6.6.3
Ek factor ek rule-based tilt hoti hai aapke portfolio mein jo historically ek return premium kamaati rahi hai. Do famous tilts:
Size (SMB): small companies tend karte hain long run mein big companies se zyada kamane ke liye.Low-volatility (LowVol): boring, low-risk stocks ne returns kamaaye hain jo wild high-risk stocks jitne ya unse bhi achhe hain — jo classic theory ke munh par ek thappad hai.
WHY care karein? Kyunki ye do factors aapko aisi portfolios banane dete hain jinke returns "sirf market" se poori tarah explain nahi hote — aur inme se ek (LowVol) asliyat mein textbook risk-reward rule ko tod deta hai.
Factor ek persistent, measurable characteristic hoti hai stocks ki (size, valuation, risk, momentum...) jo average returns mein systematic difference se associated hoti hai. Hum iska return isolate karte hain favoured group ko long karke aur unfavoured group ko short karke.
HUM kya measure karte hain — ek factor return ek long–short spread ke roop mein banta hai:
R factor = R long basket − R short basket
WHY long–short? Kyunki do baskets subtract karne se market cancel ho jaata hai . Dono baskets market ke saath upar-neeche hote hain; difference pure tilt ko isolate karta hai.
Definition Size factor (SMB)SMB ("Small Minus Big") = small-cap stocks ka average return minus large-cap stocks ka average return. Company ki "size" market capitalisation se measure hoti hai = price × shares outstanding.
HOW Fama & French ne ise banaya (simplified 2×3 sort):
Saare stocks ko market cap se rank karo; median par Small (S) aur Big (B) mein split karo.
Value (Low/Medium/High book-to-market) se bhi 3 groups mein split karo → 6 portfolios: SL SM SH BL BM BH.
Small side average = 3 1 ( R S L + R S M + R S H )
Big side average = 3 1 ( R B L + R B M + R B H )
Subtract karo:
SMB = 3 1 ( R S L + R S M + R S H ) − 3 1 ( R B L + R B M + R B H )
Intuition WHY small, big ko beat karta hai (the story)
Small firms zyada risky hoti hain: kam diversified, recessions mein fragile, thin liquidity → investors compensation ke roop mein higher expected return demand karte hain.
Small firms under-researched hoti hain aur arbitrage karna mushkil hota hai → mispricings persist karti hain.
Premium real hai lekin cyclical hai — ek decade tak gayab ho sakta hai, phir wapas aa sakta hai.
Definition Low-volatility factorLow-volatility investing un stocks ko khareedti hai jinke returns mein low variance/standard deviation (ya low beta) hoti hai aur high-volatility stocks se bachti hai. Anomaly yeh hai: low-vol stocks kam risk ke saath similar ya higher returns kamaate hain → higher risk-adjusted return.
Capital Asset Pricing Model (CAPM) predict karta hai ki expected return beta ke saath linearly badhti hai:
E [ R i ] = R f + β i ( E [ R m ] − R f )
Toh high-beta (high-vol) stocks ko zyada pay karna chahiye. Lekin empirically line flat ya downward-sloping hoti hai high-beta stocks ke liye. Woh gap low-volatility anomaly hai.
Intuition WHY low-vol jeetta hai? (behavioural + structural)
Lottery preference: investors exciting, high-vol "shot at the moon" stocks ke liye overpay karte hain → woh overpriced ho jaate hain → future returns kam hote hain.Leverage constraints: bahut se funds borrow nahi kar sakte returns boost karne ke liye, toh woh punch paane ke liye high-beta stocks khareedite hain → woh high-beta ko bid up karte hain → uska return depress ho jaata hai.Benchmarking: managers index se underperform karne se darte hain, toh woh dull low-beta names se bachte hain → woh saste rehte hain.
Volatility = returns ka standard deviation:
σ = N − 1 1 ∑ t = 1 N ( R t − R ˉ ) 2
Sharpe ratio ke zariye risk-adjusted return:
Sharpe = σ R ˉ − R f
WHY Sharpe yahan? Kyunki low-vol ka magic ek higher Sharpe hai: chahe raw return thoda sa kam ho, bahut chhote σ
Worked example Example 1 — Ek month ke liye SMB compute karoSmall portfolios ne return kiya: R S L = 3% , R S M = 2% , R S H = 4% R B L = 1% , R B M = 0% , R B H = 2%
Step 1: Small avg = 3 3 + 2 + 4 = 3% Why? SMB ko har side ke liye ek number chahiye.
Step 2: Big avg = 3 1 + 0 + 2 = 1% Why? Comparability ke liye same treatment.
Step 3: SMB = 3% − 1% = + 2% Why subtract? Size tilt isolate karta hai, market cancel karta hai.
Reading: small ne big ko is month 2% se beat kiya → positive size premium.
Worked example Example 2 — Sharpe par low-vol, high-vol ko beat karta haiStock A (low-vol): R ˉ = 8% σ = 10% R ˉ = 10% σ = 30% R f = 2%
Step 1: SharpeA = 10 8 − 2 = 0.60 Why? Risk ki har unit par return.
Step 2: SharpeB = 30 10 − 2 = 0.267 Why? Same yardstick, fair comparison.
Reading: B ka raw return higher hai lekin A kaafi behtar hai risk-adjusted basis par. A ko B ke risk tak lever up karna B ko beat kar dega — yahi low-vol edge ka essence hai.
Worked example Example 3 — Low-vol basket banana5 stocks mein se jinke σ Why? Factor characteristic par rank karo.
Step 2: 5 ka bottom 40% = 2 stocks → 12% aur 18% waale names. — Why? Hum low-risk group ko long karte hain.
Step 3 (optional long–short): factor isolate karne ke liye top 40% (40%, 55%) ko short karo.
Common mistake "Higher volatility ka matlab higher return hona chahiye — yahi poora risk-reward rule hai!"WHY sahi lagta hai: CAPM aur intuition kehte hain risk = reward, aur yeh hota bhi hai overall market aur asset classes ke liye. WHY yeh individual stocks ke liye galat hai: stock universe ke andar beta-return line flat/inverted hoti hai kyunki lottery demand aur leverage constraints ki wajah se. Fix: risk-reward broad diversified portfolios ke across hold karta hai, individual high-vol stocks ke across nahi.
Common mistake "Size factor = bas koi bhi small stock khareed lo."WHY sahi lagta hai: SMB "small minus big" hai, toh small = premium, theek hai na? WHY galat hai: premium small caps ke diversified basket se aata hai; individual small caps mein huge idiosyncratic risk hoti hai. SMB sabse chhote, most illiquid names mein concentrated hota hai aur mid-caps ke liye near-zero ho sakta hai. Fix: ek broad small-cap portfolio use karo, aur jaano ki premium cyclical hai.
Common mistake "Low-vol ek free lunch hai bina kisi risk ke."WHY sahi lagta hai: higher Sharpe ek cheat code jaisa lagta hai. WHY galat hai: low-vol mein hidden risks hain — interest-rate sensitivity (bond-like defensives), crowding, aur raging bull markets mein underperformance ke lambe stretches. Fix: ise ek risk-adjusted improvement maano, zero-risk nahi.
Recall Quick self-test (answers chhupao, pehle forecast karo)
SMB ka kya matlab hai aur ise kaise compute karte hain? → Small Minus Big; avg small-cap return − avg big-cap return.
Factor ke liye long–short spread kyun use karte hain? → Market cancel karne ke liye aur tilt isolate karne ke liye.
Kaunsa textbook model low-vol anomaly contradict karta hai? → CAPM (return beta ke saath badhna chahiye).
Do reasons batao ki low-vol kaam kyun karta hai. → Lottery preference; leverage constraints (benchmarking bhi).
Kaunsa ratio low-vol ka advantage best dikhata hai? → Sharpe ratio.
Recall Feynman: 12-saal ke bachche ko explain karoDo lemonade stands socho. "Size" idea kehta hai ki ek chhoti nayi stand ek giant company se tez grow kar sakti hai aur tumhe zyada paisa dila sakti hai — lekin yeh zyada shakeable hoti hai, toh tum extra reward demand karte ho. "Low-volatility" idea ajeeb wala hai: ek calm, steady stand jiske koi crazy days kabhi nahi hote aksar utna hi paisa kamata hai jitna ek wild, up-and-down stand kamaata hai — bahut kam heart attacks ke saath. Log exciting wild stand ke liye overpay karte hain kyunki lagta hai jaise yeh jackpot maar sakta hai, toh calm stand secretly better deal ban jaata hai.
SMB ka kya matlab hai aur kaise compute hota hai Small Minus Big = average small-cap return − average large-cap return (per period).
Factors long–short spread kyun use karte hain Market exposure cancel karne ke liye aur pure factor tilt isolate karne ke liye.
Size factor mein company ki "size" kisse measure hoti hai Market capitalisation = share price × shares outstanding.
Low-volatility anomaly kya contradict karta hai CAPM ki prediction ki expected return beta ke saath linearly badhti hai.
Low-vol kaam karne ke do behavioural/structural reasons Lottery preference (exciting stocks ke liye overpaying) aur leverage constraints (funds high-beta khareedti hain borrow karne ki jagah).
Low-vol ka advantage dikhane ke liye best metric Sharpe ratio (excess return divided by volatility).
Sharpe ratio formula (mean return − risk-free rate) / standard deviation of returns.
Small-cap return higher kyun hoti hai (risk story) Small firms riskier hoti hain, less liquid, under-researched hoti hain, toh investors premium demand karte hain.
Volatility aur single stocks ke baare mein common trap Yeh assume karna ki higher vol ka matlab hamesha higher return hota hai; stocks ke andar beta-return line flat/inverted hoti hai.
Kya low-vol ek free lunch hai Nahi — isme rate sensitivity, crowding, aur bull markets mein long underperformance hoti hai; yeh ek risk-adjusted improvement hai.
Small firms riskier and under-researched
Low variance or low beta stocks
Higher risk-adjusted return
