(44) Introduction to Fixed-Income Valuation Flashcards
LOS 53. a: Calculate a bond’s price given a market discount rate.
The price of a bond is the present value of its future cash flows, discounted at the bond’s yield-to-maturity.
Discount bonds - PV decreases as periodicity increases
Premium bonds - PV increases as preriodicity increases
LOS 53. b: Identify the relationships among a bond’s price, coupon rate, maturity, and market discount rate (yield-to-maturity).
A bond’s price and YTM are inversely related. An increase in YTM decreases the price and a decrease in YTM increase the price.
A bond will be priced at a discount to par value if its coupon rate is less than its YTM, and at a premium to par value if its coupon rate is greater than its YTM.
LOS 53. b: Identify the relationships among a bond’s price, coupon rate, maturity, and market discount rate (yield-to-maturity).
Prices are more sensitive to changes in YTM for bonds with lower coupon rates and longer maturities, and less sensitive to changes in YTM for bonds with higher coupon rates and shorter maturities.
A bond’s price moves toward par value as time passes and maturity approaches.
Coupon rate > market rate - premium bond
Coupon rate < market rate - discount bond
LOS 53. c: Define spot rates and calculate the price of a bond using spot rates.
Spot rates are market discount rates for single payments to be made in the future.
The no-arbitrage price of a bond is calculated using (no-arbitrage) spot rates as follows:
LOS 53. d: Describe and calculate the flat price, accrued interest, and the full price of a bond.
The full price of a bond includes interest accrued between coupon dates (Flat price + AI). The flat price of a bond is the full price minus accrued interest.
Accrued interest = t/T (where t = # of days between last payment and settlement date; T = # of days between each payment)
Methods for determining the period of accrued interest include actual days (typically used for government bonds) or 30-day months and 360-day years (typically used for corporate bonds).
Full price of bond (PVfull) = PV x (1 + r)t/T
LOS 53. e: Describe matrix pricing.
Matrix pricing is a method used to estimate the yield-to-maturity for bonds that are not traded or infrequently traded. The yield is estimated based on the yields of comparable bonds (i.e. similar tenor, coupons, credit quality). There are four steps:
- Find comparable bonds
- calculate YTM for each
- Find average YTM/term
- Interpolate the yield
LOS 53. f: Calculate annual yield on a bond for varying compounding periods in a year.
What is semi-annual bond basis yield or semi-annual bond equivalent yield?
Annual yield (aka interest rate) is calculated similar to the calculation for Present value: PV = FV/ (1+r)n
N changes based on periodicity. For example, if its a semi-annual bond then you multiple r by 2.
Multiplying r by the number of periods is called annualizing, which gives you the bond equivalent yield
Semi-annual bond basis yield or semi-annual bond equivalent yield is when an annual rate has a periodicity of two
Effective annual rate means compounding the rate
Bond equivalent yield means annualizing the rate
LOS 53. f: Calculate annual yield on a bond for varying compounding periods in a year. Formula to convert rate from one periodicity to another?
Going from semi-annual bond to quarterly bond:
[1+(BEY/2)]2 = [1+(BEY4/4)]4
In this equation we solve for BEY4
If going from semi to monthly, change right side of equation to 12 instead of 4
LOS 53. g,h: Calculate and interpret yield measures for fixed-rate bonds, floating-rate notes, and money market instruments. What does the effective yield of a bond depend on?
The effective yield of a bond depends on its periodicity, or annual frequency of coupon payments. For an annual-pay bond the effective yield is equal to the yield-to-maturity. For bonds with greater periodicity, the effective yield is greater than the yield-to-maturity.
LOS 53. g,h: Calculate and interpret yield measures for fixed-rate bonds, floating-rate notes, and money market instruments. What is the yield-to-maturity (YTM) quoted on a semiannual bond basis equal to?
A YTM quoted on a semiannual bond basis is two times the semiannual discount rate.
LOS 53. g,h: Calculate and interpret yield measures for fixed-rate bonds, floating-rate notes, and money market instruments. Define bond yields that follow street convention and true yields.
Bond yields that follow street convention use the stated coupon payment dates. A true yield accounts for coupon payments that are delayed by weekends or holidays and may be slightly lower than a street convention yield.
LOS 53. g,h: Calculate and interpret yield measures for fixed-rate bonds, floating-rate notes, and money market instruments. Define current yield and simple yield.
Current yield (income or running yield) is the ratio of a bond’s annual coupon payment to its price. Simple yield adjusts current yield by using straight-line amortization of any discount or premium.
Current yield = Annual coupon payment / price of bond (PV flat)
Simple yield = (Annual payment + SL amortization of gain/loss) / price of bond (PV flat)
LOS 53. g,h: Calculate and interpret yield measures for fixed-rate bonds, floating-rate notes, and money market instruments. Define yield-to-call and yield-to-worst.
For a callable bond, a yield-to-call may be calculated using each of its call dates and prices. The lowest of these yields and TYM is a callable bond’s yield-to-worst.
LOS 53. g,h: Calculate and interpret yield measures for fixed-rate bonds, floating-rate notes, and money market instruments. Define government equivalent yield
- Quoted for a corporate bond
- Restates 30/360 to actual/actual
- Results in a more accurate spread over benchmark measure
LOS 53. g,h: Calculate and interpret yield measures for fixed-rate bonds, floating-rate notes, and money market instruments. Define floating rate notes and the common day conventions, quoted margin, and required margin/discount margin.
Floating rate notes (FRN): interest payments on a floting-rate note are not fixed. They vary from period to period depending on the current level of a reference interest rate. The reference rate is usually a short-term money market rate (i.e. Libor). Intent of FRN is to offer a security with less market price risk than a fixed-rate bond. Use actual/360 and actual/365
Quoted margin - the yield spread over the reference rate; this is credit related and may be negative
Required margin/Discount margin - spread required by investors to reflect changes in credit quality; changes usually come from changes in the issuer’s credit risk
If QM = DM then PV = 100
QM > DM then PV > 100
QM < DM then PV < 100
