Fixed Income Flashcards
I Spread (Interopolated Spread)
Yield spread of a bond over swap rate of a bond with same tenure
This assumes yield curve stays flat (Yield/IRR is constant over periods)
Z Spread (Zero volatility spread)
The additional spread over the spot curve. Accounts for varying yields/discount rates
Spot Curve
Zero coupon bond
Interest indexed bonds
Only interest payment is effect by inflation not the index
Capital indexed bonds
Only the principal payment is adjusted for inflation
Make- whole bonds
A type of callable bonds. All future CF and principal payment is calculated and paid.
As opposed to embedded call option where only the fixed price principal payment is made
with the discount rate being based on a predetermined spread over the YTM of a gov bond. (The discount is typically much lower than what it would be at MV)
Bermuda Style bonds
Issuer can call bond on pre determined dates. Typically on the coupon date
Spot rates
The Yield/ discount on zero coupon bonds.
Matching different spot rates that match with coupon cf payments of a bond enables identifying arbitrage opportunities
Exp.) 1yr spot =2% 2yr spot =3% Then the price of a 2 year bond with X payment should be the PV using the spot rates as a discount
Full Price/Dirty Price Bond
The price of the bond INCLUDES Accrued Interest. This is the price that is paid for the bond
Flat Price/ Clean Price
This price does not include accrued interest. This is the price of the bond that is typically quoted
Pricing bonds that have low liquidity and no easily findable public pricing.
Matrix pricing
Actual Actual Yield Convention. Government equivalent yield
Typical with government bonds. Actual ALL days between last coupon payment and settlement day/ divided by total number of days in coupon payment.
Government bonds are typically quoted on an actual/actual basis. Corporate bonds can be converted to the government equivalent yield in order to accurately find the spread over a benchmark
30/360 - Street Convention
Typical with corporate bonds. Assumes 30 days in month 360 days in year
Current Yield/ Income Yield/ Running Yield
Sum of coupon payments divided by the flat price. A less accurate signal of yield. Ignores capital gain/loss
Simple Yield
Sum of coupon payments + straight lined ammortized gains/losses divided by flat price
Yield to worst
In regards to an embedded call with multiple call dates, it is the call date/YTM that if exercised would have the lowest yield
Option adjusted price
Flat price - the value of embedded call option
Quoted Margin
The spread on a FRN over the reference rate.
Discount Margin/ Required Spread
MRR: Money market Rate/ Reference Rate
Usually a short term money market rate used as a benchmark
Quoted Margin
Spread over the reference rate that is received in coupon payments
Discount Margin/ Required Margin
Yield spread REQUIRED by investors over reference rate
Quoted Margin> Discount margin
FRN priced at premium
Discount margin/Required margin> Quoted Margin
FRN Priced at discount
What kind of money market instruments use the market discount rate
Treasury Bills: Commercial Papers (Why)
Usually issued at a discount
What kind of money market instruments use the Add on rate
Repo Rate, CD, Index’s
What is the formula for Market discount rates
Find the PV/issuance price of the bond by calculating the multiple of Future value.
The future value/redemption value is always quoted and given
PV= FV *( days left/total days) * Discount rate
If there are alot of days left then the FV is less of a representative of the PV AKA the multiple is smaller
Calculate Discount rate:
1.) (Days in the year/ days left in maturity) > This gives the periodicity and annualizes/ standardizese the yield to the length of the bond
2.(FV-PV)/FV***
- Step 1 * 2= Discount rate
Bond Equivalent Yield(BEY)
Is a money market bond quoted on a the 365 day AoR basis
Used to compare DR quoted bonds with AOR quoted bonds
- Find the PV of the DR quoted bond.
- Calculate the AOR using the DR PV and the AOR periodicity
- Result is the BEY
AoR formula
Find the redemption value. The price is always quoted
Formula for PV/MV price is discounting the fv/(1+days/total days * Aor)
Will need to shuffle to find FV
Spot Rate
The zero coupon government rate of a security.
Treat each cf as a zero coupon bond, so that the yield is most accurate and matches with the spot rate.
Used to find the PV of a bond
Par Rate
Find the coupon rate of a security that results in the bond = par. Use spot rates as discount
When coupon=yield, the bond is priced at par
Forward Rate/ Implied Rate/ Forward Yield
Gives the incremental/marginal yield
Is useful in preventing arbitrage
Example: 3 year forward must = the geometric average of the 2 year forward and 2Y1Y/ implied forward rate of a 1 year bond purchased in 2 years
Carrying Value
purchasing price of security+- the amortized or discounted amount at the point.
Capital gain/loss only occurs if yield changes.
Capital gain = selling price+- carrying value
Full price using Accrued interest formula??? Might need to rewrite
Flat price + PV of the accrued interest
PV full price
Yield to Worst
The call price that is associated with the lowest yield if excercised
