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Fixed Income
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Terms in this set (212)
The expected return will be equal to the bond's yield only when:
The bond is held to maturity
Coupon and principal received on-time; and
All coupons reinvested at the original YTM
Forward pricing model values...
forward contracts using arbitrage free pricing
For a bond with a single cash flow remaining, par rate =
spot rate
Riding the yield curve states ff the yield curve is upward sloping, investor will...
purchase bonds with higher maturity than their holding period
Typically, par rates are used to generate spot rates using...
bootstrapping
Swap spread =
swap fixed rate - treasury yield of same maturity
I-spread =
bond rate - interpolated swap fixed rate of same maturity
Z-spread =
constant spread added to spot rate curve to force PV(CF) = market price of bond
TED Spread =
LIBOR - T-bill yield of same maturity
Libor-OIS spread =
LIBOR - overnight indexed swap rate
index rate can be federal funds rate
By and large, wider spread measures are indicative of higher...
credit and liquidity risks
Which spread is not appropriate for bonds with embedded options
z-spread
What does I-spread reflect
credit risk relative to LIBOR
TED spread is seen as an indication of...
the level of credit risk in the economy
Libor-OIS is a measure of...
credit risk and an indication of wellbeing on the banking system
Unbiased expectations theory
Forward rates are an unbiased predictor of future spot rates. Also known as the pure expectations theor
Local Expectations Theory
preserves the risk-neutrality assumption only for short holding periods, while over longer periods, risk premiums should exist
implies that over short periods every bond should earn the risk free rate
Liquidity preference theory
Investors demand a liquidity premium that is positively related to a bond's maturity
Segmented markets theory
The shape of the yield curve is the result of the interactions of supply and demand for funds in different market
Preferred Habitat Theory
It is similar to the segmented markets theory, but recognizes that market participants will deviate from their preferred maturity habitat if compensated adequately
Methods of Measuring Yield Curve Sensitivity include
Effective duration
Key rate duration
Sensitivity to parallel, steepness, and curvature movements
Effective duration measures...
price risk for small parallel shifts in yield curve
Key rate duration is used to...
quantify price sensitivity to non-parallel yield curve shifts
price sensitivity to 1% change in a single par rate, other par rates constant
The term structure of interest rate volatility is the graph of...
the old volatility versus maturity
Short-term rates are less volatile than long term rates (T/F0
F, more volatile
Short-term rates more closely linked to...
monetary policy
Long-term rates more closely linked to...
real economy and inflation
Two-thirds of the variation in short and intermediate term yields is explained by _______ with the remaining equally explained by...
inflation
economic growth and monetary policy
Bearish flattening caused by...
increase in short-term rates during expansionary times
Bullish steepening caused by...
decrease in short-term rates during recessionary times
Expansionary Fiscal policy causes increase in yield (T/F)
T
During periods of market turmoil, a flight to safety may reduce long-term government bond yields, resulting in a...
bullish flattening
In expectation of a rise in rates, investors will lower the duration of their bond portfolios (T/F)
T
Bullet Portfolio
a portfolio made up of a single maturity
Barbell Portfolio
a portfolio with both long and short maturities
Compared to a yield curve based on government bonds, swap rate curves are (more/less) comparable across countries and have a (greater/lesser) number of yields at various maturities
more
greater
Learn how to do bootstrap calculations
(R28 - Q1 #4)
okay master
Option pricing models assume a constant _________ of interest rates but not a constant _________ of interest rates
volatility
level
Market evidence shows that short-term holding period returns from investing in long-maturity bonds exceed the short-term holding period returns from investing in short-maturity bonds (T/F)
T
Does arbitrage-free valuation allow for dominance
no
What are the two types of arbitrage opportunities
value additivity
dominance
Valuation of bonds using a zero-coupon yield curve (also known as the spot rate curve) is suitable for...
option-free bonds
The tree is calibrated such that:
(1) the values of benchmark bonds using the tree are equal to the bonds' market prices
(2) adjacent forward rates at any nodal period are two standard deviations apart
(3) the midpoint for each nodal period is approximately equal to the implied one-period forward rate for that period
Lognormal random walk based on...
assumed volatility in interest rates
The process of valuing a bond using a binomial interest rate tree is...
backward induction
How many paths in a binomial tree
2^(n-1)
The binomial tree backwards-induction process is appropriate for securities with path-dependent cash flows (T/F)
F, inappropriate
Types of interest rate models:
Equilibrium term structure models
Arbitrage-free models
Other models (Gauss+)
Types of Equilibrium term structure models
The Vasicek model
The Cox-Ingersoll-Ross model
(single factor models)
Types of Arbitrage-free models
The Ho-Lee model
The Kalotay-Williams-Fabozzie (KWF) model
The Vasicek model suggests...
that interest rates are mean reverting to some long-run value
The Vasicek Model formula
The Cox-Ingersoll-Ross (CIR) Model formula
The Cox-Ingersoll-Ross (CIR) Model improves upon the ____ model in the...
Vasicek
stochastic term
Under the Vasicek model:
Volatility does not increase as the level of interest rates increase
Interest rates could become negative
Under the CIR model:
Volatility related to the current level of the interest rate (prevents negative rates)
The Ho-Lee Model formula
no pic for this :(
The Ho-Lee Model can be used to...
price zero-coupon bonds and determine the spot curve
What does the theta is the Ho-:Lee model represent
a time dependent drift
Katotay-WIliam-Fabozzi (KWF) Model fomula
Kalotay-Williams-Fabozzi (KWF) model assumes ______ volatility and a constant drift, but assumes that the short rate follows a ______ distribution
constant
lognormal
Gauss+ is a multifactor model that incorporates...
short-, medium-, and long-term rates
Gauss+. the long-term rate is designed to be...
mean reverting and depends on macroeconomic variables
Gauss+. the medium-term rate...
reverts toward the LT rate
Gauss+. the short-term rate deponds on...
central bank policy action and does not have a random component
A binomial model or any other model that uses the backward induction method cannot be used to value a mortgage-backed security (MBS) because:
the cash flows for the MBS are dependent upon the path that interest rates follow
Why is the backward induction methodology used to value a bond rather than a forward induction scheme?
The price of the bond is known at maturity
Estate puts contingent on...
death of investor
What do sinking funds do
Set aside funds to retire the bond
Value of a call option =
Value of a put option =
value of a putable bond - value of a straight bond
How does an increase in interest rate volatility affect value call and put options
increase both
When the yield curve flattens, the call option becomes ______ valuable while the put option becomes _____ valuable
more
less
The option-adjusted spread (OAS) is the...
constant spread added to each forward rate in a benchmark binomial interest rate tree, such that the sum of the present values of a credit risky bond's cash flows equals its market price
When an analyst uses a lower-than-actual level of volatility, the computed OAS for a callable bond will be too...
under or overpriced?
high
under
Effective duration =
Duration(callable or puttable) X Duration(straight)
<=
Duration(zero) X bond maturity
relatively equal
Duration(fixed rate) X bond maturity
<
Duration(floater) X time spent (years) to next rest
relatively equal
Callable Bond with option ______ will have highest key rate durations corresponding to their maturity
deep out of the money (low coupon rate
Putable bond with option ______ will have highest key rate duration corresponding to their maturity
deep out of money (High coupon rate)
Value of capped floater =
value of straight floater - value of embedded cap
Value of floored floater =
value of straight floater + value of embedded floo
Conversion ratio:
number of shares per bond
conversion value =
market price of stock × conversion ratio
Market conversion price:
effective price per share when converting
Market conversion premium =
Market conversion price - market price of stock
Market conversion premium ratio =
market conversion premium / market price
Premium over straight value =
(MV of bond / straight value) - 1
Stocks vs. CV bond:
Stock price goes down:
Stock price goes up:
Stock price flat:
CV bond outperforms stock
stock outperforms CV bond
CV bond outperforms because of coupons (assuming no change in rates or credit risk)
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
If the yield curve goes from flat to downward sloping, the bond with the highest price impact is least likely to be a _____ bond
callable
An analyst has constructed an interest rate tree for an on-the-run Treasury security. The analyst now wishes to use the tree to calculate the convexity of a callable corporate bond with maturity and coupon equal to that of the Treasury security. The usual way to do this is to calculate the option-adjusted spread (OAS) and then...
shift the Treasury yield curve, compute the new forward rates, add the OAS to those forward rates, enter the adjusted values into the interest rate tree, and then use the usual convexity formula
Does using on the run rates remove differences of credit risks in spreads
yes
Does using on the run rates remove liquidity risk
no
The duration formula given will calculate the ______ change in price for a 100 basis point change in yield,
percentage
The OAS accounts for compensation for_______ and _______ risk
credit
liquidity
If the yield curve goes from flat to upward sloping, the bond with the highest price impact is least likely to be a _____ bond
putable
Hazard rate =
= initial probability of default (conditional probability of default)
Probability of survival =
1 − the cumulative conditional probability of default
value of comparable risk-free bond - value of risky bond =
CVA
Assumed recovery rate and risk-neutral probability of default are negatively correlated (T/F)
F, positively
Credit scoring is used for...
small businesses and individuals
Credit ratings are also issued for...
corporate debt, asset-backed Securities, and government and quasi government debt
The FICO score in the US factors in...
the age of accounts, delinquencies, utilization of lines of credit, types of accounts, and number of hard inquiries
Apart from a letter grade, credit ratings also specify...
Outlook (positive, negative, or stable)
(credit migration) change in percentage of price =
-(modified duration of the bond) x (change in spread)
Value of stock =
max(0, assets - value of debt)
Value of debt =
value of assets - value of equity
= min(assets, value of debt)
Value of risky debt =
value of risk-free debt - value of a put option on the company's assets
Value of put option =
CVA
Structural models of corporate credit risk are based on...
the structure of a company's balance sheet
Structural models of corporate credit risk rely on...
insights provided by option pricing theory
Stock of a company with risky debt outstanding can be viewed as a...
call option on the company's assets
Debt investors can be thought of as being...
short a put option on company assets
Characteristics of reduced form models
Treats defaults as exogenous
Does not explain why default occurs
Uses default intensity estimated using regression model
Allows linkage of default intensity, risk-free rate, and recovery rate to the state of the economy
Structural Model Strengths
provides an economic rationale for default and explain why default occurs
Structural Model Weakness
Company assets are not actually traded and, hence, their value is not directly observable
It assumes a simple balance sheet structure
Reduced Form Strengths
Do not assume that company assets trade
Default intensity is allowed to fluctuate as company fundamentals change, as well as with business cycle
Reduced Form weaknesses
Do not explain why default occurs
Treats defaults as random surprises
Credit spread is a function of...
default probability and recovery rate
Spreads change as expectations about ______ change
state of the economy
Credit spread =
YTM of a credit risky bond - YTM of a risk-free bond
Term structure of credit spread represents the relationship of...
credit spreads to debt maturity
Term Structure Credit Spread is useful for...
relative pricing and pricing of new issues
Higher-rated sectors have _______ term structures
flatter
The shape of the term structure is influenced by:
Quality (higher rated segments have flatter credit spread curve);
Overall economic conditions (spreads narrow during economic expansions and widen during cyclical downturns);
Market demand and supply; and
Equity market volatility.
covered bonds are...
senior, secured bonds backed by a collateral pool as well as by the issuer
Covered bonds do not have recourse rights (T/F)
F, they do
Securitized debt entails financing of specific assets (e.g., auto loans, credit card receivables, mortgages) usually via a...
bankruptcy-remote SPE
Analysis of securitized debt includes analysis of...
collateral pool, servicer quality, and structure
Secured debt offers higher... for investors
diversification and risk premium
FICO scores are higher for those with:
(a) longer credit histories (age of oldest account)
(b) absence of delinquencies
(c) lower utilization (outstanding balance divided by available line)
(d) fewer credit inquires
(e) a variety of types of credit used
Do credit scores reflect default risk AND credit risk?
yes (credit risk is default risk - i think)
Is the coupon rate included in exposure
yes
Are returns for a bond depended on the bonds rating
no
An ABS security backed by a highly granular collateral pool composed of hundreds of clearly defined loans, analysis of collateral pool can be done using...
summary statistics for analyzing credit risk
What strategy would be most appropriate use of CDS given an expectation of credit curve steepening?
a curve steepening trade
In an index CDS, the lower the credit correlation, the cheaper the premium (T/F)
T
If an investor anticipates a flattening curve, they can exploit this possibility by positioning himself _________ in the short term CDS while going _________ in the long-term CDS
short (buying protection)
long (selling protection)
CDS pay off upon occurrence of a credit event, which includes
failure to pay, and bankruptcy
Restructuring refers to events such as:
reduction or deferral of principal or interest
change in the currency in which principal or interest will be paid
change in an obligation's seniority or priority
A credit default swap (CDS) is a contract between two parties in which one party...
purchases protection from the other party against losses from the default of a borrower
The protection buyer pays the seller a premium called the...
CDS spread
A CDS on an equally weighted combination of borrowers is called an...
index CDS
Credit ______ is important factor in pricing of index CDS
correlation
ISDA Credit Events include:
bankruptcy
failure to pay
restructuring
The factors that influence the pricing (i.e., spread) of CDS include...
the probability of default, the loss given default, and the coupon rate on the swap
Upfront payment (from protection buyer) =
PV(protection leg) - PV(premium leg)
PV(protection leg) is the...
expected cash flows paid by protection seller (upon default)
PV(premium leg) is the...
expected coupon payments made by protection buyer
Upfront premium % (from protection buyer) ≅
(CDS spread - CDS coupon) x duration buyer
Price of CDS ≅
$100 - upfront premium %
Profit protection buyer ≅
change in spread (in bps) x duration x notional principal
Determinants of CDS Spread
probability of default
hazard rate
loss given default
Uses of CDS
naked CDA
long sleeve short trade
curve trade
basis trade
synthetic CDO (using CDS instead of bounds)
Naked CDS
an investor with no underlying exposure buys CDS protection (bets on default)
Long sleeve short trade
an investor purchases protection on one reference entity, while selling protection on another. Investors is betting that the difference in credit spreads will change to the investors Advantage
Curve trade
a long sleeve short trade where the investor is buying and selling protection on the same reference entity but with a different maturity
Basis trade
exploiting credit spread differences between the bond market and CDS market
Synthetic CDOs
constructed using CDS (rather than actual bonds as in a cash CDO)
Flattening curve trade you should...
buy protection in a short term CDS and sell protection in a long maturity CDS
Steepening curve trade you should...
go short a long term CDS and a long a short term CDS
________ in CDS market shares makes CDS /= CDS spread
Standardization
A bond's expected rate of return will only be equal to its yield to maturity if:
the bond is held to maturity
the bond is option free and does not default
coupons are reinvested at the yield to maturity (this one rarely happens)
________ banks are more likely to use the swap rate curve as an interest rate benchmark
wholesale
________ banks are more likely to use the government bond yield curve as an interest rate benchmark
retail
Swap rates reflect the ______ risk for private commercial banks
credit
The OAS spread is used to adjust (compensate) for which types of risks relative to the bond's benchmarks
credit and liquidity risks
OAS computation is not affected if an option is out-of-the-money (T/F)
F, in-the-money
What is the OAS affected by
the assumed volatility of the interest rate tree
If the OAS is computed too high, then the computed value of the embedded options is too...
high as well
If the yield curve goes from upward sloping to more flat, a bond with a ____ option will see the least amount of appreciation
call
If an option-free bond is trading at par, the bond's ________ rate is the only one affects the bond's value
maturity-matched
For a callable bond with a low coupon rate, the rate corresponding to the _______ will be the bond's cost cirtical rate
first call date
(same thing about maturity-matched rate? - figure out what this rate is)
Do reduced forms or structural model forms use insights from option pricing models
structural
Why can't structural models be estimated using maret prices
because company assets are not traded
How is OAS interpreted
the average spread over the treasury SPOT curve
Nominal spread is measured relative to what
treasury yield curve
What is the restriction on the relationship between changes in yield and the OAS
there is no restriction
Does OAS include compensation for option risk
no, bc it is option adjusted
What does OAS compensate for
taking credit and liquidity risk
What does nominal spread compensate you for
liquidity, credit, and option risk
For a convertible bond with a call provision, with respect to the bond's convertibility feature and the call feature, the Black-Scholes option model can apply to:
The Black-Scholes model applies to the convertibility feature just as it does to the common stock. The Black-Scholes model is not appropriate for the call feature because the volatility of the bond cannot be assumed constant.
For a zero coupon bond (or very low coupon), are the key rate durations for maturity points that are shorter than the maturity of the being being analyzed usually negative or positive
negative
How do you measure expected exposure
it is the remaining cash flows on the bond
What are the assumptions of reduced form models
the risk free rate is stochastic
the state of the economy is stochastic and depends on macroeconomic variables
the probability of default (or default intensity) and the recovery rate depend on the state of the economy and are constant
Under structural models: value of risky debt =
value of risk-free debt - value of put option on company assets
Is the swap rate regulated by governments
no
Is the swap market effected by sovereign credit risk
what about technical risk factors
no to both
If the yield curve is downward sloping, the TED spread is mostly what?
why?
positive
TED = LIBOR - T-Bill yield and TED would be positive to reflect the higher credit risk
Do reduced form and structural models take into account the complex structure of an ABS
yes
Do wholesale banks have a lot of exposure to the swap market?
what about retail banks
yes
no
What curve is most appropriate for retail banks?
what about wholesale banks?
spot curve
swap rate curve
How do you compute effective convexity using the binomial model
yield curve has to be shifted upward and downward in a parallel manner and the binomial tree recalculated each time
Under which markets theory will investors in one maturity segment of the market will not move into any other maturity segments
segmented markets theory
The isolated structure of securitized assets allow what to the issuer
higher leverage and
lower cost
greater diversification
more stable cash flows
higher risk premium
When do CDSs change in value
whenever the credit quality of the reference entity changes
Do CDS spreads increase when leverage increases?
yes, bc the chance of default is higher with higher leverage
Does an increase in the probability of default increase CDS spreads
yes
How do you calculate the swap fixed rate
(
different from swap spread
)
SFR(n)*(Par1 + Par 2 +...+ Par(n)) + Par(n) = 1
Volatility in short-term rates is most likely related to uncertainty about what
monetary policy
When expected spot rates are less than the forward rates priced by the market, are bonds under or overvalued
undervalued
If rates are upward sloping, what is the relationship between spot, forward and yield curves
highest to lowest:
forward
spot
yield
When does riding the yield curve make profit
when the yield curve is upward sloping and stable (will lose money if it steepens sufficiently)
What do you do to calculate the duration of an on-the-run treasury security using a binomial tree
parallel shift up and down of the yield curve
Under the liquidity theory, does the yield curve have to be upward sloping
no, it may take any shape
Does Monte Carlo require the security to path independent
no, they can be path dependent
Does Monte Carlo require an input for an assumed level of volatility
yes
Can Monte Carlo incorporate bounds for interest rates to force mean reversion of rates
can binomial model do this?
yes
no
What causes the swap spread to increase
an increase in the credit spread embedded in the reference
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