香港Hong Kong
数据科学家 · 量化分析师 · 应用 AI 工程师
嗨，我是 Aylon。项目和研究笔记都在这里。
把杂乱的数据整理成能直接用的数据集。 Turning messy data into a dataset that just works.
研究方向Research interests从信号到组合再到归因，每一步都能复核。 From signal to portfolio to attribution — every step checkable.
研究方向Research interests把模型和文本做成可复现、可交接的流程。 Turning models and text into pipelines that others can run.
研究方向Research interests数据管道与模型评估、AI Agent 与评测框架、自动化交付 —— 把研究原型做成可复现、可追溯的流程。 Data pipelines and model evaluation, AI agents and evaluation frameworks, automated delivery — turning prototypes into reproducible, auditable processes.
风险计量、策略测试与组合优化 —— 用数据回答「这条策略在压力下还成立吗」。 Risk measurement, strategy testing and portfolio optimisation — answering whether a strategy still holds under stress.
参与学术研究项目，负责数据整理与实证分析；有论文发表。 Worked on academic research projects covering data preparation and empirical analysis; one paper published.
从原始数据到一组可检验的信号：先做诊断与合成，再看它在成本、风险与不同样本下是否还站得住。 From raw data to a set of testable signals: diagnostics and combination first, then whether it survives costs, risk and different samples.
把信号变成受约束的组合：权重上限、风险预算、换手与成本控制 —— 先定义能亏多少，再谈能赚多少。 Turning signals into a constrained portfolio: position limits, risk budgeting, turnover and cost control. Decide the downside first.
拆开收益来源：多少来自因子、多少来自风险暴露与交易成本；不成立的结论同样留档。 Breaking the return into its sources — factor, risk exposure, trading cost — and keeping a record of what did not hold.
投研RESEARCH投研项目集 · 信号与组合Quant Research Portfolio · Signals & Risk
横截面信号的完整流程 —— 从因子诊断、合成到稳健性检验。关键取舍在验证设计：宁可少报一个因子，也不留下一份换样本就反转的结论。 The full path for a cross-sectional signal — diagnostics, combination, robustness. The trade-off sits in validation design: better one fewer factor than a conclusion that flips on a different sample.
把信号变成受约束的组合：权重上限、风险预算、换手控制。先定义能亏多少，再谈能赚多少。 Turning signals into a constrained portfolio — position limits, risk budgeting, turnover control. Define the downside before the upside.
方法METHODS方法与模型知识库 · 统计 / ML / DL / LLMMethods & Models Knowledge Base · Stats / ML / DL / LLM
估计、假设检验、平稳性与时序建模 —— 这套工具决定了一个结论能不能被检验。 Estimation, hypothesis testing, stationarity and time-series modelling — the toolkit that decides whether a claim can be tested at all.
横截面建模、正则化与基线对比。重点不在模型多新，而在它相对基线多出了什么。 Cross-sectional modelling, regularisation and baselines. The question is not how new the model is, but what it adds over a baseline.
时序与横截面深度模型，以及训练与验证设计 —— 也会记录它相对传统因子模型没有优势的情况。 Sequence and cross-sectional deep models, plus training and validation design — including where they fail to beat classical factor models.
文本 → 情绪 / 事件因子 → 增量检验；哪些环节最容易制造虚假信号，同样写清楚。 Text to sentiment / event factors to incremental tests — and where spurious signal is most likely to creep in.
把杂乱的数据变成能直接用的东西：清洗、对齐、留痕，别人接手也能跑。 Turning scattered data into something usable — cleaning, aligning, leaving a trail, so someone else can run it.
训练只是开始 —— 重点是验证设计与基线对比：换个样本，这条结论还成不成立。 Training is the easy part — validation design and baselines decide whether a conclusion survives a different sample.
从信号到组合再到归因，最后把结论写成别人能复核的东西。 From signal to portfolio to attribution — then writing it up so someone else can check it.
把分散的资产配置文章整理成一条决策路径：先选基准，再分风险，处理执行，最后用 L1 形成可归因、可复核的闭环。 A single decision path through the allocation series: choose a benchmark, allocate risk, handle implementation and close the loop with L1.
进入专题地图（10 篇研究）→Open the series map (10 studies) →专题分四层：60/40 与永久组合定义比较尺子；全天候、风险平价与 1/N 讨论风险分配；再平衡、约束和负债口径处理执行；趋势覆盖与 L1 影子组合把观点、权重、成本、归因和版本治理连成一条流程。 Four layers connect the work: the 60/40 and Permanent Portfolio define the benchmark; All Weather, risk parity and 1/N examine risk allocation; rebalancing, constraints and liabilities address implementation; trend following and L1 connect views, weights, costs, attribution and governance.
结论：这个主题已经足够。下一步不是继续增加策略数量，而是统一比较口径、保留持续前向记录，并让每一篇文章都能落到一个明确的投资决策。 Conclusion: the topic is already sufficient. The next step is not more strategies, but aligned comparisons, a continuing forward record, and a clear investment decision behind every article.
一个公开多资产影子组合，用 8 个 ETF、221 个月检验 SAA/TAA、成本和归因。60/40 跑赢；留下的是可复核、可否决、可维护的投资流程。 A public multi-asset shadow portfolio tests SAA/TAA, costs and attribution over 221 months. The 60/40 wins; the durable output is an auditable investment process.
读研究案例（6 张图 · 风险与收益归因）→Read the case (6 figures · risk and return attribution) →L1 TAA 年化 5.20%、夏普 0.703；同期 60/40 为 8.43% 和 0.894。更重要的是：三只权益占资金 40%、贡献约 61% 的模型风险。政策冻结为 policy_v1，负结果保留，规则变更必须另开版本。
L1 TAA earned 5.20% a year with a 0.703 Sharpe; the 60/40 earned 8.43% and 0.894. More importantly, equities hold 40% of capital but drive roughly 61% of model risk. The policy is frozen as policy_v1, negative results are retained and rule changes require a new version.
再平衡每年多赚 0.9 个百分点，也每年放弃 0.9 个百分点——看你拿哪把尺子量。 Rebalancing earns 0.9 points a year and gives up 0.9 points a year — depending on which ruler you use.
读全文（9 张图 · 可拖容差带的交互）→Read the note (9 figures + interactivity) →用 1993-02 至 2025-09 共 392 个月的美国数据、8 条资产腿、4 个目标组合（2 / 4 / 8 / 8 条腿）与 8 种再平衡政策。分散化收益确实存在，而且与 Booth–Fama 的公式几乎完全吻合：60/40 理论 0.35% 对实测 0.33%，1/N 八腿 0.85% 对 0.88%，且随腿数上升。 392 monthly US observations from 1993-02 to 2025-09, eight asset legs, four target portfolios (two, four, eight and eight legs) and eight rebalancing policies. The diversification return is real and matches the Booth–Fama formula almost exactly: 0.35% predicted against 0.33% measured for a 60/40, 0.85% against 0.88% for 1/N — rising with the number of legs.
但同一份数据里，不再平衡比月频再平衡的年化高出 0.45–1.17 个百分点，因为不复权时权重会漂到赢家身上——60/40 三十三年后 91.9% 是股票。而按夏普排，年度再平衡在四个组合里全部胜出（0.69 对 0.65、0.79 对 0.73、0.60 对 0.56、0.64 对 0.58）。成本不是主角：放大十倍只再多损失 4–42 个基点；容差带从 1% 拉到 28% 换手单调下降，却没有一致的最优宽度。 But over the same data buy-and-hold beats monthly rebalancing by 0.45 to 1.17 points a year, because an untouched portfolio drifts into its winners — a 60/40 ends the sample 91.9% equities. Ranked by Sharpe, annual rebalancing wins in all four portfolios (0.69 against 0.65, 0.79 against 0.73, 0.60 against 0.56, 0.64 against 0.58). Cost is not the story: ten times the cost gives up only another 4–42 basis points, and widening the band from 1% to 28% lowers turnover monotonically without producing a consistent optimum.
资产端夏普垫底的组合，funding ratio 最大回撤只有 −2.4%——换成盈余端的尺子，排序整个换了一遍。 The worst portfolio on asset Sharpe drew its funding ratio down only 2.4% — change the ruler to surplus and the ranking is rewritten.
读全文（9 张图 · 可拖股票权重与久期目标的交互）→Read the note (9 figures + interactivity) →把一笔 20 年期定额年金（按当月 10 年期美国国债收益率折现，修正久期样本均值 9.00 年）当作负债，用 1993-02 至 2025-09 共 392 个月的美国数据检验七个组合。资产端夏普第一的 1/N 等权（0.71）在盈余端排第六；资产端垫底的久期匹配（0.26）盈余波动只有 2.15%、funding ratio 最大回撤只有 −2.4%。 A 20-year level annuity (discounted at the 10-year Treasury yield, average modified duration 9.00 years) becomes the liability for seven portfolios over 392 monthly US observations from 1993-02 to 2025-09. The best asset-only portfolio, 1/N at a 0.71 Sharpe, ranks sixth on surplus; the worst, duration matching at 0.26, runs 2.15% surplus volatility and a −2.4% maximum funding-ratio drawdown.
机制上，久期缺口与盈余波动是一条 U 形曲线：资产久期 0 年时 7.54%，调到 9 年（等于负债久期）降到 2.19%，再加久期重新上升。利率动 2 个百分点，缺口 −9 年的纯股组合 funding ratio 动 18%；久期匹配是 0。而可承受的风险随 funding ratio 系统性放宽：100% 时连 5% 的跌破容忍度都只允许 0% 股票，115% 时才允许 55%。同一个久期匹配组合的资产端回撤是 −30.1%——资产跌三成，盈余只跌 2.4%。 Mechanically, the duration gap and surplus volatility trace a U: 7.54% at zero asset duration, 2.19% at nine years — the liability's own duration — and rising again beyond. A two-point rate move shifts an all-equity portfolio's funding ratio by 18% against zero for duration matching. And the tolerable risk budget widens systematically with the funding ratio: at 100% even a 5% shortfall tolerance permits 0% equities; 55% needs 115%. The same duration-matched portfolio drew 30.1% down in assets while its surplus fell 2.4%.
样本内预期夏普 1.74 的最优化组合，实际拿到 0.54——和什么都不算的等权一模一样。 The portfolio that promised a 1.74 Sharpe delivered 0.54 — exactly what equal weighting earned for estimating nothing.
读全文（11 张图 · 可拖估计窗口的交互）→Read the note (11 figures + interactivity) →用 1990-02 至 2025-09 共 428 个月（样本外 392 个月）的美国数据，把 1/N 等权与八个优化器放在同一套规则下重跑：1/N 年化 5.88%、波动 6.4%、最大回撤 −25.1%、夏普 0.54，1 元变 6.47 元。八个优化器里三个赢、一个打平、四个输，而它没有估任何一个参数。 428 monthly US observations from 1990-02 to 2025-09 (392 out of sample) re-run 1/N against eight optimisers on one set of rules: 5.88% a year, 6.4% volatility, a −25.1% drawdown, a 0.54 Sharpe and 6.47× over the period. Three optimisers beat it, one ties and four lose — and it estimates nothing at all.
最锋利的一处在这里：样本最大夏普组合每年 1 月都算出一个平均 1.74 的夏普，实际拿到 0.54；九个方法里「预期」与「实现」的相关性最好只有 0.04。它不是因为算错，而是因为假设历史会重演。收缩估计能把最小方差从 0.11 修到 0.38，修不到 1/N 之上；换估计窗口（12–120 个月）、换资产数（2–8 条腿）都不改变排序。优化器的价值是条件性的——2008 年最小方差只跌 0.7%（1/N 跌 24.6%），而高通胀那三年八个优化器里只有一个赚到钱。 The sharpest point sits here: sample max-Sharpe computed an average 1.74 Sharpe every January and delivered 0.54; across nine methods the best promise-to-delivery correlation is 0.04. It is not miscalculating — it is assuming the history repeats. Shrinkage lifts minimum variance from 0.11 to 0.38 but not past 1/N, and neither the estimation window (12–120 months) nor the number of legs (2–8) changes the ordering. The optimiser's value is conditional: minimum variance lost 0.7% in 2008 against 1/N's 24.6%, while in three years of high inflation only one of the eight made money.
按风险分配而不是按资金分配——机制确实成立，代价是收益。它没跑赢 60/40，也没赢过最笨的四等分。 Allocate by risk instead of by money: the mechanism works, the return does not. It beats neither a 60/40 nor a naive four-way split.
读全文（11 张图 · 可拖杠杆与融资成本的交互）→Read the note (11 figures + interactivity) →用 1993-02 至 2025-09 共 392 个月的美国数据，把股票、长债、黄金、商品四条腿做成等风险贡献组合（每年 1 月按最近 36 个月协方差重解权重）：年化 7.40%、波动 7.2%、最大回撤 −22.5%、夏普 0.69，32.7 年 1 元变 10.3 元。同期 60/40 是 8.70% / −27.0% / 0.70，四等分四资产是 7.95% / 夏普 0.73——它确实更平，但更平不等于更高。 392 monthly US observations from 1993-02 to 2025-09 turn stocks, long bonds, gold and commodities into an equal-risk-contribution portfolio: 7.40% a year, 7.2% volatility, a −22.5% drawdown, a 0.69 Sharpe and 10.3× over 32.7 years. Over the same window a 60/40 earned 8.70% with a −27.0% drawdown, and a naive four-way split earned 7.95% with a 0.73 Sharpe. Flatter, yes — not higher.
机制本身是干净的：60/40 里 60% 的钱扛着 93.5% 的风险，等风险贡献解把它拍到 27.3 / 21.7 / 24.5 / 26.6。代价藏在别处——解出来的权重平均只离 25% 约 6.5 个百分点，所以「优化」输给了不优化；要补回那 1.3 个百分点就得上杠杆，而把融资利差压到 0，1.5 倍版年化 8.53% 仍追不平 60/40 的 8.70%，2022 年反而跌得更深（−21.3% 对 −18.1%）。273 个滚动十年窗口里它只赢 98 个，优势几乎全在 2003–2012 那一段。 The mechanism itself is clean: 60% of a 60/40's money carries 93.5% of its risk, and the equal-risk solution flattens that to 27.3 / 21.7 / 24.5 / 26.6. The cost hides elsewhere — the solved weights sit only about 6.5 points away from 25%, which is why optimising loses to not optimising. Buying the missing 1.3 points back needs leverage, and even at a zero funding spread a 1.5× version earns 8.53%, still short of the 60/40's 8.70%, while falling further in 2022 (−21.3% against −18.1%). Of 273 rolling ten-year windows it wins only 98, with the edge concentrated in 2003–2012.
它是行业基准，但不是最优：40–50% 的夏普一样，最大回撤却小 5.5 个百分点。真正让它崩的是股债同跌。 The industry benchmark, not the optimum: 40–50% earns the same Sharpe with a 5.5-point smaller drawdown. What actually breaks it is stocks and bonds falling together.
读全文（10 张图 · 可拖股票权重的交互）→Read the note (10 figures + interactive stock-weight slider) →用 1990-01 至 2025-09 共 428 个月的美国数据回测：年化 9.09%、波动 9.1%、最大回撤 −27.0%、夏普 0.70，35.7 年终值 22.3 倍。但 60% 这个数字恰好落在最差的一段：夏普峰值在 40%，40–50% 是一条平台（0.72，回撤只 −21.5%）；从 50% 加到 60%，回撤跳 5.5 个百分点，年化只多 0.6 个百分点。归因很干净：股票贡献 7.08、中债 2.06，合计 9.14 对几何 9.09。 428 monthly US observations from 1990-01 to 2025-09: 9.09% a year, 9.1% volatility, a −27.0% drawdown, a 0.70 Sharpe and 22.3× terminal wealth over 35.7 years. Sixty percent sits in the worst stretch of the curve — the Sharpe peaks at 40%, and 40–50% is a plateau (0.72, drawdown only −21.5%). Going from 50% to 60% adds 5.5 points of drawdown for 0.6 points of return. The attribution is clean: stocks 7.08 and bonds 2.06, 9.14 against a 9.09 geometric.
真正让它失效的是股债同跌：全样本相关性 −0.04，但 CPI 高于 5% 的 33 个月里翻到 +0.38——2022 年两条腿各跌 18.1%，13.5% 的月份两条腿同时下跌。修补方案里最便宜的是把 10% 挪给黄金：夏普 0.70 → 0.76、回撤 −27.0% → −22.7%，代价是终值少 4.2%；加商品（0.72）和加现金（0.71）都不如它。1.5 倍杠杆把年化推到 11.75%，代价是回撤 −39.0%——杠杆只放大结果，不改变夏普。 What breaks it is correlation: −0.04 over the full sample, but +0.38 across the 33 months with CPI above 5%. Both legs lost 18.1% in 2022, and 13.5% of all months saw both fall. The cheapest repair is shifting 10% into gold — Sharpe 0.70 → 0.76, drawdown −27.0% → −22.7%, at a 4.2% cost to terminal wealth; commodities (0.72) and cash (0.71) are worse. Levering 1.5× lifts the return to 11.75% and the drawdown to −39.0% — leverage scales the outcome, not the Sharpe.
命中率 53% 的信号是真的，但做成多空却跑不赢 60/40——问题在做空那条腿。它真正买到的是坏日子的凸性。 The 53% hit rate is real, but the long-short version still loses to a 60/40 — the short leg is the problem. What it actually buys is downside convexity.
读全文（7 张图 · 可拖目标波动率的交互）→Read the note (7 figures + interactive) →用 11 个 ETF、4,931 个交易日（2008-04 → 2026-10）检验跨资产时序动量。信号本身有效：方向命中率稳定在 53%，30 组参数全部为正，方向反转后毛夏普 −0.22。但组合结果是：多空年化 3.49% / 夏普 0.38，只做多 6.15% / 0.58，同期 60/40 是 8.26% / 0.75。 Eleven ETFs and 4,931 trading days test cross-asset time-series momentum. The signal works — a 53% direction hit rate, all 30 parameter sets positive, and −0.22 when the sign is reversed. Yet long-short earns 3.49% a year with a Sharpe of 0.38, long-only 6.15% / 0.58, and the 60/40 8.26% / 0.75.
把组合简化成 1/N 等权、只改方向用法，答案就清楚了：多空毛夏普 0.15、只做多 0.56、永远做多 0.50——价值来自「在下跌前离场」，不是「在下跌中做空」。趋势需要的不是会波动的资产，而是会跌的资产。它真正的用处写在条件收益里：标普最差 10% 的交易日，日均跌幅只有 60/40 的八分之一，2022 年 +13.9% 对 −16.6%。成本放大十倍仍为正，但 ETF 形式容量只有 50 万美元——要上规模必须走期货。 Simplify to equal weights and only change the use of direction: long-short earns a gross Sharpe of 0.15, long-only 0.56 and always-long 0.50. The value comes from leaving before declines, not from shorting them — trend needs assets that can fall. Its real use shows up in conditional returns: one eighth of the 60/40's loss on the worst 10% of days, and +13.9% in 2022 against −16.6%. Costs are not the constraint, but ETF capacity is only $0.5m — size requires futures.
股、长债、黄金、现金各 25%：夏普 0.75 是四个组合里最高的，最大回撤 −15.5% 最浅——但 CPI 高于 5% 的 26 个月里它是 −2.8%，黄金腿 −2.95%。 25% each in stocks, long bonds, gold and cash: the highest Sharpe of the four (0.75) and the shallowest drawdown (−15.5%) — yet it lost 2.8% a year across the 26 months with CPI above 5%, with gold at −2.95%.
读全文（8 张图 · 可拖黄金权重 + 播放历史）→Read the note (8 figures + animated gold-weight slider) →用 1990-01 至 2025-09 共 428 个月的美国数据检验永久组合：年化 7.18%、波动 5.8%、最大回撤 −15.5%、夏普 0.75；同期 60/40 是 9.09% / 9.1% / −27.0% / 0.70，全天候 7.90% / 7.6% / −21.7% / 0.68。它用 1.9 个百分点的年化，买了 11.5 个百分点的回撤，而且对起点最不敏感（七个起点年化 6.8%–8.5%）。 428 monthly US observations: 7.18% a year, 5.8% volatility, a −15.5% maximum drawdown and a Sharpe of 0.75, against 9.09% / 9.1% / −27.0% / 0.70 for a 60/40 and 7.90% / 7.6% / −21.7% / 0.68 for All Weather. It trades 1.9 points of return for an 11.5-point improvement in drawdown.
真正的机制不是「抗通胀」，而是四等分的资金意外地做成了等风险：25% 的资金对应风险贡献 37.5 / 33.9 / 28.4 / 0.2，因为三条腿的长期波动率都在 12–15%，而现金只有 0.7%。对照全天候宣称的「四个环境各 25% 风险」，实际是 32.4 / 53.5 / 10.5 / 2.4 / 1.2。它最亮的一年是 2008 年（−0.3%），最暗的一年是 2022 年（−11.9%），全部回撤都发生在 2021-12 至 2022-09。 The real mechanism is not inflation protection but that an even split of money turns out to be very nearly an even split of risk: 25% each produces risk contributions of 37.5 / 33.9 / 28.4 / 0.2, because the three risky legs all have volatilities of 12–15% while cash has 0.7%. All Weather's promised "25% of risk per environment" actually runs 32.4 / 53.5 / 10.5 / 2.4 / 1.2. Its best year was 2008 (−0.3%) and its worst 2022 (−11.9%), with the entire drawdown falling between December 2021 and September 2022.
它确实更稳（回撤 −22.3% 对 −29.6%），但 35 年没跑赢 60/40，而且 40% 的长债贡献了 53.5% 的风险。 It is genuinely steadier (−22.3% drawdown against −29.6%) — but over 35 years it did not beat a 60/40, and long bonds carry 53.5% of the risk.
读全文（6 张图 · 可拖权重的交互）→Read the note (6 figures + interactive weight slider) →用 1990-01 至 2025-09 共 428 个月的美国数据检验全天候的公开描述（30% 股 / 40% 长债 / 15% 中债 / 各 7.5% 黄金与商品）：年化 7.6%、波动 7.6%、最大回撤 −22.3%；同期 60/40 是 8.9% / 9.2% / −29.6%。它用 1.3 个百分点的年化，买了 7 个百分点的回撤改善，夏普并不占优（0.64 对 0.68）。
428 monthly observations test the public description of All Weather: 7.6% a year, 7.6% volatility, −22.3% maximum drawdown, against 8.9% / 9.2% / −29.6% for a 60/40. It trades 1.3 points of return for a seven-point improvement in drawdown, and Sharpe is no better.更关键的是它并没有做到「环境中性」：40% 的长债贡献了 53.5% 的风险，商品腿只有 1.2%；按失业率与通胀方向划分的四个环境里，它只在「增长下降」的两格追平或略胜 60/40。它是一台把风险从股票挪到债券的机器，而不是一台消除环境依赖的机器。 It is not environment-neutral either: long bonds carry 53.5% of the risk while commodities carry 1.2%, and across the four growth × inflation cells it only matches the 60/40 when growth falls. It moves risk from equities to bonds rather than removing dependence on the environment.
股票 8.4%、债券 1.9%、现金只有 0.1%——「投资能跑赢通胀」说的是某一类投资，不是所有投资。 Equities 8.4%, bonds 1.9%, cash just 0.1% — "investing beats inflation" describes some investments, not all of them.
读全文（6 张图 · 可拖持有期的交互）→Read the note (6 figures + interactive horizon) →用 1990 年以来 432 个月的美国数据，把五类资产放到同一把尺子（购买力）上：最初的 100 元，现金 36 年后只剩 102 元（名义 270 元，差额全被通胀吃掉）；债券 200 元；标普 500 全收益 1,850 元。年化实际收益：股票 8.4%、60/40 6.2%、黄金 4.0%、债券 1.9%、现金 0.1%。 432 months of US data on one yardstick: 100 units in cash ends at 102 after inflation (270 nominal), bonds at 200, the S&P 500 total return at 1,850. Real annualised: equities 8.4%, 60/40 6.2%, gold 4.0%, bonds 1.9%, cash 0.1%.
更反直觉的是期限那一层：股票、黄金、60/40 持有 20 年的滚动窗口里没有一个是负的实际收益，而现金持有 20 年仍有 59.9% 跑输通胀——拉长期限能救股票，救不了现金。2022 年通胀 6.5% 时五类资产实际收益全为负，连最抗跌的现金也亏了 4.7%；它们与通胀的月度相关系数全部贴近零。把「长期购买力」和「当期对冲」当成两件事，才不会用错。 The horizon layer is stranger still: no twenty-year window lost money in real terms for equities, gold or the 60/40, while cash still trailed inflation in 59.9% of its twenty-year windows. In 2022 every asset lost in real terms. Keep long-run purchasing power and inflation hedging as two separate questions.
「错过最好的 10 天，收益腰斩」只引用了对自己有利的一半——躲过最差 10 天的幅度还更大。 "Miss the ten best days and your return halves" quotes only half the evidence: avoiding the ten worst moves the number further.
读全文（6 张图 · 可拖天数的交互）→Read the note (6 figures + interactive slider) →用标普 500 从 1970 年至今 14,309 个交易日复核这句话：全仓年化 8.10%，剔除最好的 10 天降到 6.52%——数字没错。但剔除最差的 10 天，年化升到 10.12%，幅度还更大（+2.02 vs −1.58 个百分点）。 On 14,309 trading days since 1970: buy-and-hold compounds at 8.10%, and removing the ten best days cuts it to 6.52% — the arithmetic is right. But removing the ten worst lifts it to 10.12%, a bigger move (+2.02 versus −1.58 points).
它真正证明的是「精确择时非常值钱」，而不是「择时不可能」。而且这个极端情形落在随机分布的第 0 百分位——随机剔除 10 天，年化几乎不变（8.09%）。真正的论据是不可分性：最好的 10 天里有 8 天，离某个「最差 10 天」不超过 15 个交易日；最好的 20 天平均年化波动 66%、平均距高点 −33%，和坏日子住在同一栋楼里。 What it proves is that precise timing would be very valuable, not that timing is impossible. And the extreme case sits at the 0th percentile of a random distribution — removing ten random days barely changes anything (8.09%). The real argument is inseparability: eight of the ten best days fall within fifteen trading days of one of the ten worst.
58 年看黄金确实跑赢通胀（实际购买力 12.5 倍）——但 1980 年买在高点的人，要等到 2025 年才回本。 Over 58 years gold did beat inflation — but a January 1980 buyer waited until 2025 to break even.
读全文（7 张图 · 可拖权重的交互）→Read the note (7 figures + interactive weight slider) →用 1968 年以来的伦敦金价和美国 CPI（703 个月）检验「黄金抗通胀」：长期它是对的——名义价格涨 122 倍，通胀只涨 9.8 倍，实际购买力 12.5 倍。但 1980 年 1 月的高点要等到 2025 年 2 月才追平，中间实际购买力最深跌掉 83%，等了 45 年。 Using the London gold price and US CPI since 1968 (703 months): over the long run the claim holds — gold rose 122-fold against 9.8-fold inflation. But the January 1980 peak was not recovered until February 2025, an 83% real drawdown and a 45-year wait.
持有十年，四成窗口扣掉通胀后是亏的；通胀最高的 13 个年份里有 5 次黄金在跌（2022 年通胀 40 年最高，黄金只涨 0.4%）。它真正对冲的是组合波动：与股票相关性 −0.08，加 10% 进 60/40，年化几乎不变而最大回撤从 28.4% 降到 24.6%。把它放在「分散化」那一栏，不是「通胀保险」那一栏。 Forty per cent of ten-year windows lose money after inflation, and gold fell in five of the thirteen highest-inflation years. What it really hedges is portfolio volatility: correlation −0.08 with equities, and 10% in a 60/40 cuts the maximum drawdown from 28.4% to 24.6%. Put it in the diversification column, not the inflation-insurance column.
「别人恐惧我贪婪」在收益层面站得住：VIX ≥ 30 之后 12 个月的中位收益是 21.8%。但 36 年半里这样的机会只有 7 个市场阶段，其中一次买入后两年仍在亏损。 The maxim survives on returns — 21.8% median over the next twelve months. But 36 years produced only seven independent episodes, one of which was still losing money two years later.
读全文（8 张图 · 可拖阈值的交互）→Read the note (8 figures + interactive threshold) →先说结论：VIX 站上 30 之后，标普 500 后 12 个月的中位收益是 21.8%，明显高于平静期的 13.6%。但把这 36 年半翻一遍，33 个「高 VIX 月份」合并后只剩 7 个互不重叠的市场阶段——真正独立的机会是 7 次。 Median 12-month return after VIX ≥ 30 is 21.8% versus 13.6% after the calmest periods — but the 33 "high-VIX months" collapse into seven independent episodes.
那 7 次里有 1 次是亏的：互联网泡沫那一轮，任一月末入场，一年后中位数仍是 −8.1%。把规则写死（VIX≥30 满仓、≤20 空仓）年化只有 4.1%，不到买入持有的一半。所以：VIX 是风险定价的读数，不是入场信号——该用它定仓位，不是定方向。 One of the seven was a loser (−8.1% median). Written as a rule, it returns 4.1% annualised against 11.2% for buy-and-hold. VIX is a risk-pricing gauge, not a directional signal.
942 个月真实数据（美股 + 港股）：一次性投入赢约 80% 的起点，但它输的那 20% 恰好是「投完就跌」的月份。 942 months across two markets: all-in wins about 80% of starts — and loses exactly when the crash arrives immediately.
读全文（9 个图表 · 可播放动态对比）→Read the note (9 exhibits + interactive charts) →先分清两种钱：手上已有的一笔钱才有"分几次投"的选择；每月结余本来就只能定投。对历史上每一个月份回测（分 6/12/24/36 个月投完，持有 1–20 年）：标普 500 全收益上一次性投入在 79% 的起点胜出，持有 10 年中位多赚 0.13 倍本金。 Two kinds of money first. Backtesting every start month: all-in wins 79% of starts at a 10-year horizon, with a median advantage of 0.13x of principal.
定投只在"投完就跌"时赢（占起点 17–18%）：1999-02 起步定投 0.65x 输给 0.71x；2007-10 起步定投 2.34x 赢过 2.06x。换个市场结论打折——恒生指数上一次性胜率只有 63–69%。 DCA wins only when the crash comes at once: 0.65x vs 0.71x starting in 1999-02, and 2.34x vs 2.06x starting in 2007-10. In Hong Kong the all-in win rate falls to 63–69%.
同样 8% 波动预算下，四条典型机构约束一共拿走 46.8 bps/年；但样本短的时候，同样的约束是保险而不是成本。 Four ordinary institutional constraints cost 46.8 bps at an identical risk budget — and act as insurance when the sample is short.
读全文（4 张图 · 8 条文献）→Read the note (4 figures, 8 sources) →无约束的"最优"把 63.8% 押在信用债上——那不是洞察，是误差放大器。单资产上限 20% 值 27.9 bps、久期上限 2 年值 7.0、月度换手上限 25% 值 13.5、禁投清单值 10.1；四条一起 46.8 bps，小于它们单价的算术和 58.5 bps，因为约束之间会互相遮蔽。 The unconstrained optimum puts 63.8% in credit — an error amplifier, not insight. The cap costs 27.9 bps, the duration cap 7.0, the turnover cap 13.5, the exclusion list 10.1; together 46.8, below their arithmetic sum of 58.5.
反直觉的一半：估计窗口只有 24 个月时，无约束组合样本外超额夏普的 10 分位是 −0.02，加约束后是 +0.18。约束不是免费的，但它买的是对你自己的估计误差的保险。 The counter-intuitive half: with a 24-month window the 10th percentile is −0.02 unconstrained versus +0.18 constrained. A constraint is not free, but what it buys is insurance against your own estimation error.
同一份模拟数据、两档信噪比：弱信号下按 t 值挑出的前 10 名，样本内夏普 1.95、样本外 0.03。 Two signal-to-noise regimes on the same simulation: with a weak signal, the top ten factors earn 1.95 in sample and 0.03 out.
读全文（3 张图 · 11 条文献）→Read the note (3 figures, 11 sources) →400 个候选因子、8 个真因子、15 年样本：按 t 值取前 10，样本内漂亮、样本外归零，命中率只有 30%；更严格的五层过滤选出的 4 个全是噪声。附「证明一个因子需要多少年数据」的门槛计算（年化夏普 0.3 需要约 164 年）。 400 candidates, eight real factors, fifteen years: the top ten by t-statistic collapse out of sample, with a 30% hit rate; a stricter filter picked four factors and none were real. Includes the arithmetic of how many years of data a factor needs.
结论先行：筛选的天花板由信噪比决定，不由方法决定——所以我不再问「这个因子是否存在」，而是问「我的决策有多依赖它」。 The ceiling on screening is set by the signal, not the technique — so the question becomes how much the decision depends on the factor, not whether it exists.