performance-attribution

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Performance Attribution

绩效归因

Purpose

目的

Decompose portfolio returns into explainable components to understand where value was added or lost. This skill covers equity attribution (Brinson-Fachler), factor-based attribution, fixed-income attribution, currency effects, and multi-period linking methods.

将投资组合回报分解为可解释的组成部分，以了解收益或亏损的来源。本技能涵盖股票归因（Brinson-Fachler模型）、因子归因、固定收益归因、货币效应以及多期链接方法。

Layer

层级

5 — Policy & Planning

5 — 政策与规划

Direction

方向

retrospective

回顾性

When to Use

使用场景

Explaining where portfolio returns came from relative to a benchmark
Evaluating whether a manager added value through allocation, selection, or both
Decomposing returns into systematic factor exposures and residual alpha
Attributing fixed-income returns to yield, curve, spread, and credit components
Handling currency effects in international portfolio attribution
Linking single-period attribution results across multiple periods
Conducting holdings-based vs returns-based attribution analysis

解释投资组合回报相对于基准的来源
评估基金经理是否通过配置、选股或两者结合创造了超额收益
将回报分解为系统性因子暴露和剩余Alpha
将固定收益回报归因于收益率、收益率曲线、利差和信用成分
处理国际投资组合归因中的货币效应
将单期归因结果跨多个周期链接
进行基于持仓与基于回报的归因分析

Core Concepts

核心概念

Brinson-Fachler Attribution (Single Period)

Brinson-Fachler单期归因

The classic equity attribution model decomposes active return (portfolio return minus benchmark return) into three effects:

Allocation effect: Value added by over/underweighting sectors relative to the benchmark
- A_i = (w_p,i - w_b,i) × (R_b,i - R_b)
- Rewards overweighting sectors that outperform the total benchmark
Selection effect: Value added by picking better securities within each sector
- S_i = w_b,i × (R_p,i - R_b,i)
- Rewards outperforming the sector benchmark regardless of weight
Interaction effect: Combined effect of both overweighting and outperforming (or vice versa)
- I_i = (w_p,i - w_b,i) × (R_p,i - R_b,i)
- Captures the joint benefit of overweighting a sector AND selecting better securities in it
Total active return: R_p - R_b = Σ A_i + Σ S_i + Σ I_i

Where: w_p,i = portfolio weight in sector i, w_b,i = benchmark weight in sector i, R_p,i = portfolio return in sector i, R_b,i = benchmark return in sector i, R_b = total benchmark return.

经典的股票归因模型将主动回报（投资组合回报减去基准回报）分解为三个效应：

配置效应： 通过相对于基准超配/低配行业所创造的收益
- A_i = (w_p,i - w_b,i) × (R_b,i - R_b)
- 奖励超配跑赢整体基准的行业
选股效应： 在各行业内挑选更优证券所创造的收益
- S_i = w_b,i × (R_p,i - R_b,i)
- 无论权重如何，只要行业内选股跑赢行业基准即可获得收益
交互效应： 超配/低配与跑赢/跑输的联合效应
- I_i = (w_p,i - w_b,i) × (R_p,i - R_b,i)
- 捕捉超配某行业且该行业内选股跑赢基准的联合收益
总主动回报： R_p - R_b = Σ A_i + Σ S_i + Σ I_i

其中：w_p,i = 投资组合在行业i的权重，w_b,i = 基准在行业i的权重，R_p,i = 投资组合在行业i的回报，R_b,i = 基准在行业i的回报，R_b = 基准总回报。

Multi-Period Attribution

多期归因

Single-period attribution does not compound across periods. Geometric linking methods are required:

Carino method: Applies a smoothing factor to make arithmetic effects compound to the correct geometric total
Menchero method: Uses a logarithmic approach for smoother decomposition
GRAP (Geometric Return Attribution Program): Converts arithmetic effects to geometric equivalents
Key principle: the sum of linked attribution effects must equal the total geometric active return over the full period

单期归因无法跨周期复利计算，需要使用几何链接方法：

Carino方法： 应用平滑因子使算术效应复合为正确的几何总回报
Menchero方法： 使用对数方法实现更平滑的分解
GRAP（几何回报归因程序）： 将算术效应转换为几何等效值
核心原则：链接后的归因效应总和必须等于整个周期内的总几何主动回报

Factor-Based Attribution

因子归因

Decomposes returns into exposures to systematic risk factors:

Model: R_p = Σ β_k × F_k + α
- β_k = portfolio's exposure (loading) to factor k
- F_k = return of factor k during the period
- α = residual return unexplained by factors (true alpha)
Common factors: Market (MKT), Size (SMB), Value (HML), Momentum (UMD), Quality (QMJ), Low Volatility (BAB)
Factor contribution: β_k × F_k for each factor
Active factor contribution: (β_p,k - β_b,k) × F_k
The model chosen (Fama-French 3, Carhart 4, Fama-French 5, Barra, Axioma) affects results

将回报分解为对系统性风险因子的暴露：

模型： R_p = Σ β_k × F_k + α
- β_k = 投资组合对因子k的暴露度（载荷）
- F_k = 周期内因子k的回报
- α = 无法被因子解释的剩余回报（真实Alpha）
常见因子： Market (MKT)、Size (SMB)、Value (HML)、Momentum (UMD)、Quality (QMJ)、Low Volatility (BAB)
因子贡献： 每个因子的β_k × F_k
主动因子贡献： (β_p,k - β_b,k) × F_k
所选模型（Fama-French 3因子、Carhart 4因子、Fama-French 5因子、Barra、Axioma）会影响结果

Fixed-Income Attribution

固定收益归因

Decomposes bond portfolio returns into component sources:

Yield return (income): Coupon income accrued during the period (yield × time)
Roll return: Price appreciation as bonds "roll down" the yield curve toward maturity
Curve change return: Impact of parallel and non-parallel yield curve shifts
- Duration effect: -D × Δy (parallel shift)
- Curve reshaping: key rate duration contributions
Spread change return: Impact of credit spread changes: -spread_duration × Δspread
Credit/default return: Losses from defaults or credit events
Residual: Unexplained return (convexity effects, model error)

将债券投资组合回报分解为各组成部分：

收益率回报（利息）： 周期内累积的票息收入（收益率×时间）
滚动回报： 债券随时间向到期日“滚动下移”收益率曲线带来的价格上涨
收益率曲线变动回报： 收益率曲线平行和非平行移动的影响
- 久期效应：-D × Δy（平行移动）
- 曲线重塑：关键利率久期贡献
利差变动回报： 信用利差变动的影响：-利差久期 × Δ利差
信用/违约回报： 违约或信用事件带来的损失
剩余项： 无法解释的回报（凸性效应、模型误差）

Currency Attribution

货币归因

For international portfolios, returns decompose into:

Local return: Return of the asset in its local currency
Currency return: Gain/loss from exchange rate movements
Cross-product: Interaction between local return and currency return
Total return (base currency): R_base ≈ R_local + R_currency + R_local × R_currency
Hedged return: Local return + hedge cost (forward premium/discount)
Attribution of active currency decisions: actual currency exposure vs benchmark currency exposure

对于国际投资组合，回报可分解为：

本地回报： 资产以本地货币计价的回报
货币回报： 汇率波动带来的收益/损失
交叉项： 本地回报与货币回报的交互效应
总回报（基准货币）： R_base ≈ R_local + R_currency + R_local × R_currency
对冲后回报： 本地回报 + 对冲成本（远期升水/贴水）
主动货币决策的归因：实际货币暴露与基准货币暴露的差异

Holdings-Based vs Returns-Based Attribution

基于持仓与基于回报的归因

Holdings-based: Uses actual portfolio positions; more accurate but requires detailed holdings data at each evaluation point
Returns-based (style analysis): Regresses portfolio returns against a set of style indices (e.g., Sharpe style analysis); less precise but requires only return series
Transaction-based: Most accurate; accounts for intra-period trading by using actual transaction records

基于持仓： 使用实际投资组合头寸；更准确，但需要各评估时点的详细持仓数据
基于回报（风格分析）： 将投资组合回报与一组风格指数进行回归（如Sharpe风格分析）；精度较低，但仅需回报序列
基于交易： 最准确；通过使用实际交易记录考虑期内交易的影响

Key Formulas

关键公式

Formula	Expression	Use Case
Allocation effect (sector i)	A_i = (w_p,i - w_b,i) × (R_b,i - R_b)	Sector weighting decisions
Selection effect (sector i)	S_i = w_b,i × (R_p,i - R_b,i)	Security selection within sector
Interaction effect (sector i)	I_i = (w_p,i - w_b,i) × (R_p,i - R_b,i)	Joint allocation-selection effect
Total active return	R_p - R_b = Σ(A_i + S_i + I_i)	Sum of all effects equals active return
Factor return contribution	C_k = β_k × F_k	Return from factor k exposure
Duration effect	ΔP/P ≈ -D × Δy	Bond price change from yield shift
Currency return	R_fx = (S_end - S_start) / S_start	Exchange rate impact

公式	表达式	使用场景
行业i的配置效应	A_i = (w_p,i - w_b,i) × (R_b,i - R_b)	行业权重决策
行业i的选股效应	S_i = w_b,i × (R_p,i - R_b,i)	行业内证券选择
行业i的交互效应	I_i = (w_p,i - w_b,i) × (R_p,i - R_b,i)	配置-选股联合效应
总主动回报	R_p - R_b = Σ(A_i + S_i + I_i)	所有效应之和等于主动回报
因子回报贡献	C_k = β_k × F_k	因子k暴露带来的回报
久期效应	ΔP/P ≈ -D × Δy	收益率变动带来的债券价格变化
货币回报	R_fx = (S_end - S_start) / S_start	汇率影响

Worked Examples

示例演算

Example 1: Brinson-Fachler equity attribution

示例1：Brinson-Fachler股票归因

Given: Two-sector portfolio (Tech and Healthcare). Portfolio: 35% Tech (returned 15%), 65% Healthcare (returned 8%). Benchmark: 25% Tech (returned 12%), 75% Healthcare (returned 6%). Total benchmark return: 0.25×12% + 0.75×6% = 7.5%. Calculate: Allocation, selection, and interaction effects for each sector, and total active return. Solution:

Total portfolio return: 0.35×15% + 0.65×8% = 5.25% + 5.20% = 10.45%.
Total active return: 10.45% - 7.50% = 2.95%.
Tech allocation effect: (0.35 - 0.25) × (12% - 7.5%) = 0.10 × 4.5% = +0.45% (overweight a sector that beat the benchmark).
Tech selection effect: 0.25 × (15% - 12%) = 0.25 × 3% = +0.75% (stock picks in Tech beat Tech benchmark).
Tech interaction effect: (0.35 - 0.25) × (15% - 12%) = 0.10 × 3% = +0.30% (overweight AND outperformed).
Healthcare allocation effect: (0.65 - 0.75) × (6% - 7.5%) = -0.10 × -1.5% = +0.15% (underweight a sector that lagged the benchmark).
Healthcare selection effect: 0.75 × (8% - 6%) = 0.75 × 2% = +1.50% (stock picks in Healthcare beat Healthcare benchmark).
Healthcare interaction effect: (0.65 - 0.75) × (8% - 6%) = -0.10 × 2% = -0.20% (underweight but outperformed — interaction is negative).
Totals: Allocation = 0.45 + 0.15 = 0.60%. Selection = 0.75 + 1.50 = 2.25%. Interaction = 0.30 + (-0.20) = 0.10%. Sum = 0.60 + 2.25 + 0.10 = 2.95% ✓.

给定条件： 双行业投资组合（科技和医疗健康）。投资组合：35%科技（回报15%），65%医疗健康（回报8%）。基准：25%科技（回报12%），75%医疗健康（回报6%）。基准总回报：0.25×12% + 0.75×6% = 7.5%。 计算： 各行业的配置、选股和交互效应，以及总主动回报。 解答：

投资组合总回报： 0.35×15% + 0.65×8% = 5.25% + 5.20% = 10.45%。
总主动回报： 10.45% - 7.50% = 2.95%。
科技行业配置效应： (0.35 - 0.25) × (12% - 7.5%) = 0.10 × 4.5% = +0.45%（超配跑赢基准的行业）。
科技行业选股效应： 0.25 × (15% - 12%) = 0.25 × 3% = +0.75%（科技行业内选股跑赢科技基准）。
科技行业交互效应： (0.35 - 0.25) × (15% - 12%) = 0.10 × 3% = +0.30%（超配且跑赢基准）。
医疗健康行业配置效应： (0.65 - 0.75) × (6% - 7.5%) = -0.10 × -1.5% = +0.15%（低配跑输基准的行业）。
医疗健康行业选股效应： 0.75 × (8% - 6%) = 0.75 × 2% = +1.50%（医疗健康行业内选股跑赢医疗健康基准）。
医疗健康行业交互效应： (0.65 - 0.75) × (8% - 6%) = -0.10 × 2% = -0.20%（低配但跑赢基准——交互效应为负）。
总计： 配置效应=0.45+0.15=0.60%。选股效应=0.75+1.50=2.25%。交互效应=0.30+(-0.20)=0.10%。总和=0.60+2.25+0.10=2.95% ✓。

Example 2: Factor-based attribution

示例2：因子归因

Given: A fund has factor loadings: β_mkt = 1.1, β_smb = 0.3, β_hml = -0.2. During the period: MKT = 5%, SMB = 2%, HML = -1%. Risk-free rate = 1%. Fund excess return = 7%. Calculate: Factor contributions and alpha. Solution:

Market contribution: 1.1 × 5% = 5.50%.
Size (SMB) contribution: 0.3 × 2% = 0.60%.
Value (HML) contribution: -0.2 × (-1%) = +0.20%.
Total factor-explained return: 5.50 + 0.60 + 0.20 = 6.30%.
Alpha (residual): 7.00% - 6.30% = +0.70%.
Interpretation: The fund's excess return of 7% is mostly explained by above-market beta (5.5%) and a small-cap tilt (0.6%). The negative value loading helped (+0.2%) as value underperformed. After accounting for all factors, the manager generated 0.70% of true alpha.

给定条件： 某基金的因子载荷：β_mkt=1.1，β_smb=0.3，β_hml=-0.2。周期内：MKT=5%，SMB=2%，HML=-1%。无风险利率=1%。基金超额回报=7%。 计算： 因子贡献和Alpha。 解答：

市场因子贡献： 1.1×5%=5.50%。
**规模因子（SMB）贡献：**0.3×2%=0.60%。
价值因子（HML）贡献：-0.2×(-1%)=+0.20%。
**因子解释的总回报：**5.50+0.60+0.20=6.30%。
Alpha（剩余项）：7.00%-6.30%=+0.70%。
解读： 基金7%的超额回报主要由高于市场的Beta（5.5%）和小盘股倾斜（0.6%）贡献。负的价值因子暴露有所帮助（+0.2%），因为价值股表现不佳。在考虑所有因子后，基金经理创造了0.70%的真实Alpha。

Common Pitfalls

常见误区

Interaction effect is hard to interpret — some attribution models fold it into allocation or selection, which changes reported results significantly
Multi-period attribution requires geometric linking — simple arithmetic attribution does not compound correctly and residuals grow over time
Returns-based attribution (style analysis) may not reflect actual holdings, especially for managers who trade actively or change style
Factor attribution results depend heavily on the chosen factor model — different models yield different alpha estimates
Currency attribution is often overlooked in international portfolios, hiding or inflating apparent skill
Survivorship bias in manager evaluation: only surviving funds are analyzed, overstating average skill
Confusing gross-of-fee and net-of-fee returns when comparing to benchmarks
Using inappropriate benchmarks that do not match the portfolio's investment universe

交互效应难以解释——部分归因模型将其纳入配置或选股效应，这会显著改变报告结果
多期归因需要几何链接——简单的算术归因无法正确复利计算，剩余项会随时间增长
基于回报的归因（风格分析）可能无法反映实际持仓，尤其是对于交易活跃或风格转换的基金经理
因子归因结果高度依赖所选因子模型——不同模型会产生不同的Alpha估计值
国际投资组合中常忽略货币归因，这会隐藏或夸大表观投资能力
基金经理评估中的幸存者偏差：仅分析存续基金，高估了平均投资能力
与基准比较时混淆费前和费后回报
使用与投资组合投资范围不匹配的不恰当基准

Cross-References

交叉引用

investment-policy: Benchmark selection in IPS directly feeds performance attribution analysis
tax-efficiency: After-tax attribution requires adjusting returns for tax impact
savings-goals: Attribution helps assess whether investment strategy is on track to meet goals
liquidity-management: Cash drag from liquidity reserves affects portfolio-level attribution

investment-policy： 投资政策声明（IPS）中的基准选择直接为绩效归因分析提供输入
tax-efficiency： 税后归因需要针对税收影响调整回报
savings-goals： 归因有助于评估投资策略是否符合目标进度
liquidity-management： 流动性储备带来的现金拖累会影响投资组合层面的归因

Reference Implementation

参考实现

See

scripts/performance-attribution.py

for computational helpers.

详见

scripts/performance-attribution.py

获取计算工具。