Fixed Income Flashcards
Macauly Duration (time)
weighted average of time until cash flows are received;
calc PV of each coupon and final principal+coupon, weight each payment to total payment, use weight to each payment times amount ot year, add together;
if ytm is constant, MacDur decrease between coupon payments
immunization=mac duration equals investment horizon;
MacDur<investment horizon, neg duration gap, reinvestment risk dominates;
MacDur>investment horizon, positive duration gap, price risk dominates
when ytm increase or decrease, bonds final ytm always equal to initial ytm if immunization; return is determined by the YTM because the market’s current pricing reflects the present value of all future cash flows, including the final redemption value at maturity
When the Macaulay duration of a bond matches the investment horizon, the bond’s Yield to Maturity (YTM) (which represents the total return if held until maturity) and its Yield to Market (YMT) (which is the yield earned when the bond is sold in the market) are equal. This is because, with matching duration and horizon, the interest rate risk (price risk due to interest rate changes) and the reinvestment risk (risk of reinvesting coupon payments at lower rates) are effectively hedged against each other.
price risk vs reinvestment risk of bond
short term, price risk dominates, increase ytm->return fall; long term, reinvestment risk dominates, increase ytm->return increase;
1. when ytm is constant, bond hold to to maturity, final ytm the same; 2. when ytm is constant, bond sold after short period, final ytm the same;
3. when ytm increase, bond hold to maturity, price is the same, reinvestment increase, final ytm increase;
4. when ytm increase, bond sold in short term, bond price decrease, reinvestment increase, price denominates and reinvestment do not have time to manifest, final ytm return decrease;
5. when ytm decrease, bond held to maturity, price is the same, reinvestment decrease, reinvestment risk denominates, final ytm decrease
return of bond calc
PV=(princiapl+interest+reinvestment int)/([(1+ytm)^n];
use remaining maturity to calc PV of principal use ytm, use happened maturity to calc coupon FV with PV at 0, add them together to calc final ytm
duration gap
positive duration gap=mac duration>investment horizon, price risk denominate, ytm increase cause return decrease;
negative duration gap=mac duration<investment horizon, ytm decrease cause reinvestment risk return decrease
Jane Walker has set a 7% yield as the goal for the bond portion of her portfolio. To achieve this goal, she has purchased a 7%, 15-year corporate bond at a discount price of 93.50. What amount of reinvestment income will she need to earn over this 15-year period to achieve a compound return of 7% on a semiannual basis?
935(1.035)30 = $2,624
Bond coupons: 30 × 35 = $1,050
Principal repayment: $1,000
2,624 − 1,000 − 1050 = $574 required reinvestment income
modified duration (%)
multiplier to expected changes in ytm used to measure chages in bond price;
1. mac duration/(1+initial ytm); semiannual: semi-MacDur/(1+(ytm/2)). ModDur=semi-ModDur/2;
2. change in price=-mod duration*change in 1bps yield, yield and price inverse relationship assume linear instead of convex relationship so always UNDERESTIMATE bond value;
3. higher the coupon, get large cash flow back earlier so lower duartion=price is less sensitive to interest rates change;
4. longer maturity, larger maculay duration, price is more sensitive to interest rate change (tangent line);
5. lower ytm=bond price more sensitive to interest rate change, #1 and as price/yield curve is steeper slope due to convexity, price change from ytm 4-3% is greater than 8-7%
when equity performance is poor, consumer fleed to bond markets which should have higher yield
approximate modified duration (%)
average change in price to a given change in yield [rise in bond price from a yield fall V- and fall in bond price from yield rise V+] in percentage;
approx ModDur=(V- - V+)/2V0*change in ytm; positive number
spot rate assumes ytm of zero coupon bond
money duration ($)
dollar duration of mod duration; money dur=-ModDurchange in ytmmarket value; market value=bond price/100*par value;
if yield change by x%, change in price=money duration*-change in yield
duration is more accurate for small yield changes
think about the curve, larger distance, more deviation from tangent to curve
price value of a basis point (PVBP)=dollar value of a basis point (DV01)=BPV=PV01
change in bond value if ytm change by 1 bps;
money duration*1bps;
shock price by +-1bps and take gap of bond price/2=change in price
zero coupon bond mac duration=
maturity
floating rate note
price more stable than zero coupon bond; at the next coupon payment date, the coupons will reset to MRR+quoted margin, and the FRN price will reset to par; at time 0, quoted margin (coupon)=discount margin (ytm); theres a lag rest, happens next period; QM>DM, premium; QM<DM, discount;
price/yield approaches
accuracy:
1. durations (smaller yield change);
2. duration+convexity (for larger yield change more accurate);
3. full reprice, most accurate
convexity1
measure of curvature of price/yield relationship, add convexity to duration (underestimate) improves accuracy of bond/yield relationships;
calc PV of each cash flow then times weight of each cash flow by convexity at per period t=[t*(t+1)]/(1+r)^2 and divide by periodicity of the bond squared;
convexity of coupon paying bond is weighted average convexity of its each cash flows
add on yield vs discount rate
add on yield (bond equivalent yield)/365days of maturity=holding period return, calc FV; discount yield calc PV=FV/PV-1; (1+HPY)PV=FV/PV-1
price/yield curve is more sensitive when yield fall, price increase from ytm 4-3% is greater than 8-7%
price falls at decrease rate (rise at increasing rate) as yield decrease
approximate convexity
(V- + V+ - 2V0)/[V0*(change in ytm^2)];
result is same as duration+convexity;
YTM squared to make positive
convexity2
like duration, longer duration, lower coupon, lower ytm increase convexity; if two bonds have same duration, one with cash flow more dispersed over time will have the greatest convexity cuz interest rate can change more often;
Convexity = how the duration of a bond changes as the interest rate changes. If a bond’s duration increases as yields increase, the bond is said to have negative convexity. If a bond’s duration rises and yields fall, the bond is said to have positive convexity.
duration + convexity adjustment to estimate bond price changes
(positive or negative ytm) change in price= -(ModDurchange in ytm)+(0.5convexity*change in ytm^2);
new bond price=bond price*(1+change in price)
money convexity
money value of bond’s convexity=annual convexityfull price of bond position; change in bond price=-(MoneyDurchange in ytm)+(0.5MoneyConchange in ytm^2); moneyx=xmarket value; market value=price/100par value
duration is linear
when price rise, duration is not rising enough, when price fall, duration falls too much (graph)
portfolio duration and convexity
- single calc of portfolio duration and convexity based on aggregate cash flow, theoretically correct but hard to use;
- weighted average of individual asset duration, assuming parallel shift in ytm: port duration=W1D1+W2D3+…WNDN
An estimate of the change in bond prices due to changes in yield will be either too low (from yield decreases) or too high (from yield increases). Both estimates are improved by making positive adjustments for convexity.
Price change estimates based on duration alone are improved by positive convexity adjustments for both increases and decreases in yield.
negative and positive convexity
positive: normal curve=price or duration increase more when yield decreases; negative=inverted=price decrease more when yield increase
the issuer of a callable bond has an incentive to call the bond when interest rates are very low in order to get cheaper financing, this puts an upper limit on the bond price for low interest rates and thus introduces negative convexity between yields and prices.
key rate duration (for nonparallel change in yield)
(partial durations)key rate duration for each term=modified durationweight in the portfolio; change in price=-KRDchange in yield;
sum of partial key rate duration=effective duration=portfolio duration;
steepening (LT rising, ST fall), flattening, +butterfuly (MT fall, ST LT rise), -butterfly; long term change have most impact on duration; sensitivity of value of portfolio to change in the benchmark yield of a specific maturity;
shaping risk=effect of nonparallel shift in the yield curve;
KRD measure effect of nonparalell shift in yield curve
effective duration (for embedded option bond)
measure of interest rate sensitivity for option bonds; curve-based statistic;
effective duration=(V- - V+)/2V0*change in curve;
approx ModDur=(V- - V+)/2Vo*change in yield;
e.g.mortgage-backed bonds have a price-yield relationship similar to that of callable bonds
callable and puttable bonds have contingent cash flows
cuz uncertain if will be excercised and uncertain maturity
putable bond
investor have the right to sell to issuer; floor price; more valuable at higher yield as put protection; more positive convexity and valuable than straight bond: 2nd half of the curve, price is more of a rise, less of a fall due to floor
callable bond
issuer right to call (short call for investor); higher yield; investor enter callable if expect yield to be stable to capture the higher yield; if interest rate fall, issuer will call and reissue at lower int rate; if yield fall, callable bond price wont rise above call price=negative convexity
effective convexity
(V- + V+ - 2V0)/(change in curve^2*V0)
callable bond negative convexity at lower yield cuz call price ceiling, lower duration than straight bond cuz option.
puttable bond even greater positive convexity when price floored at higher yield, lower duration than straight;
approximate convexity (always positive cuz duration):
(V- + V+ - 2V0)/(change in yield^2*V0)
straight bonds are yield-based risk measures and embedded option bonds are curve-based duration risk measure
expected price change of option bond=effective duration+effective convexity adjustment
change in price=-(EffDurchange in cruve)+(0.5EffCon*change in curve^2)
straight bond’s modified duration and effective duration are different
small differences due to change in curve compared to change in ytm
analytical vs empirical duration
based on math vs based on historical relationship; empirical for risky bonds, cuz the lower the quality of bond, less accurate the model is so use empirical;
A risky bond yield and credit spread move in different directions because while a wider credit spread indicates increased risk and therefore a higher yield on a risky bond, the overall market interest rate environment can also influence the yield, causing them to sometimes move in opposite directions;
flight to quality: benchmark yield fall and credit spread rise, use empirical
A bond portfolio manager who wants to estimate the sensitivity of the portfolio’s value to changes in the 5-year yield only should use a(n):
Key rate duration refers to the sensitivity of a bond or portfolio value to a change in one specific maturity yield.
Embedded options decrease the duration of the bond relative to an equivalent option-free bond when the option has significant value.
because the issuer may choose to redeem the bond early if interest rates fall, effectively shortening the bond’s life and reducing its duration.
when an embedded option has an immaterial value, it essentially has no impact on the bond’s price behavior, meaning the duration of the option-embedded bond would be very close to that of an equivalent option-free bond, not necessarily lower.
effective annual return
(1+ytm/N)^(1/N)-1
interest rate risk
longer maturity, lower coupon rate, lower ytm cuz curvature
perpetual bond MacDur
(1+r)/r
credit risk & top-down vs bottom-up factors
loss from default of borrower failed to pay;
bottom-up factor:
-capacity=ability to pay -characteristic=willingness to pay -capital available to reduce debt - collateral -covenant;
top-down factor:
economic condition, country geopolitical environment, currency
sources of repayment
secured corporate issues backed by operating cash flows and issuer investments and cash flow from collateral;
unsecured corporate issues backed by operating cash flows and issuer investments;
secondary sources sell assets, subsidiary divestiture, issue more debt or equity
sovereign debt
backed by government cash flows tax, tariff;
secondary cash flow: debt issuance, privatization;
risk: recession, political uncertainty, fiscal deficit (limited gov spending), debt;
servicing debt=pay back debt by tax;
good if provide stable economic growth and low inflation;
sovereign creditworthiness
insolvency
L>A; illiquidity=not enough cash to meet obligations but still run daily; technically solvent still default
pari passu clauses
all bonds of a specific rank all equally default
cross default clause
any default on 1 bond causes default on all, protect investors
probability of default (PoD)
probability that borrower fail to pay interest or princiapl, annualized;
IG vs HY,
deteriorating financial strength increase PoD not LGD
loss given default (LGD)
loss if default occurs, dollar value or %;
depends on secured or unsecured, seniority
recovery rate
1-LGD
expected loss (%) [average loss]
PoD*LGD;
~inferred credit spread (market data observed)
credit spread
actual credit spread=corp bond yield-gov bond yield;
inferred credit spread=PoD*LGD;
if actual>inferred, credit spread of the bond adequately compensate investor for credit risk
credit rating
forward-looking to issuer and the debt based on quantitative and qualitative credit risk factors; could be lagged, hard to assess
transitioning risk=rating migrating, downgrading
high yield bond are equity-like; IG bond-like
credit spread risk
risk credit spread widen and bond price fall from macroeconomic (contraction), issuer-specific (litigation), market trading factors(2008);
default risk for HY, credit spread risk for IG
credit cycle moves in line with economic cycle
expansions: short term credit curves fall and steepen as PoD falls;
contractions: short term rise and flatten, may invert;
HY spreads are more sensitive to economic changes and wider disperson of yield spreads across issuers;
flight to quality=sell risky asset and buy safer, bid-ask spread widen more for HY than IG; wider spread less liquid
servicing the debt
issuer having trouble repaying the debt have higher yield to compensate higher risk
market liquidity risk
transaction cost of trading a bond;
bid-ask spread=wider, higher cost, less liquid;
larger issuers=more debt oustanding so have more actively trading bonds;
higher credit quality=more actively traded;
market stress and crisis=flight to quality, wider bid-ask spread
bid-ask spread
ask=bank asks for this price; bid=bank buy at this price
liquidity spread calc
- midprice quote=(bid+ask)/2, use this to find yield spread [yield spread=corp yield-govy yield];
- liquidity spread=plug in bid price and offer price in TVOM and calc the 2 ytm, difference is liquidity spread;
- true credit spread=yield spread-liquidity spread
higher debt/EBITDA ratio is sign of higher leverage
Conditions that cause equity markets to weaken, such as poor economic growth, also tend to widen yield spreads in the bond market. Likewise, strong equity market performance tends to coincide with tightening yield spreads.
Credit risk is calculated with the probability of default (estimated from the bond rating) and the estimated recovery value should the bond default. Yield volatility is combined with duration to estimate the price risk of a bond.
Analyzing a corporate borrower’s capacity (ability, evaluation of industry structure, industry fundamentals, and company fundamentals) to repay its debt obligations is similar to the top-down process used in equity analysis. Collateral analysis is evaluating the issuer’s assets. Analyzing covenants involves reviewing the terms and conditions of lending agreements.
Credit spreads tend to narrow in times of high demand for bonds (more liquid, compete to give higher yield) and widen in times of low demand for bonds
Credit spreads tend to widen under excess supply conditions, such as large issuance in a short period of time, and narrow when supply is low
During periods of economic expansion corporate yield spreads generally narrow, reflecting decreased credit risk. If yield spreads narrow, the prices of corporate bonds increase relative to the prices of Treasuries.
Purchase corporate bonds and sell Treasury bonds.
Selling lower-rated bonds and buying higher-rated bonds is an appropriate strategy if an economic contraction is anticipated.
sovereign creditworthiness
qualitative:
1. institutions and policy factors=economic stability and ability/willingness to pay (capacity/character);
2. fiscal flexibility factors=able to increase tax, cut spending;
3. monetary effectiveness factor=ability of central bank to vary money supply and interest rates (independence and credibility of central bank);
4. economic flexibility factors=diversity of economic growth;
5. external status factors=status of currency in international markets;
quantitative:
1. fiscal strength=low debt ratios;
2. economic growth and stability=gdp growth, large economy size;
3. external stability=high forex reserve level to GDP and external debt
nonsovereign government debt issuer
agencies=quasi-gov entities, backed by law with imiplicit gov support for specific role, similar rating to govy; ginnie mac;
government sector banks=issue bond for specific projects, similar rating to govy;
supranational issuers=collab of world banks to alleviate poverty and encourage growth; rating depend on gov support
regional governments (state, local, munis)=general obligation bond unsecured bonds, safer, backed by taxing from different sources; revenue bond backed by financing specifit source project like tolls, only the fund from project is used to service debt, higher credit risk
Debt affordability ratios compare interest payments to GDP or revenue. When these ratios are high, this suggests lower credit quality on a fiscal strength basis.
municipal bond guarantee is a form of insurance provided by a third party other than the issuer
corporate issuer evaluation
qualitative: business models changed lead to business risk, competiton in long term, deviation in revenue, covenant (para passu, asses past actions of issuer to holdders), accounting policies (aggressive vs conservative);
quantitative: financial stmts, cash flows, LGD, PoD, top down bottom up;
financial ratios in credit analysis
- EBITDA (not adjusted for capex or working capital and some not available to debt holders);
- CFO=net cash in operations, CFO=NI+non cash charges-change in working capital;
- FFO=funds from operations=NI from operation+ D+A+deferred tax+noncash charges, similar to CFO but excludes changes in working capital;
- free cash flow to firm (FCFF)=CFO-capex+net interest expensex (1-tax rate) , discretionary cash flow of the firm (BOTH DEBT and equity holder, add int exp back because it will be paid to debt holders) after all obligations met;
- retained cash flow (RCF)=operating cash flow-dividends
free cash flow to equity (FCFE)
Cash from Operations - Capital Expenditures + Net Borrowing;
Net borrowing for FCFE means Proceeds from borrowing minus repayments. Therefore the cash we get could be used for further investing in business which will increase growth rate of business and value for equity shareholders. Also, it could be used for share repurchase or dividends for equity shareholders. Therefore purpose for FCFE is free cash available for equity shareholders.
coverage (credit quality assessment ratios)
EBIT/int expense
leverage (credit quality assessment ratios)
- debt/EBITDA (low);
- RCF/(debt-cash&marketable securities) [net debt] (high)
profitability (credit quality assessment ratios)
EBIT/revenue
secured vs unsecured debt prioirty of claims
secured: backed by collateral claim by seniority;
unsecured: general claim divided by senior junior and subordinated
credit rating agencies
rate both issuer and its debt;
corporate family ratings (CFRs)=issuer rating based on unsecured debt;
corporate credit ratings (CCRs)=specific bond issue ratings [seniority, covenants, collateral];
notching=ratings differ
structural subordination
a structure where both parent and subsidary have outstanding debt;
subsidary’s debt covenant=make sure subsidary’s debt is serviced before goes to parent (priorty claim to itself)
securitization process
- bank originates the loans (ABS like auto loans, credits cards…);
- bank pool loans and sold to SPV, bank make cash from illiquid loan with lower cost and less leverage and make more loans and no long have this on b/s so lower regulatory capital;
- SPV (bankruptcy remote from bank) issue fixed income securities to investors supported by cash flow from collateral which is the loan pooled; investor can tailor risk and return, have access to certain pool and its liquidity
senior (fixed pmt)->mezzanine (fixed pmt)->equity tranche;
investor should also look at underlyings credit rating;
purchase agreement=describe the collateral sold to SPV;
prospectus=terms of securitization like fee to service (collector of pmts from borrowers) and cash flow to investors;
trustee=appointed to safekeep collateral and provide info to securitization investors disinterested and bankruptcy remote
covered bond
debt securities issued by a bank or mortgage institution and collateralised against a pool of assets that, in case of default, issuer can replace any loans to meet promised payments flexible. similar to ABS;
on balance sheet so same RWA, no SPV; covered bond assets are segregated from other other assets of the issuer in a covered pool;
dual recourse=if default, investor have claims on both cover pool and wider other issuer assets so yield lowered than abs;
mortgage loan-to-value limit=upper LTV limit, increase the collateral in case default;
80% Loan-to-Value (LTV) ratio means the mortgage amount you’re borrowing is equal to 80% of the property’s appraised value; lower yield cuz prime
overcollateralization=value of collateral usually higher than needed, lower yield
covered bond provisions
hard-bullet covered bond=default if issuer fail to pay ANY payment, leading to acceleration of payment to ALL covered bondholders;
soft-bullet covered bond=postponed payment meaning postponed default, postponed accelerated payment;
conditional pass-through covered bond=covered bond converts to pass-through (pmts from borrowers are pass through to investor) bond at maturity if any payments remain due
ABS credit enhancement structures (abs usully nonmortgage)
off balance sheet so no recourse; overcollateralization; excress spread going into reserve to earn a higher coupon, not paid out to investor unless default; tranching;
can be amortized or nonamortized;
any stream of cash flow
credit card abs
backed by credit card; cash flow are pmts of interest, principal, memberships and late payment fees; nonamortizing, borrower can pay principal at their discretion;
lockoutperiod(revolvoing period)= a period where investors only receive interest and fees paid to collateral, principal payments by credit card borrowers are used to purchase additional credit card debt, rather than paid out to the ABS holders on principal.
solar abs
backed by homeowners loans to finance solar energy systems to lower energy bill;
ESG; secured (homeowner’s property) or unsecured loans; good credit scores; internal credit enhancement-overcollateralization, excess spread
collateralized debt obligations (CDOs)
structured securities issued by SPV where collateral is pool of debts; HAVE collateral manager actively buy and sell in the pool to generate cash
collateralized bond obligations (CBO) backed by corporate and emerging markets debt;
collateralized loan obligation (CLO) backed by portfolio of leveraged bank loans, NIG loans;
recourse limited to collatereral pool
CDOs
cash flow (own loan), market value=cash flow to investor generated from trading market value of unerlying collateral (own loan), synthetic CDO (dont own loan);
synthetic CDO=SPV use credit derivatives (CDS) to recreate certain exposures without the need for underlying cash flow, no need pool.
credit default swap
synthetic CDO is a credit insurer sell credit insurance on someone else’s pool; and the CDS premiums flow down the tranches in CDO; losses goes to investors
Unsecured loans tend to charge higher interest rates than secured ones because the lender is taking a greater risk.
first lien->senior secured debt (2nd lien)->junior secured->senior unsecured debt (corp family rating to rate the issuer)->sub debt
bottoms up issuer evaluation 5C
capacity=ability to pay (generate cash day to day); capital=what other ways to finance (securities); collateral; covenants=terms; character=willingness to pay
top down issuer evaluation
conditions; country; currency
expected exposure (exposure at default)
amount investor is owed-value of collateral available
LGD%=
expected exposure*(1-recovery rate); or expected loss/PoD;
estimated spread=PoD*LGD% (same as expected loss)
illiquid vs insolvent
no cash to pay debt vs debt>A
IG vs HY
BBB- vs BB+; Baa3 vs Ba1
credit ratings are not predictions cuz lagged
not capture market pricing
distressed bond price
market price of credit risk for distressed bond is focused on default timing and expected recovery rates;
not for IG cuz it wont default
change in price of bond
-annual modified durationchange in spread+0.5annual convexity*change in spread^2;
yield increase, spread increase, price decrease
covered bond is not the same as a Collateralized Debt Obligation (CDO), although both are debt instruments backed by assets. Covered bonds are secured by a pool of assets that remain on the issuer’s balance sheet, while CDOs involve the securitization of assets into a special purpose vehicle
Time tranching
redistributes prepayment risk among different classes of ABS holders. dividing the cash flows of a pool of assets (like mortgages) into different tranches based on their maturity, creating bonds with varying average lives and durations to manage prepayment risk;
short maturity, prepayment risk, higher contraction risk=IR fall so investor repay faster, reinvesment risk (must reinvest the proceeds from maturing securities);
longer maturity, extension risk=IR increase so investor repay slower
structured finance CDO the collateral is a pool of mortgage-backed securities, asset-backed securities, or other CDOs. In a synthetic CDO the collateral is a pool of credit default swaps. In a CLO the collateral is a pool of leveraged bank loans.
Credit card ABS typically have a lockout period during which principal payments by credit card borrowers are used to purchase additional credit card debt, rather than paid out to the ABS holders.
CMBS riskier than RMBS
residential is more diversified, commercial is huge amount of loan issued to less firms;
RMBS lender has legal claim to collateral, they can take possesson of the property or foreclosure (sell); prepayment penalty; recourse or non recourse
prepayment risk (driven by int rate)
borrower prepay early;
contraction risk, interest rate fall, borrowers refinance the loans, payments increase, pool contracts, weighted average maturity of contract decrease; investor have reinvestment risk=forces investors to reinvest the repaid funds at potentially lower rates;
extension risk, interest rate increase, pmt slows, pool extent
LTV and DTI (debt-to-income ratio)
% of collateral value loaned to borrowed, default measure;
lower LTV, higher borrower’s equity in the property and lower risk for lender;
DTI ratio=monthly debt payments (calc in months);
prime loans have low LTV and DTI
MBS
borrower’s right to prepay early=prepayment risk which is like a long call;
MBS investor have no control of prepayment speed, short call=higher yield
underwater mortgage
negative equity if outstanding loan balance exceeds the property’s market value;
recourse (give out other assets) or nonrecourse
agency vs nonagency RMBS
agency guaranteed by the governemnt or a government-sponsored enterprise (GSE ginnie mae), have high minimum underwriting standard to qualify as collateral (prime loans), prepayment risk-only;
nonagency issued by private entities (banks), credit enhancements through external insurance, letters of credit, tranching, private guarantees (prime and subprime), prepayment and credit risk
CMO (collateralized mortgage obligation)
senior tranche dont have extentions risk (int rate rise, prepayment slowed) but contraction risk (reinvestment risk); mezzenine tranche dont have contraction risk, but extention risk;
z-tranches (accrual bonds)=dont receive interest payments during an accrual period so interest accures as extra principal payment;
sequential pay=tranches principal sequentially paid off, shortest tranche=top tranche paid first;
STRIP:
principal-only securities=interest rate fall, sooner the principal is paid, higher the annualized return, price increase (positive duaration, int rate increase, price fall)
interest-only securities=interest rate increase, no incentive to pay earlier, prepayment slowed, principal repay slower, reduce prepayment speed, higher annualized return of investors (negative duration, interest rate increase, price increase;
floating-rate tranche=coupon MRR+quoted margin or inverse floater;
residual tranche=like equity tranche in abs;
planned amortization class (PAC) tranche=have a support tranche to receive prepayments to protect senior tranches from extension and contraction risk; The support tranches are exposed to high levels of prepayment risk, not credit risk.
mortgage pass through security
investor have claim on cash flow from a pool of mortages, net of admin fee;
weighed average maturity (maturity weighted on each current balance), weighted average coupon=WA of loan interest rate in the pool
CMBS
focus on credit risk of property, not borrower; nonrecourse
debt service coverage (DSCR)=net operating income/debt service; cash flow coverage ratio, shows ability to service the loan;
LTV
call protection for CMO issuer
call protection=payment protection of principal:
prepayment lockout=borrower cant repay the loan within a specific time;
prepayment penalty points=penalty fee charged if prepay principal;
defeasance=borrower buy government securities sufficient to make the scheduled loan prepayments so allow borrower to remove lender’s lien if property is sold and lenders get their money back from govy
Commercial MBS typically have some type of call protection (restriction on prepayments), either in the structure of the MBS or at the loan level. Both agency RMBS and non-agency RMBS typically have no restrictions on prepayments and are subject to prepayment risk.
CMBS nonrecourse have prepayment protection, RMBS subject to prepayment risk
balloon risk
commercial mortages not fully amortized;
workout period=lender extend or modify mortgage term, create extension risk for CMBS investor
benefits to originating banks for securitization
increased business activity, profitability, lower capi reserve, better liquidity
external credit enhancement
bank guarantee issued by bank; surety bond by insurance firm; letter of credit by financial institutions; cash collateral account=borrower borrow money and invest that cash to generate revenue, that revenue could be used as collateral
only RMBS, underwater mortgage and covered bond are dual recourse
Nonconforming mortgages=do not meet the requirements to be agency RMBS e.g. government-sponsored enterprises. Private companies may securitize nonconforming mortgages
lower coupon, longer maturity->highest duration->price change the most
if no-arbitrage price of the 3-year coupon bond based on spot (zero-coupon) rates=price of a coupon paying bond, its at par
interest rates are always quoted on an annualized basis
Loss severity
money amount or percentage of a bond’s value a bondholder will lose if the issuer defaults=LGD
Aggregate indexes contain a broad selection of bonds across sectors and currencies
Because sovereign governments are the largest issuers of bonds, they typically have the largest weight in broad bond indexes.
balloon is that big last lump sum payment that is paid at the end in this question. But your only looking at one point in time! You have to consider what has been happening over the last 10 years. We have paid 9 x 1.3m =11.7m over the last 9, which is more than we borrowed. How can this happen? It’s because we were paying some principal AND interest through the course of the bond. And that act of paying both P + I In a single payment is the characteristic of amortization.
Bonds denominated in the currency of the country or region where they are issued are domestic bonds. Eurobonds are denominated in a currency other than those of the countries in which they are sold.
Accrued interest for corporate bonds is typically calculated using the 30/360 method. For government bonds, accrued interest is typically calculated using the actual/actual method. 365
G-spreads and I-spreads are only correct when the spot yield curve is flat (yields are about the same across maturities).
renote g, i, z spread!!!!
The call feature does not make a bond more sensitive to changes in interest rates, because it places a ceiling on the maximum price investors will be willing to pay. If interest rates decrease enough the bonds will be called.
calc TIPS coupon payment: principalsemi annual inflationsemiannual coupon rate
Percent price change = convexity-3.49 × (-0.005) × 100 = 1.74%
96.25 bid and 96.75 ask=0.5%=50bps relatively illiquid.
Bonds with liquid secondary markets typically have bid-ask spreads of approximately 10 to 12 basis points.
Bond ratings are forward looking, event risk is difficult for ratings firms to estimate.
yield spreads
G-spread=yield spread over government bond;
I-spreads=yield spread over MRRs used in interest rate swap;
Zero-volatility spread (z-spread)=spread added to each spot rate on the Treasury yield curve, makes the present value of a bond’s cash flows equal to its market price,trial and error, with option spread included in spread;
option-adjusted spread (OAS)=zspread if were option free;
value of an embedded option = z-spread – OAS; call positive;
accrued interest; flat price (clean price); full price
accrued interest = interest owed to the seller for buying in the interim period; (coupon payment*days from last coupon to settlement)/days in coupon period;
flat price=quoted price without accrued interest because including accrued interest would make a bond’s price appear to increase on each day of a coupon period and drop suddenly on the coupon payment date;
full price (PV) = flat price + accrued interest; full price = PV on last coupon date ×
(1+YTM/periods per year)^(days since last coupon/days in coupon period)
actual/actual convention government bond; 30/360 convention corporate bond
single payment discount (zero coupon) bond will have a YTM that can be interpreted as a spot rate
bank lines of credit (3 types)
Uncommitted line of credit=bank offer credit (MRR+fixed spread) but can refuse to lend if circumstances change (uncommitted), less reliable, no other fees than interest, can be unsecured if borrower in stable;
Committed (regular) line of credit=bank commits to an credit for a time period, more reliable, charge a commitment fee, bank need to hold reserves, can be syndicated, renewal risk if borrower unstable;
Revolving (operating) line of credit=more reliable than committed, longer term, restrictive covenants on borrowers, fees similar to committed LOC
commercial paper (CP)
short-term unsecured debt securities, interest cost less than bank loan. maturity<3months, ofter rollover (rollover risk) so borrowers have backup lines of credit aka liquidity enhancements, fund working capital, temporary source of funding before issuing long term debt; debt that is temporary until permanent funding is sorted=bridge financing;
central bank funds rate
Banks with excess reserves lend them to banks that need funds
asset-backed commercial paper (ABCP)
a type of short-term ABS; SPE sells ABCP to investors, who accept the risk and return of the collateral backing the ABCP
repo
one sells a security to another and buy it back later at a prespecified price;
loan by the security buyer to the security seller, with the security as collateral.
difference between the repurchase price and original purchase price=interest paid to the security buyer;
initial margin=protect the lender against decrease in the collateral value, meaning loan amount is discounted;
purchase price (loan amount) = market value of securities/initial margin;
haircut=(security market value-purchase amount)/security market value=1-1/initial margin;
purchase price=purchase price (loan amount)(1+de-annualized repo rate);
adjusted repayment amount=purchase price(1+de-annualized repo rate(days past/360));
variation margin=adjusted repayment amountinitial margin-security new price;
new repo price-repo price=variation margin;
variation margin negative, overcollateralized, request a release of collateral;
1 day repo=overnight repo; long term=term repo;
cuz repo is short term and high quality collateral, interst rates are less than bank loans;
repo rate higher when, underlying is low quality (buy back at higher rate), interest rate of alternate sources increase, longer term repo, undercollateralized;
bilateral repo vs tri-party repo=custodian or clearing house
high yield bonds are equity like, IG are bond like
discount bond tax=amortized and pay tax every year as interest
Commercial paper rollover = issuing new commercial paper to repay maturing commercial paper, essentially extending the life of the debt
discount rate= [(FV-PV)/ FV] * (360/t)
add on rate= [(FV-PV)/ PV] * (360/t)
EAR=(1+semiannual/2)^2
semi annual mod duration=mac du/(1+semi-annual YTM/2)
longer duration=more sensitive to IR
convexity is always positive
0.25 rescale to 25v if duration is 4
expected loss=PDLGD=~credit spread
loss severity=1-recovery rate
expected exposure=amount investor is owed-value of collateral
LGD=expected exposure(1-recovery rate)
credit ratings are lagged
debt coverage: ebit/interest expense; debt affordability=lower the better;
debt-service coverage ratio=income, mortage pmt higher the better
covered bond lower credit risk than ABS cuz dual recourse, dynamic cover pool
planned amortization class (PAC) tranche is a type of asset-backed security (ABS) that aims to provide a more predictable cash flow to investors by protecting against prepayment risk. It achieves this by create a fixed payment schedule over a set period;
support tranche=absorbs changes in prepayment rates to stabilize the principal payments to other tranches,
A Z-tranche is the lowest-ranked tranche in a structured financial product, often a collateralized mortgage obligation (CMO), and it receives payments only after all other, more senior tranches are retired.
balloon payment=not fully amortizied, some principal remain in the end;
bullet payment=all principal at the end
key rate duration for each term=modified durationweight in the portfolio; change in price=-KRDchange in yield;
sum of partial key rate duration=EFFECTIVE duration=portfolio duration;
retained cash flow=CFO-dividend; net debt=debt-cash-marketable securities; RCF to debt ratio
quoted price is flat price
putable bond, OAS is greater than z spread
pass-through securities generally receive principal prepayments pro rata. This means that when homeowners pay off their mortgages early (prepayment), the resulting principal payment is distributed to the investors in the security proportionally to their o
- single calc of portfolio duration and convexity based on aggregate cash flow, theoretically correct but hard to use;
- weighted average of individual asset duration, assuming parallel shift in ytm: port duration=W1D1+W2D3+…WNDN
commercial paper is interim financing for LT projects called bridge loans
Call protection on a mortgage is a feature that restricts the lender from calling, or demanding repayment of, the mortgage before a specified period
reduce prepayment risk
all non-competitive bids are accepted; competitive bids are ranked starting at lowest yield (highest bond price); individuals, deals and institutional investors can all bid; competitive bidders who bid higher than stop yield (lower price) do not purchase any securities where all securities are sold for a single price using a stop yield
Competitive Bidders:
They bid a specific rate, yield, or discount margin, and the Treasury accepts bids from lowest to highest until the entire amount is sold. The highest accepted bid determines the “stop-out” rate.
Noncompetitive Bidders:
They agree to accept the rate, yield, or discount margin determined by the competitive bids. They are guaranteed to receive the securities they bid for, at the stop-out yield.
In essence, the stop-out yield is the price ceiling for all successful bidders, regardless of whether they were competitive or noncompetitive.
IG debt have few embedded options
soveriegn (once issued) and private debt mostly trade on OTC
original issue discount (OID) is the difference between the original face value amount and the discounted price paid for a bond which is seen as interest income rather than capital gainsoriginal
original discount tax provision=bond price movements in a constant yield are income rather than capital gains
cross-default and pari passu are affirmative covenants because they are actions the borrower must actively perform or ensure; incurrence test is negative covenants= not continuously monitored. They only become relevant when the borrower takes a specific action that triggers the test, such as incurring new debt, paying dividends, or making an acquisition to calc financial ratio, because it restricts a borrower from taking certain actions, specifically incurring new debt or engaging in other capital events, unless they meet a specified financial test.
increase in bonds ytm reduce PV of cash flow cuz discount at higher rate hence reduce PV weighted average of time to reiceit and reduce bond’s duration
all senior unsecured bonds are treated as one class and rank pari passu regardless of maturity so both isser and issue credit ratings are same
if the reinvestment rate decrease after bond is purchased, bond held to maturity will earn realized return less than ytm when purchased
Reinvestment risk is the risk that the coupon payments received from a bond will have to be reinvested at a lower rate than the original YTM, if interest rates have fallen since the bond was purchased.
The realized return is the actual return an investor receives, taking into account the actual reinvestment rate for the coupon payments and the final price of the bond at maturity.
Imagine a bond purchased with a YTM of 5%. If the coupon payments are reinvested at a 4% rate due to lower interest rates, the realized return will be lower than the initial 5% YTM.
Domestic bonds are issued by a domestic entity in its home market and currency, subject to local regulations. (3 aligned);
foreign bonds are issued by entities that are not native to the country in which they’re traded, denominated in the country’s currency. (only 2 aligned)
Eurobond: Issued in a foreign currency in international markets, not tied to the issuer’s country or currency.
Global bonds are a type of bond that are issued simultaneously in multiple markets
