人工智能（AI）正迅速成为企业运营的核心驱动力，它既是一个重要的投资领域，也是推动各行各业收入增长和效率提升的强大引擎。企业正在战略性地整合 AI 能力，以优化产品，简化流程，并抓住新的市场机遇。

以下是 AI 在多家公司中扮演的角色及其财务影响概述：

AI 如何驱动收入增长和市场扩张

•   阿里巴巴集团 (Alibaba Group): AI 是阿里巴巴战略的核心，为业务增长做出了实实在在的贡献。

    *   云智能集团在 2025 财年第一季度报告收入同比增长 18%，其中不包括合并子公司在内的收入增长加速至 17%。这主要得益于强劲的 AI 需求和公共云采用率的提高 。

    *   AI 相关产品收入已连续七个季度实现三位数同比增长 。

    *   AI 应用正在渗透到互联网服务、金融服务乃至传统行业（如养殖业和制造业），推动工作负载向云端迁移 。

    *   在电商领域，AI 工具预计将提升变现率。对于广告业务，AI 直接改进了精准投放能力，带来了额外的广告收入。经 AI 增强的某些广告库存的点击率已提升至约3.0%，显著高于历史水平 。

•   思科 (Cisco): 公司在 AI 相关业务上取得了强劲增长，AI 订单达到 10 亿美元，比预期提前了一个季度。值得注意的是，超过 6 亿美元的系统订单中有三分之二基于以 AI 为中心的 G200 芯片，客户表示如果产能允许，他们希望购买更多芯片。这凸显了 AI 硬件带来的显著收入贡献 。
•   Alphabet (Google): AI 正在为新功能提供动力，从而提高用户参与度和商业查询量。

    *   AI 概览 (AI Overviews)表现强劲，每月用户超过 15 亿 。

    *   AI 模式 (AI Mode)收到积极反馈，用户输入的查询长度是传统搜索查询的两倍，这表明用户参与度更深，并满足了更复杂的信息需求 。

    *   Waymo自动驾驶汽车业务进展顺利，计划今年晚些时候通过优步在亚特兰大提供付费乘车服务，预示着 AI 驱动的出行解决方案未来的收入来源 。

•   英伟达 (NVIDIA): 全球对英伟达 AI 基础设施的需求“异常强劲” 。

    *   AI 推理令牌生成在一年内增长了十倍 。

    *   英伟达将主权 AI、企业 AI 和工业 AI视为新的重要增长引擎。公司目前的订单量比过去更多，并且正在大幅扩展其供应链以满足需求，全球正在规划数百个“AI 工厂” 。

•   甲骨文 (Oracle): 公司在甲骨文云基础设施（OCI）方面实现了“异常快速”的增长，这主要得益于 AI 需求以及强劲的订单。甲骨文强调其在推理领域通过 AI 数据平台产品的差异化优势 。
•   赛富时 (Salesforce): 公司斥资80 亿美元收购 Informatica，旨在将 AI CRM 与 AI 主数据管理（MDM）和抽取、转换、加载（ETL）功能整合，这反映了对 AI 驱动增长的重大投资 。公司的“Agentforce”（AI 驱动的代理）正在迅速发展，创造了新的应用并影响了投资回报率（ROI） 。
•   三星 (Samsung): S 25 系列智能手机中的Galaxy AI 体验帮助其保持了强劲的销售势头，并实现了旗舰产品收入的同比增长 。三星还将 AI 整合到新的可折叠设备中，并将其 AI 手机系列扩展到 A 系列设备和 Tab S 11 系列，旨在区分产品并确保在零部件价格上涨情况下的盈利能力 。
•   腾讯 (Tencent): AI 能力对效果广告和常青游戏贡献显著。AI 驱动的广告投放改进已直接转化为额外的广告收入。腾讯内部对 AI 的使用也使得某些广告库存的点击率显著提高，达到约3.0%。公司正在加大对新 AI 机会的投入，预计这些战略投资将在长期内带来“可观的增量回报” 。AI 整合还有望提高小型游戏作品的变现能力和用户参与度 。

AI 如何实现成本管理和效率提升

•   阿里巴巴集团 (Alibaba Group): 尽管在 AI 方面投入巨大，但现有高质量收入流的运营杠杆预计将吸收额外成本，从而在这一投资阶段保持健康的财务表现 。
•   Alphabet (Google): AI 已深入融入公司内部运营，有助于提高效率。超过 30%的提交代码现在都涉及 AI 建议的解决方案，高于此前的 25%。客户服务团队通过 AI“显著提升”了用户体验并实现了“更高效”的运营。财务团队也利用 AI 处理诸如准备财报电话会议等任务。尽管 AI 基础设施的资本支出巨大，预计 2025 年将达到约750 亿美元（高于 2024 年的略超 500 亿美元），但公司正在积极寻求效率以抵消加速折旧 [5, 14]。
•   微软 (Microsoft): 微软展示了在加速 Azure（包括 AI 计划）的同时减缓资本支出增长速度的能力，这表明其在 AI 基础设施支出方面注重效率 。
•   SAP: 云业务毛利率显著改善，这归因于毛利润的普遍增长以及销售费用、研发和一般及行政（G&A）比率的优化。这通过利用新技术（包括 AI）和控制人员增长实现，凸显了 AI 在运营效率中的作用 。
•   三星 (Samsung): MX 业务通过提高成本竞争力 2 和资源效率举措提高了营业利润，并保持了“稳健的两位数盈利能力” 。
•   腾讯 (Tencent): 尽管预计 AI 投资将导致收入增长与营业利润增长之间的差距“缩小”约1-2 年，但公司的运营杠杆预计将避免出现负盈利。腾讯正在优先进行软件优化以提高推理效率，这可能使相同硬件的GPU 容量有效翻倍。公司还利用定制的小型模型来节省推理所需的 GPU 使用量，并拥有大量高端芯片库存 。

AI 发展中的挑战和影响

•   英伟达 (NVIDIA): 由于中国 H 20 出口禁令，英伟达面临300 亿美元的库存资产减记，这些库存无法出售或再利用 。该禁令预计还将导致第二季度H 20 收入损失约 80 亿美元 。第一季度，英伟达确认了 46 亿美元的 H 20 收入，但未能发货原计划的 25 亿美元订单 。公司目前正在探索针对中国市场符合严格新限制的产品选择，中国市场此前是美国工业的 500 亿美元市场 。
•   丰田 (Toyota): 预测美国关税将在 4 月和 5 月对其营业利润产生1800 亿日元的影响。公司正在积极通过增加本地生产和供应链本地化以及与供应商合作降低成本来减轻此类影响 。

总而言之，AI 无疑是企业绩效的双重驱动力。它正在创造可观的新收入流并增强现有收入流，特别是在云服务、广告和电子商务等高增长领域。同时，企业正在将大量资本投入到 AI 基础设施中，这可能在短期内给利润带来压力，但也正在积极利用 AI 来实现令人印象深刻的运营效率和成本节约，旨在实现可持续的长期增长和盈利能力。尽管存在地缘政治不确定性以及其财务影响的不断演变，但投资 AI 的战略必要性是明确的。

Artificial intelligence (AI) is rapidly emerging as a pivotal force in corporate operations, serving as both a significant investment area and a potent driver of revenue and efficiency across diverse industries. Companies are strategically integrating AI capabilities to enhance product offerings, streamline processes, and unlock new market opportunities.

Here’s an overview of AI’s role and its financial implications for various firms:

Revenue Generation and Market Expansion:

•   Alibaba Group: AI is central to Alibaba’s strategy, contributing tangibly to business growth.

    *   The Cloud Intelligence Group reported an 18% year-over-year revenue increase in the first quarter of fiscal year 2025. Excluding consolidated subsidiaries, revenue growth accelerated to 17%, primarily driven by robust AI demand and increased public cloud adoption.

    *   AI-related product revenue has sustained triple-digit year-over-year growth for seven consecutive quarters.

    *   AI applications are expanding their penetration across a wide range of industries, including internet services, financial services, and even traditional sectors like animal farming and manufacturing, driving a migration of workloads to the cloud.

    *   In e-commerce, AI tools are expected to enhance monetization rates. For advertising, AI directly improves targeting capabilities, leading to additional advertising revenue. The click-through rate on certain ad inventories, augmented by AI, has improved to approximately 3.0%, significantly higher than historical rates.

•   Amazon (AWS): AI advancements, such as custom silicon (Graviton), contribute to improved price performance for customers, implicitly driving adoption and revenue. The new AI-powered Alexa Plus is noted for its enhanced intelligence and capability to take real action, providing a “great personal assistant” experience that could drive future value.
•   Cisco: The company has seen a strong uptake in AI-related business, with AI orders reaching $1 billion, a quarter ahead of expectations. Notably, two-thirds of over $600 million in systems orders were based on the AI-centric G200 chip, with customers indicating a desire for more if capacity were available. This underscores the significant revenue contribution from AI hardware.
•   Alphabet (Google): AI is powering new features that drive user engagement and commercial queries.

    *   AI Overviews are performing strongly, with over 1.5 billion users per month.

    *   AI Mode is seeing positive feedback, with users typing queries that are two times longer than traditional search queries, suggesting deeper engagement and more complex information needs being met.

    *   The Waymo autonomous vehicle business is progressing, with plans for paid rides in Atlanta via Uber later this year, signaling future revenue streams from AI-driven mobility solutions.

•   NVIDIA: Global demand for NVIDIA’s AI infrastructure is “incredibly strong”.

    *   AI inference token generation has surged tenfold in just one year.

    *   The new Grace Blackwell NVL72 AI supercomputer offers 40 times higher speed and throughput for reasoning AI compared to its predecessor, Hopper, designed to lower costs and improve quality.

    *   NVIDIA identifies Sovereign AI, Enterprise AI, and Industrial AI as new, significant growth engines. The company reports more orders currently than in the past and is significantly scaling its supply chain to meet this demand, with hundreds of “AI factories” being planned globally.

•   Oracle: The company is experiencing “extraordinarily fast” growth in its Oracle Cloud Infrastructure (OCI) driven by AI demand, along with strong bookings. Oracle highlights its differentiation in the inferencing space with its AI data platform product.
•   Salesforce: The acquisition of Informatica for $8 billion is poised to integrate AI CRM with AI Master Data Management (MDM) and Extract, Transform, Load (ETL) capabilities, reflecting a substantial investment in AI-driven growth. The company’s “Agentforce” (AI-powered agents) is rapidly advancing, creating new applications and impacting return on investment (ROI).
•   Samsung: The Galaxy AI experience in its S25 series smartphones has helped maintain strong sales momentum and expanded flagship revenue year-over-year. Samsung is also integrating AI into new foldable devices and expanding its AI phone lineup to its A series devices and Tab S11 series, aiming to differentiate products and secure profitability amidst rising component prices.
•   Tencent: AI capabilities contribute notably to performance advertising and evergreen games. AI-driven improvements in advertising targeting have directly translated into additional advertising revenue. Tencent’s internal use of AI has also led to a significant improvement in ad click-through rates, reaching approximately 3.0% on certain inventories. The company is stepping up spending on new AI opportunities, expecting these strategic investments to yield “substantial incremental returns” over the longer term. AI integration is also expected to improve monetization and user engagement in smaller gaming titles.

Cost Management and Efficiency:

•   Alibaba Group: While investing heavily in AI, the operating leverage from existing high-quality revenue streams is expected to absorb the additional costs, contributing to healthy financial performance during this investment phase.
•   Amazon (AWS): Investments in software and process improvements, along with the use of low-cost custom networking gear and maximizing power usage in existing data centers, are leading to optimized server capacity and lower infrastructure costs.
•   Alphabet (Google): AI is deeply embedded across internal operations, contributing to efficiencies. Over 30% of code checked in now involves AI-suggested solutions, up from 25% previously. Customer service teams have “dramatically enhanced” user experience and achieved “much more efficient” operations through AI. The finance team also leverages AI for tasks such as preparing earnings calls. Despite significant capital expenditures for AI infrastructure, expected to be approximately $75 billion in 2025 (up from just over $50 billion in 2024), the company is actively seeking efficiencies to offset accelerating depreciation.
•   Meta Platforms: The company is observing “strong traction” with AI writing code internally, suggesting potential for future efficiency gains and possibly the displacement of mid-level engineers.
•   Microsoft: Demonstrates the ability to slow down its capital expenditure growth rate while still accelerating Azure, which encompasses AI initiatives, indicating an emphasis on efficiency in AI infrastructure spending.
•   SAP: Reported strong improvement in cloud margins, attributed to broad gross profit expansion and improved selling expenses, R&D, and general and administrative (G&A) ratios. This was achieved by leveraging new technology (including AI) and containing headcount growth, underscoring AI’s role in operational efficiency.
•   Samsung: The MX business improved operating profit and maintained “solid double-digit profitability” through enhanced cost competitiveness and resource efficiency initiatives.
•   Tencent: While anticipating a “narrowing” of the gap between revenue growth and operating profit growth for approximately 1-2 years due to AI investments, the company’s operating leverage is expected to prevent negative profitability. Tencent is prioritizing software optimization to improve inference efficiency, which could effectively double GPU capacity for the same hardware. The company also utilizes custom-made smaller models to save on GPU usage for inference and has a strong stockpile of high-end chips.

Challenges and Impacts:

•   NVIDIA: Faced a $30 billion write-off on inventory that cannot be sold or repurposed due to the H20 export ban in China. This ban is also expected to result in a loss of approximately $8 billion in H20 revenue for Q2. In Q1, NVIDIA recognized $4.6 billion in H20 revenue but was unable to ship an additional $2.5 billion of planned orders. The company is now exploring options for products compliant with stringent new limits for the Chinese market, which was previously a $50 billion market for US industry.
•   Toyota: Forecasts an operating income impact of 180.0 billion yen for April and May due to US tariffs. The company is actively working to mitigate such impacts by increasing local production and supply chain localization and collaborating with suppliers to reduce costs.

AI is unequivocally a dual-pronged driver of corporate performance. It is generating substantial new revenue streams and enhancing existing ones, particularly in high-growth sectors like cloud services, advertising, and e-commerce. Simultaneously, companies are dedicating significant capital to AI infrastructure, which can pressure margins in the short term, but are also actively leveraging AI to deliver impressive operational efficiencies and cost savings, aiming for sustainable long-term growth and profitability. The strategic imperative to invest in AI is clear, despite geopolitical uncertainties and the evolving nature of its financial impact.

在追求卓越投资回报的旅程中，杠杆和复杂策略常常诱人，但也伴随着巨大的风险。通过我们之前的讨论和深入研究，我们旨在为您呈现一个将系统性方法与明智多元化原则相结合的综合投资方案。本文将总结我们的核心发现，并提出一个可行的交易框架，以期在管理风险的同时放大长期收益。

一、核心策略：利用杠杆轮动策略（LRS）驾驭市场趋势

我们讨论的基石是杠杆轮动策略（Leverage Rotation Strategy, LRS），它旨在通过系统性地调整对杠杆ETF（如TQQQ）的敞口来优化风险与回报。该策略的核心思想是波动性是杠杆的敌人，而低波动性与趋势性上涨则是杠杆的良友。

最终交易方案建议（LRS部分）：

• 启动时机： 当广义美国股票市场指数（例如S&P 500指数，或TQQQ追踪的纳斯达克100指数）的收盘价高于其200日移动平均线时，买入并持有TQQQ以放大潜在收益。这是因为它预示着未来波动性可能较低，每日平均表现较高，且正回报持续时间可能更长。

• 风险管理/规避： 当市场指数收盘价低于其200日移动平均线时，立即退出TQQQ头寸并转为国库券或现金。这一信号表明市场波动性通常会显著增加，可能导致杠杆产品遭受“持续杠杆陷阱”和巨大回撤。

• 移动平均线的价值： 200日移动平均线应被视为一个风险管理工具和波动性指标，而非仅仅是旨在最大化上涨收益的趋势指标。它能有效识别市场中高波动性时期，从而帮助投资者规避极端下跌日。

• 历史表现： 回溯测试显示，LRS策略相较于传统买入并持有非杠杆或持续杠杆策略，能够带来更高的绝对收益、更低的年化波动性、更高的风险调整后收益（夏普比率/索蒂诺比率）、更低的最大回撤以及显著的正阿尔法。这一策略在历史上最严重的熊市中，其最大回撤均低于非杠杆的标普500指数。

二、优化补充：期权策略的协同效应

为了进一步优化投资组合，尤其是在LRS策略指示持有现金/国库券的“风险规避”时期，期权策略可以作为一种有力的补充。

期权策略建议：

• 利用波动性错价： 当LRS策略处于非杠杆（现金/国库券）状态时，市场波动性往往较高。此时，可以考虑采用基于历史波动率（HV）与隐含波动率（IV）之间差异的期权策略。研究表明，当IV与HV之间存在较大差异时，期权市场可能存在错价，这可能是由于投资者对当前信息的过度反应造成的。

• 具体实施：

    ◦ 构建零成本交易策略：做多那些HV远高于IV的期权组合（被认为是“便宜”的期权），同时做空那些IV远高于HV的期权组合（被认为是“昂贵”的期权）。

    ◦ 具体期权组合可包括跨式组合（straddles）Delta对冲的看涨/看跌期权组合。这些策略的Delta值通常较低，意味着它们对标的资产方向性敞口很小，主要关注波动性而非方向。

• 优势： 这类期权策略能够提供非方向性阿尔法，从而在LRS策略不活跃（或处于低风险状态）时为投资组合带来额外的收益来源。通过分散收益来源，它有望提高整体投资组合的风险调整后收益。

• 交易成本考量： 尽管期权策略具有吸引力，但必须考虑其固有的交易成本（如买卖价差）。历史分析显示，即使在考虑交易成本后，这类策略仍能保持可观的月收益率，但流动性较低的期权通常利润更高。

三、深层洞察：风险平价与多元化原则

此次对话还深入探讨了投资组合构建的深层原理，包括风险平价和“1/N”朴素多元化规则。这些原则为我们的交易方案提供了重要的哲学基础。

• 风险平价（Risk Parity）： 传统60/40投资组合并未实现真正的多元化，因为其中60%的股票配置实际上占据了超过95%的组合风险。风险平价策略的核心是平衡高风险资产和低风险资产（主要是政府债券）的风险贡献，从而实现更强大的下行保护。下一代风险平价方法更进一步，在股票、债券和商品等资产类别内部，以及跨类别之间，实现多层次的多元化，以期获得更高的夏普比率和长期回报。LRS策略通过动态调整风险敞口，与风险平价管理风险贡献的精神不谋而合。

• “1/N”朴素多元化的力量： 尽管存在复杂的投资理论和优化模型，但朴素的“1/N”多元化规则（即在N个资产中平均分配资金）在实践中却出人意料地难以被击败。这主要是因为在资产数量（N）相对于样本量（T）较高时，传统估计方法（如马科维茨优化）的参数估计误差会大幅抵消其理论上的最优性。在一个包含可分散风险的单因子模型中，当N足够大时，“1/N”规则甚至可以渐近最优。这意味着，对于许多实际应用，特别是在第一因子占主导地位的情况下，简单、稳健的策略往往表现出色。

四、最终交易方案的整体考量

我们的最终交易方案结合了这些洞察，旨在创建一个既能捕捉市场趋势带来的杠杆收益，又能通过期权策略在特定市场环境下创造非方向性阿尔法，同时秉持风险管理和真正多元化的核心原则的投资方法：

1. 核心配置： 大部分资金遵循TQQQ杠杆轮动策略，根据200日移动平均线信号，在市场处于上涨趋势（低波动性、连续上涨）时持有TQQQ，在市场处于下跌趋势（高波动性、震荡）时转为现金/国库券。

2. 增益与对冲： 在LRS策略指示持有现金/国库券的风险规避时期，考虑部署期权波动性错价策略。这可以在市场波动性较高时（LRS规避风险时）提供额外的阿尔法来源，同时由于其低方向性敞口，有助于进一步平滑投资组合的整体波动性。

3. 组合原则： 在构建更广泛的投资组合时，秉持风险平价和真实验证的多元化原则，避免传统市场加权指数中常见的风险集中问题。对于投资范围较广的资产类别，如果存在显著的估计误差，“1/N”朴素多元化规则或与简单规则相结合的策略可能是一个稳健的基线，甚至优于看似更复杂的优化方法。

重要提示： 本文提出的策略基于历史数据和研究。过往表现不代表未来结果。 投资涉及风险，包括本金损失的可能性。实际交易中还需考虑交易成本、市场冲击、流动性以及投资者自身的风险承受能力。任何投资决策都应在咨询专业财务顾问后，结合个人财务状况和目标进行。

In the pursuit of superior investment returns, leverage and complex strategies often beckon, yet they also carry significant risks. Drawing upon our previous conversations and in-depth research, this article aims to present a comprehensive investment approach that combines systematic methodologies with sound diversification principles. We will summarize our core findings and propose a viable trading framework designed to amplify long-term gains while prudently managing risk.

I. Core Strategy: Harnessing Market Trends with the Leverage Rotation Strategy (LRS)

The cornerstone of our discussion is the Leverage Rotation Strategy (LRS), which seeks to optimize risk and return by systematically adjusting exposure to leveraged ETFs, such as TQQQ. The central idea of this strategy is that volatility is the enemy of leverage, while low volatility and sustained positive streaks are its allies.

Proposed Trading Plan (LRS Component):

• Initiation: When the closing price of the broad U.S. equity market index (e.g., S&P 500, or the Nasdaq 100 which TQQQ tracks) is above its 200-day Moving Average (MA), initiate a position in TQQQ to magnify potential returns. This signal indicates a likelihood of lower future volatility, higher average daily performance, and longer streaks of positive returns.
• Risk Management/Avoidance: When the market index’s closing price falls below its 200-day Moving Average, immediately exit TQQQ positions and rotate into Treasury bills or cash. This signal suggests that market volatility tends to increase significantly, potentially leading to the “constant leverage trap” and substantial drawdowns for leveraged products.
• The Value of the Moving Average: The 200-day Moving Average should be viewed as a risk management tool and a volatility indicator, rather than merely a trend indicator aimed at maximizing upside. It effectively helps identify periods of elevated market volatility, thereby assisting investors in avoiding extreme down days.
• Historical Performance: Backtests indicate that the LRS strategy, compared to traditional unleveraged buy-and-hold or constantly leveraged strategies, can yield higher absolute returns, lower annualized volatility, improved risk-adjusted returns (Sharpe/Sortino ratios), lower maximum drawdowns, and significant positive alpha. This strategy demonstrated lower maximum drawdowns in historical bear markets compared to the unleveraged S&P 500.

II. Optimizing Complements: The Synergistic Effect of Option Strategies

To further optimize the investment portfolio, especially during “risk-off” periods when the LRS strategy signals holding cash/Treasury bills, option strategies can serve as a powerful complement.

Option Strategy Recommendations:

• Exploiting Volatility Mispricing: When the LRS is in its unleveraged (cash/Treasury bill) state, market volatility often tends to be higher. During such times, consider employing option strategies based on the discrepancies between historical volatility (HV) and implied volatility (IV). Research suggests that when there are significant differences between IV and HV, options may be mispriced, potentially due to investor overreaction to current information.
• Specific Implementation:

    ◦ Construct zero-cost trading strategies: Go long on option portfolios where HV is significantly higher than IV (considered “cheap” options), while simultaneously going short on option portfolios where IV is significantly higher than HV (considered “expensive” options).

    ◦ Specific option combinations can include straddles and Delta-hedged call/put portfolios. These strategies typically have a low Delta, meaning they have very little directional exposure to the underlying asset and primarily focus on volatility rather than direction.

• Advantages: These types of option strategies can provide non-directional alpha, thereby offering an additional source of returns to the portfolio when the LRS is not actively leveraged (or is in a low-risk state). By diversifying revenue streams, they can potentially improve the overall risk-adjusted returns of the portfolio.
• Transaction Cost Considerations: While option strategies are appealing, their inherent transaction costs (such as bid-ask spreads) must be considered. Historical analysis shows that even after accounting for transaction costs, these strategies can maintain substantial monthly returns, though less liquid options often yield higher profits.

III. Deeper Insights: Risk Parity and Diversification Principles

This conversation also delved into the deeper principles of portfolio construction, including risk parity and the “1/N” naive diversification rule. These principles provide important philosophical underpinnings for our proposed trading plan.

• Risk Parity: Traditional 60/40 portfolios do not offer true diversification because the 60% stock allocation actually accounts for over 95% of the portfolio risk. The essence of Risk Parity is to balance the risk contribution from high-risk assets and low-risk assets (primarily government bonds), leading to stronger downside protection. The “next generation” of Risk Parity extends this concept to multiple layers of diversification within and across asset classes like equities, bonds, and commodities, aiming for higher Sharpe ratios and superior long-term returns. The LRS, by dynamically managing risk exposure, aligns with the spirit of Risk Parity in managing risk contribution.
• The Power of “1/N” Naive Diversification: Despite sophisticated investment theories and optimization models, the simple “1/N” diversification rule (investing equally across N assets) has proven surprisingly difficult to beat in practice. This is largely because, when the number of assets (N) is high relative to the sample size (T), the parameter estimation errors in traditional estimation methods (like Markowitz optimization) significantly offset their theoretical optimality. In a one-factor model with diversifiable risks, the “1/N” rule can even be asymptotically optimal when N is sufficiently large. This implies that for many practical applications, especially where a single factor dominates, simple, robust strategies often perform exceptionally well.

IV. Overall Considerations for the Final Trading Plan

Our final trading plan integrates these insights, aiming to create an investment approach that captures leveraged returns from market trends, generates non-directional alpha through option strategies in specific market environments, and adheres to core principles of risk management and true diversification:

1. Core Allocation: A significant portion of capital follows the TQQQ Leverage Rotation Strategy, holding TQQQ when the market is in an uptrend (low volatility, consistent gains) based on the 200-day MA signal, and rotating into cash/Treasury bills during downtrends (high volatility, choppy action).
2. Enhancement and Hedge: During risk-off periods when the LRS signals holding cash/Treasury bills, consider deploying option volatility mispricing strategies. This can provide an additional source of alpha when market volatility is higher (and LRS is de-risked), and due to their low directional exposure, can help to further smooth the overall portfolio volatility.
3. Portfolio Principles: When constructing a broader investment portfolio, adhere to Risk Parity and truly diversified principles, avoiding the common risk concentration issues found in traditional market-weighted indices. For broadly diversified asset classes, where significant estimation errors might exist, the “1/N” naive diversification rule or strategies combining it with simple rules can serve as a robust baseline, potentially outperforming seemingly more complex optimization methods.

Important Disclaimer: The strategies presented in this article are based on historical data and research. Past performance is not indicative of future results. Investing involves risk, including the potential loss of principal. Actual trading also entails considering transaction costs, market impact, liquidity, and an investor’s own risk tolerance. Any investment decision should be made in consultation with a professional financial advisor, based on individual financial circumstances and goals.

In the world of finance and betting, understanding how to size your bets can make or break your success. One powerful tool to guide this decision is the Kelly Criterion. Originally developed for gambling, it’s now widely applied in portfolio management to maximize long-term capital growth while managing risk.

What is the Kelly Criterion?

The Kelly formula helps determine what percentage of your capital to invest in a given opportunity when you have an edge. The basic version is:

Where:

• : probability of winning
• : net odds (reward-to-risk ratio)

If you estimate your probability of success and your upside vs downside correctly, Kelly tells you how much to invest. But real investing rarely gives you those clear odds.

Enter the Sharpe Ratio

In finance, we often use the Sharpe Ratio as a proxy to adapt Kelly to investment portfolios. The modified formula becomes:

Where:

• : expected return
• : risk-free rate
• : volatility

This gives you the optimal leverage you should use to grow capital most efficiently. For example, if your expected return is 12%, volatility is 20%, and the risk-free rate is 3%, Kelly suggests investing 225% of your capital—a signal to consider fractional Kelly for real-life applications.

Simulating the Future: Monte Carlo Method

To account for uncertainty, we use Monte Carlo simulations—a method that generates thousands of possible future scenarios based on random returns. You define assumptions like expected return and volatility, then simulate portfolio growth over decades.

This shows the range of outcomes, highlights potential downside risk, and helps answer critical questions like:

• Will I have enough to retire?
• What are the chances of losing money?

Monte Carlo visuals often reveal that even a solid plan can have a wide range of possible futures, which is a powerful reminder that risk management matters as much as return.

在投资和赌博的世界里，如何正确“下注”决定了最终的命运。凯利公式（Kelly Criterion） 是一个经典工具，帮你在有优势时决定投入多少资金，从而 最大化长期收益，并控制风险。

什么是凯利公式？

凯利公式如下：

其中：

• ：成功的概率
• ：赔率（收益与风险的比值）

如果你能准确判断成功的概率和盈亏比例，凯利公式会告诉你最合理的投资比例。但在实际投资中，这种精确的数据往往难以获得。

引入夏普比率（Sharpe Ratio）

在金融中，凯利公式常通过夏普比率进行扩展。新版凯利公式变为：

其中：

• ：预期收益率
• ：无风险利率
• ：波动率

这个公式告诉你应投入多少资金（甚至杠杆多少倍），以实现最优长期增长。例如：若预期年收益率为 12%、波动率为 20%、无风险利率为 3%，则凯利公式建议投资 225% 的本金。现实中，多数投资者会选择 半凯利 或 四分凯利，来降低风险。

蒙特卡洛模拟：预见未来的工具

为了评估不确定性，我们用 蒙特卡洛模拟 来生成成千上万个投资“平行宇宙”。通过设置预期收益和波动率，模拟几十年后的投资结果。

它展示了投资可能的全部路径，让我们看到：

• 最糟糕和最好的结果
• 有多少概率亏损或暴富

这些结果提醒我们：回报很重要，但控制风险同样关键。

交易年考察

S&P 500指数成立于1957年3月4日，统计1961年起至2023年共63个交易年的数据。

总体情况

总回报24234%，年化回报9.106%，不论是按照实际情况或是年化回报率计算，基本上每8或9年投资翻倍。

单年最大涨幅34.11%，最大跌幅-38.49%。

考察连续持有年限与回撤年份占比及数值：

	1年	5年	10年	15年	20年	25年
年份占比	17.4%	15.4%	4.4%	0%	0%	0%
最大	-37.00%	-2.35%	-1.38%	–	–	–
最小	-3.10%	-0.21%	-0.95%	–	–	–
平均	-14.45%	-1.21%	-1.17%	–	–	–
中位数	-11.89%	-0.59%	–	–	–	–

小结：连续持有10年以上可以认为绝不亏损。

极值考察

回撤

参照交易年每年回撤平均值-14.45%、中位数-11.89%，视回撤超过-15.0%为“大幅回撤”：

年份	回撤前点位	回撤后点位	最大回撤点位	最大回撤幅度	时间范围	背景原因
1962	72.6	55.9	55.9	-23.50%	1961年12月 – 1962年6月	冷战危机，经济放缓
1968	108	73	73	-32.90%	1968年12月 – 1970年6月	越战支出与经济衰退
1973	121	62	62	-48.20%	1973年1月 – 1974年10月	石油危机，滞胀环境
1980	140	102	102	-27.10%	1980年2月 – 1980年3月	高通胀与美联储加息
1987	336	224	224	-33.50%	1987年8月 – 1987年12月	黑色星期一股市崩盘
1990	368	295	295	-19.90%	1990年7月 – 1990年10月	海湾战争爆发，经济衰退
2000	1,527	768	759	-50.50%	2000年3月 – 2002年10月	科技泡沫破裂
2007	1,565	676	666	-57.70%	2007年10月 – 2009年3月	全球金融危机
2020	3,386	2,237	2,237	-33.90%	2020年2月 – 2020年3月	新冠疫情爆发
2022	4,796	3,577	3,577	-25.40%	2022年1月 – 2022年10月	加息周期，高通胀
最大				-57.70%
最小				-19.90%
绝对平均				-34.75%
等权平均				-35.26%
加权平均				-35.18%
中位数				-32.90%

小结：每一次回撤后的低点均高于上一次，自高点回撤-30%以上可视为进入底部区域。

回撤后的上涨

年份	回调后点位	下一次回调前点位	上涨幅度	背景原因
1962	55.9	108	93.20%	冷战后期美国科技与工业发展
1968	73	121	65.80%	经济繁荣推动股市上涨
1973	62	140	125.80%	滞胀结束，货币政策调整
1980	102	336	229.40%	通胀控制后经济增长
1987	224	368	64.30%	黑色星期一后市场逐渐修复
1990	295	1,527	417.60%	科技产业繁荣与经济扩张
2000	768	1,565	103.80%	经济复苏与房地产泡沫
2007	676	3,386	401%	金融危机后货币宽松政策刺激
2020	2,237	4,796	114.40%	疫情后刺激政策与科技股增长
最大			417.60%
最小			64.30%
绝对平均			179.48%
等权平均			167.81%
加权平均			174.29%
中位数			120.10%

小结：每一次大幅回撤前的上涨均超过前一次点位，少数大幅上涨推动指数提升。

附表

年份	涨跌	年回报率（含股息）	累计回报率	5年回报率（年化）	10年回报率（年化）	15年回报率（年化）	20年回报率（年化）	25年回报率（年化）
1961年	23.13%	–	–	–	–	–	–	–
1962年	-11.81%	–	–	–	–	–	–	–
1963年	18.89%	–	–	–	–	–	–	–
1964年	12.97%	–	–	–	–	–	–	–
1965年	9.06%	–	–	–	–	–	–	–
1966年	-13.09%	–	–	–	–	–	–	–
1967年	20.09%	–	–	–	–	–	–	–
1968年	7.66%	–	–	–	–	–	–	–
1969年	-11.36%	–	–	–	–	–	–	–
1970年	0.10%	4.01%	104%	–	–	–	–	–
1971年	10.79%	14.31%	119%	–	–	–	–	–
1972年	15.63%	18.98%	141%	–	–	–	–	–
1973年	-17.37%	-14.66%	121%	–	–	–	–	–
1974年	-29.72%	-26.47%	89%	-2.35%	–	–	–	–
1975年	31.55%	37.20%	122%	3.21%	–	–	–	–
1976年	19.15%	23.84%	151%	4.87%	–	–	–	–
1977年	-11.50%	-7.18%	140%	-0.21%	–	–	–	–
1978年	1.06%	6.56%	149%	4.32%	–	–	–	–
1979年	12.31%	18.44%	177%	14.76%	5.86%	–	–	–
1980年	25.77%	32.50%	234%	13.96%	8.45%	–	–	–
1981年	-9.73%	-4.92%	223%	8.10%	6.47%	–	–	–
1982年	14.76%	21.55%	271%	14.09%	6.70%	–	–	–
1983年	17.27%	22.56%	332%	17.32%	10.63%	–	–	–
1984年	1.40%	6.27%	352%	14.81%	14.78%	8.76%	–	–
1985年	26.33%	31.73%	464%	14.67%	14.32%	10.49%	–	–
1986年	14.62%	18.67%	551%	19.87%	13.83%	10.76%	–	–
1987年	2.03%	5.25%	580%	16.47%	15.27%	9.86%	–	–
1988年	12.40%	16.61%	676%	15.31%	16.31%	12.17%	–	–
1989年	27.25%	31.69%	890%	20.37%	17.55%	16.61%	11.55%	–
1990年	-6.56%	-3.10%	863%	13.20%	13.93%	13.94%	11.16%	–
1991年	26.31%	30.47%	1126%	15.36%	17.59%	14.34%	11.90%	–
1992年	4.46%	7.62%	1211%	15.88%	16.17%	15.47%	11.34%	–
1993年	7.06%	10.08%	1333%	14.55%	14.93%	15.72%	12.76%	–
1994年	-1.54%	1.32%	1351%	8.70%	14.38%	14.52%	14.58%	10.98%
1995年	34.11%	37.58%	1859%	16.59%	14.88%	14.81%	14.60%	12.22%
1996年	20.26%	22.96%	2286%	15.22%	15.29%	16.80%	14.56%	12.55%
1997年	31.01%	33.36%	3048%	20.27%	18.05%	17.52%	16.65%	13.07%
1998年	26.67%	28.58%	3919%	24.06%	19.21%	17.90%	17.75%	14.94%
1999年	19.53%	21.04%	4744%	28.56%	18.21%	18.93%	17.88%	17.25%
2000年	-10.14%	-9.10%	4312%	18.33%	17.46%	16.02%	15.68%	15.34%
2001年	-13.04%	-11.89%	3799%	10.70%	12.94%	13.74%	15.24%	13.78%
2002年	-23.37%	-22.10%	2960%	-0.59%	9.34%	11.48%	12.71%	12.98%
2003年	26.38%	28.68%	3809%	-0.57%	11.07%	12.22%	12.98%	13.84%
2004年	8.99%	10.88%	4223%	-2.30%	12.07%	10.94%	13.22%	13.54%
2005年	3.00%	4.91%	4430%	0.54%	9.07%	11.52%	11.94%	12.48%
2006年	13.62%	15.79%	5130%	6.19%	8.42%	10.64%	11.80%	13.37%
2007年	3.53%	5.49%	5412%	12.83%	5.91%	10.49%	11.82%	12.73%
2008年	-38.49%	-37.00%	3409%	-2.19%	-1.38%	6.46%	8.43%	9.77%
2009年	23.45%	26.46%	4311%	0.42%	-0.95%	8.04%	8.21%	10.54%
2010年	12.78%	15.06%	4961%	2.29%	1.41%	6.76%	9.14%	9.94%
2011年	0.00%	2.11%	5065%	-0.25%	2.92%	5.45%	7.81%	9.28%
2012年	13.41%	16.00%	5876%	1.66%	7.10%	4.47%	8.22%	9.71%
2013年	29.60%	32.39%	7779%	17.94%	7.40%	4.68%	9.22%	10.26%
2014年	11.39%	13.69%	8844%	15.45%	7.67%	4.24%	9.85%	9.62%
2015年	-0.73%	1.38%	8966%	12.57%	7.30%	5.00%	8.19%	9.82%
2016年	9.54%	11.96%	10038%	14.66%	6.94%	6.69%	7.68%	9.15%
2017年	19.42%	21.83%	12230%	15.79%	8.49%	9.92%	7.19%	9.69%
2018年	-6.24%	-4.38%	11694%	8.49%	13.12%	7.77%	5.62%	9.07%
2019年	28.88%	31.49%	15376%	11.70%	13.56%	9.00%	6.06%	10.22%
2020年	16.26%	18.40%	18205%	15.22%	13.88%	9.88%	7.47%	9.56%
2021年	26.89%	28.71%	23431%	18.48%	16.55%	10.66%	9.52%	9.76%
2022年	-19.44%	-18.11%	19189%	9.43%	12.56%	8.80%	9.80%	7.64%
2023年	24.23%	26.29%	24234%	15.69%	12.03%	13.97%	9.69%	7.56%
2024年	–	–	–	–	–	–	–	–
最大数	34.11%	37.58%	24234%	28.56%	19.21%	18.93%	17.88%	17.25%
最低数	-38.49%	-37.00%	89%	-2.35%	-1.38%	4.24%	5.62%	7.56%
中位数	12.36%	15.43%	–	14.02%	12.56%	10.71%	11.34%	10.40%