Homework 2 Fall 2023

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Homework 2 Chapter 13 4. In a discussion of the CMO market, the popular press sometimes refers to this sector of the mortgage-backed securities market as the riskiest sector and the pass-through sector as the safest sector. Comment. Answer: In discussions about the CMO market within the mortgage-backed securities sector, the popular press frequently characterizes this segment as the riskiest, while labeling the pass-through sector as the safest. The perception of CMOs as high-risk stems from their inherent complexity and extended terms compared to the straightforward nature of pass-through securities, making them potentially more challenging to comprehend and manage. Despite the elevated risk levels associated with CMOs, they present opportunities for investors to earn attractive returns. CMOs with higher interest rates often feature elevated coupons, providing investors with increased income potential. Moreover, successful performance of the underlying mortgages can lead to capital appreciation, adding to the appeal of CMO investments. The accompanying figure from the article, "The Risks of Investing in Collateralized Mortgage Obligations," visually illustrates the relative risks of CMOs in comparison to other types of mortgage- backed securities. CMOs are deemed risker but they can still provide investors with appealing returns , particularly when the underlying mortgages have strong performance . 10. Explain the role of a support bond in a CMO structure. Answer : In a collateralized mortgage obligation (CMO) structure, a support bond plays a crucial role in enhancing stability. This specific debt instrument, typically issued by a third party like an insurance company, serves to ensure the smooth functioning of the CMO by covering principal and interest payments in case the underlying collateral does not perform as anticipated. This role is pivotal as it safeguards investors from potential losses and contributes to the overall structural stability. The issuance of the support bond at a higher interest rate than the CMO itself serves as a risk- offsetting measure for the issuer. Moreover, the support bond generally has a shorter maturity period than the CMO, mitigating the risk of the issuer being locked into a long-term investment if the CMO structure faces challenges. However, it's essential to acknowledge the risks associated with support bonds. If the CMO structure fails, the support bond issuer may face significant financial obligations to the CMO holders, potentially placing them in a precarious financial position. Additionally, in the event of rising interest rates, the value of the support bond may decrease, exposing the issuer to potential losses. Support bonds can help investors stabilize their investment portfolios . 19. Consider the following CMO structure backed by 8% collateral: Tranche Par Amount (in millions) Coupon Rate (%) A $300 6.50% B $250 6.75% C $200 7.25% Page 1 of 6

D $250 7.75% Suppose that a client wants a notional IO with a coupon rate of 8%. Calculate the notional amount for this notional IO. Answer : Tranche Par Amount Excess Interest Notional amount for an 8% IO A 300 Million 1.5% (300M x 0.015)/0.08=56,250,0000 B 250 Million 1.25% (250M x 0.0125)/0.08 = 39,062,500 C 200 Million 0.75% (200 M x 0.0075) /0.08 = 18,750,000 C 250 Million 0.25% (250 M x 0.0025)/0.08=7,812,500 Total Notional Amount = 121,875,000 Chapter 14 8. Answer the below questions. a. What is the conditional default rate? b. What is the cumulative default rate? Answer: a. The conditional default rate (CDR) refers to the probability of a bond or loan defaulting within a specific period, given that it has survived up to a certain point without defaulting. In other words, it is a measure that focuses on the likelihood of default for a given time frame, conditional on the fact that the bond or loan has not defaulted up to that point. The CDR is often expressed as an annualized percentage and is a key metric in assessing credit risk. b. The cumulative default rate (CDR) represents the total proportion of bonds or loans that have defaulted over a specified period. Unlike the conditional default rate, which considers the probability of default within a given time frame, the cumulative default rate accumulates the default events over time. It provides a comprehensive view of the overall default experience of a group of bonds or loans from the beginning of the observation period until a specific point in time. The cumulative default rate is expressed as a percentage of the total number of bonds or loans in the portfolio and is a critical measure for evaluating the historical performance and credit quality of a portfolio. 12. Suppose that for a securitization with a shifting interest mechanism you are given the following information for some month: subordinate interest = 25% Page 2 of 6

shifting interest percentage = 85% regularly scheduled principal payment = $3,000,000 prepayments = $1,200,000 a. What is the senior prepayment percentage for the month? b. How much of the $3,000,000 regularly scheduled principal payment is distributed to the senior class? c. How much of the $1,200,000 is distributed to the senior class? Answer: a. Senior percentage = 100% -25%=75% b. Senior class: 0.75 x 3,000,000=2,250,000 c. Senior prepayment percentage = senior interest + (Shifting interest percentage × Subordinate interest) 75% + 0.85 × 25% = 96.25% 9 shifting percentage 0.9625 × $1,200,000 = $1,155,000 is allocated to the senior class 15. Answer the below questions. a. What is meant by an involuntary prepayment? b. Why is the distinction between a voluntary and involuntary prepayment important in nonagency RMBS? Answer : a. An involuntary prepayment occurs when a borrower is unable to meet the mortgage obligations, leading to the initiation of foreclosure proceedings. In this scenario, the prepayment is not initiated by the borrower's choice but is rather a consequence of financial distress or default. It typically involves the transfer of property ownership from the borrower to the mortgage servicer, who then takes possession with the intention of selling the property to recover the outstanding debt. b. The distinction between voluntary and involuntary prepayments is crucial in nonagency Residential Mortgage-Backed Securities (RMBS), particularly when it comes to reporting. In the context of nonagency RMBS, when a loan transitions from delinquency to default, and the servicer takes possession of the property for sale, the proceeds received (minus associated costs) are known as the recovered principal. The reporting of voluntary prepayments (traditional prepayments) and involuntary prepayments (credit-related prepayments) separately is essential for several reasons. Specifically, this distinction is vital for determining the principal payments that need to be distributed to the senior bond classes. Voluntary prepayments may be more routine and tied to changes in interest rates, while involuntary prepayments are tied to credit events and defaults. Additionally, the separation of these prepayment types is crucial for accurately assessing losses, which involve the shortfall between the mortgage balance and the recovered principal. Allocating these losses to subordinated bond classes is a critical aspect of risk management and ensuring that the impact of Page 3 of 6

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