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
