L E V E L II SC H W ESER'
C r it ic a l C o n c e pt s f o r t h e 2020 CFA® E x a m
ETHICAL AND PROFESSIONAL
STANDARDS
I
Professionalism
I (A) Knowledge o f the Law
I (B) Independence and Objectivity
I (C )
I (D)
II
II (A)
II (B)
III
HI (A)
III (B)
III (C)
III (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 of Capital Markets
Material Nonpublic Information
Market Manipulation
Duties to Clients
Loyalty, Prudence, and Care
Fair Dealing
Suitability
Performance Presentation
Preservation o f 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 of Interest
Disclosure o f Conflicts
Priority o f 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
Confidence interval for predicted Y-value:
A
Y ± t c x SE of forecast
Multiple Regression
Yj = b0 + (b, x X ,j) + (b2 x X 2j)
+ (b j X X 3i) + £;
• Test statistical significance of b; Ho: b = 0,
autocorrelation if D W < dl. 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.
Model Misspecification
• Omitting a variable.
• Variable should be transformed.
• Incorrectly pooling data.
• Using lagged dependent vbl. as independent vbl.
• Forecasting the past.
• Measuring independent variables with error.
Effects o f Misspecification
Regression coefficients are biased and inconsistent,
lack o f confidence in hypothesis tests of the
coefficients or in the model predictions.
Linear trend model: yt = b0 + bjt + £t
Log-linear trend model: ln(yt) = b0 + bjt + et
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 of residuals not significant.
Mean reverting level for AR(1):
bo
( 1 - b j)
RMSE: square root o f average squared error.
Random Walk Time Series:
xt = x t_j + et
Seasonality: indicated by statistically significant
lagged err. term. Correct by adding lagged term.
ARCH: detected by estimating:
= ao +
• Confidence Interval: b j± | t c Xsg
• SST = RSS + SSE.
• M SR = RSS / k.
• M SE = SSE / (n - k - 1).
• Test statistical significance of regression:
F = M SR / M SE with k and n —k - 1 df (1-tail).
• Standard error o f estimate (SEE = -v/MSE ).
Smaller SEE means better fit.
• Coefficient o f determination (R: = RSS / SST).
% o f variability o f Y explained by Xs; higher R~
means better fit.
Regression Analysis— Problems
• 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
Receiver operating characteristic (ROC): Shows
tradeoff between false positives and true positives.
Root mean square error (RMSE): Used when the
target variable is continuous.
n
^(Predicted. -A ctu a l.)
Risk Types:
A
Simulations
Continuous
Does not
matter
Yes
Scenario
analysis
Discrete
No
Yes
Decision trees
Discrete
Yes
No
r
Accommodates
Sequential? „
,
x
Correlated Variables?
ECONOMICS
bid-ask spread = ask quote - bid quote
Cross rates with bid-ask spreads:
'A '
'A '
vC, bid
v B , bid
x
A'
'A '
C J offer
v B , offer
'B '
CJ bid
x
/ \
B
CJ offer
Currency arbitrage: “Up the bid and down the ask.”
Forward premium = (forward price) —(spot price)
Value of fwd currency contract prior to expiration:
Vt =
(FPt — FP) (contract size)
1+ RA
days
1+ R A
Supervised learning: Algorithm uses labeled
training data (inputs and outputs identified) to
model relationships.
Unsupervised learning: Algorithm uses unlabeled
data to determine the structure o f the data.
Deep learning algorithms: Algorithms such as
neural networks and reinforced learning learn
from their own prediction errors and are used
for complex tasks such as image recognition and
natural language processing.
PREPA RIN G DATA
Normalization: Scales values between 0 and 1.
X i " Xmin
X max x min
Standardization: Centered at 0; scaled as standard
deviations from mean.
Standardized X j =
,T. . ,, .
Distribution
r
of risk
A 2
Normalized X j =
,
Appropriate
method
d2
t+1 ~~ a0 + al£t
,
n
days
\
360 /
Covered interest rate parity:
Variance o f ARCH series:
A
i=i
RM SE =
+ Bt
M A C H IN E LEA RN IN G
• Reject if |t| > critical t or p-value < a .
FIT O F A MACHINE LEARNING ALGORITHM
precision (P) = true positives / (false positives +
true positives)
recall (R) = true positives / (true positives + false
negatives)
accuracy = (true positives + true negatives) / (all
positives and negatives)
F l Score = (2 x P x R) / (P + R)
X i-p
a
360
F=
1+ R B
'0
days
360
Uncovered interest rate parity:
£ (% A SU
=
Fisher relation:
R nominal
. . = R real. + E(inflation)
v
7
International Fisher Relation:
R nominal
. ..A —R nominal
. . B — E(inflation.)
- E(inflationJ
N
A7
v
B7
Relative Purchasing Power Parity: High inflation
rates leads to currency depreciation.
%AS(A/B) = inflation^ - inflation(R)
where: % AS(A/B) = change in spot price (AIB)
Profit on FX Carry Trade = interest differential change in the spot rate o f 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)a
Growth Accounting:
growth rate in potential GDP
= long-term growth rate o f technology
+ a (long-term growth rate o f capital)
+ (1 - a) (long-term growth rate o f labor)
growth rate in potential GDP
= long-term growth rate o f labor force
+ long-term growth rate in labor productivity
Classical Growth Theory
• Real GDP/person reverts to subsistence level.
Neoclassical Growth Theory
• Sustainable growth rate is a function of
population growth, labor’s share o f income, and
the rate o f technological advancement.
• Growth rate in labor productivity driven only by
improvement in technology.
• Assumes diminishing returns to capital.
0
g* = --------(1 —a )
0
G* = --------- + A L
(1 —a )
Endogenous Growth Theory
• Investment in capital can have constant returns.
• | in savings rate —> permanent f in growth rate.
• R & D expenditures j technological progress.
Classifications o f Regulations
• Statutes: Laws made by legislative bodies.
• Administrative regulations: Issued by government.
• Ju d icial law : Findings o f the court.
Classifications o f Regulators
• Can be government agencies or independent.
• Independent regulator can be SRO or SRB. SRBs
are given government recognition.
Self-Regulation in Financial Markets
• SROs are more prevalent in common-law
countries than in civil-law countries.
Econom ic Rationale for Regulatory Intervention
• Inform ational frictions arise in the presence of
information asymmetry.
• Externalities deal with provision o f public goods.
• Weak competition can lead to lack o f innovation
and higher prices.
• Social objectives such as provision o f public goods.
Regulatory Interdependencies and Their 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 of Regulatory Intervention
• Price mechanisms, restricting or requiring certain
activities, and provision of public goods or
financing o f private projects.
Financial 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.
Prudential 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.
• Amortized cost on balance sheet; interest and realized
gain/loss on income statement.
• Fair value through OCI at FMV with unrealized
gains/losses in equity on B/S; dividends, interest,
realized gains/losses on I/S.
• Fair value through profit or loss at FMV; dividends,
interest, realized and unrealized gains/losses on I/S.
Investments in Associates: 20-50% owned, significant
influence. With equity method, pro-rata share of the
investees 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.
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.
Incom e Statem ent
• 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 of
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 Adjustm ent
IfT P P C < firm contribution, difference = A in
PBO (reclassify difference from CFF to C FO aftertax). IfT P P C > 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 Financial Statements vs. All-Current
• Pure balance sheet and income statement 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 AN D U.S. GAAP D IFFER EN C ES
Fair value accounting, investment in associates:
IFRS —Only for venture capital, mutual funds, etc.
U.S. GAAP - Fair value accounting allowed for all.
• IFRS permits either the “partial goodwill” or
“full goodwill” methods to value goodwill and
noncontrolling interest. U.S. GAAP requires the
full goodwill method.
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 OCI; amortized to P&L.
Actuarial gains/losses:
IFRS - Remeasurements in OCI 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.
RO E decomposed (extended DuPont equation)
Tax
Interest EBIT
Burden Burden Margin
NI
EBT
E B IT
RO E = ------- x --------- x ------------x
E B T E B IT revenue
T otal Asset
T urnover
Financial
Leverage
revenue
average assets
x
average assets
average equity
Accruals Ratio (balance sheet approach)
accruals ratio85 =
<N° AeND - N O A BEG)
(N OA e n d + N O A b e g ) / 2
Accruals Ratio (cash flow statement approach)
accruals ratio ^ =
(NI - C FO - CFI)
(N O A e n d + N O A BEG) / 2
Financial institutions differ from other companies
due to systemic importance and regulated status.
Basel III: Minimum levels of capital and liquidity.
CAMELS: Capital adequacy, Asset quality,
Management, Earnings, Liquidity, and Sensitivity.
Liquidity coverage ratio =
highly liquid assets
expected cash outflows
. . r ..
.
available stable funding
Net stable funding ratio = ------ -------------------required stable funding
IN SU R A N C E C O M PA N Y K EY RATIOS
Underwriting loss ratio
claims paid + A loss reserves
net premium earned
Expense ratio
underwriting expenses inch commissions
net premium written
Loss and loss adjustment expense ratio
loss expense + loss adjustment expense
net premiums earned
Dividends to policyholders ratio
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).
VL = V U
MM Prop II (No Taxes): increased use o f cheaper
debt increases cost o f equity, no change in WACC.
D,
re = r0 + — (r0 ~ rd)
E
MM Proposition I (With Taxes): tax shield adds
value, value is maximized at 100% debt.
VL = Vy + ( t x d )
M M Proposition II (With Taxes): tax shield adds
value, WACC is minimized at 100% debt.
dividends to policyholders
net premiums earned
Combined ratio after dividends
= combined ratio + divs to policyholders ratio
Total investment return ratio
= total investment income / invested assets
Life and health insurers’ ratios
total benefits paid / (net premiums written and
deposits)
commissions + expenses / (net premiums written +
deposits)
CORPORATE FINANCE
Capital Budgeting Expansion
• Initial outlay = FCInv + WCInv
• CF = (S - C - D ) ( l - T ) + D = (S - C )(l - T ) + D T
• T N O C F = SalT + NWCInv - T(SalT - BT)
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 projects 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 = NOPAT - $WACC
oo
ER
Market Value Added =
t=i (1 + WACC)1
re = 1b + ^ ( 1{ ) - rd ) ( 1 - 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)
Imputation system: effective tax rate is the
shareholder’s individual tax rate.
Signaling Effects of Dividend Changes
Initiation: ambiguous signal.
Increase: positive signal.
Decrease: negative signal unless management sees
many profitable investment opportunities.
Price change when stock goes ex-dividend:
AP =
D (1 -T d )
(1 - T c g )
Target Payout Adjustment Model
expected increase in dividends =
expected tar8et \ previous
adjustment
x payout 1 — . ,
,
earnings r • / dividend
factor
&
ratio /
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.
ESG C O N SID ER A TIO N S
The board of directors o f a company can be
structured either as a single tier board o f internal
(executive) and external (non-executive) directors,
or a two-tiered board where the management board
is overseen by a supervisory board.
CEO duality: When the CEO is also the company’s
chairperson o f the board.
ESG-Related Risk Exposures: In fixed-income
analysis, ESG considerations are primarily concerned
with downside risk. In equity analysis, ESG is
considered both in regards to upside opportunities
and downside risk.
M ERG ERS
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,
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 (HHI):
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 HHI increases 100 points (or
increases 50 points for HHI >1,800).
n
HHI = V ( M S i xlOO}
i=l
Methods to Determine Target Value
D C F method: target pro forma FCF discounted at
adjusted WACC.
Com parable company analysis: based on relative
valuation vs. similar firms + takeover premium.
Com parable transaction analysis: target value from
takeover transaction; takeover premium included.
Merger Valuations
C om binedfirm : VAT = VA+ VT + S - C
Takeover prem ium (to target): GainT = TP = PT —VT
Synergies ( to acquirer): GainA= S —TP = S - (PT - V.^
Merger Risk & Reward
Cash offer: acquirer assumes risk & receives reward.
Stock offer: some of 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:
P i-P o + C F ,
o
Pi + CFj
-1
0
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
Single-Stage F C F F /F C F E Models
Models of required equity return:
• CAPM\ r. = RF + (equity risk premium x (3.)
• M ultifactor m odel: required return = RF + (risk
premium)j + ... + (risk premium)n
• Fama-French-. r.j = RF + 1(3mkt,j x (Rmkt —RF)
+ ^SMB.j x ^ s m a ll
^ b ig ) + '^HML,j X ^ H B M
• For FCFF valuation: V0 =
• For FCFE valuation: V0 =
MVdebt
M ^debt+equity
rd (l —T ) +
^LBM^
MV' q,,i,y
-
M ^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.
• FCF is related to profitability.
• Controlling shareholder perspective.
Use residual income (RI) when:
• Firm lacks dividend history.
• Expected FCF is negative.
Gordon Growth Model (GGM)
Assumes perpetual dividend growth rate:
V0 =
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).
Present Value o f Growth Opportunities
E
V0 = ^ + PVGO
H-Model
V0 =
D o x (l + gL)] | [D o x H x (gs
r ~gL
gL)]
r ~gL
Sustainable Growth Rate: b x ROE.
Required Return From Gordon Growth Model:
r = (D, / P0) + g
Free Cash Flow to Firm (FC FF)
Assuming depreciation is the only NCC:
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 = C FO + [Int x (1 - tax rate)] - FCInv.
Free Cash Flow to Equity (FC FE)
FCFE = FCFF —[Int x (1 —tax rate)] + Net
borrowing.
FCFE = NI + Dep - FCInv - WCInv + Net
borrowing.
FCFE = NI - [(1 - DR) x (FCInv - Dep)]
- [(1 —DR) x WCInv]. ( Used to forecast.)
W ACC
FCFE!
r~g
• Pastor-Stambaugh m odel: Adds a liquidity factor to
the Fama-French model.
• M acroeconom ic m ultifactor models-. Uses factors
associated with economic variables.
• Build-up method, 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
-
FCFFj
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.
Justified P /E
leading P/E = -----r~g
trailing P/E =
( l - b ) ( l + g)
r~g
Justified dividend yield:
D0
r-g
0
!+ g
Residual Income Models
RI = Et —(r x B[_i) = (ROE —r) x Bt_i
Single-stage RI model:
V0 = B0 +
(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 Added®
• EVA - NOPAT - $WACC; NOPAT - E B IT (1-1)
Private Equity Valuation
DLOC- 1 -
1
1+Control Premium
Total discount = 1 —[(1 - D L O C )(l —DLOM )].
The DLO M varies with the following.
• An impending IPO or firm sale J DLOM .
• The payment o f dividends J, DLOM .
• Earlier, higher payments J, DLOM .
• Restrictions on selling stock J DLOM .
• A greater pool of buyers J, DLOM .
Greater risk and value uncertainty | DLOM .
FIXED INCOME
Price of a T-period zero-coupon bond:
PT =
1 T
(l + ST )
Forward price of zero-coupon bond:
Normalization Methods
• Historical average EPS.
• Average ROE.
F(i'k) = [ i + / ( j , k ) f
Price to Book (P/B) Ratio
Advantages:
• BV almost always > 0.
• BV more stable than EPS.
• Measures NAV of financial institutions.
Disadvantages:
• Size differences cause misleading comparisons.
• Influenced by accounting choices.
• BV ^ M V due to inflation/technology.
justified P / B = R Q E ~ g
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.
j ustified P /S = PMo X ( l - b ) ( l + g)
r~g
DuPont Model
sales
total assets
_
net income
x
x
RO E =
total assets
equity
sales
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.
FCFE better but more volatile.
Method of Comparables
Firm multiple > benchmark implies overvalued.
Firm multiple < benchmark implies undervalued.
Fundamentals that affect multiple should be
similar between firm and benchmark.
Forward pricing model:
F . - ^0+k)
(l’k)
p.
J
Forward rate model:
[1 +y(j>k)]k = [1 + S(j +k)](i +k>/ (1 + S.)’
“Riding the yield curve”: Holding bonds with
maturity > investment horizon, with upward
sloping yield curve.
swap spread = swap rate - treasury yield
TED spread:
= (3-month LIBO R rate) —(3-month T-bill rate)
Libor-OIS spread
= LIBO R rate —“overnight indexed swap” rate
Term Structure of 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)d t + oyfrdz
• Vasicek model: dr = a(b - r)d t + od z
• Ho-Lee model: drt - 0tdt + od z t
Managing yield curve shape risk:
AP/P - D l A x l - D sAxs - D c;A x(;
(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 of option embedded in a bond:
Vcall = Vstraight bond - V
Vput = Vputable bond - V
callable bond
straight bond
When interest rate volatility increases:
Vcall option T1 5V put option T1 ’ V callable bond ^I5V
T
putable bond 1
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.
B V Ay - BV+Ay
effective duration =
2 x BV0 x Ay
effective convexity =
BV-Ay + BV+Ay — (2 x BV q )
BV0 x A y2
Effective duration:
• ED (callable bond) < ED (straight bond).
• ED (putable bond) < ED (straight bond).
• ED (zero-coupon) « maturity o f the bond.
• 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 of a capped floater
= straight floater value - embedded cap value
Value of a floored floater
= straight floater value + embedded floor value
Minimum value o f convertible bond
= greater o f 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
Market conversion premium per share
= market conversion price - stock’s market price
Market conversion premium ratio
market conversion premium per share
market price o f common stock
Premium over straight value
/
#
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
Expected exposure: Amount a risky bond investor
stands to lose before any recovery is factored in.
Loss given default = loss severity x exposure
Probability of default: Likelihood in a given year.
Credit valuation adjustment (CVA): Sum o f the
present values o f expected losses for each period.
Credit score/rating: Ordinal rank; higher = better.
Return from bond credit rating migration: A % P
= -(modified duration o f bond) x (A spread)
Structural models of corporate credit risk:
• value of risky debt = value o f risk-free debt - value
o f put option on the company’s assets
• equity w European call on company assets
Reduced-form models: Do not explain why default
occurs, but statistically model when default occurs.
Credit spread on a risky bond = YTM o f risky
bond —YTM o f benchmark
Credit Default Swap (CDS): 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.
CDS spread: Higher for a higher probability of
default and for a higher loss given default.
Hazard rate = conditional probability o f default.
expected losst = (hazard rate)t x (loss given default)
Upfront CDS payment (paid by protection buyer)
= PV(protection leg) —PV(premium leg)
« (CDS spread - CDS coupon) x duration x NP
Change in value for a CDS after inception
« chg in spread x duration x notional principal
DERIVATIVES
Dynamic delta hedging
# o f short call options =
Forward contract price (cost-of-carry model)
FP
_
t
FP —Sq x (l + Rf )
So =
delta o f call option
# shares hedged
# o f long put options = -
T
(1 + Rf )
Price of equity forward with discrete dividends
FP(on an equity security) = (SQ- P V D )x(l+ R f)T
Value of forward on dividend-paying stock
Vt (long position) = [St — PVDt —
# shares hedged
delta o f put option
Change in option value
A C ~ call delta x AS + Vi gamma x A S2
A P ~ put delta x A S + Vi gamma x A S2
Option value using arbitrage-free pricing
FP
(l + R f F - 1)
Forward: equity index (continuous dividend)
^ _ LC , ( - h S + + C + ) Lc , ( —h S - + C T)
C a — hon H---------------------- = hoA H----------------------
0
0
(1 + Rf)
P0 = hSo +
(l + Rf)
=hSo +
(l + Rf)
(RCf - 6 c )xT
FP (on an equity index) = S0 X e ' ‘
'
Rf xT
S0 x e - 8C><T x e r
(l + Rf)
Black—Scholes—M erton option valuation model
C 0 = S0e_8TN(d1) - e-rTXN(d2)
P0 = e~rTX N (-d 2) - S0er*TSr(-d,)
where:
where:
8 = continuously compounded dividend yield
R p = continuously com pounded risk-free rate
6C = continuously com pounded dividend y ield
ln(S / X ) + (r —8 + ct 2 /2)T
Forward price on a coupon-paying bond:
a Vt
FP(on a fixed income security)
= (S0 - P V C ) x ( l + R f )T
= S o x ( l + R f )T - F V C
= dj — aV T
Value of a forward on a coupon-paying bond:
Yt(long) = [St — PVCt —
Price of a bond futures contract:
FP - [(full price)(l+Rf)T - AIT - FVC]
full price = quoted spot price + AI0
Quoted bond futures price:
(full price) (l+ R f)T - AIT - FVC
1
CF
Price of a currency forward contract:
Fr = S0 x
ft _!_
D__)T
(l
+ R
PC)
T
(! + r b c )
[FPt — FP] X (contract size)
a + n>c)(T _,)
Rc —Rc
PC
BC
xT
Swap fixed rate:
C=
1 -Z
Zj +
+ Z3 + z 4
Value of interest rate swap to fixed payer:
ij) X
^ ^ X notional
360
Binomial stock tree probabilities:
Tt(J = probability of up move = ^
U -D
1TD = probability of a down move = (1 —itA
Put-call parity:
So + Po = Co + PV(X)
Put-call parity when the stock pays dividends:
P. +
= C0 ♦ e"TX
NOIj
comparable sales price
NOI 1
cap rate
or V0 =
stabilized N O I
cap rate
Property value based on “Ail Risks Yield”:
value = V () = rentj /ARY
sales price
gross income
Term and reversion 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 of incremental rent
Debt service coverage ratio:
D SC R =
where: Z = 1/(1 +R f) = price o f zero-coupon $1 bond
= X/Z X (SFRjssfew — SFR q
cap rate =
gross income multiplier =
Currency forward price (continuous time):
F y = Sq X e
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
value = V q =
Value of a currency forward contract
Vt =
= stock price, less PV of dividends
ALTERNATIVE INVESTMENTS
FP
(l + R f F - 1)
QFP = forward price /conversion factor
Sge
first-year NOI
debt service
Loan-to-value (LTV) ratio:
LTV =
loan amount
appraisal value
equity dividend rate =
first year cash flow
equity
NAV approach to R E IT share valuation:
estimated cash NOI
+ 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)
h- 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
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 of interests
between management and PE ownership.
Valuation issues (V Cfirm s relative to Buyouts):
DCF not as common; equity, not debt, financing.
Key drivers o f equity return:
Buyout: j of multiple at exit, [ in debt.
VC: pre-money valuation, the investment, and
subsequent equity dilution.
Components o f performance (LBO): earnings
growth, | o f multiple at exit, j in debt.
Exit routes (in order o f exit value, high to low): IPOs
secondary market sales; M BO ; liquidation.
Performance Measurement: gross IRR = return
from portfolio companies. Net IRR = relevant for
LP, net o f fees & carried interest.
Performance Statistics:
• PIC = % capital utilized by GP; cumulative sum
of capital called down.
• Management fee: % of 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.
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 of Commodity 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.
Creation/redemption of ETFs: Authorized
participants (APs) create additional shares by
delivering the creation basket to the ETF manager.
Redemption is by tendering ETF shares and
receiving a redemption basket.
ETF spreads: Positively related to cost o f creation/
redemption, spread on the underlying securities,
risk-premium for carrying trades until close o f
trade, and APs’ normal profit margin. Negatively
related to probability o f completing an offsetting
trade on the secondary market.
ETF premium (discount) % =
(ETF price - NAV per share) / NAV per share
Arbitrage Pricing Theory
V ^ 'l^ in H .u io n indexed bond
BEI for longer maturity bonds
= expected inflation ( t v) + infl. risk premium (0)
Discount rate for equity = R + tv + 0 + 7 + k
A = equity risk prem ium = 7 + n
7 = risk prem ium fo r equity vs. risky debt
Discount rate for commercial real estate
= R + tt + 0 + 7 + k + 4>
k , = term inal value risk, cj> = illiquidity prem ium
Multifactor model return attribution:
k
factor return = ^ (/3pi - f a ) X (A;)
i=l
Active return
= factor return + security selection return
Active risk squared
= active factor risk + active specific risk
n
E(Rp) = R F + PP1(A,) + Pp>2(^2^ + ••• ■ M V
Expected return = risk free rate
+ £ (factor sensitivity) x (factor risk premium)
Value at risk (VaR): Estimate o f minimum loss
with a given probability over a specified period,
expressed as $ amount or % o f portfolio value.
5% annual $VaR = (Mean annual return — 1.65
x annual standard deviation) x portfolio value
Conditional VaR (CVaR): The expected loss given
that the loss exceeds the VaR.
Incremental VaR (IVaR): The change in VaR from
a specific change in the size o f a portfolio position.
Marginal VaR (MVaR): Change in VaR for a small
change in a portfolio position. Used as an estimate
o f the position’s contribution to overall VaR.
Variance for W A% fund A + W B% fund B
2_2
P o rtfo lio = W A ° A +
+ 2 W A W BC o v AB
Active return = portfolio return - benchmark return
RA= R p - R b
n
Portfolio return = Rp = ^ w P jR;
i=l
n
Benchmark return = Rg = ^ w p j R j
i=l
Information ratio
Rp — Rg
^ (R p -R g)
RA
<7A
active return
active risk
Portfolio Sharpe ratio = SRp =
Optimal level of active risk:
^--- ——
STD(Rp)
Sharpe ratio = ^ S R g 2 + IR P2
Information ratio: IR = T C x IC x VBR
= V250 x (daily standard deviation)
% change in value vs. change in YTM
= —duration (AY) + Vi convexity (AY)2
fo r M acaulay duration, replace A Y by AY/(1 + Y)
Expected active return: E(R^) = IR x crA
“Full” fundamental law of active management:
E(RA) = (TC)(IC)VBRa^
Inter-temporal rate o f substitution = mt = —
u0
Sharpe-ratio-maximizing aggressiveness level:
marginal utility of consuming 1 unit in the future
marginal utility o f current consumption of 1 unit
1 -P 0
1
P0
E(mt )
-1
Default-free, inflation indexed, zero coupon:
E ft)
Active specific risk = ^ ^(wpj — wbi)2 °ci2
i=l
Total portfolio risk: a 2 = cr 2 + ct 2
Annualized standard deviation
Bond price = P0 =
yieldnon_inflationindexed bond
Credit risky bonds required return = R + Tt + 0 + 7
where 7 = risk prem ium (spread) fo r credit risk
PORTFOLIO MANAGEMENT
Real risk-free rate o f return =
Break-even inflation rate (BEI)
+ cov(Pj, mq)
(1 + R )
Nominal short term interest rate (r)
= real risk-free rate (R) + expected inflation
( t v)
Nominal long term interest rate = R + it + 0
where 6 = risk prem ium fo r inflation uncertainty
ISBN: 978-1-4754-9547-8
© 2019 Kaplan, Inc. All Rights Reserved.
IR
STD(RA) = — — STD(Rg)
5K B
TR A N SA C TIO N C O S T ESTIM ATES
Per share effective spread transaction cost =
(side) x (transaction price - midquote price)
Effective spread = 2 x (per share effective spread
transaction cost)
VWAP transaction cost for sell orders = trade size
x (benchmark VWAP benchmark —trade VWAP)
VWAP transaction cost for buy orders = trade size
x (trade VWAP benchmark - benchmark VWAP)
Implementation shortfall: Difference in value
between a hypothetical “paper” portfolio and the
actual portfolio.
Electronic markets enable: Hidden orders,
leapfrogging, flickering quotes, electronic arbitrage
machine learning.
Abusive trading practices include front running
and market manipulation. Market manipulation:
trading for price impact, rumormongering, wash
trading, spoofing, bluffing, gunning the market,
and squeezing/cornering.