Sciences‎ > ‎CFA‎ > ‎

CFA2: Fixed Income

Credit Analysis

Credit risk types

  1. Default risk: borrower will not repay the obligation
  2. Credit spread risk: credit spread will increase and cause the value of an issue to decrease and/or cause the bond to underperform its benchmark
  3. Downgrade risk: issue will be downgraded, which will also cause the bond price to fall, and/or cause the bond to underperform its benchmark

The 4 Cs of credit analysis:

  1. Character - integrity of the management and its commitment to repay the loan. Other factors such as corporate governance structure, their business qualifications, and operating record are also important.
  2. Covenants: terms and conditions contained in the lending agreement, and include restrictions placed on management’s ability to make operating and financial decisions in the normal course of business
  3. Collateral: assets offered as security for the debt as well as other assets controlled by the issuer. The value of the pledged assets is also an important determinant of the collateral. Collateral analysis is probably the least useful in assessing corporate credit risk.
  4. Capacity to pay - corporate borrower’s ability to generate cash flow or liquidate short-term assets to repay its debt obligations. Sources of liquidity include working capital, cash flow, back-up facilities, securitization, third-party guarantees.

Ratio Analysis

  • Profitability ratios assess the issuer's ability to generate earnings sufficient to pay interest and repay principal.
ROE = NI / equity = (NI/sales)(sales/TA)(TA/equity)
  • Short-term solvency ratios determine the availability of liquid assets to meet short-term obligations.
Current ratio = current assets / current liabilities
Acid-test ratio = (current assets ? inventories) / current liabilities
  • Capitalization ratios (also known as financial leverage ratios) are evaluated with reference to the industry in order to determine the firm’s ability to take on additional risk associated with increased borrowing. (lower the better)
Long-term debt to capitalization ratio = long-term debt / (long-term debt + minority interest + shareholders’ equity)
Total debt to capitalization ratio = (current liabilities + long-term debt) / (current liabilities + long-term debt + minority interest + shareholders’ equity)
  • Coverage ratios examine the adequacy of cash flows generated through earnings to meet debt and lease obligations.
EBIT coverage ratio = EBIT / annual interest expense
EBITDA coverage ratio = EBITDA / annual interest expense
  • Limitations
    • not forward looking because it does not consider factors that can affect future cash flows
    • Ratios represent a snapshot of a particular aspect of a firm’s financial position at a given point in time
    • based on past data.
    • Traditional ratios do not fully reflect cash flow from operations and ignore factors that can alter future cash flows
    • Ratings reflect future expectations regarding a firm’s cash flows
    • A firm’s cash flow is a better measure of a firm’s financial position

Operating cash flow analysis

Net income
+ depreciation
± other noncash items
Funds from operations
+ decrease (increase) in noncash current assets
+ increase (decrease) in nondebt current liabilities
Operating cash flow
- capital expenditures
Free operating cash flow
- cash dividends
Discretionary cash flow
- acquisitions
+ asset disposals
+ other sources (uses)
Prefinancing cash flow

The typical debt structure of a high-yield issuer includes bank debt, reset notes, senior and subordinated debt (which may be zero-coupon). Typical debt structure of a high-yield issuer

  • Short-term, floating-rate, senior bank debt typically preferred over investment grade borrowers
  • Reset notes trade at a specific premium to their par value, because the coupon rate on a reset note is adjusted periodically
  • High-yield issuers are often structured as a holding company. Debt is borrowed at the parent level, and funds to pay the obligation in the future are obtained from operating subsidiaries. This makes it imperative that the operating subsidiaries’ financial ratios be examined to determine whether the subsidiaries’ financial position will help the parent meet its obligations and whether the subsidiaries’ own debt covenants will restrict their cash contributions to the parent.

Credit rating consideration factors

Asset-backed Securities

  • Collateral credit quality: The borrower’s equity in the underlying asset offered as collateral is the main determinant of whether the borrower will default/sell the asset to pay off a loan.
  • Seller/servicer quality: A third party servicer collects payments, notifies delinquent borrowers, and recovers and disposes of collateral as necessary.
  • Cash flow stress and payment structure: The rating agencies analyze ABS 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. This is an important point because the cash flow from the collateral pool may only be sufficient to meet the cash flow requirements of some, but not all, of the various ABS tranches.
  • Legal structure: A firm that securitizes assets can obtain a credit rating on the securities it issues that is higher than the issuer’s corporate credit rating by using a special purpose vehicle(SPV).

Tax-backed debt For tax-backed debt, credit worthiness is determined by:

  • Issuer’s debt structure.
  • Budgetary policy.
  • Local tax and intergovernmental revenue availability.
  • Issuers’ socioeconomic environment.

Revenue bonds issued by municipalities for financing specific projects and enterprises

  • Limits of the basic security.
  • Flow of funds structure.
  • Rate, or user charge, covenants.
  • Priority-of-revenue claims.
  • Additional-bonds tests.

Sovereign debt

  • Economic risk: ability of a national government to meet its debt obligations.
  • Political risk: willingness of a national government to meet its debt obligations.

Local currency debt - political stability; income base and economic growth; tax discipline and budgetary record; monetary policy and rate of inflation; and government debt burden and debt service experience.

Foreign currency debt - country’s balance of payments and the composition of its external balance sheet relative to its external debt (foreign currency) obligations; historically exceeded those on local currency debt

Corporate bonds

  • Capacity to pay (particularly a cash flow analysis)
  • Corporate governance structure; requires an analysis of the issuer’s operational risk.
  • Contrast to other securities
    • Asset-backed securities - assessment of collateral credit quality; efficiency and quality of the ABS servicer
    • Municipal bond credit - similar to corporate bonds except that revenue bonds have rate covenants and a priority-of-revenue claims clause.
    • Sovereign credit - analysis requires an assessment of the country’s ability to repay (economic risk) and willingness to repay (political risk)

Liquidity Conundrum

Minsky "financial instability hypothesis" framework - liquidity is a function of risk aversion, rather than central bank actions

2/28 adjustable rate subprime mortgage

  • The borrower puts no money down, i.e., it requires no equity investment.
  • Interest payments are optional.
  • The interest rate is a two-year teaser rate that subsequently adjusts up.
  • Minsky’s framework - a stable economy progresses towards greater instability
    1. Hedge unit: payments = interest + principal portion
    2. Speculative unit: payments > interest cost
    3. Ponzi unit: default rates on mortgages increase because, with declining property values, borrowers realize they have no incentive to make payments on their loans

A subprime mortgage borrower effectively granted a free at-the-money call

  • mortgage did not require a down payment.
  • full-interest payments were optional.
  • borrower’s position would be valuable if home prices rose.
  • As long as housing prices kept going up, borrowers made their monthly payment because the call had value. When house prices fell, borrowers defaulted on their mortgages because the call option was worthless.

Interest Rates

  • Parallel shift: yield on all maturities change in the same direction and by the same amount. The slope of the yield curve remains unchanged following a parallel shift.
  • Nonparallel shift: yields for the various maturities do not necessarily change in the same direction nor do they change by the same amount
  • Twists: yield curve changes when the slope becomes either flatter or more steep. A flattening of the yield curve means that the spread between short- and long-term rates has narrowed.
  • Butterfly shifts: changes in curvature of the yield curve; A positive butterfly means that the yield curve has become less curved.

Factors that explain historical Treasury returns:

  • Changes in the level of interest rates (parallel shifts - Litterman and Scheinkman 90%)
  • Changes in the slope of the yield curve (twists - 8.5%)
  • Changes in the curvature of the yield curve (butterfly shifts - 1.5%)

Theoretical spot rate curve construction

  • All on-the-run Treasury issues
+ Uses only the most accurately priced issues.
- Large maturity gaps after the five-year note.
  • All on-the-run and selected off-the-run Treasury issues
+ Reduces maturity gaps.
- 1) Still doesn't use all issues, and 2) rates may be distorted by the repo market.
  • All Treasury coupon securities and bills
+ Uses information from issues excluded by other approaches.
- 1) Some maturities have more than one yield, and 2) current prices may not reflect accurate interest rates for all maturities.
  • Treasury coupon strips
+ 1) Provides yields at most maturities and reduces maturity gaps; and 2) intuitive approach that does not require bootstrapping to derive spot rates.
- 1) Liquidity premium embedded in strip rates; and 2) tax treatment affects observed rates.

Swap rate curve (LIBOR curve): series of swap rates quoted by swap dealers over maturities extending from 2 to 30 years 
Swap rate preferred as a benchmark interest rate curve rather than a government bond yield curve:

  • Swap market is not regulated by any government, which makes swap rates in different countries more comparable.
  • supply of swaps and the equilibrium pricing that results from the interaction of supply and demand depends only on the number of participants willing to enter into a swap. It is not affected by technical market factors that can affect government bonds.
  • Swap curves across countries are also more comparable because they reflect similar levels of credit risk, while government bond yield curves also reflect sovereign risk unique to each country.
  • The swap curve typically has yield quotes at 11 maturities between 2 and 30 years. The U.S. government bond yield curve, however, only has on-the-run issues trading at four maturities of at least 2 years (2-year, 5-year, 10-year, and 30-year).

Theories of the term structure of interest rates

  • Pure expectations theory maintains that forward rates are solely a function of expected future spot rates.
    • Implications: if the yield curve is upward (downward) sloping, short-term rates are expected to rise (fall). Also, a flat yield curve implies that the market expects short-term rates to remain constant.
  • Liquidity theory proposes that forward rates reflect investors’ expectations of future rates plus a liquidity premium to compensate them for exposure to interest rate risk, and this liquidity premium is positively related to maturity.
    • Implications: forward rates are a biased estimate of the markets expectation of future rates, since they include a liquidity premium.
  • Preferred habitat theory also proposes that forward rates represent expected future spot rates plus a premium, but it does not support the view that this premium is directly related to maturity. Instead, the preferred habitat theory suggests that the existence of an imbalance between the supply and demand for funds in a given maturity range will encourage lenders and borrowers to shift from their preferred habitats (maturity range) to one that has the opposite imbalance.
    • Implications: Premiums are related to supply and demand for funds at various maturities. This means that this theory can be used to explain almost any yield curve shape.

Yield curve risk of a portfolio = sum (yield curve shifts x key rate durations)

Variance of daily yield change (assuming continuous compounding)


Option pricing model: volatility estimation using observed prices interest rate option and other observable variables

Weaknesses of use of implied volatility (:derived from solely option prices)

  • It is based on the assumption that the option pricing model is correct.
  • Models make the simplifying assumption that volatility is constant.

Yield volatility forecasts - based on the standard deviation of daily yield changes using the moving average of yield changes over some appropriate time interval

  • more appropriate to use zero as the value for the expected change in yields
  • The easiest way to compute the variance is to assign equal weights to each observation.
  • Some investors weight recent observations more heavily than distant observations.
  • Yield volatility has been observed to follow patterns over time. This pattern can be modeled and used to forecast volatility using autoregressive statistical techniques.

Embedded Options

Relative value analysis: comparison of spread to the required spread; if larger, bond is undervalued

  • Benchmark spread uesd:
  1. U.S. Treasury securities
  2. A specific sector of the bond market with a certain credit rating higher than the issue being valued
  3. A specific issuer

Backward induction: process of valuing a bond using a binomial interest rate tree from the end period

Value of the embedded call option discount and put option premium

Vcall = Vnoncallable - Vcallable
Vput = Vputable - Vnonputable
  • Embedded option value increases as volatility increases
Relative OAS Valuation
TreasuryBenchmark SectorBenchmark Issuer-Specific Benchmark
OAS > 0 Overvalued if actual OAS < required OAS; 
Undervalued if actual OAS > required OAS
Overvalued if actual OAS < required OAS;
Undervalued if actual OAS > required OAS
OAS = 0 Overvalued Overvalued Fairly priced
OAS < 0 Overvalued Overvalued Overvalued

General procedure for the use of binomial model with effective duration and convexity for option-embedded bond valuation

  1. Calculate the OAS for the issue.
  2. Impose a small parallel shift in the on-the-run yield curve by an amount equal to +?y.
  3. Build a binomial interest rate tree using the new yield curve.
  4. Add the OAS to each of the one-year rates in the interest rate tree to get a “modified” tree.
  5. Compute BV+?y using this modified interest rate tree.
  6. Repeat steps 2 through 5 using a parallel rate shift of -?y to obtain a value of BV-?y.

Convertible bond can be exchanged for common shares of the issuer; call option embedded giving he bondholder the right to buy the issuer's common stock

  • Conversion ratio = #common shares per convertible bond
  • Conversion price = issue price / conversion ratio
  • Conversion value = market price of stock × conversion ratio
  • Straight value = value of the bond if it were not convertible
  • Market conversion price = market price of convertible bond / conversion ratio
  • Market conversion premium per share = market conversion price - market price
  • Premium payback: time it takes to recoup the per-share premium.
  • Minimum value = max (straight value, conversion value).
  • Downside risk is often measured using the premium over straight value
Callable convertible bond value = straight value of bond + value of call option on stock - value of call option on bond

Effects of changes in volatilities on the convertible bond value

  • stock price volatility ↑ -> call value on stock ↑ -> value of the callable convertible bond ↑
  • interest rate volatility ↑ -> call value on bond ↑ -> value of the callable convertible bond ↓

Comparisons between underlying stock ownership and risk-return characteristics of the convertible bond:

  • stock’s price ↓ -> returns on convertible bonds > return on stock, because the convertible bond’s price has a floor = straight bond value
  • stock’s price ↑ -> bond will underperform, because of the conversion premium (main drawback of investing in convertible bonds versus investing directly in the stock)
  • If the stock’s price remains stable, the return on a convertible bond may exceed the stock return due to the coupon payments received from the bond, assuming no change in interest rates or the yield or credit risk of the issuer

Mortgage-Backed Securities

Mortgage a loan that is collateralized with a specific piece of real property, either residential or commercial. The borrower must make a series of mortgage payments over the life of the loan, and the lender has the right to “foreclose” or lay claim against the real estate in the event of loan default.

Mortgage passthrough security

  • represents a claim against a pool of securitized mortgages
  • Passthrough investors receive the monthly cash flows generated by the underlying pool
  • Prepayment risk: because the mortgages used as collateral for the passthrough can be prepaid

Monthly prepayment amount = SMM × (beginning mortgage balance for month t - scheduled principal payment for month t)

Conditional Prepayment Rate (CPR): annual rate at which a mortgage pool balance is assumed to be prepaid during the life of the pool; depends on past prepayment rates, current and expected economic state of affairs Single-monthly Mortality Rate (SMM): portion of prepayment - scheduled payment

SMM = 1 - (1 - CPR)1/12

Public Securities Association (PSA) prepayment benchmark assumes that the monthly prepayment rate for a mortgage pool increases as it ages. The model assumes prepayments start at 0.2% and increase by 0.2% per month for the first 30 months of the mortgage, and then remain at a level 6% CPR for the life of the loan.

For months < 30, CPR = 6% × (month / 30)
For months ≥ 30, CPR = 6%
  • Average life = weighted average time until both scheduled principal payments and expected prepayments are received
  • Stated maturity of a mortgage passthrough security is unlikely to equal its true life because of contraction and extension risk

Main Prepayment Factors

  1. Prevailing mortgage rate: When interest rates are low relative to the mortgage rate, prepayments increase as more borrowers refinance.
  2. Housing turnover increases as rates fall and housing becomes more affordable. This increases refinancings and prepayments. It also increases when economic growth is higher.
  3. Seasoning and property location: Prepayments are low for new mortgages but increase as the loan seasons. Local economics also influence prepayment levels, which tend to be faster in some parts of the country and slower in others.

Types of Prepayment Risk

  • Contraction risk mortgage rates ↓ -> prepayment rates ↑ -> average life of the passthrough security ↓ ->negative convexity and reinvestment risk
  • Extension risk mortgage rates ↑ -> prepayment rates ↓ -> average life of the passthrough security ↑ -> price decline due to extended duration

Collateral Mortgage Obligation (CMO): cash flows are partitioned and distributed into different risk packages(tranches)

  • CMO classes represent mixtures of contraction and extension risk, for can be matched to the unique asset/liability needs of many institutional investors and investment managers
  • Sequential pay tranches a common arrangement for separating mortgage cash flows into classes to create CMOs where each class of bond is retired sequentially
  • Z-tranche (accrual) tranche the last tranche in a sequential pay CMO to be paid principal; does not receive current interest until the other tranches have been paid off
  • 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.
  • Each PAC has a Companion (support) tranche that has a second priority claim to the cash flows
    • If prepayments are too high, the support tranche is paid off faster. If too slow, the support tranche provides the funds needed to keep the PAC on schedule.
  • The “early” tranches are protected against extension risk, while the later tranches are protected against contraction risk. The Z bond has low contraction risk, because reinvestment risk is eliminated until the other tranches have paid off.

Stripped mortgage-backed securities principal and interest are not allocated on a pro rata basis

  • Unequal allocation of principal and interest results in a price/yield relationship different from the underlying passthrough

Principal-only strips: PO strips are sold at a considerable discount to par; cash flow stream starts out small and increases with the passage of time as the principal component of the mortgage payments grows

  • The investment performance is extremely sensitive to prepayment rates.
  • Higher prepayment rates result in a higher yield.
  • PO prices are enhanced by falling interest rates.
  • The entire par value of a PO is ultimately paid to the PO investor.

Interest-only strips: IO strip cash flows start out big and get smaller over time; comparably shorter effective lives

  • The value of the cash flows that investors receive over the life of the mortgage pool may be less than initially expected and *possibly less than the amount originally invested.
  • The amount of interest produced by the pool depends on its beginning-of-month balance.
  • If market rates fall, the mortgage pool will be paid off sooner than expected, leaving IO investors with no interest cash flow.
  • IO investors want prepayments to be slow.

  • Agency CMOs are formed by splitting up a pool of passthrough securities, backed by pseudo-governmental guarantee
  • Nonagency(Whole-loan: unsecuritized) CMOs are usually created directly from the nonconforming mortgages; risk & return higher; require credit enhancement

  • Residential MBS loans: repaid by the homeowner; lender can go back to borrower personally for repayment
  • Commercial MBS loans: repaid by real estate investors who, in turn, rely on tenants and customers to provide the cash flow to repay the mortgage loan; structured as non-recourse loans: lender can only look to the collateral as a means to repay a delinquent loan if the cash flows from the property are insufficient; property credit risk determined by debt-to-service coverage ratio and the loan-to-value ratio
    • CMBS structure - segregated into tranches that are repaid in a specific sequence with the highest credit quality tranche being repaid first
    • Call protection provided at loan-level provided by the structure of the individual mortgage, and CMBS security structure
    • Means of creating loan-level call protection: Prepayment lock out, Defeasance, Prepayment penalty points, Yield maintenance charges

European Mortgage-Backed Market

Differences between the U.S. and European mortgage backed markets include the following: Key differences

  • Majority of mortgage debt funded with retail deposits rather than securitized and agency debt
  • Mortgage debt-to-GDP ratio lower
  • Home ownership lower in percentage
  • Lack of data availability and credit scoring systems

RMBS market chllenges

  • Uneven availability of data and lack of standardized credit scoring systems
  • Lack of firms with expertise in loan servicing
  • Differing growth prospects across Europe

Asset-Backed Securities

Key parties to a securitization transaction:

  • Seller: originates the loans and sells them to the SPV.
  • Issuer/trust: buys the loans from the seller and issues the ABS.
  • Servicer: services the original loans. (May be the same party as the seller)

Waterfall: flow of funds structure in a securitization transaction

  • Time tranching: MBS structures are divided into different tranches to distribute the prepayment risk to various investors using, for example, sequential-pay or PAC structures. ABS are also structured to distribute the prepayment risk
  • Credit tranching: the most common form of credit enhancement is a senior-subordinated structure in which the subordinated bonds absorb losses first up to their par value, after which losses are absorbed by the senior bonds. The result is to transfer some of the credit risk from the senior bonds to the subordinated bonds

  • Amortizing assets loans for which the borrower makes periodic scheduled payments that include both principal and interest
    • Once the assets are securitized, the composition of the loans in the pool doesn’t change. Principal payments and prepayments on the remaining loans are distributed to the bondholders according to the distribution rules of the structure.
  • Non-amortizing assets loans that do not have a scheduled payment amount. Instead, a minimum payment, which is applied against accrued interest, is required. e.g. revolving credit card bills
    • Revolving structure: Composition of the loans in the pool can and does change. During the lockout period, principal payments and prepayments are not distributed to the bondholders as is the case with amortizing assets. Instead, the cash flow from these principal payments is used to invest in new loans to replace the amounts paid off

External credit enhancements financial guarantees from third parties. Third-party guarantees impose a limit on their liability for losses up to a specified level. They protect against losses before internal credit enhancements are used.

  • Corporate guarantees: The sponsor (effectively the seller of the securities) agrees to guarantee a portion of the offer.
  • Letter of credit: The letter of credit provides a guarantee against loss, up to a certain level.
  • Bond insurance: Bond insurance provides for protection against losses through the purchase of insurance against nonperformance.
- Third-party guarantee subjects the ABS to the credit risk of the third-party guarantor
- pledge is no better than the credit of the guarantor

Internal credit enhancements commonly include setting aside reserve funds, overcollateralization, and structures that contain senior and subordinated debt.

  • Reserve accounts: Reserve accounts consist of reserve funds in the form of excess cash after paying for servicing, net coupon, and other expenses. This excess cash provides for the establishment of a reserve account to pay for future losses.
  • Overcollateralization: assigning more collateral than the face value of the loan.
  • Senior/subordinated structure: This structure contains at least two tranches: a senior tranche and a junior or subordinated tranche. The subordinated tranches absorb the first losses up to their limits. The higher the percentage of subordinate bonds, the greater the level of protection for the senior tranches.

CashFlow & Prepayment charateristics

  • Closed-end HELs secondary mortgages that are structured just like a standard fixed-rate, fully amortizing mortgage. The pattern of prepayments from HELs differs from MBS prepayment patterns, primarily because of differences in the credit traits of the borrowers. Therefore, analysts must consider the credit of the borrowers when analyzing HEL-backed securities. HEL floaters have a variable coupon rate cap called the available funds cap. HEL structures frequently include non-accelerating senior tranches and PAC tranches.
  • Manufactured housing ABS are backed by loans for manufactured homes. Prepayments for manufactured ABS are relatively stable because the underlying loans are not as sensitive to refinancing.
  • Auto loan-backed securities are backed by loans for automobiles. Auto loans are issued by auto manufacturers, commercial banks, credit unions, etc. Prepayments for auto loan-backed securities are caused by sales and trade-ins, the repossession/resale process, insurance payoffs due, borrower payoffs, and refinancing. Refinancing is of minor importance, since many auto loans are frequently below market rates due to sales promotions. Absolute prepayment speed is the measure of prepayments associated with securities backed by auto loans.
  • Student loan ABS are most often securitized by loans made under the U.S. government’s FFELP. Qualifying loans carry a U.S. government guarantee. Prepayments may occur because of defaults or loan consolidation.
  • Small Business Administration (SBA) loan-backed securities are backed by pools of SBA loans with similar terms and features. Most SBA loans are variable-rate loans, reset quarterly or monthly, and based on the prime rate.
  • Credit-card receivables ABS are backed by pools of receivables owed by banks, retailers, and other credit card issuers. The cash flow to a pool of receivables includes finance charges, annual fees, and principal repayments. Credit cards have periodic payment schedules, but since their balances are revolving, the principal is not amortized. Because of this characteristic, interest on credit card ABS is paid periodically, but no principal is paid to the ABS holders during the lockout period, which may last from 18 months to 10 years.

Collateralized Debt Obligations: ABS collateralized by a pool of debt obligations

  • One or more senior tranches.
  • Several levels of mezzanine tranches.
  • A subordinate (equity) tranche to provide prepayment and credit protection.

  • typically contains a mix of floating-rate and fixed-rate debt instruments, with majority of payments based on a floating rate. Managers often address this potential cash flow mismatch by using interest rate swaps to convert fixed-rate interest receipts into floating-rate payments.
  • Cash flow CDO: portfolio manager seeks to generate sufficient cash flow (from interest and principal payments) to repay the senior and mezzanine tranches.
  • Synthetic CDO: bondholders take on the economic risks of the underlying assets but do not take legal ownership of them. This is accomplished by linking certain contingent payments to a reference asset.

  • Motivations
    • arbitrage-driven: to generate an arbitrage return on the spread between return on the collateral and the funding costs.
    • balance sheet-driven: to remove assets (and the associated funding) from the balance sheet

Security Valuation

Cash flow yield discount rate at which security price equal to the present value of its cash flows

  • Estimate the future monthly cash flows.
  • Calculate the monthly rate of return that makes the present value of these future cash flows equal to the security's current market price.
- The cash flows will be reinvested at the cash flow yield prevailing when the MBS or ABS is priced (reinvestment risk).
- The MBS or ABS will be held until maturity (price risk).
- The cash flows will be realized

Nominal spread difference between the cash flow yield on an MBS and the yield on a Treasury security with a maturity equal to the average life of the MBS. A portion of the nominal spread represents compensation to the investor for exposure to prepayment risk.

- don’t know how much of the nominal spread reflects the significant prepayment risk associated with MBS

Zero-volatility spread spread that must be added to each Treasury spot rate that will cause the discounted value of the cash flows for an MBS or ABS to equal its price, assuming that the security is held until maturity

- only considers one path of interest rates: the current Treasury spot rate curve

Monte Carlo simulation for MBS Valuation

  1. Simulate interest rate paths and cash flows, using assumptions concerning benchmark rates, rate volatility, refinancing spreads, and prepayment rates. Non-agency MBS also require assumptions regarding default and recovery rates.
  2. Calculate the present value of the cash flows along each interest rate path.
  3. Calculate the theoretical value of the MBS as the average of the present values along each path.
  4. Calculate the OAS as the spread that makes the theoretical value = market price.
  5. Option cost = Zero-volatility spread - OAS

Sources of path dependency

  • Prepayment burnout: If mortgage rates trend downward over a period of time, prepayment rates will increase at the beginning of the trend as homeowners refinance their mortgages; but prepayments will slow as the trend continues, because many of the homeowners that can refinance will have already done so.
  • The cash flows that a particular CMO tranche receives in any one month depend on the outstanding principal balances of the other tranches in the structure, which in turn depend on the prepayment history and the interest rate path.

Option-adjusted spread(OAS): MBS spread after the "optionality" of the cash flows is taken into account; express the dollar difference between price and theoretical value as a spread.

option cost = zero-volatility spread – option-adjusted spread
  • larger OAS and low option costs are undervalued.

Reported effective durations may differ across various dealers and vendors due to:

  • Differences in Δy: If Δy, the incremental change in interest rate, is too large, the effects of convexity contaminate effective duration estimates.
  • Prepayment model differences: Prepayment models vary among dealers.
  • OAS differences: OAS is a product of the Monte Carlo simulation model. Differences in the inputs to the model will affect the measurement of OAS. This has particular relevance to the volatility assumption and the prepayment model used with a particular Monte Carlo model.
  • Differences in the spread between one-month rates and refinancing rates. The assumed spread between one-month rates and refinancing rates affects the computed values of MBS. Thus, different assumptions about this relationship will provide different values for BV+Δy and BV– Δy in the effective duration computation.

Interest-rate risk likelihood of security price change as yields change

  • Effective duration: measure of interest-rate risk
  • Convexity adjustment provides more precise estimate for larger changes in yield
% Δ in bond price ≈ duration effect + convexity effect ≈ (-ED × Δy × 100) + (EC × Δy2 × 100)

Other measures of duration

  • Cash flow duration: allows for cash flows to change as interest rates change.
- Based on the unrealistic assumption that a single prepayment rate exists over the life of a MBS for any given change in interest rates.
  • Coupon curve duration: based on a relationship between coupon rates and prices for similar MBS.
- 1) Limited to generic MBS, 2) Not readily applicable for CMO structures and other mortgage-based derivatives.
  • Empirical duration: determined using regression analysis with historical prices and yields.
- 1) Time series price data difficult to obtain, 2) Embedded options can distort the results, 3) Volatility of the spreads with reference to Treasuries can distort the price reaction to interest rate changes.
if (embedded option typically exercised?)
 if (path-dependent option)
  use OAS with Monte Carlo model // MBS & Home equity ABS
  use OAS with Binomial model // Callable corporate
 use Z-spread // Plain-vanilla corporate, Credit card ABS, Auto loan ABS