Bond Pricing and Yield Flashcards
Bond pricing
Calculate a bond’s price given a market discount rate.
The price of a bond is the PV of its future cash flows, discounted at the bond’s yield-to-maturity (YTM).
Identify the relationship among a bond’s price, coupon rate maturity, and market discount rate (yield-to-maturity).
A bond’s price and YTM are inversely related, and increase in YTM decreases the price and a decrease in YTM increases 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 par value if its coupon rate is greater than its YTM.
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.
Define spot rates and calculate the price of a bond using spot rates.
Spot rates are market discount rates for single payments be made in the future.
The no-arbitrage price of a bond is calculated using (no-arbitrage) spot rates as follows:
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.
-The flat price of a bond is the full price minus accrued interest.
-Accrued interest for a bond transaction is calculated as the coupon payment times the portion of the coupon period from the previous payment date to the settlement date. 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).
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 yields is estimated based on the yields of traded bonds with the same credit quality. If these traded bonds have different maturities than the bond being valued, linear interpolation is used to estimate the subject bond’s yield.
Calculate annual yield on a bond for varying compounding period in a year.
The effective yield of a bond depends on its periodicity, or annual frequency to 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.
Calculate and interpret yield measures for fixed-rate bonds and floating-rate notes.
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.
Current yield is the ratio of a bond’s annual coupon payments to its price. Simple yield adjusts current yield by using straight-line amortization of any discount or premium.
For callable bond, a yield-to-call may be calculated using each of its call dates and pieces. The Lowes of these yields and YTM is a callable bond’s yield-too worst.
Floating rates notes have a quoted margin relative to a reference rate, typically LIBOR. The quoted margin is positive for issuers with more credit risk than loans to these banks. The required margin on a floating rate note may be greater than the quoted margin if credit quality has decreased, or less than the quoted margin if credit quality has increased.
Calculate and interpret yield measures for money market instruments.
For money market instruments, yields may be quoted on a discount basis or an add-on basis, and may use 360-day or 365-day years. A bond-equivalent yield is an add-on based on a 365-day.
Define and compare the spot curve, yield curve on coupon bonds, par curve, and forward curve.
A yield curve shows the term structure of interest rates by displaying yields across different maturities.
The spot curve is a yield curve for single payments in the future, such as zero-coupon bonds or stripped Treasury bonds.
The par curve shows the coupon rates for bonds of various maturities that would result in bond prices equal to their par values.
A forward curve is a yield curve composed of forward rates, such as 1-year rates available at each year over a future period.
Define forward rates and calculate spot rates from forward rates, forward rates from spot rate, and the price of a bond using forward rates.
Forward rates are current lending/borrowing rates for short-term loans to be made in future periods.
The spot rate for maturity of N periods is the geometric mean of forward rates over the N periods. The same relation can be used to solve for a forward rate given spot rates for two different periods.
To value a bond using forward rates, discount the cash flows at times 1 through N by the product of one plus each forward rate for periods 1 to N, and sum them.
For a 3-year annual-pay bond:
Compare, calculate and interpret yield spread measures.
A yield spread is the difference between a bond’s yield and a benchmark yield or yield curve. If the benchmark is a government bond yield, the spread is known as a government spread or G-spread. If the benchmark is a swap rate, the spread is known as interpolated spread or I-spread.
A zero volatility spread or Z-spread is the percent spread that must be added to each spot rate on the benchmark yield curve to make the PV of a bond equal to its price.
An option-adjusted spread or OAS is used for bonds with embedded options. For a callable bond, the OAS is equal to the Z-spread minus the call option value in basis points.
