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CFA Level 2 Fixed Income
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Terms in this set (83)
Forward pricing model
F(j,k) = P (j+k) / P (j)
Forward rate model
riding the yield curve
If a yield curve is upward sloping, the investment strategy of buying long term securities, then selling them after a short period. As the bond approaches maturity, it is valued using successively lower yields and, therefore, at successively higher prices.
swap rate curve
Fix rate in an IR swap is called the swap rate. If we consider how swap rates vary for various maturities - we get the swap rate curve.
why swap rate curve is preferred over govt bond yield
1. swap rate reflects the credit risk of commercial banks
2. swap market is not regulated by any government - makes swap rates in different countries more comparable
3. swap curve has yield quotes at many maturities
Swap rate tenor
swap spread
= swap rate - treasury yield
I-spread
The amount by which the yield on the risky bond exceeds the swap rate for the same maturity. It accounts for credit and liquidity risk.
Z-Spread
A spread that when added to each spot rate on the default-free spot curve, makes the present value of a bond's cash flows equal to the bond's market price.
TED spread
The amount by which the interest rate on loans between banks exceeds the interest rate on short-term US government debt. Seen as an indication of the risk of interbank loans.
LIBOR-OIS Spread
The amount by which the LIBOR rate exceeds the OIS rate. It measures the credit risk and an indication of the overall wellbeing of the banking system. Low LIBOR-OIS spread is a sign of high market liquidity and high LIBOR-OIS spread is a sign of unwillingness to lend
OIS (overnight indexed swap)
OIS rate reflects the federal funds rate and includes minimal counterparty risk.
Unbiased Expectations Theory
the theory that the shape of the term structure of interest rates is determined by an investor's expectations about future interest rates
Local Expectations Theory
similar to unbiased expectations theory with one major difference - one exception. Local expectations theory preserves the risk-neutrality assumption only for short holding periods. Risk premiums could exist in the long run.
Liquidity preference theory
States that investors require a risk premium, in addition to expectations about future short term rates for holding longer term bonds
Segmented markets theory
Shape of the yield curve is determined by the preferences of borrowers and lenders which drives the balance between supply and demand for loans of different maturities
Preferred habitat theory
States that the existence of an imbalance between the supply and demand for funds in a given maturity range will induce lenders and borrowers to shift from their preferred habitats to one that has the opposite imbalance.
Equilibrium term structure models
attempts to describe changes in the term structure through the use of fundamental economic variables that drive interest rates e.g. CIR and Vasicek model
Cox-Ingersoll-Ross Model (CIR)
Interest rate movements are driven by individuals choosing between consumption today versus investing and consuming at a later time
change in r = a (b-r) dt + sigma SqRoot(r) dz
Vasicek Model
change in r = a (b-r) dt + sigma dz
difference between Vasicek and CIR is that there is no interest rate term in the second term therefore the volatility doesn't increase as the level of interest rates increase
Arbitrage-Free Models
able to calibrate arbitrage-free models to match current market prices e.g. Ho-Lee model
change in r = Theta x dt + sigma dzt
Effective duration
Measures price sensitivity to small parallel shifts in the yield curve. It's not accurate when the shift is not parallel
Shaping risk
Change in portfolio value due to changes in the shape of the benchmark yield curve.
Key Rate Duration
sensitivity of the value of a security to changes in a single spot rate OR
the approximate % change in the value of a bond in response to a 100 BPS change in the corresponding key rate
Decomposing yield curve
Level - parallel increase or decrease of interest rates
Steepness - long term rate increases while short term rates decrease
curvature - increasing curvature means short- and long-term rates increase while intermediate rate don't change
Two types of arbitrage opportunity
value additivity - when the value of whole differs from the sum of the values of parts
dominance - when one asset trades at a lower price than another asset with identical characteristic
backward induction
the process of valuing a bond using a binomial interest rate tree
adjacent forward rates for the same period
are two standard deviations apart
i(1,L) = i(1,U) * e^(2sigma)
pathwise valuation approach
taking the average value of each scenario. there will be 2^(n-1) scenarios
path dependency
cash flows are path dependent for MBS
Embedded options
allow an issuer to
a) manage interest rate risk and/or
b) issue the bonds at an attractive coupon rate
Bermuda style option
option can be exercised at fixed dates after the lockout period
estate put
allows the heir of an investor to put the bond back to the issuer
sinking fund bonds
require the issuer to set aside funds periodically to retire the bond
call rule
for callable bonds: use lower of price of the bond or call price at nodes
for putable bonds: use higher of price of the bond or put price at nodes
one sided durations
durations that only apply when interest rates rise (or, alternatively when rates fall)
capped floater
contains an issuer option that prevents the coupon rate from rising above a specified maximum rate known as the cap
value of a capped floater = value of a "straight" floater - value of embedded cap
floored floater
the coupon rate does not fall below a specified minimum rate known as the floor
value of floored floater = value of a straight floater + value of the embedded floor
ratchet bonds
Floating-rate bonds whose coupon can only be reset downward.
conversion value
= market price of stock * conversion ratio
straight value
the value of the bond if it were not convertible
minimum value of a convertible bond
greater of its conversion value or its straight value
market conversion
= market conversion price - stock's market price
market conversion premium ratio
= market conversion premium per share / market price of common stock
convertible, noncallable bond value
= straight value of bond + value of call option on stock
callable convertible bond value
= straight value of bond + value of call option on stock - value of call option on bond
Loss given default
value a bond investor will lose if the issuer defaults
PV of expected loss
highest price a hypothetical investor would be willing to pay to an insurer to bear the credit risk of the investment
three ways to measure credit risk
1. credit rating - least accurate, lag market and stable
2. structural model -
3. reduced form model - better than structural model due to flexibility
structural models
Structural models of corporate credit risk are based on the structure of a company's balance sheet and rely on insights provided by option pricing theory
value of risky debt = value of risk-free debt - value of put option on company's assets
reduced form model
rather than explicitly identify factors that contribute to default probability, it use the prices of liquid financial instruments and assume mkt is reasonably efficient and pricing is accurate. Input estimates can be estimated using the hazard rate estimation approach
value of debt
= min (At, K)
hazard rate estimation
technique used to estimate the inputs for reduced form models
term structure of credit spreads
the relationship of credit spreads to debt maturity
credit analysis of ABS
probability of default does not apply to ABS, we model ABS credit risk using the probability of loss, loss given default, expected loss and PV of loss
benefits of securitization
a) reducing funding costs
b) increasing liquidity
fully amortizing loan
each payment includes both an interest payment and a repayment of the principal
partially amortizing
each payment has a component of principal repayment but there is a lump sum of principal (balloon payment) in the end
interest only
no principal payment until the last payment
non-recourse loan
lender has no claim against the assets
recourse loans
lender has a claim against the borrower
mortgage pass-through securities
Bonds representing a claim on the cash flows of an underlying mortgage pool passed through to bondholders.
weighted average maturity (WAM)
equal to the weighted average of the final maturities of all mortgages in the pool weighted by its outstanding principal balance as a portion of the outstanding principal value of all the mortgages in tge oiik
weighted average coupon (WAC)
weighted average of the interest rates of all the mortgages in the pool
two types of prepayment risk
extension risk and contraction risk
extension risk
a risk that prepayments will be slower than expected
contraction risk
a risk that prepayment will be more rapid than expected
balloon risk
the possibility that a commercial mortgage borrower will not be able to refinance the principal that is due at the maturity
single monthly mortality rate (SMM)
monthly measure of the percentage of the mortgage balance available to prepay for a pool of mortgages that is projected to prepay in the given month
conditional prepayment rate (CPR)
annualized measure of prepayments
PSA (public securities association)
describe prepayment rate - above 100 means prepayment is assumed to be faster than benchmark, lower than 100 means slower than benchmark
Internal Credit Enhancements - Reserve Funds
two types:
1. Cash Reserve Funds - cash deposits that come from issuance proceeds
2. Excess Servicing Spread Funds - extra return on the collateral mortgages above that required to make the promised payments to the RMBS Holders
shifting interest mechanism
Junior tranches absorbs more credit risk than the senior tranches. However, this means that prepayment risk for senior tranches increase because they will receive principal payments sooner.
Collateralized Mortgage Obligations (CMO)
securities that are collateralized by RMBS; each CMO has multiple bond classes (CMO tranches) that have different exposures to prepayment risk
Sequential Pay CMO
a popular arrangement for separating the cash flows form a mortgage pool in which each class of bonds is retired sequentially. Short tranche has lower extension risk (principal gets repaid early) and other tranche has lower contraction risk
planned amortization class (PAC)
A PAC tranche is structured to make predictable payments, regardless of actual prepayments to the underlying MBS. PAC tranches have both reduced contraction and extension risk. The risk is shifted to the support tranches.
initial PAC collar
The upper and lower bounds on the actual prepayments rates for which the support tranches are sufficient to either provide or absorb actual prepayments to keep the PAC principal repayments on schedule. E.g. 100-300 PSA, if outside this range then we have a broken PAC
Commercial mortgage-backed securities
back by income-producing real estate, typically in the form of apartments, warehouses, shopping centers etc.
debt-to-service-coverage ratio (DSC)
= net operating income / debt service
collateralized debt obligation (CDO)
structured security issued by an SPV for which the collateral is a pool of debt obligations
CDOs have a collateral manager who buys and sells securities int he collateral pool to generate cash flows. Synthetic CDOs are made up of CDS, structured finance CDOs are made up of ABS, RMBS, CDOs etc.
Call (prepayment) protection
includes loan-level call protection such as prepayment lockout periods, defeasance, prepayment penalty points, and yield maintenance charges
structured finance CDOs
CDO where collateral is ABS, RMBS, other CDOs and CMBS
synthetic CDOs
collateral is a portfolio of CDS
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