Chapter 3: Introduction to fixed- income valuation
Bond prices and the time value of money
Bond pricing is a summary of discounted future CF
Coupon payment and principle repayment
Market discount rate (required yield or required rate of return)
For floating rate notes, Libor is quoted every 3- month
Trading
Discount (coupon rate < discount rate)
Par (coupon rate = discount rate)
Premium (coupon rate > discount rate)
Yield to maturity: internal rate of return on a bond's cash flows
Relationship of bond price and market discount rate
Inverse effect: bond price is inversely related to market discount rate
Convexity effect: percentage price change is greater when the market discount rate goes down than when it goes up
Coupon effect: lower coupon bond has greater percentage price change when market discount rate changes
Maturity effect: a longer term bond has greater percentage price change when market discount rate changes (holds on zero- coupon bonds, par bonds, and premium bonds)
Bond price: summary of the discounted future cash flows (definition)
Matrix pricing (p.109 text book)
estimation process used for bonds that are not actively traded
market discount rates are extracted from comparable bonds
required yield spread: difference between the YTM on the new bond and the benchmark rate
benchmark rate: YTM on a government bond having the same (or close to the same) time to maturity
Yield measures for fixed- rate bonds (p.24 lecture slide)
Effective annual rate
Other yield measures
Street convention yield- to- maturity: yield measures that neglect weekends and holidays
True- yield- to maturity: using calendar of weekends and bank holidays
Government equivalent yield
Current yield = coupon payment/ flat price
Simple yield = (coupon payment + amortized share of gain/ loss)/ flat price
Yield with embedded options (p.28 lecture slide)
The reference rate is determined at the beginning of the period, and the interest payment is made at the end of the period
Money market vs bond market
Spread over the benchmark ( 1 basis point = 0.01%)
Example: Callable bond
Value of the call option = price of the option- free bond - price of the callable bond
Yield- to- worst: the lowest of yield- to- call and yield- to- maturity
YTM
Bond: annualized and compounded
Money market: annualized but not compounded
Rate of return
Money market: stated on a simple interest basis
Bond: calculated using standard time- value- of money analysis
Money market: quoted using nonstandard interest rates and require different pricing equations
Bond: stated for a common periodicity
Money market: different time- to- maturity have different periodicities for the annual rate
Money market: discount rate or add- on rates (in money market, discount rate represents specific type of quoted rate)
The maturity structure of interest rates
reasons for the different in YTM
periodicity
credit risk
liquidity
tax status
currency denomination
varying- time to maturity
A forward curve
A forward market: for future delivery
A forward rate: interest rate on a bond or money market instrument traded in a forward market
An implied forward rate
calculate from spot rates
break- even reinvestment rate
links from shorter to longer term coupon bond
Yield spreads
2 components
benchmark yield
spread
Off the run: seasoned government bonds
G spread: yield spread in basis point
I- spread (or Interpolated spread)
A zero volatility spread