CH-15-16 Asset-Backed Securities – Bond Markets, Analysis and Strategies : Book Guide

This Document Contains Chapters 15 to 16 CHAPTER 15 ASSET-BACKED SECURITIES CHAPTER SUMMARY A security created by pooling loans other than residential prime mortgage loans and commercial mortgage loans is referred to as an asset-backed security (ABS). The market classifies securities backed by subprime mortgage loans as mortgage-related ABS. The two types of assets that can used as collateral for an asset-backed securitization are existing assets/existing receivables or assets/receivables to arise in the future. Securitizations with existing collateral are referred to as existing asset securitizations. Securitizations of assets/receivables to arise in the future are referred to as future flow securitizations. The types of assets that have been securitized fall into the following two general categories: (1) consumer asset-backed securities and subprime residential mortgage-backed securities (MBS) and (2) commercial asset-backed securities. The broad-based bond market indexes include an ABS sector. The five largest subsectors within this sector are: (1) credit card receivable ABS, (2) auto ABS, (3) home equity ABS, (4) rate reduction bonds (also called stranded cost ABS), and (5) manufactured housing ABS. A product that uses the securitization technology is the collateralized debt obligation (CDO). CREATION OF AN ABS A security created by pooling loans other than mortgage loans is referred to as an asset-backed security (ABS). The textbook uses the following illustration to explain how an ABS is created and the parties to a securitization. Suppose that Exception Dental Equipment, Inc. has a bulk of its sales from installment contracts (wherein the buyer agrees to repay Exceptional Dental Equipment, Inc., over a specified period of time for the amount borrowed plus interest). The dental equipment purchased is the collateral for the loan. The credit department of Exceptional Dental Equipment, Inc. makes the decision as to whether or not to extend credit to a customer. The criteria for granting a loan are referred to as underwriting standards. Because Exceptional Dental Equipment, Inc. is granting the loan, the company is referred to as the originator of the loan. Moreover, Exceptional Dental Equipment, Inc., (EDE) may have a department that is responsible for servicing the loan. As explained in previous chapters, servicing involves collecting payments from borrowers, notifying borrowers who may be delinquent, and, when necessary, recovering and disposing of the collateral (i.e., the dental equipment in our illustration) if the borrower fails to make the contractual loan payments. While the servicer of the loans need not be the originator of the loans, in our illustration we are assuming that the originator (EDE) is also the servicer. Suppose EDE has more than $300 million of installment sales contracts and wants to raise this amount. Rather than issuing corporate bonds for $300 million, the EDE’s treasurer decides to raise the funds via a securitization. To do this, EDE sets up a legal entity called a special purpose vehicle (SPV) that is called DE Asset Trust (DEAT). EDE will then sell to DEAT $300 million of the loans and so receive from DEAT $300 million in cash, the amount of funds it wanted to raise. DEAT obtains the $300 million by selling securities that are backed by the $300 million of loans. The securities are asset-backed securities. The Parties to a Securitization In our hypothetical securitization, Exceptional Dental Equipment, Inc. (EDE) is not the issuer of the ABS (although it is sometimes referred to as the issuer because it is the entity that ultimately raises the funds). Rather, it originated the loans. Hence, in this transaction, EDE is called the “seller” because it sold the receivables to DEAT. EDE is also called the “originator” because it originated the loans. DEAT (i.e., the SPV in the securitization) is referred to as the “issuer” or “trust” in the prospectus. While in our simple transaction EDE manufactured the dental equipment and originated the loans, there is another type of securitization transaction involving another company (called a conduit) that buys the loans and securitizes them. A conduit that finances dental equipment manufactures would warehouse the installment contracts purchased until it had a sufficient amount to sell to an SPV, which would then issue the ABS. There will be a trustee for the securities issued. The responsibilities of the trustee are to represent the interests of the bond classes by monitoring compliance with covenants and in the event of default enforce remedies as specified in the governing documents. Two-Step Securitizations The above description of the parties to a securitization is referred to as a “one-step securitization.” For certain reasons that are not important to investors, a securitization might involve two SPVs in order to ensure that the transaction is considered a true sale for tax purposes. One SPV is called an intermediate SPV, which is a wholly owned subsidiary of the originator and has restrictions on its activities. It is the intermediate SPV that purchases the assets from the originator. The intermediate SPV then sells the assets to the SPV that issues the asset-backed securities (i.e., the issuing entity). In the prospectus for a securitization transaction, the intermediate SPV is referred to as the depositor. Transaction Structure In creating the various bond classes (or tranches) in a securitization, there will be rules for distribution of principal and interest. All asset-backed securities are credit enhanced. Credit enhancement levels are determined relative to a specific rating desired by the seller/servicer for a security by each rating agency. Role of the Special Purpose Vehicle To understand the role of the SPV, we need to understand why a corporation would want to raise funds via securitization rather than simply issue corporate bonds. There are four principal reasons why a corporation may elect to raise funds via a securitization rather than a corporate bond. They are the potential to reduce funding costs, to diversify funding sources, to accelerate earnings for financial reporting purposes, and to achieve (if a regulated entity) relief from capital requirements. We will only focus on the first of these reasons to see the critical role of the SPV in a securitization. Suppose that Exceptional Dental Equipment, Inc. (EDE) has a BB credit rating. If it wants to raise funds equal to $300 million by issuing a corporate bond, its funding cost the going rate for a firm with a BB credit rating. If EDE defaults on any of its outstanding debt, the creditors will go after all of its assets, including the loans to its customers. Suppose that EDE can create a legal entity and sell the loans to that entity. That entity is the special purpose vehicle (SPV). In our illustration, the SPV is DEAT. If the sale of the loans by EDE to DEAT is done properly, DEAT then legally owns the receivables, not EDE. As a result, if EDE is ever forced into bankruptcy while the loans sold to DEAT are still outstanding, the creditors of EDE cannot recover the loans because they are legally owned by DEAT. The legal implication is that when DEAT issues the ABS that are backed by the loans, investors contemplating the purchase of any bond class will evaluate the credit risk associated with collecting the payments due on the loans independent of the credit rating of EDE. The credit rating will be assigned to the different bond classes created in the securitization and will depend on how the rating agencies will evaluate the credit risk based on the collateral (i.e., the loans). In turn, this will depend on the credit enhancement for each bond class. So, due to the SPV, quality of the collateral, and credit enhancement, a corporation can raise funds via a securitization where some of the bond classes have a credit rating better than the corporation seeking to raise funds and that in the aggregate the funding cost is less than issuing corporate bonds. Credit Enhancements We now review different forms of credit enhancement as applied to nonagency MBS. They include structural, originator-provided, and third-party provided credit enhancement. External credit enhancement involves a guarantee from a third party. The risk faced by an investor is the potential for the third party to be downgraded, and, as a result, the bond classes guaranteed by the third party may be downgraded. The most common form of external credit enhancement is bond insurance and is referred to as a surety bond or a wrap. Internal credit enhancements come in more complicated forms than external credit enhancements and may alter the cash flow characteristics of the loans even in the absence of default. Most securitization transactions that employ internal credit enhancements follow a predetermined schedule that prioritizes the manner in which principal and interest generated by the underlying collateral must be used. This schedule, which is explained in the deal’s prospectus, is known as the cash flow waterfall, or simply the waterfall. The cash flows that remain after all of the scheduled periodic payment obligations are met can be associated with the excess spread. The excess spread is the first line of defense against collateral losses, since deals that are structured to have a large amount of excess spread can absorb relatively large levels of collateral losses. The most common forms of internal credit enhancement are senior/subordinate structures, overcollateralization, and reserve funds. Optional Clean-Up Call Provisions For ABS there is an optional clean-up call provision granted to the trustee. There are several types of clean-up call provisions: percent of collateral call, percent of bond clean-up call, percent of tranche clean-up call, call on or after specified date, latter of percent or date call, auction call, and insurer call. The most common is the percent of collateral call where the outstanding bonds can be called at par value if the outstanding collateral’s balance falls below a predetermined percent of the original collateral’s balance. COLLATERAL TYPE AND SECURITIZATION STRUCTURE Structuring a securitization will depend on the characteristics of the underlying assets. Two characteristics affect the structure: amortization and interest rate. Specifically, the structure depends on whether (1) the assets are amortizing or non-amortizing and (2) the interest rate on the collateral is fixed or floating. Amortizing Versus Non-amortizing Assets The collateral in a securitization can be classified as either amortizing or non-amortizing assets. Amortizing assets are loans in which the borrower’s periodic payment consists of scheduled principal and interest payments over the life of the loan. The schedule for the repayment of the principal is called an amortization schedule and can be created on a pool level or a loan level. In contrast to amortizing assets, non-amortizing assets do not have a schedule for the periodic payments that the individual borrower must make. Because there is no schedule of principal payments (i.e., no amortization schedule) for a non-amortizing asset, the concept of a prepayment does not apply. Credit card receivables are examples of non-amortizing assets. Fixed-Rate Versus Floating-Rate Assets The assets that are securitized can have a fixed rate or a floating rate. The type of rate chosen impacts the structure in terms of the coupon rate for the bonds issued. For example, a structure with all floating-rate bond classes backed by collateral consisting of only fixed-rate contracts exposes bondholders to interest rate risk. CREDIT RISKS ASSOCIATED WITH INVESTING IN ASSET-BACKED SECURITIES Investors in ABS are exposed to credit risk and rely on rating agencies to evaluate that risk for the bond classes in a securitization. While the three agencies have different approaches in assigning credit ratings, they do focus on the same areas of analysis. Moody’s, for example, investigates: (1) asset risks, (2) structural risks, and (3) third parties to the structure. In addition, rating agencies analyze the legal structure (i.e., the SPV). Asset Risks Evaluating asset risks involves the analysis of the credit quality of the collateral. The rating agencies will look at the underlying borrower’s ability to pay and the borrower’s equity in the asset. If there are a few borrowers in the pool that are significant in size relative to the entire pool balance, this diversification benefit can be lost, resulting in a higher level of credit risk referred to as concentration risk. Structural Risks The decision on the structure is up to the seller. Once selected, the rating agencies examine the extent to which the cash flow from the collateral can satisfy all of the obligations of the bond classes in the securitization. In considering the structure, the rating agencies will consider (1) the loss allocation (how losses will be allocated among the bond classes in the structure), (2) the cash flow allocation (i.e., the cash flow waterfall), (3) the interest rate spread between the interest earned on the collateral and the interest paid to the bond classes plus the servicing fee, (4) the potential for a trigger event to occur that will cause the early amortization of a deal (discussed later), and (5) how credit enhancement may change over time. Third-Party Providers In a securitization, several third parties are involved. These include third-party credit guarantors (most commonly bond insurers), the servicer, a trustee, issuer’s counsel, a guaranteed investment contract provider (this entity insures the reinvestment rate on investable funds), and accountants. The rating agency will investigate all third-party providers. For the third-party guarantors, the rating agencies will perform a credit analysis of their ability to pay. While still viewed as a “third party” in many securitizations, the servicer is likely to be the originator of the loans used as the collateral. In addition to the administration of the loan portfolio as just described, the servicer is responsible for distributing the proceeds collected from the borrowers to the different bond classes in the structure according to the cash flow waterfall. Potential Legal Challenges The long-standing view is that investors in ABS are protected from the creditors of the seller of the collateral. That is, when the seller of the collateral transfers it to the trust (the SPV), the transfer represents a “true sale” and therefore in the case of the seller’s bankruptcy, the bankruptcy court cannot penetrate the trust to recover the collateral or cash flow from the collateral. However, this issue has never been fully tested. REVIEW OF SEVERAL MAJOR TYPES OF ASSET-BACKED SECURITIES The three largest sectors within the ABS market that are not backed by residential mortgage loans are: (1) credit card receivable–backed securities, (2) auto loan–backed securities, and (3) rate reduction bonds. Credit Card Receivable-Backed Securities Credit cards are issued by banks (e.g., Visa and MasterCard), retailers (e.g., JC Penney and Sears), and leading global payments and travel companies (e.g., American Express). The cash flow for a pool of credit card receivables consists of finance charge collections, principal collections, and fees collected. Structure of the Transaction Credit card issuers have a large number of credit card accounts that can be pledged to a trust. The process of structuring a transaction begins with the credit card issuer setting up a trust and pledging those credit card accounts to the trust. In credit card transactions, the type of trust used is called a master trust and is referred to in the prospectus as the trust portfolio. To be included as an account pledged to the master trust, the account must meet certain eligibility requirements. New credit card accounts can be pledged to the master trust if they meet the eligibility requirements. If a credit card account in the master trust generates a receivable, that receivable belongs to the master trust. Each series is a separate credit card deal and the trust can issue bond classes to the public. For example, a series can have a senior bond class and two subordinate bond classes. However, each series will have a different level of credit enhancement. It is the cash flow from the trust portfolio that is used to make the payments due to the bond classes for all the series. Because a card receivable is a non-amortizing asset, it therefore has a revolving structure. Throughout the revolving period (also called the lockout period), the principal payments made by credit card borrowers comprising the pool are retained by the trustee and reinvested in additional receivables to maintain the size of the pool. The revolving period can vary from 18 months to 10 years. So, during the revolving period, the cash flow that is paid out to the bond classes is based on finance charges collected and fees. The revolving period is followed by the principal amortization period where the principal received from the accounts is no longer reinvested but paid to bondholders. There are various ways principal can be repaid over the principal amortization period. There are provisions in credit card receivable-backed securities that require early amortization of the principal if certain events occur. The events are referred to as pay-out events. Such a provision, referred to as an early amortization provision or a rapid amortization provision is included to safeguard the credit quality of the structure. The only way that the principal cash flows can be altered is by occurrence of a pay-out event. When early amortization occurs, the bond classes are retired sequentially (i.e., highest rated bond class first, then the second highest rated bond class, and so on). This is accomplished by distributing the principal payments to the specified bond class instead of using those payments to acquire more receivables. The length of time until the return of principal is largely a function of the monthly payment rate. Performance of the Portfolio of Receivables Interest to the bond classes is paid periodically (e.g., monthly, quarterly, or semiannually). The interest rate may be fixed or floating. A credit card receivable is a non-amortizing asset and therefore has a revolving structure. There are provisions in credit card receivable-backed securities that require early amortization of the principal if certain events occur. Such a provision, which is referred to as either an early amortization provision or a rapid amortization provision, is included to safeguard the credit quality of the structure. The only way that the principal cash flows can be altered is by triggering the early amortization provision. The following concepts must be understood in order to assess the performance of the portfolio of receivables and the ability of the collateral to satisfy the interest obligation and repay principal as scheduled: gross portfolio yield, charge-offs, net portfolio yield, delinquencies, and monthly payment rate. The gross portfolio yield includes finance charges collected and fees. Charge-offs represents the accounts charged off as uncollectible. Net portfolio yield is equal to gross portfolio yield minus charge-offs. Delinquencies are the percentages of receivables that are past due for a specified number of months, usually 30, 60, and 90 days. They are considered an indicator of potential future charge-offs. The monthly payment rate (MPR) expresses the monthly payment (which includes finance charges, fees, and any principal repayment) of a credit card receivable portfolio as a percentage of credit card debt outstanding in the previous month. Auto Loan-Backed Securities Auto loan-backed securities are issued by the financial subsidiaries of auto manufacturers (domestic and foreign), commercial banks, and independent finance companies and small financial institutions specializing in auto loans. The cash flow for auto loan-backed securities consists of regularly scheduled monthly loan payments (interest and scheduled principal repayments) and any prepayments. Prepayments for auto loan-backed securities are measured in terms of the absolute prepayment speed (ABS). The ABS measure is the monthly prepayment expressed as a percentage of the original collateral amount. The single-month mortality rate (SMM) is the monthly conditional prepayment rate (CPR) based on the prior month’s balance. There is a mathematical relationship between the ABS and SMM. Given the SMM (expressed as a decimal), the ABS (expressed as a decimal) is obtained as follows: ABS = where M is the number of months after origination (i.e., loan age). Given the ABS, the SMM is obtained as follows: SMM = . Rate Reduction Bonds Rate reduction bonds are backed by a special charge (tariff) included in the utility bills of utility customers in. The charge, called the competitive transition charge (or CTC), is effectively a legislated asset. It is the result of the movement to make the electric utility industry more competitive by deregulating the industry. The CTC is collected by the utility over a specific period of time. Because the state legislature designates the CTC to be a statutory property right, it can be sold by a utility to an SPV and securitized. It is the legislative designation of the CTC as an asset that makes rate reduction bonds different from the typical asset securitized. The CTC is initially calculated based on projections of utility usage and the ability to collect revenues. However, actual collection experience may differ from initial projections. Because of this, there is a “true-up” mechanism in these securitizations. This mechanism permits the utility to recompute the CTC on a periodic basis over the term of the securitization based on actual collection experience. The advantage of the true-up mechanism to the bond classes is that it provides cash flow stability as well as a form of credit enhancement. DODD-FRANK WALL STREET REFORM AND CONSUMER PROTECTION ACT Because of the turmoil that occurred in the securitization market and related sectors of the financial market, in July 2010, Congress passed the Dodd-Frank Wall Street Reform and Consumer Protection Act. The key features of the act that impact securitizations are 1. The requirement that “securitizers” retain a portion of the transaction’s credit risk. 2. Requirements regarding reporting standards and disclosure for a securitization transaction. 3. The representations and warranties required to be provided in securitization transactions and the mechanisms for enforcing them. 4. Due diligence requirements with respect to loans underlying securitization transactions. The specifics regarding how the above requirements should be handled were not set forth in the act. With respect to nonagency RMBS, joint rules are to be specified by the three federal banking agencies. The rules dealing with the amount and form of credit risk that securitizers must retain differ for securitization that do not have “qualified residential mortgages” and those that have entirely such mortgages. For securitizations consisting entirely of “qualified residential mortgages,” there are no risk retention requirements. Securitizers that are required to retain credit risk are not permitted to hedge (directly or indirectly) or transfer the credit risk. COLLATERALIZED DEBT OBLIGATIONS When the ABS market began, there was a debt product that employed the securitization to pool a diversified pool of some asset type and issue securities backed by the cash flow of the asset pool. These debt products are called collateralized debt obligations (CDOs). Although many types of asset classes have been used as collateral in a CDO, the following are the major ones: investment-grade corporate bonds; high-yield corporate bonds; emerging market bonds; nonagency residential mortgage-backed securities (nonagency RMBS); commercial mortgage-backed securities (CMBS); leveraged bank loans; and, collateralized debt obligations. CDOs backed by investment-grade corporate bonds, high-yield corporate bonds, and emerging market bonds are referred to as collateralized bond obligations; those backed by nonagency RMBS and CMBS are referred to as structured finance CDOs. CDOs backed by leveraged bank loans are called collateralized loan obligations (CLOs). Finally, CDOs backed by bond classes of other CDOs are referred to as CDO-squared or CDO. Structure of a CDO In a CDO structure, there is a collateral manager responsible for managing the portfolio of debt obligations. The portfolio of debt obligations in which the collateral manager invests is referred to as the collateral. The individual issues held that comprise the collateral are referred to as the collateral assets. The funds to purchase the collateral assets are obtained from the issuance of debt obligations. These debt obligations are referred to as tranches or bond classes. The tranches include: senior tranches, mezzanine tranches and subordinate/equity tranches. The ability of the collateral manager to make the interest payments to the tranches and pay off the tranches as they mature depends on the performance of the collateral. The proceeds to meet the obligations to the CDO tranches (interest and principal repayment) can come from coupon interest payments from the collateral assets, from maturing of collateral assets, and from sale of collateral assets. In a typical structure, one or more of the tranches has a floating rate. With the exception of deals backed by bank loans that pay a floating rate, the collateral manager invests in fixed-rate bonds. The collateral manager must monitor the collateral to ensure that certain tests are being met. There are two types of tests imposed by rating agencies: quality tests and coverage tests. In rating a transaction, the rating agencies are concerned with the diversity of the assets. Consequently, there are tests that relate to the diversity of the assets. These tests are called quality tests. Distribution Rules There are three relevant periods. The first is the ramp-up period. This is the period that follows the closing date of the transaction where the collateral manager begins investing the proceeds from the sale of the debt obligations issued. This period usually lasts from one to two years. The reinvestment period or revolving period is where principal proceeds are reinvested and is usually for five or more years. In the final period, the collateral is sold and the debtholders are paid off. Income is derived from interest income from the collateral assets and capital appreciation. The income is then used as follows. Payments are first made to the trustee and administrators and then to the senior collateral manager. Once these fees are paid, then the senior tranches are paid their interest. At this point, before any other payments are made, certain tests must be passed. These tests are called coverage tests. The principal cash flow is distributed as follows after the payment of the fees to the trustees, administrators, and senior managers. If there is a shortfall in interest paid to the senior tranches, principal proceeds are used to make up the shortfall. After all the debt obligations are satisfied in full, if permissible, the equity investors are paid. Typically, there are also incentive fees paid to management based on performance. KEY POINTS Asset-backed securities are created by pooling loans and receivables through a process known as securitization. The main parties to a securitization are the seller/originator (party seeking to raise funds), special purpose vehicle, and servicer. The motivation for issuing asset-backed securities rather than issuing a corporate bond is the potential reduction in funding cost. The key to this savings is the role of the special purpose vehicle. ABS are credit enhanced to provide greater protection to bond classes against defaults. There are two general types of credit enhancement structures: internal and external. Internal credit enhancements include structural credit enhancement (senior/subordinate structures) and originator-provided credit enhancement (cash reserves, excess spread, and overcollateralization). External credit enhancements come in the form of third-party guarantees, the most common historically being bond insurance which is no longer used in deals since 2007. In analyzing credit risk, the rating agencies will examine asset risks, structural risks, and third parties to the structure. Based on this analysis, a rating agency will determine the amount of credit enhancement needed for a bond class to receive a specific credit rating. ANSWERS TO QUESTIONS FOR CHAPTER 15 (Questions are in bold print followed by answers.) 1. Why is the entity seeking to raise funds through a securitization referred to as the “seller” or the “originator”? A security created by pooling loans other than mortgage loans is referred to as an asset-backed security (ABS). To explain why an entity seeking to raise funds through a securitization is the “seller” or “originator” let us use an illustration. Suppose that Exception Dental Equipment, Inc. (EDE) has a bulk of its sales from installment contracts (wherein the buyer agrees to repay EDE over a specified period of time for the amount borrowed plus interest). The dental equipment purchased is the collateral for the loan. The credit department of EDE makes the decision as to whether or not to extend credit to a customer. EDE sets up a legal entity called a special purpose vehicle (SPV) to whom it sells its loans. Because EDE initiates the loan with the SPV, EDE is called the “seller” or “originator.” 2. In achieving the benefits associated with a securitization, why is the special purpose vehicle important to the transaction? To understand the role of the special purpose vehicle (SPV) and the benefit derived from it, we need to understand why a corporation would want to raise funds via securitization rather than simply issue corporate bonds. There are four principal reasons why a corporation may elect to raise funds via a securitization rather than a corporate bond. They are the potential to reduce funding costs, to diversify funding sources, to accelerate earnings for financial reporting purposes, and to achieve (if a regulated entity) relief from capital requirements. Let us focus on the first of these reasons to understand the critical role of the SPV in a securitization. Suppose that Exceptional Dental Equipment, Inc. (EDE) has a BB credit rating. If it wants to raise funds equal to $300 million by issuing a corporate bond, its funding cost the going rate for a firm with a BB credit rating. If EDE defaults on any of its outstanding debt, the creditors will go after all of its assets, including the loans to its customers. Suppose that EDE can create a legal entity and sell the loans to that entity. That entity is the special purpose vehicle (SPV). In our illustration, let us call the SPV by the name of DEAT. If the sale of the loans by EDE to DEAT is done properly, DEAT then legally owns the receivables, not EDE. As a result, if EDE is ever forced into bankruptcy while the loans sold to DEAT are still outstanding, the creditors of EDE cannot recover the loans because they are legally owned by DEAT. The legal implication is that when DEAT issues the ABS that are backed by the loans, investors contemplating the purchase of any bond class will evaluate the credit risk associated with collecting the payments due on the loans independent of the credit rating of EDE. The credit rating will be assigned to the different bond classes created in the securitization and will depend on how the rating agencies will evaluate the credit risk based on the collateral (i.e., the loans). In turn, this will depend on the credit enhancement for each bond class. So, due to the SPV, quality of the collateral, and credit enhancement, a corporation can raise funds via a securitization where some of the bond classes have a credit rating better than the corporation seeking to raise funds and that in the aggregate the funding cost is less than issuing corporate bonds. 3. In a securitization, what is the difference between a servicer and a special purpose vehicle? As just seen in the previous question due to the SPV (as well as quality of the collateral and credit enhancement), a corporation can raise funds via a securitization where some of the bond classes have a credit rating better than the corporation seeking to raise funds and that in the aggregate the funding cost is less than issuing corporate bonds. The role of a servicer is to see that the loan created through the SPV is serviced. This involves services such as collecting payments from borrowers, notifying borrowers who may be delinquent, and, when necessary, recovering and disposing of the collateral if the borrower does not make loan repayments by a specified time. Moreover, the servicer is likely to be the originator of the loans used as the collateral. The servicer is also responsible for distributing the proceeds collected from the borrowers to the different bond classes in the structure according to the cash flow waterfall. Where there are floating-rate securities in the transaction, the servicer will determine the interest rate for the period. The servicer may also be responsible for advancing payments when there are delinquencies in payments, resulting in a temporary shortfall in the payments that must be made to the bondholders. 4. Answer the below questions. a. What is the difference between a one-step securitization and a two-step securitization? In a one-step securitization, the originator of the loans sells the receivables to the SPV who is referred to as the “issuer” or “trust” of the asset-backed securities (ABS). In a two-step securitization, the securitization involves two SPVs. This is done to ensure that the transaction is considered a true sale for tax purposes. One SPV is called an intermediate SPV, which is a wholly owned subsidiary of the originator and has restrictions on its activities. It is the intermediate SPV that purchases the assets from the originator. The intermediate SPV then sells the assets to the SPV that issues the ABS (i.e., the issuing entity). b. What is meant by the “depositor” in a securitization? In the prospectus for a two-step securitization, the intermediate SPV is referred to as the depositor. An intermediate SPV is a wholly owned subsidiary of the originator and has restrictions on its activities. It is the intermediate SPV that purchases the assets from the originator. The intermediate SPV then sells the assets to the SPV that issues the asset-backed securities. 5. What is meant by a cash flow waterfall? Most securitization transactions that employ internal credit enhancements follow a predetermined schedule that prioritizes the manner in which principal and interest generated by the underlying collateral must be used. This schedule, which is explained in the deal’s prospectus, is known as the cash flow waterfall, or simply the waterfall. At the top of the waterfall would be cash flows due to senior bondholders (interest and principal, depending upon the principal repayment schedule) as well as some standard fees and expenses (e.g., administration and servicing fee). After the cash flow obligations at the top of the waterfall are met, cash flows down to lower priority classes (those rated AA, A, BBB bond classes and so on). The cash flows associated with the excess spread are all that remain after the scheduled periodic payment obligations are met. The excess spread is the first line of defense against collateral losses, since deals that are structured to have a large amount of excess spread can absorb relatively large levels of collateral losses. If the excess spread is fully eaten away by losses, the next lowest-rated class will begin to be negatively affected by credit losses. 6. Explain the difference in the treatment of principal received for a self-liquidating trust and a revolving trust. Typically when amortizing assets are securitized, the collateral is fixed over the life of the structure. That is, no new assets are acquired. The collateral composition stays the same except for prepayments and defaults. Consequently, all principal received by the trust is paid out to the bond classes. The structure in this case is referred to as a self-liquidating structure. In the case of non-amortizing assets, for a period of time, referred to as the lockout period or revolving period, all principal received is used to purchase new collateral. Hence, new assets are being added to the collateral, and this structure is referred to as a revolving structure. After the lockout period, called the amortization period, principal received is distributed to the bond classes. 7. Answer the below questions. (a) In a securitization, what is a revolving period? Typically when amortizing assets are securitized, the collateral is fixed over the life of the structure and all principal received by the trust is paid out to the bond classes. However, in the case of non-amortizing assets, for a period of time, referred to as the revolving period (or lockout period), all principal received is used to purchase new collateral. Hence, new assets are being added to the collateral, and this structure is referred to as a revolving structure. After the revolving period, the principal received is distributed to the bond classes. For example, a credit card receivable is a non-amortizing asset and therefore has a revolving structure. During the lockout period the principal payments made by credit card borrowers comprising the pool are retained by the trustee and reinvested in additional receivables to maintain the size of the pool. The revolving period can vary from 18 months to 10 years. So, during the revolving period, the cash flow that is paid out to the bond classes is based on finance charges collected and fees. The revolving period is followed by the principal amortization period where the principal is no longer reinvested but paid to bond holders. (b) In a securitization, what is an early amortization provision? There are provisions in credit card receivable-backed securities that require early amortization of the principal if certain events occur. Such a provision, which is referred to as either an early amortization provision or a rapid amortization provision, is included to safeguard the credit quality of the structure. The only way that the principal cash flows can be altered is by triggering the early amortization provision. Typically, early amortization allows for the rapid return of principal in the event that the three-month average excess spread earned on the receivables falls to zero or less. When early amortization occurs, the bond classes are retired sequentially (i.e., first the AAA bond then the AA rated bond, etc.). This is accomplished by distributing the principal payments to the specified bond class instead of using those payments to acquire more receivables. The length of time until the return of principal is largely a function of the monthly payment rate (MPR). MPR expresses the monthly payment (which includes finance charges, fees, and any principal repayment) of a credit card receivable portfolio as a percentage of credit card debt outstanding in the previous month. For example, suppose a $600 million credit card receivable portfolio in February realized $60 million of payments in March. The MPR for March would then be 10% ($60 million divided by $600 million). The MPR is important for two reasons. First, if the MPR reaches an extremely low level, there is a chance that there will be extension risk with respect to the principal payments to the bond classes. Second, if the MPR is very low, then there is a chance that there will not be sufficient cash flows to pay off principal. This is one of the events that could trigger the early amortization provision. 8. Answer the below questions. (a) Why is credit enhancement required in a securitization? Credit enhancement is required for all asset-backed securities to provide greater protection to investors against losses due to defaults by borrowers. More details on credit enhancement are given below. In Chapter 11, we briefly reviewed the different forms of credit enhancement for nonagency MBS. They include external credit enhancement and internal credit enhancement. The credit enhancement forms are used both individually and in combination, depending on the loan types that are backing the securities. External credit enhancement involves a guarantee from a third party. The risk faced by an investor is the potential for the third party to be downgraded, and, as a result, the bond classes guaranteed by the third party may be downgraded. The most common form of external credit enhancement is bond insurance and is referred to as a surety bond or a wrap. Internal credit enhancements come in more complicated forms than external credit enhancements and may alter the cash flow characteristics of the loans even in the absence of default. Credit enhancement levels (i.e., the amount of subordination for each form of enhancement utilized within a deal) are determined by the rating agencies from which the issuer seeks a rating for the bond classes. This is referred to as “sizing” the transaction and is based on the rating agencies’ expectations for the performance of the loans collateralizing the deal in question. Most securitization transactions that employ internal credit enhancements follow a predetermined schedule that prioritizes the manner in which principal and interest generated by the underlying collateral must be used. The most common forms of internal credit enhancement are senior/subordinate structures, overcollateralization, and reserve funds. (b) What entity determines the amount of securities needed in a securitization? While in our simple transaction example (described earlier and mentioned in the text), Exceptional Dental Equipment, Inc (EDE) manufactured the dental equipment and originated the loans, there is another type of securitization transaction involving another company, called a conduit, that buys the loans and securitizes them. For example, consider a hypothetical company Dental Equipment Financing Corporation (DEFC) whose business is to provide financing to dental equipment manufacturers who want to sell their equipment on an installment basis. DEFC would then develop a relationship with manufacturers of dental equipment (such as EDE) to purchase their installment contracts. DEFC would then warehouse the installment contracts purchased until it had a sufficient amount to sell to a special purpose vehicle (SPV), which would then issue the asset-backed securities (ABS). The SPV in a securitization is referred to as the “issuer” or “trust” in the prospectus. As issuer, the SPV would be involved in determining the details of the securities needed in the securitization. The legal implication is that when the SPV issues the ABS that are backed by the loans, investors contemplating the purchase of any bond class will evaluate the credit risk associated with collecting the payments due on the loans independent of the credit rating of EDE. The credit rating will be assigned to the different bond classes created in the securitization and will depend on how the rating agencies will evaluate the credit risk based on the collateral (i.e., the loans). In turn, this will depend on the credit enhancement for each bond class. So, due to the SPV, quality of the collateral, and credit enhancement, a corporation can raise funds via a securitization where some of the bond classes have a credit rating better than the corporation seeking to raise funds and that in the aggregate the funding cost is less than issuing corporate bonds. 9. Why is the MPR for credit card receivable-backed securities important? Credit cards are issued by banks (e.g., Visa and MasterCard), retailers (e.g., JC Penney and Sears), and travel and entertainment companies (e.g., American Express). The cash flow for a pool of credit card receivables consists of finance charges collected, fees, and principal. Finance charges collected represent the periodic interest the credit card borrower is charged based on the unpaid balance after the grace period. Fees include late payment fees and any annual membership fees. Interest to the bond classes is paid periodically (e.g., monthly, quarterly, or semiannually). The interest rate may be fixed or floating. Assuming the period is a month, then the monthly payment rate (MPR) expresses the monthly payment (which includes finance charges, fees, and any principal repayment) of a credit card receivable portfolio as a percentage of credit card debt outstanding in the previous month. For example, suppose a $600 million credit card receivable portfolio in February realized $60 million of payments in March. The MPR for March would then be 10% ($60 million divided by $600 million). The MPR is important for two reasons. First, if the MPR reaches an extremely low level, there is a chance that there will be extension risk with respect to the principal payments to the bond classes. Second, if the MPR is very low, then there is a chance that there will not be sufficient cash flows to pay off principal. This is one of the events that could trigger the early amortization provision. 10. What is the limitation of a third-party guarantee as a form of credit enhancement? As a form of external credit enhancements, the rating companies take the “weak link” approach to ratings. That is, if the rating of the third-party guarantor is downgraded, the asset-backed security’s rating will be downgraded even if the collateral is performing as expected. More details including an example are given below. All asset-backed securities are credit enhanced to provide greater protection to investors against defaults. There are two general types of credit enhancement structures: external and internal. External credit enhancements come in the form of third-party guarantees that provide for first loss protection against losses up to a specified dollar amount. Internal credit enhancements include reserve funds reserves (cash reserves and excess servicing spread), overcollateralization, and senior/subordinated structures. In earlier credit card structures, the most popular form of credit enhancement was a bank letter of credit. However, as just mentioned above, the disadvantage of a third-party guarantee is that if the guarantor is downgraded the structure will be downgraded regardless of how the collateral is performing. With the downgrading of banks that provided letters of credit for earlier credit card deals and the subsequent downgrading of the securities, this form of credit enhancement lost its popularity. 11. An asset-backed security has been credit enhanced with a letter of credit from a bank with a single A credit rating. If this is the only form of credit enhancement, explain whether this issue can be assigned a triple A credit rating at the time of issuance. The issue will not receive a triple A credit rating but a single A credit rating because there are no other forms of credit enhancements such as reserve funds (cash reserves and excess servicing spread) and overcollateralization. More details are given below. In the earlier credit card structures, the most popular form of credit enhancement was a bank letter of credit. However, the disadvantage of a third-party guarantee is that if the guarantor is downgraded the structure will be downgraded regardless of how the collateral is performing. With the downgrading of banks that provided letters of credit for earlier credit card deals and the subsequent downgrading of the securities, this form of credit enhancement lost its popularity. Today the two most popular forms of credit enhancement for credit card deals coupled with any senior/subordinated structure are the cash collateral account and the collateral invested account. Both forms of credit enhancement involve the investment of cash. In the case of the cash collateral account, funds are generally borrowed from a bank and those funds are then invested in commercial paper or other short-debt of the bank. In the collateral invested account, the funds are invested in credit card receivables within the structure rather than commercial paper or other short-term debt. 12. A corporation is considering a securitization and is considering two possible credit enhancement structures backed by a pool of automobile loans. Total principal value underlying the asset-backed security is $300 million. Principal Value for: Structure I Structure II Pool of automobile loans $304 million $301 million Senior class $250 million $270 million Subordinated class $50 million $30 million Answer the below questions. (a) Which structure would receive a higher credit rating and why? Generally, a subordinated class will receive a lower credit rating. Thus, because Structure II has a smaller subordinate class, it will likely receive a higher credit rating even though its pool of automobile loans is slightly smaller. However, through various forms of credit enhancement and features (such as options) attached to various classes, it is possible both structure could receive the same credit rating. (b) What forms of credit enhancement are being used in both structures? As with nonagency mortgage-backed securities, credit enhancement can be either insurance, corporate guarantees, or letters of credit. Internal credit enhancements include reserve funds (cash reserves and excess servicing spread), overcollateralization, and senior/subordinated structures. In both structures above, senior/subordinated structures are being used. 13. Answer the below questions. (a) What is meant by concentration risk? Concentration risk refers to a situation where a few borrowers of significant size are concentrated in a pool. This results in a loss of diversification and higher default risk. More details are given below. Analysis of the credit quality of the collateral depends on the asset type. The rating companies will look at the borrower’s ability to pay and the borrower’s equity in the asset. The latter will be a key determinant as to whether the borrower will default or sell the asset and pay off a loan. The rating companies will look at the experience of the originators of the underlying loans and will assess whether the loans underlying a specific transaction have the same characteristics as the experience reported by the issuer. The concentration of loans is examined. The underlying principle of asset securitization is that the large number of borrowers in a pool will reduce the credit risk via diversification. If there are a few borrowers in the pool that are significant in size relative to the entire pool balance, this diversification benefit can be lost, resulting in a higher level of default risk. This risk is called concentration risk. In such instances, rating companies will set concentration limits on the amount or percentage of receivables from any one borrower. (b) How do rating agencies seek to limit the exposure of a pool of loans to concentration risk? Rating agencies will seek to limit the exposure of a pool of loans to concentration risk by setting limits on the amount or percentage of receivables from any one borrower. These limits are called concentration limits. Even if the exposure cannot be perfectly limited there are still other ways to achieve a desire rating. 14. What is the difference between pool-level and loan-level analysis? The analysis of prepayments can be performed on a pool level or a loan level. In pool-level analysis it is assumed that all loans comprising the collateral are identical. For an amortizing asset, the amortization schedule is based on the gross weighted-average coupon (GWAC) and weighted-average maturity (WAM) for that single loan. Pool-level analysis is appropriate where the underlying loans are homogeneous. Loan-level analysis involves amortizing each loan (or group of homogeneous loans). Thus, the major difference is that pool-level analysis focuses upon examining a larger group of loans whereas loan-level analysis concentrates on examining a loan individually (or a small group of loans that have similar qualities). 15. How do optional call provisions in a securitization differ from that of a call provision in a standard corporate bond? To answer this question it helps to understand why a corporation would want to raise funds via securitization rather than simply issue corporate bonds. There are four principal reasons why a corporation may elect to raise funds via a securitization rather than a corporate bond. They are the potential to reduce funding costs, to diversify funding sources, to accelerate earnings for financial reporting purposes, and to achieve (if a regulated entity) relief from capital requirements. These reasons can all be viewed as involving an option that a corporate bond does not contain. Let us focus on the first of the above reasons (i.e., to reduce fund costs) using the illustration given previously and found in the text. Suppose that Exceptional Dental Equipment, Inc. (EDE) has a BB credit rating. If it wants to raise funds equal to $300 million by issuing a corporate bond, its funding cost the going rate for a firm with a BB credit rating. If EDE defaults on any of its outstanding debt, the creditors will go after all of its assets, including the loans to its customers. Suppose that EDE can create a legal entity and sell the loans to that entity. That entity is the special purpose vehicle (SPV). In our illustration, the SPV is DEAT. If the sale of the loans by EDE to DEAT is done properly, DEAT (and not EDE) then legally owns the receivables. As a result, if EDE is ever forced into bankruptcy while the loans sold to DEAT are still outstanding, the creditors of EDE cannot recover the loans because they are legally owned by DEAT. The legal implication is that when DEAT issues the ABS that are backed by the loans, investors contemplating the purchase of any bond class will evaluate the credit risk associated with collecting the payments due on the loans independent of the credit rating of EDE. The credit rating will be assigned to the different bond classes created in the securitization and will depend on how the rating agencies will evaluate the credit risk based on the collateral (i.e., the loans). In turn, this will depend on the credit enhancement for each bond class. So, due to the SPV, quality of the collateral, and credit enhancement, a corporation can raise funds via a securitization where some of the bond classes have a credit rating better than the corporation seeking to raise funds and that in the aggregate the funding cost is less than issuing corporate bonds. 16. What factors do the rating agencies consider in analyzing the structural risk in a securitization? The decision on the structure is up to the seller. Once selected, the rating agencies examine the extent to which the cash flow from the collateral can satisfy all of the obligations of the bond classes in the securitization. The cash flow of the underlying collateral is interest and principal repayment. The cash flow payments that must be made are interest and principal to investors, servicing fees, and any other expenses for which the issuer is liable. This is described by the structure’s cash flow waterfall. The rating agencies analyze the structure to test whether the collateral’s cash flows match the payments that must be made to satisfy the issuer’s obligations. This requires that the rating agency make assumptions about losses and delinquencies and consider various interest rate scenarios after taking into consideration credit enhancements. In considering the structure, the rating agencies will consider (1) the loss allocation (how losses will be allocated among the bond classes in the structure), (2) the cash flow allocation (i.e., the cash flow waterfall), (3) the interest rate spread between the interest earned on the collateral and the interest paid to the bond classes plus the servicing fee, (4) the potential for a trigger event to occur that will cause the early amortization of a deal (discussed later), and (5) how credit enhancement may change over time. We can note that in the past four nationally recognized statistical rating organizations rate asset-backed securities. These rating agencies evaluate many factors related to risk for asset-backed securities (ASB). For example, in analyzing credit risk, the rating companies focus on the following factors: credit quality of the collateral, the quality of the seller/servicer, cash flow stress and payment structure, and legal structure. In regards to the servicer, Duff & Phelps reviews the following factors when evaluating servicers: servicing history, experience, originations, servicing capabilities, human resources, financial condition, and growth/competition/business environment. Based on its analysis, Duff & Phelps determines whether the servicer is acceptable or unacceptable. More details are supplied below. 17. Why would an interest rate derivative be using in a securitization structure? To deal with situations where there may be a mismatch between the cash flow characteristics of the asset and the liabilities, interest rate derivative instruments are used in a securitization. The two common interest rate derivatives used are interest rate swaps and interest rate caps. 18. The below questions relate to auto loan-backed securities. Answer each one. (a) What is the cash flow for an auto loan-backed security? The cash flow for auto loan-backed securities consists of regularly scheduled monthly loan payments (interest and scheduled principal repayments) and any prepayments. The monthly interest rate may be fixed or floating. (b) Why are prepayments of minor importance for automobile loan-backed securities? Prepayments are less of a problem (say relative to mortgage refinancing) because auto loans are less sensitive to changes in interest rates. For example, an auto loan is a relatively small loan with short horizons so that refinancing may have little to gain. Furthermore, interest rates for the automobile loans are already substantially below market rates if they are offered by manufacturers as part of a sales promotion. More details on auto loan prepayments are given below. For securities backed by auto loans, prepayments result from sales and trade-ins requiring full payoff of the loan, repossession and subsequent resale of the automobile, loss or destruction of the vehicle, payoff of the loan with cash to save on the interest cost, and refinancing of the loan at a lower interest cost. Prepayments due to repossessions and subsequent resale are sensitive to the economic cycle. In recessionary economic periods, prepayments due to this factor increase. Whereas refinancings may be a major reason for prepayments of mortgage loans, they are of minor importance for automobile loans. Moreover, the interest rates for the automobile loans underlying several issues are substantially below market rates if they are offered by manufacturers as part of a sales promotion. (c) How are prepayments on pools of auto loans measured? Prepayments for auto loan-backed securities are measured in terms of the absolute prepayment rate, denoted not by APR but by ABS (probably because it was the first prepayment measure used for asset-backed securities). The ABS is the monthly prepayment expressed as a percentage of the original collateral amount. Recall that the SMM (monthly CPR) expresses prepayments based on the prior month’s balance. 19. The following questions relate to credit card receivable-backed securities. Answer each one. (a) What happens to the principal repaid by borrowers in a credit card receivable-backed security during the lockout period? In contrast to an auto loan-backed security, the principal repayment of a credit card receivable-backed security is not amortized. Instead, for a specified period of time, referred to as the lockout period or revolving period, the principal payments made by credit card borrowers constituting the pool are retained by the trustee and reinvested in additional receivables. The lockout period can vary from 18 months to 10 years. After the lockout period, the principal is no longer reinvested but paid to investors. This period is referred to as the principal-amortization period. (b) What is the role of the early amortization provision in a credit card receivable-backed security structure? The role of an early amortization provision in a credit card receivable-backed security structure is to provide a safeguard to protect the claims of those who purchase credit card receivable-backed securities. More details are supplied below. There are provisions in credit card receivable-backed securities that require earlier amortization of the principal if certain events occur. Such provisions, which are referred to as early or rapid amortization, are included to safeguard the credit quality of the issue. The only way that the cash flows can be altered is by triggering the early amortization provision. Early amortization is invoked if the trust is not able to generate sufficient income to cover the investor coupon and the servicing fee. For example, in the Sears Credit Account Master Trust II, Series 1995–4, if the net yield provided by the portfolio of receivables is less than the base rate for three monthly periods, early amortization is triggered. Other events that may trigger early amortization are the default of the servicer, credit support decline below a specified level, or the issuer violating agreements regarding pooling and servicing. (c) How can the cash flow of a credit card receivable-backed security be altered prior to the principal-amortization period? The cash flow of a credit card receivable-backed security can be altered prior to the principal-amortization period when credit card borrowers pay more or less than the interest due. More details are given below. In contrast to an auto loan-backed security, the principal repayment of a credit card receivable-backed security is not amortized. For a specified period of time (varying from 18 months to 10 years) before the principal-amortization period, the principal payments made by credit card borrowers constituting the pool are retained by the trustee and reinvested in additional receivables. In contrast to amortizing assets, non-amortizing assets do not have a schedule for the periodic payments that the borrower must make. Instead, a non-amortizing asset is one in which the borrower must make a minimum periodic payment. If that payment is less than the interest on the outstanding loan balance, the shortfall is added to the outstanding loan balance. If the periodic payment is greater than the interest on the outstanding loan balance, then the difference is applied to the reduction of the outstanding loan balance. There is no schedule of principal payments (i.e., no amortization schedule) for a non-amortizing asset. (d) Why is the monthly payment rate an important measure to examine when considering investing in a credit card receivable-backed security? It is important to look at the monthly payment rate so as to get a feel for how rapidly credit card borrowers are paying off their debt. More details are given below. The concept of prepayments does not apply to credit card receivable-backed securities because there is no amortization schedule during the lockout period. Instead, for this sector of the asset-backed securities market, participants look at the monthly payment rate (MPR). This measure expresses the monthly payment (which includes finance charges collected and any principal) of a credit card receivable portfolio as a percentage of debt outstanding in the previous month. For example, suppose a $500 million credit card receivable portfolio in January realized $50 million of payments in February. The MPR would then be $50 million / $500 million = 0.10 or 10%. 20. The below questions relate to rate reduction bonds. Answer each one. (a) What asset is the collateral? Rate reduction bonds are backed by a special charge (tariff) included in the utility bills of utility customers in. The charge, called the competitive transition charge (or CTC), is effectively a legislated asset. It is the result of the movement to make the electric utility industry more competitive by deregulating the industry. More details are supplied below. Prior to deregulation, electric utilities were entitled to set utility rates so as to earn a competitive return on the assets on their balance sheet. After deregulation, the setting of utility rates to recover a competitive return was no long permissible. As a result, many electric utilities had a substantial amount of assets that they acquired prior to deregulation that would likely become uneconomic and utilities would no longer be assured that they could charge a high enough rate to recover the costs of these assets. These assets are referred to as “stranded assets” and the associated costs referred to as “stranded costs.” For this reason, rate reduction bonds are also known as stranded cost bonds or stranded asset bonds. Some market participants refer to this sector of the ABS market as the “utilities” sector. The CTC is collected by the utility over a specific period of time. Because the state legislature designates the CTC to be a statutory property right, it can be sold by a utility to an SPV and securitized. It is the legislative designation of the CTC as an asset that makes rate reduction bonds different from the typical asset securitized. (b) What is a true up provision in a securitization creating rate reduction bonds? Rate reduction bonds are backed by a special charge (tariff) included in the utility bills of utility customers in. The charge, called the competitive transition charge (or CTC), is effectively a legislated asset. The CTC is initially calculated based on projections of utility usage and the ability to collect revenues. However, actual collection experience may differ from initial projections. Because of this, there is a “true-up” mechanism in these securitizations. This mechanism permits the utility to recompute the CTC on a periodic basis over the term of the securitization based on actual collection experience. The advantage of the true-up mechanism to the bond classes is that it provides cash flow stability as well as a form of credit enhancement. 21. What does the Dodd-Frank Wall Street Reform and Consumer Protection Act specify regarding a securitizer retaining credit risk in a securitization transaction? Because of the turmoil that occurred in the securitization market and related sectors of the financial market, in July 2010, Congress passed the Dodd-Frank Wall Street Reform and Consumer Protection Act. The key features of the act that impact securitizations are 1. The requirement that “securitizers” retain a portion of the transaction’s credit risk. 2. Requirements regarding reporting standards and disclosure for a securitization transaction. 3. The representations and warranties required to be provided in securitization transactions and the mechanisms for enforcing them. 4. Due diligence requirements with respect to loans underlying securitization transactions. The specifics regarding how the above requirements should be handled were not set forth in the act. Instead, Congress delegated that responsibility and its implementation to three federal banking agencies (Federal Reserve Board, Office of the Comptroller of the Currency, and the Federal Deposit Insurance Corporation) and the Securities and Exchange Commission (SEC). With respect to nonagency RMBS, joint rules are to be specified by the three federal banking agencies, the Federal Housing Finance Agency (FHFA), and the Department of Housing and Urban Development (HUD). The rules dealing with the amount and form of credit risk that securitizers must retain differ for securitization that do not have “qualified residential mortgages” and those that have entirely such mortgages. For securitizations consisting entirely of “qualified residential mortgages,” there are no risk retention requirements. The definition of what constitutes a “qualified residential mortgage” was delegated to the three federal banking agencies, SEC, FHFA, and HUD that takes into account the underwriting and product features of the loans and their historical performance. Securitizers that are required to retain credit risk are not permitted to hedge (directly or indirectly) or transfer the credit risk. 22. How does a CDO differ from an ABS transaction? When the asset-backed security (ABS) market began, there was a debt product that employed the securitization to pool a diversified pool of some asset type and issue securities backed by the cash flow of the asset pool. These debt products are called collateralized debt obligations (CDOs). CDOs are a type of structured ABS with multiple "tranches" that are issued by special purpose entities and collateralized by debt obligations including bonds and loans. CDOs differ from ABS in that the pool of assets is actively managed by an entity referred to as the collateral manager. Asset-backed securities are credit enhanced to provide greater protection to bond classes against defaults. There are two general types of credit enhancement structures: internal and external. One might note that while issuance of CDOs grew dramatically from the mid 1990s through early 2007, issuance for all but CLOs has stopped because of the dismal performance of this product. Market observers do not believe that the market for CDOs (other than CLOs) will be revived. 23. Answer the below questions. a. If there is a shortfall in interest paid to the senior tranches of a CDO, how is the shortfall made up? If there is a shortfall in interest paid to the senior tranches, principal proceeds are used to make up the shortfall. However, the principal cash flow is distributed to the senior tranches only after the payment of the fees to the trustees, administrators, and senior managers. b. If coverage tests are failed for a CDO, how is the principal received from the collateral used? If the coverage tests are failed for a CDO, the principal cash flow is used to pay down tranches in the following order: senior, mezzanine and subordinate/equity. More details are supplied below. The principal cash flow is distributed as follows after the payment of the fees to the trustees, administrators, and senior managers. If there is a shortfall in interest paid to the senior tranches, principal proceeds are used to make up the shortfall. Assuming that the coverage tests are satisfied during the reinvestment period, the principal is reinvested. After the reinvestment period or if the coverage tests are failed, the principal cash flow is used to pay down the senior tranches until the coverage tests are satisfied. If all the senior tranches are paid down, then the mezzanine tranches are paid off, followed by the subordinate/equity tranche. After all the debt obligations are satisfied in full, if permissible, the equity investors are paid. Typically, there are also incentive fees paid to management based on performance. Usually a target return for the equity investors is established at the inception of the transaction. Management is then permitted to share on some prorated basis once the target return is achieved. Finally, the collateral manager must monitor the collateral to ensure that certain tests are being met. There are two types of tests imposed by rating agencies: quality tests and coverage tests. CHAPTER 16 INTEREST-RATE MODELS CHAPTER SUMMARY In implementing bond portfolio strategies there are two important activities that a manager will undertake. First, a manager will want to determine whether the bonds that are purchase and sale candidates are fairly priced. Second, a manager will want to assess the performance of a portfolio over realistic future interest-rate scenarios. For both of these activities, the manager will have to rely on an interest rate model. The description of the uncertainty about future interest rates is mathematically described by an interest-rate model. In this chapter we provide an overview of interest-rate models. At the end of this chapter, we will see how interest-rate volatility is computed using historical data. MATHEMATICAL DESCRIPTION OF ONE-FACTOR INTEREST-RATE MODELS Interest-rate models must incorporate statistical properties of interest-rate movements. These properties are (1) drift, (2) volatility, and (3) mean reversion. The commonly used mathematical tool for describing the movement of interest rates that can incorporate these properties is stochastic differential equations (SDEs). The most common interest-rate model used to describe the behavior of interest rates assumes that short-term interest rates follow some statistical process and that other interest rates in the term structure are related to short-term rates. The short-term interest rate (i.e., short rate) is the only one that is assumed to drive the rates of all other maturities. Hence, these models are referred to as one-factor models. The other rates are not randomly determined once the short rate is specified. Using arbitrage arguments, the rate for all other maturities is determined. There are also multi-factor models that have been proposed in the literature. The most common multi-factor model is a two-factor model where a long-term rate is the second factor. In practice, however, one-factor models are used because of the difficulty of applying even a two-factor model as well as empirical evidence that supports one-factor models. While the value of the short rate at some future time is uncertain, the pattern by which it changes over time can be assumed. It is assumed that the short rate is a continuous random variable and therefore the stochastic process used is a continuous-time stochastic process. There are different types of continuous-time stochastic processes used in interest-rate modeling. In all of these models because time is a continuous variable, the letter d is used to denote the “change in” some variable. Specifically, in the models we let r = the short rate and therefore dr denotes the change in the short rate t = time and thus dt denotes the change in time (or the length of the time interval) z = a random term and dz denotes a random process A Basic Continuous-Time Stochastic Process We begin with a basic continuous-time stochastic process for describing the dynamics of the short rate given by: dr = bdt + σdz where dr, dt, and dz were defined above, σ = standard deviation of the changes in the short rate, and b = expected direction of rate change. The expected direction of the change in the short rate (b) is called the drift term and σ is called the volatility term. The change in the short rate (dr) over the time interval (dt) depends on (1) the expected direction of the change in the short rate (b) and (2) a random process (dz) that is affected by volatility The random nature of the change in the short rate comes from the random process dz. The assumptions are that (1) the random term z follows a normal distribution with a mean of zero and a standard deviation of one (i.e., is a standardized normal distribution). (2) the change in the short rate is proportional to the value of the random term, which depends on the standard deviation of the change in the short rate. (3) the change in the short rate for any two different short intervals of time is independent. Based on the assumptions above, important properties can be shown. Itô Process In the above equation, neither the drift term nor the standard deviation of the change in the short rate depends on the level of the short rate and time. There are economic reasons that might suggest that the expected direction of the rate change will depend on the level of the current short rate. The same is true for σ. We can change the dynamics of the drift term and the dynamics of the volatility term by allowing these two parameters to depend on the level of the short rate and/or time. We can denote that the drift term depends on both the level of the short rate and time by b(r,t). Similarly, we can denote the volatility term by σ(r,t). We can then write dr = b(r,t) dt + σ(r,t)dz The continuous-time stochastic model given by the above equation is called an Ito process. Specifying the Dynamics of the Drift Term In specifying the dynamics of the drift term, one can specify that the drift term depends on the level of the short rate by assuming it follows a mean reversion process. By mean reversion it is meant that some long-run stable mean value for the short rate is assumed. We denote this value by So, if r is greater than the direction of change in the short rate will move down in the direction of the long-run stable value and vice versa. In specifying the mean reversion process, we indicate the speed at which the short rate will move or converge to the long-run stable mean value. This parameter is called the speed of adjustment and we will denote it by α. The mean reversion process that specifies the dynamics of the drift term is: b(r,t) = α(r – Specifying the Dynamics of the Volatility Term There have been several formulations of the dynamics of the volatility term. If volatility is not assumed to depend on time, then σ(r, t) = σ(r). In general, the dynamics of the volatility term can be specified as follows: σrγdz where γ is equal to the constant elasticity of variance. The above equation is called the constant elasticity of variance model (CEV model). The CEV model allows us to distinguish between the different specifications of the dynamics of the volatility term for the various interest-rate models suggested by researchers. ARBITRAGE-FREE VERSUS EQUILIBRIUM MODELS Interest-rate models fall into two general categories: arbitrage models and equilibrium models. Arbitrage-Free Models In arbitrage-free models, also referred to as no-arbitrage models, the analysis begins with the observed market price of a set of financial instruments. The financial instruments can include cash market instruments and interest-rate derivatives, and they are referred to as the benchmark instruments or reference set. The underlying assumption is that the benchmark instruments are fairly priced. A random process for the generation of the term structure is assumed. Based on the random process and the assumed value for the parameter that represents the drift term, a computational procedure is used to calculate the term structure of interest rates. The model is referred to as arbitrage-free because it matches the observed prices of the benchmark instruments. The first arbitrage-free interest-rate model was introduced by Ho and Lee in 1986. In the Ho-Lee model, there is no mean reversion and volatility is independent of the level of the short rate. That is, it is a normal model. In the Kalotay-Williams-Fabozzi model, changes in the short-rate are modeled by modeling the natural logarithm of r; no allowance for mean reversion is considered in the model. The Heath-Jarrow-Morton (HJM) model is a general continuous time, multi-factor model; it has received considerable attention in the industry as well as in the finance literature. Equilibrium Models A fair characterization of arbitrage-free models is that they allow one to interpolate the term structure of interest rates from a set of observed market prices at one point in time assuming that one can rely on the market prices used. Equilibrium models, however, are models that seek to describe the dynamics of the term structure using fundamental economic variables that are assumed to affect the interest-rate process. In the modeling process, restrictions are imposed allowing for the derivation of closed-form solutions for equilibrium prices of bonds and interest rate derivatives. In these models (1) a functional form of the interest-rate volatility is assumed and (2) how the drift moves up and down over time is assumed. In characterizing the difference between arbitrage-free and equilibrium models, one can think of the distinction being whether the model is designed to be consistent with any initial term structure, or whether the parameterization implies a particular family of term structure of interest rates. Arbitrage-free models have the deficiency that the initial term structure is an input rather than being explained by the model. Basically, equilibrium models and arbitrage models are seeking to do different things. In practice, there are two concerns with implementing and using equilibrium models. First, many economic theories start with an assumption about the class of utility functions to describe how investors make choices. Second, these models are not calibrated to the market so that the prices obtained from the model can lead to arbitrage opportunities in the current term structure. EMPIRICAL EVIDENCE ON INTEREST-RATE CHANGES In any review of interest-rate models, one encounters the following issues: (1) the choice between normal models (i.e., volatility is independent of the level of interest rates) and logarithm models; and, (2) if interest rates are highly unlikely to be negative, then interest-rate models that allow for negative rates may be less suitable as a description of the interest-rate process. Volatility of Rates and the Level of Interest Rates The dependence of volatility on the level of interest rates has been examined by several researchers. The earlier research focused on short-term rates and gave inconclusive findings. Oren Cheyette found that for different periods there are different degrees of dependence of volatility on the level of interest rates. However, when interest rates were below 10%, the relationship was weak. Hence, the findings suggest that since the 1980s, interest-rate volatility has been independent of the level of interest rates. The implication is that in modeling interest rates, one can assume that interest-rate volatility is independent of the level of interest rates in an environment where rates are less than double digit. That is, in modeling the dynamics of the volatility term the normal model can be used. Negative Interest Rates While our focus is on nominal interest rates, we know that real interest rates have been found to be negative on only rare occasions. The reason is that if the nominal rate is negative, investors will simply hold cash. It is fair to say that while negative interest rates are not impossible, they are unlikely. The significance of this is that one might argue that an interest-rate model should not permit negative interest rates (or negative rates greater than a few basis points). SELECTING AN INTEREST-RATE MODEL The ease of application is a critical issue in selecting an interest-rate model. For consistency in valuation, a portfolio manager would want a model that can be used to value all financial instruments that are included in a portfolio. In practice, writing efficient algorithms to value all financial instruments that may be included in a portfolio for some interest-rate models that have been proposed in the literature is “difficult or impossible.” Based on the empirical evidence, some have concluded that the normal interest rate model is a suitable model. What is important from a practical perspective is not just whether the normal model admits the possibility of negative interest rates but whether negative interest rates may have a significant impact on the pricing of financial instruments. While the jury is still out, the consensus seems to be that negative interest rates do not have an impact in modeling interest rates. ESTIMATING INTEREST-RATE VOLATILITY USING HISTORICAL DATA One of the inputs into an interest-rate model is interest-rate volatility. Where does a practitioner obtain this value in order to implement an interest-rate model? Market participants estimate yield volatility in one of two ways. The first way is by estimating historical interest volatility. This method uses historical interest rates to calculate the standard deviation of interest-rate changes and for obvious reasons is referred to as historical volatility. The second method is more complicated and involves using models for valuing option-type derivative instruments to obtain an estimate of what the market expects interest-rate volatility is. Basically, in any option pricing model, the only input that is not observed in the model is interest-rate volatility. Since the expected interest-rate volatility obtained is being “backed out” of the model, it is referred to as implied volatility. We can calculate the historical volatility by measuring the standard deviation based on the absolute rate change and the percentage change in rates. If computing a weekly standard deviation, we must annualize the standard deviation. The formula for annualizing a weekly standard deviation is to multiply the weekly standard deviation by √52. For monthly data, we multiply by √12. For daily data, we multiply by . The difference in the calculated historical annual volatility could be significant depending on the number of trading days assumed in a year. KEY POINTS An interest-rate model is a probabilistic description of how interest rates can change over time. A stochastic differential equation is the most commonly used mathematical tool for describing interest-rate movements that incorporate statistical properties of interest-rate movements (drift, volatility, and mean reversion). In practice, one-factor models are used to describe the behavior of interest rates; they assume that short-term interest rates follow some statistical process and that other interest rates in the term structure are related to short-term rates. In a one-factor model, the SDE expresses the interest rate movement in terms of the change in the short rate over the time interval based on two components: (1) the expected direction of the change in the short rate (the drift term), and (2) a random process (the volatility term). Interest-rate models fall into two general categories: arbitrage-free models and equilibrium models. For arbitrage-free models, the analysis begins with the observed market price of benchmark instruments that are assumed to be fairly priced, and using those prices one derives a term structure that is consistent with observed market prices for the benchmark instruments. The model is referred to as arbitrage-free because it matches the observed prices of the benchmark instruments. Equilibrium models attempt to describe the dynamics of the term structure using fundamental economic variables that are assumed to affect the interest-rate process. In practice, because of the difficulties of implementing equilibrium models, arbitrage-free models are used. The classification of a model as normal or lognormal is based on the assumed dynamics of the random component of the SDE. Normal models assume that interest-rate volatility is independent of the level of rates and therefore admits the possibility of negative interest rates. The lognormal models assume that interest-rate volatility is proportional to the level of rates, and therefore negative interest rates are not possible. Empirical evidence reviewed in this chapter regarding the relationship between interest rate volatility and the level of rates suggests that the relationship is weak at interest rate levels below 10%. However, for rates exceeding 10%, there tends to be a positive relationship. This evidence suggests that in rate environments below 10%, a normal model would be more descriptive of the behavior of interest rates than the lognormal model. Empirical tests also suggest that the impact of negative interest rates on pricing is minimal, and therefore one should not be overly concerned that a normal model admits the possibility of negative interest rates. Interest-rate volatility can be estimated using historical volatility or implied volatility. Historical volatility is calculated from observed rates over some period of time. When calculating historical volatility using daily observations, differences in annualized volatility occur for a given set of observations because of the different assumptions that can be made about the number of trading days in a year. Implied volatility is obtained using an option pricing model and observed prices for option-type derivative instruments. ANSWERS TO QUESTIONS FOR CHAPTER 16 (Questions are in bold print followed by answers.) 1. What is meant by an interest-rate model? By an interest rate model, we mean a model that incorporates statistical properties of interest-rate movements. These properties are (1) drift, (2) volatility, and (3) mean reversion. The commonly used mathematical tool for describing the movement of interest rates that can incorporate these properties is stochastic differential equations (SDEs). 2. Answer the below questions. (a) Explain the drift property found in an interest-rate model. The drift term refers to that variable in an interest rate model that captures the expected direction of the change in the interest rate (e.g., a short-term nominal rate referred to as the short rate). The symbol b is used in interest rate models to represent the drift. Various assumptions must be made about the drift term. For example, it can be assumed to be zero of some positive or negative value or it can be assumed to be dependent on the level of interest rates. If the drift term is assumed to be dependent on the interest rate, one can specify that it follows a mean reversion process where it returns to its long-run stable mean value. (b) Explain the volatility property found in an interest-rate model. The volatility term refers to that variability of the interest rate or the short rate. The symbol σ is used in interest rate models to represent the volatility and is simply the standard deviation of the changes in the short rate. Like the drift term, assumptions are made such as its dependency on the level of the short rate. There have been several formulations of the dynamics of the volatility term. If volatility is assumed to depend on time, then we express volatility as σ(r,t) where r is the short rate and t is the change in time (or time period being considered). If volatility is not assumed to depend on time, then σ(r,t) = σ(r). In general, the dynamics of the volatility term can be specified as σrγdz where γ is equal to the constant elasticity of variance. This equation is called the constant elasticity of variance model (CEV model). (c) Explain the mean reversion property found in an interest-rate model. By the mean reversion property, it is meant that some long-run stable mean value for the short rate is assumed. This long-run value can be denoted by . So, if the short-rate (r) is greater than , the direction of change in the short rate will move down in the direction of the long-run stable value and vice versa. However, in specifying the mean reversion process, it is necessary to indicate the speed at which the short rate will move or converge to the long-run stable mean value. This parameter is called the speed of adjustment and can be denoted by α. The mean reversion process that specifies the dynamics of the drift term is given as b(r,t) = α(r – ) where b is the drift term (discussed previously). 3. What is the commonly used mathematical tool for describing the movement of interest rates that can incorporate the properties of an interest-rate model? The commonly used mathematical tool for describing the movement of interest rates (that can incorporate the properties of drift, volatility and mean reversion) is stochastic differential equations (SDEs). A rigorous treatment of interest-rate modeling requires an understanding of this specialized topic in mathematics. It is also worth noting that SDEs are used in the pricing of options. More details are given below. The most common interest-rate model used to describe the behavior of interest rates assumes that short-term interest rates follow some statistical process and that other interest rates in the term structure are related to short-term rates. The short-term interest rate (i.e., short rate) is the only one that is assumed to drive the rates of all other maturities. Hence, these models are referred to as one-factor models. The other rates are not randomly determined once the short rate is specified. Using arbitrage arguments, the rate for all other maturities is determined. There are also multi-factor models that have been proposed in the literature. The most common multi-factor model is a two-factor model where a long-term rate is the second factor. In practice, however, one-factor models are used because of the difficulty of applying a multi-factor models. The high correlation between rate changes for different maturities provides some support for the use of a one-factor model as well as empirical evidence that supports the position that a level shift in interest rates accounts for the major portion of the change in the yield curve. While the value of the short rate at some future time is uncertain, the pattern by which it changes over time can be assumed. In statistical terminology, this pattern or behavior is called a stochastic process. Thus, describing the dynamics of the short rate means specifying the stochastic process that describes the movement of the short rate. It is assumed that the short rate is a continuous random variable and therefore the stochastic process used is a continuous-time stochastic process. There are different types of continuous-time stochastic processes. In all of these models because time is a continuous variable, the letter d is used to denote the “change in” some variable. Terms used in these models are defined below. r = the short rate and therefore dr denotes the change in the short rate t = time and therefore dt denotes the change in time or equivalently the length of the time interval (dt is a very small interval of time) z = a random term and dz denotes a random process 4. Answer the below questions. (a) Why is the most common interest-rate model used to describe the behavior of interest rates a one-factor model? In practice, one-factor models are used because of the difficulty of applying even a two-factor model. In addition, there is empirical evidence that supports one-factor models. Thus, due to the greater simplicity and applicability of one-factor models, they are preferred over two-factor models. (b) What is the one-factor in a one-factor interest-rate model? The one-factor in a one-factor interest-rate model is short-term interest rates where it is assumed short rates follow some statistical process with other interest rates in the term structure related to the short rate. Thus, the short rate is the only factor that is assumed to drive the rates of all other maturities. 5. Answer the below questions. (a) What is meant by a normal model of interest rates? The classification of a model as normal is based on the assumed dynamics of the random component of the stochastic differential equation (SDE). Normal models assume that interest rate volatility is independent of the level of rates and therefore admits the possibility of negative interest rates. More details are given below. Consider a basic continuous-time stochastic process for describing the dynamics of the short rate given by: dr = bdt + σdz where dr and dt are the change in the short rate and time, z is a random term with dz denoting a random process, σ is the standard deviation of the changes in the short rate, and b is the expected direction of rate change. In the Vasicek specification, volatility is independent of the level of the short rate as in the above equation and is referred to as the normal model. Independence implies that it is possible for negative interest rates to be generated. The Ho-Lee model is also a normal model because volatility is independent of the level of the short rate. The Hull-White model is also a normal model where volatility does not depend on the short rate but, unlike the Ho-Lee model, it allows for mean reversion. Empirical evidence suggests that the normal model is a suitable model because the assumption about the independence of volatility relative to the short rate is generally a valid assumption. An exception is when the short-rate is greater than ten percent. (b) What is meant by a lognormal model of interest rates? Like a normal model, the classification of a model as lognormal is based on the assumed dynamics of the random component of the SDE. However, unlike normal models, lognormal models assume that interest-rate volatility is proportional to the level of rates, and therefore negative interest rates are not possible. An example of a lognormal model is the Kalotay-Williams-Fabozzi (KWF) model where changes in the short-rate are modeled by modeling the natural logarithm of r; no allowance for mean reversion is considered in the model. Empirical evidence regarding the relationship between interest-rate volatility and the level of rates suggests that the relationship is weak at interest rate levels below 10%. However, for rates exceeding 10%, there tends to be a positive relationship. This evidence suggests that in rate environments below 10%, a normal model would be more descriptive of the behavior of interest rates than the lognormal model. Moreover, empirical tests suggest that the impact of negative interest rates on pricing is minimal, and therefore one should not be overly concerned that a normal model admits the possibility of negative interest rates. 6. Answer the below questions. a. Explain the treatment of the dynamics of the volatility term for the Vasicek interest rate model. Let us begin by noting that there have been several formulations of the dynamics of the volatility term. If volatility is not assumed to depend on time, then σ(r,t) = σ(r). In general, the dynamics of the volatility term can be specified as follows: σrγdz where γ is equal to the constant elasticity of variance and z is a random term with dz denoting a random process. The above equation is called the constant elasticity of variance model (CEV model). The CEV model allows us to distinguish between the different specifications of the dynamics of the volatility term for the various interest-rate models suggested by researchers. For the Vasicek interest rate model, we look at the case for γ = 0. Substituting this value for γ into the above equation, we get the following model identified by Vasicek who first proposed it: γ = 0: σ(r,t) = σ (Vasicek specification of CEV model). In the Vasicek specification, volatility is independent of the level of the short rate as in the equation of dr = bdt + σdz (where b is the drift term) and is referred to as the normal model. In the normal model, it is possible for negative interest rates to be generated. b. Explain the treatment of the dynamics of the volatility term for the Dothan interest rate model. For the Dothan interest rate model, we look at the case for γ = 1. Substituting this value for γ into σrγdz, we get the following model identified by Dothan who first proposed it: γ = 1: σ(r,t) = σ r (Dothan specification of CEV model). In the Dothan specification, volatility is proportional to the short rate. This model is referred to as the proportional volatility model. c. Explain the treatment of the dynamics of the volatility term for the Cox-Ingersoll-Ross interest rate model. For the Cox-Ingersoll-Ross specification interest rate model, we look at the case for γ = 1/2. Substituting this value for γ into σrγdz, we get the following model identified by Cox-Ingersoll-Ross who first proposed it: γ = 1/2: σ(r,t) = σ (Cox-Ingersoll-Ross specification). The Cox-Ingersoll-Ross (CIR) specification, referred to as the square-root model, makes the volatility proportional to the square rate of the short rate. Negative interest rates are not possible in this square-root model. One can combine the dynamics of the drift term and volatility term to create the following commonly used interest rate model: dr = . This model specifies a mean reversion process for the drift term and the square root model for volatility and is referred to as the mean-reverting square-root model. While there have been many developments in equilibrium models, the best known models are the Vasicek and CIR models. To apply these models, estimates of the parameters of the assumed interest-rate process are needed, including the parameters of the volatility function for interest rates. These estimated parameters are typically obtained using econometric techniques that rely on historical yield curves without regard to how the final model matches any market prices. 7. What is an arbitrage-free interest-rate model? An arbitrage-free interest-rate model is a model that allows one to interpolate the term structure of interest rates from a set of observed market prices at one point in time assuming that one can rely on the market prices used. Thus, in arbitrage-free models, also referred to as no-arbitrage models, the analysis begins with the observed market price of a set of financial instruments. The financial instruments can include cash market instruments and interest-rate derivatives, and they are referred to as the benchmark instruments or reference set. The underlying assumption is that the benchmark instruments are fairly priced. A random process for the generation of the term structure is assumed. The random process assumes a drift term for interest rates and volatility of interest rates. Based on the random process and the assumed value for the parameter that represents the drift term, a computational procedure is used to calculate the term structure of interest rates (i.e., the spot rate curve) such that the valuation process generates the observed market prices for the benchmark instruments. The model is referred to as arbitrage-free because it matches the observed prices of the benchmark instruments. In other words, one cannot realize an arbitrage profit by pursuing a strategy based on the value of the securities generated by the model and the observed market price. Non-benchmark instruments are then valued using the term structure of interest rates estimated and the volatility assumed. 8. Answer the below questions. (a) What are the general characteristics of the Ho-Lee arbitrage-free interest-rate model? The first arbitrage-free interest-rate model was introduced by Ho and Lee in 1986. In the Ho-Lee model, there is no mean reversion and volatility is independent of the level of the short rate. That is, it is a normal model [i.e., constant elasticity of variance (γ) = 0]. (b) How does the Ho-Lee arbitrage-free interest-rate model differ from the Hull-White arbitrage-free interest-rate model? Like the Ho-Lee arbitrage-free interest-rate mode, the Hull-White model is a normal model [i.e., constant elasticity of variance (γ) = 0]. However, unlike the Ho-Lee model, the Hull-White model allows for mean reversion. Whereas the Ho-Lee model is the first arbitrage-free model, the Hull-White model is the first arbitrage-free, mean reverting normal model. 9. What is an equilibrium interest-rate model? An equilibrium interest-rate model is a model that seeks to describe the dynamics of the term structure using fundamental economic variables that are assumed to affect the interest-rate process. In the modeling process, restrictions are imposed allowing for the derivation of closed-form solutions for equilibrium prices of bonds and interest rate derivatives. In these models (1) a functional form of the interest-rate volatility is assumed and (2) how the drift moves up and down over time is assumed. More details are given below. In characterizing the difference between arbitrage-free and equilibrium models, one can think of the distinction being whether the model is designed to be consistent with any initial term structure, or whether the parameterization implies a particular family of term structure of interest rates. Arbitrage-free models have the deficiency that the initial term structure is an input rather than being explained by the model. Basically, equilibrium models and arbitrage models are seeking to do different things. To implement an equilibrium model, estimates of the parameters of the assumed interest-rate process are needed, including the parameters of the volatility function for interest rates. These estimated parameters are typically obtained using econometric techniques using historical yield curves without regard to how the final model matches any market prices. 10. Explain why in practice arbitrage-free models are typically used rather than equilibrium models. Interest-rate models fall into two general categories: arbitrage models and equilibrium models. In practice, arbitrage-free models are typically used because they are easier to implement than equilibrium models. To illustrate, there are two concerns with implementing and using equilibrium models. First, many economic theories start with an assumption about the class of utility functions to describe how investors make choices. Equilibrium models are no exception: the model builder must specify the assumed class of utility functions. Second, these models are not calibrated to the market so that the prices obtained from the model can lead to arbitrage opportunities in the current term structure. 11. Answer the below questions. (a) What is the empirical evidence on the relationship between volatility and the level of interest rates? Empirical evidence reviewed regarding the relationship between interest-rate volatility and the level of rates suggests that the relationship is weak at interest rate levels below 10%. However, for rates exceeding 10%, there tends to be a positive relationship. More details are given below. To answer this question, we need to examine from an historical perspective the issue as to whether interest rate volatility is affected by the level of interest rates or independent of the level of interest rates. If it is affected, one might suspect a higher the level of interest rates will lead to greater volatility in the interest rates. That is, there will be a positive correlation between the level of interest rates and interest-rate volatility. If the two are independent, a low correlation would exist. The dependence of volatility on the level of interest rates has been examined by several researchers. The earlier research focused on short-term rates and employed a statistical time series model called generalized autoregressive conditional heteroscedasticity (GARCH). With respect to short-term rates, the findings were inconclusive. Rather than focusing on the short-term rate, Cheyette examined all the spot rates for the Treasury yield curve for the period 1977 to early 1996, a period covering a wide range of interest rates and different Federal Reserve policies. He found that for different periods there are different degrees of dependence of volatility on the level of interest rates. (Interest-rate changes are measured as absolute rate changes in Cheyette’s study). Specifically, in the high interest-rate environment of the late 1970s and early 1980s where interest rates exceeded 10%, there was a positive correlation between interest-rate volatility and the level of interest rates. However, when interest rates were below 10%, the relationship was weak. Hence, the findings suggest that since the 1980s, interest-rate volatility has been independent of the level of interest rates. These conclusions were supported in a study by Levin of the Treasury 10-year rate from 1980 to 2003 and the 10-year swap rate from 1989 to 2003. The implication is that in modeling interest rates, one can assume that interest-rate volatility is independent of the level of interest rates in an environment where rates are less than double digit. That is, in modeling the dynamics of the volatility term the normal model can be used. (b) Explain whether the historical evidence supports the use of a normal model or a lognormal model. The support for a normal model or a lognormal model depends on the current level of interest rates as described below. Empirical evidence reviewed regarding the relationship between interest-rate volatility and the level of rates suggests that the relationship is weak at interest rate levels below 10%. However, for rates exceeding 10%, there tends to be a positive relationship. This evidence suggests that in rate environments below 10%, a normal model would be more descriptive of the behavior of interest rates than the lognormal model. Moreover, empirical tests suggest that the impact of negative interest rates on pricing is minimal, and therefore one should not be overly concerned that a normal model admits the possibility of negative interest rates. 12. Comment on the following statement: “If an interest-rate model allows the possibility of negative interest rates, then it is not useful in practice.” All because an interest-rate model allows for the possibility of negative interest rates does not imply it is not useful. Furthermore, allowing for the possibility of a negative interest rate does not mean the model will produce a negative interest rate. Allowing for the possibility of a negative interest rate may even be viewed as realistic since there are documented occasions (albeit rare) where negative rates have occurred. More details are supplied below. Our focus is on nominal interest rates. While we know that real interest rates (i.e., a nominal rate minus an inflation premium) in an economy have been negative, it is generally thought that it is impossible for the nominal interest rate to be negative. The reason is that if the nominal rate is negative, investors will simply hold cash. However, there have been time periods in countries where interest rates have been negative for a brief time period, refuting the notion that investors would not be willing to lend at negative interest rates. For example, during the Great Depression in the United States, financial historians have identified periods where Treasury securities traded at a negative yield. Japan provides another example. In early November 1998, Western banks charged Japanese banks interest of 3 to 6 basis points to hold 2- or 3-month yen deposits that Japanese banks were unwilling to deposit with local institutions because of the perceived instability of Japan’s financial system. The yield on 3-month Japanese Treasury bills during one trading day in November 1998 fell to minus 5 basis points, although the closing yield was positive. It is fair to say that while negative interest rates are not impossible, they are unlikely. The significance of this is that one might argue that an interest-rate model should not permit negative interest rates (or negative rates greater than a few basis points). Yet, this may occur in a model where volatility is measured in terms of basis points—as in the normal model. In contrast, if interest-rate volatility is measured in terms of the percentage yield change (i.e., logarithm of the yield ratio), interest rates cannot be negative. Hence, a stated advantage of using an interest-rate model whose volatility is dependent on the level of interest rates is that negative returns are not possible. 13. Answer the below questions. (a) What is meant by historical volatility? By historical volatility is meant the degree of change in interest rates over some past time period. More details are given below. Market participants estimate yield volatility in one of two methods: historical volatility or implied volatility. The historical interest volatility method uses historical interest rates to calculate the standard deviation of interest-rate changes. The text uses to explain how to calculate the historical volatility as measured by the standard deviation based on the absolute rate change and the percentage change in rates. The historical interest rates shown are the weekly returns for one-month LIBOR from 7/30/2004 to 7/29/2005. The weekly standard deviation is reported. For the absolute rate change, it is 2.32 basis points; for the percentage rate change, it is 1.33%. The weekly measures must be annualized. The formula for annualizing a weekly standard deviation is: weekly standard deviation × . Annualizing the two weekly volatility measures, we have: absolute rate change = 2.32 × = 18.86 basis points and logarithm percent change = 1.33 × = 9.62%. If we use monthly data to compute the standard deviation, the following formula would be used to annualize: monthly standard deviation × . Using daily data, we would have: daily standard deviation × . Note that annualizing of the daily volatility requires that the number of days in a year be determined. Market practice varies with respect to the number of trading days in the year that should be used in the annualizing formula above. Typically, either 250 days or 260 days are used. For many traders who use daily rates, the difference in the calculated historical annual volatility could be significant depending on the number of trading days assumed in a year. (b) What is meant by implied volatility? Market participants estimate yield volatility in one of two methods: historical volatility or implied volatility. The implied volatility method is more complicated than the historical method as it involves using models for valuing option-type derivative instruments to obtain an estimate of what the market expects interest-rate volatility is. In any option pricing model, the only input that is not observed in the model is interest-rate volatility. In practice, one assumes that the observed price for an option-type derivative is priced according to some option pricing model. The calculation then involves determining what interest-rate volatility will make the market price of the option-type derivative equal to the value generated by the option pricing model. Since the expected interest-rate volatility obtained is being “backed out” of the model, it is referred to as implied volatility. 14. Suppose that the following weekly interest rate volatility estimates are computed as: absolute rate change = 3.85 basis points and percentage rate change = 2.14%. Answer the below questions. (a) What is the annualized volatility for the absolute rate change? The formula for annualizing a weekly value is: weekly value × . Annualizing the weekly volatility measure for the absolute rate change, we get: absolute rate change = 3.85 × = 27.76 or about 28 basis points. (b) What is the annualized volatility for the percentage rate change? The formula for annualizing a weekly standard deviation is: weekly standard deviation × . Annualizing the weekly volatility measure for the percentage change, we get: percentage change = 2.14% × = 15.43176% or about 16.43%. In terms of logarithm, we would have logarithm percentage change we would get about 5.49%. Solution Manual for Bond Markets, Analysis and Strategies Frank J. Fabozzi 9780132743549, 9780133796773