Fixed Income Flashcards
Current Yield
= annual cash coupon payment / bond price
Disc: CPN < current yield < YTM
Prem: CPN > current yield > YTM
YTM in a bond assumes…
Bond held to maturity
All payments made
Coupon payments reinvested at YTM
Semi-annual pay bond inputs
N = yrs * 2 PMT = coupon/2 i = discount rate/2 FV = par value PV = -amount paid
Zero coupon bonds
Always solved as semi annual pay bonds with PMT = 0
Most price sensitive
Premium bond
Coupon rate > YTM
PV > par
Discount bond
Coupon < YTM
PV < par value
Convexity
Price increase from decrease in yield is larger than price decrease from increase in yield
Maturity effect
Other things equal, value of bonds with longer maturities is more sensitive to a change in YTM
Coupon effect
Other things equal, value of bonds with lower coupon is more sensitive to change in YTM
Calculate the price of a bond one year after issuance if the yield does not change
N = # yrs - 1
For semi-annual pay bond:
N = (#yrs - 1) • 2
All other inputs stay the same
Valuing a bond using spot rates
Given spot rates S1, S2, S3…
Value of bond
= PMT/ (1+S1)
+ PMT/ (1 + S2)^2
+ (Par + PMT) /(1 + S3)^3
Discount each CF to represent value
Matrix pricing
Use YTM of traded bonds of same credit quality to estimate bond YTM
- average of YTMs for same maturity
- linear interpolation to adjust for diff in maturities
Effective yield on a semi - annual pay bond
= [(1 + YTM/2)^2] - 1
Yield -to-first call
Calculate YTM using number if semiannual periods until the first call date and the call price for FV
Option adjusted yield
OAY < YTM for a callable bond because callable bonds have higher yields to compensate bondhders for call option
Forward rates:
1y1y=
1 year rate, 1 year from now
Implied forward rates
(1+ S3)^3 =
(1 + S1) • (1 + 1y1y) • (1 + 2y1y)
(1 + S1) • (1 + 1y2y)^2
(1 + S2)^2 • (1+ 2y1y)
Calculate 2y1y from S2 and S3
2y1y =
(1 + S3)^3 / (1+ S2)^2
FRN quoted margin
Number of bps added to reference rate
FRN required Margin or discount margin
Number of bps required to return price to par at reset date
FRN at discount
Quoted margin < required margin
FRN priced at premium
Quoted margin > required margin
Semi-annual bond basis YTM
= 2 • semi annual yield
= 2 • {[(1 + annual YTM)^1/2] - 1}
Equivalent annual-pay YTM for semi annual pay bond
= [(1 + annual YTM/2)^2] - 1
If YTM for bond increases after purchase and before first CPN, realized return will be:
Higher than YTM at purchase for buy and hold (long)
Lower than YTM at purchase for short period
If YTM for bond decreases after purchase but before CPN, rate of return be
Lower than YTM at purchase if held for long period
Macaulay duration
< # yrs to maturity
= WTD ave time until bondhders relieves cash flows
Modified duration
=Mac dur / ( 1 + YTM)
Approximate modified duration
= (V- - V+) / (2•Vo•chYTM)
Approximate change in price
= -ModDur • change in YTM
Effective duration
Approx change in price given 1% parallel shift in yield curve
For bonds with embedded options
Price value of a basis point
Change in price for a 1 bps change in yield
= abs val(initial price - price after 1 bp change in yield)
= [(V- - V+)/2] * par value * 0.01
Approximate convexity
= (V- + V+ - 2Vo) / (Vo • chYTM^2)
% change in full bond price including convexity
= - annual mod dur (ch YTM)
+ 1/2 • annual convexity • (ch YTM)^2
Option free bond
Interest rate risk = price volatility
Positive convexity
Callable bond
Negative convexity at low yields
Positive convexity at higher yields
Price compression, as yields fall prices rise at decreasing rate bc there is max price on bond
Putable bond
Positive convexity at all yields
Price compression, as yields rise prices at decreasing rate
Debenture
Unsecured and subordinated loans
Bond with no collateral
Four Cs of credit analysis
Capacity
Covenants
Collateral
Character
Repo rates with longer dates
Are higher than with shorter dates
Repo rates with high quality collateral or delivery
Are shorter than counterpart
option-adjusted spread
= z-spread - option value
money duration
= annual modified duration * full price of bond position
duration gap
= macauley duration - investment horizon
