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FINE 7650/4120: Fixed Income Valuation Exercise 2

发布时间：2023-12-14

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FINE 7650/4120: Fixed Income

Valuation Exercise 2: Modeling RMBS Cashflows

Date Assigned: 30th Nov, 2023 Date Due: End of Semester

Instructions

The valuation exercises require you to stitch together insights from various areas of Finance to solve them. They will involve concepts covered not just in the current course, but areas from the core courses, although the prime focus will be on Fixed Income. These are not simple follow-ups of class notes, instead it is meant to be a learning experience (of new materials) rather than any sort of test (on old materials). When working on valuation exercises, you may look for external sources of general information, but must consider only information known to decision-makers at the time the relevant decision is being made. Remember, there are no “right” or “wrong” answers. The grade assigned will reflect the level of attention, the novelty of your insights and the effort you put into condensing the material.

I believe that emulating real-lifework situations in the classroom is part of training professionals. As such, all homework are all group assignments. Meeting and discussing assignments with a small set of classmates is crucial to developing the skills needed to succeed in your professional career. These interactions represent a chance to learn new ideas and develop interpersonal skills, such as the ability to propose and defend ideas in a convincing, inclusive way. Note that only one grade is assigned to all members of a group task.

Guidelines: As a general guideline, the response to this exercise will be presented in the form of a write-up (Word/PDF document), with all data provided within the same document. The expected length of the write-up is 3-5 pages, with normally acceptable margins, spacing and font sizes. DO NOT UPLOAD YOUR SOLUTIONS AS EXCEL FILES. Excel work will not reflect your understanding and underlying thinking in answering the questions.

When you are done answering the questions and you are ready to submit the problem set, please first choose one group representative who will submit on your behalf. Only your FINAL attempt will be graded. Please upload only one submission per group. Remember to include the names and ID’s of all group members on your submission.

Assignment Prompt

As we approach the close of year 2023, the interest rate and mortgage market is heading into high uncertainty. Interest rates are at an all time high as are house prices, prompting risks of widespread defaults and a crash of the so-called “house price bubble” . To some experts, these developments herald an oncoming recession especially in the Mortgage Backed Securities markets, with many drawing similarities from the fundamental issues prevailing during the onset of the Subprime Mortgage Crisis of 2008.

Over the past decade and a half, financial regulators have assiduously worked to make the MBS markets safer by introducing new legislative and prudential changes that later the fundamental nature of securitization and the placement of securitized notes. These changes altogether make the concerns moot to a large extent. They, however, provide scope for an interesting thought experiment – what do macroeconomic similar to the 2008 era spell for todays’ private label RMBS?

Agency securitization was largely insulated from the risks in 2008 owing the high collateral quality, private label MBSs were the hardest hit, seeing a swathe of default across credit categories and associated ratings. Bearing this mind, in this exercise, we will explore atypical private label MBS deal structure and explain the risks and key assumptions involved in their analyses.

Deal Characteristics

The deal comprises $1,250,000,000 of collateral – all fixed rate, subprime mortgages yielding a monthly weighted average coupon (WAC) of 6.0% and a maximum maturity of 20 years. The deal is structured in four standard tranches, plus an additional fifth equity tranche, which does not typically have any access to collateral, but can benefit from excess spreads and any additional profits that flow into the deal. All notes (except the equity tranche) pay quarterly coupons, floating rate coupons indexed to the 3-month USD LIBOR. The deal structure looks as follows:

Notes	Rating	Initial Amount	Spread to LIBOR
Class A1	AAA	503,200,000	12 bps
Class A2	AAA	701,335,000	18 bps
Class B	AA	15,000,000	36 bps
Class C	BBB	30,465,000	110 bps
Class D	Equity	7,000,000
Total Rated Notes		1,250,000,000
Total Notes		1,257,000,000

Among these notes, although A1 and A2 are equal in seniority, A1 has slightly higher benefits than A2. Specifically, when both of the notes are repaid 45% or more, all principal payments first go to A1 until it is 100% paid-off and only then do principal payments go towards A2. In other words, A1 and A2 both have equal rights to principal cashflows until they are 50% redeemed, at which point, A1 becomes more senior to A2. Hence the difference in their coupon rates.

In addition to collateral, the deal contains several credit enhancement features that provide protection against collateral defaults. These include:

(a) A liquidity facility, which is effectively a credit line with a bank that the securitizer can draw upon to meet interest obligations to noteholders in the case that underlying collateral payments are insufficient to meet note holder interest obligations. The deal contains $35,000,000 in liquidity facility, which represents the maximum amount that can be borrowed. The securitizer pays 20bps over LIBOR in order to maintain this facility (known as the commitment fee). Each dollar of this facility that is actually used (or borrowed) incurs an additional fee of 40bps (i.e., LIBOR + 20bps +40bps) as long as it is not repaid (known as the drawn fee).

(b) A cash account (aka reserve fund) with an initial deposit of $7,000,000. This serves to again provide a buffer against defaults. The size of this cash account goes down to $3,142,500 when the A1 tranche has been redeemed 50%. At this point, the excess balance in the account goes towards repaying tranche A1 principal. Any balance in this account earns an interest of LIBOR.

(c) A “clean-up” call provision, which is a call option that allows the issuer to redeem all outstanding notes in entirety using any and all available cash balances, when more than 90% of the original collateral balance has been redeemed. When this call option is exercised, the deal has run its life and comes to an end.

(d) An interest rate swap, which is a derivative instrument that acts as a hedge against fluctuations in interest rate. Effectively, the presence of this swap ensures that the underlying collateral interest payments are steady over time and do not fluctuate with interest rate changes. This swap costs 1.8% of the collateral balance each year to maintain.

Instructions

Refer to the accompanying Excel model for a comprehensive cashflow model of the notes and the collateral. You will use this model to answer questions (marked by ). The other questions require you to perform your own calculations. Note that the Excel file contains several”hidden” sheets that contain certain underlying assumptions. You do not need to access these sheets for the purposes of this assignment. You can however, play around with these assumptions if you choose to do so!

Deal analysis

1. Let us first quantify the risk level of this deal and the individual notes by exploring their credit enhancement mechanisms.

(a) Calculate the level of subordination of each note

(b) The current level of the 3-month USD LIBOR is 3.8160%. Calculate the excess spread of each note and of the entire deal.

(d) Discuss whether these measures of credit enhancement are aligned with the stated coupon rates and the credit ratings of the tranches.

2. (Use the provided Excel sheet to answer this question)

Now let us understand how sizing the AAA tranche works. Use the sheet “Deal Structure” and play around with the initial amount of notes. In order to do this, try various combinations of initial note balances in column J6:J9, ensuring that the total balance of the rated notes always is lower than the total collateral balance. As you do this, look at what happens to unpaid principal balances (K46:K50). As long as a note is projected to have an unpaid principal balance, it can never attain a rating of AAA! What can you say about the size of the top tranches, their effective lives and the resulting rating?

3. (Use the provided Excel sheet to answer this question)

Next, let us explore the effects of collateral defaults, interest rates and prepayments on the note repayments. In order to do this, use the sheet titled “Indiv. Scenarios” . Using the dropdown menus, choose various combinations of the default curve assumption (D5), CPR assumption (J5) and LIBOR projections (M5). What happens to the repayment speed of each of the tranches in these scenarios? How about the unpaid principal? Discuss your interpretation of these relationships.

(Hint: You can check the Average Life of bonds from “Deal Structure” E46:E50, or from the sheet “Paydown Chart”).

4. (Use the provided Excel sheet to answer this question)

Finally, let us think about what the equity tranche signifies. Note that the principal balance of Class D Tranche exceeds that of total available collateral after accounting for its more senior classes. However, it is exactly protected by the presence of the cash account with an initial balance of $7,000,000. Now, in the model turnoff the clean-up call option using the dropdown in Cell H36 of the “Deal Structure”. What happens to the NPV and IRR of the equity tranche now?

Note that in most cases, the equity tranche is held by the issuer themselves as a way to reclaim their initial deposit to the cash account. With this in mind, discuss who does the call option favor more – the issuer or the buyer?