Introduction to Fixed-Income Valuation Flashcards
The return required by investors is also known as…
- required yield
- required rate of return
- market discount rate
Yield to maturity
- I/Y on calculator
- the implied market discount rate
- the bond’s IRR - ROR of int pmts and capital gains if held to maturity
assums:
- hold to maturity
- the issuer does not default
- investor is able to reinvest all coupons at YTM (which is unrealistic)
Convexity effect:
- the price-yield relationship of a bond is not a straight line, its convex
- price changes are not linear for the same amount of change in discount rt
- ie a 1% delta up or down will not have an equal effect on the bond’s price
“for the same coupon rate and time-to-maturity, the % price change is greater when the interest rate goes down v if int rt goes up
- ie a decreased interest rate will increase price more than an increased int rate decreases price
A decreased interest rate will ______ price _______ than an increased rate of the same amount
- a decreased int rate will increase price more than an increased rate will decrease price by the same delta rate
“Coupon effect”
The lower the coupon rate, the ____ the interest rate sensitivity
- the higher
- a bond with a lower coupon rt will have higher interest rate sensitivity
ie if interest rates go up/down by 1%, the price of a 10% bond will change more than the price of a 30% bond
Maturity effect
- for the same coupon rate, a longer-term bond has a greater percentage price change than a shorter-term bond when their market discount rates change by the same amount
ie- a 30yr bond will be affected more than a 10yr bond w/ a 1% interest rate change
Low-coupon and long-term bonds are ______ sensitive to changes in discount rates
are most sensitive
Pricing a bond using spot rates:
a one-yr spot rate is 2%, two-yr spot rate is 3%, and three-yr spot rate is 4%. What is the price of a three-yr bond that makes a 5% annual coupon pmt?
- you can draw out the timeline from T0-T3
Bond’s no-arbitrage value = (5/1.02) + (5/1.03^2) + (105/1.04^3) = 102.96
Define “Full price” or “Dirty price” and its components
Full/dirty price: - when a bond is between coupon dates, its price has two parts 1. flat price 2. accrued interest the sum of these two is the full price
PVfull = PVflat + accrued interest (AI)
PVfull = PV * (( 1 + r ) ^ t/T))
Spot rates are 1-yr: 4% 2-yr: 4.25% 3-yr: 4.5% Find the price of a 5% $1000 face value bond
coupon = .05*1000 = $50
50/1.04 + 50/1.0425^2 + 1050/1.045^3
PV = $1,014.20 YTM = 4.4836
The flat price is…
- the QUOTED PRICE
- aka CLEAN PRICE
- Flat price = Full price - AI
Accrued interest (AI) is what
- (the #of days since the last coupon pmt / the #of days between coupon pmts) * pmt
= (t / T) * PMT
can be calculated via
- actual convention: actual # of days; includes weekends, holidays, etc
- 30/360 convention: assumes 30 days in a month and 360 days in a yr
Full price formulas:
and what to look for in questions
PVfull = PVflat + accrued interest (AI)
PVfull = PV * (( 1 + r ) ^ t/T))
- note the bonds coupon %
- is it semi annual or annual: if semi, divide by 2 - note the YTM: if semi, divide by 2
- priced for settlement date
- when coupon pmts are made and when the last payment was made
- find the number of days from last payment till priced for settlement date
- find n; n will equal number of remaining yrs till maturity * two if semi ann + remaining coup date in current yr if applicable
- you start by solving for what the PV was on the most recent coup pmt date
- then PVfull = PV * (( 1 + r ) ^ t/T))
PVflat = PVfull - AI
Matrix pricing definition
- is an estimation process to find the price of a not-so-frequently traded bond
- is based on the prices of comparable bonds with similar times to maturity, types of issuer, coupon rts, and credit quality
- also used for bonds that have not been issued yet
key points:
- used when underwriting new bonds to est the required spread over the benchmark
Matrix pricing example:
- an analyst wants to value an illiquid 3-yr, 3.75% annual coupon payment corporate bond. Given the following and using matrix pricing, what is the estimated price of the illiquid bond?
additional info:
- (A) 2-yr, 4.75% annual coupon payment bond priced at 105.60
- (B) 4-yr, 3.50% annual coupon payment bond priced at 103.28
Solution: - start by finding the YTMs of the given bonds A: n=2, pmt=4.75, PV= -105.60, FV=100 solve for I/Y = 1.871% B: n=4, pmt=3.50, PV= -103.28, FV=100 solve for I/Y = 2.626%
- then, estimate the market discount rate for a 3-yr bond having the same credit quality by averaging the YTMs of the given bonds
- (1.871% + 2.626%) / 2 = 2.249% YTM
now, solve for the price of the illiquid 3-yr bond:
n=3, I/Y= 2.249%, pmt=3.75, FV=100
PV price = 104.3078
Stated annual rate of a bond
- aka: annual percentage rate or APR
- will depend on the periodicity; the number of compounding periods in a year (semi ann = 2)
- its the I/Y of a bond * the periodicity
Compounding more frequently within the year results in a _________ YTM
- in a lower YTM
ie: if a bond has a periodicity of 4 vs 1, the periodicity of 4 will result in a lower I/Y and lower stated annual rate (APR)
EAR
- effective annual rate
- the yield on an investment in one year taking into account the effects of compounding
- used to compare the rate of return on investments with different frequencies of compounding (periodicities)
Current yield
- aka income yield
- aka interest yield
= annual cash coupon payment (based on par value) / current bond price
Required margin v quoted margin
Required margin: AKA discount margin - is the spread demanded by the market
Quoted margin: for floaters, is the specified yield spread over the reference rate
The coupon rate of a floating rate note =
= reference rate + quoted margin
a 3-yr Italian floating-rate note pays 3-month Euribor plus 0.75%. Assuming that the floater is priced at 99, calculate the discount margin for the floater if the 3-month Euribor is constant at 1% (assume 30/360-day count conversion)
coupon rate of a FRN = (reference rate + quoted margin) / periodicity
= 1% + 0.75% = 1.75% / 4 = 0.4375% coupon
market discount rate:
n= 12 (3yr *4), PV= -99, FV=100, PMT= 0.4375
CPT I/Y = 0.5237 * 4 = 2.09% discount rate
THE DISCOUNT MARGIN for the floater = 2.09% - 1% reference rt
= 1.09%
Money market instrument categories:
- Discount rates:
- tbills, commercial paper (CP), and banker’s acceptance
- issued at a discount price, and pay par value at maturity
- no payments before maturity
Price:
PV = FV * (1 - (days to maturity / yr * DR) DR = discount rate
MM DR= (yr/days to maturity) * (fv - pv / fv) fv - pv = the discount (D); the interest earned on the instrument
*note that fv is denominator
- Add-on rates:
- bank term deposits, repos, certificates of deposit, libor/euribor
- interest is added to the principal to calculate the redemption amount at maturity
PV = (FV / ( 1 + (days to mat/yr * AOR))
AOR: add on rate
= yr/days to mat * (fv - pv / pv) *note that pv is in denominator
Suppose a pension fund buys a 180-day banker’s acceptance with a quoted add-on rate of 4.38% for a 365-day year. if the initial principal amount is $10m, what is the redemption amount due at maturity?
finding the redemption amount, aka the FV
add-on rate AOR = (yr/days) * (fv - pv / pv)
AOR= .0438, yr= 365, day=180, fv-pv = interest, pv = 10m
0.0438 = 365/180 * (Int / 10,000,000)
Int = .216 (216,000)
FV = 10 + .216 = 10,216,000
a FRN has a quoted margin of 50bps and required margin of 25 bps. the price of the not on its next reset date will be
MORE THAN PAR VALUE
- required margin < quoted margin
- if the required margin is less than quoted margin, it means the credit quality increased. therefore the price of the note on the reset date will be more than par, a premium
A 365 day CD with PV=95, and 300 days to maturity
Find the bond equivalent yield
BEY = yr/day * (fv-pv / pv) *not that pv is the denominator
= 365 / 300 * 100-95/95
=6.40%
