(R44) Introduction to Fixed-Income Valuation Flashcards
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 (use time value of money keys)
Discount or premium bond when coupon rate < YTM
Discount bond; premium bond is when coupon rate > YTM
Identify relationship among bond price and discount rate
Bond price is inversely related to the discount rate; when price goes up, rate goes down (this is called the inverse effect)
What is the convexity effect relationship for bond price?
Given the same coupon and time to maturity, the % change in price is greater when rates are decreasing compared to when rates in increases
What is the coupon effect relationship for bond prices?
Lower coupon bond is more price sensitive than a higher coupon bond when rates change, given the same time to maturity
What is the maturity effect relationship for bond prices?
For the same coupon rate: a longer term bond is more price sensitive than a shorter-term bond
Spot rate and calculation of PV using spot rates
Spot rates are market discount rates for single payments to be made in the future (each payment in the future has a different rate); PV = [PMT/(1+S1)] + [PMT/(1+S2)] + [PMT/(1+Sn)]
When a bond is between coupon dates, its price has two parts:
1) the flat price (PVflat) and 2) accrued interest (AI); the sum of these equal PVfull
Formula to calculate accrued interest for bonds
Accrued interest = t/T x PMT (where t = # of days between last payment and settlement date; T = # of days between each payment)
Two conventions to count days for calculating accrued interest and PVfull
30/360 (used for corporate bonds) and actual/actual (used for gov’t bonds)
Formula for PVfull
PVfull = PV x (1+r)^(t/T)
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).
Difference between effective annual rate and semi-annual bond basis yield
Effective annual rate is for bonds with a periodicity of 1 (1 coupon/year); Semi-annual bond basis yield is for bonds with a periodicity of 2 (2 coupons/year).
Relationship between periodicity and annual percentage rate
As periodicity increases, APR decreases
Formula for periodicity conversions (semi to quarterly)
[1 + (r/2)]^2 = [1+(r/4)]^4
Define bond yields that follow street convention and true yields.
Bond yields that follow street convention use the stated coupon payment dates (ignores weekend/holidays). A true yield accounts for coupon payments that are delayed by weekends or holidays and may be slightly lower than a street convention yield.
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 YTM is a callable bond’s yield-to-worst.
Define government equivalent yield
Quoted for a corporate bond
Restates 30/360 to actual/actual
Results in a more accurate spread over benchmark measure
Define floating rate notes
interest payments 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.
Define quoted margin and required margin for floating rate notes
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
Describe relationship between quoted margin, required/discount margin and PV
PV of floating rate note is > 100 when QM>DM
Calculate price of floating-rate note (PV)
Use time value of money keys: PMT=[(index + QM)/m] x 100; index is libor
Define money market instruments
Money market instruments are annualized but not compounded. For money market instruments, yields may be quoted on a discount basis or an add-on basis
Formula for two yield measures for money market instruments
Discount Rate => PV = FV x [1 - (days/yr) x DR]
DR = (yr./days) x (FV - PV) / FV
Add-on rates => PV = FV / [1 - (days/yr) x AOR]
AOR = (yr./days) x (FV - PV) / PV
Define yield curve
A yield curve (aka maturity structure or term structure of interest rates) shows the term structure of interest rates by displaying yields for a particular cluster of bonds (Same currency, liquidity, credit risk, tax status, and coupon)
Define spot curve
The spot curve includes YTMs for zero-coupon bonds for a full range of maturities (sometimes called the zero or strip curve)
Normal yield curve is upward sloping => longer maturities have higher YTMs
Define par carve
Sequence of YTMs such that each bond is priced at part. Par rates are derived from spot rates
Define a forward curve
A forward curve is a yield curve composed of forward rates, such as 1-year rates available at each year over a future period. Rates agreed on today, received/paid in the future; Forward curve is a mathematical result of the spot curve
Compare the curves when looking at them on a graph
When all curves are upward sloping (Forward > spot > par); When all curves are downward sloping (Forward < spot < par)
What does f(2,5) mean?
2 years from now, 5 year rate
Given a spot curve, what kind of curve can be derived?
Forward curve
Define forward rate and calculate the implied forward rate from a spot rate
Interest rate on a bond or money market instrument traded in a forward market (aka break-even rates or no-arbitrage rates). rates agreed on today but received/paid in the future
Ex: 3y1y means this begins in 3 years and lasts 1 years; f (3,1)
Spots: 3yr. = 3.615%; 4yr = 4.18%
Implied forward rates are calculated from spot rates using the following formula:
[1 + (.0418/2)]8 = [1 + (.0365/2)]6 [1 + (f(3,1)/2)2 we are solving for f(3,1)
What is a yield spread?
A yield spread is the difference between a bond’s yield and a benchmark yield or yield curve.
What is a zero-volatility spread (Z-spread)
A constant spread over a government spot curve (or swap curve)
Yield measures typically are annualized and compounded if they mature when?
Greater than 1 year
If maturity is less than a year, then they only annualize but no compounding
What is a G-spread
A G-spread is the difference between a bond’s yield and a benchmark yield or yield curve where the benchmark is a government bond yield.
What is an I-spread
An I-spread is the difference between a bond’s yield and a benchmark yield or yield curve where the benchmark is a interest swap rate. I-spread is more risky
