# 债券的合约现金流与价格 沿同一国债发行与重开，读清合同日程、净全价、YTM和持有结果。 Entry: zh-m06 | Node: M06 | Language: zh | Editorial revision: 2026-09-21 ## Teaching instructions 你在教M06《债券的合约现金流与价格》。先实际取得required_readings的完整指定单元，核版本/页码；PDF表头、单位与公式看原页，记录本次工具取得范围。运行日志初始为空，不把编辑端已读当成本次已读。取不到原件就说明缺口，不补造报价。 先让我用91282CNT4两份原始发行文件给出首息、末息、20期CF及每100/每1000单位；再比较原发行与重开。高密度诊断：2,000面值的票息、原价、重开全价分别多少，重开是否重启20个完整半年？只有单位与日程对了才做YTM。 用同源输入验999.5961996与1017.6171；不要把重开套成20完整期。要求我区别YTM定义与复投终值条件、约定日/财政部规则付款日/实际到账。若我把剩余票息再加到卖出价里，指出重复计量。结尾给一份未见过的发行片段或本篇双倍面值迁移题，要求解释而不只报数。 Before substantive teaching, actually retrieve every required reading unit for the selected scope. Read its complete designated section, including necessary assumptions, tables and footnotes. A working URL or an editorial access date is not a runtime reading receipt. Record the actual version, location, scope and what it supports. If unavailable, use a previously verified equivalent source; if the required unit remains unavailable, identify that gap rather than teach it from memory. Start runtime_reading_log empty. Once reading is complete, use a substantive diagnostic or follow the reader's request for direct explanation. Advance one complete reasoning task at a time; skip mastered basics. Distinguish original facts, supplied teaching assumptions and inference. ## Required readings and runtime protocol ```json { "export_mode": "public", "required_readings": [ { "source_id": "MBC-10", "access": { "kind": "html_full_text", "uri": "https://www.treasurydirect.gov/marketable-securities/treasury-notes/" }, "required_unit": { "locator": "主体及 Notes at a Glance 全表", "scope": "主体及 Notes at a Glance 全表的完整指定单元，含必要脚注与表头", "purpose": "先读票息国债的产品结构" }, "supports": "票息国债期限、半年付息与持有/出售的产品层结构；不是某CUSIP的报价。", "version": "网页；取得2026-09-21", "title": "Treasury Notes", "authors": [ "U.S. Treasury, Bureau of the Fiscal Service" ] }, { "source_id": "MBC-11", "access": { "kind": "pdf_full_text", "uri": "https://www.treasurydirect.gov/instit/annceresult/press/preanre/2025/A_20250730_1.pdf" }, "required_unit": { "locator": "PDF物理p1全文，Security Terms与Tender Information", "scope": "PDF物理p1全文，Security Terms与Tender Information的完整指定单元，含必要脚注与表头", "purpose": "原始日期与票息日" }, "supports": "原发行日期、到期日、半年票息日及报价单位。", "version": "2025-07-30", "title": "Offering Announcement: 10-Year Note 91282CNT4", "authors": [ "U.S. Treasury" ] }, { "source_id": "MBC-12", "access": { "kind": "pdf_full_text", "uri": "https://www.treasurydirect.gov/instit/annceresult/press/preanre/2025/R_20250806_2.pdf" }, "required_unit": { "locator": "PDF物理p1全文，Coupon/High Yield/Price/Accrued Interest", "scope": "PDF物理p1全文，Coupon/High Yield/Price/Accrued Interest的完整指定单元，含必要脚注与表头", "purpose": "官方收益率/价格核对" }, "supports": "4.25%票息、4.255%高收益率、每100面值99.959620、原发行无应计。", "version": "2025-08-06", "title": "Auction Results: 10-Year Note 91282CNT4", "authors": [ "U.S. Treasury" ] }, { "source_id": "MBC-13", "access": { "kind": "pdf_full_text", "uri": "https://www.treasurydirect.gov/instit/annceresult/press/preanre/2025/A_20251002_2.pdf" }, "required_unit": { "locator": "PDF物理p1全文", "scope": "PDF物理p1全文的完整指定单元，含必要脚注与表头", "purpose": "同券重开安排" }, "supports": "同一CUSIP重开、2025-10-15交付、相同票息/到期日及应计期间。", "version": "2025-10-02", "title": "Reopening Announcement: 91282CNT4", "authors": [ "U.S. Treasury" ] }, { "source_id": "MBC-14", "access": { "kind": "pdf_full_text", "uri": "https://www.treasurydirect.gov/instit/annceresult/press/preanre/2025/R_20251008_2.pdf" }, "required_unit": { "locator": "PDF物理p1全文", "scope": "PDF物理p1全文的完整指定单元，含必要脚注与表头", "purpose": "净价、应计、全价" }, "supports": "重开净价101.057226/100、应计7.04484/1000、高收益率4.117%；本包不另反算重开YTM。", "version": "2025-10-08", "title": "Reopening Auction Results: 91282CNT4", "authors": [ "U.S. Treasury" ] }, { "source_id": "MBC-09", "access": { "kind": "pdf_full_text", "uri": "https://ocw.mit.edu/courses/15-401-finance-theory-i-fall-2008/df418b972d36cd53ae5c375b8af61e53_MIT15_401F08_lec04.pdf" }, "required_unit": { "locator": "slides25–33", "scope": "slides25–33的完整指定单元，含必要脚注与表头", "purpose": "从规则期CF推PV/YTM；不偷加复投定义" }, "supports": "零息利率、票息债券现金流、YTM、久期与凸性。采用独立导数校验；不采用forward=预测的简化及slide41末项错号。", "version": "MIT 15.401, Fall 2008, lecture file 2007–2008", "title": "Finance Theory I: Fixed Income Securities", "authors": [ "Andrew W. Lo" ] }, { "source_id": "MBC-25", "access": { "kind": "pdf_full_text", "uri": "https://www.govinfo.gov/content/pkg/CFR-2025-title31-vol2/pdf/CFR-2025-title31-vol2-sec356-30.pdf" }, "required_unit": { "locator": "§356.30(a)完整段", "scope": "§356.30(a)完整段的完整指定单元，含必要脚注与表头", "purpose": "约定日与营业日支付；历史版本范围" }, "supports": "本金/票息支付与遇周末或联储非营业日顺延且不加利息的规则，用于2025发行案例。", "version": "2025-07-01 CFR edition", "title": "31 CFR §356.30: Payment of principal and interest", "authors": [ "U.S. Treasury / Government Publishing Office" ] }, { "source_id": "MBC-26", "access": { "kind": "html_full_text", "uri": "https://www.federalreserve.gov/aboutthefed/k8.htm" }, "required_unit": { "locator": "2026列及周末/假日规则", "scope": "2026列及周末/假日规则的完整指定单元，含必要脚注与表头", "purpose": "只推首笔财政部规则付款日，不声称全部未来到账" }, "supports": "2026-02-16休业与星期日2026-02-15结合，推算首次财政部规则付款日2026-02-17；非账户到账记录。", "version": "2026–2030表；更新2026-07-08", "title": "Holidays Observed — K.8", "authors": [ "Board of Governors of the Federal Reserve System" ] } ], "optional_readings": [], "runtime_reading_log": [], "supplied_inputs": { "content_version": "2026-09-21-MC-review-v2", "data": { "content_version": "2026-09-21-MC-review-v2", "cutoff": "2026-09-21", "currency": "USD", "identities": { "source_observed": "原件条款或记录", "derived": "据明确输入计算", "teaching_assumption": "非真实成交或历史曲线", "reference_quote": "非bid/ask成交报价", "conditional_cashflow": "须按约履行且满足情景" }, "note": { "cusip": "91282CNT4", "face_default": 1000, "face_identity": "teaching_assumption", "coupon_annual": 0.0425, "payments_per_year": 2, "periods": 20, "dated_date": "2025-08-15", "maturity": "2035-08-15", "original": { "announcement": "2025-07-30", "auction": "2025-08-06", "issue": "2025-08-15", "yield": 0.04255, "clean_per_100": 99.95962, "accrued_per_1000": 0 }, "reopening": { "announcement": "2025-10-02", "auction": "2025-10-08", "issue": "2025-10-15", "yield": 0.04117, "clean_per_100": 101.057226, "accrued_per_1000": 7.04484 }, "schedule": [ { "period": 1, "contract_date": "2026-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0 }, { "period": 2, "contract_date": "2026-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0 }, { "period": 3, "contract_date": "2027-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0 }, { "period": 4, "contract_date": "2027-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0 }, { "period": 5, "contract_date": "2028-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0 }, { "period": 6, "contract_date": "2028-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0 }, { "period": 7, "contract_date": "2029-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0 }, { "period": 8, "contract_date": "2029-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0 }, { "period": 9, "contract_date": "2030-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0 }, { "period": 10, "contract_date": "2030-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0 }, { "period": 11, "contract_date": "2031-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0 }, { "period": 12, "contract_date": "2031-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0 }, { "period": 13, "contract_date": "2032-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0 }, { "period": 14, "contract_date": "2032-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0 }, { "period": 15, "contract_date": "2033-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0 }, { "period": 16, "contract_date": "2033-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0 }, { "period": 17, "contract_date": "2034-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0 }, { "period": 18, "contract_date": "2034-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0 }, { "period": 19, "contract_date": "2035-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0 }, { "period": 20, "contract_date": "2035-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 1000 } ], "first_payment_rule_date": "2026-02-17", "first_payment_status": "按31 CFR §356.30(a)及2026联储休业表推得的财政部规则付款日；非持有人账户到账记录", "payment_rule": "约定付息日遇周末或联储休业日，顺延至下一营业日，不加利息；其余未来日期不预生成已核营业日日历", "slider_yield_default": 0.04255 }, "local": { "shock_bp_default": 25, "annual_yield_basis": "nominal annual, semiannual compounding" }, "curve": { "times": [ 1, 2, 3 ], "cashflows": [ 50, 50, 1050 ], "base_spot": [ 0.03, 0.035, 0.04 ], "shock_bp": 25, "compounding": "annual", "identity": "teaching_assumption", "scenarios": [ { "name": "base", "spot_rates": [ 0.03, 0.035, 0.04 ] }, { "name": "parallel_up", "spot_rates": [ 0.0325, 0.0375, 0.0425 ] }, { "name": "parallel_down", "spot_rates": [ 0.0275, 0.0325, 0.0375 ] }, { "name": "flattening", "spot_rates": [ 0.0325, 0.035, 0.0375 ] }, { "name": "steepening", "spot_rates": [ 0.0275, 0.035, 0.0425 ] } ] }, "callable": { "issuer": "Barclays Bank PLC", "cusip": "06749HU29", "pricing_date": "2026-07-15", "issue": "2026-07-17", "maturity": "2036-07-17", "denomination": 1000, "coupon_annual": 0.0525, "day_count": "30/360", "coupon_month_day": "07-17", "first_coupon": "2027-07-17", "first_call": "2029-07-17", "call_months": [ 1, 4, 7, 10 ], "notice": "至少提前5个营业日通知受托人；可全部或部分赎回", "scenario": "假设首次可赎回日全额行权、依约支付；不是赎回预测" }, "liquidity": { "sample": "2017-07 to 2024-06", "maturity_sector": "10-year", "on_the_run": { "volume_bn_usd_day": 92.05, "effective_spread_price_bp": 2.07 }, "first_off_the_run": { "volume_bn_usd_day": 6.73, "effective_spread_price_bp": 3.73 }, "identity": "NY Fed sr1170 Tables 2 and 3 sample statistics, not 2026 observations", "table3_metric": "proportional effective bid-ask spread in price basis points", "table3_values_period": "July 2017–June 2024 full-sample column; March 2020 column is separate and not used for 2.07/3.73" }, "bill": { "cusip": "912797TY3", "auction": "2026-05-26", "issue": "2026-05-28", "maturity": "2026-08-27", "days": 91, "discount_rate": 0.03595, "price_per_100": 99.091264, "investment_rate": 0.03678, "face_default": 10000 }, "repo": { "rule_card": { "version": "2026-09-16", "rate": 0.04, "tenor": "overnight", "facility": "New York Fed Standing Repo", "counterparties": "primary dealers / approved SRP counterparties", "collateral": "Treasuries / agency debt / agency MBS", "agent": "BNY tri-party", "settlement": "same-day", "margin_ratio_numeric_input": "not supplied by SRP FAQ in this lesson" }, "teaching": { "cash": 10000000, "rate": 0.04, "days": 1, "basis": 360, "margin_cash_ratio": 0.02, "lender_cash": 10000000, "borrower_eligible_collateral": 10200000, "borrower_buffer": 2000, "proceeds_spent": 0, "margin_cash_ratio_identity": "teaching assumption using FEDS Note h=(Vsec-L)/L; not SRP parameter" }, "assumptions": "教学ACT/360、一天、单一抵押比例、无外部融资，无违约处置或真实发票；公允值不变；h=(证券价值−现金)/现金" }, "fx": { "release": "2026-09-14", "url": "https://www.federalreserve.gov/releases/h10/20260914/", "identity": "reference_quote", "units": { "EUR": "USD/EUR", "JPY": "JPY/USD" }, "dates": { "2026-09-07": { "EUR": null, "JPY": null }, "2026-09-08": { "EUR": 1.1627, "JPY": 154.24 }, "2026-09-11": { "EUR": 1.1604, "JPY": 153.71 } }, "amount_default": 10000, "direction_default": "EUR_USD", "date_default": "2026-09-11" }, "fx_settlement": { "period": "2025-04", "jurisdictions": 49, "pvp_pct": 36, "mitigated_pct": 54, "gross_bilateral_pct": 10, "identity": "BIS June2026 report, actual settlement new questionnaire; not turnover/noncomparable old methods" } }, "experiments": [ "EXP-MC-M06-NOTE" ], "identity": "单一冻结输入；真实条款只读，教学项另标" } } ``` ## Supplied entry 我们先不问一只债券“收益率高不高”，而是把三件事排开：它约定在什么时候付多少钱；我们今天为取得这些权利付多少钱；用什么口径描述两者之间的关系。本篇沿着同一只美国国债的原始发行与重开走一遍。读完以后，你应当能从发行文件画出支付日程，算清取得成本，并解释票息、净价、全价和到期收益率为什么不能互换。 默认学习约 18–20 分钟。需要已经能识别金融权利的义务主体、期限和单位；有限现金流求和直接使用。 ## 一、先把真实合约读成一张时间表 主角是 CUSIP **91282CNT4**。2025 年 7 月 30 日的发行公告和 8 月 6 日的拍卖结果给了我们不同层次的信息：公告说明期限与发行安排，结果补上实际确定的票息、拍卖收益率和价格。两张纸要一起读，而不是只截一行“4.255%”。[^MBC-11][^MBC-12] | 字段 | 原件对应内容 | 对持有人的意义 | |---|---|---| | 义务主体 | 美国财政部 | 约定的本金与利息由谁支付 | | 原始发行／起息日 | 2025-08-15 | 本例现金流定价的起点 | | 到期日 | 2035-08-15 | 最后一笔本金的约定支付日 | | 年票息率 | 4.25% | 乘面值确定合同利息，不乘购买价格 | | 约定票息日 | 每年 2 月 15 日、8 月 15 日 | 每半年一次；原始发行后首个约定日为 2026-02-15 | | 拍卖高收益率 | 4.255% | 原始发行价格对应的年化报价 | | 公布价格 | 每 100 美元面值 99.959620 美元 | 不是每 1,000 面值的总付款 | 以下选择 **1,000 美元面值**做教学持仓，并不代表一笔已核实的投资者账户交易。每半年票息为 $1000\times4.25\%/2=21.25$ 美元。发行日不是首个票息日，因此不能在 2025-08-15 再凭空加一笔 21.25。完整约定日程是： | 年份 | 2月15日：票息／本金 | 8月15日：票息／本金 | |---|---:|---:| | 2026 | 21.25／0 | 21.25／0 | | 2027 | 21.25／0 | 21.25／0 | | 2028 | 21.25／0 | 21.25／0 | | 2029 | 21.25／0 | 21.25／0 | | 2030 | 21.25／0 | 21.25／0 | | 2031 | 21.25／0 | 21.25／0 | | 2032 | 21.25／0 | 21.25／0 | | 2033 | 21.25／0 | 21.25／0 | | 2034 | 21.25／0 | 21.25／0 | | 2035 | 21.25／0 | 21.25／1,000.00 | 共有 20 次票息，最后一期合付 1,021.25。425 美元票息加 1,000 美元本金，是一项**跨十年的名义金额合计**；它还没有处理资金时间，也不是“赚了 1,425”。 这张表列的是**约定日**。本例采用的财政部支付规则规定，若约定日遇周末或联储休业日，顺延到下一营业日，不额外增加利息。2026-02-15 是星期日，2 月 16 日又在联储休业日表中，因此首笔按规则推得的**财政部付款日**为 **2026-02-17**。这里说的是按财政部支付规则与联储营业日推得的付款日期，不是持有人银行或券商界面的到账时间；其余未来日期也不能仅按周末猜测银行营业日。[^MBC-25][^MBC-26] 票息把本金的使用分成期间支付，本金则在到期时归还。这种安排让出借人与借款人事先知道支付规则，但不保证投资者提前卖出时仍能拿回原来付出的价格。合同时间表与二级市场转让价格，需要分别研究。[^MBC-10] ## 二、票息、价格和 YTM 是三种不同的量 票息率乘的是面值。若以 950 美元买入同样 1,000 面值，合同每半年仍付 21.25；若以 1,050 买入也一样。市场价格改变的是取得这组现金流的成本，不会自动重写票息。 令 $CF_k$ 为第 $k$ 个半年期的合同现金流：前 19 期各 21.25，最后一期 1,021.25。按名义年率 $y$、半年复利报价，期利率是 $y/2$。在原始发行这个规则期点上，价格与收益率的关系为 $$ P(y)=\sum_{k=1}^{20}\frac{CF_k}{(1+y/2)^k}. $$ **到期收益率（YTM**）是使这组约定现金流的现值等于给定价格的那一个内部收益率表示。它不是另一个合同付款，也不需要先假定投资者已经把票息再投资，才能定义出来。对本例全为正的未来现金流，收益率 $y$ 上升时，固定现金流的价格 $P(y)$ 下降；在允许的利率范围内，较高的要求收益率对应较低的取得价格。[^MBC-09] 代入官方原始拍卖的 $y=0.04255$： $$ P=\sum_{k=1}^{20}\frac{21.25}{(1+0.04255/2)^k} +\frac{1000}{(1+0.04255/2)^{20}} \approx999.5961996. $$ 官方报价乘以十为 $99.959620\times10=999.596200$ 美元，两者在公布精度一致。现金显示到美分是 **999.60**；复算时先保留内部精度，不能一开始把每期现值都舍到分再相加。 这里使用的是 Treasury 原始发行的常规半年报价模型。它按约定票息期间折现；前节的营业日支付顺延不使合同额外生息，也不在这条拍卖报价复算里人为增加一个 2 天计息期间。若研究实际每日现金可用时点，应另用实际支付日账本，而不是默默改变报价公式。 为了看出“同一合同，不同价格”的含义，我们只改变教学收益率，保持全部现金流不动： | 教学名义年收益率，半年复利 | 每1,000面值的价格 | |---|---:| | 3.000% | 1,107.30 | | 4.255% | 999.60 | | 6.000% | 869.82 | 这三点不是历史行情。它们揭示的是价格函数：新买家要求的回报越高，愿为同样固定现金流支付的金额越少。年票息 42.50 除以今天价格所得的“当前收益率”也不是 YTM，因为它忽略了票息的时点，以及到期收到 1,000 与购买成本之间的差额。 ## 三、重开同一只债券：为什么还要付应计利息？ 2025 年 10 月 2 日公告、10 月 8 日拍卖的重开券，**CUSIP 仍是 91282CNT4**，票息仍为 4.25%，到期仍为 2035-08-15；新一批证券在 2025-10-15 交付。它不是把十年期限从十月重新开始算。[^MBC-13] 到十月中旬，首个半年票息期间已经走过一部分。新买方取得的是这只债券今后的支付权，包括下一次完整的票息；因此发行结果将净价与应计利息分列。我们把同一面值下两次取得条件放在一起：[^MBC-14] | 取得批次 | 原始发行 | 重开 | |---|---:|---:| | 交付日 | 2025-08-15 | 2025-10-15 | | 官方高收益率 | 4.255% | 4.117% | | 每100面值净价 | 99.959620 | 101.057226 | | 每1,000面值净价 | 999.596200 | 1,010.572260 | | 每1,000面值应计利息 | 0 | 7.044840 | | 每1,000面值全价 | 999.596200 | **1,017.617100** | **净价（clean price**）把本期已经积累的利息单列；**全价（dirty/full price**）把它加回，表示本例不计额外交易费用的应付对价。重开时， $$ 1{,}010.572260+7.044840=1{,}017.617100. $$ 应计利息不是把下一次 21.25 改成 $21.25+7.04484$。下一次合同票息仍是21.25；7.04484在取得证券时支付。也不能因为净价高于面值就断言收益率为负：期间还会收到票息，要把完整剩余现金流和今天的全价一起看。 这里沿用官方应计数。重开日位于票息期中，不能再把第一笔票息当作整整半年后，用前节“20 个完整半年期”公式反算 4.117%。完整的非票息日定价还需要正确的分段计息和结算日约定。本篇用原件净价加应计核对全价，把首次规则期定价和期中取得明确分开。 ## 四、YTM 算出来以后，实际回报还缺什么？ 先区分两个问题。第一，给定价格和合同现金流的 YTM 是多少？第二，我们最后实际留下多少财富？第一问是前面的内部收益率方程；第二问还涉及是否按约履行、何时出售，以及收到票息以后怎么处理。 仍用原始取得成本 999.5962，假设全部按约支付且持有至约定到期。若每次票息只保留为不生息现金，到期合计财富为 1,425。以这个**终值财富**计算十年年化约为 $(1425/999.5962)^{1/10}-1=3.6094\%$。若每笔票息均能按同一半年率 $0.04255/2$ 复投到最后一个规则期点，终值为 $$ W_{20} =\sum_{k=1}^{20}CF_k(1+y/2)^{20-k} =P_0(1+y/2)^{20}. $$ 相应有效年复合率是 $(1+y/2)^2-1=4.3003\%$，而不是把名义年率 4.255%直接当有效年率。这两个财富路径**不会改变原始合同现金流的 YTM 定义**：它们改变的是中途收款后累积到同一终点的财富。若票息被花掉，终值投资账户自然不同，也不能据此宣称当初 IRR 算错。 再换一个教学情景：收到两次票息后立即卖出，假设不计费用的出售所得是 1,010 美元。这不是一笔历史成交。投入仍为 999.5962，期间收票息42.50，终点出售1,010，则该段不复投的持有回报为 $$ \frac{1010+42.50-999.5962}{999.5962}\approx5.293\%. $$ 出售时拿不到还没发生的剩余十八次票息；它们作为剩余权利的一部分已经反映在买方愿付的价格中。把未来票息再加到卖出所得上，会重复计算。怎样分析出售价格对利率、流动性或合同条款的敏感性，下一篇再展开。 ## 五、带着日程操作一次
实验有“原始发行”和“重开”两个原件视图。先固定面值1,000，检查20行约定日程及本金只出现在最后一期；切换重开后，合同日程不重新起算，但取得日、净价和应计改变。收益率滑杆只对**原始发行的规则期现金流**开放，旁边分别保留官方报价与教学重定价，不把滑杆输出叫市场成交价。 不用交互也能完成同一任务：用第二节的3%、4.255%、6%三行价格，说明票息是否改变；再用第三节两批次表核算全价。最后把“首个约定日2026-02-15”“财政部规则付款日2026-02-17”“实际到账待账户记录核对”写成三个不同字段。 ## 六、检验理解：换了一个字段，其他字段跟着变吗？ ### 题一：首息和到期是否都数进去了？ 某同学从2025-08-15开始每半年计21.25，一直算到2035-08-15，得到21次票息。错在哪里？ **解析。** 他把原始发行日也当成付息日。首个约定票息日为2026-02-15，至2035-08-15共20期。前19期各21.25，末期1,021.25；面值1,000不能每一期都加。实际支付按营业日规则顺延，不会凭空多出一次票息。 ### 题二：面值翻倍，哪些是金额，哪些是率？ 取2,000面值，分别算原始发行成本、每半年票息和重开全价。4.255%是否也翻倍？ **解析。** 原始成本为1,999.1924，票息为42.50，重开全价为2,035.2342美元；现金展示分别约1,999.19、42.50、2,035.23。收益率、票息率及每100面值报价均不翻倍。面值只按比例放大金额。 ### 题三：净价101.057226是不是收到的利息？ **解析。** 不是。它是每100面值的净购买价格。1,000面值净价为1,010.57226，另付应计7.04484，总成本1,017.6171。下一次合同票息仍为21.25，应计不再次加进票息。仅凭净价高于100也不能判定持有回报正负。 ### 题四：不复投能不能定义YTM？ **解析。** 能。只要给定价格和约定现金流，YTM方程就已确定。把它解释为某个终点财富的复合增长率，才需要说明履约、持有期及中间现金再投资。提前出售还要用实际出售对价，不能把当初YTM当成一年的收益保证。 这四道题连在一起，得到一套可迁移的阅读顺序：**先定现金流和日期，再核面值与报价单位，随后算取得成本，最后才谈收益率和持有结果。** [^MBC-11]: U.S. Treasury，*Offering Announcement: 10-Year Note 91282CNT4*，2025-07-30。[原文](https://www.treasurydirect.gov/instit/annceresult/press/preanre/2025/A_20250730_1.pdf)。定位：PDF物理p1全文，Security Terms与Tender Information。 [^MBC-12]: U.S. Treasury，*Auction Results: 10-Year Note 91282CNT4*，2025-08-06。[原文](https://www.treasurydirect.gov/instit/annceresult/press/preanre/2025/R_20250806_2.pdf)。定位：PDF物理p1全文，Coupon/High Yield/Price/Accrued Interest。 [^MBC-25]: U.S. Treasury / Government Publishing Office，*31 CFR §356.30: Payment of principal and interest*，2025-07-01 CFR edition。[原文](https://www.govinfo.gov/content/pkg/CFR-2025-title31-vol2/pdf/CFR-2025-title31-vol2-sec356-30.pdf)。定位：§356.30(a)，印刷p406。 [^MBC-26]: Board of Governors of the Federal Reserve System，*Holidays Observed — K.8*，2026–2030表；更新2026-07-08。[原文](https://www.federalreserve.gov/aboutthefed/k8.htm)。定位：2026列及周末观察规则、注释。 [^MBC-10]: U.S. Treasury, Bureau of the Fiscal Service，*Treasury Notes*，网页；取得2026-09-21。[原文](https://www.treasurydirect.gov/marketable-securities/treasury-notes/)。定位：主体及 Notes at a Glance 全表。 [^MBC-09]: Andrew W. Lo，*Finance Theory I: Fixed Income Securities*，MIT 15.401, Fall 2008, lecture file 2007–2008。[原文](https://ocw.mit.edu/courses/15-401-finance-theory-i-fall-2008/df418b972d36cd53ae5c375b8af61e53_MIT15_401F08_lec04.pdf)。定位：slides 12–19；slides 25–33；slides 35–47。 [^MBC-13]: U.S. Treasury，*Reopening Announcement: 91282CNT4*，2025-10-02。[原文](https://www.treasurydirect.gov/instit/annceresult/press/preanre/2025/A_20251002_2.pdf)。定位：PDF物理p1全文。 [^MBC-14]: U.S. Treasury，*Reopening Auction Results: 91282CNT4*，2025-10-08。[原文](https://www.treasurydirect.gov/instit/annceresult/press/preanre/2025/R_20251008_2.pdf)。定位：PDF物理p1全文。 ## Experiment inputs and static equivalents ```json [ { "id": "EXP-MC-M06-NOTE", "title": "国债日程、原发行与重开", "anchor": "m06-experiment", "description": "两批次共享同一合同日程；重开不用原始20完整期模型。", "inputs": { "case": [ "original", "reopening" ], "face": { "default": 1000, "unit": "USD face", "step": 100 }, "yield": { "default": 0.04255, "unit": "nominal annual; q=2", "enabled_only": "original", "min": 0, "max": 0.2 } }, "outputs": { "original": { "which": "original", "face": 1000, "issue": "2025-08-15", "official_yield": 0.04255, "clean": 999.5962, "accrued": 0, "full": 999.5962, "model": { "price": 999.5961995990485, "coupon": 21.25, "mac": 8.249177066596465, "modified": 8.077331831873359, "dv01": 0.807407020204103, "convexity": 77.53054929520565, "d1": -8074.07020204103, "d2": 77499.24242831426, "effective_annual": 0.04300262562499979, "cashflows": [ 21.25, 21.25, 21.25, 21.25, 21.25, 21.25, 21.25, 21.25, 21.25, 21.25, 21.25, 21.25, 21.25, 21.25, 21.25, 21.25, 21.25, 21.25, 21.25, 1021.25 ] }, "schedule": [ { "period": 1, "contract_date": "2026-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 2, "contract_date": "2026-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 3, "contract_date": "2027-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 4, "contract_date": "2027-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 5, "contract_date": "2028-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 6, "contract_date": "2028-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 7, "contract_date": "2029-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 8, "contract_date": "2029-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 9, "contract_date": "2030-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 10, "contract_date": "2030-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 11, "contract_date": "2031-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 12, "contract_date": "2031-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 13, "contract_date": "2032-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 14, "contract_date": "2032-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 15, "contract_date": "2033-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 16, "contract_date": "2033-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 17, "contract_date": "2034-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 18, "contract_date": "2034-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 19, "contract_date": "2035-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 20, "contract_date": "2035-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 1000, "coupon": 21.25, "principal": 1000, "cashflow": 1021.25 } ], "identity": "source-backed contract; face/slider are teaching settings; actual receipt unverified" }, "reopening": { "which": "reopening", "face": 1000, "issue": "2025-10-15", "official_yield": 0.04117, "clean": 1010.5722599999999, "accrued": 7.04484, "full": 1017.6170999999999, "model": null, "schedule": [ { "period": 1, "contract_date": "2026-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 2, "contract_date": "2026-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 3, "contract_date": "2027-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 4, "contract_date": "2027-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 5, "contract_date": "2028-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 6, "contract_date": "2028-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 7, "contract_date": "2029-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 8, "contract_date": "2029-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 9, "contract_date": "2030-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 10, "contract_date": "2030-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 11, "contract_date": "2031-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 12, "contract_date": "2031-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 13, "contract_date": "2032-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 14, "contract_date": "2032-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 15, "contract_date": "2033-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 16, "contract_date": "2033-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 17, "contract_date": "2034-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 18, "contract_date": "2034-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 19, "contract_date": "2035-02-15", "coupon_per_1000": 21.25, "principal_per_1000": 0, "coupon": 21.25, "principal": 0, "cashflow": 21.25 }, { "period": 20, "contract_date": "2035-08-15", "coupon_per_1000": 21.25, "principal_per_1000": 1000, "coupon": 21.25, "principal": 1000, "cashflow": 1021.25 } ], "identity": "source-backed contract; face/slider are teaching settings; actual receipt unverified" } }, "algorithm": "P=sum(CF_k/(1+y/2)^k); clean=face*price_per_100/100; accrued=face*accrued_per_1000/1000; full=clean+accrued", "boundaries": [ "面值为100整数倍", "官方条款只读", "重开返回model=null", "日程为约定日；首日历调整另列；无账户到账证明" ], "static_equivalent": "正文二/三节价格表与第一节完整20期表；HTML静态表一致。", "source_inputs": "shared_inputs.json", "implementation": "labs/m-c/engine.js", "data_identity": "合同/报价身份按输入卡；可调项均为教学设定" } ] ``` ## Sources - [Finance Theory I: Fixed Income Securities](https://ocw.mit.edu/courses/15-401-finance-theory-i-fall-2008/df418b972d36cd53ae5c375b8af61e53_MIT15_401F08_lec04.pdf): 零息利率、票息债券现金流、YTM、久期与凸性。采用独立导数校验；不采用forward=预测的简化及slide41末项错号。 - [Treasury Notes](https://www.treasurydirect.gov/marketable-securities/treasury-notes/): 票息国债期限、半年付息与持有/出售的产品层结构；不是某CUSIP的报价。 - [Offering Announcement: 10-Year Note 91282CNT4](https://www.treasurydirect.gov/instit/annceresult/press/preanre/2025/A_20250730_1.pdf): 原发行日期、到期日、半年票息日及报价单位。 - [Auction Results: 10-Year Note 91282CNT4](https://www.treasurydirect.gov/instit/annceresult/press/preanre/2025/R_20250806_2.pdf): 4.25%票息、4.255%高收益率、每100面值99.959620、原发行无应计。 - [Reopening Announcement: 91282CNT4](https://www.treasurydirect.gov/instit/annceresult/press/preanre/2025/A_20251002_2.pdf): 同一CUSIP重开、2025-10-15交付、相同票息/到期日及应计期间。 - [Reopening Auction Results: 91282CNT4](https://www.treasurydirect.gov/instit/annceresult/press/preanre/2025/R_20251008_2.pdf): 重开净价101.057226/100、应计7.04484/1000、高收益率4.117%；本包不另反算重开YTM。 - [31 CFR §356.30: Payment of principal and interest](https://www.govinfo.gov/content/pkg/CFR-2025-title31-vol2/pdf/CFR-2025-title31-vol2-sec356-30.pdf): 本金/票息支付与遇周末或联储非营业日顺延且不加利息的规则，用于2025发行案例。 - [Holidays Observed — K.8](https://www.federalreserve.gov/aboutthefed/k8.htm): 2026-02-16为Washington’s Birthday联储休业日；与星期日2026-02-15及支付规则结合，推算财政部规则付款日2026-02-17；不是持有人账户到账记录。 ## Content relations ```json [ { "from": "zh-m06", "relation": "part_of", "to": "markets-fixed-income", "reason": "主要 topic 归属" }, { "from": "zh-m06", "relation": "requires", "to": "zh-financial-claims", "reason": "实际所需能力，不由推荐相邻推定", "required_competence": "识别义务主体、权利事项、日期和单位", "status": "external_delivered" }, { "from": "zh-m06", "relation": "illustrated_by", "to": "case-mbc-ust-91282cnt4", "reason": "2025-07-30至2025-10-15发行/重开文件" }, { "from": "m06-experiment", "relation": "illustrated_by", "to": "EXP-MC-M06-NOTE", "reason": "两批次共享同一合同日程；重开不用原始20完整期模型。" }, { "from": "m06-contract", "relation": "supported_by", "to": "MBC-11", "reason": "该单元原件依据", "locator": "PDF物理p1全文，Security Terms与Tender Information", "scope": "原发行日期、到期日、半年票息日及报价单位。" }, { "from": "m06-contract", "relation": "supported_by", "to": "MBC-12", "reason": "该单元原件依据", "locator": "PDF物理p1全文，Coupon/High Yield/Price/Accrued Interest", "scope": "4.25%票息、4.255%高收益率、每100面值99.959620、原发行无应计。" }, { "from": "m06-contract", "relation": "supported_by", "to": "MBC-25", "reason": "该单元原件依据", "locator": "§356.30(a)，印刷p406", "scope": "本金/票息支付与遇周末或联储非营业日顺延且不加利息的规则，用于2025发行案例。" }, { "from": "m06-contract", "relation": "supported_by", "to": "MBC-26", "reason": "该单元原件依据", "locator": "2026列及周末观察规则、注释", "scope": "2026-02-16休业与星期日2026-02-15结合，推算首次财政部规则付款日2026-02-17；非账户到账记录。" }, { "from": "m06-price-yield", "relation": "supported_by", "to": "MBC-09", "reason": "该单元原件依据", "locator": "slides 12–19；slides 25–33；slides 35–47", "scope": "零息利率、票息债券现金流、YTM、久期与凸性。采用独立导数校验；不采用forward=预测的简化及slide41末项错号。" }, { "from": "m06-reopening", "relation": "supported_by", "to": "MBC-13", "reason": "该单元原件依据", "locator": "PDF物理p1全文", "scope": "同一CUSIP重开、2025-10-15交付、相同票息/到期日及应计期间。" }, { "from": "m06-reopening", "relation": "supported_by", "to": "MBC-14", "reason": "该单元原件依据", "locator": "PDF物理p1全文", "scope": "重开净价101.057226/100、应计7.04484/1000、高收益率4.117%；本包不另反算重开YTM。" }, { "from": "case-mbc-ust-91282cnt4", "relation": "supported_by", "to": "MBC-11", "reason": "本例有日期的契约、规则或公开观察材料", "locator": "PDF物理p1全文，Security Terms与Tender Information", "scope": "原始交付2025-08-15、重开交付2025-10-15；同一CUSIP、4.25%票息和2035-08-15约定到期。比较价格、应计及取得日期，合同日程不重启。" }, { "from": "case-mbc-ust-91282cnt4", "relation": "supported_by", "to": "MBC-12", "reason": "本例有日期的契约、规则或公开观察材料", "locator": "PDF物理p1全文，Coupon/High Yield/Price/Accrued Interest", "scope": "原始交付2025-08-15、重开交付2025-10-15；同一CUSIP、4.25%票息和2035-08-15约定到期。比较价格、应计及取得日期，合同日程不重启。" }, { "from": "case-mbc-ust-91282cnt4", "relation": "supported_by", "to": "MBC-13", "reason": "本例有日期的契约、规则或公开观察材料", "locator": "PDF物理p1全文", "scope": "原始交付2025-08-15、重开交付2025-10-15；同一CUSIP、4.25%票息和2035-08-15约定到期。比较价格、应计及取得日期，合同日程不重启。" }, { "from": "case-mbc-ust-91282cnt4", "relation": "supported_by", "to": "MBC-14", "reason": "本例有日期的契约、规则或公开观察材料", "locator": "PDF物理p1全文", "scope": "原始交付2025-08-15、重开交付2025-10-15；同一CUSIP、4.25%票息和2035-08-15约定到期。比较价格、应计及取得日期，合同日程不重启。" } ] ``` ## Related entries ## Optional reading path 理解合约与市场机制: step 7/17 从原始发行与重开文件重建票息日程、净价、全价和持有回报。 利率与短期资金可从选读分支进入；接着把未来义务放进远期与期货合约。 Next: [远期与期货的合约结构](https://ou-liu-red-sugar.github.io/zh/notebook/forward-futures-contracts/)