(LEVEL 2) schweser, kaplan CFA 2019 schweser level 2 schweser’s quicksheet CRITICAL CONCEPTS FOR THE 2019 CFA EXAM (2019)

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.

+ Mr

Variance o f ARCH series:
A9
A
A A9
CTt+l = a0 “b alet

(tcX Sb,

_____

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

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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.
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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

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.”
• Residual income: = NI - equity charge;
Utilitarianism: Produce the highest good for the
discounted at required return on equity.
largest number o f people.
• Claims valuation separates CFs based on equity
Kantian ethics: People are more than just an
claims (discounted at cost o f equity) and debt
economic input and deserve dignity and respect.
holders (discounted at cost o f debt).
Rights theories: Even if an action is legal, it may
M M Prop I (No Taxes): capital structure irrelevant
violate fundamental rights and be unethical.

(no taxes, transaction, or bankruptcy costs).
Justice theories: Focus on a just distribution of
VL= VU
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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

最新CFA、FRM、AQF、ACCA资料欢迎添加微信
continued on next page...
286982279


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)
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,

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)2i=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.

U.S. $29.00 © 2018 Kaplan, Inc. All Rights Reserved.


2018

CRITICAL
CONCEPTS
FOR THE
CFA EXAM

CFA® EXAM REVIEW

CFA LEVEL I
SMARTSHEET
®

FUNDAMENTALS FOR CFA® EXAM SUCCESS

WCID184


efficientlearning.com/cfa

ETHICAL AND
QUANTITATIVE METHODS
PROFESSIONAL STANDARDS TIME VALUE OF MONEY
ETHICS IN THE INVESTMENT PROFESSION

STANDARDS OF PROFESSIONAL CONDUCT

PV =

FV
(1 + r) N

risk (higher is better)

• PV and FV of ordinary annuity and annuity due
PVAnnuity Duee = PVOrdinar
inary
y Annuity × (1 + r)
FVAnnuity Duee = FVOrdinar
inary
y Annuity × (1 + r)

PMT
I/Y

360 − (t × rBD )

R G =  n (1 + R1 ) × (1 + R 2 ) ×…×
×… × (1 + R n )  − 1
R MM = HPY × (360/t)

Bond Equivalent
Yieldmean: used to determine the average cost of
• Harmonic

historical performance when first claiming compliance,
then add one year of compliant performance each
subsequent year so that the firm eventually presents a
(minimum) performance record for 10 years.
• Nine major sections: Fundamentals of Compliance; Input
data; Calculation Methodology; Composite Construction;
Disclosures; Presentation and Reporting; Real Estate;

Private Equity; and Wrap Fee/Separately Managed
Account (SMA) Portfolios.

shares purchased
over time
0.5
BEY = [(1 + EAY)

− 1] × 2

Harmonic mean: X H =

N
1

N

∑x
i =1

i

• Variance: average of the squared deviations around the
mean
n

2

σ =

∑ (X i − µ)2
i =1

n

∑ (X i − X)
i =1

sp

PROBABILITY CONCEPTS
• Expected value and variance of a random variable (X)
using probabilities

E(X) = P( X1 ) X1 + P(X 2 )X 2 + … P(X
X n )X
)X n

n

σ 2 (X) = ∑ P(X i ) [X
[ X i − E (X)]2
i =1

• Covariance and correlation of returns
Corr(R A ,R B ) = ρ(R A ,R
,RB) =

2

Cov(R
R A ,R
,RB)
(σ A )(σ B )

• Expected return on a portfolio
N

E(R
R p ) = ∑ wi E
E(R
(R i ) = w1E(R
R1 ) + w 2 E
E(R
(R 2 ) +
i =1

+ w N E(R
RN )

• Variance of a 2-asset portfolio
Va R p ) = w2A σ 2 ((R
Var(
R A ) + w2B σ 2 ((R
R B ) + 2w A w Bρ((R
R A ,,R
R B )σ (R A )σ ((R
RB)

BINOMIAL DISTRIBUTION

• Probability of x successes in n trials (where the

probability of success, p, is equal for all trials) is given by:

P(X
X = x)
x) = nCx (p))x ((1 – p)n – x

• Expected value and variance of a binomial random
variable

E(x) = n × p
σ 2 = n × p × (l-p)

NORMAL DISTRIBUTION
•
•
•
•
•
•

50% of all observations lie in the interval µ ± (2/3)σ
68% of all observations lie in the interval µ ± 1σ
90% of all observations lie in the interval µ ± 1.65σ
95% of all observations lie in the interval µ ± 1.96σ
99% of all observations lie in the interval µ ± 2.58σ
A z-score is used to standardize a given observation of a
normally distributed random variable
z = (obser

erve
ved value − population mean)/standard
nda deviationn = (x − µ) /σ
ndard

• Roy’s safety-first criterion: used to compare shortfall risk
of portfolios (higher SF ratio indicates lower shortfall
risk)

Shortf
hortfal
hortf
tfall ratio (SF Ratio) =

n

s2 =

rp − rf

platykurtic (negative excess kurtosis), mesokurtic (same
kurtosis as normal distribution; i.e. zero excess kurtosis)

Professionalism
DISCOUNTED CASH FLOW APPLICATIONS
A. Knowledge of the Law
• Positive net present value (NPV) projects increase
B. Independence and Objectivity
shareholder wealth.
C. Misrepresentation

•
For mutually exclusive projects, choose the project with
D. Misconduct
the highest positive NPV.
II. Integrity of Capital Markets
• Projects for which the IRR exceeds the required rate of
A. Material Nonpublic Information
return will have positive NPV.
B. Market Manipulation
• For mutually exclusive projects, use the NPV rule if the
III. Duties to Clients
NPV and IRR rules conflict.
A. Loyalty, Prudence and Care
YIELDS FOR US TREASURY BILLS
B. Fair Dealing
C. Suitability
• Bank discount yield
D. Performance Presentation
D 360
rBD = ×
E. Preservation of Confidentiality
F
t
IV. Duties to Employers
• Holding period yield
A. Loyalty
B. Additional Compensation Arrangements
P − P + D1 P1 + D1
HPY = 1 0
=

−1
P0
P0
C. Responsibilities of Supervisors
V. Investment Analysis, Recommendations and Actions
• Money market yield
A. Diligence and Reasonable Basis
360
0 × rBD
B. Communication with Clients and Prospective
R MM =
360 − (t × rBD )
Clients
C. Record Retention
R MM = HPY × (360/t)
DiscounTeD cash floW applicaTions
VI. Conflicts of Interest
A. Disclosure of Conflicts
• Effective annual yield
B. Priority of Transactions
Effective Annual Yield
C. Referral Fees
EAY = (1 + HPY)365/ t − 1
VII. Responsibilities as a CFA Institute Member or CFA
where:
Candidate
HPY =STATISTICAL
holding period yield CONCEPTS
A. Conduct as Participants in CFA Institute Programs
t = numbers of days remaining till maturity

• Data scales: Nominal (lowest), Ordinal, Interval, Ratio
B. Reference to CFA Institute, the CFA Designation,
HPY
= (1 + EAY) t /365 − 1
(highest)
and the CFA Program
•
Arithmetic
Money Market Yield mean: simple average
GLOBAL INVESTMENT PERFORMANCE
• Geometric mean return: used to average rates of change
360 × rBD
STANDARDS (GIPS®)
(or
over time
=
R
MMgrowth)
is voluntary.

Sharpe
ar ratio =
arpe

• Positive skew: mode < median < mean
• Kurtosis: leptokurtic (positive excess kurtosis),

• PV of a perpetuity
PVPerpetuity =

• Compliance by investment management firms with GIPS

s
X

• Sharpe ratio: used to measure excess return per unit of

I.

basis in order to claim compliance.

Coefficient of variatio
ar
ariatio
n=

flow

situational influences, focusing on the immediate rather
than long-term outcomes/consequences.
• General ethical decision-making framework: identify,
consider, decide and act, reflect.
• CFA Institute Professional Conduct Program sanctions:
public censure, suspension of membership and use of
the CFA designation, and revocation of the CFA charter
(but no monetary fine).

• Third-party verification of GIPS compliance is optional.
• Present a minimum of five years of GIPS-compliant

dispersions of data sets (lower is better)

• Present value (PV) and future value (FV) of a single cash

• Challenges to ethical behavior: overconfidence bias,

• Comply with all requirements of GIPS on a firm-wide

• Standard deviation: positive square root of the variance
• Coefficient of variation: used to compare relative

E (RP ) − RT
σP

n −1

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SAMPLING THEORY

TECHNICAL ANALYSIS

MARKET STRUCTURES

• Central limit theorem: Given a population with any

• Reversal patterns: head and shoulders, inverse head

• Perfect competition
• Minimal barriers to entry, sellers have no pricing power.
• Demand curve faced by an individual firm is perfectly

probability distribution, with mean, µ, and variance,
σ2, the sampling distribution of the sample mean x,
computed from sample size n will approximately be
normal with mean, µ (the population mean), and
variance, σ2/n, when the sample size is greater than or
equal to 30.
• The standard deviation of the distribution of sample
means is known as the standard error of sample mean.
• When the population variance is known, the standard
error of sample mean is calculated as
σx = σ

• When the population variance is not known, the standard
error of sample mean is calculated as

s
sx =
n

• Confidence interval for unknown population parameter
based on z-statistic
σ
n

based on t-statistic

2

Small Sample Large Sample
n < 30
n > 30

When Sampling from a:

Normal distribution with known variance

z‐statistic

z‐statistic

Normal distribution with unknown variance

t‐statistic

t‐statistic*

Non-normal distribution with known variance

not available

z‐statistic

Non-normal distribution with unknown variance

not available

t‐statistic*

* Use of z‐statistic is also acceptable

HYPOTHESIS TESTING

H0 : μ ≤ μ0

Null
hypothesis

Alternate
hypothesis
Ha : μ > μ0

One tailed
(lower tail)
test

H0 : μ ≥ μ0

Two‐tailed

H0 : μ = μ0

Fail to reject
null if

Reject null if
Test statistic >

critical value

Test statistic ≤
critical value

P‐value represents
Probability that lies
above the computed test
statistic.

Ha : μ < μ0

Test statistic <
critical value

Test statistic ≥
critical value

Probability that lies
below the computed test
statistic.

Ha : μ ≠ μ0

Test statistic <
lower critical
value
Test statistic >
upper critical
value

Lower critical
value ≤ test
statistic ≤
upper critical
value

Probability that lies
above the positive
value of the computed
test statistic plus the
probability that lies
below the negative
value of the computed
test statistic.

• Type I versus Type II errors
Decision
Do not reject H0

H0 is True
Correct decision
Incorrect decision
Type I error
Significance level =
P(Type I error)

Reject H0

H0 is False

Incorrect decision
Type II error
Correct decision
Power of the test
= 1 − P(Type II error)

• Hypothesis test concerning the mean of a single
population
x − µ0
s n

• Hypothesis test concerning the variance of a normally
distributed population
( n − 1) s

2

σ 20

• Hypothesis test related to the equality of the variance of
two populations

F=

s12
s22

pricing power.

• Product is differentiated through non-price strategies.

• Demand curve faced by the monopoly is the industry
demand curve (downward sloping).

• An unregulated monopoly can earn economic profits
in the long run.

• Monopolistic competition
• Low barriers to entry, sellers have some degree of
pricing power.

non-price strategies.

• Own-price elasticity of demand is calculated as:

• Oligopoly
• High costs of entry, sellers enjoy substantial pricing
power.

%∆Q
QDx
… (Equation 6)
%∆Px

• Product is differentiated on quality, features,

equals 1, demand is said to be unit elastic.
• If the absolute value of price elasticity of demand
lies between 0 and 1, demand is said to be relatively
inelastic.
• If the absolute value of price elasticity of demand is

greater than 1, demand is said to be relatively elastic.
• Income elasticity of demand is calculated as:
% change in quantity demanded
% change in income

marketing and other non-price strategies.

• Pricing strategies: pricing interdependence (kinked

demand curve), Cournot assumption, game theory
(Nash equilibrium), Stackelberg model (dominant
firm).
• Firms always maximize profits at the output level where
MR = MC
• Identification of market structure
• N-firm concentration ratio.
• HHI (add up the squares of the market shares of each
of the largest N companies in the market).

AGGREGATE SUPPLY AND DEMAND

• Cross-price elasticity of demand is calculated as:
EC =

make normal profits.

• Monopoly
• High barriers to entry, single seller has considerable

• Demand curve faced by each firm is downward sloping.

• In the long run all will make normal profits.

• Positive for a normal good.
• Negative for an inferior good.

• One-tailed versus two-tailed tests

χ2 =

ECONOMICS

EI =

elastic (horizontal).

• Average revenue (AR) = Price (P) = MR.
• In the long run, all firms in perfect competition will

• Product is differentiated through advertising and other

• If the absolute value of price elasticity of demand

• When to use z-statistic or t-statistic

t-stat =

•

EDPx =

s
n

Type of test
One tailed
(upper tail)
test

•

DEMAND ELASTICITIES

• Confidence interval for unknown population parameter
x ± tα

•

•

n

x ± z α /2

•

and shoulders, double top and bottom, triple top and
bottom.
Continuation patterns: triangles (ascending/descending/
symmetrical), rectangles, flags and pennants.
Price-based indicators: moving averages, Bollinger

bands, momentum oscillators (rate of change, relative
strength index, stochastic, moving average convergence/
divergence).
Sentiment indicators: opinion polls, put-call ratio, VIX,
margin debt levels, short interest ratio.
Flow of funds indicators: Arms index, margin debt,
mutual fund cash positions, new equity issuance,
secondary offerings.
Cycles: Kondratieff (54-year economic cycle), 18-year
(real estate, equities), decennial (best DJIA performance
in years that end with a 5), presidential (third year has
the best stock market performance).

% change in quantity demanded
% change in price of substitute or complement

• Components of GDP
• Expenditure approach
GDP = C + I + G + (X
(X − M
M)

• Income approach

• Positive for substitutes.
• Negative for complements.

• Normal good: substitution and income effects reinforce
one another.

• Inferior good: income effect partially mitigates the

substitution effect.
• Giffen good: inferior good where the income effect
outweighs the substitution effect, making the demand
curve upward sloping.
• Veblen good: status good with upward sloping demand
curve.

GDP = National income + Capital consumption allowance
+ Statistical discrepancy
… (Equation 1)

• Equality of Expenditure and Income
S = I + (G − T) + ( X − M) … (Equation 7)

• To finance a fiscal deficit (G – T > 0), the private sector
must save more than it invests (S > I) and/or imports
must exceed exports (M > X).
• Factors causing a shift in aggregate demand (AD)

PROFIT MAXIMIZATION, BREAKEVEN AND
SHUTDOWN ANALYSIS

An Increase in the
Following Factors

Shifts the AD Curve

Reason

Stock prices

Rightward: Increase in AD

Higher consumption

• Profits are maximized when the difference between total

Housing prices

Rightward: Increase in AD

Higher consumption

Consumer confidence

Rightward: Increase in AD

Higher consumption

Business confidence

Rightward: Increase in AD

Higher investment

Capacity utilization

Rightward: Increase in AD

Higher investment

Government spending

Rightward: Increase in AD

Government spending a component
of AD

Taxes

Leftward: Decrease in AD

Lower consumption and investment

Bank reserves

Rightward: Increase in AD

Lower interest rate, higher
investment and possibly higher
consumption

Exchange rate (foreign
currency per unit
domestic currency)

Leftward: Decrease in AD

Lower exports and higher imports

Global growth

Rightward: Increase in AD

Higher exports

revenue (TR) and total cost (TC) is at its highest. The level
of output at which this occurs is the point where:
• Marginal revenue (MR) equals marginal cost (MC); and
• MC is not falling
• Breakeven occurs when TR = TC, and price (or average
revenue) equals average total cost (ATC) at the breakeven
quantity of production. The firm is earning normal profit.
• Short-run and long-run operating decisions
Revenue/ Cost Relationship

Short-run Decision

Long-run Decision

TR = TC

Continue operating

Continue operating

TR > TVC, but < TC

Continue operating

Exit market

TR < TVC

Shut down production

Exit market

• Factors causing a shift in aggregate supply (AS)
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An Increase in

Shifts SRAS

Shifts LRAS

Reason

Supply of labor

Rightward

Rightward

Increases resource base

Supply of natural resources

Rightward

Rightward

Increases resource base

Supply of human capital

Rightward

Rightward

Increases resource base

Supply of physical capital

Rightward

Rightward

Increases resource base

Productivity and technology

Rightward

Rightward

Improves efficiency of inputs

Nominal wages

Leftward

No impact

Increases labor cost

Input prices (e.g., energy)

Leftward

No impact

Increases cost of production

Expectation of future prices

Rightward

No impact

Anticipation of higher costs and/or
perception of improved pricing
power

Business taxes

Leftward

No impact

Increases cost of production

Subsidy

Rightward

No impact

Lowers cost of production

Exchange rate

Rightward

No impact

Lowers cost of production

• Impact of changes in AD and AS

An increase in AD
A decrease in AD
An increase in AS
A decrease in AS

Real GDP

Unemployment
Rate

Aggregate Level
of Prices

Increases
Falls
Increases
Falls

Falls
Increases
Falls
Increases

Increases
Falls
Falls
Increases

• Effect of combined changes in AD and AS
Change in AS

Change in AD

Effect on Real

GDP

Increase
Decrease
Increase
Decrease

Increase
Decrease
Decrease
Increase

Increase
Decrease
Uncertain
Uncertain

Effect on Aggregate
Price Level
Uncertain
Uncertain
Decrease
Increase

BUSINESS CYCLES
• Phases: trough, expansion, peak, contraction (or
recession)

• Theories
• Neoclassical (Say’s Law).

• Austrian (misguided government intervention).
• Keynesian (advocates government intervention during
a recession).

• Monetarist (steady growth rate of money supply).
• New Classical (business cycles have real causes, no
government intervention).

• Neo-Keynesian (prices and wages are downward

sticky, government intervention is useful in eliminating
unemployment and restoring macroeconomic
equilibrium).
• Unemployment: natural rate vs frictional vs structural
vs cyclical.
• Prices indices: using a fixed basket of goods and
services to measure the cost of living results in an
upward bias in the computed inflation rate due to
substitution bias, quality bias and new product bias.
• Economic indicators
• Leading (used to predict economy’s future state).
• Coincident (used to identify current state of the
economy).
• Lagging (used to identify the economy’s past
condition).

MONETARY AND FISCAL POLICY
• Quantity theory of money
MV = PY

• Contractionary monetary policy (reduce money supply
and increase interest rates) is meant to rein in an
overheating economy. Expansionary monetary policy
(increase money supply and reduce interest rates) is
meant to stimulate a receding economy
• Limitations of monetary policy:
• Central bank cannot control amount of savings.
• Central bank cannot control willingness of banks to
extend loans.
• Central bank may lack credibility.
• Contractionary fiscal policy (reduce spending and/
or increase taxes) is used to control inflation in an

expansion. Expansionary fiscal policy (increase spending
and/or reduce taxes) is used to raise employment and
output in a recession
• Fiscal multiplier
1
[1 − MPC(1 − t )]

FINANCIAL REPORTING
AND ANALYSIS
FINANCIAL REPORTING BASICS
• Types of audit opinions: unqualified, qualified, adverse,

• Limitations fiscal policy: recognition, action and

impact lags
• Relationships between monetary and fiscal policy
• Easy fiscal policy/tight monetary policy – results in

higher output and higher interest rates (government
expenditure would form a larger component of
national income).
• Tight fiscal policy/easy monetary policy – private
sector’s share of overall GDP would rise (as a result
of low interest rates), while the public sector’s share
would fall.
• Easy fiscal policy/easy monetary policy – this would
lead to a sharp increase in aggregate demand, lowering
interest rates and growing private and public sectors.
• Tight fiscal policy/tight monetary policy – this would
lead to a sharp decrease in aggregate demand, higher
interest rates and a decrease in demand from both
private and public sectors.

disclaimer.

• Accruals: unearned or deferred revenue (liability),

unbilled or accrued revenue (asset), prepaid expenses
(asset), accrued expenses (liability).
• Qualitative characteristics of financial information:
relevance, faithful representation, comparability,
verifiability, timeliness, understandability (first two are
fundamental qualitative characteristics).
• General features of financial statements: fair
presentation, going concern, accrual basis, materiality
and aggregation, no offsetting, frequency of reporting,
comparative information, consistency.

INCOME STATEMENTS
• Revenue recognition methods: percentage of
•

INTERNATIONAL TRADE
• Comparative advantage: a country’s ability to produce

a good at a lower opportunity cost than its trading
partners
• Ricardian model: labor is the only variable factor of
production and differences in technology are the key
source of comparative advantage.
• Heckscher-Ohlin model: capital and labor are variable
factors of production and differences in factor
endowments are the primary source of comparative
advantage.
• Effect of tariffs, import quotas, export subsidies and
voluntary export restraints
• Price, domestic production and producer surplus
increase.
• Domestic consumption and consumer surplus
decrease.
• Balance of payments components
• Current account (merchandise trade, services, income
receipts and unilateral transfers).
• Capital account (capital transfers and sales/purchases
of non-produced, non-financial assets).
• Financial account (financial assets abroad and foreignowned financial assets in the reporting country).
• Current account surplus or deficit.

•
•

•

completion, completed contract, installment method,
cost recovery method.
Discontinued operations: reported net of tax as a
separate line item after income from continuing
operations.
Unusual or infrequent items: listed as separate line
items, included in income from continuing operations,
reported before-tax.
Accounting changes
• Change in accounting principle (applied
retrospectively).
• Change in an accounting estimate (applied
prospectively).
• Correction of prior-period errors (restate all priorperiod financial statements).
Basic EPS

Basic EPS =

Net incomee − Preferred dividends
Weighted average number of share
ha s outstanding
hare

• Diluted EPS (taking into account all dilutive securities)
Diluted EPS =

Conver
Convertible
Conver
 Convertible

prefe
pref
eferred
rred + 
× (1 − t)
debt
 interest

dividends
Shares from
Shares from
Weighted
Shares
conversion
conve
convers
rsio
ion
n of
of
conversion of + issuable from
+
average +
convertible

convertible
conver
convertible
stock options
shares
prefe
ef rred shares
efe
debt

Net income − Preferred  +
dividends 


BALANCE SHEETS
• Accounting for gains and losses on marketable securities

CA = X – M = Y – (C + I + G)

CURRENCY EXCHANGE RATES

Balance Sheet

Held‐to‐Maturity
Securities
Reported at cost or
amortized cost.

• Exchange rates are expressed using the convention

A/B; i.e. number of units of currency A (price currency)
required to purchase one unit of currency B (base
currency). USD/GBP = 1.5125 means that it will take
1.5125 USD to purchase 1 GBP.
• Real exchange rate
Real exchange rate DC/FCC = SDC/
PFC //P
PDC )
C/FC
FC × ((P

• Forward exchange rate (arbitrage-free)
FDC/FC =

1
SFC/DC

×

(1 + rDC )
(1 + rDC )
or FDC/FC = SDC/FC
C/FC ×
(1 + rFC )
(1 + rFC )

• Exchange rate regimes: dollarization, monetary union,

fixed parity, target zone, crawling pegs, fixed parity with
crawling bands, managed float, independently floating

rates.

Items recognized
on the income
statement

Interest income.
Realized gains and
losses.

Available‐for‐Sale Securities
Reported at fair value.

Trading Securities
Reported at fair value.

Unrealized gains or losses due
to changes in market values are
reported in other comprehensive
income within owners’ equity.
Dividend income.
Dividend income.
Interest income.

Interest income.

Realized gains and losses.

Realized gains and losses.
Unrealized gains and losses

due to changes in market
values.

• Common-size balance sheet: expresses each balance

sheet as a % of total assets to allow analysts to compare
firms of different sizes

CASH FLOW
• CFO (direct method)
• Step 1: Start with sales on the income statement.
• Step 2: Go through each income statement account

and adjust it for changes in all relevant working capital
accounts on the balance sheet.
• Step 3: Check whether changes in these working
capital accounts indicate a source or use of cash.
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• Step 4: Ignore all non-operating items and non-cash

charges.
• CFO (indirect method)
• Step 1: Start with net income.
• Step 2: Go up the income statement account and
remove the effect of all non-cash expenses and gains
from net income.

• Step 3: Remove the effect of all non-operating activities
from net income.
• Step 4: Make adjustments for changes in all working
capital accounts.
• Free cash flow to the firm (FCFF)
FCFF = NI + NCC
C + [In
[[Int
Intt * (1 − tax rate)]] − FCI
FCInv
F
CInv
nv − WCInv
FCFF = CFO
CFO + [[Int * (1 − tax
tax rat
rrate)]
ate)
e)]] − F
FCInv

• Profitability ratios

Operating profit
of margin =
ofit

Pretax margin =

reserve

• Net income under FIFO = Net income under LIFO +
Change in LIFO reserve × (1 – tax rate)

• Equity under FIFO = Equity under LIFO + LIFO reserve ×

Operating profit
Revenue

(1 – tax rate)

• Liabilities under FIFO = Liabilities under FIFO + LIFO

EBT (earnings
ear
earnings
before tax, but afte
af r interes
nter t)
nteres
Revenue

Net profit margin =

reserve × tax rate

LONG-LIVED ASSETS

Net profit
Revenue

• Capitalizing vs expensing

Net income
ROA =
Average total assets

Adjusted ROA =

• Free cash flow to equity (FCFE)
FCFE = CFO − FCInv + Net borrowing

• COGS under FIFO = COGS under LIFO – Change in LIFO

Gross profit
Gross profit margin =
Revenue

Net incomee + Inter
nteres
est expense (1 − Tax rate)
Average total assets

Operating ROA =

Operating income or EBIT
Average total assets

FINANCIAL ANALYSIS TECHNIQUES
• Activity ratios

Return on total capital =
Cost of goods sold
Average inventory
nventor
nventory

Inventory
y tturnover =

Days of inventor
invent y on hand (DOH) =

Receivabless tturnover =

365
Inventory
nventory turnove
nventor
ur
r

Revenue
Average receivables

365
Days of sales outstanding (DSO) =
Receivables turnove
tur
r

Payabless tturnover =

Purchases
Averagee ttrade payables

Depreciation expense =
Net income
Return on equity =
Average total equity

Revenue
Average working
or
orking
capital

Revenue
Average total assets

• Liquidity ratios
Current ratio
at =
atio

Quick ratio
at =
atio

Cash ratio =

Current assets
Current liabilities

Cash + Shor
ortt-term marketable investments + Receivables
Current liabilities

Cash + Shorthor term mark
hortma etable investments
Current liabilities

Defensive interval ratio =

Cash + Shor
hortt-term marketable investments + Receivables
Daily cash expenditures

Cash conversion cycle = DSO + DOH − Number of days of payables

• Solvency ratios
Debt -to-assets
ratio =

Net incomee − Preferred dividends
Average common equity

DDB depreciatio
depr
n in Year X =

Depreciation Components

ROE =

↓

↓

ROA

Leverage

Net income
Average total assets
Revenue
×
×
Revenue
Average total assets Average share
ha holders’ equity
hare
↓

↓

Net profit margin

ROE =

Interest burden

Assett ttur
urnover
urnove

↓

↓

Leverage

Accumulated depreciation
Annual depreciation expense

Remaining useful life
lif =

Net investment in fixed assets
Annual depreciation expense

model under US GAAP).

Net income EBT
Average total assets
EBIT
Revenue
×
×
×
×

EBT
EBIT Revenue Average total assets Avg. shareholders
eholde ’ equity
eholders
↓

↓

↓

Tax burden

EBIT margin

Leverage

• Dividend-related measures
Dividend payout ratio
at =
atio

Retention Rate =

Common share
ha dividends
hare
Net income attributable
ttr
ttributable
to common share

ha s
hare

Net income attributable
ttr
ttributable
to common share
ha s − C
hare
Common share
ha dividends
hare
Net income attributable
ttr
ttributable
to common share
ha s
hare

Sustainable growth rate = Retention rate × ROE

INVENTORIES

• If revaluation initially decreases the asset’s carrying

amount, the decrease is recognized as a loss on the
income statement.
• If revaluation initially increases the asset’s carrying
amount, the increase goes directly to equity.
• Impairment of property, plant and equipment

• IFRS: asset is impaired when its carrying amount
exceeds its recoverable amount (impairment loss is the
difference between these two amounts).
• US GAAP: asset is impaired when its carrying value
exceeds the total value of its undiscounted expected
future cash flows (impairment loss is the difference
between the asset’s carrying value and its fair value).

DEFERRED TAXES
(DUE TO TEMPORARY DIFFERENCES)
• A deferred tax liability (asset) arises when:
• Taxable income is lower (higher) than pretax
accounting profit.

• Taxes payable is lower (higher) than income tax
expense.

• If a company has a DTL, a reduction (increase) in tax rates

Total debt
Shareholders
eholde ’ equity
eholders

EBIT
Interest coverage ratio =
Interest payments

Average age of asset =

• Revaluation of long-lived assets
• IFRS allows revaluation model or cost model (only cost

• LIFO vs FIFO with rising prices and stable inventory levels

Average total assets
Average total equity

Gross investment in fixed assets
Annual depreciation expense

↓

Assett ttur
urnover
urnove

Total debt
Total assets

Financial leverage ratio =

Estimated useful
ef life
eful
lif =
Net income
Average total assets
ROE =
×

Average total assets Average share
ha holders’ equity
hare

Total debt
Debt -to-capital
ratio
at =
atio
Total debtt + S
Share
ha holders’ equity
hare
Debt -to-equity
ratio =

2
× Book value att tthe beginning of Year X
Depreciable life
lif

• Depreciation components

Revenue
Fixed assett tturnover =
Averagee ffixed assets
Total assett tturnover =

Original cost − Salvage value
Depreciable life

lif

• Double declining balance (DDB)

• DuPont decomposition of ROE

365
Number of days of payables =
Payables turnove
tur
r
Working capital turnover =

Expensing
Lower
Higher
Lower
Lower
Lower
Higher
Higher
Higher

• Depreciation expense
• Straight line

EBIT
Shorthor term debt + Long-term debt + Equity
hort-

Return on common equity =

Capitalizing
Higher
Lower
Higher
Higher
Higher
Lower
Lower
Lower

Net income (first year)
Net income (future years)
Total assets
Shareholders’ equity
Cash flow from operations
Cash flow from investing
Income variability
Debt-to-equity

• LIFO to FIFO conversion with rising prices and stable or
rising inventory quantities
• Inventory under FIFO = Inventory under LIFO + LIFO
reserve

would reduce (increase) liabilities, reduce (increase)
income tax expense, and increase (reduce) equity
• If a company has a DTA, a reduction (increase) in tax rates
would reduce (increase) assets, increase (reduce) income

tax expense, and reduce (increase) equity
• DTA carrying value should be reduced to the expected
recoverable amount using a valuation allowance
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ACCOUNTING FOR BONDS

• Dividend discount model

RISK MANAGEMENT

• Effective interest method required under IFRS and

D
re = 1 + g
P0

• Financial risks: market, credit (default or counterparty

• Bond yield plus risk premium

• Non-financial risks: settlement, legal, compliance

preferred under US GAAP
• Interest expense for a given period is calculated as
the book value of the liability at the beginning of the
period multiplied by market interest rate at bond

issuance.
• Coupon payments are classified as cash outflows.
• Book value of the bond liability at any point in time is
the PV of the bond’s remaining cash flows (discounted
at the market interest rate at issuance).

LEASES
• Lease accounting from lessee’s perspective: treating a

lease as a finance lease (compared to an operating lease)
results in:
• Higher assets, current liabilities, long-term liabilities,
EBIT, CFO, leverage ratios.
• Lower net income (early years), CFF, asset turnover,
current ratio, ROA (early years), ROE (early years).
• Same total cash flow.

FINANCIAL REPORTING QUALITY
• Conditions conducive to issuing low quality financial
reports: opportunity, motivation, rationalization

• Mechanisms that discipline financial reporting

quality: markets, regulatory authorities, registration
requirements, auditors, private contracting

CORPORATE FINANCE
CORPORATE GOVERNANCE
• Key areas of interest: economic ownership and voting

control, board of directors representation, remuneration
and company performance, investors in the company,
strength of shareholders’ rights, managing long-term
risks

CAPITAL BUDGETING
• Consider incremental after-tax cash flows, externalities
•
•
•
•

•

and opportunity costs. Ignore sunk costs and financing
costs from calculations of operating cash flows
For mutually exclusive projects, use the NPV rule if the
NPV and IRR rules conflict
Payback period ignores time value of money, risk of
the project and cash flows that occur after the payback
period is reached
Discounted payback period ignores cash flows that occur
after the payback period is reached
Average Accounting Rate of Return (ratio of project’s
average net income to its average book value) is based
on accounting numbers and ignores the time value of
money
Profitability index (PI): PI exceeds 1 when NPV is positive
PI =

(including regulatory, accounting and tax risks), model,
operational, solvency
• Methods of risk modification: risk prevention/avoidance,
risk acceptance (self-insurance and diversification), risk
transfer, risk shifting/modification

re = rd + risk premium

• Project beta
• unleveraged beta for a comparable asset




1
β ASSET

ASSET = β E
EQUITY 
D


 1 + (1 − t )



E 


PORTFOLIO RISK AND RETURN

• Beta for a project using a comparable asset releveraged

• Weighted average cost of capital (WACC)
WACC = (wd )(r
)(rd ))(1
(1 − t) + (wp )(r
)(rp ) + (we )(r
)(re )

• Cost of preferred stock
dp

vp

• Cost of equity
• Capital asset pricing model (CAPM)
re = R F + β i [E(R M ) − R F ]

• Utility function
1
U = E(R
E(R)
E
(R)) − Aσ 2
2

for target company

D 

 
β PROJEC
PROJECT
PR
OJECT
T = β ASSET
ASSET 1 +  (1 − t )  
E 


• The higher the correlation between the individual assets,

MEASURES OF LEVERAGE
• Degree of operating leverage (DOL)

•

Percentage change in operating income
DOL =
Percentage change in units sold

•

• Degree of financial leverage (DFL)
DFL =

Percentage change in net income
Percentage change in operating income

•

• Degree of total leverage (DTL)
DTL =

•

Percentage change in net income
Percentage change in the number of units sold

DTL = DOL × DFL

•

• Breakeven quantity of sales = (Fixed operating costs +

the higher the portfolio’s standard deviation and the
lower the diversification benefits (no diversification
benefits with a correlation coefficient of +1)
The Markowitz efficient frontier contains all the possible
portfolios in which rational, risk-averse investors will
consider investing
Optimal capital allocation line: line drawn from the riskfree asset to a portfolio on the efficient frontier, where
the portfolio is at the point of tangency. The optimal CAL
offers the best risk-return tradeoff to an investor
The point where an investor’s indifference (utility) curve
is tangent to the optimal CAL indicates the investor’s
optimal portfolio
With homogenous expectations, the capital market line
(CML) becomes a special case of the optimal CAL, where
the tangent portfolio is the market portfolio

CML equation (slope of line is called the market price
of risk)

Equation of CML

Fixed financial costs) ÷ Contribution margin per unit

E(R
Rp ) = Rf +

• Operating breakeven quantity of sales = Fixed operating
costs ÷ Contribution margin per unit

unsystematic risk. A well-diversified investor expects to
be compensated for taking on systematic risk
• Beta captures an asset’s systematic risk (relative to the
risk of the market)

• Sources of liquidity: primary (e.g. cash balances and

short-term funds) and secondary (e.g. negotiating
debt contracts, liquidating assets, filing for bankruptcy
protection).
• Additional liquidity measures

βi =

Purchases = Ending inventory + COGS − Beginning inventory

calculate an asset’s required return given its beta (the

security market line)

Net operating cycle = Number of days of inventory + Number of days of receivables
− Number of days of payables

E(R
R i ) = R f + β i [E(
[E(R
E(R m ) − R f ]

• Trade discounts (e.g. “2/10 net 30” means a 2% discount
is available if the amount owed is paid within 10 days,
otherwise full amount is due by the 30th day)
 365


Number of days

beyond discount period 

σσ
ρi,m σ i
Cov(R
R i ,R
, R m ) ρi,m
= i,m 2i m = i,m
σm
σm
σ 2m

• The capital asset pricing model (CAPM) is used to

Operating cycle = Number of days of inventory + Number of days of receivables

Discount  
Im
Implicit
rate = Cost
Cost of trad
trade
tr
adee cre
ccredit
redi
ditt =  11+

 1− D
Discount 

E(R
Rm ) − Rf
× σp
σm

• Complete diversification of a portfolio eliminates

WORKING CAPITAL MANAGEMENT

• If an asset’s expected return using price and dividend

forecasts is higher (lower) than its CAPM required return,
the asset is undervalued (overvalued).
• Portfolio performance evaluation measures
• Sharpe ratio (uses total risk)

−1

Sharpe ratio

PV of future cash
h fflows
NPV
= 1+
Initial investment
Initial investment

COST OF CAPITAL

rp =

risks), liquidity (or transaction cost risk)

Sharpe
ar ratio =
arpe

PORTFOLIO MANAGEMENT
OVERVIEW

σp

• Treynor ratio (uses beta)

Treynor ratio

• Steps in the portfolio management process: planning

(includes developing IPS), execution (includes asset
allocation, security analysis and portfolio construction),
feedback (includes portfolio monitoring/rebalancing and
performance measurement/reporting).

INVESTMENT POLICY STATEMENT
• Investment objectives: risk objectives and return

Rp − Rf

objectives
• Investment constraints: liquidity, time horizon, tax
concerns, legal/regulatory factors, unique circumstances

Treynor ratio =

Rp − Rf
βp

• M-squared (uses total risk)
M2 = (R
(R p − R f )

σm
(R m − R f )
− (R
σp

• Jensen’s alpha (uses beta)
α p = R p − [R
[R f + β p ((R
R m − R f )]

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EQUITY INVESTMENTS
MARKET ORGANIZATION AND STRUCTURE
• Purchasing stock on margin (leveraged position)
• Leverage ratio is the reciprocal of the initial margin.
• Price at which the investor receives a margin call
(1 − Initial margin)
P0 ×
(1 − Maintenance margin)

• Types of orders
• Execution instructions, e.g. market orders, limit orders.
• Exposure instructions, e.g. hidden orders, iceberg
orders.

• Validity instructions, e.g. day orders, good till cancelled

orders, immediate or cancel orders, good on close
orders, stop orders.
• Clearing instructions, e.g. how final settlement should
be arranged (security sale orders must also indicate
whether the sale is a long sale or a short sale).
• Execution mechanisms
• Pure auction (order-driven) market: ranks buy and sell
orders on price precedence, then display precedence,
then time precedence.
• Dealer/quote-driven/price-driven market: dealers
create liquidity by purchasing and selling against their
own inventory of securities.
• Brokered market: brokers arrange trades among their
clients.
• Features of a well-functioning financial system: timely
and accurate disclosure, liquidity (which facilitates
operational efficiency), complete markets and external
(or informational) efficiency.

INDICES
• Price-weighted index: value equals the sum of the

security prices divided by the divisor (typically set to the
number of securities in the index at inception).
• Equal-weighted index: each security is given an identical
weight in the index at inception (over-represents
securities that constitute a relatively small fraction of the
target market and requires frequent rebalancing).
• Market-capitalization weighted index: initial market

value is assigned a base number (e.g. 100) and the
change in the index is measured by comparing the new
market value to the base market value (stocks with larger
market values have a larger impact on the index).

MARKET EFFICIENCY

• Cumulative preference shares are less risky than noncumulative preference shares as they accrue unpaid
dividends.

INDUSTRY ANALYSIS

RISKS OF EQUITY SECURITIES
• Preference shares are less risky than common shares.
• Putable common shares are less risky than callable or
non-callable common shares.

• Callable common and preference shares are more risky
than their non-callable counterparts.

BASIC FEATURES OF BONDS
• Types of collateral backing: collateral trust bonds,

• Porter’s five forces: threat of substitute product,

bargaining power of customers, bargaining power of
suppliers, threat of new entrants, intensity of rivalry.
• Industry life-cycle analysis
• Embryonic (slow growth, high prices, high risk of
failure).

• Growth (sales grow rapidly, improved profitability,
lower prices, relatively low competition).
• Shakeout (slower growth, intense competition,
declining profitability, focus on cost reduction, some
failures/mergers).
• Mature (little or no growth, industry consolidation,
high barriers to entry, strong cash flows).
• Decline (negative growth, excess capacity, price
competition, weaker firms leave).
• Competitive strategies: cost leadership, product/service
differentiation.

EQUITY VALUATION
• Dividend discount model (DDM) for common stock
• One-year holding period
V0 =

dividend to be received year-end pric
pr e
+
(1 + k e )1
(1 + k e )1

• Gordon growth model (constant growth rate of
dividends to infinity)

V0 =

D0 (1
(1 + gc )1

D1
=
k e − gc
(k e − gc )1

• Multi-stage DDM
D1
D2
Dn
Pn
Value =
+
+ …+
+
(1 + k e )n (1 + k e )n
(1 + k e )1 (1 + k e )2
where:
D n +1
Pn =
k e − gc
Dn = Last dividend of the supernormal growth period
Dn+1 = First dividend of the constant growth period

• Valuation of preferred stock
• Non-callable, non-convertible preferred stock with no
maturity date

• Weak form EMH: current stock prices reflect all security

market information. Abnormal risk-adjusted returns

cannot be earned by using trading rules and technical
analysis.
• Semi-strong form EMH: current stock prices reflect
all security market information and other public
information. Abnormal risk-adjusted returns cannot be
earned by using important material information after it
has been made public.
• Strong form EMH: current stock prices reflect all public
and private information. Abnormal risk-adjusted returns
cannot be earned (assuming perfect markets where
information is cost-free and available to all).
• Behavioral biases that may explain pricing anomalies:
loss aversion, herding, overconfidence, information
cascades, representativeness, mental accounting,
conservatism, narrow framing.

FIXED INCOME

V0 =

D0
r

• Non-callable, non-convertible preferred stock with
maturity at time n
n

Dt
F
t +

(1 + r)n
t =1 (1 + r)

V0 = ∑

• Price multiples: price-to-earnings, price-to-sales, priceto-book, price-to-cash flow.

• Justified P/E ratio
P0 D1 //E
E1
=
E1
r−g

• Enterprise value (EV): market value of the company’s

common stock plus the market value of outstanding
preferred stock (if any) plus the market value of debt,
less cash and short-term investments (EV can be thought
of as the cost of taking over a company).
• EV/EBITDA multiple is useful for comparing companies
with different capital structures and for analyzing lossmaking companies.

•

•
•

•

equipment trust certificates, mortgage-backed
securities, covered bonds
Credit enhancements
• Internal: subordination, overcollateralization, excess
spread (or excess interest cash flow).
• External: surety bonds, bank guarantees, letters of
credit.
Covenants
• Affirmative: requirements placed on the issuer.
• Negative: restrictions placed on the issuer.
Repayment structures
• Bullet: entire principal amount repaid at maturity.
• Amortizing: periodic interest and principal payments
made over the term of the bond.
• Sinking fund: issuer repays a specified portion of the
principal amount every year throughout the bond’s life
or after a specified date.
Bonds with contingency provisions
• Callable: issuer has the right to redeem all or part of
the bond before maturity.
• Putable: bondholders have the right to sell the bond
back to the issuer at a pre-determined price on
specified dates.
• Convertible: bondholders have the right to convert the
bond into a pre-specified number of common shares
of the issuer (can also have callable convertible bonds).
• Contingent convertible bonds (CoCos): convert
automatically upon occurrence of a pre-specified
event.

FIXED INCOME MARKETS
• Public offering mechanisms: underwritten, best efforts,
auction, shelf registration

• Corporate debt
• Bank loans and syndicated loans (mostly floating-rate
loans).

• Commercial paper (unsecured, up to a maturity of one
year).

• Corporate notes and bonds.
• Medium-term notes (short-term, medium- to longterm, structured segments).

• Short-term wholesale funds: central bank funds,
interbank funds, certificates of deposits

• Repurchase agreements (repos)
• Repo: seller is borrowing funds from the buyer and
providing the security as collateral.

• Reverse repo: buyer is borrowing securities to cover a
short position.

• Repo margin or haircut: the percentage difference

between the market value of the security and the
amount of the loan.
• Repo rate: annualized interest cost of the loan.
• Any coupon income received from the bond provided

as security during the repo term belongs to the seller/
borrower.

FIXED INCOME VALUATION
• Bond pricing with yield-to-maturity (uses constant

interest rate to discount all the bond’s cash flows)
• If coupon = YTM, the bond’s price equals par value.
• If coupon > YTM, the bond’s price is at a premium to
par.
• If coupon < YTM, the bond’s price is at a discount to par.
• Price is inversely related to yield: when the yield
increases (decreases), the bond’s price decreases
(increases).
• Bond pricing with spot rates (uses the relevant spot rates
to discount the bond’s cash flows)
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• Spot rate: yield on a zero-coupon bond for a given

maturity.
• Accrued interest when a bond is sold between coupon
payment dates
• Full price: calculated as the PV of future cash flows as
of the settlement date.
• Accrued interest (AI) included in full price: seller’s
proportional share of the next coupon, where t is the

number days from last coupon date to the settlement
date and T is the number of days in the coupon period
(actual/actual for government bonds, 30/360 for
corporate bonds)

SMMt =

• Prepayment risk: contraction risk occurs when interest

•

AI = t/T × PMT

• Flat or clean or quoted price: full price less AI, or
equivalently

•

Flat
PV Full = PV Flat
+ AI

• Yield measures
• Effective annual yield depends on periodicity of the
•
•

•
•
•

•

stated annual yield.
Annual-pay bond: stated annual yield for periodicity of
one = effective annual yield.
Semiannual-pay bond: stated annual yield for
periodicity of two = semiannual bond basis yield
= semiannual bond equivalent yield = yield per
semiannual period × 2.
Current yield: annual cash coupon payment divided by
the bond price.
Yield-to-call: computed for each call date.
Yield-to-worst: lowest yield among the YTM and the
various yields to call.
Money market pricing on a discount rate basis

 Days

ys
PV = FV ×  1 −
× DR 


year
 Year   FV − PV 
DR = 
×
 Days   FV 

• Money market pricing on an add-on rate basis

PV=

FV
ys
 1 + Days
× AOR 


Year

 Year   FV − PV 
AOR = 
×
 Days   PV 

365-day year on an add-on basis.
• Forward rate
• Interest rate on a loan originating at some point in the
future.
• Implied forward rates can be computed from spot
rates.
(1 + y s0 ) y (1 + x fy )x = (1 +

x+ ys0 )

•

•

•

rates fall (leading to an increase in prepayments), while
extension risk occurs when interest rates rise (leading
to a decrease in prepayments).
CMOs (backed by pool of mortgage pass-through
securities): sequential-pay tranches (shorter-term
tranches receive protection from extension risk, longerterm tranches receive protection from contraction
risk); PAC/support tranches (support tranche provides
protection against contraction and extension risk to
the PAC tranche); floating rate tranches (floater and
inverse floater).
Credit enhancements for non-agency RMBS: internal
(cash reserve funds, excess spread accounts,
overcollateralization, senior/subordinate structure)
and external (monoline insurers).
Commercial MBS (backed by non-recourse commercial
mortgage loans): investors have significant call
protection but are exposed to balloon risk (like
extension risk).
Non-mortgage asset-backed securities: auto-loan
receivable-backed securities (backed by amortizing
auto loans) and credit card receivable-backed
securities (with lockout period before principal
amortizing period sets in).
CDOs: structured as senior, mezzanine and
subordinated bonds (or equity class). CDO manager
engages in active management of the collateral to
generate the cash flow required to repay bondholders
and to earn a competitive return for the equity tranche.

x+ y

PVBP =

• Two types of interest rate risk
• Reinvestment risk: future value of any interim bond

cash flows increases (decreases) when interest rates
rise (decline). Matters more to long-term investors.
• Market price risk: selling price of a bond decreases
(increases) when interest rates rise (decline). Matters
more to short-term investors.
• Macaulay duration: weighted average of the time it
would take to receive all the bond’s promised cash flows.
• Modified duration: estimated percentage price change
for a bond in response to a 100 bps (1%) change in yields
MacDur
1+ r

• If Macaulay duration is not known, annual modified

duration can be estimated using the following formula:
(PV
V− ) − (PV
(PV+ )
ApproxModDur =
2 × ( ∆Yield) × (PV
V0 )

• Effective duration: measures the sensitivity of a

bond’s price to a change in the benchmark yield curve
(appropriate measure for bonds with embedded options)
EffDur =

(PV
V− ) − (PV
V+ )
2 × ( ∆Curve) × (PV
V0 )

option-free bonds based on duration to bring them close
to their actual values
ApproxCon =

• Yield spreads
• G-spread: spread over government bond yield.
• I-spread: spread over the swap rate.
• Z-spread: spread over the government spot rate.
• Option-adjusted spread: z-spread less option value

(bps per year).
• Asset-backed securities
• Residential MBS: agency RMBS vs non-agency RMBS
(require credit enhancements).
• Mortgage pass-through securities (backed by pool of
residential mortgage loans): single monthly mortality
rate (SMM).

MoneyDur = AnnModDur × PVFull

• Price value of a basis point (PVBP): estimates the change

(PV
V− ) + (PV
(PV+ ) − [2 × (PV
(PV0 ))]
( ∆Yield
Yield)
Y
ield))2 × ((PV
PV0 )

• The percentage change in a bond’s full price for a

given change in yield based on duration with convexity
adjustment is estimated as follows:
1
Full
ll
%∆PV
PV Fu
≈ (−
(− AnnM
AnnModDur
An
nMod
odDu
Durr × ∆Yield
Yield)

Y
ield)) +  × AnnConvexity
AnnConvexity × ( ∆Y
Yield)2 

2

• Effective convexity: use for bonds with embedded
options instead of approximate convexity.

• Callable bonds can exhibit negative convexity when

benchmark yields decline. Putable bonds always exhibit
positive convexity.

CREDIT ANALYSIS
• Two components of credit risk: default risk (or default

probability) and loss severity (or loss given default). Loss
severity equals 1 minus the recovery rate.
• Expected loss
Expected loss = Defaul
Default
Defa
ultt pr
pprobability
robability
obability × Loss severity
ver given default
verity

ef
efault

• Spread risk consists of downgrade risk (or credit
migration risk) and market liquidity risk.

•
•
•
•

Corporate family rating (CFR): issuer rating.
Corporate credit rating (CCR): rating for a specific issue.
Four Cs: capacity, collateral, covenants, character.
Return impact of a change in the credit spread (includes
convexity adjustment for larger changes)
Return impact ≈ −(MDurr × ∆S
Spread)) + (1/
((1/2
1/22 × C
Convexity × ∆Spread 2 )

DERIVATIVES
TYPES OF DERIVATIVES
• Forward commitments: forwards, futures, interest rate
swaps.

• Contingent claims: options, credit derivatives.

DERIVATIVE PRICING AND VALUATION

• Derivative pricing is based on risk-neutral pricing.
• Forward contracts
• Price at contract initiation (assuming underlying asset
entails benefits and costs)

• Key rate duration: measure of a bond’s sensitivity to a

change in the benchmark yield for a given maturity (used
to assess yield curve risk, i.e. non-parallel shifts in the
yield curve)
• Portfolio duration: weighted average of the durations of
the individual bonds held in the portfolio, where each
bond’s weight equals its proportion of the portfolio’s
market value
• Money duration: measure of the dollar price change in
response to a change in yields

(PV
V− ) − (PV
V+ )
2

• Approximate convexity: used to revise price estimates of

INTEREST RATE RISK

ModDur =

• Bond-equivalent yield: money-market rate stated on a

in the full price of a bond in response to a 1 bp change
in its YTM

Prepayment in month
mont t
Beginning mortgage balancee ffor mont
month
ht−S
Scheduled
cheduled principa
principal payment
payment in month
month t

F(0,T) = (S0 − γ + θ)(1
)(1 + rr))T oor F(0,T)) = S0 (1 + r)T − ( γ − θ))(1
(1 + r)T
*Note

that benefits (γ)
γγ) and costs (θ) are expressed in terms of present value.

• Value of a forward contract during its life (long
position)

Vt (0,
((0,T)
0,T)
T) = St − ( γ − θ)(1 + r ) t − [F(0, T) / (1 + r )T− t ]

• Value of a forward contract at expiration (long position)
VT (0,
((0,T)
0,T)
T) = ST − F (0,T)

• Forward rate agreement (FRA)
• Long (short) position can be viewed as the party that
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has committed to take (give out) a hypothetical loan.

• If LIBOR at FRA expiration > FRA rate, the long benefits.
• If LIBOR at FRA expiration < FRA rate, the short benefits.
• Futures: similar to forwards but standardized, exchange-

traded, marked-to-market daily, clearinghouse
guarantees that traders will meet their obligations
• Forward vs futures prices
• If underlying asset prices are positively (negatively)
correlated with interest rates, the futures price will be
higher (lower) than the forward price.
• If futures prices are uncorrelated with interest rates
or if interest rates are constant, forwards and futures
would have the same price.
• Interest rate swaps
• The swap fixed rate represents the price of the swap

(swap has zero value to the swap counterparties at
swap initiation).
• If interest rates increase after swap initiation, the swap
will have positive value for the fixed-rate payer.
• If interest rates decrease after swap initiation, the swap
will have positive value for the floating-rate payer.
• An interest rate swap can be viewed as a combination
of FRAs.
• Options
• Call (put) option gives the holder/buyer the right to buy
(sell) the underlying asset at the exercise price.
• European option: can only be exercised at the option’s
expiration.
• American option: can be exercised at any point up to
the option’s expiration.
• Call (put) option is in-the-money when the stock price
is higher (lower) than the exercise price.
• Intrinsic or exercise value: the amount an option is
in-the-money by (minimum value of 0).
• Put-call parity for European options (options and bond
have the same time to expiration/maturity T)
X
c0 +
= p 0 + S0
(1 + R F )T

• Put-call parity formula can be rearranged to create

synthetic call, put, underlying asset and bond, e.g.
synthetic call = long put + long underlying stock + short

bond).
• Factors affecting the value of an option

Impact of an increase in:

Call

Put

Value of the underlying

Increase

Decrease

Exercise price

Decrease

Increase

Risk-free rate

Increase

Decrease

Time to expiration

Increase

Increase (except for
deep in-the-money
European puts)

Volatility of the
underlying

Increase

Increase

Benefits from the
underlying

Decrease

Increase

Cost of carry

Increase

Decrease

• One-period binomial model for a call option (based on
risk-neutral probability π)

c=

πc + + (1 − π)c −
(1 + r)

π=

(1 + r − d)
(u − d)

Wheree u =

S1+
S−
and d = 1
S0
S0

ALTERNATIVE INVESTMENTS
• Potential benefits of alternative investments: low

correlations with returns on traditional investments and
higher returns than traditional investments
• Hedge funds
• Event-driven strategies: merger arbitrage, distressed/
restructuring, activist, special situations.
• Relative value strategies: fixed income convertible
arbitrage, fixed income asset backed, fixed income
general, volatility, multi-strategy.
• Macro strategies: long and short positions in broad
markets (e.g. equity indices, currencies, commodities,
etc.) based on manager’s view regarding overall macro

environment.
• Equity hedge strategies: market neutral, fundamental
growth, fundamental value, quantitative directional,
short bias, sector specific.
• Two types of fees: management fee (based on assets
under management) and incentive fee (which may be
subject to a hurdle rate or high water mark provision).
• Private equity
• Leveraged buyouts (LBOs): management buyouts (MBOs)
and management buy-ins (MBIs).
• Venture capital: formative stage financing (angel
investing, seed-stage financing, early-stage financing),
later-stage financing, mezzanine-stage financing.

• Development capital: includes private investment in
public equities (PIPEs).

• Distressed investing: buying debt of mature companies in
financial distress.

• Exit strategies: trade sale, IPO, recapitalization,
secondary sale, write-off/liquidation.

• Valuation methods for portfolio company: market or

comparables approach, discounted cash flow approach,
asset-based approach.
• Real estate
• Investment categories: residential property, commercial
real estate, REITs, timberland/farmland.

• Performance measurement: appraisal indices (tend
to understate volatility), repeat sales indices (sample
selection bias), REIT indices (based on prices of publicly
traded shares of REITs).
• Real estate valuation approaches: comparable sales
approach, income approach (direct capitalization
method and discounted cash flow method), cost
approach.
• REIT valuation approaches: income-based approaches,
asset-based approaches (NAV).
• Commodities
• Investors prefer to trade commodity derivatives to
avoid costs of transportation and storage for physical
commodities.
• Price of a commodity futures contract.
Futures price = Spot pr
pric
ice × (1 + Risk-free shorthor term rate)
hort+ Storage costs − Convenience yield

• When the futures price is higher (lower) than the spot

price, prices are said to be in contango (backwardation).

• Sources of return on a commodity futures contract: roll
yield, collateral yield, spot prices.

• Infrastructure
• Investments in real, capital intensive, long-lived assets.
• Economic infrastructure: assets such as transportation

and utility assets.

• Social infrastructure: assets such as education,
healthcare and correctional facilities.

• Brownfield investments: investments in existing
infrastructure assets.

• Greenfield investments: investments in infrastructure
assets to be constructed.

• Risk-return measures
• Sharpe ratio is not appropriate risk-return measure since
returns tend to be leptokurtic and negatively skewed.

• Downside risk measures more useful, e.g. value at risk
(VAR), shortfall risk, Sortino ratio.

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