Fixed inc Flashcards
PVfull
PVfull = PVflat + Accrued Interest
Periodicity
(1+APRm/m)^m = (1+APRn/n)^n
Discount basis
Pv=Fv(1-t/T DR)
Disc rate = t/T[(fv-pv)/fv]
Add on basis
Pv = fv/ (1+t/T AOR)
AOR = T/t[(fv-pv)/pv)]
Forward curve
2y1y
When what
2 year bond for 1 year
(1+r1)(1+implied forw rate)=(1+r2)^2
Types of yield
True yield - weekends not included
Current yield - annual PMt/PVflat
Simple yield - (ann pmt+st amort of gain/loss)/PVflat
Float Rate Note - coupon tied to libor
Libor
Libor + Quoted Margin (QM) - issuer (spread) + discount margin(DM) - market
pV = [(Libor + Qm) x Fv)/2]/m/[1+ ((Libor+DM)/m)]^n
I/y = libor + dm / n
Properties of a bond
Longer bond - more volatile
Lower pmt - more volatile
Macalay Duration
Ęweighted CF/ PVfull
Shows how long we have to keep bond so extra valuation offset the loss of reinvestmnt
Modified Duration
And
Approx Mod Dur
Annualized Macalay Dur/ (1+r)
Approx mod dur = pv- - pv+ / 2xchange in yield x PVo
Effective Duration
Pv- - Pv+ / 2xchange in curve xPVo
Curve is sensitive to benchmark yield (govt, spot, par)
Key rate Duration
Pv- - Pv+ / 2x change in rate xPVo
Duration at specific maturity of the yield curve to get %change in portfolio value
ĘKey Rate Dur = Eff Dur
Properties of Duration
Longer Time to Maturity leads to longer Duration
Lower coupon leads to longer Duration
Lower Yield to Maturity longer Duration
But its all subject to interest rate risk
Money Duration
Annual Modified Duration x PVfull
PVfull
PVfull= -money Duration x change in Yield
If 2 bonds all equal but one has lower coupon, which one is more price volatile?
If 2 bonds all equal but one has longer time to Maturity , which one is more price volatile?
Pmt lower more volatile
Ttm longer more volatile
PV per Basis Point
Pv- -PV+ /2
Convexity adjustment
Annual convexity
Pv- + Pv+ - 2PV / PVo (yield)^2
%change in PV full
(-annual Mod Dur x change in yield) + (1/2 money convexity x (yield)^2)
Change in PV full
(-Money Duration x change in yield) + (1/2 money convexity x (yield)^2)
Single Month Maturity Rate
Smm = monthly prepmt/beg amount - pmts
Prepmt amount
Smm x (end balance - pmts)
CPR
1- (1-smm)^12
What happens with ABS if int rates decr?
What if rates incr?
Refinance incr, prepmt incr, Psa incr, av life decr. Contraction risk
Refinance decr, prepmt decr, psa decr, av life incr. extension risk
Fully amort bond
Pmi + interest
Partially amort bond
Int + pmt + baloon pmt at Maturity
Callable bonds
Called at = pv of (int+fv)/govt ytm + spread
If interest rate drops company calls the bond
Convertable bonds
Conversion Ratio = Fv/ convert prixe
Conversion Val = Stock price x conv ratio
Conversion premium = BOnd Price - (stock price x conv ratio)
Conversion parity = B = (StP x ratio)
Warrants
Are not an embedded option
Credit enhancement
Internal - subordination (issue 85% senior, 15% junior)
- over collateralization ( put more collateral than tot FV of the bonds)
- excess spread
External - surety bond(issued by insurance comp)/ guarantee(issued by a bank)
- letter of credit
Time tranche
Each receives interest but principal goes a1 then a2 and so on
Redistributes prepmt risk
Collateriz Mortgage oblig
CMO only can do a time tranch
To protect from estension risked
Has non agency credit risk
To avoid it can do internal credit enhancement:
Credit tranch, build a reserve fund, overcollaterize
Or do external credit enhancement - get a guarantee
Rmbs
Loan to value ratio = mortgage/ property value
Credit quality of a mortgage holder is important
Planned Anort Class (pac)
Offers contract and extension risk
But support tranche gets all the risk
Cmbs prepmt risk
Non-recourse loan!!
Almost avoided by prep lockout
Prepmt penalty points
Yield maint charge
