Fixed Income Flashcards
Expected Loss
Expected Loss = Default Probability x Loss severity given default
Loss Severity = 1 - Recovery Rate
Cross Default Provisions
Events of default such as non-payment of interest on one bond trigger default on all outstanding debt, implies the same default probability for all issues.
Notching
Specific issues assigned different credit ratings for an issue from the same issuer due to a ratings adjustment methodology.
Structural Subordination
Can arise when a corporation with a holding company structure has debt at both its parent holding company and operating subsidiaries.
The Four C’s of Credit
Capacity
Collateral
Covenants
Character
Bond Indenture
The governing legal credit agreement and is typically incorporated by reference in the prospectus.
Return Impact
Return Impact = -Modified Duration x Change in Rate
Return Impact for Larger Rate Changes
Return Impact = (-Modified Duration x Change in Rate) + 1/2Convexity x (Change in in Rate)^2
The Swap Rate
The fixed rate in an Interest Rate Swap
Swap Spread
Swap Spread = Swap Rate - Government yield on a bond with the same maturity
Effectively, the swap spread reflects the risk of the counterparty to the swap failing to satisfy its obligation.
The Four Theories of the Term Structure of Interest Rates
1) Pure Expectations Theory
2) Liquidity Preference Theory
3) Preferred Habitat Theory
4) Market Segmentation Theory
Pure Expectations Theory
Postulates that no systematic favors other than expectations of future interest rates that affect forward rates.
Liquidity Preference Theory
States that investors will hold longer-term maturities if they are offered a long-term rate higher than the average of expected future rates by a risk premium that is positively related to the term maturity.
Preferred Habitat Theory
Adopts the view that the term structure reflects the expectation of the future path of interest rates as well as a risk premium, but rejects the assertion that the risk premium must rise uniformly with maturity.
Percentage Change in Yield
X = 100[Ln(yt/yt-1)]
yt = yield today Yt-1 = yield in previous period
Z-Spread
The spread that when added to all of the spot rates will make the present value of the bond’s cash flow equal to the bond’s market price.
Minimum Value of a Convertible Security
The greater of its conversion value or its value without the conversion option.
Conversion Value = market price of common stock x conversion ratio
Market Conversion Price
Market Conversion Price = market price of convertible security/conversion ratio
Market Conversion Premium Ratio
Market Conversion Premium Ratio = market conversion premium per share/market price of common stock
Premium Payback Period
Premium Payback Period = Market conversion premium per share/favorable income differential per share
Favorable Income Differential Per Share
Favorable Income Differential Per Share = [coupon interest - (conversion ratio x common stock dividend per share)]/conversion ratio
Value of Convertible Security
Value of Convertible Security = Straight Value + value of call option on stock - value of call option on bond
Curtailment
When a mortgage prepayment is not for the entire outstanding balance.
Conforming Mortgages
If a loan satisfied the underwriting standards for inclusion as collateral for an agency mortgage-backed security. Noncomforming loans do not meet the criteria and are used in Non-Agency MBS.
Unspecified Pools (MBS)
Trades of pools of mortgage backed securities that are ‘unspecified’ are trades that occur before any information about the pool is released. Also known as TBA’s. The two parties agree on the agency, program, coupon, face value, price, and settlement.
Pool Factor
The percentage of the pool that is still outstanding.
Single Monthly Mortality (SMM)
SMM = prepayment in month/(beginning month balance - scheduled prepayment for the month)
Conditional Prepayment Rate (CPR)
Ignoring scheduled principal payments, the CPR is the approximately the % of the outstanding mortgage balance at the beginning of the year that will be prepaid by the end of the year.
PSA
Expressed as a monthly series of CPRs. 50 PSA means half of the monthly CPR; 150 PSA means 1.5x of the monthly CPR.
Factors Affecting Prepayment Behavior
1) Prevailing mortgage rate
2) Housing turnover
3) Characteristics of the underlying residential mortgage loans
Accrual Tranche
Also know as Z Tranche, has appeal to investors who are concerned with reinvestment risk. Allocates interest payments to pay down other tranches in sequential order.
Non-Agency Mortgages
Can be for any type of real estate property. There are securities backed by 1-4 single family residential mortgages and can include home equity loans and manufactured housing.
Agency Mortgage Underwriting Standards
1) the maximum loan to value
2) the maximum payment to income
3) the maximum loan amount
Non-Agency mortgages are loans that do not meet the criteria in the above specifications.
Commercial Mortgage-Backed Securites
Securities backed by pools of commercial mortgage loans on income producing property - multifamily properties, office buildings, industrial properties, shopping centers, hotels, and health care facilities.
Non-Recourse Loans
Loans that the lender can ONLY look to the income of the property as recourse, not the borrower.
Debt Service Coverage Ratio (DSC)
DSC = NOI/debt service
CMBS Call Protection
Protection at Loan Level
1) prepayment lockout
2) defeasance - the borrower puts funds in a portfolio of treasuries that replicates the cash flows that would exist in the absence of prepayments
3) prepayment penalty
4) yield maintenance charges - make whole charge, makes it so the borrower doesn’t refinance just to get a lower rate somewhere else
Average Life (Formula)
Average Life = sum of month x principal prepay/[12(size of tranche)]
External Credit Enhancements
1) monoline insurance company
2) letter of credit
Internal Credit Enhancements
1) reserve funds
2) overcollateralization
3) senior/subordinate structures
SMM for ABS
SMM = ABS/[1 - (ABS x (M - 1))]
M = number of months after loan origination
ABS = absolute prepayment speed
Collateralized Debt Obligations (CDO)
A security backed by a diversified pool of debt obligations. When a security is backed a diversified pool of loan obligations, it is known as a CLO.
Cash CDO
A CDO backed by a pool of cash market debt instruments.
Synthetic CDO
A CDO where the investor has the economic exposure to a pool of debt instrument, but this exposure is realized via a credit derivative instrument.
Bond Equivalent Yield
BEY = 2[(1 + i)^6 - 1]
The formula for annualizing the cash flow for a monthly pay product.
Option Cost
Option Cost = Z-Spread - OAS
Cash Flow Duration
Computed assuming that if interest rates are changed, the prepayment rate will change when computing the new value.
Positive Butterfly (Shift in Yield Curve)
The yield curve becomes less humped (ie: has less curvature). This means that if yields increase, the yields in the short and long maturity sectors increase more than yields in the intermediate maturity sector.
Negative Butterfly (Shift in Yield Curve)
The yield curve becomes more humped (ie: has more curvature). If yields increase, yields in the intermediate maturity sector will increase more than yields in the short and long maturity sectors.
Implied Volatility
Estimating yield volatility based on the observed prices of interest rate options and caps.
Zero Volatility Spread
The spread that will make the present value of the cash flows from the mortgage backed security when discounted at the Treasury spot rate plus the spread equal to the price of the security.
Positive Butterfly (Shift in Yield Curve)
The yield curve becomes less humped (ie: has less curvature). This means that if yields increase, the yields in the short and long maturity sectors increase more than yields in the intermediate maturity sector.
Negative Butterfly (Shift in Yield Curve)
The yield curve becomes more humped (ie: has more curvature). If yields increase, yields in the intermediate maturity sector will increase more than yields in the short and long maturity sectors.
Implied Volatility
Estimating yield volatility based on the observed prices of interest rate options and caps.
Zero Volatility Spread
The spread that will make the present value of the cash flows from the mortgage backed security when discounted at the Treasury spot rate plus the spread equal to the price of the security.
