Monday morning. Friend's text on two MF factsheets. Same brochure 10Y return. Different ending NAV.
"Both funds list 10Y average annual return 12 pct. I started Rs 10 lakh in each ten years ago. One ended Rs 28.4 lakh. The other ended Rs 21.8 lakh." The brochure printed the arithmetic mean side by side. The standard deviation lived next to it in eight point grey type he had never opened. Fund A vol 14 pct. Fund B vol 28 pct. Same average. Half as smooth on one. The compounding noticed.
28.4lakh
Fund A . vol 14 pct
Rs 10 lakh in. Same 12 pct arithmetic mean over 10Y. Lower variance. Bigger cheque on the way out. Geometric ~ 11.0 pct.
VS
21.8lakh
Fund B . vol 28 pct
Same Rs 10 lakh in. Same 12 pct arithmetic mean. Twice the swing. Geometric drops to ~ 8.1 pct. The rupee felt every drawdown.
Same brochure number. Rs 6.6 lakh gap in the bank. The variance is the line item that ate it. Card two has the formula. Card three has the rules.