C r it ic a l C o n c e pt s f o r t h e 2019
l
r ETHICAL AND PROFESSIONAL
, STANDARDS
I
Professionalism
I (A) Knowledge of the Law
I (B) Independence and Objectivity
I (C ) Misrepresentation
I (D) Misconduct
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)
Integrity o f 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 o f 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
Machine learning: Gives a computer the ability to
improve its performance o f a task over time.
Distributed ledger: A shared database with a
consensus mechanism, ensuring identical copies.
Simple Linear Regression
Correlation:
Ny =
covXY
(sx )( sy )
t-test for r (n —2 df): t =
r>/n —2
V l-r 2
cov xy
Estimated slope coefficient:
CFA® E x a m
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).
Risk Types:
Appropriate
m ethod
D istribution
o f risk
Sequential?
Accommodates
Correlated Variables?
• Standard error o f estimate (SEE = >/MSE ).
Smaller SEE means better fit.
• Coefficient of determination (R 2 = RSS / SST).
% o f variability o f Y explained by Xs; higher R 2
means better fit.
Simulations
Continuous
Does not
matter
Yes
Scenario
analysis
Discrete
No
Yes
Decision trees
Discrete
Yes
No
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
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.
M odel M isspecification
• 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 M isspecification
Regression coefficients are biased and inconsistent,
lack o f confidence in hypothesis tests o f the
coefficients or in the model predictions.
Supervised machine learning: Inputs, outputs are
identified. Relationships modeled from labeled data.
Unsupervised machine learning: Algorithm itself
seeks to describe the structure o f unlabeled data.
Linear trend model: Yt = b 0 + b jt + £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 o f residuals not significant.
Mean reverting level for AR(1):
Estimated intercept: b0 = Y —b jX
Confidence interval for predicted Y-value:
A
(1 - b j )
RM SE: square root o f average squared error.
Y ± t c x SE of forecast
Random W alk T im e Series:
M ultiple Regression
Yi = b 0 + ( b , x X li) + (b 2 x X 2i)
+ (b 3 X X jiJ + Ej
• Test statistical significance o f b; H0: b = 0
xt = x t-i + £t
Seasonality: indicated by statistically significant
lagged err. term. Correct by adding lagged term.
ARCH: detected by estimating:
= ao +
Reject if |t| > critical t or p-value < a .
• Confidence Interval: bj ±
• SST = RSS + SSE.
(tcX Sb,
+ Mr
Variance o f ARCH series:
A9
A
A A9
CTt+l = a0 “b alet
_____
k ECONOMICS
bid-ask spread = ask quote - bid quote
Cross rates with bid-ask spreads:
Currency arbitrage: “Up the bid and down the ask.”
Forward premium = (forward price) - (spot price)
Value o f fwd currency contract prior to expiration:
(FPt — FP) (contract size)
1+ Ra
days
360 ,
Covered interest rate parity:
1 + Ra
1 + Rb
days)
360 j
So
days
[3 6 0 ,
Uncovered interest rate parity:
E (% A S)wb, = R a - R ,
Fisher relation:
R nominal = R real + E(inflation)
v
'
International Fisher Relation:
R nominal
. ..A —R nominal
. IR
= E(inflation.)
—EfinflationJ
B
v
A'
v
B'
Relative Purchasing Power Parity: High inflation
rates leads to currency depreciation.
%AS(A/B) = inflation^ - inflation(B)
where: % AS(AJB) = change in spot price (A/B)
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)Q
Growth Accounting:
growth rate in potential GDP
= long-term growth rate o f technology
+ Oi (long-term growth rate o f capital)
+ (1 - a ) (long-term growth rate of labor)
growth rate in potential GDP
= long-term growth rate o f labor force
+ long-term growth rate in labor productivity
continued on next page...
ECONOMICS continued
•••
Classical Growth T heory
• Real GDP/person reverts to subsistence level.
Neoclassical Growth T heory
• 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.
6
g** =
5
(1 - a )
G* = — - — + A L
(1 - a )
Endogenous Growth T heory
• Investment in capital can have constant returns.
• | in savings rate —» permanent j 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 of the court.
Classifications o f Regulators
• Can be government agencies or independent.
• Independent regulator can be SRO or non-SRO.
Self-Regulation in Financial M arkets
• Independent SROs are more prevalent in
common-law countries than in civil-law countries.
Econom ic Rationale for Regulatory Intervention
• Inform ationalfrictions arise in the presence of
information asymmetry.
• Externalities deal with provision of public goods.
Regulatory Interdependencies and T h eir 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 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.
Anticom petitive Behaviors and A ntitrust 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, 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 of 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
If TPPC < 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 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. IFR S
Hyperinfl. = cumul. infl. > 100% over 3 yrs. GAAP:
use temporal method. IFRS: 1st, restate foreign
curr. st. for infl. 2 nd, translate with current rates.
Net purch. power gain/loss reported in income.
Beneish model: Used to detect earnings
manipulation based on eight variables.
H igh-quality earnings are:
1 . Sustainable: Expected to recur in future.
2. Adequate: Cover company’s cost o f capital.
IF R S A N D U .S. GAAP D IF F E R E N C E S
Reclassification o f passive investments:
IFRS - Restricts reclassification into/out of 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.
• 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.
R O E decomposed (extended D uPont equation)
Tax
Interest E B IT
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 O A END - N O A BEG)
(N O A e n d + N O A BEG) / 2
Accruals Ratio (cash flow statem ent approach)
accruals ratk)
=
(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 o f capital and liquidity.
CAMELS: Capital adequacy, Asset quality,
Management, Earnings, Liquidity, and Sensitivity.
.
Liquidity coverage ratio =
Net stable funding ratio =
highly liquid assets
expected cash outflows
available stable funding
required stable funding
IN SU R A N C E C O M PA N Y K EY R A T IO S:
Underwriting loss ratio
claims paid + A loss reserves
net premium earned
continued on next page...
FINANCIAL STATEMENT ANALYSIS continued. ••
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
dividends to policyholders
net premiums earned
Combined ratio after dividends
= combined ratio - dividends to policyholders
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 Replacem ent
• Same as expansion, except current after-tax salvage
o f old assets reduces initial outlay.
• Incremental depreciation is A in depreciation.
Evaluating Projects w ith 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 O ptions
• Timing, abandonment, expansion, flexibility,
fundamental options.
Econom ic and Accounting Incom e
• 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 - $W ACC
oo
EP
• Market Value Added = X I ----t = i (1 + W A C C ) 1
• 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= VU
M M Prop II (No Taxes): increased use o f cheaper
debt increases cost o f equity, no change in WACC.
re = < b + f ( r o - r d)
E
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 = r 0 + ^ ( r 0 - r d )(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
Double 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 o f 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
(i - t d )
{l -
t c g
)
Target Payout Adjustm ent Model
expected increase in dividends =
■ target
expected
b „ \ previous
^ .
x payout I —K. . , ,
earnings r ' -q / dividend
Corporate Governance Objectives
• Mitigate conflicts of 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,
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 HHI increases 100 points (or
increases 50 points for HHI >1,800).
n
H H I = ^ ( M S j xlOO):
i=l
M ethods to D eterm ine Target Value
D C F method: target proforma 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.
M erger Valuations
C om binedfirm : VAT = VA+ VT + S - C
adjustment
factor
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 (SLA): Forces firm to
identify the most critical groups.
Ethical D ecision M aking
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 of
economic output (e.g., “veil o f ignorance”).
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 of risks & rewards shift to target. If
higher confidence in synergies; acquirer prefers cash
& target prefers stock.
Forms o f divestitures: equity carve-outs, spin-offs,
split-offs, and liquidations.
EQUITY
Holding period return:
P i— P o + C F ,
o
P i+ C F ,
-1
0
Required return: Minimum expected return an
investor requires given an asset’s characteristics.
Internal rate o f 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-C hen equity risk premium
[1 + i] x [1 + rEg] x [1 + PEg] - 1 + Y - RF
Models o f required equity return:
• CAPM\ r. = RF + (equity risk premium x (3.)
• M ultifactor m odel: required return = RF + (risk
premium) +
(risk premium) n
Fam a-French: r.j = RF + 13 mkt,j x (R mkt —RF)
+ ^SMB,j x ( P'small —
'big'
+ ^H
HML.j
M U X ^ H B M “ ^ LBM
)
continued on next page...
EQUITY continued...
• Pastor-Stambaugh model: 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
M Vequity
MV.debt
^Xdebt+equity
> a (i-T )+
^ ^ d e b t -(-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) M ethods
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 M odel (G G M )
Assumes perpetual dividend growth rate:
V0 =
r~g
Most appropriate for mature, stable firms.
Limitations are:
• Very sensitive to estimates of r and g.
• Difficult with non-dividend stocks.
• Difficult with unpredictable growth patterns (use
multi-stage model).
Present Value o f Growth Opportunities
V0 =
+ PVGO
H -M odel
_ D 0 x(l + gL)] | [P 0 x H x ( gs —gL)]
v0=
r ~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.
;ree 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.)
Single-Stage FC FF/FC FE Models
• For FCFF valuation: V 0 =
• For FCFE valuation: V 0 =
FCFFj
W ACC- g
FC FE 1
r~g
2-Stage FC FF/FC FE Models
Step 1: Calculate FCF in high-growth period.
Step 2: Use single-stage FCF model for terminal
value at end of 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 =
!+ g
1 + / ( j.k ) ]
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 M odel
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.
FCFE 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 Incom e Models
• RI = Et —(r x Br-i) = (ROE —r) x Bt_i
• Single-stage RI model:
V0 = B 0 +
T
1
.
F(i,k) = ---------------- --
justified P / B = R Q E ~ g
r~g
sales
1
(l + ST )
Forward price of zero-coupon bond:
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.
net income
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 [ DLOM .
• The payment o f dividends J, DLOM .
• Earlier, higher payments { DLOM .
• Restrictions on selling stock | DLOM .
• A greater pool of buyers J, DLOM .
Greater risk and value uncertainty | DLOM .
rT=
f-g
Normalization M ethods
• Historical average EPS.
• Average ROE.
RO E =
D LO C = 1 —
Price o f a T-period zero-coupon bond:
Justified dividend yield:
0
Private Equity Valuation
FIXED INCOME
( l - b ) ( l + g)
r~g
Do
Econom ic Value Added®
• EVA - NOPAT - $WACC; NOPAT - E B I T ( 1 - 1)
(RO E —r ) x B 0
r~g
• Multistage RI valuation: Vo = Bo + (PV of interim
high-growth RI) + (PV o f continuing RI)
Forward pricing model:
p0+k)
F(i.k) =
P;
J
Forward rate model:
[i +y(j>k)]k = [i + S(j+k)](j+k) / (i + s.)j
“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 LIBO R rate) —(3-month T-bill rate)
Libor-OIS spread
= LIBO 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)^r + a\[tdz
Vasicek model: dr = a(b - r)dt + ad z
Ho-Lee model: drt = 0t dt + ad z t
Managing yield curve shape risk:
AP/P = - D l A x l - D sA xs - D c;Axc
(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
v call„option
. |1 ,v put option
. T>v
1
callable bond1 5
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.
effective duration =
BV.Ay ~ BV+Ay
2 x BV q x Ay
continued on next page...
FIXED INCOME continued...
.
.
B V A + B V +A - ( 2 x B V 0 )
effective convexity = -------- -------------- -— -------------BV 0 x A y 2
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 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 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
DERIVATIVES
T
FP — Sq x (1 + R f )
So =
T
(1 + R f )
Value o f forward on dividend-paying stock
Vt (long position) = [St — PVD t —
(l + R f F - 1)
Forward: equity index (continuous dividend)
(R- - 8 c )xT
FP (on an equity index) = S 0 X e' *
'
^
where:
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 o f 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.
= S0 x ( l + R f )T — FVC
Return from bond credit rating migration: A % P
= -(modified duration o f bond) x (A spread)
Structural models 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
• equity » 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 CD S: Multiple borrowers, equally weighted.
Default: Occurrence o f a credit event.
Common credit events in CD S agreements:
Bankruptcy, failure to pay, restructuring.
CD S 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 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
(l + R f/ 7 - 1)
Q uoted bond futures price:
(full price)(l+Rf )T - AIT - FVC
1
C FJ
Price o f a currency forward contract:
(t x P „ J T
r bc
)
T
Value o f a currency forward contract
Vt =
[FPt — FP] x (contract size)
(i + n>c)<T-t)
Currency forward price (continuous tim e):
Fy = Sq X e
R c —R c
PC
BC
xT
Swap fixed rate:
C=
1 -Z
Z j + Z^2 + Z 3 + z 4
where: Z = 1/(1+ R J = price o f zero-coupon $1 bond
Value o f interest rate swap to fixed payer:
= X lz x (SFR jsjew —S F R o y ) x — x notional
360
Binom ial stock tree probabilities:
tcu =
probability o f up move = ^
^
U -D
tcd = probability o f a down move = (1 —i^ )
Put-call parity:
So + Po = Co + PV(X)
Put-call parity when the stock pays dividends:
P» + S„eJ,T = C 0 + e'rTX
ln(S / X ) + (r —6 + a 2 /2)T
a Vt
d-2 = dj — GyjT
Soe
FP
Price o f a bond futures contract:
FP = [(full price)(l+Rf)T - AIT - FVC]
full price = quoted spot price + AI0
(i + Rpc)
Black—Scholes—M erton option valuation model
C 0 = S 0e_8TN (d1) - e_rTXN (d2)
dl =
= (S 0 - P V C ) x ( l + R f )T
QFP = forward price /conversion factor
= h S o + i - h s + + p+ )
(1 + Rf )
5 = continuously compounded dividend yield
FP(on a fixed income security)
(i +
Po=hSo+
where:
= continuously com pounded dividend yield
F r = S0 x
„ _ LC. , ( - h S + + C + ) Lc , ( - h S - + C - )
C q — nor) H---------------------- = hon H---------------------0
0
(1 + R f )
(1 + R f )
P 0 = e~rTXN (-d 2) - S 0crnTSI(-d1)
R p = continuously com pounded risk-free rate
YtOong) = [St — PVCt —
Change in option value
A C ~ call delta x AS + Vi gamma x A S 2
A P « put delta x A S + Vi gamma x A S 2
(1 + Rf )
RfxT
S 0 x e - 6CxT X e r
straight value
# shares hedged
delta o f put option
O ption value using arbitrage-free pricing
FP
Value o f a forward on a coupon-paying bond:
market price of common stock
Premium over straight value
delta o f call option
# o f long put options = -
Price o f equity forward w ith discrete dividends
FP(on an equity security) = (SQ- P V D )x(l+ R f)T
market conversion premium per share
# shares hedged
FP
Forward price on a coupon-paying bond:
Market conversion premium per share
= market conversion price - stock’s market price
Market conversion premium ratio
market price o f convertible bond
# o f short call options =
Forward contract price (cost-of-carry model)
Sc
conversion ratio
Dynamic delta hedging
= stock price, less PV of dividends
O P T IO N S T R A T E G IE S :
Covered call = long stock + short call
Protective put = long stock + long put
Bull spread: Long option with low strike + short
option with higher strike. Profit if underlying $j\
Bear spread: strike price o f long > strike o f short
Collar = covered call + protective put
Long straddle = long call + long put (with same
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
%AP X
trading days until maturity
where
%AP =
absolute (breakeven p rice-cu rren t price)
current price
ALTERNATIVE INVESTMENTS
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 =
N O Ij
comparable sales price
,
NOL
„
stabalized NOI
value = Vq = ----------- or Vq = --------------------cap rate
cap rate
Property value based on “All Risks Yield”:
value = V () = rentj / ARY
gross income multiplier =
sales price
gross income
continued on next page...
ALTERNATIVE INVESTMENTS continued...
Term and reversion valuation approach:
total property value
= PV o f term rent + PV reversion to ERV
Layer approach:
total property value
= PV of term rent + PV o f incremental rent
Debt service coverage ratio:
first-year NO I
D SC R = ------ -------:----debt service
Loan-to-value (LTV) ratio:
^
loan amount
LTV = --------;-----------appraisal value
....
.
first year cash flow
equity dividend rate = -------------- ------------equity
NAV approach to R E IT share valuation:
estimated cash N OI
* assumed cap rate
= estimated value of operating real estate
+ cash & accounts receivable
—debt and other liabilities
= net asset value
shares outstanding
= NAV/share
Price-to-FFO approach to R E IT share valuation:
funds from operations (FFO)
shares outstanding
= FFO/share
x sector average P/FFO multiple
= NAV/share
Price-to-AFFO approach to R EIT 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 R E IT share valuation:
value o f a R EIT share
= PV(dividends for years 1 through n)
+ PV(terminal value at the end of 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: \ of multiple at exit, J, in debt.
VC: pre-money valuation, the investment, and
subsequent equity dilution.
Components o f perform ance (LBO ): earnings
growth, f o f multiple at exit, [ 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 o f Com m 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 o f 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 anagem ent 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) = R f + M V
+ M V + ••• + M V
Expected return = risk free rate
+ E (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 of 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
^Portfolio = W A°A +
+ 2W a WbCo va b
Annualized standard deviation
= V250 x (daily standard deviation)
% change in value vs. change in Y T M
= -duration (AY) + Vi 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 of consuming 1 unit in the future
marginal utility o f current consumption o f 1 unit
Real risk-free rate o f return =
1—P.0
0
E(mt)
-1
Default-free, inflation indexed, zero coupon:
E ft)
+ cov(Pj, n q )
(l + R)
Nominal short term interest rate (r)
= real risk-free rate (R) + expected inflation (tv)
Bond price = Pq =
Nominal long term interest rate = R + it + 0
where 6 = risk prem ium fo r inflation uncertainty
Break-even inflation rate (BEI)
7
^
^ n m i- in fl, r in n
in H p v p / 1 K d n H
7
^
^ i inflation
i
indexed bond
BEI for longer maturity bonds
= expected inflation (it) + infl. risk premium (0)
Credit risky bonds required return = R + it + 0 + q
where 7 = risk prem ium (spread) fo r credit risk
Discount rate for equity = R + iv + 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 + /tv + 0 + 7 + k , + <|>
k = term inal value risk, <p = illiquidity prem ium
Multifactor model return attribution:
k
factor return = ^ (/?pi — /?bi) X (Aj)
i=l
Active return
= factor return + security selection return
Active risk squared
= active factor risk + active specific risk
n
Active specific risk = ^ ^ wpi — wbi)2<Tei
i=l
Active return = portfolio return - benchmark return
R
a
= Rp" R
b
n
Portfolio return = Rp = y ^ w p j R ;
i=l
n
Benchmark return = Rg = ^ w g j R j
i=l
Information ratio
Rp — Rg
^(Rp-Rg)
R^
active return
aA
active risk
Portfolio Sharpe ratio = SRp = ^
Optimal level o f active risk:
^
STD(Rp)
Sharpe ratio = ^ S R g 2 + IR P2
Total portfolio risk: o p2 = ct b2 + a A2
Information ratio: IR = T C x IC x fiB R
Expected active return: E(RA) = IR x a A
“Full” fundamental law of active management:
E(Ra ) = (TC)(IC)V b R cta
Sharpe-ratio-maximizing aggressiveness level:
ISBN: 978-1-4754-7975-1
TR
STD(Ra ) = —— STD(Rg)
SR B
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.
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