6.3 Fixed Income Valuation: Price, Yields, Interest Rates, and Term structure Flashcards
A bond’s yield-to-maturity (YTM)
the discount rate that makes the present value of its expected future cash flows equal to its current price
it is the single discount rate that is implied by a bond’s observed price.
YTM is a promised yield because it is the internal rate of return (IRR) that an investor would earn if the following assumptions hold:
The bond is purchased today at its current market price and holding it until maturity
All cash flows (coupons and principal) are received on the scheduled dates
All coupon payments received prior to maturity are reinvested to earn the YTM
The accrued interest
the accrued interest in the period between the prior and next coupon payment date
A bond’s full price (also known as its invoice price or dirty price)
can be calculated by its present value on the last coupon payment date adjusted for the portion of the current coupon period that has passed.
The amount of interest that has accrued to the seller since the last coupon payment is included in a bond’s full price.
However, accrued interest is excluded from a bond’s flat price (or clean price)
Relationship Between Bond Prices and Bond Features
inverse relationship
Convexity effect
Coupon effect
Maturity effect
Constant-Yield Price Trajectory
Inverse relationship
A bond’s price moves in the opposite direction as its yield. A higher yield causes a lower price and vice versa.
Convexity effect
All else equal, the percentage increase in a bond’s price caused by a lower yield will be greater in magnitude than the percentage decrease caused by an equivalent increase in its yield. This effect (as well as the inverse relationship between a bond’s price and its yield) can be seen in the following graph:
Coupon effect
Bonds with lower coupon rates experience a greater percentage price change for a given change in the market discount rate than otherwise equivalent bonds with higher coupon rates.
All else equal, a zero-coupon bond is more sensitive to changes in interest rates than a coupon-paying bond.
Maturity effect
As a general rule, longer-term bonds experience a greater percentage price change for a given change in the market discount rate.
he maturity effect holds for both zero-coupon bonds and bonds that are trading at or above par.
However, exceptions to this rule can be observed among low-coupon, long-term bonds trading at a deep discount.
Constant-Yield Price Trajectory
Assuming no change in the yield curve, bonds that are trading at a discount or a premium will be “pulled to par” as they approach maturity
Matrix Pricing
Prices for some bonds must be estimated because they are traded infrequently or not yet issued.
This can be done by using quoted prices and yields for similar bonds with a process called matrix pricing.
Interpolation is used to calculate the yield for the desired maturity.
A similar process can be used to estimate a bond’s yield spread, which compensates investors for credit risk, liquidity, and tax status.
A bond’s periodicity
the number of interest compounding periods per year, which is usually the number of coupon payments per year.
The current yield
the sum of the coupon payments received over a year divided by the flat price
this yield measure ignores the frequency of coupon payments and any accrued interest. It also ignores the gain or loss from purchasing a bond at a discount or premium.
The simple yield
(total interest and compound gains/losses) / flat price
The street convention yield
assumes that a bond’s cash flows will occur on the scheduled dates, even if those happen to occur on a weekend or a holiday
calculated on the assumption of 30 days per month and 360 days per year, as is standard market practice for corporate bond quotes
A bond’s true yield
uses the actual date the cash flow will be made, such as the Monday following a weekend
calculated on the assumption of 30 days per month and 360 days per year, as is standard market practice for corporate bond quotes
The government equivalent yield
restates a bond’s yield-to-maturity based on the actual/actual day count convention.
Yield-to-call
the internal rate of return assuming the bond is called early at the stated call price
yield-to-worst.
the lowest yield possibkle for a callable bond
option-adjusted yield
This measure is calculated using a bond’s option-adjusted price, which calculated as the price of an equivalent option-free bond less the estimated value of the embedded call option.
The benchmark rate
often the yield on a comparable government bond
The benchmark yield will capture the top-down macroeconomic factors that affect all bonds.
The benchmark rate is composed of the expected real risk-free rate plus the expected inflation rate.
Yields for on-the-run government bond are commonly used as benchmark rates because these are the most liquid issues and they typically trade at prices close to their par value.
Off-the-run government bonds carry higher yields because they are not as liquid.
The following spread measures can be calculated relative to a benchmark rate:
The benchmark spread
The G-spread
The I-spread (or interpolated spread)
The benchmark spread
the difference between a bond’s yield and a specific benchmark yield.
The G-spread
the difference between a bond’s yield and an actual or interpolated government bond yield.
The I-spread (or interpolated spread)
the difference between a bond’s yield and the swap rate or a similar market refence rate (MRR) for the same tenor.
It can be interpreted as the relative cost of structuring a debt issue as a fixed-rate bond rather than a floating-rate obligation.
The I-spread indicates a bond’s credit risk relative to the MRR index.
Benchmark yield curves are typically upward-sloping because?
investors require a premium to hold longer-term securities.
Floating-rate notes (FRNs)
structured with coupon payments that move up and down with market rates, which reduces to market price risk
the quoted margin (QM)
the spread that the floating-rate issuer pays over the reference rate to compensate investors for accepting the issuer’s credit risk
The QM is set at the time an FRN is issued and it remains fixed over its life
The discount margin (DM) (or required margin)
the yield spread over the reference rate needed to make the FRN trade at par at a coupon reset date
It is the market’s assessment of the spread that is consistent with the issuer’s current credit risk.
The DM will change and deviate from the QM as new information becomes available.
if the issuer’s credit quality deteriorates, the DM will increase and the FRN will trade below its par value, reflecting the face that the QM being paid is no longer sufficient compensation for the issuer’s current credit risk
There are key differences between the money market and the bond market.
Yield measures for money market instruments are stated in annualized terms with simple (uncompounded) interest. By contrast, bond market yields are both annualized and compounded.
While bond market quotes are are standardized to a common periodicity for all maturities, quotes for money market instruments of different maturities use annual rates with different periodicities.
Unlike bond market yields, which can be calculated using standard time value of money formulas, money market instrument yield quotes are often based on nonstandard interest rates and require the use of different pricing methods.
Usually, commercial paper, Treasury bills, and bankers’ acceptances are quoted on a
discount rate (DR) basis
discount rate (DR) basis
This method understates the rate of return to the investor because it is based on the maturity value (FV) rather than the investment amount (PV).
