Understand factor investing fundamentals

6.6.1 · Stock-Market › Factor & Behavioral Finance

WHAT is a factor?

WHY do premiums exist? Do competing stories (dono partly true hain):

Risk-based: value stocks isliye sasti hoti hain kyunki woh genuinely zyada risky hoti hain (distress, illiquidity), isliye investors zyada return demand karte hain. Koi free lunch nahi — tumhe pain hold karne ka paisa milta hai.
Behavioral: investors overreact/underreact karte hain (herding, overconfidence), stocks ko systematically misprice karte hain, aur factor us mistake ko harvest karta hai. Yeh isliye persist kar sakta hai kyunki arbitrage ki limits hoti hain (costs, career risk).

HOW we express returns: from CAPM to multi-factor

Step 1 — The single-factor model (CAPM), derived

Hum assume karte hain ki stock ka excess return (return above the risk-free rate $r_{f}$ ) market ke excess return ke saath linearly move karta hai.

$R_{i} - r_{f} = α_{i} + β_{i} (R_{m} - r_{f}) + ε_{i}$

Why this form?

$R_{i} - r_{f}$ : hum excess returns mein kaam karte hain kyunki sirf guaranteed rate se upar ka reward hi risk ka compensation hai.
$β_{i}$ : sensitivity — stock $i$ kitna move karta hai jab market 1% move kare. Ise regression slope ke roop mein derive kiya jata hai: $β_{i} = \frac{Cov ( R _{i} , R _{m} )}{Var ( R _{m} )}$ Why? Best-fit line ka slope jo $E [ε^{2}]$ minimize kare woh exactly cov over var hota hai — yahi least-squares result hai.
$α_{i}$ : intercept — return jo market se explain nahi hota. Efficient CAPM world mein, $α_{i} = 0$ .
$ε_{i}$ : idiosyncratic noise, $E [ε_{i}] = 0$ , diversifiable.

Step 2 — CAPM leaves patterns behind

Empirically, small-cap aur cheap ("value") stocks ne unke $β$ ke prediction se zyada kamaya → ek positive $α$ jo random nahi tha. Woh leftover $α$ actually ek hidden factor exposure tha.

Step 3 — Add factors (Fama–French style)

Hum equation ko factor-mimicking portfolios se augment karte hain, har ek ek long-minus-short basket hai:

$R_{i} - r_{f} = α_{i} + β_{m} (R_{m} - r_{f}) + β_{s} SMB + β_{v} HML + β_{m o m} WML + ε_{i}$

Figure — Understand factor investing fundamentals

Common Mistakes (Steel-manned)

Recall Feynman: ek 12-saal ke bachche ko explain karo

Socho gym class mein bachcho ko height ke hisaab se sort kar rahe ho. Lambe bachche basketball ke liye pehle pick hote hain — "lambapan" ek factor hai jo kuch predict karta hai. Stock market mein, kuch traits — sasta hona, chhota hona, winning streak par hona — predict karte hain ki kaun se stocks thoda zyada kamate hain time ke saath. Factor investing aise kehna hai ki "main hamesha lambe, tez, aur saste-mein-milne-wale players draft karunga," aur average par meri team zyada score karti hai. Lekin kuch seasons lambe bachche injured ho jaate hain — isliye yeh har game nahi jeetta, sirf bahut saare, bahut saare games ke baad.

Recall — Flashcards

Factor investing mein factor kya hota hai?

Ek broad, persistent, investable characteristic (e.g., value, size, momentum) jo systematically securities mein return differences explain karta hai.

Factor premium kyun exist karta hai?

Ya toh risk-based compensation (tumhe genuinely riskier assets hold karne ka paisa milta hai) ya behavioral (doosron ki persistent mispricing harvest karna jo limits-to-arbitrage erase nahi kar sakti).

Market beta ka formula?

β_{i} = Cov (R_{i}, R_{m}) / Var (R_{m})

— the least-squares regression slope.

Hum excess returns (

R - r_{f}

) mein kyun kaam karte hain?

Sirf guaranteed risk-free rate se upar ka reward hi risk ka compensation hai; risk-free portion mein koi risk premium nahi hota.

SMB ka full form kya hai aur yeh kya measure karta hai?

Small Minus Big; the size premium (small caps minus large caps).

HML kya measure karta hai?

High Minus Low book-to-market; the value premium (cheap stocks minus expensive/growth stocks).

Factor portfolios long–short kyun hote hain?

Common market movement cancel karne ke liye aur characteristic ke apne pure return ko isolate karne ke liye.

Alpha aur factor premium mein difference?

Factor premium systematic return hai factor loadings se (cheaply replicable); alpha woh return hai jo saare factor exposures remove karne ke baad bachta hai — genuine unique skill.

Multi-factor model mein expected excess return?

E [R_{i}] - r_{f} = \sum_{k} β_{i, k} λ_{k}

— factor loadings aur factor premiums ka sum.

Ek genuine factor ke paanch criteria?

Persistent, pervasive, robust, investable, aur uska ek economic rationale hona chahiye ("factor zoo" se bachne ke liye).

Connections

Capital Asset Pricing Model (CAPM)
Fama-French Three-Factor Model
Momentum Anomaly
Efficient Market Hypothesis
Limits to Arbitrage
Behavioral Biases (Overconfidence, Herding)
Smart Beta ETFs
Portfolio Beta and Diversification

WHAT is a factor?

HOW we express returns: from CAPM to multi-factor

Step 1 — The single-factor model (CAPM), derived

Step 2 — CAPM leaves patterns behind

Step 3 — Add factors (Fama–French style)

The factor premium in numbers

Worked Examples

Common Mistakes (Steel-manned)

Recall — Flashcards

Connections

Concept Map