) ρi,m
R i ,R σσ ρi,m σ i
• Additional liquidity measures βi = = i,m 2i m = i,m
σ 2m σm σm
• For mutually exclusive projects, use the NPV rule if the
NPV and IRR rules conflict Purchases = Ending inventory + COGS − Beginning inventory
• The capital asset pricing model (CAPM) is used to
• Payback period ignores time value of money, risk of calculate an asset’s required return given its beta (the
the project and cash flows that occur after the payback Operating cycle = Number of days of inventory + Number of days of receivables
security market line)
period is reached
Net operating cycle = Number of days of inventory + Number of days of receivables
• Discounted payback period ignores cash flows that occur − Number of days of payables R i ) = R f + β i [E(
E(R E(R m ) − R f ]
[E(R
after the payback period is reached
• Average Accounting Rate of Return (ratio of project’s • Trade discounts (e.g. “2/10 net 30” means a 2% discount
is available if the amount owed is paid within 10 days, • If an asset’s expected return using price and dividend
average net income to its average book value) is based forecasts is higher (lower) than its CAPM required return,
on accounting numbers and ignores the time value of otherwise full amount is due by the 30th day)
the asset is undervalued (overvalued).
money 365
Im
Implicit rate = Cost
Cost of trad
trade
tradee cre ditt = 11+
ccredit
redi
Discount
Number of days
beyond discount period −1 • Portfolio performance evaluation measures
• Profitability index (PI): PI exceeds 1 when NPV is positive 1− D Discount
• Sharpe ratio (uses total risk)
Sharpe ratio
PV of future cash
h fflows NPV
PI = = 1+ Rp − Rf
Initial investment Initial investment
ar ratio =
Sharpe
arpe
σp
COST OF CAPITAL
PORTFOLIO MANAGEMENT
• Treynor ratio (uses beta)
OVERVIEW Treynor ratio
• Weighted average cost of capital (WACC) Rp − Rf
Treynor ratio =
WACC = (wd )(r (1 − t) + (wp )(r
)(rd ))(1 )(rp ) + (we )(r
)(re ) • Steps in the portfolio management process: planning βp
(includes developing IPS), execution (includes asset
• Cost of preferred stock allocation, security analysis and portfolio construction),
feedback (includes portfolio monitoring/rebalancing and • M-squared (uses total risk)
rp =
dp performance measurement/reporting).
vp σm
M2 = (R
(R p − R f ) − (R
(R m − R f )
σp
INVESTMENT POLICY STATEMENT
• Cost of equity
• Capital asset pricing model (CAPM) • Investment objectives: risk objectives and return • Jensen’s alpha (uses beta)
objectives
re = R F + β i [E(R M ) − R F ]
• Investment constraints: liquidity, time horizon, tax α p = R p − [R
[R f + β p ((R
R m − R f )]
concerns, legal/regulatory factors, unique circumstances
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EQUITY INVESTMENTS • Cumulative preference shares are less risky than non-
cumulative preference shares as they accrue unpaid FIXED INCOME
dividends.
MARKET ORGANIZATION AND STRUCTURE BASIC FEATURES OF BONDS
INDUSTRY ANALYSIS
• Purchasing stock on margin (leveraged position) • Types of collateral backing: collateral trust bonds,
• Leverage ratio is the reciprocal of the initial margin. • Porter’s five forces: threat of substitute product, equipment trust certificates, mortgage-backed
bargaining power of customers, bargaining power of securities, covered bonds
• Price at which the investor receives a margin call
suppliers, threat of new entrants, intensity of rivalry. • Credit enhancements
(1 − Initial margin) • Industry life-cycle analysis • Internal: subordination, overcollateralization, excess
P0 ×
(1 − Maintenance margin) • Embryonic (slow growth, high prices, high risk of spread (or excess interest cash flow).
failure). • External: surety bonds, bank guarantees, letters of
• Types of orders • Growth (sales grow rapidly, improved profitability, credit.
• Execution instructions, e.g. market orders, limit orders. lower prices, relatively low competition). • Covenants
• Exposure instructions, e.g. hidden orders, iceberg • Shakeout (slower growth, intense competition, • Affirmative: requirements placed on the issuer.
orders. declining profitability, focus on cost reduction, some • Negative: restrictions placed on the issuer.
• Validity instructions, e.g. day orders, good till cancelled failures/mergers). • Repayment structures
orders, immediate or cancel orders, good on close • Mature (little or no growth, industry consolidation, • Bullet: entire principal amount repaid at maturity.
orders, stop orders. high barriers to entry, strong cash flows).
• Amortizing: periodic interest and principal payments
• Clearing instructions, e.g. how final settlement should • Decline (negative growth, excess capacity, price made over the term of the bond.
be arranged (security sale orders must also indicate competition, weaker firms leave).
• Sinking fund: issuer repays a specified portion of the
whether the sale is a long sale or a short sale). • Competitive strategies: cost leadership, product/service principal amount every year throughout the bond’s life
• Execution mechanisms differentiation. or after a specified date.
• Pure auction (order-driven) market: ranks buy and sell • Bonds with contingency provisions
orders on price precedence, then display precedence,
EQUITY VALUATION
• Callable: issuer has the right to redeem all or part of
then time precedence.
• Dividend discount model (DDM) for common stock the bond before maturity.
• Dealer/quote-driven/price-driven market: dealers • Putable: bondholders have the right to sell the bond
create liquidity by purchasing and selling against their
• One-year holding period
back to the issuer at a pre-determined price on
own inventory of securities.
dividend to be received year-end pric
pr e specified dates.
• Brokered market: brokers arrange trades among their V0 =
(1 + k e )1
+
(1 + k e )1 • Convertible: bondholders have the right to convert the
clients.
bond into a pre-specified number of common shares
• Features of a well-functioning financial system: timely of the issuer (can also have callable convertible bonds).
and accurate disclosure, liquidity (which facilitates
• Gordon growth model (constant growth rate of
dividends to infinity) • Contingent convertible bonds (CoCos): convert
operational efficiency), complete markets and external
automatically upon occurrence of a pre-specified
(or informational) efficiency.
event.
(1 + gc )1
D0 (1 D1
INDICES V0 =
(k e − gc )1
=
k e − gc FIXED INCOME MARKETS
• Price-weighted index: value equals the sum of the • Public offering mechanisms: underwritten, best efforts,
security prices divided by the divisor (typically set to the • Multi-stage DDM auction, shelf registration
number of securities in the index at inception).
D1 D2 Dn Pn • Corporate debt
• Equal-weighted index: each security is given an identical Value = + + …+ +
weight in the index at inception (over-represents (1 + k e )1 (1 + k e )2 (1 + k e )n (1 + k e )n • Bank loans and syndicated loans (mostly floating-rate
securities that constitute a relatively small fraction of the where: loans).
target market and requires frequent rebalancing). Pn =
D n +1 • Commercial paper (unsecured, up to a maturity of one
k e − gc year).
• Market-capitalization weighted index: initial market
value is assigned a base number (e.g. 100) and the Dn = Last dividend of the supernormal growth period • Corporate notes and bonds.
Dn+1 = First dividend of the constant growth period
change in the index is measured by comparing the new • Medium-term notes (short-term, medium- to long-
market value to the base market value (stocks with larger term, structured segments).
market values have a larger impact on the index). • Valuation of preferred stock • Short-term wholesale funds: central bank funds,
• Non-callable, non-convertible preferred stock with no interbank funds, certificates of deposits
MARKET EFFICIENCY maturity date • Repurchase agreements (repos)
• Weak form EMH: current stock prices reflect all security • Repo: seller is borrowing funds from the buyer and
market information. Abnormal risk-adjusted returns V0 =
D0 providing the security as collateral.
cannot be earned by using trading rules and technical r
• Reverse repo: buyer is borrowing securities to cover a
analysis. short position.
• Semi-strong form EMH: current stock prices reflect • Non-callable, non-convertible preferred stock with
maturity at time n • Repo margin or haircut: the percentage difference
all security market information and other public between the market value of the security and the
information. Abnormal risk-adjusted returns cannot be n amount of the loan.
Dt F
earned by using important material information after it V0 = ∑ t +
has been made public. t =1 (1 + r) (1 + r)n • Repo rate: annualized interest cost of the loan.
• Strong form EMH: current stock prices reflect all public • Any coupon income received from the bond provided
and private information. Abnormal risk-adjusted returns • Price multiples: price-to-earnings, price-to-sales, price- as security during the repo term belongs to the seller/
cannot be earned (assuming perfect markets where to-book, price-to-cash flow. borrower.
information is cost-free and available to all). • Justified P/E ratio FIXED INCOME VALUATION
• Behavioral biases that may explain pricing anomalies:
loss aversion, herding, overconfidence, information P0 D1 //E
=
E1 • Bond pricing with yield-to-maturity (uses constant
cascades, representativeness, mental accounting, E1 r−g interest rate to discount all the bond’s cash flows)
conservatism, narrow framing.
• If coupon = YTM, the bond’s price equals par value.
• Enterprise value (EV): market value of the company’s • If coupon > YTM, the bond’s price is at a premium to
RISKS OF EQUITY SECURITIES common stock plus the market value of outstanding par.
preferred stock (if any) plus the market value of debt,
• Preference shares are less risky than common shares. • If coupon < YTM, the bond’s price is at a discount to par.
less cash and short-term investments (EV can be thought
• Putable common shares are less risky than callable or of as the cost of taking over a company). • Price is inversely related to yield: when the yield
non-callable common shares. increases (decreases), the bond’s price decreases
• EV/EBITDA multiple is useful for comparing companies
• Callable common and preference shares are more risky (increases).
with different capital structures and for analyzing loss-
than their non-callable counterparts. making companies. • Bond pricing with spot rates (uses the relevant spot rates
to discount the bond’s cash flows)
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• Spot rate: yield on a zero-coupon bond for a given in the full price of a bond in response to a 1 bp change
Prepayment in month
mont t
maturity. SMMt =
Beginning mortgage balancee ffor montht−S
month Scheduled
cheduled principa
principal payment
payment in month
month t
in its YTM
• Accrued interest when a bond is sold between coupon
payment dates • Prepayment risk: contraction risk occurs when interest V− ) − (PV
(PV V+ )
PVBP =
• Full price: calculated as the PV of future cash flows as rates fall (leading to an increase in prepayments), while 2
of the settlement date. extension risk occurs when interest rates rise (leading
to a decrease in prepayments). • Approximate convexity: used to revise price estimates of
• Accrued interest (AI) included in full price: seller’s
proportional share of the next coupon, where t is the • CMOs (backed by pool of mortgage pass-through option-free bonds based on duration to bring them close
number days from last coupon date to the settlement securities): sequential-pay tranches (shorter-term to their actual values
date and T is the number of days in the coupon period tranches receive protection from extension risk, longer-
(actual/actual for government bonds, 30/360 for term tranches receive protection from contraction V− ) + (PV
(PV (PV+ ) − [2 × (PV
(PV0 ))]
ApproxCon =
corporate bonds) risk); PAC/support tranches (support tranche provides ield))2 × ((PV
( ∆Yield
Yield)
Y PV0 )
protection against contraction and extension risk to
AI = t/T × PMT the PAC tranche); floating rate tranches (floater and
• The percentage change in a bond’s full price for a
inverse floater).
• Flat or clean or quoted price: full price less AI, or given change in yield based on duration with convexity
equivalently
• Credit enhancements for non-agency RMBS: internal adjustment is estimated as follows:
(cash reserve funds, excess spread accounts,
overcollateralization, senior/subordinate structure) 1
PV Full = PV Flat
Flat
+ AI and external (monoline insurers). PV Fu
%∆PV Full
ll
≈ (−
(− AnnM
AnnMod ield)) + × AnnConvexity
Durr × ∆Yield
AnnModDur
odDu Yield)
Y Yield)2
AnnConvexity × ( ∆Y
2
• Commercial MBS (backed by non-recourse commercial
• Yield measures mortgage loans): investors have significant call
• Effective annual yield depends on periodicity of the • Effective convexity: use for bonds with embedded
protection but are exposed to balloon risk (like
options instead of approximate convexity.
stated annual yield. extension risk).
• • Callable bonds can exhibit negative convexity when
Annual-pay bond: stated annual yield for periodicity of • Non-mortgage asset-backed securities: auto-loan
benchmark yields decline. Putable bonds always exhibit
one = effective annual yield. receivable-backed securities (backed by amortizing
positive convexity.
• Semiannual-pay bond: stated annual yield for auto loans) and credit card receivable-backed
securities (with lockout period before principal
periodicity of two = semiannual bond basis yield
amortizing period sets in).
CREDIT ANALYSIS
= semiannual bond equivalent yield = yield per
semiannual period × 2. • CDOs: structured as senior, mezzanine and • Two components of credit risk: default risk (or default
• Current yield: annual cash coupon payment divided by subordinated bonds (or equity class). CDO manager probability) and loss severity (or loss given default). Loss
the bond price. engages in active management of the collateral to severity equals 1 minus the recovery rate.
generate the cash flow required to repay bondholders • Expected loss
• Yield-to-call: computed for each call date.
and to earn a competitive return for the equity tranche.
• Yield-to-worst: lowest yield among the YTM and the
various yields to call. INTEREST RATE RISK Expected loss = Defaul
Default
Defa ultt pr obability × Loss severity
pprobability
robability ver given default
verity ef
efault
• Money market pricing on a discount rate basis
• Two types of interest rate risk • Spread risk consists of downgrade risk (or credit
Days
PV = FV × 1 −
ys
× DR • Reinvestment risk: future value of any interim bond migration risk) and market liquidity risk.
year cash flows increases (decreases) when interest rates • Corporate family rating (CFR): issuer rating.
rise (decline). Matters more to long-term investors.
• Corporate credit rating (CCR): rating for a specific issue.
Year FV − PV • Market price risk: selling price of a bond decreases
DR = ×
Days FV (increases) when interest rates rise (decline). Matters • Four Cs: capacity, collateral, covenants, character.
more to short-term investors. • Return impact of a change in the credit spread (includes
• Money market pricing on an add-on rate basis • Macaulay duration: weighted average of the time it convexity adjustment for larger changes)
would take to receive all the bond’s promised cash flows.
FV
PV= • Modified duration: estimated percentage price change Return impact ≈ −(MDurr × ∆S
Spread)) + (1/ Convexity × ∆Spread 2 )
1/22 × C
((1/2
1 + Days
ys
× AOR
Year for a bond in response to a 100 bps (1%) change in yields
MacDur
DERIVATIVES
Year FV − PV ModDur =
AOR = ×
Days PV 1+ r
• Bond-equivalent yield: money-market rate stated on a • If Macaulay duration is not known, annual modified TYPES OF DERIVATIVES
365-day year on an add-on basis. duration can be estimated using the following formula:
• Forward rate • Forward commitments: forwards, futures, interest rate
(PV V− ) − (PV
(PV+ )
swaps.
• Interest rate on a loan originating at some point in the ApproxModDur =
future. 2 × ( ∆Yield) × (PVV0 ) • Contingent claims: options, credit derivatives.
• Implied forward rates can be computed from spot DERIVATIVE PRICING AND VALUATION
rates. • Effective duration: measures the sensitivity of a
bond’s price to a change in the benchmark yield curve
(1 + y s0 ) y (1 + x fy )x = (1 + x+ y
(appropriate measure for bonds with embedded options)
• Derivative pricing is based on risk-neutral pricing.
x+ ys0 )
• Forward contracts
(PVV− ) − (PV
V+ ) • Price at contract initiation (assuming underlying asset
EffDur = entails benefits and costs)
2 × ( ∆Curve) × (PV V0 )
• Key rate duration: measure of a bond’s sensitivity to a )(1 + rr))T oor F(0,T)) = S0 (1 + r)T − ( γ − θ))(1
F(0,T) = (S0 − γ + θ)(1 (1 + r)T
change in the benchmark yield for a given maturity (used
• Yield spreads to assess yield curve risk, i.e. non-parallel shifts in the
*Note γγ) and costs (θ) are expressed in terms of present value.
that benefits (γ)
• G-spread: spread over government bond yield. yield curve)
• I-spread: spread over the swap rate. • Portfolio duration: weighted average of the durations of • Value of a forward contract during its life (long
• Z-spread: spread over the government spot rate. the individual bonds held in the portfolio, where each position)
• Option-adjusted spread: z-spread less option value bond’s weight equals its proportion of the portfolio’s
(bps per year). market value Vt (0, T) = St − ( γ − θ)(1 + r ) t − [F(0, T) / (1 + r )T− t ]
((0,T)
0,T)
• Asset-backed securities • Money duration: measure of the dollar price change in
response to a change in yields • Value of a forward contract at expiration (long position)
• Residential MBS: agency RMBS vs non-agency RMBS
(require credit enhancements). VT (0, T) = ST − F (0,T)
((0,T)
0,T)
MoneyDur = AnnModDur × PVFull
• Mortgage pass-through securities (backed by pool of
residential mortgage loans): single monthly mortality • Forward rate agreement (FRA)
rate (SMM). • Price value of a basis point (PVBP): estimates the change • Long (short) position can be viewed as the party that
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has committed to take (give out) a hypothetical loan. Impact of an increase in: Call Put • Development capital: includes private investment in
• If LIBOR at FRA expiration > FRA rate, the long benefits. public equities (PIPEs).
Value of the underlying Increase Decrease
• If LIBOR at FRA expiration < FRA rate, the short benefits. • Distressed investing: buying debt of mature companies in
Exercise price Decrease Increase financial distress.
• Futures: similar to forwards but standardized, exchange- Risk-free rate Increase Decrease • Exit strategies: trade sale, IPO, recapitalization,
traded, marked-to-market daily, clearinghouse Time to expiration Increase Increase (except for secondary sale, write-off/liquidation.
guarantees that traders will meet their obligations deep in-the-money • Valuation methods for portfolio company: market or
• Forward vs futures prices European puts) comparables approach, discounted cash flow approach,
• If underlying asset prices are positively (negatively) Volatility of the Increase Increase asset-based approach.
correlated with interest rates, the futures price will be underlying • Real estate
higher (lower) than the forward price. Benefits from the Decrease Increase • Investment categories: residential property, commercial
underlying real estate, REITs, timberland/farmland.
• If futures prices are uncorrelated with interest rates
or if interest rates are constant, forwards and futures Cost of carry Increase Decrease • Performance measurement: appraisal indices (tend
would have the same price. to understate volatility), repeat sales indices (sample
• One-period binomial model for a call option (based on selection bias), REIT indices (based on prices of publicly
• Interest rate swaps risk-neutral probability π) traded shares of REITs).
• The swap fixed rate represents the price of the swap • Real estate valuation approaches: comparable sales
πc + + (1 − π)c −
(swap has zero value to the swap counterparties at c= approach, income approach (direct capitalization
(1 + r)
swap initiation). method and discounted cash flow method), cost
• If interest rates increase after swap initiation, the swap approach.
will have positive value for the fixed-rate payer. π=
(1 + r − d)
Wheree u =
S1+ S−
and d = 1 • REIT valuation approaches: income-based approaches,
(u − d) S0 S0 asset-based approaches (NAV).
• If interest rates decrease after swap initiation, the swap
will have positive value for the floating-rate payer. • Commodities
• An interest rate swap can be viewed as a combination ALTERNATIVE INVESTMENTS • Investors prefer to trade commodity derivatives to
of FRAs. avoid costs of transportation and storage for physical
• Potential benefits of alternative investments: low commodities.
• Options
correlations with returns on traditional investments and • Price of a commodity futures contract.
• Call (put) option gives the holder/buyer the right to buy higher returns than traditional investments
(sell) the underlying asset at the exercise price. Futures price = Spot price × (1 + Risk-free short-
pric hor term rate)
hort-
• Hedge funds + Storage costs − Convenience yield
• European option: can only be exercised at the option’s • Event-driven strategies: merger arbitrage, distressed/
expiration. restructuring, activist, special situations. • When the futures price is higher (lower) than the spot
• American option: can be exercised at any point up to • Relative value strategies: fixed income convertible price, prices are said to be in contango (backwardation).
the option’s expiration. arbitrage, fixed income asset backed, fixed income • Sources of return on a commodity futures contract: roll
• Call (put) option is in-the-money when the stock price general, volatility, multi-strategy. yield, collateral yield, spot prices.
is higher (lower) than the exercise price. • Macro strategies: long and short positions in broad • Infrastructure
markets (e.g. equity indices, currencies, commodities, • Investments in real, capital intensive, long-lived assets.
• Intrinsic or exercise value: the amount an option is
etc.) based on manager’s view regarding overall macro • Economic infrastructure: assets such as transportation
in-the-money by (minimum value of 0).
environment. and utility assets.
• Put-call parity for European options (options and bond • Equity hedge strategies: market neutral, fundamental
have the same time to expiration/maturity T) • Social infrastructure: assets such as education,
growth, fundamental value, quantitative directional, healthcare and correctional facilities.
short bias, sector specific. • Brownfield investments: investments in existing
c0 +
X
= p 0 + S0 • Two types of fees: management fee (based on assets infrastructure assets.
(1 + R F )T under management) and incentive fee (which may be • Greenfield investments: investments in infrastructure
subject to a hurdle rate or high water mark provision). assets to be constructed.
• Put-call parity formula can be rearranged to create • Private equity • Risk-return measures
synthetic call, put, underlying asset and bond, e.g. • Leveraged buyouts (LBOs): management buyouts (MBOs) • Sharpe ratio is not appropriate risk-return measure since
synthetic call = long put + long underlying stock + short and management buy-ins (MBIs). returns tend to be leptokurtic and negatively skewed.
bond). • Venture capital: formative stage financing (angel • Downside risk measures more useful, e.g. value at risk
• Factors affecting the value of an option investing, seed-stage financing, early-stage financing), (VAR), shortfall risk, Sortino ratio.
later-stage financing, mezzanine-stage financing.
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