Learn about SIP vs lumpsum investing

2.2.5 · Stock-Market › Funds, ETFs & Pooled Vehicles

YE choice matter kyun karti hai?

Markets upar-neeche jaate rehte hain. Jis price par aap khareedte ho woh aapka future return decide karta hai. Agar aap sirf bottom par khareed sakte, toh aap us waqt lumpsum choose karte. Lekin koi bhi bottom pehle se nahi jaanta — yahi timing the market ki problem hai.

• Lumpsum yeh bet lagata hai ki abhi accha waqt hai (ya ki time-in-market, timing se behtar hai).
• SIP timing par bet lagane se mana karta hai; yeh purchases ko spread karta hai taaki koi ek price dominate na kare.

Rupee-cost averaging actually kaam kaise karta hai? (Derivation)

Hum kya chahte hain: SIP ke andar aap effectively per unit jo average price pay karte ho woh.

Maano aap har period ek fixed amount $A$ invest karte ho, aur period $i$ mein unit price (NAV) $p_i$ hai.

Step 1 — har period khareedI gayi units. $u_i=\frac{A}{p_i}$ Yeh step kyun? Fixed rupee amount $A$ ko price $p_i$ se divide karne par units milti hain. Kam $p_i$ ⇒ badi $u_i$.

Step 2 — $n$ periods ke baad total units. $U={\sum }_{i=1}^n\frac{A}{p_i}=A{\sum }_{i=1}^n\frac{1}{p_i}$

Step 3 — total invest kiya gaya paisa. $M=nA$

Step 4 — average cost per unit = kharcha hua paisa ÷ milayi gayi units: ${\bar{p}}_{\text{SIP}}=\frac{M}{U}=\frac{nA}{A\sum \frac{1}{p_i}}=\frac{n}{{\sum }_{i=1}^n\frac{1}{p_i}}$

Yeh prices ka ==harmonic mean== hai!

Step 5 — inequality (kyun SIP volatile market mein help karta hai). AM–HM inequality ke according, positive prices ke liye: $\text{HM}\le \text{AM},\text{equality iff all }{p}_i\text{ equal.}$ Toh ${\bar{p}}_{\text{SIP}}\le {\bar{p}}_{\text{AM}}$. SIP ki average cost kabhi bhi prices ke simple average se zyada nahi hoti, aur jab bhi prices vary karti hain toh strictly kam hoti hai. Yahi rupee-cost averaging ka mathematical core hai.

Worked Examples

Steel-manned Mistakes

80/20 Takeaway

Flashcards

#flashcards/stock-market

Connections

• Rupee-Cost Averaging
• Mutual Funds and NAV
• ETFs and Index Funds
• Time in Market vs Timing the Market
• Compounding and Power of Long-Term Investing
• AM-GM-HM Inequalities
• Dollar-Cost Averaging
• Behavioral Finance and Investor Discipline

Concept Map