CFA Level2 Formula

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

2

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

3

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 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 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 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 )

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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

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