Risks, Ratios and Yield Curves

Default Risk, Credit Spread Risk,
and Downgrade Risk
default risk - the risk that the borrower will not repay the
obligation
credit spread risk - the risk that the credit spread will increase
and cause the value of the issue to decrease and/or cause the
bond to underperform its benchmark.
downgrade risk - the risk that the issue will be downgraded by
the credit rating agencies, which will also cause the bond price
to fall, and/or cause the bond to underperform its benchmark.

Study Session 14, Reading 42

Sources of information to asses
the default risk of a bond
1. Credit Rating
2. Rating Watch
3. Rating Outlook


Four Cs of credit analysis
1. Character - management’s integrity and commitment to

meet obligations
2. Covenants - the terms and conditions, the borrowing and
lending parties have agreed to as part of the bond issue
Two types of Covenants
i.
Affirmative covenants
ii. Negative covenants

3. Collateral - the assets offered as security for the debt as well

as other assets controlled by the issuer
4. Capacity - to the corporate borrower’s ability to generate
cash flow or liquidate short-term assets to repay its debt
obligations.

Factors to Evaluate the Capacity
to Pay
Industry trends
Regulatory environment
Operating and competitive position
Financial position and sources of liquidity
Company structure
Parent company support agreements
Special event risk


Factors to Evaluate the financial
position and sources of liquidity
Working capital position of the firm
Dependable cash flow
Back up facilities
Securitized assets
Third party guarantees


Credit Analysis with Ratios
Solvency Ratios
 Current Ratio = Current Assets / Current Liabilities
 Acid Test Ratio = (Current Assets – Inventories) / Current

Liabilities

 Capitalization or Financial Leverage Ratios
 Long term debt to capitalization ratios = Long term debt / (Long

term debt + Minority Interest + Shareholders common and
preferred equity )
 Total debt to capitalization ratios = (Current Liabilities + Long term
debt) / (Current Liabilities + Long term debt + Minority Interest +
Shareholders common and preferred equity)

Credit Analysis with Ratios (cont.)
Coverage Ratios
 EBIT Coverage Ratio = EBIT / Annual Interest Expense
 EBITDA Coverage Ratio = EBITDA / Annual Interest Expense
Du Pont Analysis
 ROE = Net Income / Shareholders equity = ( Net Income / Sales) *

(Sales/Total Assets) * (Total assets / Shareholders equity)


Cash Flow Measures Used by S&P
Funds from operations = Net Income + Depreciation +/- other

non cash items
Operating cash flow = Funds from operations + decrease
(increase) in non current assets – increase (decrease) in non
current liabilities
Free operating cash flows = Operating cash flow – capital
expenditures
Discretionary cash flows = Free operating cash flow – cash
dividends
Pre-financing cash flows = Discretionary cash flows –
acquisitions + asset disposals + other sources

Ratios Used by S&P
Coverage Ratios (the higher the ratio, the stronger the

issuer’s capacity to pay):
 Funds from operations / total debt
 Funds from operations / capital spending requirement
 (Free operating cash flow + Interest) / Interest
 (Free operating cash flow + Interest) / ( Interest + Annual
Principal Repayment)
Leverage Ratio ( the lower the ratio, the stronger is the
issuer’s capacity to pay)
 Debt Payback Period = Total debt / Discretionary cash flows

Two Areas to Analyse High-Yield
Issuers
Debt Structure Analysis - includes the following types of

issues: bank debt, reset notes, and senior and subordinated
debt (which may be zero coupon bonds).

Corporate Structure Analysis - Debt is borrowed at the parent

level, and funds to pay the obligation in the future are
obtained from operating subsidiaries


Credit Analysis of Asset Backed
Securities
Collateral Credit Quality - Rating agencies evaluate whether the
collateral is of sufficient quality to be able to provide cash
flows to pay principal and interest over the life of the issue
Seller/ Servicer Quality - Rating agency looks at the servicer’s
performance history, experience, underwriting standards
adopted for loan originations, servicing capabilities (including
databases, systems, and personnel), financial strength, and
growth relative to its competitive and business environment.


Credit Analysis of Asset Backed
Securities (cont.)
Cash Flow Stress and Payment Structure - Rating agencies
analyses cash flow projections under different scenarios
related to losses, delinquencies, and economic conditions to
assess how these cash flows are distributed to the various
tranches (bonds) in the asset-backed security structure.
Legal Structure - A firm that securitizes assets, , in the event of
bankruptcy, the courts will not apply the cash flow from the
collateral toward satisfaction of general corporate liabilities


Risk Considerations
for Tax Backed Debt
Issuer’s debt structure
Budgetary policy
Local tax and intergovernmental revenue availability
Issuer’s socioeconomic environment


Risk Considerations
for Revenue Bonds
Limits of the basic security
Flow of funds structure
Rate, or user charge, covenant
Priority-of-revenue claims
Additional Bonds Test


Economic risk factors in evaluation
of Sovereign Ratings
Economic and income structure
Prospects for economic growth
Degree of fiscal flexibility
Public debt burden
Monetary policy and price stability
Balance of payments flexibility
External debt and liquidity


Political risk factors in evaluating
Sovereign Ratings
Form of government and degree of citizen participation in the

political process.
Political stability and orderliness of leadership or political
party succession.
Degree of national agreement on economic policy goals.
Integration of its economy in global trade and financial
systems.
Internal and external security risks.


Local Currency Ratings
and Foreign Currency Debt Ratings
Factors used in analysis of local currency debt ratings:
 political stability and the extent of participation by the populace in





the political process
income base and growth along with economic infrastructure
tax discipline and budgetary record
monetary policy and the rate of inflation
the government debt burden and debt service experience

Factors used in the analysis of foreign currency debt ratings:
 country’s balance of payments
 the composition of external balance sheet relative to its external

debt (foreign currency) obligations.


Multiple Discriminate Analysis (MDA)
Multiple Discriminate Analysis (MDA) - a statistical technique
used to predict default.
Z Score Model - one type of MDA
Z =1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5
Where:
X1 = Working capital/Total assets (in decimal)
X2 = Retained earnings/Total assets (in decimal)
X3 = Earnings before interest and taxes/Total assets (in decimal)
X4 = Market value of equity/Total liabilities (in decimal)
X5 = Sales/Total assets (number of times)
Z = Z-score


Credit Risk Models
Structural Models - based on option pricing theory((Brian
Scholes Option Pricing Model)
Reduced Form Models - do not look “inside the firm,” but
instead model directly the probability of default or downgrade
Popular Models:
 Jarrow and Turnbull Model
 Duffie and Singleton Model


Three Types of Yield Curves
1. normal or positively sloped yield curve –the most common

relationship are yields in which the longer the maturity, the
higher the yield
2. flat yield curve - the yield for all maturities is approximately
equal.
3. inverted or a negatively sloped yield curve - the relationship
between maturities and yields was such that the longer the
maturity the lower the yield
steepness or slope of the yield curve - The difference between
long-term Treasury yields and short-term Treasury yields

Parallel and Non Parallel Shifts
in the Yield Curve
shift in the yield curve - the relative change in the yield for each
Treasury maturity
parallel shift in the yield curve - a shift in which the change in
the yield for all maturities is the same
nonparallel shift in the yield curve - the yield for different
maturities does not change by the same number of basis
points

Types of Non Parallel Shifts
1. A downward shift in the yield curve combined with a

steepening of the yield curve.
2. An upward shift in the yield curve combined with a flattening
of the yield curve.
twist in the slope of the yield curve - a flattening or steepening
of the yield curve
butterfly shifts - nonparallel shifts in the yield curve that change
its curvature


Construction of Spot Rate Curve
shift in the yield curve - the relative change in the yield for each
Treasury maturity
Selection of Securities
Determine the methodology for constructing the curve
bootstrapping is used as a repetitive technique


Selection of Securities
Yields should not be biased on the following:
1. Default
2. Embedded options
3. Liquidity
4. Pricing errors

Treasury issues that are candidates for inclusion
1. Treasury coupon strips
2. On the run Treasury issues
3. On the run Treasury issues and selected off the run issues
4. All Treasury coupon securities and bills

Elements of Swaps and Swap Curve
Two parties “swapping” payments
 One party is paying a floating rate and receiving a fixed rate, and

 The other party is paying a fixed rate and receiving a floating rate.

Swap is described in terms of a “rate”.
The most common reference rate used in swaps is the 3-

month LIBOR. When LIBOR is the reference rate, the swap is
referred to as a “LIBOR- based swap”.


Swap Spread
Swap spread reflects the risk of the counterparty to the swap

failing to satisfy its obligation.
Swap spread primarily reflects credit risk.

Value:
Swap spread = Swap rate - Government yield on a bond with the same
maturity as the swap


Pure Expectations Theory
pure expectations theory - forward rates exclusively represent
expected future spot rates
The theory neglects the risks inherent in investing in bonds. Two
types of risks in bond investments:
1. interest rate risk
2. reinvestment risk


Liquidity Preference Theory,
Preferred Habitat Theory
Liquidity Preference Theory - the 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 to maturity
Preferred Habitat Theory - rejects the assertion that the risk
premium must rise uniformly with maturity


Measuring Yield Curve Risk
yield curve risk - the exposure of a portfolio or position to a
change in the term structure
Yield curve risk can be measured by changing the spot rate for

a particular key maturity and determining the sensitivity of a
security or portfolio to this change, holding the spot rate for
the other key maturities constant.


Measuring Historical Yield Volatility
yield volatility – Parameter measured the exposure of a
portfolio to rate changes depends on how likely and how
much interest rates may change
Formula:
Xt = 100[Ln(yt/yt- 1)]


Annualizing the Standard Deviation
Formula:
Daily standard deviation * sqrt (number of days in a year)
Some investors and traders use the number of days in the year,
365 days, to annualize the daily standard deviation. Some
investors and traders use only either 250 days or 260 days to
annualize.


ARCH Model
autoregressive conditional heteroskedasticity (ARCH) model The statistical model used to estimate this time series
property of volatility
 conditional - the value of the variance depends on or is
conditional on the value of the random variable
 heteroskedasticity - the variance is not equal for all values

of the random variable


Determination of benchmark
interest rates
The Treasury market
A sector of the bond market
The market for issuers securities


Generation of Interest Rate Trees
The interest rates on the tree are used to generate the cash

flows taking into account the embedded option.
The interest rates on the tree are used to compute the
present value of the cash flows.


Binomial Model, Trinomial Model,
Discrete Time Option Pricing Model
interest rate model - a probabilistic description of how interest
rates can change over the life of the bond
Interest Rate Tree Models:
binomial model - valuation model that assume that interest rates can
realize one of two possible rates in the next period
trinomial models - valuation model that assume that interest rates
can take on three possible rates in the next period
discrete time option pricing model – a more complex model that
assume in creating an interest rate tree that more than three
possible rates in the next period can be realized

Benchmark interest rates
Benchmark interest rates can be one of the following:
 The Treasury market
 A specific bond sector with a given credit rating
 A specific issuer
Benchmark interest rates can be based on either:
 An estimated yield curve
 An estimated spot rate curve
Thus there are six potential benchmark interest rates (2*3).

Spread Measures
nominal spread – a spread measured relative to the Treasury
yield curve and reflects compensation for credit risk, liquidity
risk and option risk
zero volatility spread – a spread relative to the Treasury spot
rate curve and reflects compensation for credit risk, liquidity
risk and option risk
option adjusted spread - a spread relative to the Treasury spot
rate curve and reflects compensation for credit risk and
liquidity risk.

OAS, Benchmark and Relative Value
When the benchmark is the Treasury spot rate curve:
 the security is expensive if the security OAS is greater than required

OAS
 the security is cheap if the security OAS is less than required OAS
 if the security OAS is equal to the required OAS, the security is fairly
priced

When a sector of the bond market with the same credit rating is the
benchmark:
 if the security OAS is greater than the required OAS, the security is

cheap
 if the security OAS is less than the required OAS, the security is
expensive
 if the security OAS is equal to the required OAS, the security is fairly
priced

Backward Induction Methodology
It is a discounting process for valuing bonds with a binomial

interest rate tree.
It refers to the process of discounting distant values in a
binomial tree, one node at a time, backwards through time to
generate a current value.


Valuation of Callable Bonds
and Putable Bonds using Binomial Model
Callable bonds can be valued by modifying the cash flows at
each node in the interest rate tree to reflect the cash flow
prescribed by the embedded call option according to the call
rule.
Putable bonds are valued using the same procedure as for a
callable bond, except that the relevant cash flows are dictated
by the rules governing the exercise of the embedded put
option.


Valuation of Bond with Embedded
Options and Floating Rate Notes
using Binomial Model
bond with an embedded option or options - can be valued by
requiring that the value at each node of the tree be adjusted
based on whether or not the option will be exercised
floating-rate note - the binomial method must be adjusted to
account for the fact that a floater pays in arrears. That is, the
coupon payment is determined in a period but not paid until
the next period.

Convertible Securities
The owner can exchange the bond for the common shares of

the issuer.
Gives the bondholder the right to buy the common stock of
the issuer.
Almost all convertible bonds are callable, and some
convertible issues are putable.


Conversion Price, Conversion Ratio
and Straight Value
conversion ratio - number of common shares for which a convertible
bond can be exchanged.
conversion price - issue price divided by the conversion ratio.
conversion value - value of the stock into which the bond can be
converted.
conversion value = market price of stock × conversion ratio
straight value - value of the bond if it were not convertible
market conversion price - price that a convertible bondholder would
effectively pay if the bond were purchased and immediately
converted.
market conversion price = market price of convertible bond/conversion
ratio

Fixed Income, Common Stock
and Hybrid Equivalents
fixed income equivalent (or a busted convertible) - the straight
value is considerably higher than the conversion value so that
the security will trade much like a straight security.
common stock equivalent - the conversion value is considerably
higher than the straight value so that the convertible security
trades as if it were an equity instrument.
hybrid equivalent - the convertible security trades with
characteristics of both a fixed income security and a common
stock instrument.

Advantages and Disadvantages
of Convertibles
Advantages:
reduction in downside risk
the price appreciation resulting from an increase in the value
of the common stock
Disadvantages:
the upside potential given-up because a premium per share
must be paid
when the stock price rises, the bond will underperform
because of the conversion premium of the bond

Mortgages
mortgage - a loan secured by the collateral of some specified
real estate property which obliges the borrower to make a
predetermined series of payments
the mortgage rate or contract rate - interest rate on the
mortgage loan


Types of Mortgage Designs
mortgage design - a specification of the interest rate, term of
the mortgage, and the manner in which the borrowed funds
are repaid
Types of Mortgage Designs:
 fixed-rate, level-payment fully amortized mortgages
 adjustable-rate mortgages
 balloon mortgages
 growing equity mortgages
 reverse mortgages
 tiered payment mortgages

Types of Mortgage Backed Securities
1. residential mortgage-backed securities - backed by

residential mortgage loans
Sectors:

 agency mortgage backed securities - issued by federal agencies
 non agency mortgage-backed securities - issued by private entities

Residential mortgage-backed securities include:
 mortgage passthrough securities
 collateralized mortgage obligations
 stripped mortgage-backed securities.

2. commercial mortgage-backed securities - backed by

commercial loans


Residential Mortgage Design
Most common mortgage design in the United States:
 fixed-rate mortgage
 level-payment mortgage
 fully amortized mortgage.
Features:
the mortgage rate is fixed for the life of the mortgage loan
the dollar amount of each monthly payment is the same for
the life of the mortgage loan
when the last scheduled monthly mortgage payment is made,
the remaining mortgage balance is zero

Residential Mortgage Servicing Fee
servicing fee - a portion of the mortgage rate
Servicing of a mortgage loan involves:
 collecting monthly payments and forwarding proceeds to owners of






the loan
sending payment notices to mortgagors
reminding mortgagors when payments are overdue
maintaining records of principal balances
initiating foreclosure proceedings if necessary
furnishing tax information to borrowers (i.e. mortgagors) when
applicable.

Residential Mortgage Prepayment
prepayment - a payment made in excess of the monthly
mortgage payment
curtailment - When a prepayment is not for the entire
outstanding balance
prepayment risk - the risk when amount and timing of the cash
flow from a mortgage loan are not known with certainty
lockout period or penalty period - a period of time over which if
the loan is prepaid in full or in excess of a certain amount of
the outstanding balance, there is a prepayment penalty


Types of Mortgage Passthrough
Securities
mortgage passthrough security - created when one or more holders of
mortgages form a collection (pool) of mortgages and sell shares or
participation certificates in the pool.
Types:
1. agency mortgage pass through securities – backed by an agency
security
Underwriting Standards:
 conforming mortgage
 nonconforming mortgage

2. non agency mortgage pass through securities - are nonconforming

mortgages used as collateral for mortgage pass-through securities
and are privately issued

Weighted Average Coupon
and Weighted Average Maturity
of Mortgage Passthrough Securities
weighted average coupon rate(WAC) - found by weighting the
mortgage rate of each mortgage loan in the pool by the
percentage of the mortgage outstanding relative to the
outstanding amount of all the mortgages in the pool.
weighted average maturity(WAM) - found by weighting the
remaining number of months to maturity for each mortgage
loan in the pool by the amount of the outstanding mortgage
balance.

Measuring the Prepayment Rates
single monthly mortality rate(SMM) - ratio of the prepayment
in a month and the amount available to prepay that month
Formula:
SMM = (Prepayment in month) / (Beginning mortgage balance for
month t – Scheduled Principal Payment in month t)

Formula: Given an assumed SMM for month t:
(Prepayment in month) = SMM * (Beginning mortgage balance for
month t – Scheduled Principal Payment in month t)


Conditional Prepayment Rate (CPR)
Formula: Given the SMM for a given month
CPR = 1 - (1 - SMM)12
Formula: Given a CPR
SMM = 1 – (CPR)1/12


PSA Prepayment Benchmark
 Expressed as a monthly series of CPRs.
 It assumes that prepayment rates are low for newly originated

mortgages and then will speed up as the mortgages become
seasoned.
 It assumes the following prepayment rates for 30-year mortgages
 a CPR of 0.2% for the first month, increased by 0.2% per year per month

for the next 30 months until it reaches 6% per year, and
 a 6% CPR for the remaining months.

Mathematically, 100 PSA can be expressed as follows:
 if t < 30 then CPR = 6% (t/30)
 if t > 30 then CPR = 6%


Average Life of Mortgage
Passthrough Securities
weighted average life or average life - measure widely used by
market participants
Formula:
Average Life = ∑ (t * Projected Principal received at time t) /
(12 * Total Principal)


Factors affecting Prepayment Behaviour
Prevailing mortgage rate
Housing turnover
Characteristics of the underlying residential mortgage loans


Contraction and Extension Risk of
Mortgage Passthrough Securities
contraction risk - undesirable consequences of declining interest
rates:
 MBS exhibit negative convexity
 cash flows must be reinvested at a lower rate.
extension risk - the drop in bond prices and the slowing of
prepayments as interest rates increase


Collateralized Mortgage Obligations
(CMOs)
Collateralized mortgage obligations are bond classes created by
redirecting the interest and principal from a pool of pass
throughs or whole loans.
CMOs are securities issued against a pool of mortgages for which
the cash flows have been allocated to different classes called
tranches.


Design of CMOs
Sequential-pay tranches - a common arrangement for
separating mortgage cash flows into classes to create CMOs
where each class of bond is retired sequentially.
Planned Amortization Class (PAC) tranches - the most common
type of CMO, have a payment schedule that is established
within a range of prepayment speeds called the initial PAC
collar.


Stripped Mortgage Backed Security
stripped mortgage-backed security - a derivative mortgagebacked security that is created by redistributing the interest
and principal payments to two different classes.
Classes:
principal-only mortgage strip (PO) - a class of securities that
receive only the principal payment portion of each mortgage
payment. The PO exhibits some negative convexity at low
rates.
interest-only mortgage strip (IO) – a classes that receive only
the interest component of each payment. The IO price is
positively related to mortgage rates at low current rates.

Non Agency Residential Mortgage
Backed Security
non agency MBS (non agency securities) - issued by private
entities and are usually backed with nonconforming mortgage
loans
nonconforming mortgage - loans that fail to meet the agency’s
underwriting standards
Non agency security cash flows are affected by mortgage default
rates and thus require credit enhancement


Commercial Mortgage Backed
Security
commercial mortgage-backed securities - backed by a pool of
commercial mortgage loans—loans on income-producing
property.
Features:
 structured as nonrecourse loans
 on two key ratios to assess the credit risk
 Debt-to-service coverage ratio
 Loan-to-value ratio.

Call Protection for CMBS
Degree of call protection available investor:
 At the loan level
 From the actual CMBS structure.
Methods of call protection at the loan level includes:
 Prepayment lock outs
 Defeasance
 Penalty fees
 Yield maintenance charges

Parties in a Securitization Process
Seller - originates the loans and sells them to the issuer/trust.
Issuer/trust - buys the loans from the seller and issues the ABS.
Servicer - who services the original loans.


Home Equity Loans
Closed-end Home Equity Loans (HELs) - secondary mortgages
that are structured just like a standard fixed rate, fully
amortizing mortgage.
Distinctive Feature: credit traits of the borrowers
Structure:
 non-accelerating senior tranches
 planned amortization class (PAC) tranches.


Manufactured Housing Backed
Securities
manufactured housing asset backed securities - backed by loans
for manufactured homes.
Distinctive feature: relatively stable prepayments


Auto Loan Backed Securities
Auto loan-backed securities - backed by loans for automobiles
Distinctive Features: Prepayments are caused by sales and tradeins, the repossession/resale process, insurance payoffs due to
thefts and accidents, borrower payoffs, and refinancing.
Auto loans have 36- to 72-month maturities and are issued by
the financial subsidiaries of auto manufacturers, commercial
banks, credit unions, etc.

Risks, Ratios and Yield Curves

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Risks, Ratios and Yield Curves