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fixed income analysis
Fixed Income Analysis Workbook 2nd Edition Frank J. Fabozzi - Solutions
12. What is the maximum amount the buyer of an option can lose?
11. Describe the following delivery options granted to the seller of the Treasury bond futures contract.a. quality or swap optionb. timing optionc. wild card option
10. Suppose that a government bond futures contract of some country has the same delivery requirements as the U.S. Treasury bond futures contract. Suppose further that there are four possible issues that are acceptable for delivery and the short has the choice of which to deliver. These issues and
9.a. What is the implied repo rate for a deliverable Treasury issue?b. What is meant by the cheapest-to-deliver issue?
8. Calculate the implied repo rate for a hypothetical issue that is deliverable for a Treasury bond futures contract assuming the following for the deliverable issue and the futures contract:Futures contract Futures price = $102 days to futures delivery date (days1) = 114 days Deliverable issue
7. Suppose that the June 200X futures contract settles at 105–08 and the issue delivered has a conversion factor of 1.21. Assume that the accrued interest for the issue delivered is$5,300 per $100,000 par value. What is the invoice price the buyer must pay the seller?
6.a. Why is it necessary to have conversion factors for a Treasury futures contract?b. How is the converted price of an issue that is acceptable for delivery for a Treasury futures contract computed?
5. George Salvich is an equity portfolio manager who uses stock index futures. He is consideringmanaging a balanced fund (i.e., a fund that includes both equities and bonds).He would like to use Treasury bond futures in managing the bond component of the fund. He was told by a broker that the
4. Eileen Morris is the manager of a bond portfolio and has recently received authorization to use Treasury futures contracts. The chief investment officer of her firm, Rita Gomez, advised Ms. Morris to be sure to keep sufficient cash available to satisfy any contingency payments that must be made
3. Explain why you agree or disagree with the following statement: ‘‘Futures and forward contracts expose the parties to the same degree of counterparty risk.’’
2. Explain why you agree or disagree with the following statement: ‘‘One difference between futures and forward contracts is that futures contracts are marked to market while forward contracts are not.’’
1. What is the counterparty risk associated with a derivative instrument?
• compute the payoff for a cap and a floor and explain how a collar is created.
• demonstrate how both a cap and a floor are packages of (1) options on interest rates and(2) options on fixed income instruments.
• compare the position of (1) the counterparties in an interest rate swap to the counterparties in an interest rate futures and (2) the counterparties in an interest rate swap to the counterparties in a floating rate bond purchased by borrowing on a fixed-rate basis.
• characterize the change in the value of an interest rate swap for each counterparty when interest rates change.
• contrast (1) interest rate options and interest rate futures, (2) exchange-traded-options and over-the-counter options, and (3) futures options on fixed income securities and options on fixed income securities.
• calculate the implied repo rate for an acceptable to-deliver bond for a Treasury futures contract and demonstrate how this rate is used to choose the cheapest-to-deliver issue.
• discuss the characteristics of interest rate futures and forward contracts.
25. Evidence by Wall Street firms on home equity loans strongly suggests that high quality borrowers do take advantage of a decline in interest rates to refinance a loan. In contrast, low quality borrowers tend not to take advantage of a decline in interest rates to refinance.a. What is the
24. Suppose that empirical evidence on prepayments for manufactured housing loans suggests that borrowers do not take advantage of refinancing when interest rates decline. Explain whether the zero-volatility spread approach or OAS approach is appropriate for valuing securities backed by
23. An investment banker has created an asset-backed security in which the collateral is the future royalties of a song writer. Which valuation approach do you think should be used to value this security, the zero-volatility spread or the option-adjusted spread?
22. Thomas Larken is a portfolio manager who is considering investing in the asset-backed securities market. In particular, Mr. Larken is considering investing in either credit card receivables, auto loan-backed securities, or prime home equity loan-backed securities.Examination of the nominal
21. Karen Brown is considering alternative measures for estimating the duration of some complex CMO tranches. One measure she is considering is empirical duration. Explain to Ms. Brown the difficulties of using empirical duration for complex CMO tranches.
20. Suppose that the coupon curve of prices for a passthrough security for some month is as follows:Coupon Price 7% 94.00 8% 97.06 9% 99.50 10% 102.60 11% 105.25 12% 106.19 What is the coupon curve duration for the 9% coupon passthrough?
19.a. What is the cash flow duration of a mortgage-backed security?b. What are the limitations of cash flow duration as a measure of the price sensitivity of a mortgage-backed security to changes in interest rates?
18. Explain why you agree or disagree with the following statement: ‘‘If the collateral for a CMO deal has negative convexity, then all the tranches in the deal must have negative convexity. The only difference is the degree of negative convexity from one tranche to another.’’
17. Joel Winters is a junior portfolio manager of a corporate bond portfolio. A decision has been made to include mortgage-backed securities in the portfolio. Mr. Winters is considering the purchase of a CMO tranche called a support bond. Before he buys this tranche, he wants to know its effective
16. How is the effective duration and effective convexity of a mortgage-backed security computed using the Monte Carlo simulation model? Be sure to explain what assumption is made regarding the option-adjusted spread when computing the effective duration and effective convexity.
15. An analysis of an agency CMO structure using the Monte Carlo simulation model based on 12% volatility found the following:OAS Z-spread Effective(basis points) (basis points) duration Collateral 90 130 8.0 Tranche PAC I A 50 60 1.5 PAC I B 70 80 3.0 PAC I C 30 120 5.0 PAC I D 30 150 9.0 PAC II A
14. Below are the results of a Monte Carlo simulation analysis using eight representative paths for two tranches of a CMO deal, Tranches M and N:Representative path 1 2 3 4 5 6 7 8 PV of path for:Tranche M 60 55 90 105 110 50 48 70 Tranche N 86 85 89 91 84 92 87 86 One of the tranches is a PAC
13. Suppose that 10 representative paths are used in the Monte Carlo simulation model and that each path has a weight of 10%. The present value for each representative path is based on discounting the cash flows on an interest rate path by the short-term interest rates on that path plus a spread.
12. Mr. Wacker is a bond analyst whose primary responsibility has been to manage the corporate bond portfolio. Recently, his firm’s analyst responsible for the mortgage-backed securities portfolio left. Mr.Wacker was asked to monitor the mortgage-backed securities portfolio until an new analyst
11. A portfolio manager is using an analytical system to value Tranche K of a CMO deal. The Monte Carlo simulation model uses eight representative interest rate paths. The present value of each of the representative interest rate paths and the weight of each path are shown below:Representative path
10. Jane Hubert is using an analytical system purchased by her firm to analyze mortgagebacked securities. The analytical system uses the Monte Carlo simulation model for valuation. She is given a choice when using the system to use either the ‘‘full Monte Carlo analysis’’ or ‘‘16
9. Assume for simplicity that only ten interest rate paths are used in the Monte Carlo simulation model to a value Tranche W of a CMO deal. Suppose further that based on a spread of 70 basis points, the present value of the interest rate paths is as follows:Interest rate path 1 2 3 4 5 6 7 8 9 10
8. Suppose that the pool of passthroughs used as collateral for a collateralized mortgage obligation is selling at a premium. Also suppose that one tranche in the deal, Tranche X, is selling at a discount and another tranche, Tranche Y, is selling at a premium.a. Explain why a slowdown in
7. Juan Rodriquez is the manager of a portfolio containing mortgage passthrough securities.He is reviewing output of his firm’s analytical system for several passthrough securities that are in the portfolio. Below is a portion of the report for three passthrough securities:Price based on an
6. What interest rates are used to value a mortgage-backed security on each interest rate path when using the Monte Carlo simulation model?
5. Nat Hawthorne, a portfolio manager, discussed the valuation of a particular mortgagebacked security with his broker, Steven Ruthledge. Mr. Hawthorne is considering the purchase of the security and asked what valuation model the brokerage firm used. Mr.Ruthledge responded that the Monte Carlo
4. The following questions have to do with the Monte Carlo simulation model.a. What assumption must be made in generating the path of short-term interest rates?b. Why must the paths of short-term interest rates be adjusted?c. In determining the path of refinancing rates, what assumption must be
3. Jane Howard is a corporate bond analyst. Recently she has been asked to extend her responsibilities to mortgage-backed securities. In researching the methodology for valuing mortgage-backed securities she read that these securities are valued using theMonte Carlo simulation model. She was
2. Suppose that the monthly cash flow yield is 0.74%. What is the cash flow yield on a bond-equivalent basis?
1. Suppose that based on a prepayment assumption of 200 PSA the cash flow yield for a specific agency passthrough security is 7.5% and the stated maturity is 15 years. Suppose further that the average life of this security is 8 years. Assume the following yield curve for Treasuries:Maturity Yield
• determine whether the nominal spread, zero-volatility spread, or the option-adjusted spread should be used to evaluate a specific fixed income security.
• discuss the merits and limitations as well as the assumptions of effective duration, cash flow duration, modified duration, coupon curve duration, and empirical duration.
• analyze the interest rate risk of a security given the security’s effective duration and effective convexity.
• calculate and interpret effective duration, cash flow duration, and coupon curve duration.
• determine and interpret theoretical value, option-adjusted spread, and option cost to judge whether a mortgage-backed security is rich, cheap, or fairly priced.
discuss path dependency in passthrough securities and the implications for valuation models.
• discuss the inputs, calibration, assumptions, appropriate discount factors, representative paths, and interest rate path present values for the Monte Carlo simulation model for valuing a mortgage-backed security.
• discuss the computation, use, and limitations of the cash flow yield, nominal spread, and zero-volatility spread for a mortgage-backed security and an asset-backed security.
38. Why have banks issued synthetic balance sheet CDOs?
37. What are the elements of the return for the junior note holders in a synthetic CDO structure?
36. Consider the following CDO transaction:1. The CDO is a $200 million structure. That is, the assets purchased will be$200 million.2. The collateral consists of bonds that all mature in 8 years and the coupon rate for every bond is the 8-year Treasury rate plus 600 basis points.3. The senior
35. What is the key factor in determining whether or not an arbitrage CDO can be issued?
34. Explain why you agree or disagree with the following statement: ‘‘By using an interest rate swap, the asset manager for a CDO increases the risk associated with meeting the obligations that must be paid to the senior tranche.’’
33. Explain why you agree or disagree with the following statement: ‘‘The asset manager for a CDO is free to actively manage the portfolio without any constraints.’’
32. What is a typical cash CDO structure?
31.a. What is meant by the monthly payment rate for a credit card deal?b. What is the significance of the monthly payment rate?c. How is the net portfolio yield determined for a credit card deal?
30. A manager of a corporate bond portfolio is considering the purchase of a credit card receivable-backed security. The manager believes that an advantage of such securities is that there is no contraction risk and no extension risk. Explain why you agree or disagree with this view.
29.a. What is the cash flow for a credit card receivable-backed security during the lockout or revolving period?b. How is the principal received from credit card borrowers handled during the lockout or revolving period?c. Explain why you agree or disagree with the following statement: ‘‘After
28.a. What are the components of the cash flow for a Small Business Administration-backed security?b. What reference rate is used for setting the coupon interest and how often is the coupon rate reset?
27. For a student loan-backed security, what is the difference between the deferment period and the grace period?
26. A trustee for a pension fund is working with a consultant to develop investment guidelines for the fund’s bond portfolio. The trustee states that the fund should be able to invest in securities backed by student loans because the loans are fully guaranteed by the U.S.government. How should
25.a. If the ABS for a security is 1.5% at month 21, what is the corresponding SMM?b. If the SMM for a security is 1.9% at month 11, what is the corresponding ABS?
24. What is the difference between a singlemonthly mortality rate and an absolute prepayment speed?
23.a. What are the components of the cash flow for an auto loan-backed security?b. How important are prepayments due to refinancing for auto loans?
22. Why are residential mortgage-backed securities outside the United States structured more like transactions in the nonagency U.S. market than the agency market.
21.a. What are the components of the cash flow for a manufactured housing-backed security?b. What are the reasons why prepayments due to refinancing are not significant for manufactured housing loans?
20. How is a non-accelerating senior tranche provided protection to reduce contraction risk and extension risk?
19. Larry Forest is an analyst reviewing for the first time a closed-end home equity loan-backed structure in order to determine whether or not to purchase the deal’s senior tranche. He understands how the shifting interest percentage schedule is structured so as to provide the senior tranches
18. Suppose that the base case shifting interest percentage schedule for a closed-end home equity loan-backed security is as follows:Years after issuance Senior prepayment percentage 1–4 100%5 90%6 80%7 50%8 20%after year 8 0%a. If there are prepayments in month 36 of $100,000, how much of the
17. Why is there is an available funds cap in an asset-backed security in which the collateral is adjustable-rate home equity loans?
16. James Tellmen is an assistant portfolio manager for amortgage-backed securities portfolio.Mr. Tellmen’s responsibility is to analyze agency mortgage-backed securities. Recently, the portfolio manager has been given authorization to purchase closed-end home equity loan-backed securities. Mr.
15. The Izzobaf Home Equity Loan Trust 2000–1 is backed by fixed-rate closed-end home equity loans. The base case prepayment for this deal is specified in the prospectus as follows:The model used with respect to the loans (the ‘‘prepayment ramp’’) assumes that the home equity loans prepay
14.a. What is the cash flow of a closed-end home equity loan?b. Indicate whether you agree or disagree with the following statement: ‘‘Typically, closed-end home equity loans are loans to borrowers of the highest credit quality.’’
13. What is a ‘‘latter of percent or call date’’ call provision?
12.a. What is meant by the ‘‘senior prepayment percentage’’ in a shifting interest mechanism of a senior-subordinate structure?b. Why does a shifting interest mechanism affect the cash flow of the senior tranche and increase the senior tranche’s exposure to contraction risk?
11.a. Explain why a senior-subordinate structure is a form of internal credit enhancement.b. Explain the need for a shifting interest mechanism in a senior-subordinate structure when the underlying assets are subject to prepayments.
10. Why is the assumption about how defaults may occur over the life of an asset-backed security transaction important in assessing the effectiveness of excess servicing spread as a form of internal credit enhancement?
9. What is the difference between a cash reserve fund and an excess servicing spread account?
8. Why is it critical for monoline insurance companies that provide insurance for asset-backed security transactions to maintain a triple A credit rating?
7. 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 why this issue is unlikely to receive a triple A credit rating.
6.a. Explain why individual loans that are of a non-amortizing type are not subject to prepayment risk.b. Explain why securities backed by collateral consisting of non-amortizing assets may expose an investor to prepayment risk.
5. Suppose that the structure for an asset-backed security transaction is as follows:senior tranche $220 million subordinate tranche 1 $50 million subordinate tranche 2 $30 million and that the value of the collateral for the structure is $320 million. Subordinate tranche 2 is the first loss
4. Suppose that the collateral for an asset-backed securities structure has a gross weighted average coupon of 8.6%. The servicing fee is 50 basis points. The tranches issued have a weighted average coupon rate of 7.1%. What is the excess servicing spread?
3. How are principal repayments from the collateral used by the trustee in a securitization transaction?
2. In the securitization process, what is the role played by the (a) attorneys and (b)independent accountants?
1. Caterpillar Financial Asset Trust 1997-A is a special purpose vehicle. The collateral(i.e., assets) for the trust is a pool of fixed-rate retail installment sales contracts that are secured by new and used machinery manufactured primarily by Caterpillar Inc. The retail installment sales
• explain the motivation of sponsors for creating a collateralized debt obligation: arbitrage and balance sheet transactions.
• describe what a collateralized debt obligation is and the different types (cash and synthetic).
• describe the cash flow and prepayment characteristics for securities backed by home equity loans, manufactured housing loans, automobile loans, student loans, SBA loans, and credit card receivables.
• explain the different conventions for measuring prepayments for asset-backed securities(conditional prepayment rate, absolute prepayment rate, and prospectus prepayment curve).
• explain the different types of credit enhancement (internal and external).
• differentiate between the payment structure of a securitization backed by amortizing assets and non-amortizing assets.
• explain prepayment tranching and credit tranching in a securitization transaction.
• describe the basic structural features of and parties to a securitization transaction.
41. What is balloon risk and how is it related to extension risk?
40.a. What types of provisions are usually included in a commercial loan to protect the lender against prepayment risk?b. In a commercial mortgage-backed securities deal, explain why the investor in a security may be afforded prepayment protection at the deal level.
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