Fixed Income Flashcards
Calculate exposure for each year of a bond
Take the final payout date and discount by the yield and add in the coupons along the way (1 year at a time)
Given exposure, default probability, and recovery amounts, calculate riskiest bonds
- find expected loss by taking (exposure - recovery) * default probability and the high expected loss is the riskiest bond
Two broad categories that cover credit risk models
1) Reduced Form
2) Structural
Reduced form credit model
- seek to predict when a default may occur, but not why
- based only on observable variables
- says credit evens are exogenous and random
Structural Model
- Based on an option perspective of the stakeholders of the company
- Bondholders are viewed as owners of the assets of the company, while shareholders have the call options on those assets
Hazard Rate
The probability that an event will occur, given that it has not already occurred
Upfront payment on a CDS
PV(protection leg) - PV(premium leg), basically whoever’s value is more has to pay the difference
Upfront premium
(credit spread - fixed coupon) *duration
Naked CDS
A position in which the holder does not have a position in the underlying
Curve Trade
buying a CDS of one maturity and selling a CDS on the same reference of a different maturity
Basis trade
A trade based on the pricing of credit in the bond market vs the price of the credit in the CDS market. To executive, go long the underpriced credit and short the overpriced credit until the two converge
Spot rate
The interest rate that is determined today for a risk-free, single unit payment at a specified future date
Spot curve
YTM’s on a series of default-risk-free zero coupon bonds
Forward Rate
An interest rate determined today for a loan that will be initiated in a future period
Forward Curve
A series of forward rates, each having the same time frame
Par Curve
A sequence of YTM’s such that each bond is priced at par value, where each bond are assumed to have the same currency, credit risk, liquidity, tax status, and annual yields stated for the same periodicity
Bootstrapping
The use of a forward substitution process to determine zero coupon rates by using the par yields and solving for the zero-coupon rates one by one
Rolling down the yield (riding the yield curve)
A maturity trading strategy that involves buying bonds with a maturity longer than the intended investment horizon
Swap rate
Fixed rate to be paid by the fixed-rate payer
Par Swap
A swap in which the fixed rate is set so that no money is exchanged at contract initiation
Swap spread
Difference between fixed rate on interest rate swap and the rate on a treasury
I Spread
Reference to linearly interpolated yield
TED spread
a measure of perceived credit risk, difference between Libor and t bill
OIS Spread
difference between LIBOR and overnight indexed swap rate
Local expectations theory
Return for all bonds over short periods is the risk free rate
3 Factors that explain yield curve shape changes
1) Level - explains the most
2) Steepness
3) Curvature
Bearish flattening
Short-term bond yields rise, curve goes flat
Bullish steepening
Short-term rates fall, curve goes steep
Bullish flattening
Long-term rates fall, curve goes flat
Bullet portfolio
A fixed income portfolio concentrated in a single maturity
Dominance principle
arbitrage opportunity when a financial asset with a risk-free payout in the future must have a positive price today
Cox-Ingersoll-Ross Model (CIR)
Model that assumes interest rates are mean reverting and interest rate volatility is directly related to the level of interest rates
Vasicek Model
Interest rates are mean reverting and interest rate volatility is constant
Ho-Lee Model
- The first arb model, calibrated to market data and uses a binomial lattice approach to generate a distribution of possible future interest rates
- Can be calibrated to closely fit an observed yield curve
Kalotay-Williams-Fabozzi Model (KWF)
Describes the dynamics of the log of the short-rate and assumes constant drift, no mean reversion, and constant volatility
Effective duration definition and formula
sensitivity of the bond’s price to an instant parallel shift in a benchmark yield curve, for example, the government par curve
(v minus - v plus) / (2v0change in yield)
Conversion Price
For a convertible bond, the price per share at which the bond can be converted into shares
Market price of convertible bond / conversion ratio
Conversion Rate (ratio)
The number of stock that bondholder receives from converting the bond into shares
When would a forced conversion happen
when underlying share prices increases above the conversion price
Conversion Value
- Parity Value
- market price of stock * conversion ratio
Expected Exposure
Projected amount of money an investor could lose if an event of default occurs, before factoring in possible recovery
Credit Valuation Adjustment
The value of the credit risk of a bond in present value terms
Index CDS
A type of CDS that involves a combination of borrowers
Credit correlation
the correlation of credit risks of the underlying single name CDS contained in an index CDS
Roll
When an investor moves its investment position from an older series to the most current series
Protection Leg
The contingent payment that the credit protection seller may have to make to the credit protection buyer
Calculate the spread the market expects for credit and liquidity component of the YTM
The swap spread is measured over the “on-the-run” swaps, so calculate the on the run ytm and then the sap rate and subtract the two
CDS Trade - Flattening of Curve
- sell long-term CDS
- buy short term CDS
CDS trade - steepening of curve
- buy long-term CDS
- sell short-term CDS
Advantages of using Monte Carlo to simulate interest rate paths
1) increases the number of paths increases the estimate’s statistical accuracy
Does monte carlo provide a closer value to bond’s true fundamental value
No
Credit Score
- Used primarily in retail lending market and for small businesses
- sometimes only negative information, like delinquent or default is included
Advantages of using swap curve as a benchmark of interest rates relative to government bond yield curve
Some countries do not have active government bond markets with trading at all maturities, so with an active swap market, there are typically more points available to construct
Segmented Market vs. Preferred Habitat Theories
- Both try to explain the shape of any yield curve in terms of supply and demand
- Segmented market theory says investors are limited to purchase maturities that match the timing of their liabilities
- Preferred habitat says investors have a preferred maturity for asset purchases, but may deviate if they feel returns in other maturities offer sufficient compensation
OAS on callable bond when volatility drops
increases
Callable bond = value of straight bond - value of call option
OAS on puttable bond when volatility drops
decrease
Puttable bond = value of straight bond + value of put option
Typical impact of credit rating migration on the expected return on a bond
Typically reduces the expected return for two reasons:
1) Probabilities for rating changes are not symmetrically distributed, they are skewed towards a down rating
2) Increase in the credit spread is much larger for downgrades than is the decrease in the spread for upgrades
Long-Short Trade when economy strengthens using HY and IG
selling CDS on HY and buying CDS on IG because credit spreads narrow
One benefit of testing that the binomial interest rate tree has been properly calibrated to be arbitrage-free
Enabling the model to price bonds with embedded options
Conversion premium ratio
1) Par Value (1,000) / current conversion price = current conversion ratio
2) Current trading price / current conversion ratio = market conversion price
3) Market conversion premium = market conversion price / current share price
Value of embedded put option when interest rates increase
Put option increases
Value of embedded call option when yield curve flattens
Call options increases
Value of a convertible bond with an embedded call option and put option
Value of straight bond + value of call option on stock - value of issuer call option + value of put option
Market conversion premium per share
1) Market conversion price = convertible bond price / conversion price
2 Market conversion premium per share = market conversion price - underlying share price
Value of put option when yield curve moves from being upward sloping to flat to downward sloping
Value of put option decreases
Z spread
single rate that when added to the rates of the spot yield curve, provide the correct discount rate to price a corporate bond
Spot rate determined by using forward substitution
1 = (par rate in year you want / 1+spot rate in year 1) + (par rate in year you want / 1 + spot rate in year 2) … + (1 + par rate in year you want / 1 + spot rate in final year (which you are solving for))
What is the typical term structure of interest rate volatility
downward sloping
Spread that reflects risks and liquidity in money market securities
MRR-OIS Spread
spread that reflects risk in the banking sector
TED spread
A swap curve is a type of what curve
par curve
which theory of term structure interest rates does not have a supply and demand argument
liquidity preference
where does short-term interest rate volatility come from and where does long-term interest rate volatility come from
short-term = monetary policy uncertainty
long-term = real economy and inflation
effective duration of floating rate bond
close to the time to next market reset
Effective duration formula
[(PV-) - (PV+)]/ [2* delta I-rate*(PV0)]
Loss Severity
1 - Recovery Rate
Expected price change as a result of credit rating change
- Duration * (New credit rating credit spread - old credit rating credit spread)
Risk neutral probability of default
100 = (exposure * (1-p) + cash flow in default * p) / (1 + r )
cash flow in default = default probability * exposure
Gain/Loss in CDS trade
change in credit spread * duration * notional amount
CDS up front premium
(credit spread - CDS fixed coupon) * duration
On what level of debt is single name CDS typically issued
senior unsecured debt
Price of CDS
1 - CDS up front premium
Which approach for evaluating credit risk is most predictive
reduced form model
Which approach for evaluating credit risk is least predictive
credit rating
do credit spreads predict probability of default
no
Impact of volatility on CVA
almost no impact
why is a risk-neutral probability of default much higher than historically observed rates of default
the resulting credit spread should reflect uncertainty of payments
term structure of credit spread of HG vs. IG vs. Distressed
HG = upward sloping
IG = flat to upward sloping
Distressed = downward sloping
which credit model predicts probability of default
none of them
How should MBS be valued
Using Monte Carlo
When underlying options are at or near the money, one sided down duration vs one sided up duration callable bonds
Lower
When underlying options are at or near the money, one sided down duration vs one sided up duration on putable bonds
Higher
When underlying options are at or near the money, one sided down duration vs one sided up duration on putable bonds
Higher
Expected loss on CDS
Hazard rate * LGD
Options analogies in structural model
- Equity investors have call option on assets
- Debt investors short a put option on assets
- Value of put option = CVA
Value of call and put options when volatility increases
Both increase
Value of callable bond when volatility increases
Decreases
Value of putable bond when volatility increases
Increases
OAS and value of callable bond when lower than actual volatility is used
OAS is too high so bond is underpriced
OAS and value of putable bond when lower than actual volatility is used
OAS too low and putable bond is overpriced
Standardized rate on CDS contract for HY
5%
Standardized rate on CDS contract for IG
1%
CDS trade for when credit curve shifts up at all points
sell short buy long
the underlying of a CDS
the credit quality of the borrower
CVA Formula
LGD * POD * discount factor
LGD = 1-recovery rate
CVA Formula
LGD * POD * discount factor
LGD = 1-recovery rate * expected exposure
