Jo cheez quietly returns destroy karti hai woh koi ek bura saal nahi hai — woh hai fee jo har saal compounding mein kaatti jaati hai.
Pehle principles se shuru karte hain. Ek saal mein fund ke assets pehle gross return g se badhte hain, jo factor (1+g) deta hai. Phir TER fassets ke percentage ke roop mein lagaya jaata hai (return ke nahi), jo bacha hua hisse ko (1−f) se multiply karta hai. Toh ek saal ka net growth factor product hai:
1+r=(1+g)(1−f)
N saalon mein, ₹1 badh kar ho jaata hai:
Vnet(N)=[(1+g)(1−f)]N=(1+g)N(1−f)N
Fee-free version Vgross(N)=(1+g)N ke comparison mein, fees mein gaya wealth ka fraction hai:
L(N)=1−Vgross(N)Vnet(N)=1−(1+g)N(1+g)N(1−f)N
(1+g)N saaf cancel ho jaata hai — fee drag gross return par depend hi nahi karta:
Active aur passive funds ke beech primary GOAL ka difference kya hai?
Active ek benchmark ko beat karne ki koshish karta hai; passive use match karne ki.
Costs ke baad average active investor kyun underperform karta hai?
Sharpe ki arithmetic — costs se pehle active investors collectively market return kamaate hain; zyaada fees ghataao toh woh average par peeche rah jaate hain.
N saalon ke liye sahi fee-drag formula likho.
L(N)=1−(1−f)N (kyunki TER assets ko har saal (1−f) se multiply karta hai).
Fee ko gross return se simply subtract kyun nahi karte?
TER assets ka percentage hai, multiplicatively apply hota hai: net factor =(1+g)(1−f) hai, 1+g−f nahi.
Kya fee drag L(N) gross return g par depend karta hai?
Nahi — (1+g)N cancel ho jaata hai, isliye L(N)=1−(1−f)N sirf f aur N par depend karta hai.
Typical expense ratio range: active vs passive?
Active ≈ 0.5–2%; passive ≈ 0.03–0.5%.
Passive fund ki success kaise judge karte ho?
Chhote tracking error/difference se apne index ke saath, outperformance se nahi.
Fund ke return ka apne benchmark ke return se deviation.
Recall Feynman: 12-saal ke bacche ko explain karo
Socho ek badi class jahan sabke grades average kiye jaate hain. Kuch bacche thoda better karte hain, kuch thoda worse, lekin milake woh average ke barabar hote hain — yahi "market" hai. Ab, ek active fund ek tutor ki tarah hai jo tumhe bahut charge karta hai aur promise karta hai ki woh tumhe average se upar le jayega. Lekin kyunki saare tutored bacche milake bhi class average ke barabar hi average hote hain, aur unhone tutor ko pay kiya, poore taur par tutored bacche average se neeche reh jaate hain tutor ki fee ke barabar. Ek passive fund ek chhoti si fee mein class average accept karne jaisa hai. Sasta, boring, aur zyaadatar aage nikalta hai. Aur woh fee? Har saal tumhare pure dher ka ek hissa liya jaata hai — toh saal dar saal yeh quietly use chhota karta rehta hai. Bas itna hi!
