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FINE 7650/4120: Fixed Income Problem Set 3: Corporate Bonds and Mortgage-Backed Securities

发布时间：2023-12-15

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FINE 7650/4120: Fixed Income

(Optional) Problem Set 3: Corporate Bonds and Mortgage-Backed Securities

Date Assigned: 5th Dec, 2023 Date Due: End of Semester

This problem set is optional. If you choose to run it in, it will subsume the lower of your grades from the two previous problem sets. The two best scores from the three problem sets will be used to compute the problem set component of the final grade.

To help you practice the material, there are problem sets that accompany each of the topics we study. The problem sets account for 15% of your grade. The file should include scanned handwritten pages on which you show how you solved the problems and/or an Excel file with your work. If you use a financial calculator, write down what numbers you enter into the special keys of the financial calculator. Alternatively, you can choose to do all the problems in Excel and send the Excel file rather than scanned handwritten pages. Either way, I should be able to see your work, not just your final answers.

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.

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. The representative should login to Canvas and click on “Problem Set 3” under “Assignments.” Click on the “Upload” button at the bottom of the screen. Click on “Choose a file to Upload” on the right side of the screen, (Alternatively, you can drag and drop you chosen files) to open a window that allows you to browse for your saved file. Highlight the file and click “Open.” Your filename will now appear to the right of the “Choose File” button. You can upload more than one file (e.g., handwritten notes and an Excel file) by clicking on “+ Add Another File”. When you are done uploading the file (or files), click on the green “Submit Assignment” button. You should see a confirmation of your submission on the top right corner of the screen. If you want to update your submission or make corrections, click on “Try Again” at the bottom right corner and repeat the steps above. 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.

This problem set contains 4 questions. Answering the 4 questions correctly will earn you full credit. Partial/incorrect solutions will be graded accordingly.

1. Callable and puttable bonds.

Consider the following set of bonds, all issued on the same day by FINE Corp with 15 years to maturity. Each bond carries a coupon of 5% payable semi-annually

(a) Callable on any day after the fifth anniversary of bond issuance

(b) Callable only if at least 10 years have passed since the bond’sissuance. (c) Puttable on any day following the 5th anniversary of bond issuance.

(d) Puttable only if at least 10 years have passed since the bond’sissuance. (e) No callability or puttability features (plain vanilla bond).

Discuss the risks faced by the issuer and bond investor in each of these bonds. Finally, rank the bonds in the order of their likely price atissue.

2. Default Risks.

Suppose that you invest $250,000 in a AA-rated senior secured corporate bond issued by FAMA Corp. historically, such bonds have a default rate of 8.5%, and when defaulted, 65% of the capital is recovered. What is your expected loss in the bond?

3. Agency RMBS

On October 1, 2005, Fannie Mae issued a mortgage pass-through security and the prospectus stated the following:

FANNIE MAE*

MORTGAEG_BACKES SECURITIES PROGRAM

$464,927,576.04

ISSUE DATE OCTOBER 01, 2005

SECURITY DESCRIPTION FNMS 05.0000 CL-844801

5.0000 PERCENT PASS-THROUGH RATE

FANNIE MAE POOL NUMBER CL-844801

CUSIP 31407YRW1

PRINCIPAL AND INTEREST PAYABLE ON THE 25TH OF EACH MONTH

BEGINNING NOVEMBER 25,2005

POOL STATISTICS

SELLER

NUMBER OF MORTGAGE LOANS

AVERAGE LOAN SIZE

MATURITY DATE

WA COUPON RATE

WA LOAN AGE

WA LOAN TERM

WA REMAINING MATURITY

WA LTV

WA CREDIT SCORE

WELLS FARGO BANK, N.A.

1,986

$234,312.06

10/01/2035

5.7500%

1 mo

360 mo

359 mo

73%

729

(a) What does the “pass-through rate” of 5% for this security mean?

(b) What is the average interest rate being paid by the borrowers in the loan pool for this security?

(c) Why does the pass-through rate differ from the average interest rate paid by the borrowers in the loan pool for this security?

(d) The “maturity date” for this security is shown as 10/01/2035An investor in this security might be concerned about its very long maturity (30 years). Why is the maturity date a misleading measure for this security’smaturity?

(e) If an investor purchased $15 million principal of this security, and in some month,

the cash flow available to be paid to the security holders (after all fess are paid) is $12 million, how much is the investor entitled to receive?

(f) Each month the security would report a “pool factor,” which denotes the percentage of original collateral balance remaining on that month. If, on a given month, the pool factor is 0.92, what is the outstanding principal balance of the collateral pool for the month?

(g) Why does the WA loan term differ from the WA remaining maturity? What does this denote?

4. Monthly cashflows of PL MBS.

Consider the following Alt-A private label MBS issuance, where the collateral balance at the beginning of the month is $500,000,000. The mortgage pool pays a WAC of 8% (in annual terms), paid monthly.

Tranche	Current balance	Spread to 3m LIBOR
Class A	$300,000,000	15bps
Class B	$150,000,000	20bps
Class C	$25,000,000	22bps
Class D	$25,000,000	25 bps

Suppose that the current CPR assumption stand at 2% (annual) and the default rate assumption (CDR) is 1% for the current month. Also suppose that the collateral pool has a default recovery rate of 70%, with no lag between defaults and recovery. $300,000 of the collateral balance is scheduled to be repaid in the current month. Further, the 3m USD LIBOR is 5.64%. Given this information, calculate the following:

(a) Total cashflows from the collateral for the current month (principal and interest). (b) Principal and interest cash flows to each tranche for the current month.

(c) Remaining principal balance at the end of current month for each tranche, accounting for scheduled repayments, excess prepayments and defaulted principal.