This tutorial is the second of two parts covering fixed income.  The subject of asset backed securities (of which <a href="https://financetrain.com/introduction-to-mortgage-backed-securities/">mortgage backed securities</a> are technically a large subset) may sound intimidating to some candidates, but this module is actually heavily conceptual.  Beyond memorizing a few formulas, there are a lot of definitions and ideas to absorb.  The few formulas presented should not be ignored, but ABS/MBS are commonly valued with sophisticated computer programs, which is beyond the scope of the exam.

With a general expectation of two fixed income item sets (twelve questions) on the exam, as much as one full item set’s worth of questions, six give or take, could come from the second fixed income session.

This module aligns with Study Session 15 material in the Level II CFA Program Curriculum ©.

<strong>NOTES:</strong>

The Fixed Income topics of the Level 2 exam draw heavily upon the foundation created in Level 1.  Candidates are strongly encouraged to review the following from Level 1:
<ul>
	<li>How to value annual pay bonds with a <a href="https://financetrain.com/cfa-calculator-financial-calculator-for-cfa-exam/">CFA approved calculator</a>.</li>
	<li>How to value zero coupon bonds with a CFA approved calculator.</li>
	<li>The relationship between par, spot, and forward interest rates.</li>
	<li>The concept and formula to calculate a bond’s effective <a href="https://financetrain.com/what-is-macaulay-duration/">duration</a>.</li>
<ul>
	<li>Effective Duration = (Bond Price <sub>lower rate</sub> – Bond Price <sub>higher rate</sub>) / (2 * Bond Price <sub>current</sub> * change in interest rate)</li>
</ul>
	<li>The concept and formula to calculate a bond’s convexity.</li>
<ul>
	<li>Effective Convexity = (Bond Price <sub>lower rate</sub> + Bond Price <sub>higher rate</sub> - (2 * Bond Price <sub>current</sub>)) / (2 * Bond Price <sub>current</sub> * Δinterest rate<sup>2</sup>)</li>
</ul>
	<li>Negative convexity of callable bonds on the price-yield graph.</li>
	<li>Price floor of a putable bond on the pried-yield graph.</li>
</ul>
Never, ever, ever, ever forget that the value of a bond moves inversely with interest rate changes!  If interest rates go up, then the value of the bond will drop.

<strong>Material:</strong>

I.          Mortgage Backed Securities (MBS)

II.        Asset Backed Securities (ABS) Market

III.       Valuation of MBS and ABS

<strong> <br clear="all" /> </strong>

CFA Level 2: Fixed Income Part 2 – Introduction

<ul><li>Simply put, a mortgage is a debt instrument that is backed by real estate as collateral.</li><li><b>Fully Amortized Mortgage Loan:</b> Borrower makes an equal monthly payment that includes an interest component and a principal repayment component.
<ul>
<li>In the early years of the repayment schedule, interest makes the largest share of the monthly payment, as principal repayment takes over as the largest share in the later years.</li>
</ul>
</li></ul>



<div class="formula1">With a TI BA2+ calculator, the monthly payment can be obtained by entering the following:
<p>&nbsp;</p>
<ul>
<li>PV = Mortgage Amount</li>
<li>I/Y = Monthly interest rate (i.e. the annual interest rate / 12)</li>
<li>N = Number of months in mortgage (i.e. 12 * number of years)</li>
<li>CPT PMT: Will generate monthly mortgage payment</li>
</ul>
</div>



<ul><li style="list-style-type: none;">&nbsp;</li><li>When a private investor purchases a mortgage from a financial institution as an investment, the financial institution will take out a service fee from the mortgage's coupon rate.</li></ul>



<div class="formula1">Investor's Net Interest/Net Coupon = Gross Coupon - Service Fee</div>



<ul><li>Commonly mortgages can be wholly or partially pre-paid at the borrower's discretion, without penalty. <ul><li>NOTE: when evaluating asset backed securities it is critical to know whether or not the borrower can prepay without penalty. This will impact the security valuation approach; more to come. </li></ul></li><li><b>Prepayment:</b> Payment in excess of the required monthly minimum; commonly applied as a reduction of principal.</li><li><b>Curtailment:</b> Borrower prepays only a portion of the debt principal. <ul><li>Example: a borrower with an amortizing mortgage loan pays above the monthly minimum, but not so much that the payment covers the full remaining balance of the debt. </li></ul></li><li>In the event the mortgage market rates drop below the borrower's existing rate, then the borrower has an incentive to refinance.</li><li><b>Refinancing:</b> Taking out a new lower rate mortgage to repay the existing higher rate mortgage.</li><li><b><a href="https://financetrain.com/call-and-prepayment-risk/" class="rank-math-link">Prepayment Risk</a>:</b> Risk to the lender (investor) that the borrower will repay the mortgage principal sooner than expected and the lender will be forced to reinvest (or relend) the funds at a lower interest rate.</li></ul>

Mortgage Cash Flow Characteristics

<ul>
	<li>Mortgage Pass-through Security: shares in a pool of mortgages sold by a financial institution or government agency, where mortgage payments less fees are passed through to the security investors.</li>
		<ul>
			<li>A mortgage pass-through security is a type of MBS.</li>
		</ul>
	<li>Following issuance, pass-throughs can be resold by investors on the secondary market.</li>
		<ul>
			<div class="formula1">Pass-through Rate = Mortgage Rate - Service Fee</div>
			<li>Note that while mortgage payments are due on the first of the month, investors do not receive the pass-through payment for several days thereafter, enabling the servicing institution to collect several days worth of interest (which is called the "float").</li>
		</ul>
	<li>WAC = weighted average coupon rate of the mortgages in the security pool</li>
	<li>WAM = weighted average of maturity of the mortgage in the security pool</li>

</ul>
<h2>Pass-through Types</h2>
<ul>
	<li><b>Agency Pass-throughs:</b> Guaranteed by U.S. government agencies (Fannie Mae, Freddie Mac, and Ginnie Mae).</li>
		<ul class="list2">
			<li>Technically, Fannie Mae and Freddie Mac pass-throughs are corporate and do not carry the full faith and credit of the U.S. government, but there has been considerable debate over the "implied backing" of these securities.</li>
			<li>Mortgage Pass-throughs: Issued by Ginnie Mae and Fannie Mae</li>
			<li>Participation Certificates: Issued by Freddie Mac</li>
			<li>Conforming Mortgages: Meet standards to obtain agency backing</li>
			<li>Jumbo Mortgages: Mortgages that do not qualify for agency backing because of their size (too large)</li>
		</ul>
	<li><b>Non-agency Pass-throughs:</b> Are issued by private financial institutions and do not have the backing of a government agency; the mortgages in a non-agency pass-through are usually non-conforming.</li>
</ul>
<h2>Risks of Mortgage Pass-through Securities</h2>

<ul>
	<li><b>Interest Rate Risk:</b> As rates rise, the security's value will fall.</li>
	<li><b>Prepayment Risk:</b> Because mortgages can usually be prepaid at any time without penalty, mortgages essentially take the form of a callable bond that has a strike price at par.</li>
		<ul>
			<li>Prepayments are unpredictable, but directionally they increase as interest rates fall and decrease as interest rates rise.</li>
			<li>Prepayment risk is form of reinvestment risk, as the investor will be forced to re-invest at lower interest rates.</li>
			<li>MBS securities exhibit negative convexity as a result of the ability to prepay.</li>
		</ul>
	<li><b>Credit Risk:</b> Agency securities tend to have low credit risk.</li>
</ul>


Mortgage Pass-through Securities: Characteristics and Risks

Prepayment risk is the risk that a borrower will repay the mortgage before its due date. Mortgages can usually be prepaid at any time without penalty.

<h3>Two Types of Prepayment Risk</h3>
<ol>
	<li><strong>Contraction Risk:</strong> This is the risk that the investor (holder of the fixed income security) is forced to re-invest for a lower return following refinancing of mortgages in response to declining interest rates. The contraction risk increases as the interest rates decline. This is because as interest rates decline, the prepayments increase.</li>
	<li><strong>Extension Risk:</strong> Inability of an investor to re-invest principal at higher rates following pro-longed rising interest rates because mortgage borrowers opt not to refinance (which extends the average life of mortgages in the asset pool). When interest rates are rising, the borrowers are less likely to prepay. So, the investor's capital is locked in the securities at a lower rate and they cannot invest this capital in higher-interest instruments.</li>
</ol>
<h3>Variables that Impact Prepayment Risk</h3>

<ul>
	<li><strong>Mortgage Rates:</strong> In the event that mortgage rates drop far enough below the security's WAC, then borrowers are likely to refinance.</li>
	<li><strong>Interest Rate Path:</strong> The trend in interest rate changes will impact prepayment patterns.</li>
</ul>

<div class="special-area">For example, if interest rates follow a pattern of dropping, then increasing, the refinancing will steadily decline as most borrowers are likely to become "burned out" (that is they refinanced following the initial rate drop and subsequent rate drops are not sufficient to warrant another refinancing).

Understanding the interest rate path is critical for evaluating MBS.</div>

<ul>
	<li><strong>Mortgage Characteristics:</strong> The mortgages in the security pool will all be different from one another (to varying degrees) and these differences will result in different refinancing behaviors.</li>
	<li><strong>Seasonality:</strong> Real estate sales tend to be higher in the spring and summer, so prepayment may be higher during these months.</li>
	<li><strong>Economic Climate:</strong> Real estate turnover tends to be higher during periods of economic expansion.</li>
</ul>

Cash Flows and Prepayment Risk

<h2>Conditional Prepayment Rate (CPR) </h2>

CPR is the annualized percentage of the existing mortgage pool that is expected to be prepaid in a year. This assumes a constant rate for <a href="https://financetrain.com/cash-flows-and-prepayment-risk/">prepayment</a>, i.e., after every coupon, a constant percentage of the mortgages will be prepaid. This is also called the Constant Mortgage Mortality (CMM).

For example, if CPR is 8%, then the investor can expect 8% of the mortgages within the security pool to be prepaid within the year.

CPR is estimated based on various factors such as the characteristics of the underlying pool, historical prepayment rates and future predictions.

<h2>Single Monthly Mortality Rate (SMM)</h2>

CPR is an annual rate. However, since the mortgage payments happen monthly, we need to calculate the monthly prepayment rate. SMM is a measure of the monthly mortgage prepayment rate of the security’s mortgage pool.

Let’s take an example to understand how SMM can be calculated.

Assume that the outstanding loan is $100,000, the scheduled principal and interest payments are $500 and $10,000. If the actual payments in the first month are $12,000, the SMM will be calculated as follows:

<div class="formula1">SMM = (12,000 – 10,000 - 500)/(100,000 - 500) = 1.51%</div>

This means that 1.51% of the month’s scheduled principal balance has been prepaid.

<h2>Relationship between SMM and CPR</h2>

The following formula shows the relationship between SMM and CPR.

<div class="formula1">SMM = 1 – (1 – CPR)<sup>1/12</sup></div>

<div class="formula1"><strong>Example:</strong>

Assuming a CPR of 6%, the SMM will be calculated as follows:

SMM = 1 – (1 – 0.06)<sup> 1/12</sup> = 0.514%

Alternatively,

CPR = 1 – (1 – SMM)<sup> 12</sup>

If SMM is 1.5%, CPR will be calculated as follows:

CPR = 1 – (1 – 1.5%)^12 = 16.6%
</div>
<h2>Calculating Prepayment</h2>

The SMM can be used to calculate a dollar amount for the monthly principal prepayment.

<div class="formula1">Prepayment <sub>i</sub><sup>th</sup><sub> month</sub> ($) = SMM * (Principal Bal. <sub>i</sub> – Principal Pmt. <sub>i</sub>)</div>

Single Monthly Mortality (SMM) & Conditional Prepayment Rate (CPR)

<h2><strong>PSA Standard Benchmark</strong></h2>
The Public Securities Association’s (now known as the Bond Market Association) established convention for expressing <a href="https://financetrain.com/cash-flows-and-prepayment-risk/" title="Cash Flows and Prepayment Risk">prepayments</a> on a <a href="https://financetrain.com/mortgage-pass-through-securities-characteristics-and-risks/">mortgage pass-through</a>.

The PSA Benchmark is expressed as a series of monthly prepayment rates. It’s also referred to as a prepayment model suggesting that it can be used to estimate prepayment rates.

It assumes the following prepayment rates for a 30-year mortgage.

The first month prepayments = 1/30<sup>th</sup> of 6% (0.2%), then prepayments rise at a linear rate for 30 months. In the 30<sup>th</sup> month the prepayment rate reaches 6%. After that it maintains a 6% CPR for the remaining life of the mortgage. This benchmark is referred to as 100% PSA.

“100 PSA”: investor expectations that mortgage principal repayments in a security pool will all (100%) follow the PSA Benchmark.

The prepayment speeds can be made slow or fast by altering the percentage.  If a mortgage pool is 50 PSA, then half of the mortgage prepayments are expected to follow the PSA Benchmark, i.e., 0.1% prepayment in the first month that will linearly increase to 3% in the first 30 months after which it will remain constant at 3%. 150 PSA means 1.5 times the speed of PSA benchmark (i.e., based on 9% - 6% * 1.5).

The following chart illustrates the PSA for 50 PSA, 100 PSA, and 150 PSA.
<h2><strong>Calculating <a href="https://financetrain.com/single-monthly-mortality-smm-conditional-prepayment-rate-cpr/" title="Single Monthly Mortality (SMM) & Conditional Prepayment Rate (CPR)">SMM and CPR</a> using PSA</strong></h2>
PSA benchmark can be used to calculate SMM and CPR. The following examples illustrates this.
<div class="formula1">
<strong>Example 1</strong>

Using the PSA benchmark, CPR = 6% * t/30

For month 10,

CPR = 6% * 10/30 = 2%

SMM = 1 – (1 – 2%)^(1/12) =  0.17%

<strong>Example 2</strong>

Using 150 PSA, CPR = 9% * t/30

For month 5,

CPR = 9% * 5/30 = 1.5%

SMM = 1 – (1 – 1.5%)^(1/12) =  0.126%</div>

PSA Prepayment Benchmark

With <a title="Mortgage Pass-through Securities: Characteristics and Risks" href="https://financetrain.com/mortgage-pass-through-securities-characteristics-and-risks/">mortgage pass-through securities</a>, investors share equally in interest coupon and principal cash flows and therefore all assume equal prepayment, extension, and contraction risk.

CMO structures will take one or more pass-through securities, divide up the cash flows, and then prioritize the cash flows from the collateral to different bond classes called tranches. These tranches will have different risk and return profile. So, there will be several classes of bondholders with varying maturities or different date of maturities, known as tranches.

The tranches do not change the overall <a title="Cash Flows and Prepayment Risk" href="https://financetrain.com/cash-flows-and-prepayment-risk/">prepayment risk</a> of the underlying assets; the tranches simply reallocate that risk among the CMO’s investors.

<strong>CMO Tranches</strong>

<strong>Sequential Pay Tranches</strong>

Each tranche receives its pro-rata share of interest payments, but principal prepayments will first be allocated to Tranche A bonds until those bonds are retired, then to Tranche B bonds, etc.

Tranche A will be protected against extension risk, but the other bonds will be protected from contraction risk until Tranche A principal is retired.

<strong>Accrual Bonds or Z-tranche</strong>

Accrual bonds or Z-tranches do not receive cash payments from interest on the underlying collateral, rather interest is accrued to the accrual bonds’ principal value and then paid once the other tranches are paid off.

Accrual bonds allow investors to avoid reinvestment risk since no coupon interest is paid until all sequential bonds have been retired.

<strong>Planned Amortization Class (PAC) Tranche</strong>

These bonds will help an investor manage prepayment risk.<strong> </strong>Commonly the PAC is split into two tranches: a PAC tranche and a Support tranche (or companion tranche).

The PAC tranche will have a band or collar that sets controls on the principal payments allocated to it.

The initial PAC collar will have a minimum and maximum PSA speed.

Prepayment fluctuations outside the PAC collar band are then absorbed by the <strong>Support tranche</strong>.  Therefore the support tranche absorbs most of the prepayment risk.

Collateralized Mortgage Obligations (CMO) and CMO Tranches

<a title="Mortgage Pass-through Securities: Characteristics and Risks" href="https://financetrain.com/mortgage-pass-through-securities-characteristics-and-risks/">Mortgage backed securities </a>can be stripped into principal only (PO) strips and interest only (IO) strips. The principal component of the MBS payment is used to pay down the PO strip MBS, while the interest component of the payment is used to pay the IO strip MBS.

The bonds of stripped MBS therefore do not have a pro-rata principal and interest payment distribution to investors.
<h2>PO Strips</h2>
PO strips receive the entire mortgage principal and only the mortgage principal.
<ul>
	<li>PO strips have a known dollar amount but an unknown timing.</li>
	<li>The PO strip will be sold to investors at a significant discount to the gross principal balance; the discount amount will be based on the level of interest rates and the prepayment speed.</li>
	<li>Generally, PO strip bonds are more volatile than conventional MBS.</li>
	<li>Declining interest rates increase PO repayment speed, lowering the discount rate and increasing the PO price.</li>
	<li>Rising interest rates cause prepayments to decelerate and increases the discount rate applied to cash flows, thus lowering the PO price.</li>
	<li>The yield on PO strips varies based on the <a title="PSA Prepayment Benchmark" href="https://financetrain.com/psa-prepayment-benchmark/">prepayment speed</a>. The higher the prepayment, the faster the principal is repaid, and the higher is the yield for the investors.</li>
	<li>The investor is protect from the <a title="Cash Flows and Prepayment Risk" href="https://financetrain.com/cash-flows-and-prepayment-risk/">contraction risk</a>.</li>
</ul>
<h2>IO Strips</h2>
IO strip investors receive only the interest component of the mortgages in the security pool.
<ul>
	<li>Assuming that a mortgage is held to maturity, the IO payments would be very high in the early years and very low in the later years.</li>
	<li>High prepayments tend to reduce IO values.</li>
	<li>As interest rates decline and prepayments increase, less dollars of interest are paid to IO investors, so IO prices can drop when interest rates decline.</li>
	<li>As interest rates increase, prepayments decrease, so mortgages last longer and the total dollars paid to IO holders rises; therefore IO prices can rise when interest rates rise.</li>
</ul>
 

&nbsp;

Stripped MBS – Interest Only (IO) and Principal Only (PO)

Non-agency <a title="Mortgage Pass-through Securities: Characteristics and Risks" href="https://financetrain.com/mortgage-pass-through-securities-characteristics-and-risks/">Mortgage-backed Securities</a> are securities issued by private institutions in contract with the agency MBS which is issued by governmental or quasi-governmental agencies. The underlying collateral for non-agency MBS usually consists of mortgages which do not conform to the requirements, such as size, documentation, loan-to-value ratios, etc., of MBS issued by government agencies such as Ginnie Mae, Fannie Mae or Freddie Mac.

The mortgages in non-agency MBS can be prime mortgages, Alternative-A mortgages, Option Adjustable rate Mortgages (option ARMS), or Subprime mortgages.

Even though non-agency mortgage pass-throughs lack a government guarantee, many retain a high credit rating through the use of credit enhancement techniques.

In order to “conform” to agency standards, mortgages have loan size limits, loan to value limits, and debt to income ratio limits for the borrower.

Because borrowers can exceed these limits or may wish to have customized loan terms, many mortgages are non-conforming.

Non-agency mortgage securities are commonly structured as CMOs.

Given that the underlying mortgages of non-agency security pools have different characteristics from those of agency conforming security pools, prepayment patterns for the two types will differ.

For example, given the larger size of mortgages in a non-agency MBS security, borrowers have a high incentive to refinance whenever rates fall, so non-agency <a title="Cash Flows and Prepayment Risk" href="https://financetrain.com/cash-flows-and-prepayment-risk/">prepayment rates</a> can be higher in a declining interest rate environment.

Residential Non-Agency MBS

Commercial Mortgage Backed Securities (CMBS) are securities that are collateralized by commercial real estate mortgages on income generating properties.

Income generating properties backing CMBS commonly include: apartment buildings, office buildings, industrial properties, hotels, shopping malls, and elderly care facilities.

<strong>Differences between CMBS and residential MBS</strong>
<ul>
	<li><strong>Commercial Mortgages are Nonrecourse:</strong> Residential mortgages are recourse loans, whereas commercial mortgages are nonrecourse.  This means that the lender has legal recourse for a residential mortgage default.  In the event of a commercial mortgage default, however, the lender can only sell the underlying property in order to obtain repayment.</li>
</ul>
<ul>
	<li><strong>Collective Credit Risk for RMBS:</strong> residential mortgage backed securities have their credit assessed on a collective basis, as loans with similar profiles are pooled together.  Alternatively, CMBS loans have their credit assessed on an individual basis and this assessment must be continuously refined as different loans are paid off.</li>
</ul>
<strong>CMBS Structure</strong>

CMBS bonds are commonly sliced into tranches and the credit rating assigned to each tranche will reflect its specific credit risk.

CMBS have sequential pay structures and the highest rated tranche will be paid first.

As a result of the sequential pay structure, the lowest rated tranches have higher credit risk as they are the first to absorb losses from borrower defaults.

<strong>CMBS Deal Types (3)</strong>
<ul>
	<li><strong>Liquidating Deal Trusts:</strong> Backed by non-performing mortgage loans.</li>
</ul>
<ul>
	<li><strong>Multi-property Single Borrower:</strong> Security pool is composed of multiple loans from one borrower.</li>
</ul>
<ul>
	<li><strong>Multi-property Conduit:</strong> This is the most common type of CMBS, where the security pool includes loans for multiple properties from multiple commercial lending institutions.</li>
</ul>
<strong>CMBS and Call Protection</strong>

A CMBS investor holds a bond that is backed by a pool of underlying commercial mortgages.

When a borrower prepays a commercial mortgage, the mortgage is effectively “called away” from the investor.

CMBS investors can obtain call protection at both the loan level and by way of the CMBS structure.

<strong>Loan Level CMBS Call Protection Forms</strong>
<ul>
	<li><strong>Prepayment Lockout:</strong> Contractually prevents borrower from prepaying during a specified lockout period, which is commonly two to five years from loan origination.</li>
	<li><strong>Defeasance:</strong> Borrower invests prepayment funds in a portfolio of Treasuries that replicate mortgage cash flows.</li>
	<li><strong>Prepayment Penalty Points:</strong> Borrower must pay a fixed rate premium for prepayments made over the life of the loan.  The penalty declines over time.</li>
	<li><strong>Yield Maintenance or “Make Whole” Charge:</strong> Requires the borrower to pay a premium on prepayment that allows the lender to maintain the yield of the original mortgage contract.  With this type of protection, the lender becomes indifferent to prepayment timing and such a loan clause dis-incentivizes the borrower from refinancing.</li>
</ul>
<strong>Structural CMBS Call Protection</strong>
<ul>
	<li>The sequential pay structure offers investors will call protection as well.</li>
</ul>
<ul>
	<li>The higher rated tranches will be paid down first and have lower risk of principal loss resulting from borrower default.</li>
</ul>
<strong>CMBS Balloon Risk</strong>
<ul>
	<li>This is the risk that a commercial mortgage buyer will be unable to make a lump-sum principal payment at the end of the loan term.</li>
	<li>Balloon risk translates to extension risk as the borrower may be forced to extend the life of the loan.</li>
	<li>As a result of the tranche structure of a CMBS, significant refinancing may need to take place in the event of a balloon payment default so that obligations to the senior tranche can be met.</li>
</ul>
 

CMBS: Structure and Call Protection

<h2>Amortizing Loan</h2>
In an amortizing loan, the borrower makes regularly scheduled payments, called equated monthly installments, over the life of the loan to pay off the debt.  Each payment is consists of part interest and part principal.

The payment every month is fixed and is calculated in such a way that the interest portion of the payment is equal to the interest due for the month on the balance principal outstanding. The remaining portion of the payment is paid towards the principal. As more principal is paid every month, the outstanding principal balance keeps reducing. For this reason, this type of loan is also called a reducing-balance loan.

During the early years of the loan, the payment is primarily interest, as the principal outstanding is large. However, in the later years the payment is mostly principal.

Amortizing loans can usually be prepaid without penalty, so <a title="Cash Flows and Prepayment Risk" href="https://financetrain.com/cash-flows-and-prepayment-risk/">prepayment rates</a> must be calculated for an ABS bond supported by amortizing loans.
<h2>Non-amortizing Loan</h2>
In a non-amortizing loan, the borrower does not have a schedule of payments to repay the debt, rather the borrower is only required to make minimum monthly payments. This is the common structure of a credit card in the U.S. Other examples are balloon mortgages and deferred interest programs.

When the borrower makes a periodic payment that is less than the accrued interest, the balance of the unpaid interest is added to the debt principal.

When the borrower makes a periodic payment that is greater than the accrued interest, the excess balance is applied to reduce the debt principal.

Since a non-amortizing loan has no determined repayment schedule, there is no clear definition for “prepayment”.

Amortizing Loans vs. Non-Amortizing Loans

While <a title="Mortgage Pass-through Securities: Characteristics and Risks" href="https://financetrain.com/mortgage-pass-through-securities-characteristics-and-risks/">Mortgage-backed Securities (MBS)</a> and <a title="Collateralized Mortgage Obligations (CMO) and CMO Tranches" href="https://financetrain.com/collateralized-mortgage-obligations-cmo-and-cmo-tranches/">Collateralized Mortgage Obligations (CMO)</a> securities are a form asset backed securities (and technically the largest class of ABS), the acronym “ABS” is commonly used to refer to those securities whose underlying assets are not mortgage loans.

ABS collateral includes: auto loans, credit card receivables, student loans, home equity loans, manufactured housing loans, Small Business Administration loans, and collateralized bond obligations.

<strong>Securitization Process for an ABS</strong>
<ul>
	<li>The loan originator (commonly a bank) makes a loan, such as a home equity loan where the borrower is borrowing against the equity (home value in excess of remaining mortgage balance) in his or her house.</li>
	<li>The bank then pools similar loans and sells these loans to a special purpose vehicle (SPV).</li>
	<li>The SPV holds the loans as assets and issues ABS bonds backed by the loan pool.</li>
	<li>Proceeds from the ABS issuance allow the SPV to fund the purchase of the loans from the bank.</li>
	<li>The SPV employs a third part (the third part can actually be the loan originator) as the servicer to collect monthly payments.</li>
	<li>The servicer then delivers the payments to the SPV’s trustee.</li>
	<li>The SPV’s trustee forwards payments on to the ABS bondholders and files financial reports for the collateral.</li>
</ul>
<img class="aligncenter size-full wp-image-6422" title="ABS" src="https://financetrain.com/wp-content/uploads/ABS.png" alt="" />

From a legal perspective, a non-mortgage ABS is very similar to an MBS, but non-mortgage ABS may have significantly lower credit quality collateral and the non-mortgage ABS collateral may be amortizing or non-amortizing.

<strong>Payment Structure</strong>

The payment structure to an ABS investor is commonly driven by whether or not the underlying collateral is amortizing or non-amortizing.
<ul>
	<li><strong>ABS with Amortizing Collateral:</strong> Prepayment is commonly passed through to ABS investors.</li>
	<li><strong>ABS with Non-amortizing Collateral:</strong> Principal repayments from borrowers during a “lock-out period” are used by the trustee to purchase additional collateral.</li>
	<li><strong>Revolving Structure:</strong> The ABS investors will not receive any principal repayments until the lock out period ends.  After the lock out period ends, no new collateral will be acquired and principal payments will then be passed through to investors.  This is called a revolving structure.</li>
</ul>
&nbsp;

Overview of Asset Backed Securities (ABS)

Because most <a title="Mortgage Pass-through Securities: Characteristics and Risks" href="https://financetrain.com/mortgage-pass-through-securities-characteristics-and-risks/">mortgage-backed securities</a> have higher credit quality collateral than non-mortgage <a title="Overview of Asset Backed Securities (ABS)" href="https://financetrain.com/overview-of-asset-backed-securities-abs/">ABS</a>, many non-mortgage ABS offer credit enhancements to make their risk level more tolerable to investors.

Credit enhancement can be internal or external.

<strong>Internal Credit Enhancements</strong>
<ul>
	<li><strong>Cash Reserve Accounts:</strong> ABS issuer sets aside a portion of the fees earned in the security underwriting process, so this cash is available to draw upon if necessary.</li>
	<li><strong>Excess Servicing Spread Accounts:</strong> This spread creates an additional basis point buffer beyond the servicing fee between the gross weighted average coupon of the assets and weighted average coupon paid to ABS investors.  This excess spread is deposited into an account and is available to draw upon if necessary.</li>
	<li><strong>Overcollateralization:</strong> The value of the assets supporting an ABS is greater than the outstanding principal owed to bond investors.  Therefore, in the event of a default, excess assets can be used to pay ABS investors.</li>
	<li><strong>Senior/Subordinate Structure:</strong> More than one tranche is issued for the asset pool and in the event of a default; the subordinate tranches absorb losses before the senior tranches do.</li>
</ul>
<strong>External Credit Enhancements </strong>

Commonly, external credit enhancements are third party employed measures to back up the internal credit enhancements.
<ul>
	<li>For example, bond insurance could be purchased for the asset pool from an insurance company.</li>
	<li>Keep in mind that if the credit quality of the third party insurer or guarantor declines, then the credit quality of the ABS will decline as well.</li>
</ul>

Internal and External Credit Enhancements

<a title="Overview of Asset Backed Securities (ABS)" href="https://financetrain.com/overview-of-asset-backed-securities-abs/">Asset-backed securities</a> can be issued as pass-through or pay-through securities.

<strong>ABS Pass-through Structure:</strong> In a pass-through structure, the cash flows generated by the asset pool are passed through to investors, less a servicing fee, on a pro-rata basis (this is the same general structure as that of the <a title="Mortgage Pass-through Securities: Characteristics and Risks" href="https://financetrain.com/mortgage-pass-through-securities-characteristics-and-risks/">mortgage pass through securities</a> previously discussed).

<strong>ABS Pay-through Structure:</strong> This is similar to a collateralized mortgage obligation, where tranches with different characteristics are paid out differently based on their risk-return profile.

The tranching within a pay-through structure can be of two types: credit tranching and prepayment tranching. Tranching is a type of internal credit enhancement.

<strong>Two Types of Pay-through Structures</strong>
<ul>
	<li><strong>Credit Tranching: </strong>This is the most common form of tranching and creates a senior/subordinate structure. A typical senior/subordinate structure consists of several tranches varing in their seniority. Cash flows are divided among senior and subordinated tranches. The senior tranches are the first ones to be paid the principal from the available cash flow. Subordinate tranches are the first to absorb default losses, so the subordinate tranches provide protection to the senior tranches. This protection structure is also called waterfall structure. The structure redistributes credit risk and is considered a credit enhancement.</li>
	<li><strong>Prepayment Tranching:</strong> Cash flows are divided among tranches that have different principal payment parameters.  These tranches can be sequential pay or planned amortization class, for example.  This structure redistributes prepayment risk. The senior tranche is divided into tranches with different exposure to prepayment risk. In this way, senior tranches can be transferred among the senior tranches.</li>
</ul>
 

Pay-through Structures: Prepayment Tranching vs. Credit Tranching

HELs are loans backed by a residential property lien.  An HEL is commonly used to finance the purchase of goods other than the home itself.

An HEL may be amortizing (also called “closed-end”) or non-amortizing (also called “open-end”). The closed-ended home equity loans are primarily used as collateral in asset-backed securities. The closed-ended HEL works just like an amortizing mortgage; it has a fixed maturity and equated payments that amortize the loan by its maturity date. HELs can be fixed-rate or floating-rate.

<strong>HEL Prepayments:</strong> While HELs have <a title="Cash Flows and Prepayment Risk" href="https://financetrain.com/cash-flows-and-prepayment-risk/">prepayment risk</a>, it is very specific to the loans in the asset pool and their respective borrowers. The prospectus for an HEL collateralized ABS will contain a prospectus prepayment curve (PPC) which serves a similar purpose as the <a title="PSA Prepayment Benchmark" href="https://financetrain.com/psa-prepayment-benchmark/">PSA</a> for mortgage pass-throughs.  While the PSA is a general benchmark, the PPC will be specific to the ABS.

<strong>HEL Payment Structure:</strong> Available Funds Cap
<ul>
	<li>ABS secured by HELs may be issued to investors with floating interest rates, but the underlying assets may have fixed rates.</li>
	<li>Available Funds Cap is stipulation employed by an ABS issuer to prevent a situation where interest paid on the ABS to investors does not exceed interest earned by the collateral in the asset pool.</li>
</ul>
In HEL ABS, the tranches are structured so as to provide some senior tranches more prepayment protection that other senior tranches. This is done through two structures: Non-Accelerating Senior (NAS) Tranche, and Planned Amortization Class (PAC) Tranche.

<strong>HEL ABS Non-Accelerating Senior (NAS) Tranche</strong>
<ul>
	<li>The NAS tranche gives greater prepayment protection than that provided to subordinate tranches.</li>
	<li>The NAS tranche will get principal payments based on a schedule that is a percentage of the tranche’s pro rata share.</li>
	<li>The NAS tranche will have more stable average lives in the early years of an ABS bond.</li>
</ul>
<strong>HEL ABS Planned Amortization Class (PAC) Tranche</strong>
<ul>
	<li>Like the NAS tranche, the PAC tranche is another method of offering prepayment protection to specific ABS investors.</li>
	<li>Support tranches will receive principal prepayments in line with the parameters of the PAC collar.</li>
</ul>
 

Home Equity Loans (HEL) Backed Securities

An <a title="Overview of Asset Backed Securities (ABS)" href="https://financetrain.com/overview-of-asset-backed-securities-abs/">asset-backed security</a> can be collateralized with a pool of loans for manufactured houses. Manufactured houses (commonly known as mobile homes in the United States) are a type of prefabricated houses that are largely assembled in factories and then transported to sites where they need to be installed.

These securities may (not always) be issued by Ginnie Mae.  When issued by Ginnie Mae, the securities have the credit backing of the U.S. government.

Manufactured housing ABS are similar to MBS in that the loans are typically 15 to 20 years, and have a repayment schedule similar to a regular home mortgage. The loan itself could be a mortgage loan or a consumer installment loan.

The prepayment is measured in terms of CPR. <a title="Cash Flows and Prepayment Risk" href="https://financetrain.com/cash-flows-and-prepayment-risk/">Prepayment risk</a> for manufacture housing ABS tends to be lower than MBS because:
<ul>
	<li>The loans are smaller and therefore the borrowers have less incentive to refinance;</li>
</ul>
<ul>
	<li>Manufactured homes tend to depreciate in value faster than the loan principal declines, which makes refinancing difficult to obtain; and</li>
</ul>
<ul>
	<li>Manufactured home buyers tend to have low credit quality and might not be able to refinance.</li>
</ul>
&nbsp;

Manufactured Housing Backed Loans

Institutions that lend funding for the purchase of automobiles may issue auto loan backed ABS.

Auto loans are typically amortizing with a term of three to five years.

Prepayment risk exists because borrowers may sell or trade-in their vehicles to buy new ones, the car can be repossessed, borrowers may destroy their cars in accidents and have the loans paid off with insurance money, or borrowers may refinance if rates drop far enough.

Prepayment can be measured by absolute prepayment speed, which is a percentage of the collateral.  The absolute prepayment speed can then be used to create a <a title="Single Monthly Mortality (SMM) &amp; Conditional Prepayment Rate (CPR)" href="https://financetrain.com/single-monthly-mortality-smm-conditional-prepayment-rate-cpr/">single monthly mortality (SMM) rate</a>.

Auto loans represent the second largest sub-sector of the ABS market.

Auto loan ABS can be <a title="Mortgage Pass-through Securities: Characteristics and Risks" href="https://financetrain.com/mortgage-pass-through-securities-characteristics-and-risks/">pass-through</a> or <a title="Pay-through Structures: Prepayment Tranching vs. Credit Tranching" href="https://financetrain.com/pay-through-structures-prepayment-tranching-vs-credit-tranching/">pay-through structures</a>.

Auto loan ABS are generally issued as an owner trust structure, which allows for a time tranching of the senior class, and credit tranching to issue subordinated debt. The sequential senior bonds allow issuers to tailor issuance to meet the different maturity preferences of fixed-income investors.

Auto loan ABS can also be structured as a grantor trust in which certificates represent a proportionate beneficial interest in the trust. Principal is passed through to investors on a pro rata basis. The certificates can be tranched into senior and subordinated classes, but it does not allow time tranching.

Auto Loans Backed Securities

As the name suggests, SLABS are asset backed securities collateralized by student loans.

The majority of U.S. student loans are backed by the U.S. government, which reduces credit risk for the investor.

The most common student loans are the Federal Family Education Loan Program (FFELP) loans, which are guaranteed by the U.S. Department of Education ("DOE"). Under this program, the government provides loans to students through private lenders. These private lenders give loans to students based on their repayment capacity. They also give you the ability to <a href="https://www.credible.com/refinance-student-loans" target="_blank" rel="noopener">consolidate student loans</a>. In case of a default on the loans, the government will guarantee upto 95-98% of the principal plus interest payments.

The second type of loans are the non-FFELP or private sector student loans. Students use private student loans to bridge the gap between what they can borrow through federal programs and what they actually need for the education.

A government-sponsored enterprise called Student Loan Marketing Association (Sallie Mae) was created to purchase student loans in the secondary market and to securitize pools of student loans.

<a title="Cash Flows and Prepayment Risk" href="https://financetrain.com/cash-flows-and-prepayment-risk/">Prepayment risk</a> is largely associated with defaults; the student defaults and the guarantor pays off the loan.

Student loans are commonly issued with floating interest rates, so declining interest rates might not induce prepayments from refinancing.

Student Loan Backed Securities (SLABS)

SBA backed <a title="Overview of Asset Backed Securities (ABS)" href="https://financetrain.com/overview-of-asset-backed-securities-abs/">ABS</a> are securities whose underlying assets are loans from the Small Business Administration of the U.S. government.

The SBA is a US Government agency that guarantees the loans made by approved SBA lenders to qualified borrowers. Since, the SBA loans are backed by the U.S. government, it lowers credit risk.

The pooled loans must have similar terms and features, such as capped or uncapped. The different maturities used for pooling loans together are 7, 10, 15, 20 and 25 years.

SBA loans are commonly floating rate. The reference rate is the prime rate. The payments are made monthly and include both interest and principal repayments.

The <a title="Cash Flows and Prepayment Risk" href="https://financetrain.com/cash-flows-and-prepayment-risk/">prepayments</a> are largely driven by the borrowing purpose. Shorter maturity loans tend to have higher prepayment speed. Studies suggest that the loans with maturities of less than 10 years made for the purpose of working capital needs have the fastest prepayment speed. On the other hand, loans for real estate purposes have the slowest prepayment rates. Loans with capped interest rates prepay slower than uncapped loans.

SBA Loan Backed Securities

When institutions that issue consumer credit cards do not wish to keep the receivables on their balance sheets, these institutions can issue credit card receivable backed securities.

Credit card loans are non-amortizing and are issued by banks, retailers, as well as travel companies.

The cash flows from credit cards consist of finance charges (interest), fees (annual fee and late payment fee) and principal repayments.

Because a principal retirement schedule does not exist for the credit card receivables, a lock out period may be established for the <a title="Overview of Asset Backed Securities (ABS)" href="https://financetrain.com/overview-of-asset-backed-securities-abs/">ABS</a>.

During the lock-out period, any principal paid by the borrowers is loaned to other credit card users (invested in receivables) to maintain the size of the pool.  Therefore the investors only receive interest payments during the lockout period. The lockout period ranges from 18 months to 10 years. After the lock-out period the principal is not reinvested, instead it is pad back to the investors. This period is called principal amortization period.

<strong>Amortization Structures</strong>

Principal payment can be structured as:
<ul>
	<li><strong>Pass-through:</strong> Principal is paid to ABS investors as received</li>
	<li><strong>Controlled Amortization Schedule:</strong> Principal is returned at a set schedule or there can be some range of prepayment speeds.</li>
	<li><strong>Soft Bullet:</strong> Principal payments are held by the trustee during an accumulation speed and then paid to investors at once; the title soft bullet is used because the maturity of the payment is a goal rather than a legal guarantee.</li>
</ul>
<strong>Performance Measure: Portfolio Yield</strong>
<ul>
	<li>A large credit card portfolio will have defaults.</li>
	<li>These losses are charged against the portfolio’s gross yield to obtain a net yield for the ABS.</li>
	<li>ABS investors will be paid from net yield.</li>
</ul>
<strong>Performance Measure: Monthly Payment Rate &amp; Early Amortization Provisions</strong>
<ul>
	<li>Monthly Payment Rate (MPR) is the ratio of monthly payments as a percentage of the prior month’s loan balance.</li>
	<li>When MPR is low, the investor can be exposed to extension risk.</li>
	<li>When MPR is extremely low, it could be inferred that the borrowers in the credit card pool may fail to repay principal (i.e. it is a sign of default risk).</li>
	<li>Early Amortization Provisions: offer credit card backed ABS investors protections which force early principal repayment if specified monthly payment metric levels are crossed (or triggered).</li>
</ul>
 

&nbsp;

Credit Card Receivable Backed Securities

CDOs are a form of <a title="Overview of Asset Backed Securities (ABS)" href="https://financetrain.com/overview-of-asset-backed-securities-abs/">asset-backed securities</a> where the underlying collateral is a diversified pool of debt instruments such as junk bonds, bank loans, or emerging market debt.

<strong>Collateralized Loan Obligations (CLOs):</strong> This is the case where the loan pool is entirely bank loans.

<strong>Collateralized Bond Obligations (CBOs):</strong> This is the case where the loan pool is entirely bond like instruments.
<h2>CDO Tranche Structure</h2>
<ol start="1">
	<li><strong>High Quality Senior Tranche:</strong> These bonds are typically floating rate and will be entitled to the majority of the cash flows generated by the asset pool.</li>
	<li><strong>Lower Quality Junior Tranches:</strong> These bonds are typically fixed rate and will absorb some of the default risk.</li>
	<li><strong>Equity Tranche:</strong> This tranche receives payments from the asset pool that are not paid to the senior and junior tranches.</li>
</ol>
In the case where the underlying assets are fixed rate, interest rate derivatives will need to be employed to manage obligations to the senior tranche.
<h2>CDO Life Cycle</h2>
<ul>
	<li><strong>Start-up Phase:</strong> For a period of one to two months, CDO securities are sold to the investing public and the sale proceeds are used to purchase debt instruments for portfolio.</li>
	<li><strong>Reinvestment Phase:</strong> A period of three to five years; the portfolio manager will reinvest prepayments from the asset portfolio.</li>
	<li>Pay-down Phase: principal is repaid to investors based on the sequence prescribed in the ABS indenture.</li>
</ul>
<h2>Cash Vs. Synthetic CDO</h2>
<strong>Cash CDO:</strong> The CDO actually holds the underlying securities.

<strong>Synthetic CDO:</strong> The CDO uses derivatives to obtain economic exposure to desired securities.
<h2>CDO Objective</h2>
CDO sponsor motivation determines whether the objective category is arbitrage driven or balance sheet driven.
<ul>
	<li><strong>Arbitrage Driven CDOs:</strong> The goal of these CDOs is to earn a positive spread between the cost of funds (the interest paid to CDO investors) to acquire the asset collateral and the return on the collateral.  In other words, the CDO issuer seeks to generate a return from the assets that is greater than the rate paid to investors.</li>
	<li><strong>Balance Sheet Driven CDOs:</strong> The goal of these CDOs is to allow banks to remove loan assets from their balance sheets in order to remove credit risk exposure.</li>
</ul>
 

Collateralized Debt Obligations (CDOs) and Synthetic CDOs

<h2>Cash Flow Yield</h2>
Unlike bonds, cash flows for <a title="Mortgage Pass-through Securities: Characteristics and Risks" href="https://financetrain.com/mortgage-pass-through-securities-characteristics-and-risks/">MBS</a>/<a title="Overview of Asset Backed Securities (ABS)" href="https://financetrain.com/overview-of-asset-backed-securities-abs/">ABS</a> investments are commonly monthly.  The cash flows will be made up of interest, scheduled principal repayments, and principal prepayments.  In order for the cash flow expectations to approximate reality, prepayment assumptions must be made.

<div class="formula1">r <sub>bond equiv. yield</sub> = 2[(1 + i <sub>monthly</sub>)<sup>6</sup> – 1]</div>

An investor actually realizing the cash flow yield return depends upon the following taking place:
<ul>
	<li>Cash flows are re-invested every month at the cash flow yield;</li>
	<li>Prepayments equal the assumed prepayment schedule;</li>
	<li>The investor holds the ABS/MBS until it is retired.</li>
</ul>
<h2>Nominal Spread</h2>
Compares the cash flow yield of the ABS/MBS to the yield to maturity of a Treasury security with a maturity equal to the average life of the ABS/MBS.

<div class="formula1">Nominal Spread = CF Yield – YTM of comparable Treasury</div>

The nominal spread may be a flawed measure of comparison as the spread may not reflect risk premiums unique to the ABS/MBS, such as prepayment risk.
<h2>Zero-Volatility Spread (aka Z-spread or static spread)</h2>
The Z-spread is the spread that an ABS/MBS investor will receive over the complete Treasury spot rate curve, if the security is held to maturity.

The Z-spread will be closer to the nominal spread when: the ABS/MBS has a short average life and/or when the yield curve is relatively flat.

The Z-spread assumes that the timing and amount of principal payments are known, regardless of future interest rate path changes.  In other words, the Z-spread assumes interest rates are constant, so prepayments are known.

Given the material prepayment risk inherent in ABS/MBS, the Z-spread may not be appropriate for relative valuation analysis.
<h2>Option Adjusted Spread (OAS)</h2>
Since the OAS adjusts for option risk, it is a good measure of relative risk after adjusting for the impact of prepayments.

Cash Flow Yield, Nominal Spread, and Zero Volatility Spread for ABS/MBS

Because the binomial interest rate tree model is a backward induction process that does not consider current interest rates in comparison to historical interest rates in estimating prepayments (i.e. the interest rate path), it cannot be used to value ABS/MBS securities.

Understanding the interest rate path is critical for valuing <a title="Overview of Asset Backed Securities (ABS)" href="https://financetrain.com/overview-of-asset-backed-securities-abs/">ABS</a>/<a title="Mortgage Pass-through Securities: Characteristics and Risks" href="https://financetrain.com/mortgage-pass-through-securities-characteristics-and-risks/">MBS</a> because the interest rate path will inform prepayment assumptions, as borrowers tend to refinance when interest rates drop.
<h2>Steps in a Monte Carlo Simulation</h2>
<ol>
	<li>A Monte Carlo simulation program will create thousands of interest paths that the ABS/MBS could follow over its life.</li>
	<li>The paths are adjusted so the model is “arbitrage free”, meaning that the model correctly values current on the run Treasuries.</li>
	<li>For each interest rate path modeled, the simulator will forecast monthly prepayments for the life of the security.</li>
	<li>The simulator calculates cash flows paid on each interest rate path utilizing forecasted prepayment rates.</li>
	<li>A present value of each path is calculated by the simulator based on the cash flows and discount rates for each path.</li>
	<li>The simulator averages the present values for each path in step 5.  This value is the expected value of the security, if it were risk free.</li>
	<li>A constant spread is added by the simulator to the arbitrage free Treasury rates calculated in step 2; the cash flows from step 4 are discounted with the new discount rate.</li>
	<li>The simulator averages all the present values for step 7 and compares this to the current price of the security.  If the average present value is too low, then the constant spread in step 7 will be reduced.</li>
</ol>
<h2>Monte Carlo Simulation and the Option Adjusted Spread (OAS)</h2>
The difference between the OAS and the Z-spread can be interpreted as the value of the embedded option, stated in basis points. The Z-spread will be greater than the OAS spread.

In order for the OAS to be accurate:
<ul>
	<li>Volatility assumptions must closely approximate future volatility.</li>
	<li>Prepayment assumptions must closely approximate prepayment realized.</li>
	<li>The Monte Carlo simulator model correctly values on the run Treasuries</li>
	<li>The OAS ensures that the average price across all interest rate paths equals the security’s current price.</li>
</ul>
If the assumptions are accurate and comparable for multiple ABS/MBS securities, then the ABS/MBS with the higher OAS is considered the better value.

OAS = Z-spread, when interest rate volatility is assumed to be zero.

Monte Carlo Simulation for ABS/MBS

Effective <a title="Bond Duration and Convexity Simplified – Part 1 of 2" href="https://financetrain.com/bond-duration-and-convexity-simplified-part-1-of-2/">Duration and Convexity</a> for ABS/MBS are calculated with the same formulas as those used for bonds valued with a binomial interest rate tree model (see the notes at the beginning of the module).

Different ABS/MBS security dealers may calculate different effective durations because:
<ul>
	<li>Different dealers may use different interest rate changes in the calculation (i.e. not all dealers may use the standard 100 basis points/1%).</li>
	<li>Different dealers may use different <a title="Cash Flows and Prepayment Risk" href="https://financetrain.com/cash-flows-and-prepayment-risk/">prepayment</a> assumptions in valuing the ABS/MBS.</li>
	<li>Different dealers may use different interest rate paths and interest rate volatility.</li>
</ul>
<strong>Various Duration Measures for MBS</strong>
<ul>
	<li><strong>Cash Flow Duration:</strong> This is the same as effective duration. The problem with this measure is that the effect of changes in prepayment rates is not fully captured, which may change due to changes in cash flow yield. It assumes one prepayment rate throughout the life of the MBS.</li>
	<li><strong>Modified Duration:</strong> Modified duration indicates the percentage change in the price of a bond for a given change in yield. It is a more adjusted measure of Macaulay duration that produces a more accurate estimate of bond price sensitivity. This less accurate than cash flow duration because modified duration does not consider how prepayments may change. Cash flow duration, on the other hand, does recognize prepayments, even though with a very simple assumption. Duration is obtained by rolling up and rolling down the coupon, as the price changes.</li>
	<li><strong>Coupon Curve Duration:</strong> In this method, the market prices are used to calculate the duration of the MBS. The coupon curve is the curve of various MBS with different coupons and prices. You will generally take different MBS from an issuer with different coupon rates.</li>
	<li><strong>Empirical Duration:</strong> It does not use any theoretical formula, rather uses historical pricing data for calculating duration.</li>
</ul>
&nbsp;

Duration and Convexity for ABS/MBS

<ul>
	<li>A key driver in selecting the appropriate <a href="https://financetrain.com/cash-flow-yield-nominal-spread-and-zero-volatility-spread-for-absmbs/" title="Cash Flow Yield, Nominal Spread, and Zero Volatility Spread for ABS/MBS">spread</a> is the nature of the asset pool backing the security because this will influence prepayment behavior.</li>
	<li>Cash flow classes of the underlying loans:</li>
		<ul>
			<li>1. The underlying loans cannot be prepaid.</li>
			<li>2. The underlying loans can be prepaid, but refinancing is not a significant reason to prepay, so interest rate movements do not affect prepayment; this is most commonly the case with auto loan backed securities.</li>
			<li>3. The underlying loans can be prepaid and prepayment is largely driven by refinancing, so prepayment depends on the level of interest rate activity. This class is comprised of two sub-classes:</li>
				<ul class="list2">
					<li>3a) The current interest rate level determines prepayment; which would be the case with callable bonds.</li>
					<li>3b) Both the current interest rate level and the prior path of interest rate determine prepayment; which would be the case with mortgage backed securities and some other asset backed securities.</li>
				</ul>
		</ul>
<li>Securities backed by assets from cash flow classes 1 and 2 can be analyzed with the Z-spread.</li>
	<ul>
		<li>The OAS can also be used for these securities because cash flows are not interest rate level dependent.  In this instance, Z-spread = OAS.</li>
	</ul>
<li>Securities backed by assets from cash flow class 1 can be analyzed with the nominal spread; the Z-spread should be similar and is technically superior.</li>
<li>Cash Flow Class 3a: If a bond has an embedded option, the binomial interest rate tree model can be applied to generate an OAS; a callable corporate bond, for example.</li>
<li>Cash Flow Class 3b: If the security is backed by assets that are interest rate path dependent, such as a mortgage pass through security, a Monte Carlo based OAS should be applied.</li>
<li>OAS can be used for any debt security, but it is mandatory when borrower refinancing heavily influences future cash flows received by investors.</li>
<li>Analysts should not apply the nominal spread to evaluate bonds with embedded options as this spread will not account for the impact of the options on investor returns.</li>
</ul>
<table class="mytable">
<tr>
<th scope="colspan">YIELD CURVE & RATE VOLATILITY</th>
<th scope="colspan">APPROPRIATE SPREAD</th>
</tr>
<tr>
  <td>Flat & zero volatility.</td>
  <td>Analyst can use any spread as nominal = Z-spread = OAS.</td>

</tr>
<tr>
  <td class="alt">Non flat & non-zero volatility.</td>
  <td>Conventional bonds without embedded options: can use either nominal or Z-spread, but Z is superior.</td>

</tr>
<tr>
  <td>Non flat & non-zero volatility.</td>
  <td>Amortizing securities where interest rates do not influence prepayments: Z-spread.</td>

</tr>
<tr>
  <td class="alt">Non flat & non-zero volatility.</td>
  <td>Securities whose prepayments are affected by current interest rates: OAS from binomial interest rate tree model.</td>

</tr>
<tr>
  <td>Non flat & non-zero volatility.</td>
  <td>Securities whose prepayments are affected by interest rate levels and interest rate path: OAS from a Monte Carlo model.</td>

</tr>
</table>


Choosing an Appropriate Spread for ABS/MBS

Fixed Income Part 2

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COURSE

Fixed Income Part 2

Lessons

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