LEV EL II SCHW ESER'
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r it ic a l
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2018
C F A ®
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ETHICAL AND PROFESSIONAL
STANDARDS
I
I (A)
I (B)
I (C )
I (D)
IIII (A)
II (B)
IIIHI (A)
HI (B)
HI (C)HI (D)
HI (E)
IVIV (A)
IV (B)
IV (C)
V
v (A)
V (B)
V (C)
VIVI (A)
VI (B)
VI (C)
VIIVII (A)
VII (B)
Professionalism Knowledge of the Law Independence and Objectivity Misrepresentation
Misconduct
Integrity of 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 of 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 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 =
(sx)(s y)
t-test for r (n - 2 d f): t = rVn — 2
Estimated slope coefficient: covxy
<J\
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 l i ) + (b2 x X 2l)
+ (b3 X X 3i) + £;
• Test statistical significance of b; H (): b = 0,
A /
t = y , n — k — 1 df
Reject if |t| > critical t or p-value < a . Confidence Interval: bj ± |tc X sg 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 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.
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.
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 of confidence in hypothesis tests of 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 of residuals not significant. Mean reverting level for A R(1):
bo (1 — b j)
RM SE: square root of 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 of ARCH series:
A 2 A A A 2 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
ECONOMICS
bid-ask spread = ask quote - bid quote Cross rates with bid-ask spreads:
'A '
vC,
'A 'vC,
bid 'A '
B ,
n >
X
bid
.B
C
offer /A X \ B ,
V ^ /
/ T-x \ X
offer bid B C \ ^ /offer
Currency arbitrage: “Up the bid and down the ask.” Forward premium = (forward price) - (spot price) Value of fwd currency contract prior to expiration:
(FPt — FP)(contract size) Vt =
1 + RA days
360 \
Covered interest rate parity:
1 + Ra
F = ^ ---days 360 / •0
1 + RB days
360 Uncovered interest rate parity:
e(%a s w , = R , - K Fisher relation:
R nominal real= R . + E(inflation) International Fisher Relation:
R . — R . nominal A 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 of 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 of 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. Neoclassical Growth T heory
• Sustainable growth rate is a function of population growth, labor’s share of income, and the rate of technological advancement.
Assumes diminishing returns to capital.
0 0
g* =
( 1 - a ) G* = ( 1 - a ) + A L
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 icial 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 ational friction s arise in the presence of information asymmetry.
• Externalities deal with provision of 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. 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 of 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 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. OCI).
• 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 Adjustment
If TPPC < firm contribution, difference = A in PBO (reclassify difference from CFF to CFO after-tax). 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 OCI; 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 E B T E B IT RO E = ---x ---x ---x
E B T E B IT revenue
T otal Asset T urnover
revenue X
Financial Leverage
average assets average assets average equity
Accruals Ratio (balance sheet approach)
(NOAEn d — NOABEg) accruals ratio ^ =
(NOAe n d + NOABEg) / 2
Accruals Ratio (cash flow statem ent approach)
(NI - CFO - CFI) accruals ratio ^ =
(NOAe n d + NOABEg) / 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 + NWCInv - T(Salr - B.r)
Capital Budgeting Replacement
• Same as expansion, except current after-tax salvage of 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:
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).
V = VV L V U
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 c g )
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 = previous
dividend +
expected increase in EPS
\
X /
target payout
ratio \
x 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 (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 of 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
H H I = ^ ( M S i X l 0 0 ) 2
i= l
Methods to Determ ine Target Value
D C F m ethod: target proforma FCF discounted at adjusted WACC.
Com parable company analysis-, target value from relative valuation metrics on similar firms + takeover premium.
Com parable transaction analysis: target value from takeover transaction; takeover premium included.
M erger Valuations
C om binedfirm :
Ya t = Va + Vt + 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 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:
= r = P l ~ p0 +c f i= p1 + c f l x
Po 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
+ ^ S M B .j X ^
Models of required equity return:
•
CAPM:
r. = RF + (equity risk premium x 0.) • M ultifiactor model: required return = RF + (riskpremium) j + ... + (risk premium) n • Fam a-French: r. = RF + 0 , . x (R — RF)j 1 mkt,j x mkt '
"small _ P y g) + ^ H M L .j X ~~ Pastor-Stam baugh model: 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
MVdebt
^ ^ d e b t+ equity
rd (l - T ) +
MV.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.
• 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: V „ = - ^
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 r
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 r ~gL
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 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 = 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 - WCInv + 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 A C C - 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.
Justified P /E
leading P/E = 1 - b r “ g trailing P/E = ^ - b) ( 1 + g)
r - g Justified dividend yield:
D o _ r - g 0 ! + g
Normalization Methods
• Historical average EPS. • Average ROE.
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:
(RO E — r ) x B 0 V0 = 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
1 D LO C = 1
-1 + Control Premium
Total discount = 1 - [(1 - D L O C )(l - DLOM )]. The D LO M varies with the following.
• An impending IPO or firm sale [ 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 o f a T-period zero-coupon bond: Py =
---y-(! + St )
Forward price o f zero-coupon bond:
Sno= —
i + Z O ’ k)) Forward pricing model:
B P()+k> F0 ’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: dr =Q dt+ ad zt t t Managing yield curve shape risk:
AP/P » - DlAx l - DsAxs - 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 straight V bond - Vcallable bond V = put putable V bond - Vstraight bond W hen interest rate volatility increases:
v . . T , v call option 1 put option . T> v1 callable bond'1 'k 5 V tputable 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 - BVhAy 2 x BV0 x Ay
. . BV Ay + BV+Ay - (2 > errective convexity = --- -—
BV0 x A y2 Effective duration:
One-sided durations: Callables have lower down- duration; 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
= greater0/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 of 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
recovery rate = % money received upon default Loss given default (%) = 100 — recovery rate Expected loss = prob. of 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
• equity « 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 of 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 CDS agreements: Bankruptcy, failure to pay, restructuring. C D 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) 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)
T - FP
FP — S0 x (l + R f ) So =
(i + R f)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 — PVDt — FP (l + R f F - ' J
Forward on equity index with continuous dividends
(r£ - 8c)xT FP (on an equity index) = SqX r
S o X e " 6CxT x e RrXTt where:
R Cf = continuously com pounded risk-free rate 8C = continuously com pounded dividend y ield
Forward price on a coupon-paying bond:
FP (on a fixed income security) = (S0 - PVC) x (1 + R f )T or
= SQ x (1 + R f )T — FVC
Value o f a forward on a coupon-paying bond:
Vt (long) = [St - P V C t ] - FP (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
Price o f a currency forward contract:
(l + R p c )T
1 C F j
Fr = S 0 x
(! + r Bc)T
Value o f a currency forward contract
_ [FPt - FP] X (contract size)
V t= (l + * c ) (T- r)
Currency forward price (continuous time)
F p = S0 x e
\
R c — R c PC B C) x T
Swap fixed rate:
1 - Z 4 C =
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:
= YjZ x (SFRjqew — SFRq 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)
Put-call parity:
S0 + Po = C o + PV (X)
Put-call parity when the stock pays dividends:
Po + S0e-*T = C 0 + e"rIX
Dynam ic delta hedging
# o f short call options = # shares hedged delta of 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
O ption value using arbitrage-free pricing portfolio
„ _ uc ( - h S + + C + ) Lc , (—h s - + c - )
C 0 — hoQ H--- --- -— = hS0 H—
Pq — hSn +0
(1 + R f ) (—hS~ + P ~ )
(l + R f)
— hS0 +
(1 + R f )
(—hS+ + P + )
(1 + R f )
Black-Scholes-M erton option valuation model
C 0 = S0e ^ N (d [) - e'rIXN (d2) P0 = e-*X N (-d 2) - S0e-6TN (-d 1) where:
8 = continuously compounded dividend yield
di =
ln(S/X) + ( r - 6 + a 2 /2)T a V T
d2 = di — a^/T
Sge ^ = stock price, less PV o f dividends
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 of short
Collar = covered call + protective put
Long straddle = long call + long put (with 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
252
trading days until maturity where
% A P = absolute (breakeven price — current 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
NOIf
cap rate
comparable sales price
value = Vq = NOIl
cap rate or V0 =
stabalized NOI cap rate Property value based on “All Risks Yield”:
value = V Q = rentj / ARY
Value o f a property using gross income multiplier: sales price gross income multiplier =
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
Debt service coverage ratio:
D SC R = firSt' year N Q I debt service
Loan-to-value (LTV) ratio:
loan amount LTV =
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 of a R EIT 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 C firm s relative to Buyouts): DCF not as common; equity, not debt, financing. Key drivers o f equity return:
Buyout: t 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, | of multiple at exit, [ in debt.
E xit routes (in order o f exit value, high to low): IPOs secondary mkt sales; M BO ; liquidation.
Performance M easurement: gross IR R = return from portfolio companies. Net IR R = relevant for LP, net of fees & carried interest.
Perform ance Statistics:
• PIC = % capital utilized by GP; cumulative sum of 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 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 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 long-dated 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) + Pp,A ) + ••• + Pp,A )
Expected return = risk free rate
+ E (factor sensitivity) x (factor risk premium)
Value at risk (VaR) is an estimate of 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 of 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 % fluid A + W °/o fluid BA D
^Portfolio = Wa4 + + 2 WaWbCo v a 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)
ISBN: 978-1-4754-5984-5
U.S. $ 29 .00 © 2 0 17 Kap l an , Inc. Al l Ri ght s Reser ved.
Inter-temporal rate of 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 =l - P o _ 1 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 jndCXed bond yield^a^op indexed bond BEI for longer maturity bonds
= expected inflation (t t) + infl. risk premium (0) Credit risky bonds required return = R + tt + 0 + 7
where7 = 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<Tei i=l
Active return = portfolio return - benchmark return
RaA - R b n
Portfolio return = Rp = ^ ^ w p j R ; i=l
n Benchmark return = Rg = ^ w g jRj
i=l
Information ratio
_ Rp — Rg _ R A _ active return ^(Rp—Rg) a A 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
dmizing aggressiveness
TR
— — ST D (R g)
jKr
Execution Algorithms: Break an order down into smaller pieces to minimize market impact.
