asset-allocation

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Asset Allocation

资产配置

Purpose

用途

Provides frameworks for determining how to distribute capital across asset classes and strategies. Covers strategic and tactical allocation, mean-variance optimization, Black-Litterman, risk parity, glide paths, and practical implementation approaches. Asset allocation is the primary driver of long-term portfolio performance and risk.

提供各类框架指导如何在不同资产类别和策略之间分配资金，涵盖战略配置与战术配置、均值方差优化、Black-Litterman模型、风险平价、下滑路径及实际落地方法。资产配置是决定长期投资组合收益和风险的核心因素。

Layer

层级

4 — Portfolio Construction

4 — 投资组合构建

Direction

适用方向

both

双向

When to Use

适用场景

Setting long-term strategic asset allocation targets
Making tactical allocation decisions based on market views
Running mean-variance optimization with constraints
Implementing Black-Litterman to blend market equilibrium with investor views
Building risk parity or equal risk contribution portfolios
Designing glide paths for target-date or lifecycle strategies
Evaluating core-satellite portfolio structures
Matching assets to liabilities for pensions or insurance portfolios

设定长期战略资产配置目标
基于市场观点制定战术配置决策
带约束条件的均值方差优化运算
落地Black-Litterman模型融合市场均衡预期与投资者主观观点
构建风险平价或等风险贡献投资组合
为目标日期或生命周期策略设计下滑路径
评估核心-卫星投资组合结构
为养老金或保险投资组合做资产负债匹配

Core Concepts

核心概念

Strategic Asset Allocation (SAA)

战略资产配置（SAA）

The long-term policy portfolio based on an investor's risk tolerance, return objectives, time horizon, and constraints. SAA determines the baseline target weights (e.g., 60% equity / 30% bonds / 10% alternatives) and is the dominant driver of long-term portfolio returns. SAA should be revisited when investor circumstances change, not in response to market movements.

基于投资者风险承受能力、收益目标、投资期限和约束条件制定的长期政策组合。SAA确定基准目标权重（例如60%股票/30%债券/10%另类资产），是长期投资组合收益的核心决定因素。仅当投资者自身情况发生变化时才需要重新调整SAA，不应随市场波动随意变动。

Tactical Asset Allocation (TAA)

战术资产配置（TAA）

Short-to-medium-term deviations from the SAA based on market views, valuations, or momentum signals. TAA requires a disciplined process to avoid becoming ad hoc market timing. Key considerations:

Define allowable deviation bands (e.g., +/- 10% from SAA)
Have a clear signal framework (valuation, momentum, macro)
Set reversion rules: when to return to SAA weights

基于市场观点、估值或动量信号，在短期到中期维度偏离SAA基准的配置调整。TAA需要有纪律的执行流程，避免演变为随意的择时操作。核心考量点：

定义允许的偏离区间（例如相对于SAA基准上下浮动10%）
建立清晰的信号框架（估值、动量、宏观指标）
设定回归规则：何时回归SAA基准权重

Mean-Variance Optimization (MVO)

均值方差优化（MVO）

Markowitz's framework for finding optimal portfolio weights that maximize risk-adjusted return:

max w'*mu - (lambda/2) * w'Sigmaw

subject to: sum(w_i) = 1, w_i >= 0 (if long-only), and any additional constraints.

Where:

w = weight vector
mu = expected return vector
Sigma = covariance matrix
lambda = risk aversion parameter

MVO requires three inputs: expected returns, the covariance matrix, and risk aversion. The solution is highly sensitive to expected return inputs.

马科维茨提出的框架，用于求解最优投资组合权重，最大化风险调整后收益：

max w'*mu - (lambda/2) * w'Sigmaw

约束条件：sum(w_i) = 1, w_i >= 0（仅做多时），以及其他额外约束。

其中：

w = 权重向量
mu = 预期收益向量
Sigma = 协方差矩阵
lambda = 风险厌恶系数

MVO需要三类输入：预期收益、协方差矩阵、风险厌恶系数，求解结果对预期收益输入的敏感度极高。

Black-Litterman Model

Black-Litterman模型

Combines market equilibrium returns with investor views to produce more stable, intuitive portfolio weights. Two-step process:

Step 1 — Implied Equilibrium Returns: Pi = lambda * Sigma * w_mkt

where w_mkt is the market-capitalization weight vector, lambda is the risk aversion parameter, and Sigma is the covariance matrix. These are the returns the market implicitly expects given current prices.

Step 2 — Blending with Views: E(R) = [(tau*Sigma)^(-1) + P'*Omega^(-1)P]^(-1) * [(tauSigma)^(-1)*Pi + P'*Omega^(-1)*Q]

where:

tau = scalar (uncertainty of equilibrium, typically 0.025-0.05)
P = pick matrix (identifies assets in each view)
Q = view vector (expected returns from views)
Omega = diagonal matrix of view uncertainties

The result is a posterior expected return vector that tilts away from equilibrium toward the investor's views, proportional to confidence.

融合市场均衡收益与投资者主观观点，生成更稳定、更符合直觉的投资组合权重。分为两步：

步骤1 — 隐含均衡收益： Pi = lambda * Sigma * w_mkt

其中w_mkt是市值权重向量，lambda是风险厌恶系数，Sigma是协方差矩阵。这类收益是当前定价下市场隐含的预期收益水平。

步骤2 — 与主观观点融合： E(R) = [(tau*Sigma)^(-1) + P'*Omega^(-1)P]^(-1) * [(tauSigma)^(-1)*Pi + P'*Omega^(-1)*Q]

其中：

tau = 标量参数（均衡收益的不确定性，通常取值0.025-0.05）
P = 选择矩阵（标识每个观点涉及的资产）
Q = 观点向量（观点对应的预期收益）
Omega = 观点不确定性的对角矩阵

输出结果是后验预期收益向量，会根据观点置信度按比例从均衡水平向投资者主观观点方向倾斜。

Risk Parity

风险平价

Equalizes the risk contribution from each asset (or factor) rather than equalizing capital allocation:

RC_i = w_i * (Sigma*w)_i / sigma_p

Set RC_i = RC_j for all i, j.

In a simple two-asset case with no correlation: w_i is proportional to 1/sigma_i

Risk parity portfolios allocate more capital to lower-volatility assets (typically bonds) and often require leverage to achieve competitive return targets.

让每个资产（或因子）的风险贡献相等，而非资金分配相等：

RC_i = w_i * (Sigma*w)_i / sigma_p

令所有i,j满足RC_i = RC_j。

在无相关性的简单双资产场景下：w_i与1/sigma_i成正比

风险平价组合会给低波动资产（通常是债券）分配更多资金，通常需要加杠杆才能达到有竞争力的收益目标。

Glide Path

下滑路径

An age-based or time-based allocation that systematically shifts from growth assets to defensive assets as the investor ages or the target date approaches:

Common rule of thumb: Equity % = 110 - Age

Target-date fund glide paths typically:

Start at 90% equity for young investors
Decrease by ~1-2% per year
Reach 30-40% equity at retirement
Continue to "through" allocation post-retirement

基于年龄或时间的配置规则，随着投资者年龄增长或目标日期临近，系统性地从成长类资产转向防御类资产：

常见经验法则：股票占比 = 110 - 年龄

目标日期基金的下滑路径通常：

年轻投资者初始配置90%股票
每年降低1-2%左右的股票占比
退休时股票占比降至30-40%
退休后仍会继续调整配置

Core-Satellite

核心-卫星

A hybrid approach combining:

Core (60-80%): Low-cost, broadly diversified index funds or ETFs
Satellites (20-40%): Active strategies, factor tilts, alternatives, or concentrated positions

This structure captures the market return efficiently (core) while allowing alpha generation or specific exposures (satellites).

混合配置思路，包含：

核心部分（60-80%）： 低成本、宽基分散的指数基金或ETF
卫星部分（20-40%）： 主动策略、因子倾斜、另类资产或集中持仓

该结构既可以通过核心部分高效获取市场收益，又可以通过卫星部分获取alpha或特定风险暴露。

Asset-Liability Matching

资产负债匹配

For investors with defined liabilities (pensions, insurance, endowments with spending rules):

Match asset duration and cash flows to liability duration and timing
Surplus optimization: optimize the portfolio relative to liabilities, not absolute return
Liability-driven investing (LDI): hedge liability risk with duration-matched bonds, invest surplus in return-seeking assets

适用于有明确负债的投资者（养老金、保险、有支出规则的捐赠基金）：

匹配资产久期和现金流与负债的久期和支付时间
盈余优化：相对于负债优化投资组合，而非追求绝对收益
负债驱动投资（LDI）：用久期匹配的债券对冲负债风险，将盈余投资于收益型资产

Key Formulas

核心公式

Formula	Expression	Use Case
MVO Objective	max w'mu - (lambda/2)w'Sigmaw	Optimal portfolio weights
Equilibrium Returns	Pi = lambda * Sigma * w_mkt	Black-Litterman starting point
BL Posterior	E(R) = [(tauSigma)^(-1) + P'Omega^(-1)P]^(-1) [(tauSigma)^(-1)Pi + P'Omega^(-1)Q]	Blended expected returns
Risk Contribution	RC_i = w_i * (Sigma*w)_i / sigma_p	Risk parity target
Risk Parity Condition	RC_i = RC_j for all i, j	Equal risk contribution
Glide Path Rule	Equity % = 110 - Age	Age-based allocation

公式	表达式	适用场景
MVO目标函数	max w'mu - (lambda/2)w'Sigmaw	求解最优投资组合权重
均衡收益	Pi = lambda * Sigma * w_mkt	Black-Litterman模型起点
BL后验收益	E(R) = [(tauSigma)^(-1) + P'Omega^(-1)P]^(-1) [(tauSigma)^(-1)Pi + P'Omega^(-1)Q]	融合主观观点的预期收益
风险贡献	RC_i = w_i * (Sigma*w)_i / sigma_p	风险平价目标
风险平价条件	RC_i = RC_j for all i, j	等风险贡献
下滑路径规则	股票占比 = 110 - 年龄	基于年龄的配置

Worked Examples

实操案例

Example 1: Three-Asset Mean-Variance Optimization

案例1：三资产均值方差优化

Given:

Assets: US Equity (mu=8%, sigma=16%), Int'l Equity (mu=7%, sigma=18%), US Bonds (mu=3%, sigma=4%)
Correlations: US/Intl Equity = 0.75, US Equity/Bonds = 0.10, Intl Equity/Bonds = 0.05
Risk aversion: lambda = 4
Constraints: long-only, fully invested

Calculate: Optimal weights

Solution:

Covariance matrix:

Cov(US,US) = 0.16^2 = 0.0256
Cov(Intl,Intl) = 0.18^2 = 0.0324
Cov(Bond,Bond) = 0.04^2 = 0.0016
Cov(US,Intl) = 0.75 * 0.16 * 0.18 = 0.0216
Cov(US,Bond) = 0.10 * 0.16 * 0.04 = 0.00064
Cov(Intl,Bond) = 0.05 * 0.18 * 0.04 = 0.00036

MVO with lambda=4 (solving numerically or via quadratic programming):

Optimal weights (approximate):

US Equity: 35%
Int'l Equity: 15%
US Bonds: 50%

Portfolio: expected return = 5.25%, volatility = 7.8%

Note: The high bond allocation results from the optimization penalizing variance heavily (lambda=4). Reducing lambda or adding a minimum equity constraint would shift toward equities.

已知条件：

资产：美股（mu=8%, sigma=16%）、国际股票（mu=7%, sigma=18%）、美债（mu=3%, sigma=4%）
相关性：美股/国际股票=0.75，美股/债券=0.10，国际股票/债券=0.05
风险厌恶系数：lambda=4
约束：仅做多，满仓

计算： 最优权重

求解：

协方差矩阵：

Cov(美股,美股) = 0.16^2 = 0.0256
Cov(国际股票,国际股票) = 0.18^2 = 0.0324
Cov(债券,债券) = 0.04^2 = 0.0016
Cov(美股,国际股票) = 0.75 * 0.16 * 0.18 = 0.0216
Cov(美股,债券) = 0.10 * 0.16 * 0.04 = 0.00064
Cov(国际股票,债券) = 0.05 * 0.18 * 0.04 = 0.00036

lambda=4时的MVO求解（数值求解或二次规划求解）：

最优权重（近似值）：

美股：35%
国际股票：15%
美债：50%

投资组合：预期收益=5.25%，波动率=7.8%

注：高债券占比是因为优化对方差的惩罚力度较高（lambda=4）。降低lambda或添加最低股票占比约束会提升股票配置比例。

Example 2: Black-Litterman with a View on Emerging Markets

案例2：带新兴市场观点的Black-Litterman模型

Given:

Market-cap weights: US 55%, Developed Ex-US 30%, EM 15%
Equilibrium returns (from Pi = lambdaSigmaw_mkt): US 6.5%, Dev Ex-US 5.8%, EM 7.2%
Investor view: EM will outperform US by 2% (medium confidence)
tau = 0.05

Calculate: Posterior expected returns and implied weight shift

Solution:

View specification:

P = [-1, 0, 1] (EM minus US)
Q = [2%] (EM outperforms US by 2%)
Omega = [0.001] (medium confidence; lower = higher confidence)

After applying the Black-Litterman formula:

Posterior expected returns (approximate):

US: 6.2% (decreased from 6.5%)
Dev Ex-US: 5.9% (slight increase due to correlation effects)
EM: 7.8% (increased from 7.2%)

The posterior tilts returns toward the view. When these posterior returns are fed into MVO, the resulting weights shift from market-cap weights toward EM and away from US, but the shift is moderate and proportional to confidence, avoiding the extreme concentrations that raw MVO can produce.

已知条件：

市值权重：美股55%，发达市场非美股30%，新兴市场15%
均衡收益（由Pi = lambdaSigmaw_mkt计算）：美股6.5%，发达非美股5.8%，新兴市场7.2%
投资者观点：新兴市场将跑赢美股2%（中等置信度）
tau=0.05

计算： 后验预期收益和隐含权重偏移

求解：

观点定义：

P = [-1, 0, 1]（新兴市场减美股）
Q = [2%]（新兴市场跑赢美股2%）
Omega = [0.001]（中等置信度，值越小置信度越高）

应用Black-Litterman公式后：

后验预期收益（近似值）：

美股：6.2%（较6.5%下降）
发达非美股：5.9%（受相关性影响小幅上升）
新兴市场：7.8%（较7.2%上升）

后验收益向主观观点方向倾斜，将该后验收益输入MVO后，得到的权重会从市值基准向新兴市场偏移、降低美股占比，但偏移幅度适中，与置信度成正比，避免了原始MVO可能产生的极端集中持仓问题。

Common Pitfalls

常见误区

MVO is highly sensitive to expected return inputs and has been called an "error maximizer" — small changes in returns produce large changes in weights
Unconstrained MVO often produces extreme, concentrated positions — always add constraints (long-only, max weight, turnover limits)
Black-Litterman requires the analyst to specify confidence in views (Omega), which is itself uncertain
Risk parity portfolios require leverage to achieve equity-like returns, introducing borrowing costs and leverage risk
Ignoring implementation costs: transaction costs, bid-ask spreads, and taxes can significantly erode theoretical optimal returns
Ignoring liquidity constraints: some asset classes (private equity, real estate) cannot be rebalanced quickly
Glide paths assume a generic investor — individual circumstances may require customization
Over-reliance on historical covariance matrices that may not reflect future relationships

MVO对预期收益输入高度敏感，被称为「误差放大器」——收益的微小变化会导致权重的大幅变动
无约束的MVO通常会生成极端集中的持仓，必须添加约束（仅做多、单资产最大权重、换手率限制）
Black-Litterman模型需要分析师指定观点置信度（Omega），该参数本身存在不确定性
风险平价组合需要加杠杆才能达到股票级别的收益，会引入借贷成本和杠杆风险
忽略落地成本：交易成本、买卖价差和税费会大幅侵蚀理论最优收益
忽略流动性约束：部分资产类别（私募股权、房地产）无法快速调仓
下滑路径假设是通用投资者，个人实际情况可能需要定制化调整
过度依赖历史协方差矩阵，可能无法反映未来的相关性关系

Cross-References

交叉参考

historical-risk (wealth-management plugin, Layer 1a): volatility and correlation inputs for mean-variance optimization
forward-risk (wealth-management plugin, Layer 1b): expected return forecasts and scenario analysis for portfolio optimization
diversification (wealth-management plugin, Layer 4): diversification principles underpin all allocation frameworks
bet-sizing (wealth-management plugin, Layer 4): position sizing within the allocated asset classes
rebalancing (wealth-management plugin, Layer 4): maintaining allocation targets over time
quantitative-valuation (wealth-management plugin, Layer 3): valuation signals can inform TAA decisions

historical-risk（财富管理插件，层级1a）：均值方差优化的波动率和相关性输入
forward-risk（财富管理插件，层级1b）：投资组合优化的预期收益预测和情景分析
diversification（财富管理插件，层级4）：所有配置框架的基础分散化原则
bet-sizing（财富管理插件，层级4）：已分配资产类别内的仓位设定
rebalancing（财富管理插件，层级4）：长期维持配置目标
quantitative-valuation（财富管理插件，层级3）：估值信号可支撑TAA决策

Reference Implementation

参考实现

See

scripts/asset_allocation.py

for computational helpers.

计算工具请查看

scripts/asset_allocation.py

。