📘 AM, GM, HM, IRR
1. Arithmetic Mean (AM)
Used when investing in multiple stocks for 1 year.
AM = (x₁ + x₂ + x₃ + ... + xₙ) / n
If weighted: Weighted AM = (w₁x₁ + w₂x₂ + ...) / (w₁ + w₂ + ...)
Use when time is same, amount is different.
2. Geometric Mean (GM)
Used when investment is done for multiple years in the same stock.
GM = [(1 + x₁)(1 + x₂)(1 + x₃)...]^(1/n) - 1
Use for compounding returns.
3. Harmonic Mean (HM)
Used when equal money is invested in each stock to find average price.
HM = n / (1/x₁ + 1/x₂ + ... + 1/xₙ)
| Stock | Invested (₹) | Price | Shares |
|---|---|---|---|
| X | 100 | 10 | 10 |
| Y | 100 | 50 | 2 |
| Z | 100 | 5 | 20 |
Wrong average price: (10 + 50 + 5)/3 = 21.67 ❌
Correct HM: 3 / (1/10 + 1/50 + 1/5) = ₹9.375 ✅
4. IRR (Internal Rate of Return)
Used when investment is made in different years and amounts.
- Year 0: ₹100
- Year 1: ₹50
- Year 2: ₹200
- Year 3: Return ₹457
IRR gives true return with varying cash flows.
📝 Summary
- AM: Different stocks, same time
- GM: Same stock, different years
- HM: Equal ₹ in different stocks
- IRR: Different amounts, different years
If numbers are same: AM = GM = HM
If variation increases: AM > GM > HM