Fixed Income 10% - 12%

Explain: - 30/360 interest: What type of bonds use? - Actual/actual interest: What type of bonds use? Ex) Investor buys a $1,000 par value bond w/ 6% annual coupon paid on July 15th. Trade settles on August 12th. Calculate 30/360 & actual/actual. What is a: - Full price: Other two names? - Flat price: Other two names? What are the steps to calculate accrued interest for 30/360? Ex) What's the full price & flat price based on 30/360 if bond is purchased to settle on Nov 20, 2015? Annual coupon rate: 6% ; YTM: 7% Frequency: Semiannual (Feb 15th & Aug 15th) Face value: $100,000 Maturity: Aug 15, 2035

30/360: Corporate bonds. 30days/month. 360days/year. Actual/Actual: Gov't Bonds. 365days/year & the actual # of days in each month Ex) Investor buys $1,000 par value bond w/ 6% annual coupon paid on July 15th. Trade settles on August 12th. Calculate 30/360 & actual/actual. - 30/360) 15 days left in July & 12 days left August = 27 total days / 360 x (Coupon pmt) = $4.50 - Actual/actual: July actually has 31 days so 16 are left. 12 actual days used in August = 28 total days / 365 x (Coupon pmt) = $4.60 Full Invoice Dirty Price: Price including accrued interest. Uses price at last coupon; Ex) Semi annual: = (PV on Last Coupon Date)•[(1 + YTM/n)^(Days)/(Days in Period)] Flat Clean Quoted Price: Full price w/o accrued interest; = (FullP - Accrued interest) Acc Int = (1 Coupn Pmt)•[(Days Used)/(Days in Period)] Accrued Interest on 30/360: - Step 1) Calculate PV of bond on last coupon date. Find PV on Aug 15, 2015 ; PV = 89.32 Semiannual, coupon rate is 3%. YTM (I/Y): 7/2 = 3.5 FV = 100,000 N = 40 coupon pmts b/w last & maturity - Step 2) How many days since last coupon pmt date? Nov 20th - Aug 15th = 95 days bc 30 days per month FullP = PV•[(1 + YTM/n)^(Days Used)/(Days in Period)] = 89.32(1.035)^95/180 = 90.95904 x 1,000 - Step 3) Calculate Accrued Interest: Acc Int = (1 Coupn Pmt)•[(Days Used)/(Days in Period)] = 3,000 x (95/180) = 1,583.33 - Step 4) FlatP = FullP 90,959.04 - 1,583.33 = 89, 375.71

Explain: - Asset backed securities (ABS): - Cash collateral account:

ABS: Collateralized by underlying pool of assets. Firm sells securities to SPE (removes them from BS). No legal claim to asset anymore. Cash Collateral Account: Cash borrowed by issuer that's invested at inception into low risk ST debt securities to cover any future issues

Explain: - Affirmative covenants: - Negative covenants: - Cross default: - Pari passu covenant: - Negative covenants: - Restricted payment covenant: - Restricted subsidiaries' cash flows: - Change of control put: - Domestic bonds: - Foreign bonds: - National bond market: - Eurobonds - Global bonds:

Affirmative Covenants: Actions issuer must perform/do (pay on time, insure assets, comply with laws) - Cross Default: If one bond issued defaults then all the others are also considered in default - Pari Passu Covenants: Bonds have same priority of claims as the issuer's other senior debt issues Negative Covenants: Restrictions on issuer's actions to protect bondholders (eg can't pay divs before bond payments, can't sell pledged collateral asset, additional borrowing restrictions, etc) Protects bondholder. Restricted Payment Covenant: Protects lenders. Limits the amount of cash paid to equity holders Structural Subordination: Subsidiaries must service their own debt (has priority) before upstreaming dividends to parent. Holding company debt is subordinated to subsidiary debt. - Restricted Subsidiary: Makes parent company's debt rank pari passu w/ subsidiary's debt. Credit related consideration. Protects lenders. Change of Control Put: Protects lenders. Requires borrower to buy back their debt if company is sold Domestic Bonds: Domestic issuer & currency ($US Microsoft bonds, issued in the US) Foreign Bonds: Trade in home currency, but have a foreign issuer National Bond Market: Includes trading of both domestic & foreign bonds Eurobonds: Denominated in currency other than market in which they are sold & held (other than issuer's domestic currency) - Issued outside jurisdiction of any one country - Sold by international syndicate & issued simultaneously to investors in many countries - Avoids regulation & less tax constraints - Issuing USD bonds in other countries & not required to register them w/ SEC (can't be traded in US) - Reaches large pool of global investors (primarily eurozone, Asia Pacific & US) Global Bonds: Eurobonds that also trade in the national bond market; Ex) World Bank bonds

Explain: - Street convention: - Bond true yield: - What's higher: Street convention or True yield? - Yield to call (YTC): - Yield to worst: Who does a bond with options favor? What do investors require on callable bonds? Why? What is an option adjusted yield? When/why would you use option adjusted yield? How do you use it? What are the steps: Option free bond price = Which is more valuable; putable bonds or option free bonds? For putable bonds, how do you get the option adjusted price?

All Fixed Coupon Bond Related: Fixed Coupon Bonds: Held to maturity, no default & CFs can be reinvested at YTM (flat yield curve) Effective Annual Yield (EAY): Compounded rate of return. I/Y is always annual. EAY for a bond w/: - Annual Yield = I/Y = EAY = [1 + (YTM/n)]ⁿ − 1 - Semiannual: Calculate I/Y. Then, EAY = (1 + I/Y)² - 1 - Monthly: Calculate I/Y. Then, EAY = (1 + I/Y)¹² - 1 Changing Semiannual to Monthly: - Step 1) YTM of 4% semiannual has effective yield of 2% per 6 months. Semiannual's EAY: 1.02² − 1 = 4.04% - Step 2) Annual YTM on monthly bond is EAY times 12. Monthly yield = to 2% per 6 months is = [(1.02¹⸍² − 1) • 12] Street Convention: Coupon pmts are made on the scheduled dates. Higher yield than true yield. True Yield: Uses actual coupon dates to ensure dates don't happen over a weekend/holiday. Lower yield than street convention bc dates are pushed out further Current Yield (income, running): Limited. Ignores g/l as price moves toward par = (Annual coupon pmt)/Price Simple Yield: Adjusts current yield by using SL amor for premium & discount bonds. It declines evenly over remaining years to maturity = (Annual coupon pmt ± Amor) / Price Option Adjusted Yield: Removes effect of embedded option from YTM. For comparing to option free bonds. - Call Value < Option Free: = CallableP + Call Value - Putable Value > Option Free: = PutableP - Put Value Option Adjusted Spread (OAS): Similar to Z-spread, but removes extra yield from embedded options, to compare to option free bonds. Credit & liquidity risk. - Option Value in bp = Z-spread - OAS - Option value > 0 for callables & < 0 for putables Yield to Call: Each possible call date & price. Yield to Worst: Lowest/worst YTM out of all the possible call dates

What type of options are these? Explain: - Contingency provisions: - Callable bonds: - Make whole provision: - Putable bonds: - Convertible bonds: - Warrants: - Contingent convertibles (coco's):

All Have Embedded Options: Contingency Provisions: Actions issuer or bondholder may take if the contingency event occurs Bond w/ (call) Option: Benefits issuer bc they can call early. Investors require a higher yield to compensate for this added risk Callable Bonds: Attractive to issuer. Trades at a ↓Price, but has a ↑Yield (vs bond w/o call) as added risk comp. - Issuer can redeem before maturity on call dates at call price. Issuer benefits. Call protection (no calls for X years). Highest YTM at issuance. - ↑Yield unless bond has Make Whole Provision: Call price includes PV of future coupons pmts. Stops from "refinancing", taking advantage of low rates Putable Bonds: Attractive to investors. Trades at a ↑Price, but has a ↓Yield (vs bond w/o put). Bondholder can sell bonds back to issuer at par. Bondholder benefits through interest rate protection. Convertible Bonds: Attractive to investors. Trades at ↑Price, but has a ↓Yield. Bondholder benefits. Bondholder can exchange bond's for common. Warrants: Gives bondholder right to buy common at X price, but still keep the bond. Lower yield vs bonds w/o warrants. Gives a bond upside when attached. Contingent Convertibles (Coco): Automatically converts to common, if specified event occurs. Used to meet regulator's minimum equity/capital requirements.

Explain: - Auto loan ABS: Prepayment risk & loan type? - Credit card ABS: Prepayment risk & loan type? - Lockout period: - Rapid amortizing provision: What are all the sources of a bond's return?

Auto loan ABS: Fully amortized loans. Needs credit enhancement to attract investors, due to default risk. Prepayment occurs if car is sold, traded in, paid early or loan is prepaid w/ insurance proceeds if the car is wrecked or stolen. Credit card ABS: Non amortized loans. Backed by pool of credit card receivables. No prepayment risk. - Lockout period: In beginning, no principal is paid & any principal paid by card holders is used to purchase more receivables making principal value stays the same. - Early (rapid) amortizing provisions: Provides earlier principal amortization (preserving credit quality) that gets triggered if things go wrong (bad credit, sudden defaults increase, etc). Usually includes seniors/subordinated structure.

Explain: - Bank borrowing: - Bilateral loan: - Syndicated loan: - Commercial paper: - US commercial paper: - Eurocommercial paper: - HPY: - Discount interest basis: - Add on interest basis: - Rollover risk: - Combatting rollover risk:

Bank Borrowing: Corporations borrow from banks - Bilateral Loan: Single bank (ie two parties involved) - Syndicated Loan: Multiple banks involved Commercial Paper: Interim financing for LT projects. Short maturity to avoid regulation. Usually issued by top credit companies. Reissued or rolled over. Has secondary market. US Commercial Paper: Matures in < 270 days. Doesn't register w/ SEC. Sold on discount interest basis (Borrow $98 & pay you back $100). Settles (T + 0) Eurocommercial Paper: Matures < 364 days. Doesn't register(T+2). Limited secondary market. Low rates for high quality borrowers HPY: Effective return over a period. Discount Yield (interest): Priced at < Par Commercial paper with HPY of 1.35% $100 / 1.0135 = 98.668. Borrows $98. Pays back $100 Discount from par = 100 - 98.668 = 1.332% Add On Yield (interest): Multiply par value. Paper issued at 100. Pay 100(1.0135) = 101.35 at maturity Ex) Buy $100 par value bond. Pay back $102 at maturity Rollover Risk: Company unable to sell new commercial paper to replace maturing paper. Happens from credit deterioration (ability to pay debt) or systemic failure (ie 2008 financial crisis) Combat Rollover Risk: Firms get backup lines of credit so bank agrees to fund matured paper unless material adverse change significant financial deterioration

Explain: - Benchmark yield curve: - Relationship b/w liquidity & yield spreads relative to the benchmark: - Spread to benchmark: - Price effect from changes in spread: Formula: - Top heavy: - Structural subordination:

Benchmark yield curve: Composed of RFR & expected inflation. Includes premiums for credit risk & illiquidity The less liquidity a bond has: The higher its yield spread is relative to its benchmark bc investors require a higher yield to compensate them for giving up liquidity. Spread to benchmark (parallel): Includes premiums for credit risk & illiquidity. Estimates price effect of Δ in spread using duration & convexity Price effect from Δspread using duration & convexity (same formula as price effect from ΔYTM) = -Dur(ΔSpread) + ½Convexity(ΔSpread)² Top Heavy: High yield companies were secured bank debt is a high proportion of capital structure. Can't borrow during stressful times. Higher chance of default. Structural Subordination: Subsidiaries must service their own debt (has priority) before upstreaming dividends to parent. Holding company debt is subordinated to subsidiary debt.

All about CDOs: - Explain collateralized debt obligations (CDOs): - Types of CDOs: - CDO structure: - What's key to a CDOs viability: - Synthetic CDO: - Arbitrage CDO:

CDOs: Pool of collateralized debt obligations. Managed to generate CFs by a collateral manager to make promised payments to investors. Only CDOs buy/sell their securities. Types of CDOs: ~ Structured finance CDO: Collateral is a pool of MBS, ABS or other CDOs ~ Corporate, emerging market bond (CBOs) ~ Collateralized loan obligation CLO: Collateral is a pool of leveraged bank loans. CDO structure: Issue three classes of bonds - Senior tranches: 70% - 80% of principal total. Sold at floating rate debt - Mezzanie tranches: Middle tranche. Has fixed coupon - Equity (residual, subordinated, 1st loss) tranches: Provides prepayments & credit protection Key to CDO's viability: Creating structure w/ a competitive return for subordinated tranche. (Senior & mezzanie tranche are easily to sell. The concern is if the equity tranche is sellable) Synthetic CDO: Takes on economic risk (not legal ownership) of underlying assets by using a credit default swap, rather than a cash market position. Synthetics acts like a CDO, but collateral is a pool of credit default swaps (not debt securities) Arbitrage CDO: CDOs structured to earn returns from spread b/w collateral interest paid (portfolio returns) & funding costs (ABS promised interest)

Explain Portfolio Duration: - How do you calculate? - Portfolio duration Method #1: - Portfolio duration Method #2: Money duration: - Formula & interpretation: - How does duration effect price: Price value of a basis point: - What is it & what does it measure: - Useful for: - Formula to calculate price value of a Bp:

CF Yield Approach (Portfolio Dur Method): Weighted avg periods until entire portfolio receives CFs - Rarely used. Generates portfolio IRR, but can't be used w/ embedded options Weighted Avg Portfolio Dur Approach/Method: Weighted avg of each bond's dur in the portfolio. Most common. - This method includes embedded options so it uses EffDur. Future CFs are unknown & depend on interest rate movements. Shows interest rate risk. - Limitation: YTM of every bond in portfolio must Δ by same amount. Assumes parallel shift in YC = [(FP₁/Port)•(FP₁ Dur)] + [(FP₂/Port)•(FP₂ Dur)] +..+ Total = Total value (duration) of portfolio or market FP = Bond full price (not par) Port = Sum of entire portfolio FP₁ Dur = Bond Duration Money Dur: = MonDur x Bond's full price - Interpretation: Δ in full price for an ↑ in yield of X - Since yield ↑ & the answer $ it must ↓. - Dur Overestimates Price↓ & Underestimates Price↑. W/ MonDur, if yield↑, make yield negative in formula to show P↓ in answer = - X(MonDur) = ↓ of $amount Price Value of a Basis Point: Δ in price from a 1bp Δ in YTM. Measures sensitivity to small yieldΔ. - Useful for uncertain CFs like callable bonds Step 1) If not given, solve for I/Y V₋ = PV of 1bp below YTM; subtract 1bp from I/Y V₊ = PV of 1bp above YTM; add 1bp to I/Y Input +1bp & -1bp w/ two decimal places for I/Y Step 2) PVBP = (V₋ - V₊) /2 ** If solving in semiannual, Δanswer back to annual rate. - Ex) For 5% YTM: Input I/Y as 5.01 & 4.99 (not 4.9)

Commercial Mortgage Backed Securities (CMBS) Explain: - What is CMBS: What do analysts focus on? - CMBS structures: Why is it necessary? - Debt service coverage ratio: Formula. Want high or low? - Loan to value ratio: Formula? - CMBS level call protection: - Prepayment lockout: - Defeasance: - Prepayment penalty points: - Yield maintenance charges:

CMBS: Nonrecourse loans. Focuses on property's risk & what it can generate. Paid by investors who, rely on tenants' rental payments to cover mortgage. Partially amortizing w/ balloon risk. Borrower defaults if unable to pay balloon payment (extension risk). Typically feature call protection. CMBS Structures: Since nonrecourse w/ extension risk, lenders want protection. Each CMBS is segregated into tranches. Default losses 1st absorbed by lowest priority tranche (also called equity/residual/1st loss tranche) Debt service coverage ratio: Higher ratios show better credit quality (borrower has more income to pay) = Net operating income / Debt services Loan to value ratio: = Current mortgage $ / Current appraised value CMBS Level Call Protection: To reduce prepayment risk (vs residential). Structures tranches repayments sequence so loan defaults 1st affect lower tranches, protecting senior, higher credit rating tranches. Also provides call protection to senior tranches. Loan Protection only for CMBS: - Prepayment Lockout: Prohibits prepmts for X years - Defeasance: Insisted prepmts are used to purchase gov't securities to generate interest. ↑Pool's credit. - Prepayment Penalty Points: Penalty expressed in points. 1 point = 1% of principal amount prepaid - Yield Maintenance Charges: Borrower pays fee to lenders as comp for lost interest from prepayment

All about CMOs: - Collateralized mortgage obligations (CMO): - Reasons to issue CMOs: - Sequential pay CMO: Tranche A vs last tranche risks - Planned amortization class CMO (PAC): - In PAC tranche, when is there extension or contraction risk? - In Support tranche, what's the outcome of slow/fast prepayments? - PAC collar: - Broken collar:

CMOs: Collateralized pass through MBS for investors w/ different risk needs. Risk is redistributed through tranches w/ varying contractions/extension risks. - Can raises funds at low cost bc tranches appeal to many investor risk needs Sequential Pay CMO: Type of time tranching. All principal pmts flow to each tranche (starting w/ shortest) in chronological order, until it's paid off. - Tranche A: Highest contraction risk from getting all the prepayments - Last Tranche: Highest extension risk, but lowest contraction risk PAC: Two tranches. Limits contraction & extension risk - PAC Tranche: Low extension & contraction risk. Has predictable CF & ave life. PSA↓ = Small extension risk PSA↑ = Small contraction risk - Support Tranche: Absorbs contraction & extension risks. Faster prepmts goes to Support. When prepmts↓, Support gives PAC Tranche principal pmts to keep it on schedule. High extension & contraction risk ~ Slow Prepmts: ↑Extension. Support avg life↑ more ~ Fast Prepmts: ↑Contraction. Support avg life↓ more PAC Collar: Upper & lower limit that Support Tranche can sufficiently provide/absorb prepmts for PAC - Broken PAC: Pmts to PAC Tranche are outside limit

Explain: - Corporate bonds: - Structured financial instruments: Includes? - Credit linked notes (CLN): Instrument type? - Credit default swap (CDS): Buyer & seller view points - Capital protected instrument: - Guarantee certificate: - Participation instrument: - When is a floater leveraged, deleveraged & not leveraged: - Term maturity structure: Bond type? - Serial bond issue: Similar to? Bond type? - Medium term notes (MTNs): Bond type? - Structured note:

Corporate Bonds: Various coupon structures w/ both fixed & floating rate coupon payments. Secured by collateral or unsecured. Can have call, put, or conversion provisions. Structured Financial Instruments: Changes risk profile of underlying security by redistributing risk through combining a debt security w/ a derivative. Includes ABS & CDOs. Credit Linked Note (CLN): Regular coupon payments, but redemption value is dependent upon if specific credit event occurs. Like buying a note & simultaneously selling a CDS. Yield enhancer instrument. - If credit event doesn't occur: Par value is paid - If CNL occurs: Will be redeemed for < par value Credit Default Swap (CDS): CDS buyer makes periodic pmts to seller. Seller only pays if credit event occurs. Yield enhancer instrument. - Buyer: Makes pmts to seller. If event occurs, seller pays buyer (like buying fire insurance) - Seller: The bondholder. Receives premium pmts (extra yield) as comp for assuming asset's risk. Gains if no default. Low pmts at maturity if event occurs (defaults) Capital Protected Instrument: Guarantees min value at maturity + potential upside based on asset returns. Ex) Combining zero coupon w/ call option - Guarantee Certificate: If minimum payment at maturity equals purchase price. Ie you're at least guaranteed the purchase price if there's no gain on upside. Participation Instrument: Payments based on value of underlying instruments (eg stock index) or on MRR. When MRR↑, coupon payment↑ ; Ex) Floating rate note Annual yield for pricing w/ negative YTM: Can be done w/ calc: Future value/ (1 - YTM)ⁿ Leveraged Inverse Floater: △ in coupon rate is a multiple of△ in MRR. Coupon = Fixed rate - (Multiplier x Reference rate) Leveraged Inverse Floater: When multipliers is > 1 Deleveraged Inverse Floater: When multiplier is < 1 Not Leveraged Floater: When multiplier = 1 Term Maturity Structure: All bonds mature on same date. Corporate bond. Serial Bond Issue (Structure): Matures on several dates. At issuance, you know when bonds will be redeemed (unlike sinking bonds). Corporate bonds. Medium Term Notes (MTNs): Continuous offerings by issuer's agent. Many maturity ranges. Investor specifies desired par/maturity. Agent confirms w/ issuer, then enacts transaction on issuer's behalf. Corporate bonds. Structured Notes: MTN (ie debt securities) combined w/ derivatives (options, futures, swaps, etc.)

All about covered bonds: - Where are they issued? - What's the difference b/w them and ABS? - Which has the advantage, ABS or covered bonds? - How are they backed? For covered bonds, explain: - Dual coverage: - Replacement: - Single class: - If default happens: - Hard bullet covered bond: - Soft bullet covered bond: - Conditional pass through covered bond:

Covered Bonds: Replaces ABS in Europe, Australia & Asia. Similar, but underlying assets are segregated on issuer's BS. Assets aren't sold. No SPE is created. Less default risk. Advantages over ABS. Backed by segregated assets (residential, commercial mortgages) Similar to ABS, but legislation protects underlying assets, that are segregated, but still owned by the firm & on firm's BS. - Segregated asset that are unable to make payments are augmented (ie put more assets into pool) creating bondholder protection. Bondholders now have recourse to both firm & segregated assets (ABS doesn't) In Covered Bonds: - Dual Coverage: Recourse to issuer & asset pool. Claim against asset pool & claim against issuer (unlike ABS) - Replacement: Any prepaid or nonperforming assets must be replaced to maintain dynamic pool. No contraction risk. Credit risk↓ by replacing bad assets. - Single Class: No tranches bc most risk is left w/ issuer - Default: If default there's special provisions to adjust terms/collateral + replacement & dual coverage - Hard bullet covered bond: Defaults if issuer fails to make scheduled payments - Soft bullet covered bond: Postpones originally scheduled maturity date up to 1 year - Conditional pass through covered bond: Converts to pass through bond on maturity date if pmts remain due

Explain: - Factors considered to estimate credit risk of bond? - Factors considered to estimate price risk of bond? - Default risk: - Loss severity: Formula? - Expected loss formula: - Recovery rate: Formula? - What happens w/ ↑recovery rate: - Low recovery rate = - What do ratings & spreads reflect? - What is spread: - Market liquidity risk: - Example of benchmark yield curve & why:

Downgrade Risk (Credit Migration): Credit rating downgrade due to earnings shortfalls. ↑Spread bc issuer becomes less creditworthy. Rating↓. Two Components of Credit Risk: Default prob & Loss severity Factors to Est Credit Risk: Bond rating & recovery rate. ; ie Prob of default risk (from bond rating) & loss severity (from recovery rate). Factors to Est Price Risk: Yield volatility & Duration Default Risk: Prob issuer fails to pay. Credit ratings reflect a bond's default risk (not %). ↑Credit rating = ↓Prob of default Loss severity: Amount or % bondholder loses if default. = (1 - Recovery rate) Expected loss = Default risk prob x Loss severity Recovery rate: % of bond's value a bondholder receives if default An ↑recovery rate means loss severity↓ which ↓expected loss Low recovery rate = High loss severity Ratings reflect: Default risk. Spreads reflect: Expected loss. Market liquidity risk: Receiving < market value when selling a bond. Reflected in bid ask spread. Benchmark yield: Very safe & liquid bonds (Treasury bonds)

What is: - Duration: - Low duration vs high duration: Macaulay Duration: - What effects sensitivity: - When is MacDur less: - How do coupon payments effect it: What are the formulas for: - Modified Duration: What is it? What does it measure? - Approximate Modified Duration (AMD): What is it? What type of bonds can be calculated from each of these? Is MacDur or ModDur always larger? When & why?

Duration: # of years it takes to be repaid on a bond. Measures interest risk/price sensitivity from Δ in yield - Long Maturity =↑Duration, ↑Interest rate risk - Short/Low Maturity = ↓Duration, ↓Interest rate risk - Low Coupon Rate = ↑Dur, ↑Interest rate risk - ↑Coupon = ↓Dur, ↓Interest rate risk - YTM↑ = ↓Dur - Zero Coupon (MacDur): Have Highest duration Macaulay Dur (MacDur): Weighted Dur avg. Weights are the PV of each CF. %PΔ for a 1%ΔYTM - MacDur is lowest with: The highest YTM & shortest maturity - Used for option free bonds - Always > ModDur, if YTM > 0. ModDur is 7, MacDur > 7 Modified Dur: Measures Yield duration & by ΔYTM - Limitation: Assumes parallel shift in a flat yield curve is from a 1%Δ in yield (YTM). ModDur = [MacDur/(1+YTM)] Approx Modified Dur (AMD): ΔYTM. Assumes curve is parallel. Best for small yield Δs. Option free bonds. - Step 1) Calculate: PV₁: (bp + I/Y) & PV₂: (I/Y - bp) ΔYTM = Basis points in decimal (5bp = 0.05% = 0.0005) - Step 2) = (V₋ - V₊) / (2 • V₀ • ΔYTM) V₊ = PV₁ w/ YTM↑; adding bp to I/Y V₋ = PV₂ w/ YTM↓; subtracting bp from I/Y

Effective duration: - What is it? - How do you calculate? - How does it move? - What does it measure? Key Rate Duration: Other name? - What is it? - What does it measure? - What does the sum equal?

Effective Dur: Parallel shifts entire benchmark yield curve by same amount, at each maturity. - Used for bonds w/ embedded options. Bc their CFs depend on interest rate levels & paths (measures interest rate risk) - Measures curve duration, but doesn't Δcurve shape EffDur = (V₋ - V₊) / (2 • V₀ • decimal Δ in curve) V₋ = PV w/ curve↓; subtracting basis points from I/Y V₊ = PV w/ curve↑; adding basis points to I/Y Decimal Δ in curve = Shifts the the benchmark curve up/down by the same amount at each maturity Key Rate (Partial) Duration: Impacts of nonparallel shifts. Measures price sensitivity to Δs in the spot rate at a specific/single maturity (eg steepening or flattening) - Bond's sensitivity to shaping risk. Estimates effect on bond prices of Δ in shape of yield curve. - Sum of Key Rate Durations = EffDur

For floating rate notes, explain: - The rate at next coupon reset date: - Quoted margin: - Required margin: Other name? What happens to required margin & price if: - Issuer's credit quality got worse: - Issuer's credit quality got better: How do basis points relate to interest rate? Ex) 110 basis points to interest rate?

FRN Coupon at Next Reset Date: Reference rate at previous reset date +/- quoted margin Quoted Margin: Margin used to calculate coupon pmt amount. # of bp added to MRR Required or Discount Margin: # of bp that must be added to LIBOR to return price to par at reset date. Credit quality△ can causes required margin to differ from quoted margin. - Issuer Credit Quality↓ Requird Marg > Quoted Marg, FRN is priced at discount on reset date - Issuer Credit Quality↑: Requird Marg < Quoted Marg, FRN priced at premium on reset date. Bp: One 100th of interest rate: 110bp = 1.1% interest rate

Explain: - How do you calculate EBITDA? - Financial ratios: - What to include when analyzing company's total debt: - Profit & CF metrics: - Funds from operations (FFO): Formula? - Leverage ratios: High or low? - Coverage ratios: High or low?

Financial Ratios: Credit analysts focus on leverage ratios and coverage ratios Analyzing Company Total Debt, include: Obligations such as operating lease payments & underfunded pension plans EBITDA = Operating income + Depr + Amort ** Doesn't include capital expenditures Profit & CF metrics: - EBITDA (non cash charges available for debt), EBIT - FFO: NI from continuing operations + depr/amor + deferred taxes + noncash items - FCF before/after dividends Leverage Ratios: Lower is better ~ High ratio = High leverage = High risk ~ Debt to capital, debt to EBITDA, debt to equity ~ Lower ratio = Less debt. Better chance to make payments Coverage Ratios: Higher is best. ~ High ratio = High coverage = Low credit risk ~ FFO to debt, EBITDA to interest expense, EBIT to interest expense: ~ Higher ratio = Higher operating earnings, CFs, credit, etc so better chance to make payments.

Explain floating rate notes (FRN): - What is it: Formula? - FRN Cap: Who benefits? - FRN Floor: Who benefits? - Floating rate notes: - Inverse floater: How do you calculate coupon rate for interest payments when given a floating rate note & MRR?

Floating Rate Bonds: Coupon rate ↑ & ↓ w/ market interest rates. Reference rate must match frequency of rate resets; = Reference rate +/- Margin/bp - 3% LIBOR on June 30th. 4% LIBOR on Dec 31. The LIBOR paid on Dec 31st is 3% bc LIBOR now sets the interest rate for the next period. FRN: Coupon rate based on market reference rate (MRR) +/- Fixed Margin (eg +80 bp) for risk. Bps are added on for the additional risk bond has over MRR - FRN Cap: Benefits issuer. Maximum the interest rate can float up too, regardless of reference rate & margin. - FRN Floor: Benefits bondholder. Minimum the interest rate can float down to, regardless of reference rate & margin; Ex) Rate will never be less than X% Floating Rate Notes: Interest rate is tied to the benchmark rate. Pays periodic interest dependent on current market interest rates. Less risk from interest rate movement. Type of participation instrument. When MRR↑, coupon pmt↑ Inverse Floater: Coupon rate △s in opposite direction to market interest rate, inverse relationship w/ benchmark rate. Coupon rate↓ & Interest rates↑. - Type of leveraged instrument. Coupon rate for interest payments when given a floating rate note & MRR: Use the previous coupon date's MRR + given basis points. **Note: +80bp is .80

What's included in Four Cs of credit analysis: - Capacity: - Collateral: - Higher depr vs capital spending implies: - Stock price < BV implies: - Intangible assets as collateral imply: - Covenants: - Character: What are Porter's Five Forces?

Four Cs of credit analysis: Capacity: Industry structure (Porter's 5), Industry fundamentals (cyclicality, growth prospects), Company fundamentals, ability to repay debt Collateral: Firm's intellectual capital, depr & intangible assets. Value/quality of assets. Important for less creditworthy companies. ~ High Depr Expense vs Capital Spending: Implies insufficient investment, low quality assets ~ Stock price < BV: May indicate low quality assets ~ Intangible Assets: Can be sold (patents, intellectual property) may have collateral value Covenants: Bond's legal terms & conditions. Protects lender. Lender accepts lower rates when stricter. ~ Affirmative Covenants: Actions issuer must take (pay interest/principal on time, pay taxes) ~ Negative Covenants: Actions issuer can't take (issue more debt, pledge same assets); May constrain firm's operations & impose significant costs Character: Mgmt's integrity, past performance, fraud, accounting policies, prior treatment of debtholders vs equity, soundness of strategy Porter's Five Forces: 1st level of a credit analysis. Industry competition intensity depends on: - Barriers to Entry: High barriers is best - Power of Suppliers: High # of suppliers is best. If suppliers can keep raising prices, it puts lid on ur profit - Power of Buyers: High # of buyers is best. W/ few buyers, buyers have power to take your profit (ie if gov't is primary buyer) - Substitution Risk: Low is best - Rivalry among existing competitors: Low is best

Explain: - Spread outcome from higher & lower yields? - Yield spread formula: How do these factors affect yield spread? - Bond quality: - Credit cycle: - Economic conditions: - Issuer financial performance: - Broker dealer supply of capital: - High supply of new issues: - High demand of bonds:

Higher Yield = Wider Spread = High Risk Lower Yield = Narrow Spread = Low Risk Yield Spread = Liquidity premium + Credit spread Spread Risk: Risk of spread widening. Bond yield spread to benchmark yield △ing due to credit migration risk or market liquidity risk. Spread: Amount above benchmark for a risky bond. Spread Considerations: - Credit Spread: Depends on credit rating & economic conditions. Bigger dif = Higher Spread - Embedded Call: Widens spread - Embedded Put or Conversion: Narrows spread - Greater liquidity/large issue size: Narrows spread Bond Quality: Spreads more volatile for low quality bonds than high quality bonds. High Yield Bonds: Higher default risk. Increase focus on loss severity. Analyze debt structure. Credit Cycle: When credit is widely available (at credit peak) & credit cycle improves, spread narrows. As credit cycle improves, spread are also narrow. Economic Conditions: In weaker economy, things look more risky, spread widens. In strong economy, spread narrows. Issuer Financial Performance: If issuer has poor performance& higher yield, spread widens. If the issuer has good performance, the spread narrows. BD Supply of Capital: BDs finance their portfolio so w/ less capital, wider spread. W/ a lot of capital for OTC trading, spread narrows. Supply of New Issues (bonds): Wider spreads bc of excess supply condition (large issuance in short period) High volume drives prices down & yields up. Higher Bond Demand: Spread narrows

Explain: - Index linked bonds: Most common type & structure? - Inflation indexed bonds: Other name? - Interest indexed: - Capital indexed: - Indexed annuity bonds: - Principal protected: - Deferred coupon bond: Other name? - Step up coupon bond: - Securitized bonds: - American style callable bond: - European style callable bond: - Bermuda style callable bond:

Index Linked Bonds: Coupon or principal △s based on a published index (commodity, equity index, etc) - Ex) Inflation Index Bonds (linkers): Most common type. Payments adjusted based on CPI (inflation index) Interest Indexed: Coupon rate adjusted for inflation, principal/par remains fixed Capital Indexed: Principal/Par increases for inflation. Coupon remains fixed. Most common structure. - Ex) Treasury Inflation Protected Securities (TIPS) Indexed Annuity Bonds: Fully amortizing w/ payments adjusted for inflation or deflation Principal Protected: Indexed bonds that still pays original par value even if index decreases. Ex) TIPS Deferred (Split) Coupon Bond: Coupon payments don't begin until X time period after issuance Step Up Coupon Bond: Coupon rate increases over time on a schedule. Typically callable. Securitized Bonds: Reduce LT borrowing cost for low credit rating companies. CFs are linked to pool of underlying loans or financial instruments. American Style Callable: Callable at any time after 1st call date European Style Callable: Callable only on call dates Bermuda Style Callable: Callable on specified dates after 1st call date

Explain: - Interbank market: - Central bank funds market: - Central bank funds rate: - Reference rate: Formula? - LIBOR: What's replacing it? Primary Bond Market: - Public offering: - Shelf registration: - Underwritten offerings: - Grey market: Other name? - Best efforts offerings: - Auctions:

Interbank Market: Other than reserves on deposit w/ central bank, funds that are loaned by one bank to another. Interbank funds are ST unsecured loans/borrowing b/w banks. Central Bank Funds Market: Banks that deposit more than required amount w/ central bank have excess reserves. They lend excess to other banks in the central bank funds market. The interest rates on these loans is the central bank funds rate. Central Bank Funds Rate: The interest rate on excess reserves borrowed by one bank from another bank Reference Rates: Coupon rate on floating rate debt is Floating rate = market reference rate (MRR) + a margin based on the issuer's credit risk Libor Rates: Many different banks' quotes use interbank money market. Each rate refers to a specific maturity (ranging overnight to one year) & currency. LIBOR is being phased out. In US, secured overnight financing rate (SOFR) is replacing LIBOR. SOFR is based on actual repurchase transactions. Public Offering: Issues must be registered w/ securities regulators Shelf Registration: Registers entire issue of bonds w/ regulators. Shelf them & issues to public over time. Underwritten Offerings: Investment or syndicate bank buys entire issue at one price & then resells to dealers & investors at a different price - Grey Market: Bonds traded on "when issued" basis. Bonds trade before they're issued in forward delivery, but promised to be delivered upon issuance. Best Efforts Offerings: Investment banks gives best effort to sell as many bonds as they can on the specific commission basis Auction: Gov't bonds are primary dealer

Explain: - How interest is taxed: - How municipal bond interest is taxed: - Original issue discount bonds (OID): - Zero coupon bonds: Other name? - Bullet structure: Other name? - Partially amortized: - Balloon payment: - Interest only lifetime mortgage: - Fully amortized: - Sinking fund:

Interest: Is taxed as ordinary income Municipal bond interest: Tax exempt Original Issue Discount Bonds (OID): Bonds issued w/ coupon rate < market rate - Price increases over time. Taxed as interest income. Ex) Zero coupon (pure discount) bonds: No interest (coupon) pmts, but increase in bond's value is treated as taxable interest income Bullet Structure (Plain Vanilla) Bond: Periodic interest pmts, all principal paid in one lump sum at maturity Partially Amortized: Periodic payments include interest & some principal. Balloon pmt of remaining principal repaid at maturity Balloon Pmt: Lump sum of principal that remains to be paid at the end of the loan period Interest only lifetime mortgage: Partially amortizing. No principal repayment for lifetime of loan. Balloon payment = original loan principal amount. Fully Amortized: Equal periodic pmts each period of interest & principal. No principal is owed beyond last pmt (no balloon risk); Ex) Mortgage or car payments Sinking Fund: Bonds mature on several different dates, but when bonds will be redeemed is unknown. Part of bond issue is redeemed periodically. Can be redeemed early, creating redemption risk prior to maturity.

Explain: - How investment horizon & MacDur relate: - When is MacDur almost = to YTM? - Duration gap formula: - Positive duration gap: YTM, returns, risk, rates & yield - Negative duration gap: YTM, returns, risk, rates & yield

Investment horizon: When you expect to sell the bond Macaulay Dur, when MacDur = Investment Horizon, MarketP Risk & Reinvestment Risk just offset each other - Ex) MacDur is 3.0 & YTM is 4.5%. Bond sold after 3 years. MacDur & # years are equal so the annualized horizon return is approx 4.5% Short Holding Period: MarketP Risk > Reinvestment Risk Long Holding Period: Reinvestment risk > MarketP Risk Duration Gap = MacDur - Investment horizon Positive Dur Gap: Short investment horizon. ST investment (left side of timeline pic) - ↑YTM, ↓Returns. Price risk dominates. Investor at risk of ↑interest rates. Horizon yield < MacDur Negative Dur Gap: Long investment horizon. LT investment (right side of timeline pic) - No price risk. ↓YTM, ↓Returns bc reinvestment risk dominates from ↓interest rates. Increases horizon yield

Explain: - Issuer: - Maturity date: - Tenor: - Par (face) value: - Coupon rate: - Coupon frequency: - Dual currency bond: - Currency option bond: - Bond Indenture: Other name? - Covenants:

Issuer: Entity that pays interest, repays principal Maturity date: Date of final payment Tenor: Time remaining until bond matures Ex) 30 year bond we will always call a 30 year bond, even though there might only be 2 or 3 years left Par (face) value: Principal to be repaid Coupon Rate: Annual interest as percent of par Periodicity (Coupon Frequency): # of coupon pmts per year Dual Currency Bond: Coupon interest payments are in one currency & principal repayment at maturity in another currency Currency Option Bond: Gives bondholders a choice of which of two currencies they would like to receive their payments in. Bond Indenture (Trust deed): Legal contract b/w issuer & bondholder, held by trustee Covenants: Provisions of an indenture

What does: - MacDur, ModDur & EffDur measure vs Key Rate Duration: - Read the answers of MacDur, ModDur & EffDur: - ModDur & MacDur have as a limitation of interest risk - Duration relate to price, interest rate & interest rate risk? - High & low duration mean: How do these factors affect duration & interest rate risk: - Increase in maturity → - Higher coupon rate → - Higher YTM → What does low maturity do to price?

Key Rate (Partial) Duration: Nonparallel shifts. Sensitivity to shaping risk. Measures price sensitivity to Δ in yield curve shape & Δ in spot rates. MacDuc, ModDur & EffDur: Measure price sensitivity to a parallel shift in yield curve. Duration is the % priceΔ bc of a 1% Δ in yield - Answer interpretation: With a 1% YTM ↑/↓, the bond price will ↑/↓ by approximately __Duration% If duration is 7.5, the bond price will Δ by approx 7.5% EffDur: Measures curve duration. Price sensitivity Δs in the benchmark yield curve. Parallel shifts in a curve. - Use EffDur to measure interest rate risk bc bonds future CFs depend on the path of interest rate changes, like w/ embedded options - Adding a put or call to a bond ↓EffDur ModDur & MacDur: Measures yield duration. Sensitive to YTM. No distinction b/w Δs in the benchmark yield and Δs in the spread Limitation for interest risk: We assumed a parallel shift to the flat yield curve is from a 1%Δ in yield. Parallel shift in a YTM figure (ie in a flat curve) With higher duration (an investor is waiting longer to their money back) a bond's price drops more as interest rates increase, creating high interest rate risk. If rates rise 1%, a 5 year bond will lose 5% of its value. Interest rate risk/sensitivity = Duration = Interest rate Coupon rates are inversely related to duration. The higher the coupon (ie interest rate) the lower the duration. Duration & interest rate risk w/ other factors unchanged: - Long/↑Maturity will↑Duration &↑Interest rate risk - An ↑Coupon rate, will ↓Duration & ↓Interest rate risk - ↑YTM & ↑Current yield = ↓Interest rate risk - An ↑YTM will ↓Duration & ↓Interest rate risk Lower Dur = Lower sensitivity in price to a Δin yield Low/short maturity (low duration) = Small %Δ in price High interest rate sensitivity → Zero coupon bond

What is Matrix pricing? What does it use? Explain Matrix pricing steps using below example: Ex) Estimate the value of a nontraded 4% annual-pay, A+ rated bond that has 3 years remaining until maturity. Here are YTMs on similar corporate bonds: - A+ rated, 2-year annual-pay, YTM = 4.3% - A+ rated, 5-year annual-pay, YTM = 5.1% - A+ rated, 5-year annual-pay, YTM = 5.3%

Matrix Pricing: Ests unknown YTM (price) of bonds traded infrequently or not currently traded. - Use YTM of traded bonds w/ same credit quality - Use linear interpolation to adjust for diff in maturities - Step 1) Calculate avg YTM of bonds w/ same # of years. 5-year bonds: (5.1 + 5.3) / 2 = 5.2%. - Step 2) Interpolate Yr 3 YTM based on Yr2 & Yr 5 YTM Interpolated: = Yr2%+ [(1/3)•(Yr5% − Yr2%)] = 4.6% Interpolated YTM: = 4.3%+ [(1/3)•(5.2% − 4.3%)] = 4.6% 1/3 is: YTMs we're using are b/w Yr 2 & Yr 5. The YTM we need is Yr 3, which is 1/3 of the way b/w Yr 2 & Yr5. - Step 3) Price Nontraded using interpolated 4.6% YTM N = 3; PMT = 40; FV = 1,000; I/Y = 4.6; CPT→PV = -983.54

Explain these mortgage characteristics: - Maturity: - How long is maturity US, Europe & Japan? - Variable rate mortgage: Other name? - Renegotiable mortgage: Other name? - Hybrid mortgage: - Convertible mortgage: - Prepayment provision/penalty: - Recourse loans: - Nonrecourse loans: - Strategic default:

Maturity: Time until last loan payment is made. Usually 15-30 years in US, 20-40 years in Europe, up to 100 years in Japan Variable (adjustable) rate mortgage: Interest rates can change over life of the mortgage Renegotiable (rollover) mortgage: Initial fixed interest rate changes to a different fixed rate during its life Hybrid mortgage: Initial fixed rate changes to a variable rate during its life Convertible mortgage: Can be changed from fixed rate to variable rate or vice versa at the borrower's option Prepayment provision: Paying back principal faster than what's scheduled may result in a penalty Recourse loans: Lender has claim against borrower. If borrower defaults on payment & collateral is repossessed, lender sells the collateral & goes after the borrower for outstanding principal on the loan Nonrecourse loans: Lender has no claim (recourse) to the borrower, only has claim against the asset Strategic default: Can't sell an asset if value drops below your loan amount bc you'd still owe. In a nonrecourse, there's no claim against borrower so borrower voluntarily returns asset (default) to lender

Explain: - Money market instruments: How are they quoted? - Bond equivalent yield (BEY): - Steps to calculate BEY: - When calculating BEY, what do you do w/ add on yield, discount rate, 360 day year & 365 day year:

Money Market Instruments: Yield on debt securities w/ < 1 yr. Based on 360 day or 365 day year. Discount basis from par or add on yields. BEY (Gov't Equivalent Yield): Add on yield using 365 day year; Corporate & gov't bond yields can be restated based on actual/actual (365 day year) ; Used for calculating spread to benchmark gov't bond yields. When money market securities are quoted on diff basis, to compare, put them all in BEY. Step 1) Use 360 or 365 day year based on question. If Current Price (PV) is not given, calculate: PV = Par• { 1 +/- [(Yield%)•(Days Used/Days in Yr)]} - Yield% = Given discount or add on % as a decimal - Days used = Days til maturity = Days given - (1 +) for add on yield. (1 -) for discount rate/yield. Step 2) Calculate BEY using HPY: HPY = [(Par / PV) - 1 ] BEY = (HPY)•(365/Days Used) ** BEY calculation always uses 365 day year - Based on 360/Yr: Use 360 to calculate CurrentP. Must use 365 to calculate BEY. - Based on 365/Yr: Use 365 to calculate CurrentP & BEY

Forward rates: How do you read: - 1y1y: - 2y1y: - 1y2y: - 2y3y: What are they expressed as? Implied forward rates: Three different ways to write (1 + S3)³ How do you calculate: - Price between two spot rates? - Spot rate from forward rates: - Bond value w/ forward or spot rates:

N Period Rate at Some Future Date: - 1y1y: One year from now this is the 1 year rate - 2y1y: Two years from now this is the 1 year rate - 1y2y: One year from now this is the 2 year rate - 2y3y: Two years from now this is the 3 year rate - Sₙ & Zₙ: The N year spot rate All: Are compounded annual rates (1 + S₃)³: Rate paid back/owed at end of 3 years (1 + S₃)³ = (1 + S₁)(1 + 1y1y)(1 + 2y1y) (1 + S₃)³ = (1 + S₁)(1 + 1y2y)² (1 + S₃)³ = (1 + S₂)² (1 + 2y1y) Cost of borrowing for 3 year at the spot rate; S₃ is = to: - Borrowing for 1 year at S₁, 1 year at 1y1y & 1 year at 2y1y - Borrowing for 1 year at S₁ & 2 years at 1y2y - Borrowing for 2 years at S₂ & for 1 year at 2y1y Guessed Formula: - X Yr forward Rate, is the exponent in num (1 + S)^ - X Yrs from now, exponent in den (1 + S)^ - 1 yr forward rate, normal division - 2 yr forward rate +, use goemetric mean exponent at end of answer - Just for spot rate: Treat like geometric mean by multiplying all spot rates (1 + S) together, then 1/n exponent Approximation Formulas: - Given: Forward rates ; Asked for: 3Yr Spot rate S₃ = {[(1+S₁)+(1+S₂)+(1+S₃)]/3} - 1 - Given: Spot rate. ; Asked for: Forward rate 1y1y = S₂% - S₁% ; 2y2y = (S₄ - S₂)/2 - Bond Value w/ Spot,Forward: 5% 3yr annual pay bond = CP/(1+S₁) + CP/(1+S₁)(1+S₂) + (CP+Par)/(1+S₁)(1+S₂)(1+S₃)

Nonagency RMBS external credit enhancements: Nonagency RMBS internal credit enhancements options: - Reserve funds: - Overcollaterilization: - Senior/Subordinated structure:

Nonagency RMBS External Credit Enhancements: 3rd party gives enhancement through: Corporate guarantee by seller, Bank letter of credit, surety bonds (insurance) Nonagency RMBS Internal Credit Enhancements: Based on fund's structure. Happens through: 1. Reserve funds: Cover defaults & excess servicing spread funds (spread b/w paid interest & amount promised on nonagency RMBS. Covers difference if paid is < what's promise) 2. Overcollateralization: Adds more mortgages to pool to absorb losses if: FV is < underlying collateral value 3. Senior/Subordinated Structure: Reapportion credit risk. Subordinated tranches absorb losses 1st which raises credit on senior tranches Internal Credit Enhancement: Built into bond's structure. Protection methods to make bonds less risky: - Overcollateralization: Pledged collateral > par value of issued debt - Excess spread: Pool's yield > Issued bond's yield Protection if asset's yield less than anticipated. - Tranches: Different priority of claims for different bond classes. Ex) Waterfall structure: Available funds go 1st to senior tranches, then next highest priority, etc.

Explain: - Positive convexity: - Negative convexity: - Approximate convexity: Formula? - Approximate effective convexity: Formula? - Callable bond price yield: - Putable bond price yield: - Price effect from changes in yield: Formula? - Duration's effect on price: - How bondholder feel about the types of convexity:

Positive Convexity: Price↑ from a ↓YTM is > a Price↓ from an ↑YTM, by the same amount. Curved relationship. Prices rise faster than they fall. - Bondholders like convexity bc when yield↓ they gain more than they'd lose if yield↑ - As yields↑, prices↓, price curve gets flatter & yieldΔs have a smaller effect on prices Option Free Bond: Price yield curve is convex towards origin, positive. P↓ at a ↓ing rate & Yield↑ (Convexity) Putable Bond Price Yield: W/ ↑Convexity, yield↑, making put more valuable. Put value falls slower than option free bonds. Put EffDur↓. Positive convexity. - As yields↑, prices↓ at a decreasing rate. Callable Bond Price Yield: Call prices puts ceiling on price↑, causing negative convexity at ↓yields. Call prices cause an ↑limit on bond's value. - As interest rates/yields↓, Price↑ at a decreasing rate. Negative Convexity: P↑ from ↓YTM < P↓ from ↑YTM Approximate Convexity: Yield convexity. Assumes expected CFs don't Δ when yield Δs = (V₋ + V₊ - 2V₀) / [(ΔYTM)² • V₀] ΔYTM = Bp in decimal (5bp = 0.05% = 0.0005) Approximate Effective Convexity: Curve convexity. For bonds w/ embedded options. ; V₀ = Price = (V₋ + V₊ - 2V₀) /[(ΔCurve)² • V₀] Duration Effect: %Price Δ w/ EffDur = (-ModDur)(Δ in bp) Convexity Effect: %Price Δ w/ Convexity = (½ Convex)(Δ in bp)² Full Bond Price Δ = Duration effect + Convexity effect Price Effect from YieldΔs: Answer = the approximate Δ in price &/or impact on bondholder's return Full Bond Price Δ / Impact on Return = [(-EffDur)•(Δbp)] + {(½ApproxConvex)•[(Δbps)²]} = Duration Effect + Convexity Effect %Price Δ w/ EffDur: Duration Effect = [(-EffDur)•(Δbp)] = -X%, make duration negative since this is for money %Price Δ w/ Convexity: Convexity Effect = (½ApproxConvex)•[(Δbps)²]} **Note: One calculation using given bp (no V₋ & V₊) Dur Overestimates P↓ & Enderestimates P↑ - Reason why ModDur is neg in price effect formula. Convexity fixes Dur by (ΔYTM)², making it positive

Explain: - Prepayment risk: - Contraction risk: - Extension risk: - Prepayments are slowing when: Measures of prepayments rates: - Single monthly mortality rate (SMM): When does it decrease? - Conditional prepayment rate (CPR): - What does CPR measure? - Public securities associations (PSA): - 100 PSA, 50 PSA, and 135 PSA:

Prepayment risk: Receiving principal back sooner (contraction risk) or later (extension risk) than expected Contraction risk: Lower interest rates → more refinancing so prepayments increase → shorter average MBS life. Gets principal back faster than expected. Extension risk: Higher interest rates → less refinancing so prepayments decreases → longer average MBS life. Receives payments later, ie extending payments longer Prepmts are slowing. When extension risk↑ or contraction risk↓ SMM: Measures monthly % by which prepayments reduce principal balance vs no prepayments. Measures prepayment speed, varies over MBS life. Decreases as contraction risks falls. CPR: Measures annualized prepayments from a pool based on WAC, interest rates & prior prepayments PSA: Prepayment benchmark assumes monthly prepmts↑ w/ age. Expressed as monthly series of prepayment rates (CPRs). Conditional prepmt rates (CPR) are annual rate, not monthly. - If MBS CPR is = PSA Benchmark CPR, PSA is 100 (100% of benchmark CPR) ~ PSA 50: Prepayments are 50% of PSA benchmark CPR for loans of this age (ie pool has slower prepayments) ~ PSA 130: Prepayments are 130% of the CPR of the 100 PSA benchmark

Explain: - Examples of credit rating agencies: - What's a bond rating? - Corporate family rating (CFR): What are they rated on? - Corporate credit rating (CCR): - Notching: When are they larger? - Moody's, S&P & Fitch what are C & D ratings: Risks in relying on credit ratings: - What are they? - Explain subprime mortgage and how it applies: - How do price and spreads adjust? - What does rating and spread reflect?

Rating agencies: Moody's, S&P & Fitch - In Moody's, C rating means: It's already in default - In S&P & Fitch, D rating means: It's already in default Bond ratings: Forward looking & assess the probability of future default. Lower bond ratings are less stable than higher bond ratings. Event risk is difficult for ratings firms to estimate. Investment Grade: Baa3/BBB- or higher Noninvestment Grade: Ba1/BB+ or lower Corporate Family Rating (CFR): Credit rating of issuer's senior unsecured debt. CFR is AA while CCR is lower. (CCR) is lower bc bonds may have low seniority ranking. If newly issued bond is a senior subordinated debt, it has a lower priority of claims & hence lower rating. Corporate Credit Rating (CCR): Rating of a debt issue. May be notched above or below CFR depending on bond's characteristics. Additional covenants protecting bondholders ↑CCR rating. Notching: Credit rating agencies use notching to distinguish b/w an issuer's rating & issue's rating. Notching adjustments are larger w/ lower CFR. Risks of relying on credit ratings: - Credit rating are dynamic: Can change (downgrade or upgrade) - Rating agencies make mistakes. Ex) Subprime mortgage: When security is assigned much higher ratings than it deserve - Issuer specific risk & event risk is unpredictable (litigation, natural disasters, LBO, acquisitions, etc) - Credit ratings lag market price: Prices & spreads adjust faster than credit ratings.

Explain: - Repurchase agreement: - Repo agreement for buyers & sellers point of view: - Overnight repo: - Term repo: - Repo rate: Formula? - Repo risks: - Repo margin: Other name? What causes: - Both repo rate & margin ↑: - Both repo rate & margin ↓: - Repo rater to be lower: - Repo margin to be lower:

Repurchase (Repo) Agreement: Bond sold to counterparty w/ promise to buy it back at higher price on repo(future) date. Cheap source of short term borrowing for bond dealers - Buyer: Lends funds & buys security, but will sell it back - Borrower: Sells the security & promises to buy it back - Overnight Repo: 1 day repurchase agreement - Term Repo: Agreements > 1 day - Repo Rate: Implied interest rate. The % diff b/w SalesP & RepurchaseP = [(RepurchaseP) / (SaleP)] - 1 Repo Margin (Haircut): Diff b/w loan amount (salesP) & bond/market value. Gives lender protection & reduces risk by: Lending < Market Value Repo Rate (Interest) & Repo Margin (Haircut): - Both ↓ w/ ↑Collateral credit quality - Both ↓ when security is in ↑Demand: ↓Returns & interest rates bc lender requires less protection - Both ↑ w/ repo terms (maturity): If ↑Returns then lender requires more protection - ↓Repo rate: W/ required delivery - ↓Repo margin: W/ good counterparty credit Repo Risks: Both face counterparty risk - Buyer risk: If security value is < repo price & if borrower doesn't repurchase the security on repo date - Borrower risk: Security won't be delivered

Explain: - Convexity: - Maturity effect: - Coupon effect: - Inverse price yield relationship: - Constant yield price trajectory: When is a bond trading at a: - Premium: - Discount: - Par value: What is the outcome on yield when price is up or down?

Required rate of return = Required yield = Market discount rate = YTM = I/Y = Yield Coupon = PMT = Required margin/interest Inverse Price Yield Relationship: YTM↓, Price↑ Convexity: Curved relationship b/w yield & price. Price↑ from a yield↓ is > than a price↓ from a yield↑ Constant Yield Price Trajectory: P↑at an ↑ing rate. Convergences towards par at maturity. Shows how price would △ if YTM remains constant. - Capital g/ls are measured relative to this Maturity Effect: Bond w/ long maturities are more sensitive to △s in YTM Coupon Effect: Bond w/ low coupons are more sensitive to △s in YTM Premium: Coupon rate > YTM = Overvalued, don't buy Discount: YTM > Coupon rate = Undervalued, buy At Par: Coupon rate = YTM

What are residential mortgage loans? - Explain loan to value (LTV) ratio: High or low, why? Residential mortgage backed securities (RMBS) explain: - Agency vs nonagency RMBS: Loan criteria? - Confirming vs nonconforming RMBS: Prepayment risk for both - What happens w/ pass through for agency RMBS? - Pass through securities: Servicer role? Type of RMBS? Pass through securities types: - Weighted average maturity (WAM): - Weighted average life (WAL): - Weighted average coupon (WAC):

Residential mortgage loans: Loans w/ residential real estate as collateral. Repaid by homeowners. Lenders look at credit worthiness. - LTV: % of collateral value that is borrowed. - Low LTV ratio = Lower prob of default. High recovery % if default does occur. Gives lender better protection. Agency RMBS: Pool of mortgages as collateral issued by gov't agency w/ full faith of gov't (Ginnie Mae), or gov't sponsored enterprises not backed by gov't but have high credit quality (Fannie Mae, Freddie Mac) Agency RMBC loans: Fully amortizing loans. Only includes conforming loans (ie meet agency standards) that have Loans criteria: Min % down payment, max LTV ratio, max size, minimum documentation & purchase insurance Both agency & nonagency RMBS: No prepayment restrictions. Subject to prepayment risk Nonagency RMBS loans: Securitized by private companies. No gov't guarantee or gov't sponsor. More credit risk & needs credit enhancement. Mortgage pass through securities: Agency RMBS. They pass through pool to diversify risk (not reallocate contraction & extension risk) Each mortgage represents a large # of debts. Servicer collects issuance costs/fees, then passes profits to holders/investors who receive pro rata share of all CFs. WAM: Maturities weighted by each mortgage's outstanding principal as a proportion of total outstanding principal WAL: WA time until principal is repaid. Bc they're fully amortized < WAM. Ex) 30 year mortgage has WA life < than 30 years WAC: Interest rates weighted by entire pool's outstanding principal bc loans have diff coupon rates

Type of Bond Market, Explain: - Dealer market: - Tender offer: - What does bid ask spread convey? - What are the basis points for a liquid & illiquid market? - Trade settlement: - T + 2 or T + 3: Example - What type of bonds have same day? Explain: - Sovereign bonds: Explain credit rating - On the run vs off the run: - Fixed rate debt - Floating rate debt: - Nonsovereign government bonds: - Quasi gov't bonds: Other name? Give example - Supranational bonds: Give examples How are these classified: Municipal & supranational bonds, capital markets, money & capital markets, MRR & emerging markets:

Secondary Bond Market: Previously issued bonds. - Dealer Market: OTC trading - Bid ask spread is profit margin. Conveys info about issue's liquidity - Tender Offer: Issuer offers to repurchase some discounted outstanding bonds at X price Liquid Market: Spread b/w bid & bid ask of 10 to 12bp Illiquid Market: Spread b/w bid & bid ask of < 10bp Trade Settlement: When bond & cash exchange hands - Settlement for Corporate Bonds: T+2 or T+3 - Same Day Settlement: (cash settlement): Money market securities & some gov't bonds (most gov't bonds are T+1) Sovereign Bonds: Issued by national Gov't. Issued in local or foreign currency, ↑Credit rating for local currency debt (lower default risk bc they can print $) - On the Run: Most recently issued, best price information, actively trading (off the run is not) - Fixed rate debt: Have interest rate risk - Floating rate debt (floaters): Less interest rate risk Nonsovereign Gov't Bonds: Other gov't types (not nat'l) like state, city, etc. Paid from taxes, fees, or specific project rev Quasi Gov't bonds (Agency): Bonds issued by gov't sponsored entities for specific purposes (small businesses or mortgage financing). Typically T + 1. Might be guaranteed by national gov't. Ex) Fannie Mae (US) Supranational Bonds: Issued by multinational agencies (operate globally). Classified by issuer type - Ex) IMF, World Bank, European Investment Bank Classified By: - Municipal bonds: Tax status or issuer type - Emerging (developed) markets: Geography - Supranational bonds: Issuer type - Money/Capital market securities: Origin maturities - MRR: Coupon structure

All about securitization: - What is it: - Explain the process for seller, buyer, investors & servicer: - Benefits: - Bankruptcy remote: - Two securitization structures: - Credit tranching: Other name? Example - Sequential structure: Other name? - Waterfall structure:

Securitization: Process when financial assets are purchased by an SPE & put into a pool, legally separate from the company. SPE then issues securities which are funded by CFs from the financial assets. SPE: Legal corporation to which assets used as ABS collateral are sold. This transaction separates assets used as collateral from other assets of the company seeking financing through an ABS. ~ Seller (company holding the assets): Wants to remove assets from their BS so they sell to issuer (ie SPE) **Securitization does not remove liabilities from BS. Financial assets are securitized, not liabilities. ~ Issuer/SPE (legally separate from the seller) Puts assets into a pool & then issues ABS (tradable securities) which are backed by CFs from the assets. ~ Investors: Buys the created securities from SPE & receive CFs from interest ~ Servicer (often seller): Collects payments & recovers assets if payment defaults Securitization Benefits: Creates tradable securities w/ greater liquidity than the original loan - Reduces funding costs: for firms selling bc they get lower interest rates - Increases liquidity: for assets, bc now actively trading - Banks can raise more & increases their lending ability - Offers investors exposure to new asset classes - SPE is bankruptcy remote. If sellers gets into financial trouble, it doesn't effects ABS owner bc ABS may have higher credit rating than seller's corporate bonds Securitization Structures (can have both): 1. Senior/Subordinate Structure (Credit Tranching): Ex) Non agency RMBS, CMBS ~ Subordinated Tranches: Takes on credit risk by absorbing all credit defaults/losses. High yields due to risk. ~ Senior Tranches: Paid 1st, low yield, High credit rating - Waterfall Structure: Tranches w/ differing priority of claims. In liquidation, each subordinated tranche receive only the "overflow" from senior tranches 2. Sequential Structure (Time Tranching): Investors choose level of prepayment risk bc tranches have different exposure to contraction & extension. Ex) CMO - 1st (Sequential) Tranche: Receives all principal payments & prepayments until paid off. - 2nd starts to get both payments, and so on

Explain: - Seniority ranking: - Highest & lowest ranks of unsecured debt: - Secured debt: Example? - Unsecured debt: Other name? - What has priority of claims, secured or unsecured debt? - Collateral trust bonds: - Equipment trust certificates: - Pari passu: - Priority of claims in bankruptcy:

Seniority Ranking: Different bonds from same issuer have different seniority/priority of claims: - Highest) First lien/Senior Secured: - 2nd) Second lien/Secured: Has collateral - 3rd) Senior Unsecured - 4th) Senior Subordinated - 5th) Subordinated - 6th) Junior Subordinated: Lowest priority - 7th) All debt has priority over preferred, which has priority over common Unsecured Debt/Bond (Debenture): Have claim to overall assets & CFs of issuer (no collateral). Never has priority over secured - Unsecured highest rank: Senior Unsecured Debt - Unsecured lowest rank: Junior Subordinated. Secured Debt/Bonds: All secured has priority over any unsecured. Claim to asset owned by issuer. Secured is backed by collateral. Ex) Mortgages, auto loans, trust bonds, lien Collateral Trust Bonds: Collateral/Asset backed such as stocks & bonds. Secured bond. Held by trustee. Equipment Trust Certificates: Physical assets sold to a trust & then leased back to firm. Secured bond. Pari Passu: All debt in same category have same priority of claims Priority of Claims: Not always strictly followed in bankruptcy bc creditors may negotiate different outcomes to limit delays & issuing firm bankruptcy costs or judge orders a different outcome.

What is & How do you calculate: - Annualized holding period rate of return: - FV of reinvested coupon payments at end of holding period: - Capital G/L from sale of asset at end of holding period: - Annual compound rate of return - Assuming all coupons are reinvested over holding period, an investor's investment horizon:

Sources of Returns from Fixed Income Investing: - Coupons, principal pmts & G/L if sold before maturity - Reinvestment of coupon pmts. If reinvested coupon interest return < YTM, your realized yield must be < YTM Realized rate of return = YTM, if held to maturity Assumed Reinvestment rate = YTM at coupon date Annualized HPR: Earned compound annual return from bond / investor's holding period Investment Horizon: The time an investor hold's a bond. Investor who sells bond prior to maturity, we assume, coupon reinvested rate of return = YTM, if YTM changes after purchase, but prior to 1st coupon date, To calculate: Horizon when coupons are reinvested: Part 1) Calculate FV of reinvested coupon payments at end of the holding period. Use Holding Yrs for N. Part 2) Calculate G/L from sale at end of holding perid - Step 1) Calculate PV for the remaining years left until the bond's matures. Use remaining years for N. - Step 2) G/L = (PV - Par Value) = If negative, capital loss (20 year bond, sold after 5 years, N=15, 15 years remain) - If YTM > Coupon = Discount - If YTM < Coupon = Premium Part 3) Calculate investor's X years horizon yield - Step 1) Calculate total CFs = FV Reinvested coupon pmts + G/L from sale = Answer #1 + #2 - Step 2) Calculate ending value realized yield Horizon yield = Annual compound rate of return: = [Step 1 total CFs answer / Par ]¹⸍ⁿ - 1 N = Years in holding period (years bond was held before it was sold) Interest portion of a bond's return= Sum of coupon payments + interest earned from reinvesting coupon payments over holding period

Explain: - Sovereign entities: - Municipal entities: - General obligation bonds: - Revenue bonds: - Municipal bond guarantee: - Yield for revenue bonds:

Sovereign Entities (National Gov't): Can print money & raise taxes to repay debt. Municipal Entities (Local Gov't): Can't print money. Tax free bonds. Low default vs corporate bonds. Issues municipal & nonsovereign bonds. Municipal Bond Guarantee: 3rd party guarantee from insurance provided. Improves bond credit rating which ↓yield. More liquid in secondary market. General Obligation Bonds: Municipal backed by local gov't taxing revenue power (not collateral) which depends on local economy & LT obligations (pensions, retirement benefits) - GOB: ↓Yield than Rev bonds, but ↑Yield than Municipal 3rd Party Guarantee bonds Revenue Bonds: Municipal security backed by specific project revenue (not taxes). ↑Yields bc of ↑Risk vs GBO

Term structure of yield volatility, Explain: - Term structure: - What drives short & long term rates: - Term structure of yield volatility relationship: - When does duration increase? - When does the yield volatility term structure slope downwards? - When could price volatility for a short term bond be higher than for a long term bond? Explain analytical duration vs empirical duration: - Flight to quality & its effects: - When to use empirical duration: - Difference b/w analytical & empirical duration in reference to risky bonds:

Term structure: At different maturities Short term rates: Driven by monetary policy. Monetary authorities control it (fed reserves, central banks, etc) Long term rates: Driven by expected inflation, economic growth, macro factors Term structure of yield volatility: Relationship b/w yield volatility & maturity - ST bonds w/ low Dur, but more yield volatility could have more price risk than LT bonds. - When a ST yield is more volatile than LT, yield volatility term structure slopes downward Analytical duration: Using calculations & Δs in benchmark yields for risky bonds assumes benchmark yields & spreads for risky bonds are uncorrelated. This is not always true (eg flight to quality) Flight to quality: Investors get nervous & sell risky assets to buy safe ones (treasury bonds). Effect: Spread increases from risky bonds sold (yield↑) & safe bonds are purchased (price↑ & yield↓). The benchmark yield curve comes down, but the spread also widens causing minimal ΔYTM. This reduces duration effect. For this, use empirical duration. Empirical Dur: Historical relationship b/w Δs in gov't benchmark yield & bond prices. Includes correlation b/w Δs in benchmark & spread Δs - Use when: Portfolio many bonds/issuers. Especially high yield bonds (have greatest widening spread to benchmark curve)

Explain: - Yield curve: - Spot yield curve: - Coupon bond yield curve: - Par yield curve value: Formula? - Forward yield curve: - Spot rate annual yield: Other names? - No arbitrage bond price: How do you calculate a bond's price using spot rates?

Yield Curve (Term Structure): Yields at different maturities, but same rate (currency, risk, liquidity, tax) Coupon Bond Yield Curve: Newly issued, actively traded & close to par bonds w/ coupons at various maturities. Converts Month maturity yields - Long maturities are based on linear interpolation Spot Yield Curve (Strip, Zero Curve): Bond is priced by discounting each pmt at the appropriate spot rate for its maturity. Bonds have same rates (currency, risk, liquidity, tax), but aren't actively traded. - Ex) Benchmark curve. Gov't zero coupons YTM Spot (Zero) Rate/Yield: Market rate for a single pmt received in the future. Discount rates (YTM) for (pure discount) zero coupons are spot rates Par Yield Curve Value: Uses spot yield curve to determine what each bond price must be for it to be priced at par. Values bonds at par, for each spot rate. Doesn't use YTM. Par Value = Pmt/(1+S₁) + Pmt/(1+S₂)² +...+(100+Pmt)/( 1+S)ⁿ Forward Yield Curve: Forward rates of same tenor at different future periods. Ex) 1 yr forward rates 1 yr & 2 yrs from now Forward Rate: Rate today for a loan made in the future. No Arbitrage Bond Price: Price, calculated using spot rates, bc if priced differently, there will be a profit opportunity from arbitrage among bonds. Calculating Bond Price Using Spot Rates: PV = [CP/(1+S₁)] + [CP/(1+S₂)²] +....+ [CPₙ+Par/(1+Sₙ)ⁿ] - Given Semiannual Spot Rate: 1) Rates are always given annual. So divide each spot rate by 2 = 6 month rate. 2) Num: 6 month coupon pmt. Den: (1 + each spot rate)ⁿ N = # of periods. For 1.5, N = 3. This spot rate is compounding for 3 periods

Explain: - Yield spreads: - RFR: Driven by? - Bond's spreads: Driven by? - Benchmark yield: Affected by? - G spread: Formula? - On the run bond yields: - Eurozone bonds: - Interpolated yields: Other name? - Zero volatility spread: Other name? - Disadvantage of G & I spreads? - Option adjusted spread (OAS): Formula? When is it callable vs putable? - Option value formula: Ex) 5 year corporate euro coupon bond as "mid swap + 80 bp: What's the mid swap & spread? What does spread represent?

Yield Spreads: Allows separation of changes in RFR, from changes in yield premiums for credit risk & liquidity RFR: Driven by macroeconomic factors Bond's Spreads: Driven by micro factors (quality, liquidity, taxes status, quality rating, etc) Benchmark Yield: Affected by macro factors G-Spread: Gov't spread to benchmark yield for same maturity (US, UK, Japan) = YTMcorporate − YTMgov't - On the Run Bond Yields: Most recently issued bonds. Actively trading. Great price information Interpolated Yields (I-Spread): Bps over the swap rate. Spread is relative to swap rates. Bonds usually denominated in euros. Ex) Eurozone bonds = YTMcorporate - Swap rate of same tenor G & I Spread Disadvantages: Only correct if yield curve is flat (same maturities), but curve is upward sloping (ie LT yields are higher than ST) Eurozone Bonds: Spread relative to swap rates. One party pays fixed & other pays floating rate. - Ex) 5yr corporate euro coupon at "mid swap + 80 bp" Mid swap: B/w bid & ask +80 bp: Spread shows credit risk diff b/w interbank lending (LIBOR) & the bond. Z-Spread (Static, Zero, Zero Volatility): Parallel to gov't spot rate. Adds equal amount to each gov't spot rate to discount bond's pmts to get market rate (actual price) - Risks: Credit, liquidity & options Option Adjusted Spread (OAS): Similar to Z-spread, but removes extra yield from embedded options, to compare to option free bonds. Credit & liquidity risk. - Option Value in bp = Z-spread - OAS - Option value > 0 for callables & < 0 for putables