# 日期现金、结果分布与Risk-Reward 用日期现金与同状态普通股结果合并粗权重，区分两种年化、代表点亏损及资金限制。 Entry: zh-p31 | Node: P31 | Language: zh | Editorial revision: 2026-09-21 ## Teaching instructions 你正在教授P31《日期现金、结果分布与Risk-Reward》，读者具有高年级本科至研究生数学背景。 先确认本次节点和读者所选分支。先实际取得required_readings中该范围的全部完整单元，核对版本、期间、币种与模型身份；目录、摘要、搜索节选和成功打开标题不算正文。记录实际工具/文件、单元起止、读到的关键约定及其支持范围，runtime_reading_log从空表开始，不预填“已读”。本站方法和公司案例从access.uri所列公开正文读取，外部原件从指定URL读取；不得假设访问任何私人盘符。读取失败先用明示的已核等价来源，仍缺则具体说明缺的单元，不凭记忆声称已核该事实。读者要求直接讲解时可直接推进；互动时一次要求一个完整推理任务，不逐格问四则运算。引用紧随所用材料。案例固定2026-09-20信息与2026-09-18价格，不更新报价、不接账户、不重估公司；不执行或换名恢复股票DCF/WACC。所有操作标原状态、具名已算替代或纯教学扰动，不能把点击当新增证据。最后用迁移题检验，给完整解析，并指出剩余条件。 本篇任务与反馈尺度： 先让读者列−253.71和2029末一股售价两笔现金，核1200/365.25；企业救援发行不是旧股东强制追加。由全概率/全期望公式接四代表点，保留近似身份；重算361.428923、11.372500%及8.347799%，并用非线性/Jensen解释T>1的方向。严格亏损的等号边界须说清。用第二类80/120的练习证明条件均值可能保留ETW却丢失亏损概率；当前参数区间没有全类支持身份。实验只在4定价×4权重16项内切换，具名经营替代另回P04。Tail损失84.4023不是最坏5%平均。概率翻转固定原价格和Base/Tail；16.886105pp不是通用隐含概率。最后用一年末股息再投资题检验日期现金和不重复计利。 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": "PBCD-METHOD-RR", "title": "业务状态下的条件定价、普通股桥与Risk-Reward", "version": "2026-09-21 局部准确摘编", "access": { "kind": "site_body", "uri": "https://ou-liu-red-sugar.github.io/zh/notebook/conditional-pricing-common-equity-risk-reward/", "availability": "staged_site_body; accessible after adoption" }, "required_unit": { "locator": "pm-conditional-rr-dated-shareholder-results", "scope": "完整日期结果节", "purpose": "投资者与企业现金分开" }, "supports": "规定估值组、盈利/参照、普通股桥、状态权重和日期现金的输入输出与边界。", "authors": [ "本站方法" ] }, { "source_id": "PBCD-CASE-AMZN", "title": "Amazon：2026-09-20历史条件研究案例", "version": "研究截止2026-09-20；教学摘编2026-09-21", "access": { "kind": "site_body", "uri": "https://ou-liu-red-sugar.github.io/zh/notebook/amzn-research-20260920/", "availability": "staged_site_body; accessible after adoption" }, "required_unit": { "locator": "case-amzn-probabilities、case-amzn-equity、case-amzn-distributions", "scope": "所用状态、终点、权重及16组分布", "purpose": "代表点近似、零途中现金和恒利率比较" }, "supports": "原研究的事实/分析代理、四条未来路径、5项具名替代、4套权重与16组已算分布。报价冻结，代表点不是条件均值。", "authors": [ "本站历史研究" ] } ], "optional_readings": [], "runtime_reading_log": [], "supplied_inputs": { "case_id": "CASE-AMZN-20260920", "uri": "https://ou-liu-red-sugar.github.io/notebook/labs/p-bcd/inputs.json", "identity": "冻结2026-09-20输入；不同JSON字段保留事实/假设/条件结果身份", "selected_keys": [ "case_id", "metadata", "states", "probabilities", "pricing", "identity_notes", "teaching_examples" ], "data": { "case_id": "CASE-AMZN-20260920", "metadata": { "information_cutoff": "2026-09-20", "purchase_date": "2026-09-18", "valuation_date": "2029-12-31", "purchase_price": 253.71, "currency": "USD", "money_unit": "billion", "share_unit": "billion", "quote_type": "regular_close", "quote_time": "16:00 EDT", "years": 3.2854209445585214, "cash_distributions": 0, "original_shareholder_additional_cash": 0, "result_identity": "历史研究的未来条件结果；不是当期目标价；期间分配为零；救援发行不等于原股东强制追加现金" }, "states": [ "Bull", "Base", "Bear", "Tail" ], "probabilities": { "adopted": { "Bull": 0.31, "Base": 0.44, "Bear": 0.2, "Tail": 0.05 }, "capital_pressure": { "Bull": 0.2, "Base": 0.42, "Bear": 0.3, "Tail": 0.08 }, "platform_durable": { "Bull": 0.37, "Base": 0.43, "Bear": 0.16, "Tail": 0.04 }, "mixed_retail_pressure": { "Bull": 0.27, "Base": 0.41, "Bear": 0.26, "Tail": 0.06 } }, "pricing": { "representative": { "prices": { "Bull": 556.4431539969916, "Base": 347.4461331923256, "Bear": 170.3830229466745, "Tail": 39.57284315295868 }, "distributions": { "adopted": { "identity": "weighted representative-point discrete approximation; not identified conditional means", "weights": { "Bull": 0.31, "Base": 0.44, "Bear": 0.2, "Tail": 0.05 }, "expected_terminal_wealth": 361.4289230906735, "annualized_expected_terminal_wealth": 0.11372500084263093, "probability_weighted_annualized_return": 0.08347799170226604, "representative_point_loss_probability": 0.25, "benchmark_terminal_wealth": 296.2384031031345, "expected_net_gain": 107.71892309067348, "expected_holding_return": 0.42457499937201315, "arithmetic_fields_derived_from_frozen_inputs": [ "expected_net_gain", "expected_holding_return" ] }, "capital_pressure": { "identity": "weighted representative-point discrete approximation; not identified conditional means", "weights": { "Bull": 0.2, "Base": 0.42, "Bear": 0.3, "Tail": 0.08 }, "expected_terminal_wealth": 311.49674107641414, "annualized_expected_terminal_wealth": 0.06444851095331705, "probability_weighted_annualized_return": 0.02739362318963135, "representative_point_loss_probability": 0.38, "benchmark_terminal_wealth": 296.2384031031345, "expected_net_gain": 57.78674107641413, "expected_holding_return": 0.22776690345833472, "arithmetic_fields_derived_from_frozen_inputs": [ "expected_net_gain", "expected_holding_return" ] }, "platform_durable": { "identity": "weighted representative-point discrete approximation; not identified conditional means", "weights": { "Bull": 0.37, "Base": 0.43, "Bear": 0.16, "Tail": 0.04 }, "expected_terminal_wealth": 384.1300016491731, "annualized_expected_terminal_wealth": 0.13456741963153296, "probability_weighted_annualized_return": 0.10756073466601901, "representative_point_loss_probability": 0.2, "benchmark_terminal_wealth": 296.2384031031345, "expected_net_gain": 130.4200016491731, "expected_holding_return": 0.5140514825949829, "arithmetic_fields_derived_from_frozen_inputs": [ "expected_net_gain", "expected_holding_return" ] }, "mixed_retail_pressure": { "identity": "weighted representative-point discrete approximation; not identified conditional means", "weights": { "Bull": 0.27, "Base": 0.41, "Bear": 0.26, "Tail": 0.06 }, "expected_terminal_wealth": 339.3665227433541, "annualized_expected_terminal_wealth": 0.09257717616699845, "probability_weighted_annualized_return": 0.05849624773953117, "representative_point_loss_probability": 0.32, "benchmark_terminal_wealth": 296.2384031031345, "expected_net_gain": 85.65652274335409, "expected_holding_return": 0.3376158714412285, "arithmetic_fields_derived_from_frozen_inputs": [ "expected_net_gain", "expected_holding_return" ] } } }, "aws_low": { "prices": { "Bull": 501.9201160419391, "Base": 307.23516017809226, "Bear": 142.662843118597, "Tail": 32.729060876469404 }, "distributions": { "adopted": { "identity": "weighted representative-point discrete approximation; not identified conditional means", "weights": { "Bull": 0.31, "Base": 0.44, "Bear": 0.2, "Tail": 0.05 }, "expected_terminal_wealth": 320.9477281189046, "annualized_expected_terminal_wealth": 0.07417660466152975, "probability_weighted_annualized_return": 0.04260405124858831, "representative_point_loss_probability": 0.25, "benchmark_terminal_wealth": 296.2384031031345, "expected_net_gain": 67.23772811890458, "expected_holding_return": 0.2650180446923833, "arithmetic_fields_derived_from_frozen_inputs": [ "expected_net_gain", "expected_holding_return" ] }, "capital_pressure": { "identity": "weighted representative-point discrete approximation; not identified conditional means", "weights": { "Bull": 0.2, "Base": 0.42, "Bear": 0.3, "Tail": 0.08 }, "expected_terminal_wealth": 274.8399682888832, "annualized_expected_terminal_wealth": 0.024647981645059325, "probability_weighted_annualized_return": -0.013972336275786732, "representative_point_loss_probability": 0.38, "benchmark_terminal_wealth": 296.2384031031345, "expected_net_gain": 21.12996828888319, "expected_holding_return": 0.08328393949344992, "arithmetic_fields_derived_from_frozen_inputs": [ "expected_net_gain", "expected_holding_return" ] }, "platform_durable": { "identity": "weighted representative-point discrete approximation; not identified conditional means", "weights": { "Bull": 0.37, "Base": 0.43, "Bear": 0.16, "Tail": 0.04 }, "expected_terminal_wealth": 341.9567791461314, "annualized_expected_terminal_wealth": 0.0951087194514817, "probability_weighted_annualized_return": 0.06691970990061341, "representative_point_loss_probability": 0.2, "benchmark_terminal_wealth": 296.2384031031345, "expected_net_gain": 88.24677914613139, "expected_holding_return": 0.3478253878291411, "arithmetic_fields_derived_from_frozen_inputs": [ "expected_net_gain", "expected_holding_return" ] }, "mixed_retail_pressure": { "identity": "weighted representative-point discrete approximation; not identified conditional means", "weights": { "Bull": 0.27, "Base": 0.41, "Bear": 0.26, "Tail": 0.06 }, "expected_terminal_wealth": 300.54092986776476, "annualized_expected_terminal_wealth": 0.052911001655461254, "probability_weighted_annualized_return": 0.017289746862522194, "representative_point_loss_probability": 0.32, "benchmark_terminal_wealth": 296.2384031031345, "expected_net_gain": 46.83092986776475, "expected_holding_return": 0.18458448570322328, "arithmetic_fields_derived_from_frozen_inputs": [ "expected_net_gain", "expected_holding_return" ] } } }, "retail_low": { "prices": { "Bull": 518.7315541002855, "Base": 316.295337911165, "Bear": 153.7165513620935, "Tail": 32.3000212248235 }, "distributions": { "adopted": { "identity": "weighted representative-point discrete approximation; not identified conditional means", "weights": { "Bull": 0.31, "Base": 0.44, "Bear": 0.2, "Tail": 0.05 }, "expected_terminal_wealth": 332.33504178566096, "annualized_expected_terminal_wealth": 0.08563661920994514, "probability_weighted_annualized_return": 0.05434228003363471, "representative_point_loss_probability": 0.25, "benchmark_terminal_wealth": 296.2384031031345, "expected_net_gain": 78.62504178566095, "expected_holding_return": 0.3099012328471915, "arithmetic_fields_derived_from_frozen_inputs": [ "expected_net_gain", "expected_holding_return" ] }, "capital_pressure": { "identity": "weighted representative-point discrete approximation; not identified conditional means", "weights": { "Bull": 0.2, "Base": 0.42, "Bear": 0.3, "Tail": 0.08 }, "expected_terminal_wealth": 285.2893198493603, "annualized_expected_terminal_wealth": 0.03635196615726377, "probability_weighted_annualized_return": -0.001923265807132167, "representative_point_loss_probability": 0.38, "benchmark_terminal_wealth": 296.2384031031345, "expected_net_gain": 31.579319849360303, "expected_holding_return": 0.12447014248299348, "arithmetic_fields_derived_from_frozen_inputs": [ "expected_net_gain", "expected_holding_return" ] }, "platform_durable": { "identity": "weighted representative-point discrete approximation; not identified conditional means", "weights": { "Bull": 0.37, "Base": 0.43, "Bear": 0.16, "Tail": 0.04 }, "expected_terminal_wealth": 353.8243193858345, "annualized_expected_terminal_wealth": 0.1065396937848615, "probability_weighted_annualized_return": 0.07855824157161317, "representative_point_loss_probability": 0.2, "benchmark_terminal_wealth": 296.2384031031345, "expected_net_gain": 100.11431938583448, "expected_holding_return": 0.39460139287310114, "arithmetic_fields_derived_from_frozen_inputs": [ "expected_net_gain", "expected_holding_return" ] }, "mixed_retail_pressure": { "identity": "weighted representative-point discrete approximation; not identified conditional means", "weights": { "Bull": 0.27, "Base": 0.41, "Bear": 0.26, "Tail": 0.06 }, "expected_terminal_wealth": 311.64291277828846, "annualized_expected_terminal_wealth": 0.06460052109503844, "probability_weighted_annualized_return": 0.02938465337265891, "representative_point_loss_probability": 0.32, "benchmark_terminal_wealth": 296.2384031031345, "expected_net_gain": 57.932912778288454, "expected_holding_return": 0.22834304039371123, "arithmetic_fields_derived_from_frozen_inputs": [ "expected_net_gain", "expected_holding_return" ] } } }, "both_low": { "prices": { "Bull": 464.20851614523303, "Base": 276.08436489693173, "Bear": 125.99637153401603, "Tail": 25.45623894833421 }, "distributions": { "adopted": { "identity": "weighted representative-point discrete approximation; not identified conditional means", "weights": { "Bull": 0.31, "Base": 0.44, "Bear": 0.2, "Tail": 0.05 }, "expected_terminal_wealth": 291.8538468138921, "annualized_expected_terminal_wealth": 0.043552908344197894, "probability_weighted_annualized_return": 0.01050543847442972, "representative_point_loss_probability": 0.25, "benchmark_terminal_wealth": 296.2384031031345, "expected_net_gain": 38.14384681389211, "expected_holding_return": 0.1503442781675619, "arithmetic_fields_derived_from_frozen_inputs": [ "expected_net_gain", "expected_holding_return" ] }, "capital_pressure": { "identity": "weighted representative-point discrete approximation; not identified conditional means", "weights": { "Bull": 0.2, "Base": 0.42, "Bear": 0.3, "Tail": 0.08 }, "expected_terminal_wealth": 248.63254706182948, "annualized_expected_terminal_wealth": -0.006134289196877973, "probability_weighted_annualized_return": -0.0465101641443272, "representative_point_loss_probability": 0.38, "benchmark_terminal_wealth": 296.2384031031345, "expected_net_gain": -5.077452938170524, "expected_holding_return": -0.020012821481890875, "arithmetic_fields_derived_from_frozen_inputs": [ "expected_net_gain", "expected_holding_return" ] }, "platform_durable": { "identity": "weighted representative-point discrete approximation; not identified conditional means", "weights": { "Bull": 0.37, "Base": 0.43, "Bear": 0.16, "Tail": 0.04 }, "expected_terminal_wealth": 311.6510968827928, "annualized_expected_terminal_wealth": 0.06460903062550782, "probability_weighted_annualized_return": 0.03506603435849147, "representative_point_loss_probability": 0.2, "benchmark_terminal_wealth": 296.2384031031345, "expected_net_gain": 57.94109688279278, "expected_holding_return": 0.22837529810725932, "arithmetic_fields_derived_from_frozen_inputs": [ "expected_net_gain", "expected_holding_return" ] }, "mixed_retail_pressure": { "identity": "weighted representative-point discrete approximation; not identified conditional means", "weights": { "Bull": 0.27, "Base": 0.41, "Bear": 0.26, "Tail": 0.06 }, "expected_terminal_wealth": 272.8173199026991, "annualized_expected_terminal_wealth": 0.02234686284916987, "probability_weighted_annualized_return": -0.014897488794448313, "representative_point_loss_probability": 0.32, "benchmark_terminal_wealth": 296.2384031031345, "expected_net_gain": 19.107319902699118, "expected_holding_return": 0.07531165465570577, "arithmetic_fields_derived_from_frozen_inputs": [ "expected_net_gain", "expected_holding_return" ] } } } }, "identity_notes": { "market_debt": "期末有息借款余额（模型口径），不是未来债券市场公允价值", "cash": "期末账面可用现金/证券模型余额，经营保留未被支出", "finance_claims": "融资租赁及融资义务；与有息借款分列", "investment_net": "已扣模型实现税的非经营投资；不是流动性储备", "other_claims": "模型取0；未作全体潜在权利为零的审计结论", "pricing_range": "同一经营/资金路径的定价参数范围；不是置信区间或条件支持", "probability": "主观粗判断，不是统计后验；按钮操作不新增研究证据", "quarters": "每季已继承此前融资；融资前余额不是全期无融资轨迹，也不保证季内资金充足", "quote_vs_cutoff": "9月18日参考进入价格，9月20日研究信息截止；无实际成交或仅用9月18日信息的样本外回测声明。", "share_count_proxy": "11.0274十亿股是冻结模型规划代理：10.783普通股 + 0.2444 outstanding RSU；公司另披露普通股加全部 outstanding stock awards 对应股份约11.0十亿股。该代理不是官方完全稀释股数，也不是EPS加权平均股数。" }, "teaching_examples": { "mixed_equity_bridge": { "industrial_ev": 600, "industrial_debt": 120, "bank_equity": 200, "bank_debt_already_in_equity": 1000, "nonoperating_cash": 30, "parent_debt": 40, "shares": 10, "common_equity": 670, "price": 67, "identity": "纯教学设定；不是任何公司披露" }, "brier": { "hypothetical_observation": "Base", "adopted": 0.4522, "capital_pressure": 0.4728, "normalization": "sum over four classes, no one-half; range0–2" } } } }, "reading_resolution": "Use public access.uri and its specified complete unit; the teaching runtime must actually fetch it. Site candidates are not claimed publicly published.", "experiment_ids": [ "EXP-P31-RISK-REWARD" ] } ``` ## Supplied entry 一张列着Bull、Base、Bear、Tail四个价格的表，还没有完成风险回报分析。我们还要知道：这些结果属于哪一天，投资者在途中实际付出或收到什么，各类有多少权重，哪些损失可能被代表点遮住，以及有没有资金压力迫使我们到不了终点。 本篇把前面两条支线合起来：P30提供同日期普通股结果，P05提供公司状态与权重。我们沿用2026年9月20日的 Amazon 历史研究，不更新报价或重新估值。读完之后，你应能重算一组结果分布，并解释结论为何会因经营、定价、概率或融资条件的不同而翻转。[^case] ## 1. 先站在同一个股东的现金视角 本案例假设投资者于2026年9月18日以253.71美元买入一股，在2029年12月31日按相应条件值退出，中途分配和个人追加均取零。按实际日期/365.25计算，期间为1200/365.25，即3.2854209446年。没有把这个时间简称为“三年”后直接套立方根。 9月18日是研究采用的参考买入价，而信息截止为9月20日；这不是宣称当时已经成交，也不是仅凭9月18日可得信息完成的样本外回测。 若一般情况下买入付款为 $P_0$，期间实际收到分配 $D_i$、追加付款 $A_j$，期末剩余权益售价 $P_T$，未做再投资合并之前，净损益为 $$ \Pi=P_T+\sum_iD_i-P_0-\sum_jA_j. $$ 各笔现金有日期。相同净损益，早收到钱与晚收到钱对持有回报可能不同。存在复杂出入金时，应回到日期现金表，不能仅用 $P_T/P_0-1$。IRR是这条现金路径的结果，不用来生成期末条件价格；多根或无合理根时应保留原流水，而不是挑一个好看的解。[^method] 企业自己的资本开支不是股东个人追加；企业借钱或向其他人增发，也不是原股东自动再付款。Tail中的救援增发已经进入公司现金和期末股数，未参与认购的原股东通过稀释承担影响。若再给该股东虚构一笔个人出资，会重复压低回报。同样，回购已经减少公司现金并改变股份数，不能在每股价值之外另加一份“回购收益”。 ## 2. 从状态集合到结果分布 令 $S_s$ 为互斥穷尽的四类公司状态，$p_s=P(S_s)$，$W_T$ 为同一资金安排下的终点财富。完整分布应满足 $$ P(W_T\le w)=\sum_sp_sP(W_T\le w\mid S_s), \qquad E[W_T]=\sum_sp_sE[W_T\mid S_s]. $$ 第一个式子把每类内的分布混合起来，第二个式子是全期望公式；期望公式要求财富可积。实际研究可能还不能识别每类的完整分布，于是只提供代表点 $w_s$。此时 $\widehat E[W_T]=\sum_sp_sw_s$ 是**四点近似**；除非代表点确为条件均值，否则不要把近似的帽子悄悄去掉。 本案例的四个代表点如下。中途现金为零，所以该情景的一股终点售价也是终财富。[^case] | 状态 | 采用权重 | 2029年末每股条件值 | 持有期回报 | |---|---:|---:|---:| | Bull | 31% | 556.443154 | 约+119.32% | | Base | 44% | 347.446133 | 约+36.95% | | Bear | 20% | 170.383023 | 约−32.84% | | Tail | 5% | 39.572843 | 约−84.40% | 因此四点近似期望终财富为 $$ \begin{aligned} \widehat E[W_T] &=0.31(556.443154)+0.44(347.446133)\\ &\quad+0.20(170.383023)+0.05(39.572843)\\ &\approx361.428923. \end{aligned} $$ 对应期望净收益107.718923、期望持有期回报42.457500%。这些“期望”是基于给定粗权重和代表点的模型量，不保证哪一次投资会得到平均结果。 ## 3. 两种年化为什么不相等 把期望终财富换成年化尺度，得到 $$ r_{EW}=\left(\frac{361.428923090674}{253.71}\right)^{1/3.285420944559}-1 =11.372500\%. $$ 若先把每个情景年化，再按概率平均，则得到 $$ \bar r=\sum_sp_s\left[\left(\frac{w_s}{253.71}\right)^{1/T}-1\right] =8.347799\%. $$ 一个是在问“期望终财富相当于怎样的恒定复合速度”，另一个是在平均各条路径的年化数，两者的研究对象不同。它们也都不是已经实现的长期几何复合回报。 数学上，当前 $T>1$，函数 $f(x)=(x/P_0)^{1/T}-1$ 在非负财富上凹，所以 $f(\sum p_s w_s)\ge\sum p_sf(w_s)$。当结果并不相同且权重为正时，通常严格不等。若观察期小于一年，幂次改变，这个不等式方向也不能原封不动搬用。真正稳妥的做法，是先说清对象，再按实际日期计算。 ## 4. 25%的亏损权重究竟是什么 Bear和Tail代表点低于253.71，因此相应权重相加为25%。这只是“**代表点亏损权重**”。真正的亏损概率应是 $$ P(W_T ## 5. 把不同分歧分开比较 先固定四条经营与资金路径、固定条件价格，只改变概率，可以得到： | 概率判断 | 期望终财富 | 期望终财富年化 | 概率平均路径年化 | 四点亏损权重 | |---|---:|---:|---:|---:| | adopted | 361.428923 | 11.3725% | 8.3478% | 25% | | capital_pressure | 311.496741 | 6.4449% | 2.7394% | 38% | | platform_durable | 384.130002 | 13.4567% | 10.7561% | 20% | | mixed_retail_pressure | 339.366523 | 9.2577% | 5.8496% | 32% | 接着固定经营路径，分别选择两组业务的低倍数参照。仍是同一公司的既定盈利，只改变市场在该状态下愿意给予的定价： | 定价框架 | 采用权重下期望终财富 | 年化 | 资本压力权重下期望终财富 | 年化 | |---|---:|---:|---:|---:| | 原代表定价 | 361.428923 | 11.3725% | 311.496741 | 6.4449% | | AWS低倍数 | 320.947728 | 7.4177% | 274.839968 | 2.4648% | | 非AWS低倍数 | 332.335042 | 8.5637% | 285.289320 | 3.6352% | | 两组均低倍数 | 291.853847 | 4.3553% | 248.632547 | −0.6134% | 四种定价乘四套概率，共有16组已保存的结果。它们不是16种新经营预测。真正改变需求、成本或资本的具名经营替代，在P04实验中单独查看；不要把一个“悲观开关”同时改利润、倍数和权重，却不说明经济理由。 历史研究另用4.83%的三年美债收益率作常利率再投比较，将253.71延长至同一终点，得到296.238403。它没有指定一只完全匹配3.2854年期限的证券，也没有完整处理票息、再投资与交易税费，因而是近似资本用途基准，不是本公司的折现率或必要回报率。 可以看到，两组低倍数下的采用分布终财富291.853847已经低于这一近似基准；再采用资本压力权重则低于本金。这个结果说明结论依赖哪些条件，并不证明这些不利条件必然同时发生。 ## 6. 概率要改变多少，比较才会翻转 我们还可以明确一次有边界的反向问题：固定所有价格与Base/Tail权重，只把 $\delta$ 从Bull转到Bear。新的期望财富为 $$ \widehat E_\delta[W_T]=\widehat E_0[W_T]-\delta(w_{Bull}-w_{Bear}). $$ 若要与指定目标 $K$ 相等，则 $$ \delta=\frac{\widehat E_0[W_T]-K}{w_{Bull}-w_{Bear}}, \qquad 0\le\delta\le p_{Bull}. $$ 对近似国债终值296.238403，转移约16.886105个百分点；对本金253.71，转移约27.902110个百分点。它们都在原Bull31%的可转移范围内。若分母为零或所需转移超过可用权重，就不能宣称这条特定转移路径上存在可行翻转。 这两个数不等于市场隐含概率，也不是所有可能概率变化的通用阈值。只移动Tail，或同时改变条件价格，会产生不同结果。反向问题的价值在于把“我对哪个判断还不放心”变得具体，而不是给一个单一股价赋予唯一信念。 ## 7. 操作与迁移
[打开Risk-Reward实验](/notebook/labs/p-bcd/interactions.html#EXP-P31-RISK-REWARD)。先只切换概率，保持定价不变；再只切换定价。观察终财富、两种年化与亏损权重哪些变化、哪些不变。图中两条参考线分别标出本金和近似国债终财富，图下注明其身份。无脚本时，上述两表就是默认和主要对照结果，完整16组表也保留在实验静态区。 最后返回P04的现金路径：高终值并不能支付之前已经到期的账款。这里的终点普通股价值依赖条件融资路径能够走通。即使某状态的利润最终恢复，季度内部融资关闭、抵押分割或资金晚到也可能迫使调整。这一层不应被期望终财富的单一均值盖住。 **解释题。** 某状态权重40%，代表点高于买入价。为什么不能直接认为这40%全部是盈利概率？ **解析。** 代表点没有描述类内分布。若该类有一半结果亏损，其对总亏损概率贡献就是20%；若全部盈利才贡献零。缺少类内权重时应保留未知或有证据的界限，不能从一个代表点反推整类。当前AMZN参数区间不具完整支持身份，不能拿来填补这个缺口。 **计算题。** 另一个纯教学投资本金100，两个互斥状态权重各50%。第一类总是终值150；第二类内部以各50%得到80或120。求期望终值与真正亏损概率，并比较只用第二类中点100的两点近似。 **解析。** 第二类条件均值为100，总期望 $0.5\times150+0.5\times100=125$。真正亏损概率为 $0.5\times0.5=25\%$。若只用150与100两个点，期望恰好仍是125，但严格亏损点权重为零。即使代表点碰巧等于条件均值，它也不一定保留亏损概率；均值信息不能代替分布。 **日期题。** 本金100，两年后股票卖得100，一年末还收过10股息。无再投资时净损益多少？若把股息在收到后按明确的5%利率投资一年，终财富又是多少？ **解析。** 无再投资净损益为10，现金日期是−100、+10、+100，不能仅据终股价说回报为零。若确实按5%再投，终财富为 $100+10\times1.05=110.5$。此时不能再把原10股息加一次。该5%是题目给定的现金安排，不用于股票估值；税费、再投资可得性亦按题目假设。 **结论题。** 两低倍数和资本压力权重下年化为−0.6134%，是否足以证明原研究“必然亏损”？ **解析。** 不足。它说明在这组具名条件和概率近似下，期望终财富略低于本金。我们应该检查低资本转化的定价解释、资本压力的证据及共同成立条件，而不是把敏感性结果当成事件已经发生。同样，原采用分布的11.3725%也不是回报保证。Risk-Reward的结论应保留条件、替代与途中资金，而不是只留下一个漂亮年化数。 [^case]: [CASE-AMZN-20260920](/zh/notebook/amzn-research-20260920/#case-amzn-distributions)，冻结报价、日期、四状态价格、四套权重和16组已算分布；资本用途比较沿同一历史版本，不使用现在报价。 [^method]: [日期股东结果短参考](/zh/notebook/conditional-pricing-common-equity-risk-reward/#pm-conditional-rr-dated-shareholder-results)。收益口径延续P02：外部出入金、公司内部资金与分红再投资分别记账。 ## Experiment inputs and static equivalents ```json [ { "id": "EXP-P31-RISK-REWARD", "title": "日期现金、结果分布与Risk-Reward", "anchor": "p31-experiment", "description": "用日期现金与同状态普通股结果合并粗权重，区分两种年化、代表点亏损及资金限制。", "inputs": { "pricing_id": { "allowed": [ "representative", "aws_low", "retail_low", "both_low" ], "default": "representative" }, "weight_id": { "allowed": [ "adopted", "capital_pressure", "platform_durable", "mixed_retail_pressure" ], "default": "adopted" }, "flip_target": { "allowed": [ "treasury", "capital" ], "default": "treasury" } }, "outputs": { "distribution": "ETW, net gain, HPR, annETW, mean path annual, representative loss mass, Tail representative loss", "flip": "fixed original probability transfer only" }, "units": { "money": "USD billion for company amounts; USD per share for outcomes", "shares": "billion", "probabilities": "fractions summing to one" }, "identity": "frozen dated research or explicitly marked bounded teaching arithmetic", "static_equivalent": { "reader": "https://ou-liu-red-sugar.github.io/zh/notebook/dated-cash-outcome-risk-reward/#p31-experiment", "lab": "https://ou-liu-red-sugar.github.io/notebook/labs/p-bcd/interactions.html#EXP-P31-RISK-REWARD", "without_javascript": "默认完整表和主要对照保留；不把参数规格当运行结果" }, "algorithm": "engine.distribution读取16个已有价格/权重对，复算所有字段；flip始终固定原repr/adopted，不随其他下拉框混算。", "boundaries": [ "未知定价/权重拒绝", "无类内支持故不发布true P(loss)", "严格亏损用<", "期间分配/追加0；其他现金例只在练习", "比较利率非估值折现" ], "default_values": { "identity": "weighted representative-point discrete approximation; not identified conditional means", "weights": { "Bull": 0.31, "Base": 0.44, "Bear": 0.2, "Tail": 0.05 }, "expected_terminal_wealth": 361.4289230906735, "annualized_expected_terminal_wealth": 0.11372500084263093, "probability_weighted_annualized_return": 0.08347799170226604, "representative_point_loss_probability": 0.25, "benchmark_terminal_wealth": 296.2384031031345, "expected_net_gain": 107.71892309067348, "expected_holding_return": 0.42457499937201315, "arithmetic_fields_derived_from_frozen_inputs": [ "expected_net_gain", "expected_holding_return" ] }, "inputs_uri": "https://ou-liu-red-sugar.github.io/notebook/labs/p-bcd/inputs.json" } ] ``` ## Sources - [Amazon：2026-09-20历史条件研究案例](https://ou-liu-red-sugar.github.io/zh/notebook/amzn-research-20260920/): 原研究的事实/分析代理、四条未来路径、5项具名替代、4套权重与16组已算分布。报价冻结，代表点不是条件均值。 - [业务状态下的条件定价、普通股桥与Risk-Reward](https://ou-liu-red-sugar.github.io/zh/notebook/conditional-pricing-common-equity-risk-reward/): 规定估值组、盈利/参照、普通股桥、状态权重和日期现金的输入输出与边界。 ## Content relations ```json [ { "from": "zh-p31", "relation": "part_of", "to": "portfolio-valuation", "reason": "主要 topic 归属" }, { "relation": "requires", "to": "zh-p05", "reason": "本篇承重步骤实际使用该能力", "required_competence": "能解释公司状态权重与证据身份", "from": "zh-p31" }, { "relation": "requires", "to": "zh-p30", "reason": "本篇承重步骤实际使用该能力", "required_competence": "能构造同日期普通股结果", "from": "zh-p31" }, { "relation": "uses_method", "to": "zh-pmconditionalrr", "reason": "调用短参考中本篇对应的输入输出与条件，不反向要求读完六篇", "from": "zh-p31" }, { "relation": "illustrated_by", "to": "zh-amzn-research-20260920", "reason": "固定日期案例；不新建第二个别名案例", "period": "2025Q4–2029", "cutoff": "2026-09-20", "from": "zh-p31" }, { "relation": "uses_method", "to": "zh-p02", "reason": "日期现金与回报定义在本文就地给出；P-A已交付，本包不重新发布", "scope": "正式站点接入时解析P02既有身份", "from": "zh-p31" }, { "from": "p31-experiment", "relation": "illustrated_by", "to": "EXP-P31-RISK-REWARD", "at_section": "p31-experiment", "reason": "用日期现金与同状态普通股结果合并粗权重，区分两种年化、代表点亏损及资金限制。" } ] ``` ## Related entries