R65 练习: 抵押贷款支持证券
考纲范围
Define prepayment risk and describe time tranching structures in securitizations and their purpose.
Describe fundamental features of residential mortgage loans that are securitized.
Describe types and characteristics of residential mortgage-backed securities, including mortgage pass-through securities and collateralized mortgage obligations, and explain the cash flows and risks for each type.
Describe characteristics and risks of commercial mortgage-backed securities.
Q1.
A collateralized mortgage obligation (CMO) has a PAC tranche and one support tranche, and the initial PAC collar is from 100 PSA to 150 PSA. If the prepayment rate goes up to 170 PSA, the average life of the PAC tranche will most likely:
A. remain unchanged.
B. get larger.
C. get smaller.
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答案：C
解析：当提前还款速度(170 PSA)超出PAC collar上限(150 PSA)时，超出部分的提前还款首先由support tranche吸收。但如果support tranche无法完全吸收（已耗尽），PAC tranche的平均寿命也会缩短。即使在collar范围内PAC保持稳定，超出collar后平均寿命会缩短。
选项 判断 解析 A ✗ 170 PSA超出了PAC collar上限150 PSA B ✗ 提前还款加速时平均寿命缩短，不是变长 C ✓ 提前还款速度超出collar上限，PAC tranche平均寿命缩短
Q2.
A collateralized mortgage obligation (CMO) investor who wants to avoid prepayment risk is most likely to buy products from:
A. a PAC tranche.
B. the highest tranche in a sequential-pay structure.
C. a floating-rate tranche.
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答案：A
解析：PAC tranche(Planned Amortization Class)设计了特定的偿还计划和collar范围，在一定提前还款速度范围内能保持稳定的现金流，最好地保护投资者免受提前还款风险。Sequential-pay结构中的最高层级最先收到还款，面临较大的contraction risk。
选项 判断 解析 A ✓ PAC tranche有collar保护，最好地规避提前还款风险 B ✗ sequential-pay最高层级面临较高contraction risk C ✗ floating-rate tranche仅解决利率风险，不解决提前还款风险
Q3.
Which of the following characteristics of a mortgage loan would be most beneficial to lenders in the presence of strategic defaults by borrowers?
A. Recourse loan
B. Non-recourse loan
C. Prepayment option
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答案：A
解析：追索权贷款(recourse loan)允许贷款人在借款人违约时不仅可以没收抵押房产，还可以追索借款人的其他资产。面对战略性违约，这为贷款人提供了最大程度的保护。非追索权贷款只能处置抵押品。
选项 判断 解析 A ✓ recourse loan允许追索借款人其他资产，最利于贷款人 B ✗ non-recourse loan只能处置抵押品，不利于贷款人 C ✗ prepayment option对借款人有利，不特别保护贷款人免受违约
Q4.
It is an advantage for a borrower if the mortgage loan:
A. is a recourse loan.
B. has a prepayment option.
C. has a prepayment penalty provision.
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答案：B
解析：提前还款选择权(prepayment option)对借款人有利，允许在利率下降时以更低利率再融资。追索权贷款对贷款人有利。提前还款罚金条款限制了借款人的灵活性，对借款人不利。
选项 判断 解析 A ✗ recourse loan对贷款人有利，对借款人不利 B ✓ prepayment option给予借款人提前还款的灵活性，有利于借款人 C ✗ prepayment penalty限制借款人灵活性，对借款人不利
Q5.
James, a fund manager, is considering adding a collateralized mortgage obligation (CMO) to his portfolio. The CMO has three sequential-pay tranches: Tranche A, Tranche B, and Tranche C. If James predicts that interest rates will fall, which tranche is least suitable for him to avoid the risk of reinvesting at lower interest rates?
A. Tranche C
B. Tranche A
C. Tranche B
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答案：B
解析：在sequential-pay结构中，Tranche A最先收到本金偿还。当利率下降时，提前还款加速，Tranche A首当其冲收到大量提前还款本金，这些资金需要在更低利率下再投资，面临最大的再投资风险(contraction risk)。
选项 判断 解析 A ✗ Tranche C最后收到本金，再投资风险最小 B ✓ Tranche A最先收到加速偿还的本金，再投资风险最大，最不适合 C ✗ Tranche B风险居中
Q6.
Sunchip Advisory offers advice for clients on collateralized mortgage obligations management. A client is concerned about the rising interest rate level and asks if any CMO structures can best mitigate the extension risk?
A. Principal-only securities.
B. Z-tranche.
C. Senior tranche.
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答案：C
解析：利率上升 → 提前还款减慢 → 投资者收到本金的时间被推迟，这就是 extension risk（延期风险）。题目问哪种 CMO 结构能最好地缓解这种风险，本质是问哪种结构在利率上升场景下最不暴露于 extension。
在 sequential-pay CMO 结构中，本金按顺序优先偿还给 senior（高级）tranche，之后才轮到次级 tranche，最后才是 Z-tranche。因此 senior tranche 平均期限最短，extension risk 最低。
CMO 结构 利率上升时的表现 Extension Risk Senior tranche（顺序偿还结构中的优先档） 最先收到本金，平均期限短 最低 ✓ Principal-only (PO) 价格大跌（本金延后→NPV 下降） 极高 Z-tranche（应计累积档） 在其他档全部偿完前不收现金流 最高
选项 判断 解析 A ✗ PO 严重受 extension risk 伤害：利率上升→提前还款减慢→本金折现期延长→PO 价格大跌。PO 反而是受益于 contraction（利率下降提前还款加速），并非缓解 extension。 B ✗ Z-tranche 在其他档未还清前不收现金流（利息累积进本金），是 CMO 中 extension risk 最高的结构，与题目要求完全相反。 C ✓ Sequential-pay 结构下 senior tranche 最先收到本金偿还，平均期限最短，在 A/B/C 三个选项中 extension risk 暴露最小，最能缓解延期风险。 ⚠️ 易错点：
- 不要混淆 PO 和 IO 对利率方向的反应：PO 受益于 contraction（rates ↓），受损于 extension（rates ↑）；IO 正好相反。
- “缓解 extension risk” ≠ “在 extension 中受益”，而是降低对 extension 的暴露。Senior tranche 通过结构性优先偿还实现这一点；标准最佳答案是 PAC tranche（计划摊还档），但本题三个选项中 senior tranche 是最佳次优解。
Q7.
Glenn Smith is a private wealth consultant working on mortgage-backed security analysis. He expects the central bank to lower the 5-year-and-beyond loan prime rates soon. Which of the following CMO structures least protects investors from risk associated with falling interest rates?
A. An inverse floater in floating-rate tranche.
B. Interest-only securities.
C. Planned amortization tranche.
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答案：B
解析：利率下降时提前还款加速，导致contraction risk。Interest-only securities(仅利息证券)在利率下降时受损最严重，因为本金加速偿还导致利息基数缩小，现金流大幅减少。IO securities最不保护投资者免受利率下降风险。
选项 判断 解析 A ✗ inverse floater在利率下降时收益增加 B ✓ IO securities在利率下降/提前还款加速时损失最大，最不保护 C ✗ PAC tranche有collar保护，能一定程度保护投资者
Q8.
As commercial mortgage-backed securities (CMBS) are usually partially amortized, the CMBS investors may face:
A. liquidity risk.
B. contraction risk.
C. balloon risk.
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答案：C
解析：CMBS通常是部分摊销的(partially amortized)，到期时仍有大量未偿本金(balloon payment)需要偿还。如果借款人无法再融资来偿还这笔大额到期付款，就产生了balloon risk（气球风险）。CMBS通常有call protection，contraction risk较低。
选项 判断 解析 A ✗ 流动性风险不是部分摊销直接导致的 B ✗ CMBS有call protection，contraction risk较低 C ✓ 部分摊销导致到期时有大额balloon payment，产生balloon risk
Q9.
Which of the following statements about the difference between CMBS and RMBS are correct?
Statement 1: Compared with RMBS, CMBS investors pay more attention to the balloon risk.
Statement 2: Compared with RMBS, CMBS have call protection to reduce prepayment risk.
A. Only Statement 1
B. Only Statement 2
C. Both are correct
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答案：C
解析：CMBS通常是部分摊销的，因此有balloon risk（RMBS通常完全摊销，balloon risk较小）。CMBS通常有call protection（如lockout periods、prepayment penalties等）来减少提前还款风险，而RMBS的提前还款风险更大。两个说法都正确。
选项 判断 解析 A ✗ Statement 2也正确 B ✗ Statement 1也正确 C ✓ CMBS确实更关注balloon risk且有call protection