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

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

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l C r it ic a l C o n c ept s f o r t h e 2019 CFA® E x a m

r ETHICAL AND PROFESSIONAL

, STANDARDS

I

I (A)

I (B)

I (C )

I (D)

II

II (A)

II (B)

III

HI (A)

HI (B)

HI (C)

HI (D)

HI (E)

IV

IV (A)

IV (B)

IV (C)

V

v (A)

V (B)

V (C )

VI

VI (A)

VI (B)

VI (C)

VII

VII (A)

VII (B)

Professionalism

Knowledge of the Law

Independence and Objectivity

Misrepresentation

Misconduct

Integrity of Capital Markets

Material Nonpublic Information

Market Manipulation

Duties to Clients

Loyalty, Prudence, and Care

Fair Dealing

Suitability

Performance Presentation

Preservation of Confidentiality

Duties to Employers

Loyalty

Additional Compensation Arrangements

Responsibilities of Supervisors

Investment Analysis, Recommendations,

and Action

Diligence and Reasonable Basis

Communication with Clients and

Prospective Clients

Record Retention

Conflicts of Interest

Disclosure of Conflicts

Priority of Transactions

Referral Fees

Responsibilities as a CFA Institute

Member or CFA Candidate

Conduct in the CFA Program

Reference to CFA Institute, CFA

Designation, and CFA Program

QUANTITATIVE METHODS

Machine learning: Gives a computer the ability to

improve its performance of a task over time

Distributed ledger: A shared database with a

consensus mechanism, ensuring identical copies

Simple Linear Regression

Correlation:

covXY

Ny =

(sx)(sy)

t-test for r (n — 2 df): t = r>/n — 2

V l - r2

Estimated intercept: b0 = Y — bjX

Confidence interval for predicted Y-value:

A

Y ± t c x SE of forecast

Multiple Regression

Yi = b0+ ( b , x X li) + (b2x X 2i)

+ (b3 X X jiJ + Ej

• Test statistical significance of b; H0: b = 0

Reject if |t| > critical t or p-value < a

• Confidence Interval: bj ± (tcXSb,

• SST = RSS + SSE

M SR = RSS / k

• MSE = SSE / (n - k - 1)

• Test statistical significance of regression:

F = M SR / MSE with k and n - k — 1 df (1-tail)

• Standard error of estimate (SEE = >/MSE )

Smaller SEE means better fit

means better fit

Regression Analysis— Problems

• Heteroskedasticity Non-constant error variance

Detect with Breusch-Pagan test Correct with White-corrected standard errors

• Autocorrelation Correlation among error terms Detect with Durbin-Watson test; positive autocorrelation if DW < dl Correct by adjusting standard errors using Hansen method

• Multicollinearity High correlation among Xs

Detect if F-test significant, t-tests insignificant

Correct by dropping X variables

Model Misspecification

• Omitting a variable

• Variable should be transformed

• Incorrectly pooling data

• Using lagged dependent vbl as independent vbl

• Forecasting the past

• Measuring independent variables with error

Effects o f Misspecification Regression coefficients are biased and inconsistent, lack of confidence in hypothesis tests of 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 of unlabeled data

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

Dickey Fuller test

Unit root: coefficient on lagged dep vbl = 1 Series with unit root is not covariance stationary First differencing will often eliminate the unit root

Autoregressive (AR) model: specified correctly if autocorrelation of residuals not significant

Mean reverting level for AR(1):

(1- b j ) RMSE: square root of average squared error

Random W alk Tim e Series:

xt = xt-i + £t Seasonality: indicated by statistically significant lagged err term Correct by adding lagged term

ARCH: detected by estimating:

Variance of ARCH series:

CTt+l = a0 “b alet

Risk Types:

Appropriate method

Distribution

o f risk Sequential?

Accommodates Correlated Variables?

Scenario

Cross rates with bid-ask spreads:

Currency arbitrage: “Up the bid and down the ask.” Forward premium = (forward price) - (spot price) Value of fwd currency contract prior to expiration:

(FPt — FP) (contract size)

1 + Ra days

360 , Covered interest rate parity:

1 + Ra days)

1 + Rb days [3 6 0 , Uncovered interest rate parity:

E(% A S)wb, = Ra - R , Fisher relation:

R = nominal real v R + E(inflation)' International Fisher Relation:

R nominal A — R IR = E(inflation.) — EfinflationJnominal 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 of investment currency Mundell-Fleming model: Impact of monetary and fiscal policies on interest rates & exchange rates Under high capital mobility, expansionary monetary policy/restrictive fiscal policy —> low interest rates —> currency depreciation Under low capital mobility, expansionary monetary policy/ expansionary fiscal policy —> current account deficits —> currency depreciation

Dornbusch overshooting model: Restrictive monetary policy —> short-term appreciation of currency, then slow depreciation to PPP value Labor Productivity:

output per worker Y/L = T(K/L)Q Growth Accounting:

growth rate in potential GDP

= long-term growth rate of technology

+ Oi (long-term growth rate of capital)

+ (1 - a) (long-term growth rate of labor) growth rate in potential GDP

= long-term growth rate of labor force + long-term growth rate in labor productivity

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ECONOMICS continued

Classical Growth Theory

• Real GDP/person reverts to subsistence level

Neoclassical Growth Theory

• Sustainable growth rate is a function of

population growth, labor’s share of income, and

the rate of technological advancement

• Growth rate in labor productivity driven only by

improvement in technology

• Assumes diminishing returns to capital

Endogenous Growth Theory

• 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 dicial 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 Markets

• Independent SROs are more prevalent in

common-law countries than in civil-law countries

Econom ic Rationale for Regulatory Intervention

• Inform ational frictions arise in the presence of

information asymmetry

• Externalities deal with provision of public goods.

Regulatory Interdependencies and Their Effects

Regulatory capture theory: Regulatory body is

influenced or controlled by industry being regulated

Regulatory arbitrage: Exploiting regulatory differences

between jurisdictions, or difference between

substance and interpretation of a regulation

Tools o f Regulatory Intervention

• Price mechanisms, restricting or requiring certain

activities, and provision of public goods or

financing of private projects

Financial m arket regulations: Seek to protect

investors and to ensure stability of financial system

Securities m arket regulations: Include disclosure

requirements, regulations to mitigate agency

conflicts, and regulations to protect small investors

Prudential supervision: Monitoring institutions to

reduce system-wide risks and protect investors

Anticompetitive Behaviors and Antitrust Laws

• Discriminatory pricing, bundling, exclusive dealing

• Mergers leading to excessive market share blocked

N et regulatory burden: Costs to the regulated

entities minus the private benefits of regulation

Sunset clauses: Require a cost-benefit analysis to be

revisited before the regulation is renewed

FINANCIAL STATEMENT ANALYSIS

Accounting for Intercorporate Investments

Investment in Financial Assets: <20% owned, no

significant influence

• Held-to-maturity at cost on balance sheet; interest and

realized gain/loss on income statement

• Available-for-sale at FMV 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 of 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 Method 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

Income Statement

• Total periodic pension cost (under both IFRS and GAAP) = contributions — A funded status

• IFRS and GAAP differ on where the total periodic pension cost (TPPC) is reflected (Income statement vs OCI)

• Under GAAP, periodic pension cost in P&L

= service cost + interest cost ± amortization of actuarial (gains) and losses + amortization of 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 Cost TPPC = ending PBO - beginning PBO + benefits paid - actual return on plan assets TPPC = contributions — (ending funded status — beginning funded status)

Cash Flow Adjustment

If TPPC < firm contribution, difference = A in PBO (reclassify difference from CFF to CFO after-tax) IfTPPC > firm contribution, diff = borrowing (reclassify difference from CFO to CFF after-tax)

M ultinational Operations: Choice o f Method 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

• COGS, depreciation at historical rate

• Exposure = monetary assets - monetary liabilities

Net asset position & depr foreign currency = loss

Net liab position & depr foreign currency = gain

Original F/S vs All-Current

• Pure BS and IS ratios unchanged

• If LC depreciating (appreciating), translated mixed ratios will be larger (smaller)

Hyperinflation: GAAP vs IFRS Hyperinfl = cumul infl > 100% over 3 yrs GAAP:

use temporal method IFRS: 1st, restate foreign curr st for infl 2nd, translate with current rates

Net purch power gain/loss reported in income

Beneish model: Used to detect earnings manipulation based on eight variables

High-quality earnings are:

1 Sustainable: Expected to recur in future

2 Adequate: Cover company’s cost of capital IFR S AN D U S GAAP D IFFE R E N C E S Reclassification of 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 of 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 DuPont equation)

Burden Burden Margin

ROE = -x -x -x

EBT EBIT revenue

T otal Asset

T urnover revenue

x

Financial Leverage average assets average assets average equity Accruals Ratio (balance sheet approach)

Accruals Ratio (cash flow statement approach)

(NI - CFO - CFI)

Financial institutions differ from other companies due to systemic importance and regulated status Basel III: Minimum levels of capital and liquidity CAMELS: Capital adequacy, Asset quality, Management, Earnings, Liquidity, and Sensitivity

Liquidity coverage ratio = Net stable funding ratio =

expected cash outflows available stable funding required stable funding

IN SU R A N C E CO M PA N Y KEY RA TIO S: Underwriting loss ratio

claims paid + A loss reserves net premium earned

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• • 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

• TN O C F = SalT + NWCInv - T(SalT - BT)

Capital Budgeting Replacement

• Same as expansion, except current after-tax salvage

of old assets reduces initial outlay

• Incremental depreciation is A in depreciation

Evaluating Projects with Unequal Lives

• Least common multiple of lives method

• Equivalent annual annuity (EAA) method:

annuity w/ PV equal to PV of project cash flows

Effects o f Inflation

• Discount nominal (real) cash flows at nominal (real)

rate; unexpected changes in inflation affect project

profitability; reduces the real tax savings from

depreciation; decreases value of fixed payments to

bondholders; affects costs and revenues differently

Capital Rationing

• If positive NPV projects > available capital,

choose the combination with the highest NPV

Real Options

• Timing, abandonment, expansion, flexibility,

fundamental options

Econom ic and Accounting Income

• Econ income = AT CF + A in projects MV

• Econ dep based on A in investment’s MV

• Econ income is calculated before interest expense

(cost of 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

-t= i (1 + W A C C ) 1

• Residual income: = NI - equity charge;

discounted at required return on equity

• Claims valuation separates CFs based on equity

claims (discounted at cost of equity) and debt

holders (discounted at cost of debt)

MM Prop I (No Taxes): capital structure irrelevant

(no taxes, transaction, or bankruptcy costs)

MM Prop II (No Taxes): increased use of cheaper debt increases cost of equity, no change in WACC

re = < b + f ( r o - r d)

E

MM Proposition I (With Taxes): tax shield adds

VL = Vu + (txd)

MM Proposition II (With Taxes): tax shield adds

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 of 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:

A P =

{ l - t c g ) Target Payout Adjustment Model expected increase in dividends =

■ target expected ^ x payout I — K , , b „ \ previous

earnings r ' -q / dividend

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

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

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 Decision Making Friedman Doctrine: Only responsibility is to increase profits “within the rules of the game.”

Utilitarianism: Produce the highest good for the largest number of people

Kantian ethics: People are more than just an economic input and deserve dignity and respect

Rights theories: Even if an action is legal, it may violate fundamental rights and be unethical

Justice theories: Focus on a just distribution of economic output (e.g., “veil of ignorance”)

Corporate Governance Objectives

• 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 (HHI): market power = sum of squared market shares for all industry firms In a moderately-concentrated industry (HHI 1,000 to 1,800), a merger is likely

to be challenged if HHI increases 100 points (or increases 50 points for HHI >1,800)

n

HHI = ^ ( M S j xlOO):

i=l Methods to Determine Target Value

D C F method: target proforma FCF discounted at

adjusted WACC

Comparable company analysis: based on relative

valuation vs similar firms + takeover premium

Comparable transaction analysis-, target value from

takeover transaction; takeover premium included Merger Valuations

C om binedfirm : VAT = VA + VT + S - C Takeover premium (to target): GainT = TP = PT — VT Synergies (to acquirer): GainA = S - TP = S - (PT - VT)

Merger Risk & Reward

Cash offer: acquirer assumes risk & receives reward Stock offer: some of risks & rewards shift to target If

higher confidence in synergies; acquirer prefers cash

& target prefers stock

Forms of divestitures: equity carve-outs, spin-offs, split-offs, and liquidations

EQUITY Holding period return:

- 1

Required return: Minimum expected return an investor requires given an asset’s characteristics Internal rate of return (IRR): Equates discounted cash flows to the current price

Equity risk premium:

required return = risk-free rate + ((3 x ERP) Gordon growth model equity risk premium:

+ consensus long-term earnings growth rate

- long-term government bond yield Ibbotson-Chen equity risk premium

[1 + i] x [1 + rEg] x [1 + PEg] - 1 + Y - RF Models of required equity return:

• CAPM\ r = RF + (equity risk premium x (3.)

• M ultifactor model: required return = RF + (risk

Fama-French: r = RF + 3 j 1 mkt,j x (R — RF)mkt

+ ^SMB,j x ( P'small — 'big'+ ^H M U X ^ H B M “ ^LBM HML.j )

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• Pastor-Stambaugh model: Adds a liquidity factor to

the Fama-French model

• M acroeconomic multifactor 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

EQUITY continued

MV.debt

^Xdebt+equity > a ( i- T ) + MVequity

^ ^ d eb 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) Methods

Use dividend discount models (DDM) when:

• Firm has dividend history

• Dividend policy is related to earnings

• Minority shareholder perspective

Use free cash flow (FCF) models when:

• Firm lacks stable dividend policy

• Dividend policy not related to earnings

• FCF is related to profitability

• Controlling shareholder perspective

Use residual income (RI) when:

• Firm lacks dividend history

• Expected FCF is negative

Gordon Growth Model (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 =

H-M odel

+ PVGO

v0 =_ D 0 x(l + gL)] | [P 0x H x ( gs — gL)]

r ~ g L r ~ g L

Sustainable Growth Rate: b x ROE

Required Return From Gordon Growth Model:

r = (D, / P0) + g

Free Cash Flow to Firm (FCFF)

Assuming depreciation is the only NCC:

FCFF = NI + Dep + [Int x (1 — tax rate)] — FCInv

- WCInv

FCFF = [EBIT x (1- tax rate)] + Dep - FCInv

- WCInv

FCFF = [EBITDA x (1 - tax rate)] + (Dep x tax

rate) - FCInv - WCInv

FCFF = CFO + [Int x (1 - tax rate)] - FCInv

;ree Cash Flow to Equity (FCFE)

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 FCFF/FCFE Models

FCFFj

• For FCFE valuation: V0 =

W A C C - g

r ~ g

2-Stage FCFF/FCFE 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 of earnings makes interpretation difficult

• Management discretion over accounting choices affects reported earnings

Justified P/E leading P/E = -trailing P/E =

r ~ g

( l - b ) ( l + g)

r ~ g

Justified dividend yield:

Normalization Methods

• Historical average EPS

• Average ROE

Price to Book (P/B) Ratio Advantages:

• BV almost always > 0

• BV more stable than EPS

• Measures NAV of financial institutions

Disadvantages:

• Size differences cause misleading comparisons

• Influenced by accounting choices

• BV ^ MV due to inflation/technology.

justified P / B = R Q E ~ g

r ~ g Price to Sales (P/S) Ratio Advantages:

• Meaningful even for distressed firms

• Sales revenue not easily manipulated

• Not as volatile as P/E ratios

• Useful for mature, cyclical, and start-up firms

Disadvantages:

• High sales ^ imply high profits and cash flows

• Does not capture cost structure differences

• Revenue recognition practices still distort sales

justified P / S = PMoX (1 - b)(1 + g)

r ~ g DuPont Model

net income ROE =

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

Method o f Comparables Firm multiple > benchmark implies overvalued

Firm multiple < benchmark implies undervalued

Fundamentals that affect multiple should be similar between firm and benchmark

Residual Income Models

• RI = Et — (r x Br-i) = (ROE — r) x Bt_i

• Single-stage RI model:

V0= B0 +

r ~ g

• Multistage RI valuation: Vo = Bo + (PV of interim high-growth RI) + (PV of continuing RI)

Econom ic Value Added®

Private Equity Valuation

1

1 +Control Premium Total discount = 1 - [(1 - D LO C )(l - DLOM)] The DLOM varies with the following

• An impending IPO or firm sale [ DLOM.

• The payment of 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 FIXED INCOME

Price of a T-period zero-coupon bond:

(l + ST )T Forward price of zero-coupon bond:

F(i,k) =

1 + / ( j k ) ]

Forward pricing model:

p0+k)

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 LIBOR rate) — (3-month T-bill rate) Libor-OIS spread

= LIBOR 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 + adz Ho-Lee model: dr = 0 dt + ad zt t t

Managing yield curve shape risk:

AP/P =

(L = level, S = steepness, C = curvature) Yield volatility: Long-term <— uncertainty regarding

the real economy and inflation

Short term <— uncertainty re: monetary policy

Long-term yield volatility is generally lower than volatility in short-term yields

Value of option embedded in a bond:

V = V call straight bond - Vcallable bond

V = V put putable bond - Vstraight bond When interest rate volatility increases:

-DlAx l - D sAxs -D c;Axc

v „ | ,v call option 1 put option 1 T>v v

1 5 putable bond 1 callable bond

Upward sloping yield curve: Results in lower call value and higher put value

When binomial tree assumed volatility increases:

• computed OAS of a callable bond decreases.

• computed OAS of a putable bond increases.

2x BVq x Ay

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

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FIXED INCOME continued

effective convexity = - -—

-BV0 x A y2

Effective duration:

• ED (callable bond) < ED (straight bond)

• ED (putable bond) < ED (straight bond)

• ED (zero-coupon) ~ maturity of the bond

• ED of floater « time (years) to next reset

One-sided durations: Callables have lower down-

duration; putables have lower up-duration

Value of a capped floater

= straight floater value — embedded cap value

Value of a floored floater

= straight floater value + embedded floor value

Minimum value of convertible bond

= greater o f conversion value or straight value

Conversion value of convertible bond

= market price of stock x conversion ratio

Market conversion price

market price of convertible bond

conversion ratio

Market conversion premium per share

= market conversion price - stock’s market price

Market conversion premium ratio

market conversion premium per share

market price of common stock

Premium over straight value

straight value

Callable and putable convertible bond value

= straight value of bond

+ value of call option on stock

- value of call option on bond

+ value of put option on bond

Expected exposure: Amount a risky bond investor

stands to lose before any recovery is factored in

Loss given default = loss severity x exposure

Probability of default: Likelihood in a given year

Credit valuation adjustment (CVA): Sum of the

present values of expected losses for each period

Credit score/rating: Ordinal rank; higher = better

Return from bond credit rating migration: A% P

= -(modified duration of bond) x (A spread)

Structural models of corporate credit risk:

• value of risky debt = value of risk-free debt - value

of 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 of risky

bond — YTM of benchmark

Credit Default Swap (CDS): Upon credit event,

protection buyer compensated by protection seller

Index CDS: Multiple borrowers, equally weighted

Default: Occurrence o f a credit event

Common credit events in CDS agreements:

Bankruptcy, failure to pay, restructuring

CDS spread: Higher for a higher probability of

default and for a higher loss given default.

Hazard rate = conditional probability of default

expected losst = (hazard rate)t x (loss given default)

Upfront CDS payment (paid by protection buyer)

= PV(protection leg) — PV(premium leg)

« (CDS spread - CDS coupon) x duration x NP

Change in value for a CDS after inception

» chg in spread x duration x notional principal

DERIVATIVES Forward contract price (cost-of-carry model)

(1 + R f )T Price o f equity forward with discrete dividends FP(on an equity security) = (SQ - PV D )x(l+Rf)T Value o f forward on dividend-paying stock

(l + R f F - 1) Forward: equity index (continuous dividend)

(R- - 8 c )xT

FP (on an equity index) = S0 X e' * '

RfxT

X e r

S0x e - 6CxT

where:

Rp = continuously compounded risk-free rate

Sc = continuously compounded dividend yield

Forward price on a coupon-paying bond:

FP(on a fixed income security)

= (S0- P V C ) x ( l + R f )T

= S0 x ( l + R f )T — FVC Value o f a forward on a coupon-paying bond:

(l + R f/ 7 - 1) Price o f a bond futures contract:

FP = [(full price)(l+Rf)T - AIT - FVC]

Quoted bond futures price:

QFP = forward price / conversion factor (full price)(l+Rf )T - AIT - FVC Price o f a currency forward contract:

(t x P „ J T

Fr = S0 x

1

CFJ

(i + Rpc) (i + r b c)T Value o f a currency forward contract

(i + n>c)<T-t) Currency forward price (continuous time):

Swap fixed rate:

1 - Z

C =

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:

U - D

Put-call parity:

So + Po = Co + PV(X) Put-call parity when the stock pays dividends:

P» + S„eJ,T = C0 + e'rTX

# of short call options =

Dynamic delta hedging

# shares hedged delta of call option

delta of put option Change in option value

A C ~ call delta x AS + Vi gamma x A S2

O ption value using arbitrage-free pricing

„ _ LC , ( - h S + + C + ) Lc , ( - h S - + C - )

Cq — nor) = hon

Black—Scholes—M erton option valuation model

C0 = S0e_8TN (d1) - e_rTXN (d2)

P0 = e~rTXN (-d 2) - S0crnTSI(-d1) where:

5 = continuously compounded dividend yield

dl = ln(S / X ) + (r — aVt6 + a2 / 2)T

d-2 = dj — GyjT

O P T IO N ST 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 of long > strike of 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

current price ALTERNATIVE INVESTMENTS Value of 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

N OIj cap rate =

comparable sales price

value = Vq = - or Vq =

Property value based on “All Risks Yield”:

value = V() = rentj / ARY

gross income

continued on next page

Trang 6

Term and reversion valuation approach:

total property value

= PV of term rent + PV reversion to ERV

Layer approach:

total property value

= PV of term rent + PV of incremental rent

Debt service coverage ratio:

first-year NO I

DSCR = -

-: -debt service

Loan-to-value (LTV) ratio:

LTV =

-; -appraisal value

equity dividend rate = -

-equity NAV approach to R EIT share valuation:

estimated cash NOI

* 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 REIT share valuation:

funds from operations (FFO)

shares outstanding

= FFO/share

x sector average P/FFO multiple

= NAV/share

Price-to-AFFO approach to REIT share valuation:

funds from operations (FFO)

— non-cash rents

— recurring maintenance-type capital

expenditures

= AFFO

shares outstanding

= AFFO/share

x property subsector average P/AFFO multiple

= NAV/share

Discounted cash flow R EIT share valuation:

value of a REIT 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 (VCfirms 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 performance (LBO): earnings

growth, f of 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 of 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)

ALTERNATIVE INVESTMENTS continued

• 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 Commodity Futures

1 Insurance theory: Contract buyers compensated for providing protection to commodity producers

Implies backwardation is normal

2 Hedging pressure hypothesis: Like insurance theory, but includes both long hedgers ( —>

contango) and short hedgers (—» backwardation)

3 Theory of storage: Spot and futures prices related through storage costs and convenience yield

Total return on fully collateralized long futures

= collateral return + price return + roll return Roll return: positive in backwardation because long-dated contracts are cheaper than expiring contracts

PORTFOLIO MANAGEMENT Portfolio Management 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) = Rf + M V + M V + ••• + M V Expected return = risk free rate

+ E (factor sensitivity) x (factor risk premium) Value at risk (VaR): Estimate of minimum loss with a given probability over a specified period, expressed as $ amount or % of 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

of the position’s contribution to overall VaR

Variance for W % fund A + W % fund BA B

Annualized standard deviation

= V250 x (daily standard deviation)

% change in value vs change in YTM

= -duration (AY) + Vi convexity (AY)2

fo r M acaulay duration, replace AY by A Y/(1 + Y)

ISBN: 978-1-4754-7975-1

Inter-temporal rate of substitution = mt = —

u0

marginal utility of consuming 1 unit in the future

Real risk-free rate of return =1 — P.0

Default-free, inflation indexed, zero coupon: Bond price = Pq = E f t ) + cov(Pj, n q )

(l + R) Nominal short term interest rate (r)

= real risk-free rate (R) + expected inflation (tv) Nominal long term interest rate = R + it + 0

where 6 = risk premium fo r inflation uncertainty

Break-even inflation rate (BEI)

7 ^ ^ n m i - i n f l , r i n n in H p vp / 1 K d n H 7 ^ ^ i i inflation 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 premium (spread) fo r credit risk

Discount rate for equity = R + iv + 0 + 7 + k,

A = equity risk premium = 7 + K

7 = risk premium fo r equity vs risky debt

Discount rate for commercial real estate

= R + /tv + 0 + 7 + k, + <|>

k = term inal value risk, <p = illiquidity premium

Multifactor model return attribution:

k factor return = ^ (/?pi — /?bi) X (Aj)

i=l Active return

= factor return + security selection return Active risk squared

= active factor risk + active specific risk

n

Active specific risk = ^ ^ wpi — wbi)2<Tei

i=l Active return = portfolio return - benchmark return

R a = R p " R b n

Portfolio return = Rp = y ^ w p j R ;

i=l

n

i=l Information ratio

Portfolio Sharpe ratio = SRp = ^ ^

Sharpe ratio = ^ SR g2 + IRP2

Total portfolio risk: o p2 = ctb2 + aA2

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)VbRcta

Sharpe-ratio-maximizing aggressiveness level:

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

Trang 7

CFA ® LEVEL I SMARTSHEET

2018

CRITICAL CONCEPTS FOR THE CFA EXAM

Trang 8

efficientlearning.com/cfa

ETHICAL AND

PROFESSIONAL STANDARDS

ETHICS IN THE INVESTMENT PROFESSION

• Challenges to ethical behavior: overconﬁ dence bias,

situational inﬂ uences, focusing on the immediate rather

than long-term outcomes/consequences

• General ethical decision-making framework: identify,

consider, decide and act, reﬂ ect

• 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 ﬁ ne)

STANDARDS OF PROFESSIONAL CONDUCT

A Knowledge of the Law

B Independence and Objectivity

C Misrepresentation

D Misconduct

II Integrity of Capital Markets

A Material Nonpublic Information

B Market Manipulation

III Duties to Clients

A Loyalty, Prudence and Care

B Fair Dealing

C Suitability

D Performance Presentation

E Preservation of Conﬁ dentiality

IV Duties to Employers

A Loyalty

B Additional Compensation Arrangements

C Responsibilities of Supervisors

V Investment Analysis, Recommendations and Actions

A Diligence and Reasonable Basis

B Communication with Clients and Prospective

Clients

C Record Retention

VI Conﬂ icts of Interest

A Disclosure of Conﬂ icts

B Priority of Transactions

C Referral Fees

VII Responsibilities as a CFA Institute Member or CFA

Candidate

A Conduct as Participants in CFA Institute Programs

B Reference to CFA Institute, the CFA Designation,

and the CFA Program

GLOBAL INVESTMENT PERFORMANCE

STANDARDS (GIPS®)

is voluntary.

• Comply with all requirements of GIPS on a ﬁ rm-wide

basis in order to claim compliance

• Third-party veriﬁ cation of GIPS compliance is optional.

• Present a minimum of ﬁ ve years of GIPS-compliant

historical performance when ﬁ rst claiming compliance,

then add one year of compliant performance each

subsequent year so that the ﬁ rm 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

QUANTITATIVE METHODS TIME VALUE OF MONEY

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

ﬂ ow

(1 r) N

• PV and FV of ordinary annuity and annuity due

PV A

PV nnuity Due e e e = = = = = = = = = = = = = = = = = = PV PV PV PV O O O O rd rd inar inar inary A inar inar inar y A y A y A nnuity nnuity × × × × × × × × × × × × × × × × × × A

FVA

FVnnuity Dueeee = = = = = = = = = = = = = = = = = = FV FV FV FVOOOO rd rd inar inar inary A inar inar inar y A y A y A nnuity nnuity × × × × × × × × × × × × × × × × × ×

• PV of a perpetuity

I/Y Perp

PVPerp

PV etuity=

DISCOUNTED CASH FLOW APPLICATIONS

• Positive net present value (NPV) projects increase shareholder wealth

• For mutually exclusive projects, choose the project with the highest positive NPV

• Projects for which the IRR exceeds the required rate of return will have positive NPV

• For mutually exclusive projects, use the NPV rule if the NPV and IRR rules conﬂ ict

YIELDS FOR US TREASURY BILLS

• Bank discount yield

F 360 t BD

r BD r

• Holding period yield

HPY PP − −PP + + D P

P + D

1 − 0 +

P 1 P 0

P − P +

P 1 − − P 0 + +

P − P + 1 0

P 0 P

1 + 1

P1 D1

P + D

P 1 + + D 1

P + D 0

P 0 P

• Money market yield

=

− ×

R 360 r0 r × ×

360 (t − × − × r ) (t

MM 0 r 0 rBDBD

BD

r ) BD

r )

R MM = = = H PY PY × × × (360/t)

• Eﬀ ective annual yield

DiscounTeD cash floW applicaTions

4

Effective Annual Yield

EAY (1 HPY) 365/t 1 where:

HPY = holding period yield

t = numbers of days remaining till maturity

HPY (1 EAY) t/365 1

Money Market Yield

− ×

360 (t r )

BD

R MM HPY (360/t)

Bond Equivalent Yield

BEY [(1 EAY) 0.5 1] 2

STATISTICAL CONCEPTS

• Data scales: Nominal (lowest), Ordinal, Interval, Ratio

(highest)

• Arithmetic mean: simple average

• Geometric mean return: used to average rates of change (or growth) over time

R = = ( + +

R = =   ( + +

R = =   ( + +

R = = = =   ( + + + +

RGGGG= = = = = = = =  ( 1 R 1 R + + + + + + ) ( + + 1111) ( × + × + × + × + 1 R 1 R ) ) ) ×… ×…× + × + × + × + ( ( ( 1 R 1 R ) ) ) )  ) 1  − − 1 1 1 1

RG= = ( + + 1

R = = ( + +

RG= = ( + + 1

R = =   ( + +

RG= = = =   ( + + + + 1

R = =  ( + +

R  (

R G   ( 1

R = = = =   ( + + + +

RG= = = = = = = =   ( + + + + + + + + 1

RGG= = = = = = = =  ( 1 R 1 R 1 R 1 R + + + + + + + + 11 2222222) ) ) ) ) ) ×… ×… ×… ×…× + × + × + × + × + × + × + × + × + × + ( ( ( ( ( ( 1 R 1 R 1 R 1 Rnnnnnnn

R = = n ( + +

R = = ( + +

RG= = ( + + 1

R = = n ( + +

RG= = ( + + 1

• Harmonic mean: used to determine the average cost of shares purchased over time

∑

=

1 x H i

i 1 =

i 1 = N

• Variance: average of the squared deviations around the mean

∑

σ =

− µ

n 2

σ = 2

σ =

i 1 =

i 1 = n

∑

=

− s

n 1 −

2

i 1 =

i 1 = n

• Standard deviation: positive square root of the variance

• Coeﬀ icient of variation: used to compare relative dispersions of data sets (lower is better)

Coefficient of variatio ariatio ar n s

X

=

• Sharpe ratio: used to measure excess return per unit of risk (higher is better)

Sharpe arpe ar ratio r r

s

p f

r p r f

p

=rr−rr

• Positive skew: mode < median < mean

• Kurtosis: leptokurtic (positive excess kurtosis), platykurtic (negative excess kurtosis), mesokurtic (same kurtosis as normal distribution; i.e zero excess kurtosis)

PROBABILITY CONCEPTS

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

E(X) P( = = = = = = = = = = = = = = = = P( X ) X ) X ) X ) X ) X )1111 1 X X X X1111 1 + + + + + + (X )X + + + + + + + + + + P P P P 22)X )X 22 P(X )X X ) X )XnnnXnnn

∑

σ (X =

σ ) ) =∑ ∑P P

σ 2 = (X ) [X X − − (X)] E E

σ = i i i ) [ ) [X X i i i E E 2

i 1 =

i 1 = n

• Covariance and correlation of returns

Corr(R ,R ) A A ,R ,R B B ) = ρ = ρ R ,R ) ( ( R , R ,R ) A A A R ) B B B Cov(R ,R )((σσσσR , R ,R )))((AAAσσσσR )))BBB

A B

σ A σ B

( A ) B ( σ ) σ ( σ σ A ) σ σ B ( σ σ σ σ σ A A ) ( ( ( ( σ σ σ σ σ B B ) ) ) )

• Expected return on a portfolio

E(R ) R ) R )ppp w E(R ) w E(R ) w E(R ) w E w Eiii ii) w ) w11 R ) R ) w E111 w E222 22) ) w E(R ) w wNN R ) R )NN

i 1

N

2 ) ) w w N

2 ) w N

∑

p ∑ i

p = = = = w E w E(R i (R ) w ) w = = = =

p w E i

p = w E w E i =

p = = = w E i iiii) w ) w ) w ) w = = = 1111

p =∑ ∑ i =

p ∑ i

p i 1111+ + + + + + + + w E w E(R w E w E w E w E2222(R )222222) ) ) ) ) ) ) ) ) ) ) + + + + + + + + + + w w w w w w w w w w w wNNNNNN

i 1 =

i 1

• Variance of a 2-asset portfolio Var(

Va R ) w R ) R ) wppppppp= = = = = w w w w w w w w w w w w w 2 2 2 2AAAAAAAσ σ σ σ σ 2 2 2 2 (R ) w ( ( ( ( ( ( ( ( ( ( ( ( ( ( R ) R ) wAAAAAAA+ + + + + w w w w w w w w w w w w wBBB2 2BBBB2 2 σ σ σ σ σ 2 2 2 2 (R ) 2w w (R ,R ) (R ) (R ) ( ( ( ( ( ( ( ( ( ( ( ( ( ( R ) R )BBBBBB+ + + + + + + 2w 2w w ( 2w 2w 2w 2wAAAAAAw ( w (R , w ( w ( w ( w ( w (BBBBBBBρ ρ ρ ρ ρ ρ ρ R ,AAAAAAAR ) R ) (RBBBBBBBσ σ σ σ σ (R (R (R ) ( (R (R (R (RAAAAAAA) ( σ σ σ σ σ R ) R )BB

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 X x) = = = = = = ) ) ) n x n x C (p) (1 – p) C C C C ) ( ) ( x x n – x

• Expected value and variance of a binomial random variable

= × E(x) n p = × = × n p

σ = × × 2 n p n p × × × × (l-p)

σ = 2

σ =

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

• A z-score is used to standardize a given observation of a normally distributed random variable

z ( = = = = = = = = = = = = = = = obs obs er er erve er er er ve ve ve d v d v alue alue − − − − − − − − − − − − − − − population mean)/standard ndard nda deviation ( n ( = − = − = − = − µ σ x x x µ σ µ σ µ σ ) ) ) / /

• Roy’s safety-ﬁ rst criterion: used to compare shortfall risk

of portfolios (higher SF ratio indicates lower shortfall risk)

Shortf hortf hor al tfal tf l ratio (SF Ratio) E RP P RR R T T

P ( )

E R( )

E R( )P P T T

Trang 9

SAMPLING THEORY

• Central limit theorem: Given a population with any

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

σ =

σ = σ x n

σ = x

σ =

• When the population variance is not known, the standard

error of sample mean is calculated as

=

n

x

• Conﬁ dence interval for unknown population parameter

based on z-statistic

x z ±

x z ± /2 n

• Conﬁ dence interval for unknown population parameter

based on t-statistic

± α

x t ±

x t ± sn

2

• When to use z-statistic or t-statistic

When Sampling from a: Small Sample n < 30 Large Sample n > 30

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

• One-tailed versus two-tailed tests

Type of test hypothesis Null hypothesis Alternate Reject null if Fail to reject null if P‐value represents

One tailed

(upper tail)

test

H 0 : μ ≤ μ 0 H a : μ > μ 0 Test statistic >

critical value Test statistic ≤ critical value Probability that lies above the computed test statistic.

One tailed

(lower tail)

test

H 0 : μ ≥ μ 0 H a : μ < μ 0 Test statistic <

critical value Test statistic ≥ critical value Probability that lies below the computed test statistic.

Two‐tailed H 0 : μ = μ 0 H a : μ ≠ μ 0 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 H 0 is True H 0 is False

Do not reject H 0 Correct decision Incorrect decision

Type II error

Reject H 0 Incorrect decision

Type I error

Significance level =

P(Type I error)

Correct decision Power of the test

= 1 − P(Type II error)

• Hypothesis test concerning the mean of a single

population

= − µ

t-stat x

s n

0

• Hypothesis test concerning the variance of a normally

distributed popu lation

( )

χ = 2 ((((((n 1 n 1 − −σ))))))s

χ = 2

0

• Hypothesis test related to the equality of the variance of

two populations

s

1

2

=

TECHNICAL ANALYSIS

• Reversal patterns: head and shoulders, inverse head and shoulders, double top and bottom, triple top and bottom

• Continuation patterns: triangles (ascending/descending/

symmetrical), rectangles, ﬂ ags 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 oﬀ erings

• 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)

ECONOMICS DEMAND ELAST ICITIES

• Own-price elasticity of demand is calculated as:

% P

Px x x

% P x

% P

= ∆% Q% Q% P% P∆∆∆ … (Equation 6)

• If the absolute value of price elasticity of demand 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:

=

E % change in quantity demanded

% change in income

I

• Positive for a normal good

• Negative for an inferior good

• Cross-price elasticity of demand is calculated as:

E % change in quantity demanded

% change in price of substitute or complement

C =

• Positive for substitutes

• Negative for complements

• Normal good: substitution and income eﬀ ects reinforce one another

• Inferior good: income eﬀ ect partially mitigates the substitution eﬀ ect

• Giff en good: inferior good where the income eff ect outweighs the substitution eff ect, making the demand curve upward sloping

• Veblen good: status good with upward sloping demand curve

PROFIT MAXIMIZATION, BREAKEVEN AND SHUTDOWN ANALYSIS

• Proﬁ ts are maximized when the diﬀ erence between total 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 ﬁ rm is earning normal proﬁ t

• Short-run and long-run operating decisions

TR = TC Continue operating Continue operating

TR > TVC, but < TC Continue operating Exit market

TR < TVC Shut down production Exit market

MARKET STRUCTURES

• Perfect competition

• Minimal barriers to entry, sellers have no pricing power

• Demand curve faced by an individual ﬁ rm is perfectly elastic (horizontal)

• Average revenue (AR) = Price ( P) = MR

• In the long run, all ﬁ rms in perfect competition will make normal proﬁ ts

• M onopoly

• High barriers to entry, single seller has considerable pricing power

• Product is diﬀ erentiated through non-price strategies

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

• An unregulated monopoly can earn economic proﬁ ts

in the long run

• Monopolistic comp etition

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

• Product is diﬀ erentiated through advertising and other non-price strategies

• Demand curv e faced by each ﬁ rm is downward sloping

• In the long run all will make normal proﬁ ts

• Oligopoly

• High costs of entry, sellers enjoy substantial pricing power

• Product is diﬀ erentiated on quality, features, marketing and other non-price strategies

• Pricing strategies: pricing interdependence (kinked demand curve), Cournot assumption, game theory (Nash equilibrium), Stackelberg model (dominant

ﬁ rm)

• Firms always maximize proﬁ ts at the output level where

MR = MC

• Identiﬁ cation of market structure

• N-ﬁ rm 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

• Expenditure approach

GDP C I G (X M) = + = + C I C I+ + + + G ( G (X M X M −

+ GDP Nati = = = = = = = = = = Nati ona ona l i l i ncom ncom e C e C + + + + + + + + + + apital consumption allowance Statistical discrepancy … (Equation 1)

• Equality of Expenditure and Income

S I= +

S I = + G T( ( ( (G T G T G T G T− − − − − − ) ) ) ) + + + + + + ( ( (X M X M X M X M− − − − ) ) ) … (Equation 7)

• To fi nance a fi scal defi cit (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)

An Increase in the Following Factors Shifts the AD Curve Reason

Stock prices Rightward: Increase in AD Higher consumption 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

• Factors causing a shift in aggregate supply (AS)

Trang 10

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

Real GDP Unemployment Rate Aggregate Level of Prices

• Eﬀ ect of combined changes in AD and AS

Change in AS Change in AD

Effect on Real GDP Effect on Aggregate Price Level

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)

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 ﬁ xed basket of goods and

services to measure the cost of living results in an

upward bias in the computed inﬂ ation 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 ﬁ scal policy (reduce spending and/

or increase taxes) is used to control inﬂ ation in an

expansion Expansionary ﬁ scal policy (increase spending and/or reduce taxes) is used to raise employment and output in a recession

• Fiscal multiplier

1 [1 MP − − − − − − MP C( C( 1 t 1 t − − − − − − )]

• Limitations ﬁ scal policy: recognition, action and impact lags

• Relationships between monetary and ﬁ scal policy

• Easy ﬁ scal policy/tight monetary policy – results in higher output and higher interest rates (government expenditure would form a larger component of national income)

• Tight ﬁ scal 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 ﬁ scal policy/easy monetary policy – this would lead to a sharp increase in aggregate demand, lowering interest rates and growing private and public sectors

• Tight ﬁ scal 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

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 diﬀ erences in technology are the key source of comparative advantage

• Heckscher-Ohlin model: capital and labor are variable factors of production and diﬀ erences in factor endowments are the primary source of comparative advantage

• Eﬀ ect of tariﬀ s, import quotas, export subsidies and voluntary export restraints

• Price, domestic production and producer surplus increase

decrease

• Current account (merchandise trade, services, income receipts and unilateral transfers)

• Capital account (capital transfers and sales/purchases

of non-produced, non-ﬁ nancial assets)

• Financial account (ﬁ nancial assets abroad and foreign-owned ﬁ nancial assets in the reporting country)

• Current account surplus or deﬁ cit

CA = X – M = Y – (C + I + G)

CURRENCY EXCHANGE RATES

• 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/FC C C C C C = = = = = = = S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S D D D D D D C/ C/ C/FC C/ C/ C/ C/ C/ C/ C/ C/ C/ FC FC FC FC FC FC FC × × × × × × × (P /P ) ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( P /P ) P / P / P / FC FC P ) P ) DC DC

• Forward exchange rate (arbitrage-free)

S (1 r ) (1 r )or F S

(1 r ) (1 r )

DC

F DC

F /FC FC/DC DC

r )DC

r )

FC

r ) FC

r ) F F F F F F DC DC /F /F C C S S S S S S D D C/FC C/ DC

r )DC

r )

FC

r ) FC

r )

= × ++ F F F F F F C C C C = = = = = = = S S S S S S D D D D C/ C/FC C/FC C/ C/FC C/ FC × × × × × × × +

+

• Exchange rate regimes: dollarization, monetary union,

fi xed parity, target zone, crawling pegs, fi xed parity with crawling bands, managed fl oat, independently fl oating rates

FINANCIAL REPORTING AND ANALYSIS

FINANCIAL REPORTING BASICS

• Types of audit opinions: unqualiﬁ ed, qualiﬁ ed, adverse, disclaimer

• Accruals: unearned or deferred revenue (liability), unbilled or accrued revenue (asset), prepaid expenses (asset), accrued expenses (liability)

• Qualitative characteristics of fi nancial information: relevance, faithful representation, comparability, verifi ability, timeliness, understandability (fi rst two are fundamental qualitative characteristics)

• General features of ﬁ nancial statements: fair presentation, going concern, accrual basis, materiality and aggregation, no oﬀ setting, frequency of reporting, comparative information, consistency

INCOME STATEMENTS

• Revenue recognition methods: percentage of completion, completed contract, installment method, cost recovery method

• Discontinued operations: reported net of tax as a separate line item aft er 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 period errors (restate all prior-period ﬁ nancial statements)

• Basic EPS

= Basic EPS Net income Pe P − − referred dividends Weighted average number of share hare ha s outstanding

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

Net income dividendsPreferred ConvertibleConverpref d

dividends Convertible Conver debt interest (1 t) Weighted

average shares

Shares from conversion of convertible conver prefe efe ef rred shares

Shares from conversion of convertible conver debt

Shares issuable from stock options

=

−

 +++++++ prprefefeefeefefeef rreerredd +++++++ × −× −(1(1















+ conver f + + convertible + + convertibleconvertible + + convertibleconver + +

BALANCE SHEETS

• Accounting for gains and losses on marketable securities

Held‐to‐Maturity

Balance Sheet Reported at cost or

amortized cost.

Reported at fair value Reported at fair value Unrealized gains or losses due

to changes in market values are reported in other comprehensive income within owners’ equity.

Items recognized

on the income statement

Interest income.

Realized gains and losses.

Dividend income.

Interest income.

Realized gains and losses.

Dividend income Interest income 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

ﬁ rms of diﬀ erent 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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