Variance drag . why the same average return ends with different money
Two portfolios. Same arithmetic average. Different ending balances. The volatile one loses to the math.
Toy run . start Rs 100 . two years . each portfolio averages 10 pct per year . Portfolio A swings hard . Portfolio B stays steady.
Path
Year 1
Year 2
Ending Rs
Portfolio A. high vol
+50 pct . Rs 150
-30 pct . Rs 105
105
Portfolio B. low vol
+10 pct . Rs 110
+10 pct . Rs 121
121
Arithmetic mean. both
10 pct
10 pct
tie
Geometric truth
A compounds at 2.5
B compounds at 10.0
16 Rs gap
Same average return. 16 rupees difference. The volatile path forfeits the gap to variance, not to bad picks.
Sigma squared is the cost of being volatile. Two portfolios can earn the same average year by year and the lower-vol one still ends with more money. The difference is paid by variance.