grad-fama-french
用 Fama-French 三因子模型拆解資產報酬，評估基金的因子曝險和 alpha
中文翻譯
--- name: "grad-fama-french" description: "用 Fama-French 三因子模型，把資產報酬拆解成市場、規模與價值因子。當使用者需要解釋報酬的橫斷面差異、評估基金在 CAPM alpha 之外的績效、評估投資組合的小型股或價值股傾斜，或問到「為什麼小型股報酬比較高」「價值溢酬是真的嗎」「什麼因子驅動報酬」時，就用這個 skill。" metadata: category: "WP-26 財務理論" tags: ["Fama-French", "three-factor", "SMB", "HML", "factor-model", "asset-pricing"] --- # Fama-French Three-Factor Model ## Overview Fama 和 French（1993）在 CAPM 上加了兩個因子，也就是規模（SMB）和價值（HML），用來解釋 CAPM 單獨無法捕捉的股票報酬橫斷面變異。這個模型顯示，小型股和高帳面市值比的股票會賺到系統性的溢酬。 ## When to Use - 解釋為什麼某些投資組合的 CAPM alpha 不為零 - 在控制因子曝險之後，評估基金經理人的能力 - 建構傾斜特定因子的投資組合 - 資產定價異常現象的學術研究 ## When NOT to Use - 固定收益或衍生性商品定價（這些是股票導向的因子） - 該市場沒有可用的因子資料 - 當作完整的模型：獲利能力和投資因子也可能重要（五因子） ## Assumptions ``` IRON LAW: Single-factor models (CAPM) underestimate expected returns for small-cap and value stocks. Size and value represent systematic risk factors that command their own premia. ``` 關鍵假設： 1. SMB 和 HML 捕捉的是系統性風險，不是錯誤定價 2. 因子溢酬在不同時期和市場中是持續的 3. 因子是由可觀察、有再平衡的投資組合建構出來的 ## Methodology ### Step 1 — Obtain Factor Data - Rm-Rf：市場超額報酬 - SMB（Small Minus Big）：小型股投資組合報酬減大型股投資組合報酬 - HML（High Minus Low）：高 B/M 投資組合報酬減低 B/M 投資組合報酬 ### Step 2 — Run Time-Series Regression Ri - Rf = ai + bi(Rm-Rf) + si(SMB) + hi(HML) + ei。建構細節見 `references/`。 ### Step 3 — Interpret Factor Loadings - bi：對市場的敏感度（和 CAPM 的 beta 相同） - si：規模曝險（正值 = 傾向小型股） - hi：價值曝險（正值 = 傾向價值股，負值 = 傾向成長股） ### Step 4 — Evaluate Alpha 如果 alpha（ai）在統計上不顯著，報酬就是由因子曝險解釋，表示沒有經理人的能力。 ## Output Format ```markdown ## Fama-French Analysis: [Fund / Portfolio] ### Regression Results | Factor | Loading | t-stat | Interpretation | |--------|---------|--------|----------------| | Market (Rm-Rf) | x.xx | x.xx | [market exposure] | | SMB | x.xx | x.xx | [size tilt] | | HML | x.xx | x.xx | [value tilt] | | Alpha | x.xx% | x.xx | [skill or luck] | ### R-squared - Three-factor R2: x% vs CAPM R2: x% ### Conclusions - [Factor attribution summary] - [Manager skill assessment] ``` ## Gotchas - 因子溢酬會隨國家和時期而變，不保證會持續 - HML 在論文發表後減弱了，有人把這歸因於套利 - 五因子模型（2015）加入了獲利能力（RMW）和投資（CMA），三因子可能不夠 - 因子的建構方法很重要，不同的切分點會得出不同結果 - 高 R-squared 不代表模型「正確」，只代表因子解釋了變異 - 因子代表風險還是錯誤定價，爭論還在持續 ## References - Fama, E. & French, K. (1993). Common risk factors in the returns on stocks and bonds. *Journal of Financial Economics*, 33(1), 3-56. - Fama, E. & French, K. (2015). A five-factor asset pricing model. *Journal of Financial Economics*, 116(1), 1-22. - Fama, E. & French, K. (1992). The cross-section of expected stock returns. *Journal of Finance*, 47(2), 427-465.
英文原文
--- name: "grad-fama-french" description: "Apply the Fama-French three-factor model to decompose asset returns into market, size, and value factors. Use this skill when the user needs to explain cross-sectional return differences, evaluate fund performance beyond CAPM alpha, assess small-cap or value tilts in a portfolio, or when they ask 'why do small caps earn more', 'is value premium real', or 'what factors drive returns'." metadata: category: "WP-26 財務理論" tags: ["Fama-French", "three-factor", "SMB", "HML", "factor-model", "asset-pricing"] --- # Fama-French Three-Factor Model ## Overview Fama and French (1993) extended CAPM by adding two factors — size (SMB) and value (HML) — to explain cross-sectional variation in stock returns that CAPM alone cannot capture. The model shows that small-cap and high book-to-market stocks earn systematic premiums. ## When to Use - Explaining why CAPM alpha is nonzero for certain portfolios - Evaluating fund manager skill after controlling for factor exposures - Constructing factor-tilted portfolios - Academic research on asset pricing anomalies ## When NOT to Use - For fixed income or derivatives pricing (equity-focused factors) - When factor data is unavailable for the market in question - As a complete model — profitability and investment factors may also matter (five-factor) ## Assumptions ``` IRON LAW: Single-factor models (CAPM) underestimate expected returns for small-cap and value stocks. Size and value represent systematic risk factors that command their own premia. ``` Key assumptions: 1. SMB and HML capture systematic risk, not mispricing 2. Factor premia are persistent across time periods and markets 3. Factors are constructed from observable, rebalanced portfolios ## Methodology ### Step 1 — Obtain Factor Data - Rm-Rf: market excess return - SMB (Small Minus Big): return of small-cap portfolio minus large-cap portfolio - HML (High Minus Low): return of high B/M portfolio minus low B/M portfolio ### Step 2 — Run Time-Series Regression Ri - Rf = ai + bi(Rm-Rf) + si(SMB) + hi(HML) + ei. See `references/` for construction details. ### Step 3 — Interpret Factor Loadings - bi: market sensitivity (same as CAPM beta) - si: size exposure (positive = small-cap tilt) - hi: value exposure (positive = value tilt, negative = growth tilt) ### Step 4 — Evaluate Alpha If alpha (ai) is statistically insignificant, returns are explained by factor exposures — no manager skill. ## Output Format ```markdown ## Fama-French Analysis: [Fund / Portfolio] ### Regression Results | Factor | Loading | t-stat | Interpretation | |--------|---------|--------|----------------| | Market (Rm-Rf) | x.xx | x.xx | [market exposure] | | SMB | x.xx | x.xx | [size tilt] | | HML | x.xx | x.xx | [value tilt] | | Alpha | x.xx% | x.xx | [skill or luck] | ### R-squared - Three-factor R2: x% vs CAPM R2: x% ### Conclusions - [Factor attribution summary] - [Manager skill assessment] ``` ## Gotchas - Factor premia vary across countries and time periods — not guaranteed to persist - HML has weakened post-publication; some attribute this to arbitrage - Five-factor model (2015) adds profitability (RMW) and investment (CMA) — three-factor may be insufficient - Factor construction methodology matters; different breakpoints yield different results - High R-squared does not mean the model is "correct" — it means factors explain variance - Debate persists whether factors represent risk or mispricing ## References - Fama, E. & French, K. (1993). Common risk factors in the returns on stocks and bonds. *Journal of Financial Economics*, 33(1), 3-56. - Fama, E. & French, K. (2015). A five-factor asset pricing model. *Journal of Financial Economics*, 116(1), 1-22. - Fama, E. & French, K. (1992). The cross-section of expected stock returns. *Journal of Finance*, 47(2), 427-465.