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Chapter 8 Managing interest rate risk using loan sales and securitisation Answers to end-of-chapter questions Questions and problems 1 What is the difference between loans sold with recourse and loans sold without recourse from the perspective of both sellers and buyers? Loans sold without recourse means that the credit risk is transferred entirely to the buyer. In the event the loan is defaulted, the buyer of the loan has no recourse to the seller for any claims. Thus, the originator of the loan can take it off the balance sheet after selling the loan. In the case of a sale with recourse, credit risk is still present for the originator because the buyer could transfer ownership of the loan back to the originator. Thus, from the perspective of the buyer, loans with recourse bear the least amount of credit risk. 2 What is the difference between loan participations and loan assignments? In a loan participation, the buyer does not obtain total control over the loan. In an assignment, all rights are transferred upon sale, thereby giving the buyer a direct claim on the borrower. Monitoring incentives are higher under loan assignments as opposed to loan participations because the buyer is the sole holder of the loan. Thus, there is no free-rider problem. Monitoring costs are lower because the loan assignment buyer must only monitor the borrower’s activities, while the loan participation buyer must monitor both the borrower and the originating FI. Risk exposure is greater under loan participations than under loan assignments because participations have a ‘double risk’ exposure. The buyer of the loan participation is exposed to the credit risk of the originating FI as well as the credit risk of the borrower. 3 A bank has made a three-year $10 million loan that pays annual interest of 8 per cent. The principal is due at the end of the third year. (a) The bank is willing to sell this loan with recourse at an interest rate of 8.5 per cent. What price should it receive for this loan? If the bank sells with recourse, it should expect: ($0.80m) × PVA n=3, k=8.5 + ($10m) × PV n=3, k=8.5 = $9.8723 million (b) The bank has the option to sell this loan without recourse at a discount rate of 8.75 per cent. What price should it receive for this loan? If the bank sells without recourse, it should expect: ($0.80m) × PVA n=3, k=8.75 + ($10m) × PV n=3, k=8.75 = $9.8093 million (c) If the bank expects an 0.5 per cent probability of default on this loan, is it better to sell this loan with or without recourse? It expects to receive no interest payments or principal if the loan is defaulted. If sold with recourse and the expected probability of default is taken into account, it should expect to receive (0.995) × $9.8723 = $9.8229, which is still higher than selling it without recourse. So, it should sell it with recourse. (d) Explain how the sale of the loan with recourse will change the duration characteristics of the balance sheet. If the average duration of the bank’s asset prior to the sale is greater than three years, then the sale of the loan will increase the duration. However, if the average duration of the bank’s assets is less than three years, then the sale of the loan will lower the average duration of the assets remaining on the balance sheet. The only other situation would be if the average duration of the bank’s assets prior to sale was equal to three years, in which case the sale of the loan would have no impact on the average duration of the on-balance-sheet assets. 4 Why are yields higher on loan sales than on commercial paper issues with similar maturity and issue size? Commercial paper issuers generally are blue chip corporations that have the best credit ratings. Banks may sell the loans of less creditworthy borrowers, thereby raising required yields. Indeed, since commercial paper issuers tend to be well-known companies, information, monitoring and credit assessment costs are lower for commercial paper issues than for loan sales. Moreover, since there is an active secondary market in commercial paper, but not for loan sales, the commercial paper buyer takes on less liquidity risk than does the buyer of a loan sale. 5 In addition to managing credit risk, what are some other reasons for the sale of loans by FIs? The reasons for an increase in loan sales, apart from hedging credit risk, include: (a) Removing loans from the balance sheet by sale without recourse reduces the amount of deposits necessary to fund the FI, which in turn decreases the amount of regulatory reserve requirements that must be kept by the FI. (b) Originating and selling loans is an important source of fee income for the FIs. (c) One method to improve the capital to assets ratio for an FI is to reduce assets. This approach often is less expensive than increasing the amount of capital. (d) The sale of FI loans to improve the liquidity of the FIs has expanded the loan sale market which has made the FI loans even more liquid, thus reducing FI liquidity even further. Thus, by creating a market, the process of selling the loans has improved the liquidity of the asset for which the market was initially developed. (e) Finally, loan sales have been considered a substitute for securities underwriting. 6 An FI is planning the purchase of a $5 million loan to raise the existing average duration of its assets from 3.5 years to 5 years. It currently has total assets worth $20 million, $5 million in cash (0 duration) and $15 million in loans. All the loans are fairly priced. (a) Assuming it uses the cash to purchase the loan, should it purchase the loan if its duration is seven years? The duration of the existing loan is: 0 + $15m/$20m(X) = 3.5 years  Existing loan duration = 4.667 years If it purchases $5 million of loans with an average duration of 7 years, its portfolio duration will increase to $5m/$20m(7) + $15m/$20m(4.667) = 5.25 years. In this case, the average duration will be above 5 years (of its liabilities). The FI may be better off seeking another loan with a slightly lower duration. (b) What asset duration loans should it purchase in order to raise its average duration to five years? The FI should seek to purchase a loan of the following duration: $5m/$20m(X) + $15m/$20m(4.667 years) = 5 years  X = duration = 6 years. 7 In addition to assisting in the management of interest rate risk, what are four factors that are expected to encourage loan sales in the future? Discuss the impact of each factor. The reasons for an increase in loan sales, apart from hedging credit risk, include: New capital requirements for credit risk, which suggests a further need for FIs to reduce their risky portfolios and replace them with lower risk assets. This suggests increased loan sales activity. The trend towards market value accounting makes it easier to trade different categories of loans. Loan sales as trading instruments, which makes it attractive for commercial banks and investment banks to specialise in specific loan categories and to market them effectively, since they require only brokerage functions as opposed to performing asset transformations. Loan sales allow an FI to remove credit risk from their balance sheet as long as the loans are sold without recourse. The ability to allocate loan credit ratings should cause more investors to enter the market. The growth of distressed loans in international markets should provide opportunities for domestic investors to enter this market at substantially reduced prices. 8 Outline the costs and benefits of securitising car loans. The costs of securitising car loans are: Features of car loans are not standardised and are therefore difficult to pool into securities. Since each car loan is typically small in face value, many loans must be pooled to construct securities of any substantial face value. Since each security pool will be composed of many small loans, monitoring costs for ultimate securities holders would be very large. Servicing costs will be significant given the frequency of cash flows and the number of underlying creditors. The benefits of securitising car loans are: Since each security pool will be composed of many small loans, securitisation provides risk diversification benefits. As a result of risk-adjusted capital requirements, it is more costly for banks to finance car loans. Securitising car loans would increase the availability of financing to this sector of the economy. 9 Consider a mortgage pool with principal of $20 million. The maturity is 30 years with a monthly mortgage payment of 10 per cent per annum. (Assume no prepayments.) (a) What is the monthly mortgage payment (100 per cent amortising) on the pool of mortgages? The monthly mortgage payment, R, is (the monthly interest rate is R = $175 514.31 (b) If the mortgage-backed security insurance fee is 60 basis points and the servicing fee is 40 basis points, what is the yield on the pass-through security? The annual yield is 10% – 0.44% – 0 .06% = 9.5%. The monthly yield is (c) What is the monthly payment on the pass-through security in part (b)? The monthly payment, R, is: R = $168 170.84 (d) Calculate the first monthly servicing fee paid to the originating banks. The first monthly servicing fee, R, is (the monthly fee rate is ): 10 Calculate the value of (a) the mortgage pool and (b) the pass-through security in question 9 if interest rates increased 100 basis points. (Assume no prepayments.) (a) The mortgage pool’s value, V, is (the monthly discount rate is (b) The pass-through security’s value, V, is (the monthly discount rate is 11 A bank originates a pool of 500 30-year mortgages, each averaging $150 000, with an annual mortgage coupon rate of 8 per cent. If the mortgage-backed security insurance fee is 60 basis points and the bank’s servicing fee is 19 basis points: (a) What is the present value of the mortgage pool? $500 × $150 000 = $75 million. (b) What is the monthly mortgage payment? There are 360 monthly mortgage payments (30 years × 12 months). Monthly mortgage payments are: R = $550 323.43 (c) For the first two payments, what portion is interest and what is principal repayment? For the first monthly payment, the monthly interest is: 8%/12 × $75 million = $500 000. Therefore, for the first monthly mortgage payment, $500 000 is repayment of interest and $50 323.43 is repayment of principal. For the second monthly payment, the principal outstanding is: $75m – $50 323.43 = $74 949 676.57. The monthly interest payment is: $499 664.51. The principal payment in the second month is: $550 323.43 – $499 664.51 = $50 658.92. (d) What are the expected monthly cash flows to securitised bondholders? The annual securitised bond rate is 8% – (6 + 19) basis points = 7.75%. Bondholders receive monthly payments of: R = $537 309.18 (e) What is the present value of the pass-through security bonds? (Assume that the risk-adjusted market annual rate of return is 8 per cent compounded monthly.) The discount yield is 8 per cent annually, compounded monthly. The present value of the pass-through bonds is: (f) Would actual cash flows to securitised bondholders deviate from expected cash flows as in part (d)? Why or why not? Actual payments will equal expected payments if and only if no prepayments are made. If any mortgages are prepaid as a result of refinancing or homeowner mobility, the monthly payments will change. In the month in which prepayments are made monthly payments will increase (to reflect the principal repayments). In all subsequent months, monthly payments will decline (to reflect the lower face value of the pass-through bonds). (g) What is the bank’s expected monthly cash flows? The bank gets the difference between the monthly mortgage payments and the pass-through payments: $550 323.43 – $537 309.18 = $13 014.25. (h) If all of the mortgages in the pool are completely prepaid at the end of the second month, what is the pool’s weighted average life? (Hint: Use your answer to part (c).)
Time Expected principal payments Timex principal
1 month $50 323.43 $50 323.43
2 month $74 949 676.57 $149 899 353.10
$75 000 000.00 $149 949 676.50
After the first two months, principal payments total: $50 323.43 + $50 658.92 = $100 982.35. Total principal outstanding after two months is: $75 million – 100 982.35 = $74 899 017.65. Therefore, the second month’s principal payment is: $50 658.92 + $74 899 017.65 = $74 949 676.57. (i) What is the price of the pass-through security if its weighted-average life is equal to your solution for part (h)? (Assume no change in market interest rates.) The pass-through security with a weighted-average life of 1.9993 months has only two cash flows. The first month’s cash flow is $537 309.18. The second month’s cash flow is
$537 309.18 plus the extra principal repayment of $74 899 017.65 = $75 436 326.83. The present value of the pass-through security is: (j) What is the price of the pass-through security with a weighted-average life equal to your solution for part (h) if market yields decline by 50 basis points? Market yields decline 50 basis points to 7.5% per annum compounded monthly. The present value of the pass-through security is: 12 If 150 $200 000 mortgages are expected to be prepaid in three years and the remaining 150 $200 000 mortgages in a $60 million 15-year mortgage pool are to be prepaid in four years, what is the weighted-average life of the mortgage pool? Mortgages are fully amortised with mortgage coupon rates set at 10 per cent to be paid annually. The annual mortgage payment is: R = $7 888 426.61 Annual mortgage payments, with no prepayments, can be decomposed into principal and interest payments:
Yr Balance Payment (R) (fixed) Interest payment Principal payment Remaining principal
1 $60 m $7.888 m $6 m $1.888 m $58.112 m
2 58.122 7.888 5.811 2.077 56.034
3 56.034 7.888 5.603 2.285 53.749
4 53.749 7.888 5.375 2.513 51.236
The first year’s interest is $6 million (0.10 × $60 million). Deducting this from the first year’s mortgage payment yields a principal payment of $1 888 426.61 at the end of the first year. Outstanding principal is $58 111 573.39. The second year’s interest payment is 0.10 × $58 111 573.39 = $5 8111 157.34. Deducting this from the annual mortgage payment yields a second annual principal payment of
$2 077 269.27 for a principal outstanding of $56 034 304.12. The third year’s regular interest payment is $5.603 million. Deducting this from the annual mortgage payment yields a third annual principal payment of $2.285 million for a principal outstanding of $53 749 307.92. The principal outstanding at the end of the fourth year, without prepayments, is $51 235 812.10. However, at the end of the third year, half of the mortgages in the mortgage pool are completely prepaid. That is, at the end of the third year, an additional principal payment of 50% × $53 749 307.92 = $26 874 653.96 is received for a remaining outstanding principal balance of $26.875 million. Total third-year principal payment is therefore $29.16 million = the regular principal payment of $2.285 million plus an extra payment of $26.875 million. The fourth year annual interest payment is 10% × $26.875 million = $2.687 million, leaving a regular fourth year principal payment of $7.888 million – $2.687 million = $5 200 961.21. This end-of-fourth-year principal payment would have left an outstanding principal balance of $21 673 692.75, which is paid in full at the end of the year. Fourth-year principal payments total $26.875 million = $5.201 million plus $21.674 million. Prepayments alter the annual cash flows for years 3 and 4 as follows:
Yr Balance Payment (R) (fixed) Interest payment Principal payment Remaining principal
3 56.034 7.888 5.603 29.16 26.875
4 26.875 7.888 2.687 26.875 0
$60 m
Calculating the weighted-average life:
Time Expected principal payments Time × princ.
1 1.888 1.888
2 2.077 4.154
3 29.160 87.480
4 26.875 107.500
60 201.022
13 What would be the impact on mortgage-backed security pricing if the pass-through security was not fully amortised? What is the present value of a $10 million pool of 15-year mortgages with an 8.5 per cent monthly mortgage coupon per annum if market rates are 5 per cent? (The mortgage-backed security guarantee fee is assumed to be 60 basis points and the bank servicing fee 40 basis points. Assume that the pass-through security is fully amortised.) There are 180 monthly payments (15 years × 12 months). The pass-through security monthly coupon rate is 8.5% – 0.5% = 8% p.a. The monthly pass-through payment is: R = $95 565.21 The present value of the pass-through security at a 5% market rate is: PV = $12.085 million 14 What factors affect prepayment probability? Prepayment probabilities are affected by homeowners’ expectations about future interest rates, mobility rates and financial awareness. In addition, prepayments increase as the costs of refinancing decrease (this is determined in part by the competitive structure of the financial services industry). Finally, the structure of existing mortgages relative to maturity, fixed versus floating rates, or existing mortgage covenants (e.g. against assumption of mortgages) will all impact on prepayment probabilities. 15 Consider $200 million of 30-year mortgages with a coupon of 10 per cent per annum paid quarterly. (a) What is the quarterly mortgage payment? There are 120 quarterly payments over 30 years. The quarterly mortgage payments are: R = $5 272 358.60 (b) What are the interest repayments over the first year of life of the mortgages? What are the principal repayments?
Qtr Balance Payment (R) (fixed) Interest payment Principal payment Remaining principal
1 $200m $5.272m $5m $0.272m $199.728m
2 199.728 5.272 4.993 0.279 199.449
3 199.449 5.272 4.986 0.286 199.163
4 199.163 5.272 4.979 0.293 198.87
(c) Construct a 30-year CMO using this mortgage pool as collateral. There are three tranches (where A offers the least protection against prepayment and C offers the most). A $50 million Tranche A makes quarterly payments of 9 per cent per annum; a $100 million Tranche B makes quarterly payments of 10 per cent; and a $50 million Tranche C makes quarterly payments of 11 per cent. (i) Assume non amortisation of principal and no prepayments. What are the total promised coupon payments to the three classes? What are the principal payments to each of the three classes for the first year? (ii) If, over the first year, the trustee receives quarterly prepayments of $10 million on the mortgage pool, how are the funds distributed? (iii) How are the cash flows distributed if in the first half of the second year prepayments are $20 million quarterly? (iv) How can the CMO issuer earn a positive spread on the CMO? Tranche A: 9%/4 × $50 million = $1 125 000 quarterly Tranche B: 10%/4 × $100 million = $2 500 000 quarterly Tranche C: 11%/4 × $50 million = $1 375 000 quarterly Total interest payments: $5 million quarterly Regular Tranche A payments are $1.125 million quarterly. If there are no prepayments the regular pass-through security quarterly payment of $5.272 million is distributed among the three tranches. $5 million is the total coupon payment for all three tranches. Therefore, $0.272 million of principal is repaid each quarter even if there are no prepayments. Tranche A receives all principal payments. Tranche A cash flows are $1.125 million + $0.272 million = $1.397 million quarterly.
Qtr Balance Payment (R) (fixed) Interest payment Principal payment Remaining principal
1 $50m $1.397m $1.125m $0.272m $49.728m
2 49.728 1.397 1.119 0.278 49.45
3 49.45 1.397 1.113 0.284 49.166
4 49.166 1.397 1.106 0.291 48.875
Quarterly prepayments on the entire mortgage pool are $10 million. They are credited entirely to Tranche A until all principal is paid off. The payments are distributed as follows:
Qtr Balance Payment (R) (fixed) Interest payment Principal payment Remaining principal
1 $50m $11.937m $1.125m $10.812m $39.188m
2 39.188 11.937 0.882 11.055 28.133
3 28.133 11.937 0.633 11.304 16.829
4 16.829 11.937 0.379 11.558 5.271
In the second year, quarterly payments on the entire mortgage pool are $20 million. The quarterly payment on Tranche A is $1.125 plus $20.272 million for a total quarterly payment of $21.397 million. The payments are distributed as follows:
Qtr Balance Payment (R) (fixed) Interest payment Principal payment Remaining principal
5 5.271 21.397 0.119 21.278 0
After the fifth quarter, Tranche A is completely paid off. There is $16.007 million cash flow remaining ($21.278 less the remaining Tranche A principal of 5.271). That leaves $16.007 million in prepayments to be applied towards Tranche B. The way the terms of the CMO are structured, the average coupon rate on the three classes equals the mortgage coupon rate on the underlying mortgage pool. However, given the more desirable cash flow characteristics of the individual classes, the FI may be able to issue the CMO classes at lower coupon rates. The difference between the sum of all coupon payments promised on all CMO tranches and the mortgage coupon rate on the underlying mortgage pool is the FI’s servicing fee. 16 How does securitisation impact on the FI’s role as a delegated monitor? If the FI packages loans and sells them without recourse, then the FI does not perform any monitoring function over the life of the loan. The FI may simply service the loan on behalf of the ultimate securities holders. 17 How does the FI use securitisation to manage its risk exposure? (Be sure to consider interest rate, currency, liquidity and credit risks.) In the process of intermediation on behalf of its customers, the FI assumes risk exposure. The FI can reduce that risk exposure by altering its product base, thereby affecting the portfolio mix obtained in the course of intermediation. However, this is likely to be quite costly in terms of customer goodwill and loss of business. Securitisation enables FIs to manage risk exposure by changing their portfolio mix without alienating customers. That is, customers are still serviced and the FI continues to intermediate. Balance sheet alterations are made subsequent to and independent of the intermediation activity. Thus, the FI can make portfolio changes and still fulfil the franchise of the intermediary. Interest rate risk exposure is reduced by matching the durations of assets and liabilities. Securitisation enables the FI to accomplish this since the FI can determine which loans to package and sell off. Credit risk exposure is minimised by selling loans without recourse. Foreign exchange rate risk exposure is reduced by matching the foreign currencies in which the assets and liabilities are denominated. Securitisation allows the FI to sell off unmatched assets. Finally, securitisation reduces liquidity risk since the FI does not have to fund the asset. Web questions 18 Go to the website of the Australian Treasury Department and find information about the government’s ‘Stream Two: Support smaller lenders to compete with the big banks’ and describe how this scheme also assists the Australian securitisation market. The answer will depend on the date of the assignment. At the website, click on ‘Reports’ and then use the search function to find the required report. As of my last update in January 2022, I'm unable to access or retrieve real-time data from specific websites such as the Australian Treasury Department. However, I can provide you with general information about the Australian government's initiatives to support smaller lenders and how they might impact the securitization market. The Australian government has implemented various schemes and initiatives aimed at supporting smaller lenders to compete with larger banks. One such initiative is likely to be the "Stream Two: Support smaller lenders to compete with the big banks," which may involve measures to increase competition in the banking sector and improve access to finance for smaller financial institutions. Here's how such a scheme might assist the Australian securitization market: 1. Enhanced Funding Opportunities: By supporting smaller lenders, the government helps diversify the sources of funding available in the market. This could lead to increased securitization activity as smaller lenders seek to access capital markets to fund their lending activities. Securitization allows lenders to package loans into tradable securities, thereby accessing additional funding beyond traditional deposit-taking. 2. Reduced Reliance on Banks: Smaller lenders may use securitization as a means to reduce their reliance on traditional bank funding. By accessing capital markets through securitization, these lenders can raise funds directly from investors, bypassing the need for bank intermediaries. This can lead to greater competition in the lending market and potentially lower borrowing costs for consumers. 3. Risk Management: Securitization allows lenders to transfer credit risk from their balance sheets to investors. This can improve the overall risk management of smaller lenders by reducing their exposure to credit losses. As a result, smaller lenders may be more willing to extend credit to a broader range of borrowers, including those traditionally underserved by the banking sector. 4. Market Liquidity and Efficiency: Increased securitization activity contributes to the liquidity and efficiency of the financial markets. It provides investors with access to a diverse range of investment opportunities and allows for the efficient allocation of capital across the economy. By supporting smaller lenders in accessing securitization markets, the government helps promote market liquidity and resilience. Overall, government initiatives aimed at supporting smaller lenders to compete with larger banks can have positive spillover effects on the Australian securitization market. By facilitating greater access to funding, improving risk management, and enhancing market liquidity, these initiatives contribute to a more competitive and dynamic financial landscape. 19 Go to the website of the Reserve Bank of Australia and find a speech by Chris Aylmer, head of domestic markets department, to the Australian Securitisation Forum on 11 November 2013, titled ‘Developments in Secured Issuance and RBA Reporting Initiatives’. From this, determine the total bond issues by banks, and discuss the difference between covered bond issues and unsecured issues and the advantages of each for an FI manager. The answer will depend on the date of the assignment. At the website, click on ‘Speeches’ and then on ‘2004’ and find the speech referred to. Difference between Covered Bond Issues and Unsecured Issues: 1. Covered Bond Issues: • Covered bonds are debt securities backed by a pool of assets, typically residential or commercial mortgages, which remain on the issuer's balance sheet. • In the event of default, covered bondholders have recourse to the cover pool of assets, providing an additional layer of security. • Covered bond issues are typically secured by specific assets, providing investors with a higher level of security and lower credit risk compared to unsecured bonds. • Covered bonds usually have lower interest rates compared to unsecured bonds due to their secured nature. 2. Unsecured Issues: • Unsecured bonds are debt securities that are not backed by specific assets or collateral. • In the event of default, unsecured bondholders have a claim on the issuer's general assets but do not have specific recourse to any particular asset pool. • Unsecured issues carry higher credit risk compared to covered bonds since they lack collateral backing. • Unsecured bonds typically offer higher interest rates compared to covered bonds to compensate investors for the higher risk. Advantages for FI Managers: 1. Covered Bond Issues: • Lower Funding Costs: Covered bonds generally carry lower interest rates compared to unsecured bonds, allowing FI managers to access cheaper funding sources. • Diversification of Funding: Covered bonds provide FI managers with an additional funding avenue, diversifying their funding sources and reducing reliance on traditional unsecured debt markets. • Enhanced Liquidity: Covered bonds are often more liquid than unsecured bonds due to their higher credit quality and investor demand, providing FI managers with greater flexibility in managing their funding and liquidity needs. 2. Unsecured Issues: • Flexibility: Unsecured bonds offer FI managers greater flexibility in terms of asset allocation and use of proceeds since they are not backed by specific assets. • No Asset Encumbrance: Unsecured bonds do not encumber specific assets on the issuer's balance sheet, allowing FI managers to maintain flexibility in managing their asset base. • Access to Different Investor Base: Unsecured bonds may appeal to a broader investor base compared to covered bonds, providing FI managers with access to different segments of the capital markets. In summary, covered bond issues offer lower funding costs, diversification, and enhanced liquidity for FI managers, while unsecured issues provide flexibility and access to a broader investor base. The choice between covered and unsecured issues depends on factors such as funding needs, investor preferences, and risk management objectives. Solution Manual for Financial Institutions Management Anthony Saunders, Marcia Cornett, Patricia McGraw 9780070979796, 9780071051590

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