CFA 2023 Schweser - Level I Schwesers Quicksheet

6 Pages·1.996 MB·English

by  Kaplan Schweser

L E V E L I
2 0 2 3 CFA®
C C E
r i t i c a l o n c e p t s f o r t h e x a m
|
^ETHICAL AND PROFESSIONAL
Required Rate of Return Correlation and Covariance
Components: Correlation: covariance divided by product of the
.STANDARDS
1. Real risk-free rate (RFR). two standard deviations.
2. Expected inflation rate premium (IP).
I Professionalism C O V (R i,R j)
3. Risk premium. corr^RpRj j =
1(A) Knowledge of the Law.
a ( R [) a ( R ])
1(B) Independence and Objectivity. E(R) = (l + RFRreal)(l + IP)(l + RP) - 1
1(C) Misrepresentation.
Expected return, variance o f 2-stock portfolio:
Approximation formula for nominal required rate:
1(D) Misconduct.
II Integrity of Capital Markets E(R) = RFR + IP + RP E(Rp) = w AE(Ra ) + w bE (R b)
11(A) Material Nonpublic Information.
Means
11(B) Market Manipulation.
V ar( R p) = w Af f 2 ( R A) + w B ^ 2 ( R B)
Arithmetic mean: sum of all observation values in
III Duties to Clients
+2wAwBcr(RA)(7(RB)p (R A,R B)
HI (A) Loyalty, Prudence, and Care. sample/population, divided by # of observations.
III(B) Fair Dealing. Geometric mean: used when calculating investment Normal Distributions
III(C) Suitability.
returns over multiple periods or to measure Normal distribution is completely described by its
III(D) Performance Presentation.
compound growth rates. mean and variance.
III(E) Preservation of Confidentiality.
Geometric mean return: 68% of observations fall within ± la .
IV Duties to Employers
90% fall within ± 1.65a.
IV(A) Loyalty. R = [(l + R ,)x ...x (l + RN) f - l
g
95% fall within ± 1.96a.
IV(B) Additional Compensation Arrangements.
N
99% fall within ± 2.58a.
IV(C) Responsibilities of Supervisors.
Harmonic mean =
N
V Investment Analysis, Recommendations, 1
Computing Z-Scores
E
and Actions
Z-score: “standardizes” observation from normal
i=i
V(A) Diligence and Reasonable Basis.
distribution; represents # of standard deviations a
V(B) Communication with Clients and
Trimmed mean (x%): Exclude highest and lowest
given observation is from population mean.
Prospective Clients.
x/2 percent of observations.
V(C) Record Retention. observation — population mean x — fi
Winsorized mean (x%): Substitute values for highest
VI Conflicts of Interest
standard deviation a
and lowest x/2 percent of observations.
VI (A) Disclosure of Conflicts.
VI (B) Priority of Transactions. Variance and Standard Deviation Binomial Models
VI(C) Referral Fees. Variance: average of squared deviations from mean. Binom ial distribution: assumes a variable can take
VII Responsibilities as a CFA Institute
one of two values (success/failure) or, in the case of
n
Member or CFA Candidate
E ( x i - x ) 2 a stock, movements (up/down). A binomial model
VII(A) Conduct as Participants in CFA Institute
2 i=l can describe changes in the value of an asset or
sample variance = s =
Programs.
n — 1
portfolio; it can be used to compute its expected
VII(B) Reference to CFA Institute, the CFA
value over several periods.
Standard deviation: square root of variance.
Designation, and the CFA Program.
Sampling Distribution
Target Downside Deviation
Global Investment Performance Standards
Sampling distribution: probability distribution of
D efinition o f firm : Corporation, subsidiary, or
( X j - target) all possible sample statistics computed from a set of
division held out to clients as a business entity. e
target
equal-size samples randomly drawn from the same
n —1
All fee-paying discretionary portfolios must be
population. The sam pling distribution o f the mean is
included in at least one composite.
the distribution of estimates of the mean.
Holding Period Return (HPR)
Verification: Optional, but if chosen it must be
Central Limit Theorem
carried out by an independent third party.
R = P[~P 1+D or Pt+C>t - 1
c c c
C entral lim it theorem: when selecting simple
GIPS standards fo r firm s:
P.-1 Pt-i
random samples of size n from population with
1. Fundamentals of Compliance
2. Input Data and Calculation Methodology Coefficient of Variation mean p and finite variance a 2, the sampling
Coefficient o f variation (CV): expresses how much distribution of sample mean approaches normal
3. Composite and Pooled Fund Maintenance
4. Composite Time-Weighted Return Report dispersion exists relative to mean of a distribution; probability distribution with mean p and variance
allows for direct comparison of dispersion across equal to a 2In as the sample size becomes large.
5. Composite Money-Weighted Return Report
different data sets. CV is calculated by dividing
6. Pooled Fund Time-Weighted Return Report
Standard Error
7. Pooled Fund Money-Weighted Return Report standard deviation of a distribution by the mean or
Standard error o f the sample mean is the standard
expected value of the distribution:
8. GIPS Advertising Guidelines deviation of distribution of the sample means.
CV = =
known population variance: cr^ =
X —j=
vn
QUANTITATIVE METHODS
Roy’s Safety-First Ratio
unknown population variance: s^ =
Time Value of Money Basics
rp rtarget
• Future value (FV): amount to which investment
a„
Confidence Intervals
grows after one or more compounding periods.
C onfidence interval: gives range of values the mean
Expected Return/Standard Deviation
• Future value: FV = PV(1 + I/Y)N.
value will be between, with a given probability (say
• Present value (PV): current value of some future
Expected return-. E(X) = ^ ^ P (x j) xn
90% or 95%). With known variance, formula for a
cash flow PV - FV/(1 + I/Y)N.
E(X) = P (Xl) Xl + P (x2)x 2 + ... + P(xn)x n
confidence interval is:
• Annuities: series of equal cash flows that occur at
evenly spaced intervals over time. Probabilistic variance-. x za/2 r~
V n
• Ordinary annuity: cash flow at end-o$-xvcs\e.
< C x ) = E p M h - E(x ) f
1.645 for 90% confidence intervals
period.
• Annuity due: cash flow at beginning-of-time period. = P (x ,)[x 1 - E ( X ) ] 2 + P ( x 2)[x -E (X )] (significance level 10%, 5% in each tail)
E(x)f
• Perpetuities: annuities with infinite lives. 1.960 for 95% confidence intervals
+ - + P(xn)[x„ —
PV . = PMT/(discount rate). (significance level 5%, 2.5% in each tail)
perpetuity v
Standard deviation: take square root of variance.
continued on next page.
QUANTITATIVE METHODS continued... M onopoly: Single firm with significant pricing Financial account: government-owned assets
power; high barriers to entry; advertising used to abroad; foreign-owned assets in the country.
z = 2.575 for 99% confidence intervals
a/2
compete with substitute products.
Regional Trading Agreements
(significance level 1%, 0.5% in each tail)
In all market structures, profit is maximized at
Free trade area: Removes barriers to goods and
the output quantity for which marginal revenue =
Null and Alternative Hypotheses
services trade among members.
marginal cost.
Null hypothesis (H0): hypothesis that contains the
Customs union: Members also adopt common trade
equal sign (=, <, >).
Gross Domestic Product policies with non-members.
Alternative hypothesis (Ha): concluded if there is
Real GDP = consumption spending + investment + Common market: Members also remove barriers to
sufficient evidence to reject the null hypothesis.
government spending + net exports. labor and capital movements among members.
Economic union: Members also establish common
Savings, Investment, Fiscal Balance, and Trade
Difference Between One- and Two-Tailed Tests
institutions and economic policy.
Balance
O ne-tailed test: tests whether value is greater than or
M onetary union: Members also adopt a common
Fiscal budget deficit (G - T) = excess of saving over
less than a given number.
currency.
domestic investment (S - I) - trade balance (X - M)
Two-tailed test: tests whether value is equal to a
Foreign Exchange Rates
given number. Equation of Exchange
For the exam, FX rates are expressed as p rice
MV = PY, where M = real money supply, V =
Type I and Type II Errors
currency / base currency and interpreted as the
velocity of money in transactions, P = price level,
• Type I error: rejection of null hypothesis when it is
number of units of the price currency for each unit
and Y = real GDP
actually true.
of the base currency.
Business Cycle Phases
• Type II error: failure to reject null hypothesis when
Real Exchange Rate
Expansion; peak; contraction; trough.
it is actually false.
base currency CPI
Economic Indicators
nominal FX rate X
Hypothesis Tests
price currency CPI
Leading: Turning points occur ahead of peaks and v
Test of: Stat d . f troughs (stock prices, initial unemployment claims,
No-Arbitrage Forward Exchange Rate
manufacturing new orders)
Mean t or z n - 1
forward 1 + price currency interest rate
Coincident: Turning points coincide with peaks
Difference in means t n - 1 and troughs (nonfarm payrolls, personal income, spot 1 + base currency interest rate
manufacturing sales)
Mean differences t n - 1
Exchange Rate Regimes
Lagging: Turning points follow peaks and troughs
Formal dollarization: country adopts foreign
Variance n - 1
x2 (average duration of unemployment, inventory/
currency.
sales ratio, prime rate)
Equal variances F n, - 1, n2- 1
M onetary union: members adopt common currency.
Factors Affecting Aggregate Demand
Correlation t n — 2 Fixed peg: ± 1 % margin versus foreign currency or
Consumers’ wealth; business expectations;
basket of currencies.
Independence ( r - U ( c - l ) consumers’ income expectations; capacity
x2
Target zone: Wider margin than fixed peg.
utilization; monetary and fiscal policy; exchange
Regression slope: Crawling peg: Pegged exchange rate adjusted
rates; global economic growth.
Significance F 1, n - 2 periodically.
Factors Affecting SR Aggregate Supply
Value t n - 2 Crawling bands: Width of margin increases over
Input prices; labor productivity; expectations for
time.
output prices; taxes and subsidies; exchange rates;
M anaged floating: Monetary authority acts to
all factors that affect LR aggregate supply.
influence exchange rate but does not set a target.
ECONOMICS Independently floating: Exchange rate is market-
Factors Affecting LR Aggregate Supply
determined.
Size of labor force; human capital; supply of natural
Elasticity
resources; stock of physical capital; level of technology.
%A quantity demanded
Own p rice elasticity Types of Unemployment
FINANCIAL STATEMENT ANALYSIS
%A price
Frictional: time lag in matching qualified workers
If absolute value > 1, demand is elastic. with job openings.
Revenue Recognition
If absolute value < 1, demand is inelastic. Structural: unemployed workers do not have the
Two requirements: (1) completion of earnings
On a straight line dem and curve, total revenue is skills to match newly created jobs.
process and (2) reasonable assurance of payment.
maximized where price elasticity = — 1. Cyclical: economy producing at less than capacity
Five-step revenue recognition model:
during contraction phase of business cycle.
%A quantity demanded
Incom e elasticity 1. Identify contracts
%A income Policy Multipliers
2. Identify performance obligations
If positive, the good is a normal good. 3. Determine transaction price
money multiplier = -------------------------
If negative, the good is an inferior good. 4. Allocate price to obligations
reserve requirement
. . . . %A quantity demanded 5. Recognize when (as) obligations are satisfied
Cross p rice elasticity = -------- -----------------------
%A price of related good fiscal multiplier = -------------------
Unusual or Infrequent Items
l - M P C ( l - t )
• Gains/losses from disposal of a business segment.
If positive, related good is a substitute.
• Gains/losses from sale of assets or investments in
If negative, related good is a complement. where MPC = marginal propensity to consume,
subsidiaries.
t = tax rate.
Breakeven and Shutdown
• Provisions for environmental remediation.
Breakeven: total revenue = total cost. Expansionary and Contractionary Policy
• Impairments, write-offs, write-downs, and
Operate in short run if total revenue is greater than M onetary policy is expansionary when the policy
restructuring costs.
total variable cost but less than total cost. rate is less than the neutral interest rate (real trend
• Integration expenses associated with businesses
Shut down in short run if total revenue is less than rate of economic growth + inflation target) and
recently acquired.
total variable cost. contractionary when the policy rate is greater than
Discontinued Operations
the neutral interest rate.
Market Structures
To be accounted for as a discontinued operation, a
Fiscal policy is expansionary when a budget
Perfect com petition: Many firms with no pricing
business—assets, operations, investing, financing
deficit is increasing or surplus is decreasing, and
power; very low or no barriers to entry;
activities—must be physically/operationally distinct
contractionary when a budget deficit is decreasing
homogeneous product.
from rest of firm. Income/losses are reported net of
or surplus is increasing.
M onopolistic com petition: Many firms; some
tax after net income from continuing operations.
pricing power; low barriers to entry; differentiated Balance of Payments
Compute Cash Flows From Operations (CFO)
products; large advertising expense. Current account: merchandise and services; income
D irect method: start with cash collections (cash
Oligopoly: Few firms that may have significant receipts; unilateral transfers.
equivalent of sales); cash inputs (cash equivalent of
pricing power; high barriers to entry; products may Capital account: capital transfers; sales/purchases of
be homogeneous or differentiated. nonfinancial assets.
continued on next page...
FINANCIAL STATEMENT ANALYSIS continued-
Basic and Diluted EPS
_ . operating profit EBIT
operating profit margin = ---------- -------- —
cost of goods sold); cash operating expenses; cash Basic EPS calculation does not consider effects of
revenue net sales
interest expense; cash taxes. any dilutive securities in computation of EPS:
net income
Indirect method: start with net income, subtracting
net income — preferred dividends
net profit margin =
basic EPS =
back gains and adding back losses resulting from
revenue
wtd. avg. no. of common shs. outstanding
financing or investment cash flows, adding back all
Return on assets [return on total capital (ROTC)]:
, , , „ adj. income avail, for common shares
noncash charges, and adding and subtracting asset
diluted EPS = ---- ------------------------------------------—
return on assets _ EBIT
and liability accounts that result from operations.
wtd. avg. common shares plus potential
(total capital) average total capital
common shares outstanding
Free Cash Flow
Debt to equity ratio and total debt ratio:
Free cash flo w (FCF) measures cash available for
Therefore, diluted EPS is:
discretionary purposes. It is equal to operating cash
total debt
debt-to-equity ratio = convertible convertible
flow less net capital expenditures.
net _ pfd
total equity
+ preferred + debt 0 - t )
income div
Critical Ratios
dividends interest
total debt
Common-size fin a n cia l statem ent analysis:
total-debt-ratio = wtd shares from sh ’ s from shares
• Common-size balance sheet expresses all balance total assets
avg + conversion of + conversion + issuable from
sheet accounts as a percentage of total assets. sh’s conv. pfd. sh’s conv. debt stock options
Interest coverage and fix ed charge coverage: V /
• Common-size incom e statem ent expresses all
EBIT Long-Lived Assets Capitalizing vs. Expensing
income statement items as a percentage of sales.
interest coverage = 7
Capitalizing: lowers income variability and
interest
• Common-size cash flow statement expresses each
increases near-term profits. Increase assets, equity.
line item as a percentage of total cash inflows EBIT + lease payments
fixed charge coverage = 7 Expensing: opposite effect.
(outflows), or as a percentage of net revenue.
interest + lease payments
Depreciation
Horizontal com m on-size fin an cial statem ent analysis:
Growth rate (g): g = RR x ROE
expresses each line item relative to its value in a
cost — residual value
Straight-line: ---------------------------
common base period.
dividends declared
useful life
retention rate = 1 —
Liquidity ratios:
operating income after taxes
D ouble declining balance:
current assets
\
/ ^
current ratio = ---------- 7— 7-7-7—
Liquidity ratios indicate company’s ability to pay its
current liabilities
(cost —accum. depreciation)
short-term liabilities.
useful life /
cash + marketable securities + receivables V
quick ratio — Operating perform ance ratios indicate how well
current liabilities Units o f production:
management operates the business.
cash + marketable securities cost — salvage value
DuPont Analysis
cash ratio = output units
X
current liabilities Traditional DuPont equation: useful life in units
cash + mkt. sec. + receivables
Revaluation of Long-Lived Assets
net income sales assets
defensive interval =
return on equity =
daily cash expenditures IFRS: revaluation gain recognized in net income
„ sales , assets,
, equity,
only to the extent it reverses previously recognized
Receivables, inventory, payables turnover, and days
impairment loss; further gains recognized in equity
You may also see it presented as:
supply ratios—all o f which are used in the cash
as revaluation surplus. (For investm ent property,
conversion cycle: net profit asset equity
return on equity = all gains and losses from marking to fair value are
annual sales margin turnover multiplier
receivables turnover = recognized as income.)
average receivables
Extended DuPont equation further decomposes net U.S. GAAP: revaluation is not permitted.
profit margin:
cost of goods sold
Deferred Taxes
inventory turnover =
• Created when taxable income (on tax return) ^
average inventory
net income EBT' ' EBIT '
ROE = v v pretax income (on financial statements) due to
A A
EBT EBIT, revenue
purchases
/
V, temporary differences.
payables turnover ratio =
revenue avg. total assets
average trade payables
• D eferred tax liabilities are created when taxable
x
v
A
avg. total assets} avg. equity
income < pretax income. Treat DTL as equity if
365
days of sales outstanding = not expected to reverse.
receivables turnover You may also see it presented as:
• D eferred tax assets are created when taxable income
ROE = tax burden x interest burden x
> pretax income. Must recognize valuation
365
days of inventory on hand = 7 EBIT margin x asset turnover x leverage
allowance if more likely than not that DTA will
inventory turnover
Marketable Security Classifications
not be realized.
_______ 365_______ H eld-for-trading: fair value on balance sheet;
Long-Term Liabilities
number of days of payables =
dividends, interest, realized and unrealized G/L
payables turnover ratio
• Premium bond: coupon rate > market rate at
recognized on income statement.
issuance.
days of inventory
Available-for-sale: fair value on balance sheet;
cash conversion cycle = • Discount bond: coupon rate < market rate at issuance.
on hand
dividends, interest, realized G/L recognized
• Interest expense equals book value at the beginning
on income statement; unrealized G/L is other
days of sales number of days
of the year multiplied by the market rate of interest
+
comprehensive income.
outstanding of payables
at the time the bonds were issued.
H eld-to-maturity: amortized cost on balance
Leases
Total asset, fixed-asset, and working capital turnover
sheet; interest, realized G/L recognized on income
Lessee reporting: Under IFRS, lessee recognizes asset
ratios:
statement.
and liability equal to PV of lease payments. Interest
revenue
Inventory Accounting
total asset turnover =
portion of each payment is interest expense,
average total assets
In periods of rising prices and stable or increasing
principal portion decreases liability.
inventory quantities:
revenue U.S. GAAP is same except that for an operating
fixed asset turnover =
LIFO results in: FIFO results in: lease, entire lease payment is an expense.
average fixed assets
Higher COGS Lower COGS
Lessor reporting, fin a n ce lease: Remove asset from
revenue Lower gross profit Higher gross profit
balance sheet, recognize lease receivable asset,
working capital turnover =
Lower inventory Higher inventory
average working capital report interest income.
balances balances
Lessor reporting, operating lease: Keep asset on
Gross, operating, and net profit margins:
balance sheet, report lease payments as income,
gross profit record depreciation expense.
r .
gross profit margin = ------------
—
revenue
continued on next page...
r
PORTFOLIO MANAGEMENT
FINANCIAL STATEMENT ANALYSIS continued
• ••
L.
Pensions
Investment Policy Statement
D efined contribution: employer contribution
Investm ent objectives:
expensed in period incurred.
• Return objectives.
D efined benefit: overfunded plan recognized as
• Risk tolerance.
asset, underfunded plan recognized as liability.
Constraints:
• Liquidity needs.
• Time horizon.
CORPORATE ISSUERS
• Tax concerns.
• Legal and regulatory factors.
Weighted Average Cost of Capital
• Unique circumstances.
WACC = (wd) [kd (1—t)] + (wps) (kps) + (wce )(ks)
Combining Preferences with the Optimal Set of
Risk-Adjusted Returns
Cost of Preferred Stock
Portfolios
Sharpe ratio and M -squared measure excess return
Markowitz efficient frontier is the set of portfolios
per unit of total risk.
that have highest return for given level of risk.
Treynor measure and Jensens alpha measure excess
Cost of Equity Using CAPM
return per unit of systematic risk.
ke = RFR + /3(Rmkl — RFR)
E(R)
Capital Allocation
CF, CR CF
n
NPV = CF0 + + + ... +
( i+ k )1 a + k ) (l + k)n
IRR: discount rate that makes NPV equal to zero.
Nonpublic/Thinly Traded Stock Beta
Delevered asset beta for comparable company:
Security Market Line (SML)
0 = 0
■
f asset ^ equity
Investors should only be compensated for risk
relative to market. Unsystematic risk is diversified
away; investors are compensated for systematic risk.
Relevered beta for target company:
The equation of the SML is the CAPM, which is a
D
3 target 3,---* y^ H I l( -i -tt l) return/systematic risk equilibrium relationship.
target asset
^
/
total risk = systematic + unsystematic risk Behavioral Biases
Adjusted beta = 2/3 x unadjusted beta +1/3
C ognitive errors, b elie f perseverance: Conservatism,
E(R)
Measures of Leverage
confirmation, representativeness, control,
Total leverage: percent change in net income hindsight
from a given percent change in sales.
Cognitive errors, inform ation processing: Anchoring
Operating leverage: percent change in EBIT from
and adjustment, mental accounting, framing,
a given percent change in sales. availability
Financial leverage: percent change in net income
E motional biases: Loss aversion, overconfidence,
from a given percent change in EBIT.
self-control, status quo, endowment, regret
aversion
breakeven quantity of sales =
T echnical Analysis
fixed operating & financing costs
Reversal patterns: head and shoulders, inverse H&S,
price — variable costs per unit
double/triple top or bottom.
Continuation patterns: triangles, rectangles,
operating breakeven quantity of sales =
pennants, flags.
Price-based indicators: moving averages, Bollinger
fixed operating costs
E(Ri)
bands, momentum oscillators (rate of change, RSI,
price — variable costs per unit
stochastic, MACD).
Corporate Governance Sentiment indicators: put/call ratio, VIX, margin debt.
Stakeholder groups: Shareholders, board of
directors, senior managers, employees, creditors,
^SECURITIES MARKETS
suppliers.
Board committees: Audit, governance,
& EQUITY INVESTMENTS
nominations, compensation, risk, investment.
ESG in Investment Analysis
Well-Functioning Security Markets
N egative screening: Exclude companies with poor
• Operational efficiency (lowest possible
ESG records.
transactions costs).
Positive screening: Invest in companies with good
• Informational efficiency (prices rapidly adjust to
ESG records.
new information).
The SML and Equilibrium
Thematic investing: Invest to promote a specific
Identifying mispriced stocks: Margin Purchases
ESG goal.
Consider three stocks (A, B, C) and SML. For margin transactions:
Active ownership: Use share voting, access to
Estimated stock returns should plot on SML. • Leverage factor = 1/margin percentage.
managers to promote ESG goals.
• A return plot over the line is underpriced. • Levered return = HPR x leverage factor.
• A return plot under the line is overpriced..
Margin Call Price
P0(l — initial margin %)
1 — maintenance margin %
continued on next page...
SECURITIES MARKETS & EQUITY INVESTMENTS continued... Critical relationship between k and g\
full price = PV at last coupon date x (1 + YTM)t/T
• As difference between k and g widens, value of accrued interest = coupon payment x (t/T)
Computing Index Prices
stock falls. where:
stock prices
• As difference narrows, value of stock rises.
t = days from most recent coupon payment to
Price-weighted Index =
adjusted divisor • Small changes in difference between k and g trade settlement
cause large changes in stock’s value. T = days in coupon payment period
Value-weighted Index
Critical assumptions of infinite period DDM:
Matrix pricing: For illiquid bonds, use yields of bonds
XXcurrent prices) (# shares)
• Stock pays dividends; constant growth rate. with same credit quality to estimate yield; adjust for
x base value
XXbase year prices) (# base year shares) • Constant growth rate, g , never changes. maturity differences with linear interpolation.
• ke must be greater than g (or math will not work).
Bond Markets
Typ es of Orders
Earnings Multiplier Model National bond market includes domestic bonds and
Execution instructions: how to trade; e.g., market
v
foreign bonds.
orders, limit orders.
P0 Ej payout ratio
• Domestic bonds. Domestic issuer and currency.
Validity instructions: when to execute; e.g., stop
Ei k - g k - g • Foreign bonds. Foreign issuer, domestic currency.
orders, day orders, fill-or-kill orders.
Eurobond market is outside any one country, with
Clearing instructions: how to clear and settle; for sell
Price Multiples bonds denominated in currencies other than those
orders, specify short sale or sale of owned security.
price per share of countries in which bonds are sold.
leading P/E =
Market Structures
Global bonds trade in both a national bond market
forecast EPS next 12 mo.
Q uote-driven markets: investors trade with dealers.
and the eurobond market.
Order-driven markets: buyers and sellers matched price per share
trailing P/E = Bond Issuance
by rules.
EPS previous 12 mo.
Underwritten offering: Investment banks buy entire
Brokered markets: brokers find counterparties.
issue, sell to public.
price per share
Forms of EMH
P/B =
Best efforts offering: Investment banks act as brokers.
book value per share
• Weak form . Current stock prices fu lly reflect
S h elf registration: Register entire issue with
available security market info. Volume
regulators but sell over a period of time.
price per share
information/past price do not relate to future P/S =
Embedded Options
sales per share
direction of security prices. Investor cannot
Callable: Issuer may repay principal early. Increases
achieve excess returns using tech analysis.
price per share
yield and decreases duration.
P/CF =
• Semi-strong form . Security prices instantly adjust
cash flow per share Putable: Bondholder may sell bond back to issuer.
to new p u b lic information. Investor cannot achieve
Decreases yield and duration.
excess returns using fundamental analysis.
Convertible: Bondholder may exchange bond for
• Strong form . Stock prices fu lly reflect all information
FIXED INCOME issuer’s common stock.
from public and private sources. Assumes perfect
Embedded warrants: Bondholder may buy issuer’s
markets in which all information is cost free and
Basic Features of Bonds common stock at exercise price.
available to everyone at the same time. Even with
Issuer. Household, nonfinancial corporations,
Yield Measures
inside info, investor cannot achieve excess returns.
governments, financial institutions.
Effective y ield depends on periodicity. YTM =
Maturity. Money market (one year or less); capital
effective yield for annual-pay bonds.
EQUITY INVESTMENTS market (greater than one year).
Semiannual bond basis: YTM = 2 x semiannual
Par value. Bond’s principal value (face value).
discount rate.
Industry Life Cycle Stages Coupon. Annual percent of par; fixed or floating.
Current y ield = annual coupon / price.
Embryonic: slow growth, high prices, large Divide by periodicity to get periodic rate.
Simple y ield = current yield ± amortization.
Currency. Single, dual, currency option.
investment needed, high risk of failure.
Yield to call is based on call date and call price.
Growth: rapid growth, falling prices, limited Indenture. Affirmative and negative covenants.
Yield to worst is lowest of a bond’s YTCs or YTM.
competition, increasing profitability.
Price, Yield, Coupon Relationships M oney market yields may be on a discount or add­
Shakeout: slower growth, intense competition,
Bond prices and yields are inversely related. on basis and may use a 360- or 365-day year.
declining profitability, cost cutting, weaker firms
Increase in yield decreases price; decrease in yield B ond-equivalent y ield is an annualized add-on yield
fail or merge.
increases price. based on a 365-day year.
M ature: slow growth, consolidation, stable prices,
Coupon < yield: Discount to par value.
Forward and Spot Rates
high barriers to entry.
Coupon > yield: Premium to par value.
Forward rate is a rate for a loan that begins at a
D ecline: negative growth, declining prices,
Constant-yield p rice trajectory: Price approaches
future date. “Iy3y” = 3-year forward rate 1 year
consolidation.
par as bond nears maturity from amortization of
from today.
Five Competitive Forces discounts and premiums. Capital gains and losses
Example of spot-forward relationship:
are calculated relative to this trajectory.
1. Rivalry among existing competitors.
(1 + S2)2 = (1 + Sj)(l + lyly)
2. Threat of entry.
Cash Flow Structures
Yield Spreads
3. Threat of substitutes.
Bullet: All principal repaid at maturity.
G-spread: Basis points above government yield.
4. Power of buyers.
Fully amortizing: Equal periodic payments include
I-spread: Basis points above swap rate.
5. Power of suppliers.
both interest and principal.
Z-spread: Accounts for shape of yield curve.
One-Period Valuation Model Partially amortizing: Periodic payments include
Option-adjusted spread: Adjusts Z-spread for effects
interest and principal, balloon payment at maturity
of embedded options.
Di Pi
V0 = +
repays remaining principal.
(1 + k .) (l + k„) Interest Rate Risk
Sinking fu n d : Schedule for early redemption.
Interest rate risk has two components: reinvestment risk
Be sure to use expected dividend in calculation.
Floating-rate: Coupon payments based on reference
and market price risk from YTM changes. These risks
rate plus margin.
Infinite Period Dividend Discount Models
have opposing effects on an investor’s horizon yield.
Supernormal grow th m odel (multi-stage) DDM:
Bond Pricing
• Bond investors with short horizons are more
There are two equivalent ways to price a bond:
D
D concerned with market price risk.
n n
V0 = + + + • Constant discount rate applied to all cash flows
• Bond investors with long horizons are more
(1 + k.) (1 + k J" (1 + k.)"
(YTM) to find PV. This is a bond’s fla t p rice (does
concerned with reinvestment risk.
D
not include accrued interest).
n+1
where: Pn = • The horizon at which market price risk and
• Discount each cash flow using appropriate spot
(ke - g c )
reinvestment risk just offset is a bond’s M acaulay
rate for each. This is a bond’s no-arbitrage price.
duration. This is the weighted average of times
Constant grow th model:
Full p rice includes accrued interest. Government
until a bond’s cash flows are scheduled to be paid.
D,
V - Do(! + gc) _ bonds use actual day counts; corporate bonds use
vo — —
30/360 method.
k e - gc
k e - Sc
continued on next page...
ALTERNATIVE INVESTMENTS
Forward Contract Value
FIXED INCOME continued...
At time tr.
M odified duration is the approximate change in a
Hedge Funds
V (T) = [S + PV (costs) - PV (benefits)]
bonds price given a 1% change in its YTM:
Event-driven strategies: merger arbitrage; distressed/
- CF0(T )a + Rf)-(T-t)I
restructuring; activist shareholder; special
Futures vs. Forwards
Macaulay duration ( V_) — (V+ )
situations.
Futures are standardized, exchange-traded forward
~~ 0 + 0 2V0(Ay)
Relative value strategies: convertible arbitrage;
contracts that require daily cash settlement of
asset-backed fixed income; general fixed income;
mark-to-market gains and losses.
Effective duration is required if a bond has
volatility; multi-strategy.
Forward Rate Agreements (FRA)
embedded options:
Equity strategies: market neutral; fundamental
Can be viewed as a forward contract to borrow/
growth; fundamental value; quantitative
( V - ) - ( y +) lend money at a certain rate at some future date.
directional; short bias.
2Vq (Acurve) Interest Rate Swaps M acro strategies: based on global economic trends.
May be replicated by a series of FRAs with present
Hedge fund fees:
Price change estimates based on duration only are
values at swap initiation that sum to zero.
• “2 and 20”: 2% management fee plus 20%
improved by adjusting for convexity:
Options incentive fee.
1
%Aprice = —duration (Ay) H— convexity (Ay) • Buyer of a call option—long asset exposure. • Hard hurdle rate: incentive fee only on return
• Writer (seller) of a call option—short asset above hurdle rate.
• Soft hurdle rate: incentive fee on whole return,
exposure.
Asset-Backed Securities
• Buyer of a put option—short asset exposure. but only paid if return is greater than hurdle rate.
Residential MBS', home mortgages are collateral.
• Writer (seller) of a put option—long asset • High water mark: no incentive fee until value
Agency RMBS include only conforming loans;
exceeds previous high.
exposure.
nonagencv RMBS may include nonconforming
intrinsic value of a call option = Max[0, S — X]
loans and need credit enhancement. Private Capital
intrinsic value of a put option = Max[0, X — S]
Prepayment risk: contraction risk from faster Leveraged buyouts: management buyouts (existing
prepayments; extension risk from slower
American vs. European Options managers), management buy-ins (new managers)
prepayments. American options allow the owner to exercise the Venture capital stages of development:
CMOs: pass-through MBS are collateral. May have option any time before or at expiration. European • Formative stage: angel investing, seed stage, early
sequential-pay or PAC/support structure. options can be exercised only at expiration. stage.
Commercial MBS: non-recourse mortgages on • Later stage: expand production, increase sales.
Factors that Affect Option Values
commercial properties are collateral. • Mezzanine stage: prepare for IPO.
Increase in: Calls Puts
Auto ABS: auto loans are collateral. Exit strategies: trade sale; IPO; recapitalization;
Credit card ABS: credit card receivables are Asset price Increase Decrease secondary sale; write-off.
collateral.
Real Estate
Exercise price Decrease Increase
CDOs: Bonds, bank loans, MBS, ABS, or other
Includes residential property; commercial property;
Risk-free rate Increase Decrease
CDOs are collateral.
real estate investment trusts (REITs); whole loans;
Collateral and Credit Enhancement Volatility Increase Increase construction loans.
Secured bonds are backed by specific collateral and
Commodities
Time to Increase Increase*
senior to unsecured bonds.
expiration Contango: futures price > spot price.
Unsecured bonds are general claims to issuer’s cash
Backwardation: futures price < spot price.
Holding costs Increase Decrease
flows and assets.
futures price « spot price(l + Rf) + storage costs
Internal credit enhancem ent: Excess spread,
Holding Decrease Increase
- convenience yield
overcollateralization, waterfall structure.
benefits
Infrastructure
External credit enhancem ent: Surety bonds, letters of
* Except some deep-in-the-money European puts.
Long-lived assets for public use, including
credit, bank guarantees.
Put-Call Parity transportation, utility, communications, social.
Credit Analysis
The put-call parity relationship for European Brownfield: Existing infrastructure.
Investm ent grade: Baa3/BBB- or above
options at time P. Greenfield: Infrastructure to be built.
N on-investment grade: Bal/BB+ or below
c + X(1 + Rf) T = S + p
Corporate family rating (CFR): issuer rating.
Each security in the put-call parity relationship can
Corporate credit rating (CCR): security rating.
be expressed as:
“Four Cs”: capacity, collateral, covenants, character,
S = c - p + X(1 + RfVT
default risk = probability of default
p = c - S + X(1 + RfVT
loss severity = percent of value lost if borrower
c = S + p - X(1 + RfVT
defaults
X(1 + Rf)"T = S + p - c
expected loss = default risk x loss severity
Put-Call Forward Parity
recovery rate = 1 — expected loss percentage
The present value of the forward price of the
underlying asset, F0(T)(1 + Rf)~T, can be
DERIVATIVES substituted for S in any of the put-call parity
relationships at time 0.
Arbitrage and Replication
• Law o f one price-, two assets with identical cash
flows in the future, regardless of future events,
should have the same price.
• Two assets with uncertain returns can be combined
in a portfolio that will have a certain payoff. If a
portfolio has a certain payoff, the portfolio should
ISBN: 978-1-0788-2583-2
yield the risk-free rate. For this reason, derivatives
values are based on risk-neutral pricing.
Derivatives Values vs. Prices
The price of a forward, futures, or swap contract
is the forward price stated in the contract and is
9 7 8 1 0 7 8 8 2 5 8 3 2
set such that the contract has a value of zero at
initiation. Value may change during the contract’s
life with opposite gains/losses to the long and short.
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