Noesis
6.6.3Factor & Behavioral Finance

Understand size and low-volatility factors

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🇮🇳 Yeh note Hinglish mein padho →

1. What is a factor? (foundation)

WHAT we measure — a factor return is built as a long–short spread:

Rfactor=Rlong basket−Rshort basketR_{\text{factor}} = R_{\text{long basket}} - R_{\text{short basket}}

WHY long–short? Because subtracting the two baskets cancels out the market. Both baskets rise and fall with the market; the difference isolates the pure tilt.

2. The Size factor (SMB = Small Minus Big)

Deriving SMB from scratch

HOW Fama & French built it (simplified 2×3 sort):

  1. Rank all stocks by market cap; split at the median into Small (S) and Big (B).
  2. Also split by value (Low/Medium/High book-to-market) into 3 groups → 6 portfolios: SL SM SH BL BM BH.
  3. Small side average =13(RSL+RSM+RSH)= \tfrac{1}{3}(R_{SL}+R_{SM}+R_{SH}).
  4. Big side average =13(RBL+RBM+RBH)= \tfrac{1}{3}(R_{BL}+R_{BM}+R_{BH}).
  5. Subtract:

SMB=13(RSL+RSM+RSH)−13(RBL+RBM+RBH)\text{SMB} = \tfrac{1}{3}(R_{SL}+R_{SM}+R_{SH}) - \tfrac{1}{3}(R_{BL}+R_{BM}+R_{BH})

3. The Low-Volatility factor

Why this is shocking — a first-principles clash

The Capital Asset Pricing Model (CAPM) predicts expected return rises linearly with beta:

E[Ri]=Rf+βi (E[Rm]−Rf)E[R_i] = R_f + \beta_i\,(E[R_m]-R_f)

So high-beta (high-vol) stocks should pay more. But empirically the line is flat or even downward-sloping for high-beta stocks. That gap is the low-volatility anomaly.

Measuring the risk we exploit

Volatility = standard deviation of returns:

σ=1N−1∑t=1N(Rt−Rˉ)2\sigma = \sqrt{\frac{1}{N-1}\sum_{t=1}^{N}(R_t-\bar R)^2}

Risk-adjusted return via the Sharpe ratio:

Sharpe=Rˉ−Rfσ\text{Sharpe} = \frac{\bar R - R_f}{\sigma}

WHY Sharpe here? Because low-vol's magic is a higher Sharpe: even if raw return is a touch lower, dividing by a much smaller σ\sigma gives a bigger number.

Figure — Understand size and low-volatility factors

4. Worked examples

5. Common mistakes (steel-manned)

6. Active recall

Recall Quick self-test (hide answers, forecast first)
  • What does SMB stand for and how is it computed? → Small Minus Big; avg small-cap return − avg big-cap return.
  • Why do we use a long–short spread for a factor? → To cancel the market and isolate the tilt.
  • What textbook model does the low-vol anomaly contradict? → CAPM (return should rise with beta).
  • Give two reasons low-vol works. → Lottery preference; leverage constraints (also benchmarking).
  • Which ratio shows low-vol's advantage best? → Sharpe ratio.
Recall Feynman: explain to a 12-year-old

Imagine two lemonade stands. The "size" idea says a tiny new stand can grow faster and make you more money than a giant company — but it's shakier, so you demand extra reward. The "low-volatility" idea is the weird one: a calm, steady stand that never has crazy days often makes you just as much money as a wild, up-and-down stand — with way fewer heart attacks. People overpay for the exciting wild stand because it feels like it could hit the jackpot, so the calm stand secretly becomes the better deal.

Connections

SMB stands for what and how computed
Small Minus Big = average small-cap return − average large-cap return (per period).
Why do factors use a long–short spread
To cancel out market exposure and isolate the pure factor tilt.
What is a company's "size" measured by in the size factor
Market capitalisation = share price × shares outstanding.
What does the low-volatility anomaly contradict
CAPM's prediction that expected return rises linearly with beta.
Two behavioural/structural reasons low-vol works
Lottery preference (overpaying for exciting stocks) and leverage constraints (funds buy high-beta instead of borrowing).
Best metric to show low-vol's advantage
Sharpe ratio (excess return divided by volatility).
Sharpe ratio formula
(mean return − risk-free rate) / standard deviation of returns.
Why is small-cap return higher (risk story)
Small firms are riskier, less liquid, under-researched, so investors demand a premium.
Common trap about volatility and single stocks
Assuming higher vol always means higher return; within stocks the beta-return line is flat/inverted.
Is low-vol a free lunch
No — it has rate sensitivity, crowding, and long underperformance in bull markets; it's a risk-adjusted improvement.

Concept Map

isolated via

cancels

example

example

equals

size measured by

built by

averages value groups

explained by

buys

contradicts

delivers

Factor: rule-based tilt

Long-short spread

Market return

Size factor SMB

Low-volatility factor

Small minus Big returns

Market capitalisation

Fama-French 2x3 sort

Neutralises value tilt

Small firms riskier and under-researched

Low variance or low beta stocks

CAPM risk-reward rule

Higher risk-adjusted return

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, factor investing ka matlab hai ki tum apne portfolio mein ek soch-samajh kar tilt lagate ho — jaise "chhoti companies zyada khareedo" ya "kam risk waali stocks khareedo". Har factor ko hum long-short spread se measure karte hain: jo group pasand hai usko long, jo nahi pasand usko short — isse market ka effect cancel ho jaata hai aur sirf pure factor ka return bachta hai.

Size factor (SMB = Small Minus Big): yeh kehta hai ki chhoti market-cap waali companies, badi companies ko long run mein beat karti hain. Kyun? Kyunki chhoti companies risky hoti hain, kam liquid hoti hain, aur inpe research kam hoti hai — is compensation ke badle investors extra return maangte hain. Formula simple hai: small stocks ka average return minus big stocks ka average return.

Low-volatility factor sabse interesting hai. Textbook (CAPM) kehta hai "zyada risk = zyada return", lekin real data mein boring, kam volatility waali stocks utna hi ya usse bhi zyada return de deti hain — kam risk ke saath! Iska reason behavioural hai: log exciting, "lottery-type" high-vol stocks ke liye zyada paisa dete hain, jisse woh overpriced ho jaati hain aur unka future return gir jaata hai. Isliye Sharpe ratio (return divided by risk) low-vol stocks ka bahut behtar aata hai.

Yaad rakhne ka trick: "Small beats Big; Slow & Steady wins the race." Par ek warning — ye premiums cyclical hote hain, kai saal tak gaayab ho sakte hain, aur single chhoti stock kabhi mat kharido, hamesha diversified basket lo. Low-vol bhi free lunch nahi hai — bull market mein peeche reh sakti hai. Risk-adjusted edge samajhna zaroori hai, na ki "no risk".

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Connections

Learn Fama-French three - five factor modelsStock-Market · 6.6.4Understand CAPM and betaStock-Market · 5.5.5