Learn Fama-French three - five factor models

6.6.4 · Stock-Market › Factor & Behavioral Finance

YE MODEL EXIST KYU KARTA HAI? (CAPM ki failure ko steel-man karna)

CAPM predict karta hai ki har asset Security Market Line par hoga: $E [R_{i}] - R_{f} = β_{i} (E [R_{m}] - R_{f})$

KYA GALAT HUA: Jab aap stocks ko size aur book-to-market ( $B / M$ ) ke hisaab se sort karte ho aur realized average returns dekhte ho, to small & value stocks apne $β$ ke prediction se zyada kamaate hain. Jo residual (alpha) bachta hai wo noise nahi hai — wo persistent aur cross-sectional hai.

CAPM sahi kyun laga: Ek factor elegant hai aur "market hi wo ek risk hai jo diversify nahi ho sakta." Fair baat hai. Fix: Agar koi return premium bahut saare stocks aur time mein pervasive hai, to wo ek priced systematic risk hai, isliye uska apna factor hona chahiye — usse alpha mein dumpna theek nahi.

Three-Factor Model — scratch se banate hain

Hum ek portfolio ka excess return $R_{i} - R_{f}$ explain karna chahte hain. CAPM se shuru karo aur do mimicking portfolios add karo jo size aur value effects ko isolate karte hain.

YE KAISE CONSTRUCT HOTE HAIN (2×3 sort):

Saare stocks ko market cap ke hisaab se Small / Big mein split karo (median breakpoint).
Independently $B / M$ ke hisaab se Low (30%) / Medium / High (30%) mein split karo.
Isse 6 value-weighted portfolios milte hain: SL, SM, SH, BL, BM, BH.
Phir: $SMB = \frac{1}{3} (S L + S M + S H) - \frac{1}{3} (B L + B M + B H)$ $HML = \frac{1}{2} (S H + B H) - \frac{1}{2} (S L + B L)$

Five-Factor Model (2015) — aur do kyun add kiye?

3-factor model bhi profitability aur investment ke hisaab se sort kiye stocks mein alpha chhodta tha. To Fama & French ne add kiya:

Figure — Learn Fama-French three - five factor models

Worked Examples

Common Mistakes

#flashcards/stock-market

What are the three factors in the Fama-French 3-factor model?

Market excess return (Rm−Rf), SMB (size), HML (value).

What does SMB stand for and capture?

Small Minus Big; the size premium (small-cap stocks earning more than large-cap).

What does HML stand for and which stocks does positive HML favor?

High Minus Low book-to-market; positive HML = value (cheap) stocks over growth.

What two factors are added in the 5-factor model?

RMW (profitability: Robust Minus Weak) and CMA (investment: Conservative Minus Aggressive).

In the equation, what is the difference between a loading (e.g. s_i) and a premium (E[SMB])?

Loading = regression sensitivity (dimensionless slope); premium = the factor's expected return. Expected extra return = loading × premium.

What does alpha represent in a factor model?

The average return NOT explained by the included factors; ideally ≈0. Not automatically "skill".

Why were profitability and investment added?

The dividend-discount/valuation identity implies expected return rises with profitability and falls with investment, for given price & B/M.

How is SMB constructed to be a "pure" size bet?

Average small-cap portfolios across all B/M levels minus average big-cap across all B/M, so the value effect cancels.

CAPM predicts return from what single quantity?

Market beta only: E[Ri]−Rf = βi(E[Rm]−Rf).

A growth stock typically has what sign of HML loading?

Negative h (low book-to-market).

Recall Feynman: 12-saal ke bacche ko explain karo

Socho toy cars ko do cheezein se sort kar rahe ho: kitni chhoti hain aur kitni sasti hain. Tumhe pata chalta hai chhoti cars aur sasti cars dhalaaN par tez chalti hain. CAPM sirf "dhalaaN kitni bhaari hai" (market) check karta tha. Fama & French ne kaha: ye bhi check karo "kya ye chhoti car hai?" (SMB) aur "kya ye bargain thi?" (HML). Baad mein unhone add kiya "kya iska engine bahut paisa banata hai?" (RMW) aur "kya ye cheezein banane mein paisa barbaad karta hai?" (CMA). Ab, agar koi car tez jaati hai, tum explain kar sakte ho kyun — instead of ise magic (alpha) kehne ke.

Connections

CAPM and the Security Market Line — wo one-factor ancestor jise ye generalize karta hai.
Arbitrage Pricing Theory (APT) — multi-factor theoretical framework jiska FF ek instance hai.
Momentum Factor (Carhart 4-factor) — wo famous factor jo FF ne originally chhodha tha.
Book-to-Market and Value Investing — HML ke peeche ki economic story.
Behavioral Explanations vs Risk-Based Explanations — kya premium risk hai ya mispricing?
Regression and R-squared — factor loadings ki statistical machinery.
Smart Beta and Factor Investing — kaise funds in tilts ko package karte hain.