CFA 2018 level 2 schweser s quicksheet
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L E V E L II SC H W ESER'
C r it ic a l C o n c e pt s
ETHICAL AND PROFESSIONAL
STANDARDS
I
Professionalism
I (A) Knowledge of the Law
I (B) Independence and Objectivity
I (C )
I (D)
II
II (A)
II (B)
III
HI (A)
HI (B)
HI (C)
HI (D)
HI (E)
IV
IV (A)
IV (B)
IV (C)
V
v (A)
V (B)
V (C)
VI
VI (A)
VI (B)
VI (C)
VII
VII (A)
VII (B)
Misrepresentation
Misconduct
Integrity o f Capital Markets
Material Nonpublic Information
Market Manipulation
Duties to Clients
Loyalty, Prudence, and Care
Fair Dealing
Suitability
Performance Presentation
Preservation of Confidentiality
Duties to Employers
Loyalty
Additional Compensation Arrangements
Responsibilities o f Supervisors
Investment Analysis, Recommendations,
and Action
Diligence and Reasonable Basis
Communication with Clients and
Prospective Clients
Record Retention
Conflicts o f Interest
Disclosure o f Conflicts
Priority of Transactions
Referral Fees
Responsibilities as a CFA Institute
Member or CFA Candidate
Conduct in the CFA Program
Reference to CFA Institute, CFA
Designation, and CFA Program
QUANTITATIVE METHODS
Simple Linear Regression
Correlation:
covXY
rXY =
( s x )( s y )
t-test for r (n - 2 d f): t =
rVn —2
Estimated slope coefficient:
cov xy
Estimated intercept: b0 = Y —bjX
Confidence interval for predicted Y-value:
A
Y ± tc x SE of forecast
M ultiple Regression
Yi = b0 + ( b 1x X li) + (b2 x X 2l)
+ (b3 X X 3i) + £;
• Test statistical significance o f b; H (): b = 0,
A
t= y
Regression Analysis— Problem s
• Heteroskedasticity. Non-constant error variance.
Detect with Breusch-Pagan test. Correct with
White-corrected standard errors.
• Autocorrelation. Correlation among error
terms. Detect with Durbin-Watson test; positive
autocorrelation if D W < d(. Correct by adjusting
standard errors using Hansen method.
• Multicollinearity. High correlation among Xs.
Detect if F-test significant, t-tests insignificant.
Correct by dropping X variables.
• Omitting a variable.
• Variable should be transformed.
• Incorrectly pooling data.
• Using lagged dependent vbl. as independent vbl.
• Forecasting the past.
Confidence Interval: bj ± |tc X sg
SST = RSS + SSE.
M SR = RSS / k.
M SE = SSE / ( n - k - 1).
Test statistical significance o f regression:
F = M SR / M SE with k and n —k — 1 df (1-tail)
ECONOMICS
bid-ask spread = ask quote - bid quote
Cross rates with bid-ask spreads:
n>
.B
'A '
'A '
X
vC, bid
B , bid
'A '
/A X
vC, offer
\ B , offer
VC
^ /bid
/ T-x \
B
X
\C
^ /offer
Currency arbitrage: “Up the bid and down the ask.”
Forward premium = (forward price) - (spot price)
Value o f fwd currency contract prior to expiration:
Vt =
(FPt — FP)(contract size)
\
days
1+ R A
360
Covered interest rate parity:
Uncovered interest rate parity:
e
• Measuring independent variables with error.
Effects o f M isspecification
Regression coefficients are biased and inconsistent,
lack o f confidence in hypothesis tests o f the
coefficients or in the model predictions.
Linear trend model: yt = b0 + b,t + £t
Log-linear trend model: ln(yt ) = b0 + b,t + £t
Covariance stationary: mean and variance don’t
change over time. To determine if a time series is
covariance stationary, (1) plot data, (2) run an AR
model and test correlations, and/or (3) perform
Dickey Fuller test.
Unit root: coefficient on lagged dep. vbl. = 1. Series
with unit root is not covariance stationary. First
differencing will often eliminate the unit root.
Autoregressive (AR) model: specified correctly if
autocorrelation o f residuals not significant.
Mean reverting level for A R(1):
bo
(1 — b j)
RM SE: square root o f average squared error.
Random W alk T im e Series:
xt = xt-i + £t
Seasonality: indicated by statistically significant
lagged err. term. Correct by adding lagged term.
ARCH: detected by estimating:
= ao + ai^t-i + Bt
Variance o f ARCH series:
A
E xa m
days
1+ R a
•0
360 /
F = ^ -------days
1+ R B
360
M odel M isspecification
A2
Reject if |t| > critical t or p-value < a .
C FA®
Standard error of estimate (SEE = VM SE ).
Smaller SEE means better fit.
• Coefficient of determination (R2 = RSS / SST).
% of variability of Y explained by Xs; higher R2
means better fit.
/
, n —k —1 df
2018
fo r t h e
(% a s w , = R , - K
Fisher relation:
R nominal = R real. + E(inflation)
International Fisher Relation:
R nominal
. A —R nominal
. B = E(inflation.)
v
A'
E(inflationB)
Relative Purchasing Power Parity: High inflation
rates leads to currency depreciation.
%AS(A/B) = inflation Xj - inflation,B)
where: % AS(A/B) = change in spot price (A/B)
Profit on FX Carry Trade = interest differential change in the spot rate of investment currency.
Mundell-Fleming model: Impact o f monetary
and fiscal policies on interest rates & exchange
rates. Under high capital mobility, expansionary
monetary policy/restrictive fiscal policy —>low
interest rates —> currency depreciation. Under low
capital mobility, expansionary monetary policy/
expansionary fiscal policy —> current account
deficits —» currency depreciation.
Dornbusch overshooting model: Restrictive
monetary policy —» short-term appreciation of
currency, then slow depreciation to PPP value.
Labor Productivity:
output per worker Y/L = T(K/L)‘'
Growth Accounting:
growth rate in potential GDP
= long-term growth rate of technology
+ a (long-term growth rate o f capital)
+ (1 - a) (long-term growth rate of labor)
growth rate in potential GDP
= long-term growth rate of labor force
+ long-term growth rate in labor productivity
Classical Growth T heory
• Real GDP/person reverts to subsistence level.
A A2
CTt+l = a0 + al£t
Risk Types:
Appropriate
m ethod
Distribution
o f risk
Sequential?
Accommodates
Correlated Variables'
Simulations
Continuous
Does not
matter
Yes
Scenario
analysis
Discrete
No
Yes
Decision trees
Discrete
Yes
No
Neoclassical Growth T heory
• Sustainable growth rate is a function of
population growth, labor’s share o f income, and
the rate of technological advancement.
• Growth rate in labor productivity driven only by
improvement in technology.
Assumes diminishing returns to capital.
g* =
0
(1-a)
G* =
0
(1-a)
+ AL
Endogenous Growth Theory
• Investment in capital can have constant returns.
• | in savings rate —> permanent T in growth rate.
• R & D expenditures ] technological progress.
Classifications o f Regulations
• Statutes: Laws made by legislative bodies.
• A dm inistrative regulations: Issued by government.
• Ju d icia l law : Findings o f the court.
Classifications o f Regulators
• Can be government agencies or independent.
• Independent regulator can be SRO or non-SRO.
Self-Regulation in Financial Markets
• Independent SROs are more prevalent in
common-law countries than in civil-law countries.
Econom ic Rationale for Regulatory Intervention
• Inform ationalfriction s arise in the presence o f
information asymmetry.
• Externalities deal with provision o f public goods.
Regulatory Interdependencies and T heir Effects
Regulatory capture theory: Regulatory body is
influenced or controlled by industry being regulated.
Regulatory arbitrage: Exploiting regulatory differences
between jurisdictions, or difference between
substance and interpretation o f a regulation.
Tools o f Regulatory Intervention
• Price mechanisms, restricting or requiring certain
activities, and provision o f public goods or
financing o f private projects.
Regulations Covering Com m erce
• Company law, tax law, contract law, competition
law, banking law, bankruptcy law, and dispute
resolution system.
F in an cial m arket regulations: Seek to protect
investors and to ensure stability o f financial system.
Securities m arket regulations: Include disclosure
requirements, regulations to mitigate agency
conflicts, and regulations to protect small investors.
P rudential supervision: Monitoring institutions to
reduce system-wide risks and protect investors.
Anticompetitive Behaviors and Antitrust Laws
• Discriminatory pricing, bundling, exclusive dealing.
• Mergers leading to excessive market share blocked.
N et regulatory burden: Costs to the regulated
entities minus the private benefits o f regulation.
Sunset clauses: Require a cost-benefit analysis to be
revisited before the regulation is renewed.
FINANCIAL STATEMENT ANALYSIS
Accounting for Intercorporate Investments
Investment in Financial Assets: <20% owned, no
significant influence.
• Held-to-maturity at cost on balance sheet; interest
and realized gain/loss on income statement.
• Available-for-sale at FM V with unrealized gains/
losses in equity on B/S; dividends, interest,
realized gains/losses on I/S.
• Held-for-trading at FMV; dividends, interest,
realized and unrealized gains/losses on I/S.
• Designated as fair value —like held for trading.
Investments in Associates: 20—50% owned,
significant influence. With equity method, prorata share o f the investee’s earnings incr. B/S inv.
acct., also in I/S. Div. received decrease investment
account (div. not in I/S).
Business Combinations: >50% owned, control.
Acquisition method required under U.S. GAAP
and IFRS. Goodwill not amortized, subject to
annual impairment test. All assets, liabilities,
revenue, and expenses o f subsidiary are combined
with parent, excluding intercomp, trans. If <100%,
minority interest acct. for share not owned.
Joint Venture: 50% shared control. Equity method.
Financial Effect o f Choice o f M ethod
Equity, acquisition, & proportionate consolidation:
• All three methods report same net income.
• Assets, liabilities, equity, revenues, and expenses
are higher under acquisition compared to the
equity method.
Differences between IFRS and U .S. GAAP
treatm ent o f intercorporate investments include:
• Unrealized FX gains and losses on available-for-sale
debt securities recognized on income statement
under IFRS and as O CI under U.S. GAAP.
• IFRS permits either the “partial goodwill” or
“full goodwill” methods to value goodwill and
noncontrolling interest. U.S. GAAP requires the
full goodwill method.
Pension Accounting
• PBO components: current service cost, interest
cost, actuarial gains/losses, benefits paid.
Balance Sheet
• Funded status = plan assets —PBO = balance sheet
asset (liability) under GAAP and IFRS.
Income Statement
• Total periodic pension cost (under both IFRS and
GAAP) = contributions —A funded status.
• IFRS and GAAP differ on where the total
periodic pension cost (TPPC) is reflected (Income
statement vs. O CI).
• Under GAAP, periodic pension cost in P&L
= service cost + interest cost ± amortization o f
actuarial (gains) and losses + amortization o f past
service cost —expected return on plan assets.
• Under IFRS, reported pension expense = service
cost + past service cost + net interest expense.
• Under IFRS, discount rate = expected rate o f return
on plan assets. Net interest expense = discount rate
x beginning funded status. If funded status was
positive, a net interest income would be recognized.
Total Periodic Pension C ost
TPPC = ending PBO —beginning PBO + benefits
paid - actual return on plan assets
TPPC = contributions —(ending funded status beginning funded status)
Cash Flow Adjustment
If TPPC < firm contribution, difference = A in
PBO (reclassify difference from CFF to CFO aftertax). If TPPC > firm contribution, diff = borrowing
(reclassify difference from CFO to CFF after-tax).
M ultinational Operations: Choice o f M ethod
For self-contained sub, functional ^ presentation
currency; use current rate method:
• Assets/liabilities at current rate.
• Common stock at historical rate.
• Income statement at average rate.
• Exposure = shareholders’ equity.
• Dividends at rate when paid.
For integrated sub., functional = presentation
currency, use temporal method:
• Monetary assets/liabilities at current rate.
• Nonmonetary assets/liabilities at historical rate.
• Sales, SGA at average rate.
• CO G S, depreciation at historical rate.
• Exposure = monetary assets - monetary liabilities.
Net asset position & depr. foreign currency = loss.
Net liab. position & depr. foreign currency = gain.
Original F/S vs. All-Current
• Pure BS and IS ratios unchanged.
• If LC depreciating (appreciating), translated
mixed ratios will be larger (smaller).
Hyperinflation: GAAP vs. IFRS
Hyperinfl. = cumul. infl. > 100% over 3 yrs. GAAP:
use temporal method. IFRS: 1st, restate foreign
curr. st. for infl. 2nd, translate with current rates.
Net purch. power gain/loss reported in income.
Beneish model: Used to detect earnings
manipulation based on eight variables.
High-quality earnings are:
1. Sustainable: Expected to recur in future.
2. Adequate: Cover company’s cost o f capital.
IFRS A N D U .S. GAAP D IFFER E N C ES
Reclassification of passive investments:
IFRS —Restricts reclassification into/out o f FVPL.
U.S. GAAP —No such restriction.
Impairment losses on passive investments:
IFRS —Reversal allowed if due to specific event.
U.S. GAAP —No reversal o f impairment losses.
Fair value accounting, investment in associates:
IFRS —Only for venture capital, mutual funds, etc.
U.S. GAAP —Fair value accounting allowed for all.
Goodwill impairment processes:
IFRS - 1 step (recoverable amount vs. carrying value)
U.S. GAAP — 2 steps (identify; measure amount)
Acquisition method contingent asset recognition:
IFRS —Contingent assets are not recognized.
U.S. GAAP —Recognized; recorded at fair value.
Prior service cost:
IFRS —Recognized as an expense in P&L.
U.S. GAAP - Reported in O CI; amortized to P&L.
Actuarial gains/losses:
IFRS —Remeasurements in O CI and not amortized.
U.S. GAAP —OCI, amortized with corridor approach.
Dividend/interest income and interest expense:
IFRS —Either operating or financing cash flows.
U.S. GAAP —Must classify as operating cash flow.
R O E decomposed (extended D uPont equation)
Tax
Interest EBIT
Burden Burden Margin
NI
EBT
E B IT
R O E = -------x ---------x ------------x
E B T E B IT revenue
Financial
Leverage
T otal Asset
T urnover
revenue
average assets
X
average assets
average equity
Accruals Ratio (balance sheet approach)
accruals ratio ^ =
(N OAEn d — N OABEg )
(N OA e n d + NOABEg ) /2
Accruals Ratio (cash flow statem ent approach)
accruals ratio ^ =
(NI - CFO - CFI)
(N OA e n d + N OABEg ) /2
CORPORATE FINANCE
Capital Budgeting Expansion
• Initial ouday = FCInv + WCInv
• CF = (S - C - D ) ( l - T ) + D = (S - C )(l - T ) + D T
• T N O C F = SaLr + NW CInv - T(Salr - B.r)
Capital Budgeting Replacement
• Same as expansion, except current after-tax salvage
o f old assets reduces initial outlay.
• Incremental depreciation is A in depreciation.
Evaluating Projects with Unequal Lives
• Least common multiple o f lives method.
• Equivalent annual annuity (EAA) method:
annuity w/ PV equal to PV o f project cash flows.
Effects o f Inflation
• Discount nominal (real) cash flows at nominal (real)
rate; unexpected changes in inflation affect project
profitability; reduces the real tax savings from
depreciation; decreases value of fixed payments to
bondholders; affects costs and revenues differently.
Capital Rationing
• If positive NPV projects > available capital,
choose the combination with the highest NPV.
Real Options
• Timing, abandonment, expansion, flexibility,
fundamental options.
Econom ic and Accounting Income
• Econ income = AT CF + A in project’s MV.
• Econ dep. based on A in investment’s MV.
• Econ income is calculated before interest expense
(cost o f capital is reflected in discount rate).
• Accounting income = revenues - expenses.
• Acc. dep’n based on original investment cost.
• Interest (financing costs) deducted before
calculating accounting income.
Valuation Models
• Economic profit = NO PAT - $WACC
• Market Value Added =
t= i (1 + W A C C ) r
• Residual income: = NI —equity charge;
discounted at required return on equity.
• Claims valuation separates CFs based on equity
claims (discounted at cost o f equity) and debt
holders (discounted at cost o f debt).
M M Prop I (No Taxes): capital structure irrelevant
(no taxes, transaction, or bankruptcy costs).
VV L= VVU
M M Prop II (No Taxes): increased use o f cheaper
debt increases cost o f equity, no change in WACC.
r e = < b + f O b - r d)
M M Proposition I (With Taxes): tax shield adds
value, value is maximized at 100% debt.
VL = Vu + ( t x d )
M M Proposition II (With Taxes): tax shield adds
value, WACC is minimized at 100% debt.
re = *0 + ^ 0 b - r d) ( ! - T c )
E
Investor Preference Theories
• M M ’s dividend irrelevance theory: In a no-tax/
no-fee world, dividend policy is irrelevant because
investors can create a homemade dividend.
• Dividend preference theory says investors prefer the
certainty o f current cash to future capital gains.
• Tax aversion theory: Investors are tax averse to
dividends; prefer companies buy back shares.
Effective Tax Rate on Dividends
D ouble taxation or split rate systems:
eff. rate = corp. rate + (1 - corp. rate)(indiv. rate)
Im putation system: effective tax rate is the
shareholder’s individual tax rate.
Signaling Effects o f Dividend Changes
In itiation : ambiguous signal.
Increase: positive signal.
D ecrease: negative signal unless management sees
many profitable investment opportunities.
Price change when stock goes ex-dividend:
A r = ° ( 1 - T° )
(1_
t
cg)
Target Payout Ratio Adjustment Model
If company earnings are expected to increase and
the current payout ratio is below the target payout
ratio, an investor can estimate future dividends
through the following formula:
expected dividend =
\
target
expected
adjustment
increase X payout x
factor
ratio /
in EPS /
\
previous
dividend +
Dividend Coverage Ratios
dividend coverage ratio = net income / dividends
FCFE coverage ratio
= FCFE / (dividends + share repurchases)
Share Repurchases
• Share repurchase is equivalent to cash dividend,
assuming equal tax treatment.
• Unexpected share repurchase is good news.
• Rationale for: (1) potential tax advantages, (2) share
price support/signaling, (3) added flexibility, (4)
offsetting dilution from employee stock options,
and (5) increasing financial leverage.
Dividend Policy Approaches
• Residual dividend: dividends based on earnings
less funds retained to finance capital budget.
• Longer-term residual dividend: forecast capital
budget, smooth dividend payout.
• Dividend stability: dividend growth aligned with
sustainable growth rate.
• Target payout ratio: long-term payout ratio target.
Stakeholder impact analysis (SIA): Forces firm to
identify the most critical groups.
Ethical Decision Making
Friedman Doctrine: Only responsibility is to
increase profits “within the rules o f the game. ”
Utilitarianism: Produce the highest good for the
largest number o f people.
Kantian ethics: People are more than just an
economic input and deserve dignity and respect.
Rights theories: Even if an action is legal, it may
violate fundamental rights and be unethical.
Justice theories: Focus on a just distribution o f
economic output (e.g., “veil o f ignorance”) .
Corporate Governance Objectives
• Mitigate conflicts o f interest between
(1) managers and shareholders, and (2) directors
and shareholders.
• Ensure assets used to benefit investors and
stakeholders.
Merger Types: horizontal, vertical, conglomerate.
Merger Motivations: achieve synergies, more
rapid growth, increased market power, gain access
to unique capabilities, diversify, personal benefits
for managers, tax benefits, unlock hidden value,
achieving international goals, and bootstrapping
earnings.
Pre-Offer Defense Mechanisms: poison pills
and puts, reincorporate in a state w/ restrictive
takeover laws, staggered board elections, restricted
voting rights, supermajority voting, fair price
amendments, and golden parachutes.
Post-Offer Defense Mechanisms: litigation,
greenmail, share repurch, leveraged recap, the
“crown jewel,” “Pac-Man,” and “just say no”
defenses, and white knight/white squire.
The Herfindahl-Hirschman Index (H H I):
market power = sum o f squared market shares for
all industry firms. In a moderately-concentrated
industry (HHI 1,000 to 1,800), a merger is likely
to be challenged if H H I increases 100 points (or
increases 50 points for H H I >1,800).
n
HHI = ^ ( M S i X l 0 0 ) 2
i= l
Methods to Determine Target Value
D C F m ethod: target proforma FCF discounted at
adjusted WACC.
C om parable company analysis-, target value from
relative valuation metrics on similar firms + takeover
premium.
C om parable transaction analysis: target value from
takeover transaction; takeover premium included.
M erger Valuations
C om binedfirm :
Y a t = Va + V t + S — C
Takeover prem ium (to target):
GainT = TP = PT — VT
Synergies (to acquirer):
GainA = S — TP = S — (PT — VT )
M erger Risk & Reward
Cash offer: acquirer assumes risk & receives reward.
Stock offer: some o f risks & rewards shift to target. If
higher confidence in synergies; acquirer prefers cash
& target prefers stock.
Forms of divestitures: equity carve-outs, spin-offs,
split-offs, and liquidations.
EQUITY
Holding period return:
= r = P l ~ p0 + c f i = p1 + c f l
Po
x
Po
Required return: Minimum expected return an
investor requires given an asset’s characteristics.
Internal rate of return (IRR): Equates discounted
cash flows to the current price.
Equity risk premium:
required return = risk-free rate + ((3 x ERP)
Gordon growth model equity risk premium:
= 1-yr forecasted dividend yield on market index
+ consensus long-term earnings growth rate
- long-term government bond yield
Ibbotson-Chen equity risk premium
[1 + i] x [1 + rEg] x [1 + PEg] - 1 + Y — RF
Models of required equity return:
• CAPM: r. = RF + (equity risk premium x 0.)
• M ultifiactor m odel: required return = RF + (risk
premium) j + ... + (risk premium) n
• Fam a-French: r.j = RF + 10 mkt,j
, . x (R
—RF)'
x mkt
+ ^ S M B .j X ^ "small _
P y g) + ^ H M L .j X
~~
Pastor-Stam baugh m odel: Adds a liquidity factor to
the Fama-French model.
• M acroeconom ic multifiactor models: Uses factors
associated with economic variables.
• Build-up m ethod: r = RF + equity risk premium +
size premium + specific-company premium
Blume adjustment:
adjusted beta = (2/3 x raw beta) + (1/3 x 1.0)
WACC = weighted average cost of capital
MV.equity
MVdebt
rd (l - T ) +
^ ^ d e b t+ equity
M V debt+ equity
Discount cash flows to firm at WACC, and cash
flows to equity at the required return on equity.
Discounted Cash Flow (D C F) Methods
Use dividend discount models (DDM ) when:
• Firm has dividend history.
• Dividend policy is related to earnings.
• Minority shareholder perspective.
Use free cash flow (FCF) models when:
• Firm lacks stable dividend policy.
• Dividend policy not related to earnings.
Justified P /E
• FCF is related to profitability.
• Controlling shareholder perspective.
Use residual income (RI) when:
• Firm lacks dividend history.
• Expected FCF is negative.
leading P/E =
r“ g
trailing P/E = ^ - b) ( 1 + g)
r-g
Gordon Growth Model (GGM )
Assumes perpetual dividend growth rate:
+ PVGO
2 -Stage Growth Model
Step 1: Calculate high-growth period dividends.
Step 2: Use G G M for terminal value at end of
high-growth period.
Step 3: Discount interim dividends and terminal
value to time zero to find stock value.
H-M odel
V0 =
D o x ( l + gL)] | [Dq x H x ( g s
r ~gL
Price o f a T-period zero-coupon bond:
Do _ r - g
Present Value o f Growth Opportunities
r
FIXED INCOME
Justified dividend yield:
V „ = -^
r-g
Most appropriate for mature, stable firms.
Limitations are:
• Very sensitive to estimates o f r and g.
• Difficult with non-dividend stocks.
• Difficult with unpredictable growth patterns (use
multi-stage model).
V0 =
Earlier, higher payments J, DLOM .
Restrictions on selling stock J DLOM .
A greater pool o f buyers J, DLOM .
Greater risk and value uncertainty | DLOM .
1 -b
gL )
r ~gL
Sustainable Growth Rate: b x ROE.
Solving for Required Return
For Gordon (or stable growth) model:
Di
r= ^ + g
Ao
Free Cash Flow to Firm (FC FF)
Assuming depreciation is the only N CC:
FCFF = NI + Dep + [Int x (1 —tax rate)] - FCInv
- WCInv.
FCFF = [EBIT x (1 —tax rate)] + Dep —FCInv
- WCInv.
FCFF = [EBITDA x (1 —tax rate)] + (Dep x tax
rate) —FCInv - WCInv.
FCFF = CFO + [Int x (1 —tax rate)] —FCInv.
Tee Cash Flow to Equity (FC FE)
FC FE = FCFF — [Int x (1 —tax rate)] + Net
borrowing.
FC FE = NI + Dep - FCInv - W CInv + Net
borrowing.
FC FE = NI - [(1 - DR) x (FCInv - Dep)]
- [(1 - DR) x WCInv]. ( Used to forecast.)
Single-Stage F C F F /F C F E Models
FCFF
• For FCFF valuation: V0 = ----------- -—
W ACC- g
FCFF
• For FCFE valuation: V0 = -------- r~g
2-Stage F C F F /F C F E Models
Step 1: Calculate FCF in high-growth period.
Step 2: Use single-stage FCF model for terminal
value at end o f high-growth period.
Step 3: Discount interim FCF and terminal value
to time zero to find stock value; use WACC
for FCFF, r for FCFE.
Price to Earnings (P /E ) Ratio
Problems with P/E:
• If earnings < 0, P/E meaningless.
• Volatile, transitory portion o f earnings makes
interpretation difficult.
• Management discretion over accounting choices
affects reported earnings.
0
!+ g
Py = ------------y(! + S t )
Normalization Methods
• Historical average EPS.
• Average ROE.
Forward price o f zero-coupon bond:
Price to Book (P /B ) Ratio
Advantages:
• BV almost always > 0.
• BV more stable than EPS.
• Measures NAV o f financial institutions.
Disadvantages:
• Size differences cause misleading comparisons.
• Influenced by accounting choices.
• BV ^ M V due to inflation/technology.
j ustified P /B =
—&
r“ g
Price to Sales (P/S) Ratio
Advantages:
• Meaningful even for distressed firms.
• Sales revenue not easily manipulated.
• Not as volatile as P/E ratios.
• Useful for mature, cyclical, and start-up firms.
Disadvantages:
• High sales ^ imply high profits and cash flows.
• Does not capture cost structure differences.
• Revenue recognition practices still distort sales.
justified P/S = PMo x (1~ b)(1 + g)
r- g
D uPont Model
ROE =
net income
sales
x
sales
total assets
x
total assets
equity
Price to Cash Flow Ratios
Advantages:
Cash flow harder to manipulate than EPS.
More stable than P/E.
Mitigates earnings quality concerns,
disadvantages:
Difficult to estimate true CFO.
FC FE better but more volatile.
M ethod o f Comparables
Firm multiple > benchmark implies overvalued.
Firm multiple < benchmark implies undervalued.
Fundamentals that affect multiple should be
similar between firm and benchmark.
Residual Income Models
• RI = Et —(r x Bt_i) = (ROE —r) x Bt_i
• Single-stage RI model:
V0 = B 0 +
(R O E —r ) x B 0
r“ g
• Multistage RI valuation: Vo = Bo + (PV o f interim
high-growth RI) + (PV o f continuing RI)
Econom ic Value Addedđ
ã EVA = NOPAT - $WACC; NOPAT = E B IT (1-1)
Private Equity Valuation
D LO C = 1 -
1
1 + Control Premium
Total discount = 1 - [(1 - D L O C )(l - DLO M )].
The D LO M varies with the following.
• An impending IPO or firm sale [ DLOM .
The payment o f dividends J, DLOM .
Sno= —
i + Z O ’ k))
Forward pricing model:
B
F0 ’k)
P()+k>
p.
AJ
Forward rate model:
[1 +/j,k)]k= [ l + S((<10]«*k» / ( l + S()i
“Riding the yield curve”: Holding bonds with
maturity > investment horizon, with upward
sloping yield curve.
swap spread = swap rate - treasury yield
T E D spread:
= (3-month L IB O R rate) —(3-month T-bill rate)
Libor-OIS spread
= L IB O R rate - “overnight indexed swap” rate
Term Structure o f Interest Rates
Traditional theories:
Unbiased (pure) expectations theory.
Local expectations theory.
Liquidity preference theory.
Segmented markets theory.
Preferred habitat theory.
Modern term structure models:
Cox-Ingersoll-Ross: dr = a (b -r)^ + a fr d z
Vasicek model: dr = a(b - r)d t+ ad z
Ho-Lee model: drt = Qt dt+ a d z t
Managing yield curve shape risk:
AP/P » - D l A x l - D sAxs - D cAxc
(L = level, S = steepness, C = curvature)
Yield volatility: Long-term <— uncertainty regarding
the real economy and inflation.
Short term <— uncertainty re: monetary policy.
Long-term yield volatility is generally lower than
volatility in short-term yields.
Value o f option embedded in a bond:
V call = Vstraight bond - V callable bond
V put = Vputable bond - V straight bond
W hen interest rate volatility increases:
v call
. option
. T1 , vput option. 1T> v callable bond'1'k 5 V putable bond t1
Upward sloping yield curve: Results in lower call
value and higher put value.
W hen binomial tree assumed volatility increases:
• computed OAS o f a callable bond decreases.
• computed OAS o f a pu table bond increases.
_ BV Ay - BV hAy
effective duration =
2 x BV0 x Ay
.
.
BV Ay + BV+Ay - (2 >
errective convexity = -------------------------- -—
BV0 x A y2
Effective duration:
• ED (callable bond) < ED (straight bond).
• ED (putable bond) < ED (straight bond).
ã ED (zero-coupon) ô maturity o f the bond.
ã ED fixed-rate bond < maturity o f the bond.
• ED o f floater « time (years) to next reset.
One-sided durations: Callables have lower downduration; putables have lower up-duration.
Value o f a capped floater
= straight floater value - embedded cap value
Value o f a floored floater
= straight floater value + embedded floor value
Minimum value o f convertible bond
= greater 0/conversion value or straight value
Conversion value o f convertible bond
= market price o f stock x conversion ratio
Market conversion price
market price o f convertible bond
conversion ratio
FP (on an equity index) = Sq X
where:
8C = continuously com pounded dividen d y ield
P0 = e-*X N (-d 2) - S0e-6TN (-d 1)
Forward price on a coupon-paying bond:
where:
FP (on a fixed income security)
8 = continuously compounded dividend yield
= (S0 - PVC) x (1 + R f )T
or
= SQ x (1 + R f )T — FVC
market price o f convertible bond
straight value
Callable and putable convertible bond value
= straight value o f bond
+ value o f call option on stock
— value o f call option on bond
+ value o f put option on bond
recovery rate = % money received upon default
Loss given default (%) = 100 —recovery rate
Expected loss = prob. o f default x loss given default
Present value o f expected loss
= (risky bond value) - (risk-free bond value)
Structural model o f corporate credit risk:
• value o f risky debt = value o f risk-free debt —value
o f put option on the company’s assets
ã equity ô European call on company assets
Reduced form models: Impose assumptions on the
output o f a structural model.
Credit analysis o f ABS:
• ABS do not default but lose value w/defaults.
• Modeled w/probability o f loss, loss given default,
expected loss, present value o f the loss.
Credit Default Swap (C D S): Upon credit event,
protection buyer compensated by protection seller.
Index CDS: Multiple borrowers, equally weighted.
Default: Occurrence o f a credit event.
Common credit events in CD S agreements:
Bankruptcy, failure to pay, restructuring.
C D S spread: Higher for a higher probability o f
default and for a higher loss given default.
Hazard rate = conditional probability o f default,
expected losst = (hazard rate) t x (loss given
default) t
Upfront CD S payment (paid by protection buyer)
= PV(protection leg) - PV(premium leg)
« (CDS spread - CDS coupon) x duration x NP
Change in value for a CD S after inception
« chg in spread x duration x notional principal
DERIVATIVES
Forward contract price (cost-of-carry model)
FP
T
Price o f equity forward with discrete dividends
FP(on an equity security) = (SQ- P V D )x(l+ R f) !
Value o f forward on dividend-paying stock
Vt (long position) = [St — PVD t —
, (—h s - + c - )
Black-Scholes-M erton option valuation model
C 0 = S0e ^ N (d [) - e'rIXN (d2)
RC
f = continuously com pounded risk-free rate
Vt (long) = [St - P V C t ] -
(i + R f)
( - h S + + C + ) Lc
di =
ln(S/X) + ( r - 6 + a 2 /2)T
aVT
d2 = di — a^/T
market price o f common stock
Premium over straight value
So =
_ uc
C 0 — hoQ H------ ---------- -— = hS0 H—
(1 + R f )
(1 + R f )
(—hS+ + P + )
(—hS~ + P ~ )
— hS0 +
Pq — hSn0 +
(1 + R f )
(l + R f)
Value o f a forward on a coupon-paying bond:
market conversion premium per share
T
„
(r £ - 8 c )x T
r
RrXT
S o X e " 6CxT x e t
Market conversion premium per share
= market conversion price —stock’s market price
Market conversion premium ratio
FP — S0 x (l + R f )
O ption value using arbitrage-free pricing
portfolio
Forward on equity index with continuous
dividends
FP
(l + R f F - ' J
FP
Sge ^ = stock price, less PV o f dividends
(l + R f )(T+t)
Price o f a bond futures contract:
FP = [(full price) (l+ R f)T - AI.r - FVC]
full price = quoted spot price + AI
Q uoted bond futures price:
QFP = forward price /conversion factor
(foil price) (1+Rf )T - AIT - FVC
1
CFj
Price o f a currency forward contract:
Fr = S 0 x
(l + R p c )T
T
(! + r Bc )
Value o f a currency forward contract
_ [FPt - FP] X (contract size)
V t=
(l + * c ) (T- r)
O P T IO N STRA TEG IES:
Covered call = long stock + short call
Protective put = long stock + long put
Bull spread: Long option with low exercise price
+ short option with higher exercise price. Profit if
underlying $|.
Bear spread: exercise price o f long > exc. price o f
short
Collar = covered call + protective put
Long straddle = long call + long put (w ith sam e
strike). Pays off if future volatility is higher.
Calendar spread: Sell one option + buy another at a
maturity where higher volatility is expected.
Long calendar spread: Short near-dated call + long
long-dated call. (Short calendar spread is opposite.)
Breakeven volatility analysis
^annual = % A P X
Currency forward price (continuous time)
\
R c —R c
xT
PC
BC)
F p = S0 x e
252
trading days until maturity
where
%AP =
absolute (breakeven price — current price)
current price
Swap fixed rate:
C =
1-Z 4
ALTERNATIVE INVESTMENTS
Z j + Zo + Z * + Z,
where: Z = 1/(1+ R J = price o f n-period zero-coupon
bon d p er $ o f prin cipal
Value o f interest rate swap to fixed payer:
= Yj Z x (SFRjqew —SFR q j j ) x — — x notional
360
Binomial stock tree probabilities:
Ttu = probability o f up move = ^
^
U -D
t t d = probability o f a down move = (1 —Ttu)
Value o f property using direct capitalization:
rental income if fully occupied
+ other income
= potential gross income
—vacancy and collection loss
= effective gross income
—operating expense
= net operating income
cap rate
NOIf
comparable sales price
Put-call parity:
S0 + Po = C o + PV (X)
Put-call parity when the stock pays dividends:
Po + S0e-*T = C 0 + e"rIX
Dynamic delta hedging
# o f short call options =
# shares hedged
delta o f call option
# o f long put options = -
# shares hedged
delta o f put option
Change in option value
A C « call delta x A S + Vi gamma x A S2
A P ps put delta x A S + Vi gamma x A S2
value = V q =
NOI l
stabalized NOI
or V0 =
cap rate
cap rate
Property value based on “All Risks Yield”:
value = V Q= rentj /ARY
Value o f a property using gross income multiplier:
gross income multiplier =
sales price
gross income
Term and reversion property valuation approach:
total property value
= PV o f term rent + PV reversion to ERV
Layer approach:
total property value
= PV o f term rent + PV o f incremental rent
Debt service coverage ratio:
D SC R = firSt' year N Q I
debt service
Loan-to-value (LTV) ratio:
LTV =
loan amount
appraisal value
first year cash flow
equity dividend rate = ------------- ;----------equity
Net asset value approach to REIT share
valuation:
estimated cash NO I
4- assumed cap rate
= estimated value o f operating real estate
+ cash & accounts receivable
—debt and other liabilities
= net asset value
± shares outstanding
= NAV/share
Price-to-FFO approach to REIT share valuation:
funds from operations (FFO)
* shares outstanding
= FFO/share
x sector average P/FFO multiple
= NAV/share
Price-to-AFFO approach to REIT share valuation:
funds from operations (FFO)
—non-cash rents
—recurring maintenance-type capital
expenditures
= AFFO
4- shares outstanding
= AFFO/share
x property subsector average P/AFFO multiple
= NAV/share
Discounted cash flow REIT share valuation:
value o f a R E IT share
= PV(dividends for years 1 through n)
+ PV (terminal value at the end o f year n)
Private Equity
Sources o f value creation: reengineer firm, favorable
debt financing; superior alignment o f interests
between management and PE ownership.
Valuation issues (V C firm s relative to Buyouts): DCF
not as common; equity, not debt, financing.
Key drivers o f equity return:
Buyout: t o f multiple at exit, j in debt.
VC: pre-money valuation, the investment, and
subsequent equity dilution.
Components o f perform ance (LBO ): earnings
growth, | o f multiple at exit, [ in debt.
E xit routes (in order o f exit value, high to low): IPOs
secondary mkt sales; M BO ; liquidation.
Perform ance M easurement: gross IR R = return from
portfolio companies. Net IR R = relevant for LP,
net o f fees & carried interest.
Perform ance Statistics:
• PIC = % capital utilized by GP; cumulative sum
o f capital called down.
• Management fee: % o f PIC.
• Carried interest: % carried interest x (change in
NAV before distribution).
• NAV before distrib. = prior yr. NAV after distrib.
+ cap. called down - mgmt. fees + op. result.
• NAV after distributions = NAV before
distributions - carried interest - distributions
• DPI multiple = (cumulative distributions) / PIC
= LP s realized return.
• RVPI multiple = (NAV after distributions) /
PIC = LP’s unrealized return.
• TVPI mult. = DPI mult. + RVPI mult.
N PV VC & IRR methods-, calculate pre-money value,
post-money value, ownership fraction, & price per
share. NPV methods starts with POST, IR R with
expected future wealth.
Assessing Risk: (1) adjust discount rate for prob of
failure; (2) use scenario analysis for term.
Commodities
Contango: futures prices > spot prices
Backwardation: futures prices < spot prices
Term Structure o f Comm odity Futures
1. Insurance theory: Contract buyers compensated
for providing protection to commodity producers.
Implies backwardation is normal.
2. Hedging pressure hypothesis: Like insurance
theory, but includes both long hedgers ( —>
contango) and short hedgers (—>backwardation).
3. Theory of storage: Spot and futures prices related
through storage costs and convenience yield.
Total return on fully collateralized long futures
= collateral return + price return + roll return
Roll return: positive in backwardation because longdated contracts are cheaper than expiring contracts.
PORTFOLIO MANAGEMENT
Portfolio M anagement Planning Process
• Analyze risk and return objectives.
• Analyze constraints: liquidity, time horizon, legal
and regulatory, taxes, unique circumstances.
• Develop IPS: client description, purpose, duties,
objectives and constraints, performance review
schedule, modification policy, rebalancing
guidelines.
Arbitrage Pricing Theory
E(Rp) = Rp + Piu^i) + P p ,A ) + ••• + Pp,A )
Expected return = risk free rate
+ E (factor sensitivity) x (factor risk premium)
Value at risk (VaR) is an estimate o f the minimum
loss that will occur with a given probability over a
specified period, expressed as a currency amount or
as percentage o f portfolio value.
5% annual $VaR = (Mean annual return — 1.65
x annual standard deviation) x portfolio value
Conditional VaR (CVaR) is the expected loss given
that the loss exceeds the VaR.
Incremental VaR (IVaR) is the estimated change in
VaR from a specific change in the size o f a portfolio
position.
Marginal VaR (MVaR) is the estimate o f the
change in VaR for a small change in a portfolio
position and is used as an estimate o f the position’s
contribution to overall VaR.
Variance for W A % fluid A + W D °/o fluid B
^Portfolio = W a 4
+
+ 2 W a Wb C o va b
Annualized standard deviation
= V250 x (daily standard deviation)
% change in value vs. change in YTM
= -duration (AY) + V2 convexity (AY)2
fo r M acaulay duration, replace A Y by A Y/(1 + Y)
Inter-temporal rate o f substitution = mt =
u0
marginal utility o f consuming 1 unit in the future
marginal utility o f current consumption o f 1 unit
Real risk-free rate o f return =
1
l-P o _
Po
E(mt)
-1
Default-free, inflation indexed, zero coupon:
Bond price = Pn = ^- + cov(Pi, m i)
v
0
(1 + R )
1 1
Nominal short term interest rate (r)
= real risk-free rate (R) + expected inflation (it)
Nominal long term interest rate = R + tt + 9
where 6 = risk prem ium fo r inflation uncertainty
Break-even inflation rate (BEI)
^^non-inflation jndCXedbond yield^a^op indexedbond
BEI for longer maturity bonds
= expected inflation (t t ) + infl. risk premium (0)
Credit risky bonds required return = R + tt + 0 + 7
where 7 = risk prem ium (spread) fo r credit risk
Discount rate for equity = R + tt + 0 + 7 + k ,
A = equity risk prem ium = 7 + k
7 = risk prem ium fo r equity vs. risky debt
Discount rate for commercial real estate
= R + TT + 0 + 7 + K + cj>
K, = term inal value risk, p = illiquidity prem ium
Multifactor model return attribution:
k
factor return = ^ ( / 3 pi - ( 3 bi) x ( \ )
i=l
Active return
= factor return + security selection return
Active risk squared
= active factor risk + active specific risk
n
Active specific risk = ^ ] (w pi —wbi)2
Active return = portfolio return - benchmark return
Ra A - R b
n
Portfolio return = Rp = ^ ^ w p j R ;
i=l
n
Benchmark return = Rg = ^ w g j R j
i=l
Information ratio
_ Rp — Rg _ R A _ active return
^(Rp—Rg)
aA
active risk
Portfolio Sharpe ratio = S R P = —
1
ST D (R p )
Optimal level of active risk:
Sharpe ratio = ^ S R g 2 + I R P2
Total portfolio risk: a p2 = a B2 + o f
Information ratio: IR = T C X IC x V BR
Expected active return: E(RA) = IR x crA
“Full” fundamental law of active management:
E (R a ) = (T C )(IC ) a/BRcta
ISBN: 978-1-4754-5984-5
dmizing aggressiveness
TR
— — ST D (R g)
j
Kr
Execution Algorithms: Break an order down into
smaller pieces to minimize market impact.
High-Frequency Algorithms: Programs that trade
on real-time market data to pursue profits.
U.S. $29.00 © 2017 Kaplan, Inc. All Rights Reserved.
