CFA二级公式表

CFA 公式表-Level II

Quantitative Methods

1. Simple Linear Regression Correlation: ()()xy

xy x y Cov r s s =

t-test for r (df = n-2): t = Estimated slope coefficient: 2xy

x Cov σ Estimated intercept: 01

??b y b =-x Confidence interval for predicted Y-value: ^

c y t SE ±?of forecast

2. Multiple Regression

0112233()()()i i i Y b b X b X b X i i ε=+?+?+?+

● Test statistical significance of b; 0:0

?,1b

H b b t df n k s ===-- Reject if t or p-value < 0h ||t critical >α

● Confidence Interval: ?()j

j c b b t s ±?●

SST = RSS+SSE ●

MSR = RSS/k ●

MSE = SSE / (n-k-1) ● Test statistical significance of regression: F = MSR / MSE with df k and

n-k-1 (1-tail)

●

Standard error of estimate (SEE =), Smaller SEE means better fit. ● Coefficient of determination (2/R RSS SST =). % of variability of Y

explained by X’s; Higher R 2 means better fit.

3. Regression Analysis-Problems

● Heteroskedasticity. Non-constant error variance. Detect with Breusch-Pagan

test. Correct with White-corrected standard errors.

● Autocorrelation. Correlation among error terms. Detect with Durbin-Watson

test; positive autocorrelation if DW

using Hansen method.

● Multicollinearity. High correlation among X’s. Detect if F-test significant,

t-test insignificant. Correct by dropping X variables.

4. Model Misspecification

● Omitting a variable.

● Variable should be transformed.

● Incorrectly pooling data.

● Using lagged dependent variable as independent variable.

● Forecasting the past.

● Measuring independent variables with error.

5. Effects of Misspecification

Regression coefficients are biased and inconsistent, lack of confidence in hypothesis tests of the coefficients or in the model predictions.

6. Linear Trend Model: 01t t y b b t ε=++

7. Log-Linear Trend Models: 01ln()t t y b b t ε=++

8. Covariance Stationary: Mean and var. don’t change over time. To determine

if a time series is covariance stationary, (1) plot data, (2) run an AR model and test correlations, and/or (3) perform Dickey Fuller test.

9. Unit Root: Coefficient on lagged dep.vb1=1. series with unit root is not

covariance stationary. First differencing will often eliminate the unit root. 10. Autoregressive (AR) Models: Specified correctly if autocorrelation of

residuals not significant: 01122......t t t p t p x b b x b x b x t ε---=+++++

11. Mean Reverting Level For AR(1): 01(1)

b b - 12. RMSE: square root of avg squared error.

13. Random Walk Time Series: 1t t x x t ε-=+

14. Seasonality: Indicated by statistically significant lagged err. term. Correct by

adding lagged term.

15. ARCH: Detected by estimating: 22011t t a a εεμ-=++

Variance o ARCH series: 22101t t a a σε+=+

ECONOMICS

1. One Third Rule: at given technology level, 1% increase in capital/labor hour

leads to 1/3 % increase in real GDP per hour.

2. Rule of 70: approximate to double GDP = 70/growth rate.

3. Classical Growth Theory

●

4. Neoclassical Growth Theory

●

Economic growth stops when real return = target return. ●

Pop. Growth independent of economic growth. 5.

New Growth Theory ●

Economic growth continues indefinitely ad technology advances. ●

↓real rate => incentive to discover new products and methods. ●

Discovery => real return > target return. 6.

Nominal & Real Exchange Rate ●

Nominal ex. Rate (E): price of one currency in terms of another; observed in EX markets. ●

Real exchange rate = E ×(P/P *) 7.

Balance of Payment: current account + capital account + official reserve account = 0 8.

Foreign Exchange: Direct quotes: ●

if quote is ? per $ (or USD:GBP), this is a direct quote from the perspective of the pound. ● Bid-ask spread stated as percent of asking price:

%(100)askprice bidprice spread askprice -=

● Foreign currency is at forward discount (premium) if F is below (above) S, using direct quotes: 360(/)(1)()day min fwdrate fwdprem disc spotrate ter s

=-● Currency appreciates due to: (1) Lower relative income growth rate. (2)

Lower relative inflation rate. (3) Higher domestic real interest rate. (4) Improved investment climate.

9. Unanticipated shift to exp. Monetary Policy: Higher income, accelerated

inflation, lower real interest rates, leads to currency dept, current acct surplus, and financial acct deficit.

10. Unanticipated shift to exp. Fiscal Policy: currency appr, current acct deficit,

& financial account surplus.

11. 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 depreciate.

01()1CounterCurrency t BaseCurrency I S E I ??+= ? ?+??

S 12. International Fisher Relation: Assumes real interest rates are equal across borders, so interest differential equals expected inflation difference.

11(11(b b a a r E I r E I ???++= ? ++???))???

()()b a b a r r E I E I -≈-

13. Uncovered Interest Rate Parity: Countries with high nominal interest rates should see their currencies depreciate.

01360()1360CounterCurrency n BaseCurrency n r S E n r ????+ ? ??????=????+ ? ????

?S 14. Interest Rate Parity: Countries with high nominal interest rates will have their currencies sell at forward discount to prevent arbitrage.

()()

11b a r F S r +=+ 15. Currency Arbitrage: up the bid and down the ask

Financial Statement Analysis

1. Accounting for InterCorp Investments

a) Minority passive: < 20% owned, no significant influence.

i. Held-to-maturity at cost on B/S; interest and realized gain/losses on I/S ii. Available-for-sale at FMV with unrealized gains/loss in equity on B/S;

dividends, interest, realized gains/losses on I/S

iii. Held-for-trading at FMV , dividend, interest, realized and unrealized

gains/losses on I/S.

b) Minority active: 20-50% owned, significant influence. With equity

method, pro-rata share of the investee’s earnings increase, B/S investment account, also in I/S. Div. received decrease investment account. (div. not in I/S)

c) Controlling: >50% owned, control. Consolidation, all assets, liability,

revenue, and expense of sub combined with parent, excluding

d)

preferred, similar to regular consolidation, except only include pro-rata share. US GAAP: equity method.

2.

Financial Effect of Choice of Method: equity, consolidation, proportionate

consolidation.

a)

All three methods report same net income.

b)

All three methods report same ROE

c) Asset, liabilities, sales are highest under consolidation; lowest under

equity method; proportionate consolidation in between.

3. a) b)

c)Pension expense components: current service cost, interest cost, expected

return on plan assets, prior (past) service cost, net actuarial gains/losses. d) Aggressive assumptions/low earnings quality: high discount rate, low

compensation growth rate, high expected return.

4.Economic pension expense: if < firm contribution, diff = ↓ in overall pension

obligation. If > firm contribution, diff = borrowing (and reclass from CFO to CFF)

5.Balance sheet: GAAP vs. IFRS: GAAP: net assets/liability = funded status =

economic reality. IFRS: net assets/liab = funded status adj. for unrecognized items.

6.Underlying Economic Pension Expense: Sum of all changes in PBO (except

benefits paid) less actual ROA. Also = change in funded status exclude firm’s contributions. Service cost= operating expense. Interest and actual ROA repeated as non operating income.

7.Business Combinations:

a)Purchase method required under U.S. GAAP and IFRS

b)Goodwill not amortized, subject to annual impairment test.

8.Purchase Method Attributes:

a)Acquirer assumes assets/liabilities of acquired company.

b)Excess FMV of acquired net assets allocated first to intangible assets,

then goodwill.

c)Prior operating results not restated.

9.Pooling Method Attributes

a)Company f/s combined at book value.

b)Prior operating results restated.

10.Impact of Purchase vs. Pooling

a)Asset and equity higher, net income lower under purchase method.

b)Profit margin, ROA, ROE lower under purchase method.

11.Entity is VIE if any of:

12.Multinational Operations: Choice of Method

a)Insufficient at-risk equity investment.

b)Shareholder lack decision-making rights.

c)Shareholder do not absorb losses

d)Shareholder do not receive residual benefits.

The primary beneficiary consolidates the VIE.

Qualifying SPE: GAAP allows – no consol. (use equity method). Not permitted under IFRS.

13.Multinational Operations: Choice of Method

For self-contained sub, functional ≠presentation currency; use all-current method:

a)Assets/liabilities at current rate.

b)Common stock at historical rate.

c)Income statement at average rate.

d)Exposure = shareholder’s equity

e) Dividend at rate when paid.

For integrated sub, functional = presentation currency, use temporal method: f) Monetary assets/liabilities at current rate.

g) Nonmonetary assets / liabilities at historical rate.

h) Sales, SGA at average rate.

i) COGS, depreciation at historical rate.

j) Exposure = monetary assets – monetary liabilities

Net asset position & Depr, foreign currency = loss

Net liab, position & depr, foreign currency = gain.

14. Original F/S vs. All-Current

a) Pure B/S and I/S ratios unchanged

b) If Local currency depreciating, translated mixed ratios will be larger c) If local currency appreciating, translated mixed ratios will be smaller. 15. Hyperinflation: GAAP vs. IFRS: Hyperinflation = cumulative inflation >

100% over 3 years,GAAP, use temporal method. IFRS: 1. restate foreign currency st. for inflation. 2. translate with all-current. Net purchase power gain/losses reported in income.

16. Accrual-based income: accrual part less persistent ten cash part.

17. Measure of earning quality:

()()

()()/2/2BS END BEG

END BEG BS

END BEG CF END BEG Accruals NOA NOA NOA NOA AccrualsRatio NOA NOA NI CFO CFI AccrualsRatio NOA NOA =--=+--=+ 18. Mean Reversion: occurs faster with larger accrual earnings component. 19. Detecting Manipulation:

a) Revenue recognize: large changes in receivable & unearned revenue. ↑

DSO, compare revenue to cash collected.

b) Expense recognize: large changes in fixed assets & inventory, ↑DOH,

LIFO liquidation, compare depreciation. Exp, calculate core operate margin = (sales-COGS- SG&A)/sales.

c) B/S: capitalize operating lease; impaired goodwill

d) CF: compare growth of operating leases to asset grow, look for ↓in

discretionary spend at year end.

20. Fair value hedge: gain/loss from derivative & hedged BS item reported in IS. 21. Cash flow hedge: gain/loss from derivative bypass IS- reported in

shareholder’s equity.

22. Net investment hedge of a foreign sub: gain/loss recognize in equity along

with transaction gain/loss.

CORPORATE FINANCE

1. Capital budgeting expansion

a)

Initial outlay = FCinv + WCinv

b) CF = (S-C-D)(1-T) +D = (S-C)(1-T) + DT

c) TNOCF = Sal T + NWCInv – ( Sal T – B T ) ×T

2. Capital budgeting replacement

a) Same as expansion, except current after – tax salvage of old assets reduces initial outlay.

b) Incremental depreciation is Δ in depth.

3. Projects with unequal lives

a) Least common multiple of lives.

b) Equivalent annual annuity (EAA): annuity equal to PC of project CFs. 4. Effects of inflation: Discount nominal (real) cash flows at nominal (real) rate;

unexpected changes in inflation affect project profitability; reduces the real tax savings from depreciation; decreases value of fixed payments to bondholders; affects costs and revenues differently.

5. Capital rationing: If +NPV > capital, choose combination with highest NPV .

6. Real options: Timing, abandonment, expansion, flexibility, fundamental

options.

7. Economic and accounting income

a) Economic Income = AT CF + Δ in project’s MV .

b) Economic depr based on Δ in investment’s MV .

c) Economic income calculated before interest expense (cost of capital reflected in discount rate)

d) Account income = project revenue –costs

e) Account dep based on original investment cost.

f) Interest (financing costs) deducted before calculating accounting income. 8. Valuation models:

a) Econ profit = NOPAT -$WACC; discounted at WACC.

b) Residual income = NI – equity charge; discounted at required return on equity.

c) Claims valuation separates CFs based on equity claims (discounted at cost of equity) and debt holders (discounted at cost of debt).

9. Operating leverage: variable/fixed cost tradeoff

%DOL %EBIT Sales

?=? ()()qty sales Q P V DOL Q P V F S VC DOL S VC F

-=

---=-- 10. Financial leverage: refers to use of fixed-income securities (debt and preferred stock).

%%i %()(%)EPS EBIT DFL EBIT EBIT erest EPS DFL EBIT ?=

=?-?=?nt

11. Total leverage: measures effect on EPS of given change in sales. DTL=DOL

×DFL

12. Breakeven:BE F Q P V

=- 13. MM Prop I (No taxes): Capital structure irrelevant (no taxes, transaction cost

or bankruptcy costs).

14. MM Prop II (No Taxes): increased use of cheaper debt increases cost of

equity, no change in WACC.

15. MM Proposition I (With taxes): tax shield adds value, value maximized at

100% debt.

16. MM Proposition II (With taxes): tax shield adds value, WACC minimized at

100% debt.

17. Corporate Governance Objectives

a) Mitigate conflicts of interest between (1) managers and shareholders, and (2) directors and shareholders.

b) Ensure assets used to benefit investors and stakeholders.

18. EPS after a share repurchase

tan TotalEarnings AfterTaxCostofFunds EPS SharesOuts dingAfterBurback

-= If after-tax cost of debt is less then earnings yield, a share repurchase will increase EPS. If after-tax cost of debt is greater than earnings yield, a share repurchase will decrease EPS.

19. BV per share after a share repurchase: If the share price is greater than the

original BVPS, a share repurchase will decrease BVPS. If the share price is less the original BVPS, a share repurchase will increase BVPS.

20. Effective tax rate on dividends:

a) Double taxation or split rate systems: effective rate = corp rate + (1- corp rate)(indiv rate)

b) Imputation system: effective tax rate is the shareholder’s individual tax rate.

21. Signaling Effects of Dividend Changes

a) Initiation: ambiguous signa

b) Increase: positive signal

c) Decrease: negative signal unless management sees many profitable investment opportunities.

22. Share Repurchase

a) Share repurchase is equivalent to cash dividend, assuming equal tax treatment.

b) Unexpected share repurchase is good news.

c) Rational for: 1) prevent EPS dilution; 2) supplement a regular dividend;

3) good investment for company; 4) positive signal to investor; 5) change capital structure.

23. Dividend Policy Approaches

a)Residual dividend: dividends based on earnings less funds retained to

finance capita budget.

b)Longer-term residual dividend: forecast capital budge, smooth dividend

payout.

c)Dividend stability: dividend growth aligned with sustainable growth rate.

d)Target payout ratio: long-term payout ratio target.

24.Merger Types: Horizontal, vertical, conglomerate.

25.Merger Motivations: Achieve synergies, more rapid growth, increase market

power, gain access to unique capabilities, diversify, manager personal

benefits, tax benefits unlock hidden value, achieving intl goals, and

bootstrapping earning.

26.Pre-offer Defense Mechanisms: poison pills and puts, reincorp. In a state

where restrictive takeover laws, staggered board elections, restrict voting

rights, supermajority voting, fair price amendments, and golder parachutes.

27.Post-offer Defense Mechanisms: litigation, greenmail, sare repurch,

leveraged recap, th “crown jewel”, ”Pac man”, and “just say no” defense,

and white knight/white squire.

28.The Herfindahl-Hirschman Inex (HHI): market power = sum of squared

market shres for all industry firms. High or increase HHI mean regulators

more likely to challenge a merger.

29.Methods to determine Target Value

a)DCF method: target performance FCF discounted at adjusted W ACC

b)Comparable company analysis: target value from relative valuation

metrice on similar firms + takeover premium.

c)Comparable transaction analysis: target value from takeover transactionl

takeover premium included

30.Merger Valuations

a)Combined firm: V AT=V A + V T +S –C

b)Takeover premium (to target): Gain T = TP = P T -V T

c)Synergies ( to acquirer): Gain A = S- TP = S- (P T-V T)

31.Merger Risk & Reward

a)Cash offer: acquirer assumes risk & receives reward.

b)Stock offer: some of risks & rewards shift to target. If higher confidence

in synergies; acquirer prefers cash & target prefers stock.

32.Forms of Divestitures: equity carve –outs, spin –offs, split – offs, and

liquidations.

EQUITY & ALTERNATIVE INVESTMETNS

1.Alpha:

a)Ex ante α = expected return – required return from CAPM or APT

b)Ex post α = historical holding period return – historical return on similar

assets

2.Franchise value and growth process

Tangible P/E =1/r

Franchise P/E = franchise factor ×growth factor = FF × GF

a)if ROE>r, firm has sustainable competitive advantage, franchise factor >

0.

b)If ROE

3.Inflation effects on valuation

a)Higher flow- through rate implies higher P/E, all else equal

b)If inflation flow-through < 100%, higher inflation implies lower P/E, all

else equal.

4.Porter’s Five Forces/competitive strategy

a)Threat of new entrants. Increase = more pricing pressure, lower industry

profits.

b)Threat of substitutes. Is there a price ceiling? More cost effective, more

pricing pressure. Buyer propensity to substitute. Switching costs.

c)Bargaining power of buyers = function of bargaining leverage/price

sensitivity.

d)Bargaining power of suppliers: determined by differentiation of inputs,

presence of sub. Inputs, supplier concentration, importance to supplier,

threat of forward integration.

e)Rivalry among existing competitors. Increasing rivalry = increasing risk

of destructive price/feature/marketing wars. Function of industry growth,

fixed costs, value added, product differences, branding, diversity of

competitors, exit barriers. Key point: who captures value added?

Eliminating rival risky, attracts competition.

5.Strategic alternatives

a)Positioning firm where five forces weakest.

b)Project and exploit changes in industry.

c)Induce industry changes to play to firm strength.

6.Industry Analysis

a)Industry life cycle: Pioneer – Growth – Mature – Decline.

b)External factors: Technology, government, social change, demography,

foreign influence.

7.Nominal vs. Real: distinction Matters

●Income taxes: forecast nominal earnings before taxes.

●Real cash flow from WC = Δ real WC; convert nominal WC to real CF.

●Forecast real capex, dep, and EBITDA

8.Discounted Cash flow (DCD) methods

Use dividend discount models (DDM) when:

●Firm has dividend history,

●Dividend policy related to earnings,

●Minority shareholder perspective

Use free cash flow (FCF) models when:

●Firm lacks stable dividend policy

●Dividend policy not related to earnings.

●FCF is related to profitability

●Controlling shareholder perspective.

Use residual income (RI) when:

● Firm lacks dividend history.

● Expected FCF is negative

9. Gordon Growth Model (GGM) Assumes perpetual dividend growth rate:

10D V r g

=- Most appropriate for mature, stable firms.

Limitations are:

● Very sensitive to estimates of r and g

● Difficult with non-dividend stocks

● Difficult with unpredictable growth patterns (use multi-stage model) 10. Present Value of Growth Opportunities

10E V PVGO r

=+ 11. 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.

12. H- Model

()()0001L s L L

D g D H g g V r g r g ?+??-????

??=+--L ?? 13. Solving for Required Return

For Gordon (or stable growth) model, solving for return yields:

10

D r g P =+ 14. Free Cash flow to firm (FCFF)

Assuming DEP is only NCC:

● FCFF = NI + Dep +[Int × (1- tax rate)] – FCInv – WCInv

● FCFF = [EBIT ×( 1- tax rate)] + Dep – FCInv – WCInv

● FCFF = [EBITDA × (1-tax rate)] + (Dep × tax rate) – FCInv –

WCInv

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

15. Free cash flow to Equity (FCFE)

● FCFE = FCFF - [Int × (1- tax rate)] + Net Borrowing

● FCFE = NI + Dep – FCInv – WCInv + Net Borrowing

● FCFE = NI – [(1-DR) × (FCInv -Dep)] - [(1-DR) ×WCInv]( Used to

forecast)

16. Single-stage FCFF/FCFE models

● For FCFF valuation: 10FCFF V WACC g

=- ● For FCFE valuation: 10FCEF V r g =

- 17. Two-stage FCFF/FCFE models

Step 1: Calculate FCF in high – growth period.

Step 2: Use single – stage FCF model for terminal value at end of high – growth period.

Step 3: Discount interim FCF and terminal value to time zero to find stock value, use W ACC for FCFF, r for FCFE.

18. Price to Earning (P/E) ratio

Problems with P/E:

● If earnings < 0, P/E meaningless.

● V olatile, transitory portion of earnings makes interpretation difficult. ● Management discretion over accounting choices affects reported

earnings

19. Justified P/E Leading P/E = 1b r g

-- Trailing P/E =

(1)(1)b g r g -+- 20. Normalization Methods:

● Historical average EPS.

● Average ROE.

21. Price to Book (P/B) ratio

Advantages:

● BV almost always > 0

● BV more stable than EPS

● Measures NA V of financial institutions.

Disadvantages:

● Size differences cause misleading comparisons

● Influenced by accounting choices.

● BV ≠ MV due to inflation/technology Justified P/B = ROE g r g

-- 22. Price to Sales (P/S) ratio

Advantages:

● Meaningful even for distressed firms

● Sales revenue not easily manipulated

● Not as volatile as P/E ratios

● Useful in valuing mature, cyclical, and start-up firms

Disadvantages:

● High sales do not imply high profits and cash flows

● Does not capture cost structure difference.

● Revenue recognition practices still distort sales. Justified P/S = 0(1)(1)PM b g r g

?-+- 23. Price to Cash Flow Ratios

Advantages:

● Cash flow harder to manipulate than EPS

● More stable than P/E

● Mitigates earnings quality concerns

Disadvantages:

● Difficult to estimate true CFO

● FCFE better but more volatile

24. Method of Comparables

● Firm multiple > benchmark implies overvalued

● Firm multiple < benchmark implies undervalued

● Fundamentals that affect multiple should be similar between firm and

benchmark.

25. Residual Income Models

11()()t t t RI E r B ROE r B --=-?=-?

Single stage RI model: ()000ROE r B V B r g -???=+??-??

Multistage RI valuation: V 0 = B 0 + (PV of interim high-growth RI) + (PV of continuing RI)

26. Economic value added

EV A=NOI-$WACC NOPAT=EBIT(1-t)

27. Real estate (RE) investment analysis

● CFAT = NOI – debt service – taxes payable

● ERAT = net selling price – mortgage balance – taxes

● Recaptured depreciation: depr. Taken in anticipation of decrease in

asset’s value that did not materialize

28. Types of Real estate investment

Raw land: passive and illiquid; for speculators and developers.

Apartments and office building: active, moderately liquid; tax-shelters for high- income investors

Warehouses: passive, moderately liquid; for passive investors & those seeking tax shelter

Shopping centers: moderately active, low-liquidity, for wealthy investors.

Hotels and motels: active, moderately liquid; for those seeking tax shelter 29. Income Property Analysis: Cap Rate Market extraction: 0()NOI R ME MV

=, use when income data is available. 30. Valuing Income Properties Direct income capitalization technique: 110NOI NOI MV r g R

==- Gross income multiplier technique

MV=gross income ×income multiplier Gross income multiplier Pr ()Sales ice M GrossIncome

= 31. Sustainable Growth rate: b ×ROE

32. Private Equity

Sources of value creation: reengineer firm, favorable debt financing; superior alignment of interests between management and PE ownership

Valuation issues (VC firms relative to Buyouts): DCF not as common; equity, not debt, primary financing.

Key driver of equity return

Buyout: ↑of multiple at exit, ↓ in

debt VC: pre-money valuation, the investment, and subsequent equity dilution. Components of performance (LBO): earnings growth, ↑of multiple at exit, ↓in debt.

Exit routes ( in order of exit value, high to low): IPOs secondary market sales; MBO; liquidation.

performance measurement: Gross IRR= return from portfolio companies. Net IRR = relevant for LP, net of fees & carried interest.

Performance statistics:

● PIC = % capital utilized by GP; Cumul, sum of capital called down. ● Mgmt fee: % of PIC

● Carried Interest: % carried int ×(change in NA V before distrib)

● NA V before distrib = prior yr NA V after distrib + cap. Called dwn- mgmt

fees + op result

● NA V after disturb = NA V befoe distrib- carried int – distrib

● DPI mult = (cumul distrib)/PIC = LP’s realized return

● RVPI mult = (NA V after distrib)/PIC = LP’s unrealized return.

● TVPI mult = DPI mult + RVPI mult.

NPV VC: IRR methods: calculate pre-money val. Post-money val.

analysis for term.

LBO CF. start with net income, add back non-cash depr & amoriz of def, charges. Subtract ↑in NWC and appop capex.

33.Hedge Funds

Performance measurement difficult due to diff in leverage, short positions, Δ in style, & port. TO.

Exposed to investment, fraud and operational risk.

Use downside measure of risk, such as maximum drawdown and/or value at risk (Var)

Prices: inversely related to stock prices over ec. Cycle & inflation.

FIXED INCOME

1.Credit Analysis

High-yield debt

●Issuer has senior, short-term, floating bank debt.

●Analyze corporate structure, debt structure.

Asset-backed debt

●Quality of collateral

●Servicer quality

●Cash flow stress and payment structure

●Legal structure

Municipal bonds

●Tax-backed municipal bond analysis involves: issuer’s debt structure,

budgetary policy, local tax and intergovernmental revenue availability,

and issuer’s socioeconomic environment.

●Municipal bond credit analysis: limits of the basic security, flow of funds

structure, rate covenants, and additional bonds tests.

Sovereign debt

●Local vs. foreign currency rating.

●Economic risk: ability to pay

●Political risk: willingness to pay.

2.Theories of the Term Structure

Pure (unbiased) expectations. Forward rates (F) function of expected future spot rates E(S).

●If up sloping. ST spot rates rise.

●If down sloping, ST rate spot rates fall

●If flat, ST spot rates constant.

Liquidity theory: F rates reflect expectations of E(S) plus liquidity premium.

Preferred habitat theory: Imbalance between fund supply/demand at maturity range induces lenders to shift from preferred habitats to one with opposite imbalance.

3.Key rate duration

●%Δvalue from 100 bps Δ in key rate.

●Have several key rates (5-yr, 10-yr)

●Estimate effect of non-parallel yield curve shift on bond portfolio value.

4.Valuing Option Free Bonds

To value option free bond with the binomial tree, start at end discount back through the tree (backwards induction method).

Value 2-yr, option-free bond:

Step 1: Find the time one up-node value:

Nodal value 1,U =2,2,1,1,1211UU UD U u NodalValue NodalValue i i ?????+?? ? ? ++???????

???? Step 2: Find time one down-node value

Step 3: find time zero value:

Nodal value 01,1,001211U D NodalValue NodalValue i i ??????+?? ? ?++??????

5. Value Bond with Embedded Option

For bonds with embedded options, assess whether option will be exercised at each node. New step 3 is: (Callable bond). Find time 0 value assuming year 1 down-node calculated value > that call price.

Nodal value 0=1,1,001211U D NodalValue NodalValue i i ?????+?? ? ++?????

??? Call = noncallable bond-callable bond

Put = putable bond – nonputable bond

6. Option Adjust Spread

● “Option – removed spread”

● Compensation for liquidity and credit risk relative to benchmark

● Spread that forces model price = market price

● Nominal spread = OAS + option cost.

7. Relative Valuation Analysis

If benchmark is Treasuries or higher-rated bond sector:

● Bond is undervalued if OAS > 0

● Bond is overvalued if OAS < 0

8. Convertible Bonds

● Conversion value = stock price ×conversion ratio

● Minimum value = max (straight value, conversion value)

● Market conversion premium = straight bond + call on stock – call on

bond

9. MBS Prepayment Risk

Prepayment speed factors

● Spread of current vs. original mortgage rates

● Mortgage rate path (refinancing burnout)

● Housing turnover

● Loan seasoning and property location

Contraction risk occurs as rates fall, prepayments rise, average life falls. Extension risk occurs as rate rise, prepayments fall (slow), average lift rises. 10. CMO Prepayment Risk

● PAC I tranches: low contraction and extension risk (due to PAC collar) ● PAC II tranches: somewhat higher contraction and extension risk.

● Support tranches: higher contraction and extension risk

● IO strips: value positively related to interest rates at low current rates. ● PO strips: negative convexity at low rates, high interest rate sensitivity. 11. Commercial MBS

● Non-recourse, so focus on property credit risk,

● Loan-level call protection: prepayment lockout; defeasance; prepayment

penalty; yield maintenance charge.

● Pool-level call protection: senior and subordinated tranches.

12. ABS Credit Enhancement

● External: corporate guarantees, letters of credit, bond insurance.

● Internal: reserve funds, overcollateralization, senior/sub structure.

13. ABS Prepayment Risk

● Closed-end HEL: prepayments also affected by borrower credit traits. ● Manufactured housing loan: low prepayment risk; small balances, high

depreciation, low borrower credit ratings.

● Auto loan: low prepayment risk; small balances, high depreciation

● Student loan: prepayment from default, loan consolidation.

● Credit card receivable: low prepayment risk; lockout period, no

prepayment on credit cards.

14. Collateralized Debt Obligation (CDO)

● Structure: senior tranches, mezzanine tranches, equity tranche

● Arbitrage – driven cash CDO: use interest rate swap.

● Cash flow CDO: actively managed, no short-term trading.

● Synthetic CDO, Bondholders take on economic risks of assets but not

legal ownership of them; link contingent payments to reference asset (e.g., a bond indee)

● Advantages of synthetic CDO: no funding, shorter ramp-up period,

acquire exposure more cheaply through credit-default swap.

15. MBS/ABS Spread Analysis

● Plain-vanilla corporate: use Z-spread

● Callable corporate: use OAS (binomial model)

● MBS: use OAS (Monte Carlo model)

● Credit card/auto ABS: use Z-spread

● High-quality home equity ABS: use OAS (Monte Carlo model)

DERIV ATVES

1. Forwards: No arbitrage Pricing

0(1)T f FP S R =?+

(1)long t T t f FP V S R -??=-??+????

2. Equity Forward

()0()(1()(1)T

Equity f long t t T t f FP S PVD R FP V S PVD F -=-?+??=--??+????

) 3. Forward on Fixed Income Securities

()0()(1()(1)T

FixedIncome f long t T t f FP S PVC R FP V S PVC F -=-?+??=--??+????

) 4. Forward Rate Agreement (FRA)

● FRA is forward contract on interest rate; long wins when rates increase,

loses when rates decrease.

● FRA “price” is implied forward interest rate for period beginning when

FRA expires to underlying “loan ” maturity.

● FRA value at maturity is interest savings at maturity of “loan”

discounted back to FRA expiration at current LIBOR.

● FRA value prior to maturity is interest savings estimated by implied

forward rate discounted back to valuation date at current LIBOR.

5. Currency Forward (Interest Rate Parity)

()0(1)(1)T DC currency T

FC R FP S R +=?+ F and S in DC/FC

(1)(1)t long T t T t FC DC S FP V R R --???=-???++??????

6. Futures Price

0(1)T f FP S R =?+

● Futures > forward when rates and asset values positively correlated. ● Futures < forward when rates and asset values negatively correlated. 7. 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 future today; collect loan, buy asset under futures contract, deliver to cover short sale.

8. Costs and Non- Monetary Benefits

● Holding costs increase futures price; non monetary benefits reduce

futures price.

● Backwardation: Futures price < spot price.

● Contango: Futures price > spot price.

● Normal backwardation: Futures price < expected spot price.

● Normal contango: Futures price > expected spot price.

9. Treasury Bond Futures

1Pr (1)T f FP Bond ice R FVC CF

??=?+-??? 10. Equity Futures

()0()()0(1)T stock f R T index FP S R FVD

FP S e δ-=?+-=?

11. Eurodollar Futures

● Priced as discount yield; LIBOR-based deposits priced as add-on yield

→ deposit value not perfectly hedged by Eurodollar contract.

● Can’t price Eurodollar futures using no-arb framework

12. Put-call party Call + RF bond = Put + Underlying

00(1)

T X C P r +=+0S + 13. 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.

14. Binomial Option Pricing Model

Step 1: calculate option payoffs at end in all states. Step 2: calculate expected value using probabilities.

1R D U D

π+-=- Step 3: Discount to today at risk-free rate.

15. BSM Assumptions & Limitations

● Assumption: Price of underlying follows lognormal distribution;

(continuous) risk-free rate constant and known; σ of underlying asset

constant and known; frictionless markets; underlying asset has no CF,

European options.

● Limitation: Not useful for pricing options on bond prices/interest rates; σ

must be estimated; σ not constant over time; frictionless markets

assumption not realistic.

16. Effect of each variable on a call option:

● Asset price: positively related.

● V olatility of asset price: positively related.

● Risk free rate: positively related.

● Time to expiration: value → $0 as call → maturity

● Exercise price: negatively related.

17. Delta

Estimates the change in value of option for a one unit change in stock price.

● Call delta between 0 and 1; increases as stock price increases.

● Call delta close to 0 for far out-of-the-money calls; close to 1 for far

in-the-money calls.

● Put delta between -1 to 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 far

in-the-money puts.

18. Delta Neutral Hedging # calls for delta hedge = #SharesOfStock DeltaOfCallOption

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.

19. Gamma

Measures rate of change in delta as underlying stock price changes; largest when option is at-the-money.

20. Currency Swaps

Parties swap payments in two currencies at fixed or floating rates.

21. Interest Rate Swaps

Plain vanilla interest rate swap: trading fixed interest rate payments for floating rate payments.

22. 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.

23. Swap Pricing and Valuation

● Swap rate is set so PV of floating rate payments = PV of fixed rate payments; swap value is zero to both parties:

121...N N N

Z C Z Z Z -=+++ Z n = PV of $1 on n th date

● Value to fixed pay side = PV of floating –PV of fixed; value increase

when rates increase.

● Value to floating pay side = PV of fixed – PV of floating; value increase

when rates decrease.

24. Credit Derivatives

Credit default swap: compensates buyer when credit event occurs on referenced bond/loan. Pricing depends on credit risk of reference obligation, not interest rate risk.

Strategies: basis, curve, index, options, capital structure, and correlation trades. PORTFOLIO MANAGEMENT

1. CAL: Efficient front. With R F becomes straight line.

()()T F c F T E R R E R R C σσ??-=+????