A portfolio gains 50% in year 1 and loses 50% in year 2. What are its arithmetic and geometric average annual returns?
Arithmetic mean = (50 − 50)/2 = 0%. Geometric = √(1.5 × 0.5) − 1 = √0.75 − 1 ≈ −13.4%; ₹100 actually becomes ₹75.
The concept: Arithmetic vs geometric mean
Worked example
Choice 1 returns −50% then +100%. Choice 2 returns +10% then +10%. • Arithmetic mean (AMR): 25% vs 10%. • Geometric mean (GMR): 0% vs 10%. > ₹1,00,000 ends at ₹1,00,000 under choice 1 and at ₹1,21,000 under choice 2. Choice 2 is clearly better.