CFA Level II 公式
Contents ETHICAL AND PROFESSIONAL STANDARDS..........................................................................5 QUANTITATIVE METHODS .........................................................................................................6 Hypothesis Testing ....................................................................................................................6 Test Population Means ..............................................................................................................6 ·Difference in means test for independent samples Equal Variance..........................................6 Unequal Variance : ....................................................................................................................6 ·Mean differences test for dependent samples...........................................................................6 Variance Tests............................................................................................................................6 Correlation Coefficient, r ..........................................................................................................7 Multiple Regression ..................................................................................................................7 Regression Analysis Problems ..................................................................................................7 ECONOMICS ...................................................................................................................................8 Growth Accounting Equation....................................................................................................8 Neoclassical Growth Theory.....................................................................................................8 Endogenous Growth Theory .....................................................................................................8 Factors Promoting Economic Growth.......................................................................................8 Purchasing Power Parity ...........................................................................................................8 International Fisher Relation.....................................................................................................8 Uncovered interest Rate Parity..................................................................................................9 Interest Rate Parity....................................................................................................................9 Asset Market Approach.............................................................................................................9 Currency Arbitrage....................................................................................................................9 Real Exchange Rate Risk ..........................................................................................................9 Foreign Currency Risk Premium (FCRP) ...............................................................................10 International CAPM................................................................................................................10 Currency Exposure..................................................................................................................10 Product Life Cycle ..................................................................................................................10 Regression to Mean.................................................................................................................10 PORTFOLIO MANAGEMENT .....................................................................................................11 Measuring Risk .......................................................................................................................11 Portfolio Risk and Return .......................................................................................................11 Efficient Frontier and Optimal Portfolio .................................................................................11 Systematic Risk vs. Unsystematic Risk ..................................................................................11 Capital Market Line(CML) .....................................................................................................12 SML and CAPM .....................................................................................................................12 SML vs. CML .........................................................................................................................12 Arbitrage Pricing Theory(APT) ..............................................................................................12 Testing CAPM.........................................................................................................................12 Multifactor Models .................................................................................................................13 Portfolio management Planning Process.................................................................................13 FINANCIAL STATEMENT ANALYSIS .......................................................................................14 Inventory Analysis ..................................................................................................................14
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CFA Level II 公式
Depreciation and Impairment..................................................................................................14 Off-Balance Sheet Debt ..........................................................................................................14 Lease Classification ................................................................................................................14 Effect of Classification on Lessor ...........................................................................................15 Marketable Securities Classification.......................................................................................15 Account for Inter-corporate Investments ................................................................................15 Business Combinations ...........................................................................................................15 Purchase Method: Constructing Consolidated Statements......................................................15 Effect of Pension Plan Assumptions .......................................................................................16 Pension Calculations ...............................................................................................................16 Pension Adjustments ...............................................................................................................16 Multinational Operations ........................................................................................................17 Cash Flow Measures ...............................................................................................................17 Basic and Diluted EPS ............................................................................................................17 Most Critical Ratios ................................................................................................................17 3-component DuPont: .............................................................................................................18 5-component DuPont: .............................................................................................................18 Sustainable Growth Rate.........................................................................................................18 CORPORATE FINANCE ...............................................................................................................19 Weighted Average Cost of Capital ..........................................................................................19 Capital Budgeting Expansion Project .....................................................................................19 Operating Leverage.................................................................................................................19 Financial Leverage..................................................................................................................19 Total Leverage.........................................................................................................................19 Optimal Capital Structure .......................................................................................................19 Dividend Signaling Hypothesis...............................................................................................19 Good Reasons for Mergers......................................................................................................19 Bad Reasons for Mergers ........................................................................................................19 NPV of Merger........................................................................................................................20 Takeover Defense Measures ...................................................................................................20 EQUITY INVESTMENTS .............................................................................................................21 Alpha.......................................................................................................................................21 Taxes and International Investing ...........................................................................................21 Methods to Reduce Execution Costs.......................................................................................21 American Depository Receipts (ADRs)..................................................................................21 Franchise Value and Growth Process ......................................................................................21 Inflation Effects on Valuation .................................................................................................21 Valuation in Emerging Markets...............................................................................................21 Porter’s Five Forces ................................................................................................................22 Generic Competitive Strategies...............................................................................................22 Industry Analysis.....................................................................................................................22 Discounted Cash Flow (DCF) Methods..................................................................................22 Gordon Growth Model (GGM)...............................................................................................23 Present Value of Growth Opportunities ..................................................................................23
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CFA Level II 公式
Two – Stage Growth Model ....................................................................................................23 H-Model..................................................................................................................................23 Solving for Required Return ...................................................................................................23 Strengths of multistage growth models:..................................................................................23 Limitations of multistage models:...........................................................................................24 Free Cash Flow to Firm (FCFF)..............................................................................................24 Free Cash Flow to Eqauity (FCFE).........................................................................................24 Single-Stage FCFF / FCFE Models ........................................................................................24 Two – Stage FCFF / FCFF Models .........................................................................................24 Price to Earnings (P/E) Ratio ..................................................................................................24 Justified P/E ............................................................................................................................24 Normalization Methods: .........................................................................................................25 Price to Book (P/B) Ratio .......................................................................................................25 Price to Sales (P/S) Ratio ........................................................................................................25 Price to Cash Flow Ratios.......................................................................................................25 Method of Comparables..........................................................................................................26 Residual Income (RI)Valuation...............................................................................................26 Economic Value Added ...........................................................................................................26 Growth Duration Model..........................................................................................................26 DEBT INVESTMENTS .................................................................................................................27 Credit Analysis........................................................................................................................27 Bond Price Yield Relationship ................................................................................................27 Duration and Convexity ..........................................................................................................28 Yield Curve(Term Structure ) Shifts .......................................................................................28 Theories of the Term Structure................................................................................................28 Key Rate Duration ..................................................................................................................28 Valuing Option Free Bonds.....................................................................................................28 Value Bond with Embedded Option........................................................................................29 Option Adjusted Spread ..........................................................................................................29 Convertible Bonds...................................................................................................................29 MBS Prepayment Risk............................................................................................................29 CMO prepayment Risk ...........................................................................................................30 ABS Prepayment Risk ............................................................................................................30 MBS /ABS spread Analysis ....................................................................................................30 DERIVATIVES ...............................................................................................................................31 Forwards-No Arbitrage Pricing...............................................................................................31 Equity Forward .......................................................................................................................31 Forward on Fixed Income securities .......................................................................................31 Forward Rate Agreements.......................................................................................................31 Currency Forward(Interest Rate Parity ).................................................................................31 Futures Price ...........................................................................................................................31 Futures Arbitrage.....................................................................................................................32 Treasury Bond Futures ............................................................................................................32 Equity Futures .........................................................................................................................32
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CFA Level II 公式
Put-Call Parity.........................................................................................................................32 Caps and Floors.......................................................................................................................32 Binomial option Pricing Model...............................................................................................32 Black-Scholes Option Pricing Model......................................................................................32 Delta........................................................................................................................................33 Delta Neutral Hedging ............................................................................................................33 Gamma....................................................................................................................................33 Currency Swaps ......................................................................................................................33 Interest Rate Swaps.................................................................................................................33 Equity Swaps ..........................................................................................................................33 Swap Pricing and Valuation ....................................................................................................33 Swptions..................................................................................................................................34
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CFA Level II 公式
ETHICAL AND PROFESSIONAL STANDARDS I Fundamental Responsibilities I(A) Comply with laws Code/Standards I(B) Do noe participate/assits in violations II Responsibilities to Profession II (A ) Use of Professional designation II(B) professional nisconduct II(C) prohibition against plagiarism III Responsibilities to Employer III (A) Inform employer of Code/Standards III (B) duty to employer III (C) disclosure of conflicts to employer III (D)Disclosure of additional compensation III (E) Responsibilities of supervisors IV Responsibilities to Clients IV (A.1) Reasonable basis and represent tations IV (A.2) Research reports IV (A.3) Independence and objectivity IV(B.1) Fiduciary duties IV(B.2) Portfolio recommendations/actions IV(B.3) Fair dealing IV(B.4) Priority of transactions IV(B.5) Preservation of confidentiality IV(B.6) Prohibition against misrepresentation IV(B.7) Disclosure of conflicts to clients IV(B.8) Disclosure of referral fees V Responsibilities to Public V(A) Don’t use material nonpublic info V(B) Performance presentation
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CFA Level II 公式
QUANTITATIVE METHODS Hypothesis Testing ·Type I error Rejecting H 0 when true ·Type II error Failing to reject H 0 when false ·a=probability of Type 1 error Test Population Means z=
x − µ0 x − µ0 ;t = , n − 1, df s/ n s/ n n<30 Z
n≥30 Z
Normal distribution Known variance Normal distribution t t or z Unknown variance ·Difference in means test for independent samples Equal Variance
t=
( x1 − x2 ) − ( µ1 − µ 2 ) 1/ 2
⎛ s 2p s 2p ⎞ ⎜ + ⎟ ⎜n n ⎟ 2 ⎠ ⎝ 1
, n1 + n2 − 2 df
(n1 − 1) s12 + (n2 − 1) s22 s = n1 + n2 − 2 2 p
Unequal Variance :
t=
( x1 − x2 ) − ( µ1 − µ 2 ) 1/ 2
⎛ s12 s22 ⎞ ⎜⎜ + ⎟⎟ ⎝ n1 n2 ⎠
·Mean differences test for dependent samples t=
d , n − 1 df sd / n
Variance Tests Population variance x 2 =
(n − 1) s 2
Equality of variances : F =
σ 02
, n − 1 df
s12 , n1 − 1, n2 − 1 df s12 > s 22 s 22
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CFA Level II 公式
Correlation Coefficient, r Measure of strength of linear relationship (correlation ) between two variables
r1, 2 =
cov(1,2) s1 × s2
Test H 0 :ρ=0:
t − stat =
r n−2 1− r 2
, n − 2 df
Multiple Regression Yi = bo + (b1 × X li ) + (b2 × X 2i ) + (b3 × X 3i ) + ε i
·Test statistical significance of b:Ho:b=0 t = bˆ / sbˆ , n − k − 1 df
(
·Confidence Interval: bˆ j ± t c × sbˆj
)
·SST=SSR+SSE ·MSR=SSR/k ·MSE=SSE/(n-k-1) ·Test statistical significance of regression F=MSR/MSE with k and n-k-1 df(1-tailed ) ·Standard error of the estimate (SEE=MSE ) smaller SEE means better fit ·Coefficient of determination(R2=SSR/SST).% of variability of Y explained by X’s ;higher R2 means better fit Regression Analysis Problems ·Heteroskedasticity: Non-constant error variance Detect with Breusch-Paen test ·Autocorrelation: Correlation among error terms Detect with Durbin Watson test positive autocorrelation if DW< d1 ·Multicollinearity: High correlation among X’s. Detectif F-test significant t-tests insignificant
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CFA Level II 公式
ECONOMICS Growth Accounting Equation Total economic output growth=(labor share ×labor input growth)+(growth of total factor productivity ) (a,k,a technological progress ) (Percapita economic output growth)=( capital share)×(capital-labor ratio growth )+(growth of total factor productivity ) Neoclassical Growth Theory z Assumes diminishing marginal product of capital (MPC) and curved savings function Predicts that an increase in savings rate will Increase the level of per capita output Not change long-run growth in total output which equals population growth in long-run Not change growth rate in per capita output withch equals technological progress in long-run Endogenous Growth Theory z Assumes constant MPC to society and a straight line savings curve but diminishing MPC to individual firms Predicts that an increase in savings rate will increase long run growth in per capita output Factors Promoting Economic Growth z High savings/capital investment z Human capital development z Balanced budgets tight monetary policy z Free trade z Adequate legal system z Low population growth z Technological advancement and sharing Purchasing Power Parity Law of one price a single clearly comparable good should have same real price in all countries Relative PPP Countries with high inflation rates should see their currencies depredate
s1 1 + iFC = , Sin FC / DC s0 1 + iDC International Fisher Relation Assumes real interest rates are equal across borders so interest differential equals inflation differential
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CFA Level II 公式
1 + rFC 1 + E (iFC ) = 1 + rDC 1 + E (iDC ) rFC − rDC ≈ E (iFC ) − E (iDC )
Uncovered interest Rate Parity Countries with high minimal interest rates should see their currencies depreciate
E ( s1 ) 1 + rFC , S _ in FC / DC = s0 1 + rDC %∆S ≈ rFC − rDC
Interest Rate Parity Countries with high minimal interest rates will have their currencies sell at forward discount to prevent arbitrage
F 1 + rFC = , Sand F in FC / DC S 0 1 + rDC F − S0 ≈ rFC − rDC S0 Asset Market Approach Money supply increase will cause: z Short-run DC depreciation form inflation Increase and rate decrease. z Long-run DC appreciation to PPP level. z Overall, DC depreciates from initial level PPP level. Currency Arbitrage 2-currency arbitrage bid-ask midpoint range =
1 ⎛⎜ 1 1 ⎞⎟ ± − 2 S f ⎜⎝ S f (1 − TC ) S f ⎟⎠
·Triangular arbitrage opportunity if :
⎛ FC1 ⎞ ⎜ ⎟ ⎝ DC ⎠bid
⎛ DC ⎞ ⎟⎟ × ⎜⎜ FC 2 ⎠ bid ⎝
⎛ FC2 ⎞ ⎟⎟ ≠ 1 × ⎜⎜ FC 1 ⎠ bid ⎝
Real Exchange Rate Risk Real exchange rate (X) is:
⎛P X = S × ⎜⎜ FC ⎝ PDC
⎞ ⎟⎟ , S in DC/FC ⎠
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CFA Level II 公式
Real exchange rate is possibility of nominal exchange rate changes not explained by inflation differentials.
Foreign Currency Risk Premium (FCRP) Expected foreign currency appreciation less interest rate differential: FCRP = E (%∆S ) − (rDC − rFC ) , S in
DC/FC
International CAPM DC return =FC interest rate +FC appreciation = DC interest rate + FCRP. E ( R ) = RF + ( β G × MRPG ) + (γ 1 × FCRP1 ) + (γ 2 × FCRP2 )
γ = γ FC + 1 Currency Exposure ·Exporters are hurt ad importers are helped by domestic currency appreciation. ·Traditional model predicts domestic currency depreciation will improve competitiveness and increase equity prices (negative currency exposure). ·Money demand model predicts positive currency exposure; decreased LR economic activity causes currency depreciation and lower equity prices. Product Life Cycle Development Expansion
Maturity
Decline
Regression to Mean Industry competition drives margins to long-run normal level; economic profit = 0.
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CFA Level II 公式
PORTFOLIO MANAGEMENT Measuring Risk From expectation data N
{
}
variance= σ 2 = ∑ [ri − E(r)] × Pi i=1
2
s tan dard deviation = σ = σ 2
Portfolio Risk and Return · E (rp ) = wa E (ra ) + Wb E (rb ) 2 · σ ab = ( wa2σ a2 ) + ( wb2σ b2 ) + (2wa wb pa，bσ aσ b )
·The lower the correlation the greater the benefits of diversification Efficient Frontier and Optimal Portfolio ·Efficient portfolios have highest return for given level of risk or lowest risk for given level of return ·Optimal portfolio is intersection of efficient frontier with I curves E(RP)
Risk σP
Systematic Risk vs. Unsystematic Risk ·Systematic risk cannot be diversified away ;relevant risk for security measured with beta
βi =
cov(stock , market ) var(market )
·Unsystematic risk can be diversified away
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CFA Level II 公式
Capital Market Line(CML) E (rM ) − rf ⎫ ⎧ E (rp ) = rf + ⎨σ p × ⎬ σM ⎩ ⎭
Capital market line
E(RP) Efficient Frontier Market Portfolio Risk σP
SML and CAPM
E (ri ) = rf + {β i × [ E (rm ) − r f ]} Security market line
E(RP)
E(RM) Market Portfolio Rf Risk σP 1
SML vs. CML · Risk measure for CML is total risk only market portfolio and risk-free asset plot on CML ·Risk measure for SML is beta all properly priced securities and portfolios plot on SML Arbitrage Pricing Theory(APT) Main advantage over CAPM is that APT requires fewer assumptions to derive APT may be a more general model Specifically APT does not require the following (historic ) assumptions that are requited by CAPM ·Investors have quadratic utility functions ·Security returns are normally distributed ·All investors hold market portfolio Testing CAPM ·security betas are unstable portfolio betas are stable ·Roll’s Critique CAPM not testable because cannot observe market portfolio ·Benchmark error problem cannot identify market portfolio empirical SML is too flat 12
CFA Level II 公式
Multifactor Models Macroeconomic factors Unexpected changes in inflation real GDP consumer confidence yield curve Microeconomic factors (Fama-French model ) Excess market returns large-cap minus small cap returns value ninus growth returns stock return momentum Portfolio management Planning Process z Analyze risk constraints liquidity time horizon legal and regulatory taxes unique circumstances z Develop IPS client description purpose duties objectives and constraints performance review schedule modification policy rebalancing guidelines z Determine investment strategy passive active semi-active z Select strategic asset allocation asset class weightings based on capital market expectations
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CFA Level II 公式
FINANCIAL STATEMENT ANALYSIS Inventory Analysis z INVEND=INVBGN + Pur-COGS z IF Price↑ LIFO →COGS↑，others↓(taxes↓, net income↓, inventory balances↓, NWC↓)→so determine the relevant ratios. FIFO →COGS↓，others↑(taxes↑, net income↑, inventory balances↑, NWC↑)→so determine the relevant ratios. FIFO COGs
LIFO COGS
Depreciation and Impairment z accelerated → SL depreciation: depreciation↓，future net income↑, ROA↑, ROE↑. z Asset Impairment Obligation (AIO) : today’s assets↓, shareholders’ equity↓, net income↓, ROA↓, and ROE↓; increases today’s debt/equity future depreciation expense↓, debt/equity↓; future net income↑, ROA↑ , ROE ↑, and asset turnover↑. Off-Balance Sheet Debt z Sale of A/R with recourse and take-or-pay contracts parent assets↑, liabilities↑. Lease Classification Lease is capital lease to lessee if one holds: z Title is transferred to lessee at end z Bargain purchase option z Lease period ≥ 75% of asset’s life. z PV of payments > 90% of FV. Lease is capital lease to lessor if all hold: z If lessee regards the lease as Capital Lease z Predictable collectability of the A/R. z Cost can be determnined. Sales-type (capital) lease:; Direct financing :.
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CFA Level II 公式
Effect of Classification on Lessor z Sales-type lessor is equipment dealer Will report profits and has higher assets at the beginning; earlier profits, same total CF, CFO↓(Because of Less interest revenue). z Direct Financing if the lessor is not the equipment dealer Will reports no profits, no change in assets at the beginning; later profits, same total CF, and more CFO↑(Because of More interest revenue) Marketable Securities Classification z Held to-maturity B/S: Cost ; I/S : interest, realized gains/losses z Available for sale B/S: FMV, unrealized gains/losses; I/S: interest, realized gains/losses, dividends z Trading B/S: FMV; I/S: interest, realized gains/losses, dividends, realized and unrealized gains/losses Account for Inter-corporate Investments z Cost/market Equity ratio <20%; no influence. z Equity 20% ≤Equity ratio≤ 50%; significant influence. z Consolidation Equity ratio >50%; control. Business Combinations Under IASB GAAP pooling method: z No identification of acquirer and acquired. z B/S values consolidated at historical cost. z Prior operating results restated. Under IASB and U.S. GAAP purchase methods: z Acquirer and acquired identified. z Acquired firm B/S restated to FMV. z Prior results disclosed, not restated. z Goodwill U.S- annual impairment test; IASB – annual amortization. z In-process R&D U.S –expense immediately; IASB – capitalize and amortize. Purchase Method: Constructing Consolidated Statements z Revalue all tangible assets/liability of acquired to FMV. 15
CFA Level II 公式
z z z
Recognize intangible assets/liabilities of acquired firm. Allocate remaining purchase price to goodwill (net of assumed liabilities). Eliminate common equity of acquired firm; replace with MV of shares issued.
Effect of Pension Plan Assumptions z Higher discount rate： ↓PBO, ABO, service cost, pension expense; ↑ funded status; interest cost. z Lower compensation growth rate： ↓PBO, service cost, interest cost, pension expense; ↑funded status. z Higher expected return ↓pension expense. z Lower healthcare cost inflation rate： ↓decrease APBO & post-retirement benefit expense. Pension Calculations FV of plan assets (beginning) + actual ROA + contributions +/- other factors benefits paid = FV of plan assets (ending) PBOt-1 + service cost + interest cost +/- actuarial losses/gains and amendments +/- other factors - benefits paid PBOt Funded status = FV of plan assets – PBO funded status +/- unrecognized actuarial losses (gains) + unrecognized prior service cost +/- unrecognized prior transfer obligation (asset ) +/- amortization of actuarial losses/gains = net pension asset (liability)
Pension Adjustments z Adjust pension liability/asset to reflect funded status. z Recurring cost = Service cost + Interest cost z Gross pension cost = Recurring cost + actuarial losses + Plan amendments z Non-smoothed cost (credit) = Gross pension cost – Actual ROA 16
CFA Level II 公式
Multinational Operations z All-current method: condition Local currency → functional currency z Method assets/liabilities: current rate. common stock: historical rate . I/S : average rate. z
z
Temporal method. Local currency → Reporting currency Functional currency → Reporting currency sub in inflationary environment, parent currency is functional currency. Method B/S monetary assets/liabilities: current rate. B/S non-monetary assets/liabilities: historical rate. I/S sales, SG&A : average rate. COGS& depreciation: historical rate.
Cash Flow Measures z Traditional cash flow = net income + depreciation + change in deferred taxes. z Cash flow from operations (CFO) = traditional cash flow net changes in non-cash current assets and liabilities. Basic and Diluted EPS NI − Pr ef div Basic EPS= WA common sharesO / S
Diluted EPS=
Adj NI available for common shares WA common shares + potential connom shares O/S
Most Critical Ratios Internal liquidity: z Current ratio = current assets / current liabilities. z Quick ratio = (current assets - inventory) / current liabilities. z Receivables turnover = sales / average accounts receivable z Average collection period = 365/ receivables turnover. z Inventory turnover = COGS / average inventory.. z Payables turnover = COGS / average trade payables. z Payables payment period = 365 / payables turnover. Evaluating operating efficiency: z Total asset turnover = sales / average total assets. 17
CFA Level II 公式
z z z z z z
Fixed asset turnover = sales / average fixed assets. Gross profit margin = gross profit / sales. Operating profit margin = EBIT / sales. Net profit margin =net income / sales. Return on total assets (ROA) = net income/ average total assets. Return on total equity (ROE) = net income / average total equity.
Evaluate business and financial risk: z Debt-equity ratio = total long –term debt/ total equity. z Long – term debt to total capital = long –term debt / long –term capital. Note: long – term capital = long – term debt+ preferred stock + equity. z Debt to assets = total debt / total assets. Note: also called “debt to total capital.” z Interest coverage = EBIT / interest expense.
3-component DuPont: ⎛ netincome ⎞ ⎛ sales ⎞ ⎛ assets ⎞ ⎟⎟ ROE = ⎜ ⎟×⎜ ⎟ × ⎜⎜ ⎝ sales ⎠ ⎝ assets ⎠ ⎝ equity ⎠
5-component DuPont: ⎛ assets ⎞ ⎡⎛ EBIT ⎞ ⎛ sales ⎞ ⎛ int erest exp ense ⎞ ⎟⎟ × (1 − t ) ROE = ⎢⎜ ⎟ ×⎜ ⎟−⎜ ⎟ ] × ⎜⎜ assets ⎠ ⎣⎝ sales ⎠ ⎝ assets ⎠ ⎝ ⎝ equity ⎠
Sustainable Growth Rate g = ROE×RR, RR=Retention Ratio.
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CFA Level II 公式
CORPORATE FINANCE Weighted Average Cost of Capital WACC = (wd)[kd(1-t)]+(wps)(kps)+(wce)(ks), weighted by the market value. Capital Budgeting Expansion Project z Initial investment : Cost , changes in NWC z Operating cash flows = (R-C) (1-t)+(D×t), D is Depreciation. z Terminal cash flows: after-tax salvage return of NWC Operating cash flows at the last period Operating Leverage Variable vs. fixed cost tradeoff. DOL = (△EBIT/EBIT) / (△Q/Q) DOLQ=Q(P-V) / [Q(P-V)-F] DOLS= (S-VC)/ (S-VC-F) Financial Leverage Use of fixed – incomes in capital structure DFL =(△EPS /EPS) / (△EBIT/EBIT) DFL = EBIT / [EBIT – I] Total Leverage DTL = DOL×DFL=(△EPS /EPS) / (△Q/Q) Optimal Capital Structure Trade–off between tax shelter benefit from more debt and higher expected bankruptcy costs from higher leverage. Dividend Signaling Hypothesis Unexpected dividend cut is bad news; dividend increase is good news. Good Reasons for Mergers z Economies of scale. z Vertical integration. z Complementary resources. z Surplus cash. z Eliminating operating inefficiencies. Bad Reasons for Mergers z Diversification. z Lower financing costs. 19
CFA Level II 公式
z
Bootstrapping
NPV of Merger NPV (cash merger)=gain – cost =VBT-(cash price – VT) Cost of stock merger = (N＊PBT)-VT Takeover Defense Measures z Staggered boards. z Supermajority. z Fair price amendment z Restricted voting rights z Waiting period. z Poison pill z Litigation. z Asset or liability restructuring .
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CFA Level II 公式
EQUITY INVESTMENTS Alpha ex ante α = expected return – required return from CAPM or APT ex post α = holding period return - return on similar assets. Taxes and International Investing Three forms of tax: transaction, capital gain, income. Methods to Reduce Execution Costs Program trading, Internal / external crossing, Principal trades, agency trades, futures contract. American Depository Receipts (ADRs) Advantage: Reduce administration / duty costs on each transaction. Disadvantage: Do not eliminate inherent currency / economic risks. Franchise Value and Growth Process Tangible P/E =1/r Franchise P/E = franchise factor ╳ growth factor = FF×G 1 1 FF = − r ROE G=
g r−g
IF ROE>r, firm has sustainable competitive advantage, Franchise Factor>0. If FF>0, higher retention ratio implies higher GF, higher franchise P/E.
Inflation Effects on Valuation Higher flow-through rate implies higher P/ E, all else equal. If inflation flow-through <100%, higher inflation implies lower P/E, all else equal.
P0 1 = , k is the required rate of return, I is the inflation rate, λis the E1 k + (1 − λ ) × I inflation flow-through rate.
Valuation in Emerging Markets Adjust cash flows rather than discount rate: z Country risks are diversifiable. z Differing response to country risk. z Country risk is one- sided. z ID cash flow aids in risk management.
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CFA Level II 公式
Porter’s Five Forces 1. Entry barriers(or threat of new entrants) z function of economies of scale, product differentials, brand identity, capital requirements, access to distribution channels, government policy, cost advantages, 2. Threat of substitutes z function of relative price performance of substitutes, buyer propensity to substitute, switching cost. 3. Bargaining power of buyers z function of bargaining leverage / price sensitivity. 4. Bargaining power of suppliers z determined by differentiation of inputs, presence of substitute inputs, supplier concentration, importance of volume to supplier, threat of forward integration. 5. Rivalry among existing competitors: z function of industry growth, fixed costs, value added, product differences, brand identity, diversity of competitors, exit barriers, informational complexity. Generic Competitive Strategies z Cost leadership Try to be low- cost producer. z Differentiation. Try to set products apart from competitor’s products. z Cost focus Cost leader in industry segment. z Differentiation focus. Differentiate in industry segment. Industry Analysis z Industry life cycle: Pioneer Growth Mature Decline z External factors: Technology, government, social change, demography, foreign influences. Discounted Cash Flow (DCF) Methods Use dividend discount models (DDM) when: z Firm has dividend history. z Dividend policy related to earnings. z Minority shareholder perspective. Use free cash flow (FCF) models when: z Firm lacks stable dividend policy. z Dividend policy not related to earnings. z FCF is related to profitability. 22
CFA Level II 公式
z Controlling shareholder perspective. Use residual income (RI) when: z Firm lacks dividend history. z FCF is negative. Three ways to determine cost of equity: z CAPM: r=rf+ß(rm-rf). z Multi–factor APT. z Add equity risk premium to firm’s LT bond yield. Gordon Growth Model (GGM) Assumes perpetual dividend growth rate V0 =
D1 r−g
Most appropriate for mature, stable firms. Limitations are: z Very sensitive to estimates of r and g, z Difficult with non-dividend stocks. z Difficult with unpredictable growth patterns (use multi-stage model). Present Value of Growth Opportunities E Vo = 1 + PVGO r
Two – Stage Growth Model Step 1: Calculate dividends in high-growth period. Step 2: Use GGM for terminal value at end of high-growth period. Step 3: Discount interim dividends and terminal value to time zero to find stock value. H-Model
Vo = H=
[D0 × (1 + g L )] + [D0 × H ( g s − g L )] r − gL t 2
Solving for Required Return For Gordon (or stable growth) model, solving for return yields:
r=
D1 +g P0
Strengths of multistage growth models: z Flexibility. z Use in forward or reverse. z Relationship between assumptions and value estimates. 23
CFA Level II 公式
z
Easy with spreadsheet software.
Limitations of multistage models: z Garbage-in, garbage-out. z Can’t determine effects of assumptions unless model is clearly understood. z Value estimates sensitive to assumptions of growth and required return. z Difficult to ID data / input errors. Free Cash Flow to Firm (FCFF) Assuming DEPreciation is only NCC: z FCFF= NI+Dep+[Int×(1-tax rate)]-FCInv-WCInv. z FCFF = [EBIT]×(1-tax rate)]+Dep-FCInv – WCInv. z FCFF = [EBITDA×(1-tax rate)]+(Dep×tax rate)-FCInv-WCInv. z FCFF = CFO + [Int×(1-tax rate)]-FCInv. Free Cash Flow to Eqauity (FCFE) z FCFE = FCFF – [Int×(1-tax rate)]+Net borrowing. z FCFE = NI + Dep – FCInv-WCInv+Net borrowing. z FCFE = NI-[(1-DR)×(FCInv-Dep)]-[(1-DR)×WCInv]. z Single-Stage FCFF / FCFE Models z
For FCFF valuation: Vo =
FCFF1 WACC − g
z
For FCFF valuation: Vo =
FCFF1 r−g
Two – Stage FCFF / FCFF 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. z If earnings <0, P/E meaningless. z Volatile, transitory portion of earnings makes interpretation difficult. z Management discretion over accounting choices affects reported earnings. Justified P/E Leading P / E1 =
1− b r−g
24
CFA Level II 公式
Trailing P / E0 =
(1 − b)(1 + g ) r−g
Normalization Methods: z Historical average EPS. z Average ROE. Price to Book (P/B) Ratio Advantages: z BV almost always>0, z BV more stable than EPS. z Measures NAV of financial institutions. Disadvantages: z Size differences cause misleading comparisons. z Influenced by accounting choices. z BV≠MV due to inflation/ technology. Justified = P / B =
ROE − g r−g
Price to Sales (P/S) Ratio Advantages: z Meaningful even for distressed firms. z Sales revenue not easily manipulated. z Not as volatile as P/E ratios. z Useful in valuing mature, cyclical, and start-up firms. Disadvantages: z High sales do not imply high profits and cash flows. z Does not capture cost structure differences. z Revenue recognition practices still distort sales. Justified P / S =
PM 0 × (1 − b)(1 + g ) r−g
Price to Cash Flow Ratios Advantages: z Cash flow harder to manipulate than EPS. z More stable than P/E z Mitigates earnings quality concerns. Disadvantages: z Difficult to estimate true CFO z FCFE better but more volatile.
25
CFA Level II 公式
Method of Comparables z Firm multiple > benchmark implies overvalued z Firm multiple < benchmark implies undervalued. z Fundamentals that affect multiple should be similar between firm and benchmark. Residual Income (RI)Valuation z RIt=Et-(r×Bt-1) z Firm value = adjusted BV0+ PV of expected future RI. z
Single-stage residual income model: V0 = B0 +
z
PV of continuous residual income in T-1:
ROE − r × B0 r−g
RI T , ω is the persistence factor, 1+ r − ω
between 0 and 1.
Economic Value Added EVA = NOPAT - $WACC; NOPAT = EBIT(1-t) $WACC = WACC×Invested capital; Invested capital = NWC + Net PP&E Ways to increase EVA : Increase revenues, reduce expenses, less invested capital , find + NPV projects, reduce WACC. Growth Duration Model ⎛1 + gH + dH ⎞ ⎛ High, Growh, P / E ⎞ ⎟⎟ ln⎜ ⎟ = T × ln⎜⎜ ⎝ Cons tan tGrowthP / E ⎠ ⎝ 1 + gC + dC ⎠
26
CFA Level II 公式
DEBT INVESTMENTS Credit Analysis Liquidity sources z Working capital z Cash flow. z Back-up facilities z Third-party guarantees. High-yield debt z Issuer has senior, short-term, floating bank debt. Asset-backed debt z Quality of collateral. z Servicer quality z Payment structure. z Legal structure (VIE, SPV) Municipal bonds z Tax-backed: repaid with tax revenue z Revenue: repaid with project CF. Sovereign debt z Local vs. foreign currency rating. z Economic risk; ability to pay. z Political risk: willingness to pay. Bond Price Yield Relationship Option free bond exhibits positive convexity.
Callable bond exhibits negative convexity. price
price
Strike price
yield
yield
27
CFA Level II 公式
Duration and Convexity
ED =
(BV−∆Y − BV+∆Y ) 2 × BVO × ∆Y
%△BV (from duration)≈-ED×△y Convx =
BV− ∆y − BV+ ∆y − (2 × BVo ) 2 × BVo × ∆y 2
%△BV (from convx)≈Convx×△y
2
Yield Curve(Term Structure ) Shifts ·Parallel shift ·Nonparallel shift slope changes ·Butterfly twist change in “humped ” shape Theories of the Term Structure z Pure (unbiased) expectations Forward rates (F) function of expected future spot rates E(S) If up sloping, spot rates rise If down sloping , spot rates fall If flat, spot rates constant z Liquidity theory F rates reflect expectation of E(S) plus liquidity premium z Preferred habitat theory Imbalance between fund supply demand at maturity range induces lenders to shift from preferred habitats to one with opposite imbalance z Market segmentation theory Imbalance between fund supply demand at maturity range induces lenders to shift from preferred habitats to one with opposite imbalance z Market segmentation theory Yield curve shape determined by supply demand for securities at each maturity Key Rate Duration ·% △value from 100 bps △in key rate ·Have several key rates (5-yr, 10-yr ) ·Estimate effect of non-parallel yield curve shift on bond portfolio value Valuing Option Free Bonds To value option free bond with the binomial tree start at end and discount back though the tree (backwards induction method ) Value 2-year option free bond step1: Find the time one up node value
28
CFA Level II 公式
Nodal value 1,U =
1 ⎡⎛⎜ nodal _ value2UU ⎢ 2 ⎢⎣⎜⎝ 1 + i1,U
⎞ ⎛ nodal _ value2UD ⎟+⎜ ⎟ ⎜ 1 + i1,U ⎠ ⎝
⎞⎤ ⎟⎥ ⎟ ⎠⎥⎦
Step 2 Find time one down-node value nodal value 1,D =
1 ⎡⎛⎜ nodalvalue2, DD ⎢ 2 ⎣⎢⎜⎝ 1 + i1, D
⎞ ⎛ nodalvalue2,UD ⎟+⎜ ⎟ ⎜ 1 + i1, D ⎠ ⎝
⎞⎤ ⎟⎥ ⎟ ⎠⎦⎥
Step 3: Find time zero value : nodal value 0 =
1 ⎡⎛ nodal _ value1,U ⎢⎜ 2 ⎣⎜⎝ 1 + i0
⎞ ⎛ nodalvalue1, D ⎞⎤ ⎟⎟ + ⎜⎜ ⎟⎟⎥ 1 + i0 ⎠ ⎝ ⎠⎦
Value Bond with Embedded Option For bonds with embedded options assess whether option will be exercised at each node New Step 3 is Step 3 (callable bond ) Find time 0 value assuming year 1 down node calculated value> than call price nodal value 0 =
1 ⎡⎛ nodal _ value1,U ⎢⎜ 2 ⎣⎜⎝ 1 + i0
⎞ ⎛ nodal _ value1,D ⎞⎤ ⎟⎟ + ⎜⎜ ⎟⎟⎥ + 1 i 0 ⎠ ⎝ ⎠⎦
Call=noncallable bond –callable bond
Option Adjusted Spread ·“Option-removed spread.” ·Compensation for liquidity and credit risk ·Spread that forces model price =marker price ·z-spread =OAS+option cost Convertible Bonds ·Conversion value =stucco price x conversion ratio ·Minimum value =min(straight value conversion value ) ·Market conversion premium=conversion price market price ·Callable convertible bond=straight bond - call on stock call on bond MBS Prepayment Risk z Prepayment speed factors Spread of current vs original mortgage rates. Mortgage rate path (refinancing burnout ) Level of mortgage rates Underlying mortgage rates Seasonal factors z Contraction risk occurs as rates fall prepayments rise average life falls z Extension risk occurs as rates rise prepayments fall slow average life rises
29
CFA Level II 公式
CMO prepayment Risk z PAC I tranches: low contraction and extension risk (due to PAC collar) z PAC II tranches: somewhat higher contraction and extension risk z Support tranches: higher contraction and extension risk z IO strips: value positively related to interest rates at low current rates z PO strips: negative convexity at low rates high interest rate sensitivity ABS Prepayment Risk z External credit enhancement corporate guarantees leers of credit bond insurance z Internal credit enhancement reserve funds over-collateralization senior sub structure z Auto loan low prepayment risk small balances high depreciation z Credit card receivable low prepayment (lockout period no prepayments on crddit cards ) MBS /ABS spread Analysis z Plain vanilla corporate: Z-spread z Callable corporate: OAS (binomial model ) z MBS: OAS (Monte Carlo model ) z Credit card auto ABS: Z-spread z High quality home equity ABS: OAS (Monte Carlo model )
30
CFA Level II 公式
DERIVATIVES Forwards-No Arbitrage Pricing FP = S 0 × (1 + R f ) T Vlong = S t −
FP (1 + R f )T −t
Equity Forward FP (equity ) = ( S 0 − PVD ) × (1 + R f )T Vlong = S t − PVDt −
FP (1 + R f )T −t
Forward on Fixed Income securities FP ( fixedincome) = ( S 0 − PVD ) × (1 + R f )T Vlong = S t − PVC −
FP (1 + R f )T −t
Forward Rate Agreements ·Long position in FRA is party that would borrow If LIBOR at end is above forward rate in FRA long in effect has right to borrow at below market rates and receives a payment ·FRA“Price”is forward rate implied by current sport rates j+k ⎤ ⎡ ⎢1 + L(1+ k ) 360 ⎥⎛ 360 ⎞ − 1⎥⎜ FR ( j , k ) = ⎢ ⎟ ⎢ 1 + L( j ) ( j ) ⎥⎝ k ⎠ 360 ⎣ ⎦ Currency Forward(Interest Rate Parity ) FP (currency ) = S 0
T ( 1 + Rdomestic ) ×
(1 + R foreign ) T
F and S in DC/FC Vlong =
St (1 + R foreign )
T −t
－
FP (1 + Rdomestic )T −t
Futures Price FP = S 0 × (1 + R f ) T
·Futures> forward when rates and asset values positively correlated ·Futures< forward when rates and asset values negatively correlated 31
CFA Level II 公式
Futures Arbitrage Cash and carry: Borrow, buy spot, sell futures today deliver asset, repay loan at end Reverse cash and carry: short spot, invest, buy futures today; collect loan, buy asset under futures contract, deliver to cover short sale . Treasury Bond Futures FP = bond price × (1 + R f )T − FVC
Equity Futures FP( stock ) = S 0 × (1 + R f ) T − FVD
FP(index) = S 0 × e ( R −δ )T Put-Call Parity Call+Risk-free Bond=Put+Underlying Co +
X = P0 + S 0 (1 + r )T
Caps and Floors ·Cap=portfolio of calls on LIBOR ·Floor=portfolio of puts on LIBOR ·Collar=buy cap and sell floor or sell cap and buy floor Binomial option Pricing Model Step 1: Calculate option payoffs at end in all stares Step 2:Calculate expected value using probabilities
1+ R − D U −D Step 3: Discount to today at risk –free rate
π up =
Black-Scholes Option Pricing Model
Ct = [ S t × N (d1 )] − [ X × e − r (T −t ) × N (d )]
[
]
⎛S ⎞ ln⎜ t ⎟ + r + (0.5 × σ 2 ) × (T − t ) X d1 = ⎝ ⎠ σ × T −t
d 2 = d1 − (σ × T − t ) Pt = Ct − St + (e − r (T −t ) × X ) Effect of each variable on a call option Asset price positively related 32
CFA Level II 公式
z z z z z
Asset price: positively related Volatility of asset price: positively related Risk free rate: positively related Time to expiration: positively related Exercise price: Negatively related
Delta Estimates the change in value of option for a one-unit change in stock price ·Call delta between o and 1 increases as stock price increases · Call delta close to 0for far out of the money calls close to 1 for fan in the money calls ·Put delta between I and 0 increases from 1 to 0 as stock price increases ·Put delta =call delta -1 (all else equal ) ·Delta close to 0 for far out –of the money puts close to -1 for fan in the money puts Delta Neutral Hedging #Calls for delta hedge =
# shares of stock delta of call option
Delta neutral position only holds for very small changes in value of underlying stock Delta neutral portfolio must be frequently (continuously) rebalanced to maintain hedge called a dynamic hedge
Gamma Measures rate of change in delta as underlying stock price changes largest when option is at the money Currency Swaps Parties swap payments in two currencies at fixed or floating rates Interest Rate Swaps Plain vanilla interest rate swap trading fixed interest rate payments for floating rate payments Equity Swaps Return on stock portfolio or stock index is paid each period by one party in return for a fixed payment Return can be capital appreciation or total return including dividends on the stock or portfolio Swap Pricing and Valuation ·Swap rate is set so PV of floating rate payments PV of fixed rte payments swap value is zero to both parties
CN =
1 − BN B1 + B2 + L + BN 33
CFA Level II 公式
Bn = PV of ＄1 on n th date
·Value to fixed pay side =PV of floating –PV of fixed ·Value to floating –pay side=PV of fixed –PV of floating Swptions ·Payer swaption value increases as rates rise ·Receiver swaption value increases as rates fall
34
