Fixed Income Flashcards
riding the yield curve
when yld curve is UPWARD sloping, holding long-maturity bonds, earns an excess return as the bond “rolls down the yield curve)
swap rate curve
reflect credit risk of commercial banks rather than gov’t
swap market is not regulated by any gov’t
swap curve typically has yield quotes at many maturities
swap spread
swap rate - t-bill
z-spread
when added to each spot rate on the yld curve, makes the pv of a bond’s cf equal to the bond’s market price
appropriate spread measure for option-free corp. bonds, credit CDS, and ABS.
TED spread
3-month libor - 3-month T-bill rate
Libor-OIS spread
amount by which the LIBOR rate exceeds the overnight indexed swap rate.
it’s a useful measure of credit risk and provides an indication of the overall well-being of the banking system.
unbiased expectations theory
pure expectation
forward rates are an unbiased predictor of future spot rates
local expectations theory
preserves the risk-neutrality assumption only for short holding periods, whole over long periods, risk premiums should exist
This implies that over ST period, every bond should earn rf.
liquidity preference theory
investors demand a liquidity premium that is positively related to a bond’s maturity
segmented markets theory
shape of the yld curve is the result of the interactions of supply and demand for funds in diff. market segments
investors in one maturity segment of the market will not move into any other maturity segments.
preferred habitat theory
similar to segmented markets theory, but recognizes that market participants will deviate from their preferred maturity habitat if compensated adequately.
equilibrium term structure models
CIR
Assumes the economy has a natural long-run interest rate (b) that short-term rate converges to.
dr=a(b-r)dt+sigma sqr(r)dz
equilibrium term structure models - Vasicek model
assumes that interest rate volatility level is independent of the level of ST interest rates
constant volatility
dr = a(θ − r)dt + σdz
arbitrage models -Ho-Lee model
is calibrated by using market prices to find the time-dependent drift time that generates the current term structure.
dr(t) = theta dt + σdz
effective duration
sesitivity of a bond’s price to parallel shifts in the bmk yld curve
=BV(-change in yld) - BV(+ change in yld)
/ 2BV0*change in yld
key rate duration
measures bond price sensitivity to a change in a specific par rate, keeping everything else constant
sensitivity to parallel, steepness, and curvature movemtns
measures sensitivity to three distinct categories of changes in the shape of the benchmark yield curve.
binomial interest rate tree framework
lognormal random walk model with 2 equally likely outcomes
pathwise valuation
value of the bond is the avg of the values of the bond at each path
2^(n-1) possible paths
monte carlo forward-rate simulation
uses pathwise valuation and a large number of randomly generated simulated paths
used to value MBS
Value of Call option
=Vs-Vcallable
Value of Put option
=Vputable-Vs
OAS
the constant spread added to each forward rate in a bmk binomial interest rate tree, such that the sum of the pv of a credit risky bond’s cash flows equals its market price
=z-spread - option cost
one-sided duration
when interest rates rise versus when they fall
better at capturing interest rate sensitivity than regular effective durations
when option is at-or-near-the-money, callable/putable bonds will have lower/higher one-sided down-duration than one-sided up-duration
effective convexity
positive for straight and putable bonds
callable bond have negative convexity
BV-+BV+-2BV0
/ (BV*CHANGE IN YLD^2)
value of capped floater
=value of straight floater - value of embedded cap
value of a floored floater
=value of straight floater + value of embedded floor
conversion value
market price of stock * conversion ratio
market conversion price
market price of convertible bond / conversion ratio
market conversion premium/share
market conversion price - market price
minimum value of convertible bond
max(straight, conversion value)
callable and putable convertible bond value
= straight value of bond
+ value of call option on stock
- value of call option on bond
+ value of put option on bond
recovery rate
% recovered in the event of default
LGD=
loss severity (1-recovery rate) * exposure
POD
likelihood of default
CVA
sum of pv of expected loss
% change in Price
-(md)*change in spread
structural models of corp. credit risk
are based on structure of bs and rely on insights provided by option pricing option theory
assumes that rf is not stochastic
Structural models do not account for the impact of interest rate risk of the value of a company’s assets.
value of stock = max (At-K,0)
Value of debt = min(K,At)
value of risky debt
value of rf debt - value of a put option on assets
CVA= value of put option
short a put option on company’s assets for debt investors
reduced form models
do no explain why default occurs
explain when default occurs
default under RF is randomly occurring exogenous variable - the default intensity (pod over the next period)
allow for company fundamentals change as well as when the state of economy changes
credit spread on a risky bond
YTM of a risky bond - YTM of bmk
CDS
CDS buyer get paid when default occur, pays the premium - CDS spread
buyer shorts credit risk
expected loss
harzard rate * LDG
upfront payment by protection buyer
PV(protection leg) - pv(Premium leg)
=(CDS spread - CDS coupon)* CDS duration
profit for protection buyers (%)
change in spread (%) - CDS duration
is said to be short the reference entity’s credit risk and is bearish on the financial condition of the reference entity
naked trade
investor with no exposure to the underlying purchases protection in the CDS market
curve trade
long/short trade where the investor is buying and selling protection on the same reference entity but with diff. maturities
short-term better, buy long-term CDS and selling ST CDS
Changes in the shape of yield curve is explained by (in order of importance):
level, steepness and curvature.
under structure model, owning risky debt is equivalent to a long position in a similar rf bond and
a short position in a pot option on assets of the companys
valuation of bond based on OAS
OAS <0 or < required OAS, overvalued
OAS> required OAS, undervalued
tranched CDS
covers a combination of borrowers but only up to a pre-specified levels of losses, much in the same manner that abs are divided into tranches.
