LM 3: Fixed Income Valuation: Prices, Yields, Interest Rates, & Term Structure Flashcards
What is the market discount rate?
Rate of return required by investor.
What is the price of a bond?
Present value of its expected future cash flows
What three factors effect the bond price? STD
- Size of cash flows
- Timing of cash flows
- Discount rate
What is the formula for PV of bond?
(PMT/(1+r)^1) + (PMT/(1+r)^2) + (PMT+FV / (1 + r) ^N)
PMT= coupon payment per period
FV= Par value of the bond
r= market discount rate per period
N= number of periods until maturity
How is the PV formula of an annual paying bond different than the PV formula of a semiannual paying bond?
semi-annual bond would require you to divide the PMT and the discount rate by 2 since its semi-annually
semi-annual bond would require you to multiple N by 2
What happens to coupon rate vs market discount rate and bond price vs par value when bond is selling at par?
Coupon rate is equal to discount rate
Bond price is equal to par value
What happens to coupon rate vs market discount rate and bond price vs par value when bond is selling at premium?
Coupon rate is greater than discount rate
Bond price is greater than par value
What happens to coupon rate vs market discount rate and bond price vs par value when bond is selling at discount?
Coupon rate is less than discount rate
Bond price is less than par value
Yield to maturity is a promised yield if what 3 assumptions are met?
- bond purchased today and you hold 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
What is yield to maturity?
rate of return earning by the investor if three conditions are met:
- Hold until maturity
- Reinvest all coupon & principal at YTM
- Receive coupon payments on time & in full
What happens if bond sold is between coupon dates?
must allocate coupon payment between seller and buyer
What is accrued interest formula due to the seller when a bond is sold between coupon payments?
AI = t/T * PMT
t = number of days between the last coupon payment and the trade settlement date
T= number of days in the coupon period
PMT = amount of next coupon payment
What does 30/360 day count mean?
30 days in month /360 number of days each year
What is a bonds full price?
PV of a bond + adjusted for the present value of the coupon payment that has to be split between the seller and buyer
What is the equation for a bond’s full price?
PV full = PV * (1+R) ^t/T
t = number of days between the last coupon payment and the trade settlement date
T= number of days in the coupon period
r = market discount rate
PV = present value of bond
What is a bond’s flat price
and formula?
flat price = PV - accrued interest
PV = present value of bond
AI = accrued interest of the coupon payment being split between buyer and seller
the agreed upon bond price (excluding interest)
What are the 5 relationships between bond prices and bond features? ICCMC
- Inverse effect
- Convexity effect
- Coupon effect
- Maturity effect
- constant yield price trajectory
What is an inverse effect on bond relationships?
A bond’s price moves in the opposite direction as its yield. A higher yield causes a lower price and vice versa.
What is convexity effect?
Bond price is more sensitive to a decrease in discount rate and less sensitive to an increase in discount rate
What is coupon effect?
Lower coupon rate bonds have a greater interest rate sensitivity than higher interest rate coupon bonds
What is the maturity effect?
Longer-term bonds have a greater percentage price change than shorter-term bonds
What is the constant yield price trajectory?
bonds trading at either discount or premium will be pulled to par as they get closer to maturity
What is matrix pricing?
determine the estimated required yield spread over a benchmark rate
estimating what a bond’s price should be by looking at similar debt issues, and then applying algorithms and formulas to tease out a reasonable value.
Used for bonds not yet issued or infrequently traded
What is interpolating?
figuring out yields for bonds that are between maturities
What is periodicity for bonds?
number of coupon payments per year
eg. semi-annual has 2
What is effective annual rate and formula?
used to convert a non-annual yield into an
annual yield
EAR = (1+(APR/M)^M) -1
APR = bond yield
M = number of compound periods per year
What is current yield and formula?
yield to maturity that neglects time value of money and principal gain or loss.
sum of coupon payments in year/ market price of bond
What is simple yield and formula?
adjusted current yield calculation to include the amortized gain or loss
(sum of coupon payments in year + amortized gain or loss) / market price
What is street convention yield?
assumes cash flows are made on the scheduled dates, even if on holidays or weekends
What is true yield?
focus on the actual timing of cash flows, excludes weekends and holidays.
Why is street convention yields greater than true yield?
true yield may delay payments if it falls on weekend producing a smaller yield
What is a government equivalent yield?
yield to maturity that does actual/actual instead of 30/360
What is yield to call?
measures internal rate of return assuming bond is called early by issuer at stated call price
What is yield to worst?
most conservative (lowest) rate of return for a callable bond
What is option adjusted yield?
an expected yield of the bond, accounting for the embedded call
represents yield consistent with the current bond price (takes into account the value of the option)
What is the benchmark rate?
benchmark rate is often the yield on a comparable government bond
What 2 things are benchmark rates composed of?
- expected real risk-free rate
- plus the expected inflation rate
What 2 things are yield-to-maturity rates composed of?
- benchmark rate
- bond specific spread (risk premiums)
What is the benchmark spread and formula?
difference between corporate bond yield and a specific benchmark yield
benchmark spread = corporate bond yield - benchmark yield
What is the G spread and formula?
difference between bonds yield to maturity and government bond yield
g spread = corporate bond yield - government bond yield
What is the I spread and formula?
difference between a corporate bonds yield and a similar market reference rate for the same tenor
I spread = corporate bond yield - swap rate (or MRR)
What is Z spread?
Z-spread is the constant spread added to each spot rate in the benchmark curve to make the present value of future cash flows match the bond’s current price.
What is the Z-spread formula?
PV = (PMT / (1+spot rate + z)^1) + (PMT / (1+spot rate + z)^2) + ((PMT + FV)/(1+spot rate + Z)^n)
spot rate = rate right now
PMT = coupon payment
z = spot rate
What is the option-adjusted spread formula?
OAS = Z spread - options value (in basis points)
What is the difference between the quoted margin and the discount margin?
quoted margin: the spread that the floating-rate issuer pays over the reference rate to compensate investors for accepting the issuer’s credit risk
discount (required) margin: the markets assessment of issuers current credit risk
the spread (a security’s yield relative to the yield of its benchmark) that equates the security’s future cash flow to its current market price
What is the present value formula of a floating rate note?
((index + qm)*fv)/m) / (1+ (index+dm/m))^n
index = reference rate state as annual percentage
QM= quoted margin stated as annual percentage rate
FV= Par value of bond
m= number of payment periods per year
DM= required margin stated as annual percentage rate
n= number of event spaced periods to maturity
What is the formula for pricing money market instruments using discount rates, specifically for commercial paper, Treasury bills, and bankers’ acceptances?
PV = FV (1 - Days/ 360 *DR)
DAYS = # of days between settlement and maturity
Year = # of days in year
DR = discount rate stated in an annual percentage rate
What is the formula for pricing money market instruments using add-on rates, specifically for certificates of deposits and repos?
PV = FV / (1+ DAYS/360 *AOR)
DAYS = # of days between settlement and maturity
Year = # of days in year
AOR = add-on rate stated in an annual percentage rate
What is the formula for calculating money market discount rates and add-on rates?
DR = (# of days in Year (365) / Days) * (FV - PV / FV)
AOR = (# of days Year (365) / Days) * (FV - PV / PV)
What is maturity structure?
Yields varying by maturity is called maturity structure
What are spot curves?
yield on zero-coupon government bonds
What are the 3 types of yield curves?
- upward sloping (spot curve) means long loans have higher yields.
- flat yield curve
- inverted yield curve (shorter bonds have high yields)
What is par rate?
represents the coupon rate for that makes a government security of a given duration trade at par.
What is a par curve?
par curve plots yield to maturity for different maturities for bonds that are priced at par.
What is the formula for par rate per period?
PMT / 100
What is the par rate formula?
100= (PMT/(1+Z1)^1)
+ (PMT(1+Z2)^2)
+ PMT+100(1+ZN)N
z= spot rate
How do notations on forward rates work?
-first number refers to length of forward period in years from today
-second number refers to the tenor of the underlying bond
What is a forward curve?
plots forward rates each having the same maturity. the forward rates is an estimation of what investors expect the short-term interest rates to be
What’s the formula for calculating the implied forward rate?
IFR (a,b) = [((1-Spot Rate B)^ Year for B) / ((1-Spot Rate A)^ Year for A)] ^ (1/(Year B - Year A) -1
What’s the formula for calculating the spot rate from forward rates?
{[(1 + IFR 0,1) * (1 +IFR 1,1)] (^1/N)} -1= ((1+ two year spot rate (aka z)) ^2)
When would a corporate bonds yield be less than the yield of a government bond or negative compared to a yield of a government bond?
if corporate bond contains an embedded option
What is required margin (aka discount margin)?
yield spread over or under a reference rate, reflecting the credit risk of an issuer. change in the required margin come from change in issuers credit risk
What’s the difference between forward rate and spot rate?
spot rate represents the current exchange rate, while the forward rate is a predetermined rate for future transactions
What is the formula for linear interpolation?
lower year spot rate yield + ((year you looking for spot rate - lower year) / (high year- lower year) * (higher year spot rate yield - lower year spot rate yield)
Eg. The current 5-year and 10-year Treasury spot yields are 2.10% and 2.85%, respectively.
Use linear interpolation to calculate the yield on a 7-year security.
2.10% + ((7-5)/(10-5)) * (2.85 -2.10)
What is the one exception to the maturity effect?
the only exception is for low coupon, long-term bonds trading at a discount
