Fixed Income Flashcards
trust deed / bond indenture
legal contract between the bond issuer (borrower) and bondholders (lenders)
Negative covenants
restricts the activities of the borrower to protect bondholders
e.g. negative pledge of collateral / restrictions on additional borrowings
Affirmative covenants
promises to bondholders
e.g. cross-default provisions - if issuer defaults on one loan - it defaults all round.
pari passu clause - bond repayments have same priority as issuer’s other senior debt issues.
domestic bonds
bonds issued and traded in same country
foreign bonds
bonds issued in a foreign country and traded on national bond market
e.g. Foreign bonds traded in China and denominated in Yuan (Panda bonds)
Eurobonds (global bonds)
bonds issued in one country’s currency and sold in a different country
A Eurobond is an international bond issued outside the jurisdiction of any one country and not denominated in the currency of the country where it is issued.
covered bonds
A covered bond is a package of loans that were issued by banks and then sold to a financial institution for resale.
- bankruptcy remote (but remain on b/s)
- dual recourse to asset pool and issuing company
∴ issuer must replace non-performing assets
- no credit tranching
- less risk, lower yields compared to ABS
External credit enhancements (additional insurance options for bondholders)
Bank guarantee - issued by bank
Surety bond - issued by insurance company
Letter of credit - issued by financial institution
Cash collateral account for issuer (emergency account)
Internal credit enhancements (built into the bond structure)
- Overcollateralization: collateral > amount borrowed
- Excess spread: yield on asset pool > yield of bonds
- Tranches: different priority of claims for different bond classes (waterfall structure)
Tax on income from US municipal bonds
None
Original issue discount (OID) bonds
coupon < market rate
- as the price increases towards par over the life of the bond this can create a tax liability as interest income.
fully amortizing loan
equal payments of principal and coupon each month e.g. a mortgage
sinking fund
some bonds are retired/redeemed early (some of principal paid off when bonds are redeemed bit by bit)
floating rate notes
Coupon rate based on a reference rate (e.g. LIBOR) +/- a fixed margin. Maximum rate (benefits issuer)
- Cap/maximum rate (benefits issuer paying the loan back)
- Floor/minimum rate (benefits bondholder)
IR ↑ bond value ↓
inverse floater
coupon rate = coupon - reference rate
IR ↑ coupon payments ↓
Step-up coupon
Coupon rate that increases according to a pre-defined schedule
Credit-linked coupon
Credit rating ↓ coupon rate ↑
Payment-in-kind
coupon paid by increasing principal owed
Deferred (split) coupon
delayed coupon payments by a certain period
Index-linked bonds
Coupon/principal changes based on index. These can be interest-indexed (relating to coupon) or capital-indexed (relating to principal). Indexed-annuity bonds are fully amortizing.
e.g. CPI, equity-linked notes, commodity-indexed bonds
Contingency provisions
actions the issuer/bondholder can take
Callable bonds
Bonds that the issuer may redeem before maturity at certain dates.
- make-whole provision: call price includes PV of future coupons
Putable bonds
Bondholder can sell bonds back to the issuer, typically for par value.
Convertible bonds
bondholder exchanging bonds for common stock according to conversion ratio
Warrants
Sometimes attached to bonds, but are separate to the bonds - give the bondholders the right to buy the stock at a specified price
Contingent Convertibles (co-cos)
converts the bonds automatically to common stock is if a particular event occurs
Characteristics of a a bond
- type of issuer
- credit quality
- original maturities
- coupon structure
- currency denomination
- geography
- indexing
- tax status
Structured overnight financing rate (SOFR)
based on the actual rates of repurchase (repo) transactions and reported daily by the Federal Reserve.
Issuing bonds in primary markets
- underwritten offering
- best efforts offering
- auction
- shelf registration
public offering / private placement
- Underwritten offering: entire bond issue is purchased from the issuing firm by the investment bank
- Best efforts offering: investment banks sell the bonds on a commission basis (do not commit to
purchase/underwrite the whole issue) - Auction e.g. govt bonds
- Shelf registration: a bond issue is registered with securities regulators in its aggregate value with a master prospectus (available only to qualified investors)
Issuing bonds in secondary markets
dealer / OTC
e.g. Tender offer: an issuer offers to repurchase some of its outstanding bonds at a specified price
Sovereign bonds
issued by national governments
Non-sovereign bonds
issued by states / provinces / cities
Quasi-govt. / agency bonds
issued by govt.-sponsored entities
e.g. Fannie Mae (US)
Supernational bonds
issued by multilateral agencies
Sovereign bonds are described as on-the-run when they:
are the most recent issue in a specific maturity.
Commercial paper (working capital, bridge financing)
- US Commercial Paper (maturities up to 270 days, sold on a discount interest basis, settles T+0)
- Eurocommercial Paper (maturities up to 364 days, sold on discount or add-on interest basis, settles T+2)
Rollover risk: risk that new paper cannot be issued to pay for maturing paper.
Term maturity structure (corporate bonds)
entire issue matures on same date
serial bond issue (corporate bonds)
multiple maturity dates
Medium-term notes (MTNs) (corp. bonds)
- issuer provides a range of maturities, bondholder specifies amount and maturity.
- continuous offering by issuer’s agent
medium-term notes typically have less liquidity than a regular bond issue from the same issuer. Medium-term notes can have any maturity and are sold through agents.
Structured financial instruments
Securities designed to change the risk profile of an underlying debt security, often by combining a debt security with a derivative.
e.g. credit-linked note, capital protected instruments, participation instruments, leveraged instruments
Credit-linked note (CLN)
a security with an embedded credit default swap permitting the issuer to shift specific credit risk to credit investors.
Lower redemption value if credit event occurs (e.g. credit rating downgrade or default on reference asset).
Capital protected instruments
Guaranteed minimum value at maturity and potential upside gain (which is based on return of another asset) - usually paired with a call option
Participation instruments
Payments based on underlying instrument, often a reference interest rate or equity index e.g. floating rate notes
Short-term funding for banks:
- Customer deposits
- Certificates for deposits (CDs)
- Central bank funds market
- Interbank funds
Repurchase agreements (Repos)
Source of short-term funding for bond dealers
- Sell bond to counterparty, and repurchase it for a higher price on the repo date.
1 day = overnight repo
> 1 day = term repo
reverse repo = dealer acts as lender and buys back bond
repo rate
% difference between sale price and repurchase price. Lower when delivery is required,
- credit quality of collateral (underlying bonds) ↑ repo rate ↓
- demand for security ↑ repo rate ↓
- term of repo ↑ repo rate ↑
repo-margin / ‘haircut’
% difference between sale price and value of bond. Lower when counterparty credit is better
- credit quality of collateral (underlying bonds) ↑ repo margin ↓
- demand for security ↑ repo margin↓
- term of repo ↑ repo margin ↑
interbank market
short-term borrowing and lending among banks of funds other than those on deposit at a central bank
central bank funds market
loans of reserves on deposit with a central bank
Typical bid-ask spread in liquid market
10 to 12 basis points
Settlement for corporate bond trades
T+2 or T+3
Yield-to-maturity (YTM)
The market discount rate appropriate for discounting a bond’s cash flows. If known, you can calculate the PV (price) of the bond.
Impact of higher yields on a bond’s market value
bond yields (discount rate) ↑ PV of bond payments ↓ market value of bond ↓
‘constant-yield price trajectory’
convergence to par value over the life of the bond
‘no-arbitrage price’
PV of bond calculated using spot rates (profit opportunity from arbitrage among bonds)
Matrix pricing
method of estimating the required YTM/PV of bonds that are currently not traded or infrequently traded
street convention
assumes payments are made on scheduled dates
true yield
uses actual payment dates, taking holidays and weekends into account
govt. equivalent yield
corp. bond yield restated based on actual/actual (used for calculating spread to benchmark govt. bond yield).
current yield
annual coupon / flat price
- ignores movement towards par value
- discount bond: current yield < YTM
- premium bond: current yield > YTM
flat price of a bond
full price - accrued interest
quoted price
simple yield
(annual coupon +/- amortisation of premium/discount) / flat price
- assumes straight-line amortisation of premium/discount
option-adjusted yield
- calculate value of call option and add to flat price (minus for put option)
- calculate YTM
more precise yield measure for callable bonds
Valuing floating rate notes
coupon = prev. reference rate +/- quoted margin
‘quoted margin’: the margin used to calculate the bond coupon payments (PMT)
‘required/discount margin’: the margin required to return the FRN to its par value (I/Y)
If the required margin > quoted margin (for a floating rate note)
The credit quality of the issue has decreased and the price on the reset date will be less than par value.
Yield curve
shows yields for bonds at different maturities
Spot rate yield curve
- YTM of government zero-coupon bonds
- Not actively traded across different maturities so yield curves are constructed using coupon bond yields (bootstrapping).
Coupon bond yield curve
- Semi-annual bonds issued for specific maturities (e.g. 1, 3 , 5 etc.)
Par yield curve
- Calculates the coupon payment for each bond maturity with the bond priced at par, using spot rates
Forward yield curve
- Forward rates are rates for loans to be made in the future. Typically, the forward curve would show the yields of 1-year securities for each future year (quoted semi-annually).
e. g. a two-year rate, issued one-year from now, is expressed as 1y2y.
3-period spot rate (S3)
= ( ( 1 + S1 ) ( 1 + 1y1y ) ( 1 + 2y1y ) )^1/3 - 1
yield spread
- Yield - RFR
- Difference between the yields of two different bonds
benchmark spread
yield spread relative to a benchmark bond
e.g. if a 5-year corporate bond has a yield of 6.25% and its benchmark, the 5-year Treasury note, has a yield of 3.50%, the corporate bond has a benchmark spread of 625 − 350 = 275 bps
G-spread
yield spread over a government bond
e.g an A-rated, 10yr corporate bond with an 8% yield, and a govt. bond with the same maturity has a yield of 6%, the spread would be 2%.
interpolated spreads / I-spreads
Yield spreads relative to swap rates
Z-spread / static spread
the amount added to each spot rate so that price = PV
Option-adjusted spread (OAS)
Z spread - option value
option value: cost to issuer in bps per year.
periodicity
number of bond payments per year
Bond Equivalent Yield (BEY)
(FV - PV) / PV * 365/d
Securitization
Where financial assets (e.g. mortgages, accounts receivable) are purchased by an entity that then issues securities supported by cash flows from those assets.
Benefits of securitization
- Reduces funding costs for firms that securitize financial assets.
- Increases liquidity for the financial assets.
- Offers investors exposure to new asset classes.
Time tranching (securitization structures)
Tranche 1 bonds receive all the principal repayments until paid off, then Tranche 2….. etc.
Credit tranching (securitization structures)
Tranches have different credit risks: Tranche C bear credit losses up to their par value, then Tranche B, then Tranche A (e.g. Tranche A more senior)
Weighted average maturity (WAM) (mortgage pass-through securities)
maturities weighted by outstanding principal of mortgages in pool
Weighted average coupon (WAC) (mortgage pass-through securities)
interest rates weighted by outstanding principal of mortgages in pool
Agency Residential mortgage-backed securities (RMBS)
issued by the Government National Mortgage Association (GNMA), Federal National Mortgage Association or the Federal Home Loan Mortgage Corporation.
- these are ‘mortgage pass-through securities’ - each security represents a claim on cash flows from the pool of mortgages. Mortgages are referred to as ‘securitized mortgages’.
Non-Agency RMBS
Credit enhancement provided either externally (e.g. corporate seller, bank letter, bond insurance) or internally (e.g. reserve funds, overcollateralization, senior/subordinated structure)
Nonrecourse mortgage loans
Lender has no claim against assets apart from property itself.
∴ If value of house falls, borrowers may voluntarily return property to lender.
Recourse mortgage loans
Lender has a claim against the borrower for the amount by which the sale of a repossessed collateral property falls short of the principal outstanding on the loan.
In a securitization, the issuer of asset-backed securities is best described as:
the seller.
ABS are issued by a special purpose entity (SPE), which is an entity created for that specific purpose. In a securitization, the firm that is securitizing financial assets is described as the seller because it sells the assets to the SPE. The servicer is the entity that deals with collections on the securitized assets. (LOS 42.b)
extension risk (MBS)
The risk that prepayments on mortgage backed securities will be slower than expected
i.e. the average life of the tranche increases more than than that of the PAC
Can be caused by IR ↑, prepayments ↓, life of MBS ↑
contraction risk (MBS)
The risk that prepayments on mortgage backed securities will be more rapid than expected.
- rapid prepayment reduce the amount of principal outstanding on the loans supporting the MBS so the total interest paid over the life of the MBS is reduced.
i. e. the average life of the tranche decreases more than than that of the PAC
Can be caused by IR ↓, prepayments ↑, life of MBS ↓
Collateralized Mortgage Obligations (CMOs)
created from pass-through mortgage-backed securities (MBS) (collateral) for investors with different risk needs (via different tranches / risk structures)
Single monthly mortality rate (SMM) (prepayment risk)
% by which prepayments reduce the principal balance, compared to no prepayments.
prepayment
a payment ahead of schedule
Conditional prepayment rate (CPR) (prepayment risk)
Annualised prepayment rate (based on WAC, interest rates and prior prepayments)
Commercial mortgage
Non-recourse loans, partially amortizing, balloon payment (balloon risk)
Debt service coverage ratio
NOI / debt service ( salary / mortgage payments )
LTV
mortgage (loan) / appraised value
Synthetic CDOs
exposure to underlying assets through credit default swaps as opposed to a cash market position (economic risk but no legal ownership of underlying positions).
Arbitrage CDOs
generate return on spread between collateral and funding costs
Default provisions for covered bonds:
- Hard-bullet covered bond: bond is default if issuer fails to make a scheduled payment
- Soft-bullet covered bond: issuer may postpone scheduled maturity for up to a year.
- Conditional pass-through: converts pass-through on maturity date if any payments remain due.
Balloon risk
risk of a commercial mortgage borrower not being able to refinance the principal that is due at maturity.
relationship between SPE and seller in securitzation
separate legal entities (so that the seller’s creditors do not have a claim against the securitized assets).
Call protection
prohibits the issuer from buying bond back for a specified period of time.
e.g. Commercial MBS typically have some type of call protection (restriction on prepayments), either in the structure of the MBS or at the loan level.
Public Securities Association (PSA)
Prepayment benchmark for MBS that assumes the monthly pre-payment rate increases with time. It consists of a monthly series of conditional prepayment rates (CPRs).
e.g. 50 PSA: prepayment speed is assumed to be 50% of PSA
PAC tranches (CMOs)
A type of structure that makes predictable payments, regardless of actual prepayments, to the underlying MBS. This is achieved by increasing the prepayment risk of support tranches.
How are CMBS mortgages structured
As nonrecourse loans (lender has no claim against assets apart from property itself)
∴ analysis of CMBS securities focuses on credit risk of the property not of the borrower,
Methods of establishing loan-level call protection
- Prepayment lockout: prohibits borrower from repaying loan for specified period of time.
- Defeasance: using early payments of principal to invest in govt. securities that ensure cash flows remain as planned.
- Prepayment penalty points: penalty fee expressed in points may be charged for early repayments of principal.
- Yield maintenance charges: borrower is charged the amount of interest lost by the lender for their prepayments.
Renegotiable (rollover) mortgages,
Hybrid mortgages &
Convertible mortgages
Renegotiable (rollover): mortgages with an initial fixed-rate interest, that can be amended to another fixed-rate.
Hybrid: mortgages with an initial fixed-rate that can be amended to have a variable rate.
Convertible: mortgages that can change between fixed/variable rates at the borrower’s option
‘Pass-through rate’ / ‘net-interest rate’
The interest rate on a securitized asset, net of fees
Three sources of returns from investing in a fixed-rate bond
- coupon/principal payments
- interest on coupon payments (that are reinvested)
- capital gains if bond is sold prior to maturity
For a fixed-rate bond that does not default and has a reinvestment rate equal to the YTM, what rate of return will an investor who holds the bond to maturity earn if purchased at a discount/premium?
A return equal to the YTM at purchase.
For an investor who sells a bond prior to maturity, what rate of return will the investor earn (if the YTM has not changed since purchase)?
A return equal to the YTM at purchase.
How are the impacts of non-parallel shifts in the yield curve measured?
Key rate duration (partial duration).
Key rate duration (partial duration)
the sensitivity of the value of the bond to changes in the spot rate for a specific maturity.
The sum of a bond’s key rate durations = effective duration
duration of a perpetuity
( 1 + YTM ) / YTM
effect of a higher coupon on interest rate risk?
C ↑ IR risk ↓
a higher coupon means that more of the bond’s value will be from coupon payments received sooner so value of bond will be less sensitive to yield changes.↓
effect of a higher YTM on interest rate risk?
YTM ↑ IR risk ↓
due to convexity of price-yield curve
effect of adding a call/put provision on a bond on interest rate risk?
IR risk ↓
Two ways of measuring duration of a portfolio?
- weighted average no. periods until cash flows are received.
- weighted no. of durations of the individual bonds in portfolio (more common)
Money duration of bond
annual modified duration * full price of bond position
money duration * Δ YTM = Δ bond value
Price value of a basis point (PVBP)
the money change in the full price of a bond when its YTM changes by 1bp.
initial price - price if YTM changed by 1bp
approximate convexity
assumes expected cash flows do not change when yield changes
effective convexity
Unlike approx. convexity, effective convexity considers changes in cash flows due to embedded options
duration gap
maximum duration - investment horizon
empirical duration
duration estimated from historical data
impact on PV following convexity adjustment (of modified duration)
always increases, despite the yield change
credit risk
risk of losses if the borrower fails to pay (broader than just default risk)
spread risk
risk of a spread widening
credit migration (downgrade risk)
issuer’s creditworthiness declines and bond ratings fall
default risk
probability of borrower defaulting
expected loss
default risk * loss severity (monetary value)
recovery rate
1 - loss severity (%)
corporate family rating (CFR)
issuer credit rating, applied to senior unsecured debt
corporate credit rating (CCR)
applies to specific debt issue (may be notched up or down from CFR)
Factors to consider when evaluating industry fundamentals
- cyclicality
- growth prospects
- published statistics
Factors to consider when evaluating company fundamentals
- competitive position
- operating history
- strategy and execution
- ratios
Factors to consider when evaluating collateral
- intangible assets
- depreciation
- equity market cap
- human and intellectual capital
Factors to consider when evaluating character (management’s commitment to repaying loan)
- soundness of strategy
- track record
- accounting policies and tax strategies
- fraud record
- prior treatment of bondholders
Five factors that impact yield spread
- credit cycle
- economic conditions
- broker-dealer capital
- market supply and demand
- issuer’s financial performance
Six sources of liquidity analysts look for:
- B/S cash
- working capital
- CFO
- bank credit
- issued equity
- sales of assets
Important covenants for HY debt
- Change of control put: forces the issuer to buyback debt in the event of an acquisition.
- Restricted payments: limits the amount of cash paid to equity holders.
- Limitations on liens: limits amount of secured debt the issuer can carry.
- Restricted subsidiaries: using a subsidiary’s cash flow and assets to service the parent company’s debt.
Enterprise value
Mkt cap + total debt - cash
Five key areas to look at when assessing sovereign debt:
- Institutional
- Economic
- External
- Fiscal
- Monetary
General obligation bonds
unsecured bonds backed by full faith credit of issuing govt. entity (e.g. their taxing power)
Revenue bonds
non-sovereign bonds issued to finance specific projects.
Market liquidity risk
risk of receiving less than market value when selling a bond and is reflected in the size of the bid-ask spreads
Factors to consider when estimating the credit risk of a bond
- bond rating
- recovery rate
bearer bonds
Bonds for which the trustee does not keep records of ownership.
In contrast, domestic and foreign bonds are typically registered bonds for which ownership is recorded by either name or serial number.
OTC
In over-the-counter (OTC) markets, buy and sell orders are initiated from various locations and then matched through a communications network.
Most bonds are traded in OTC markets
organized exchanges
buy and sell orders may come from anywhere, but the transactions must take place at the exchange according to the rules imposed by the exchange
open market operations
Central banks buy and sell bonds, usually sovereign bonds issued by the national government, as a means to implement monetary policy.
Wholesale funds
Sources of short-term financing for banks, include central bank funds, interbank funds, and negotiable certificates of deposit
bearer bonds
Most Eurobonds are bearer bonds, meaning that the trustee does not keep records of who owns the bonds; only the clearing system knows who the bond owners are.
dual-currency bond
coupon payments are denominated in one currency, and the par value is denominated in a different currency.
Equipment trust certificates
bonds secured by specific types of equipment or physical assets, such as shipping containers.
collateral trust bonds
secured by securities such as common shares, other bonds, or other financial assets.
Credit migration risk or downgrade risk
Risk that a bond issuer’s creditworthiness may deteriorate or migrate lower. The result is that investors view the risk of default to be higher, causing the spread on the issuer’s bonds to widen.
Market liquidity risk
Risk that the price at which investors transact may be different from the price indicated in the market.
Increased by (1) less debt outstanding and/or (2) a lower issue credit rating
If goodwill makes up a large percentage of a company’s total assets, this most likely indicates that:
a large percentage of the company’s assets are not of high quality.
Goodwill is viewed as a lower quality asset compared with tangible assets that can be sold and more easily converted into cash
In order to determine the capacity of a company, it would be most appropriate to analyze the:
The growth prospects of the industry provide the analyst insight regarding the capacity of the company.
EBITDA
Operating profit (EBIT) + Depreciation and amortization
The two components of credit risk are
default probability and loss severity.
loss severity
(1 – Recovery rate)
Loss severity is the portion of a bond’s value (including unpaid interest) an investor loses in the event of default.
Notching
Process for moving ratings up or down relative to the issuer rating when rating agencies consider secondary factors, such as priority of claims in the event of a default and the potential loss severity.
this is done, not on the probability of default of the issuer, but for secondary reasons such as:
- priority of payment in the event of default.
- potential severity of loss in the event of default.
Structural subordination
When a corporation with a holding company structure has debt at parent and operating subsidiaries.
Debt at the operating subsidiaries is serviced by the cash flow and assets of the subsidiaries before funds are passed to the parent holding company.
When determining the capacity of a borrower to service debt, a credit analyst should begin with an examination of:
Credit analysis starts with industry structure—for example, by looking at the major forces of competition, followed by an analysis of industry fundamentals—and then turns to examination of the specific issuer.
Convexity of a putable bond
positive
When interest rates rise, a putable bond is more likely to be sold back to the issuer by the investor, limiting the loss of value and giving the bond more positive convexity than an option-free bond.
Convexity of a callable bond
negative
a callable bond is likely to be called from the investor when interest rates fall, limiting the gain in value and giving the bond negative convexity.
Convexity of an option-free bond
positive but less positive convexity than a putable bond
