Volatility Drag

Monday morning. Friend forwards two MF factsheets. Both print "10Y average annual return 12 pct" in big type at the top.

He had run the same Rs 10 lakh through each one ten years ago. One ended at Rs 28.4 lakh today. The other ended at Rs 21.8 lakh. Six lakh gap on the same headline number.

Asked himself the question I would have asked.

The answer was sitting next to the return on the same page, in eight point grey type he had never opened. Standard deviation. Fund A vol 14 pct. Fund B vol 28 pct. Same average, twice the swing on one of them. The compounding noticed, even though the brochure did not say so.

The math is the part most factsheets refuse to print. The geometric return, the one that actually compounds in your account, sits roughly at the arithmetic mean minus sigma squared over two. Vol 14 pct costs about a percentage point of compounding. Vol 28 pct costs almost four. Double the swing, four times the drag. The penalty scales with vol squared, not vol.

The reason is asymmetric recovery. A 10 pct drawdown needs an 11 pct gain to break even. A 20 pct drawdown needs 25. A 30 pct needs 43. A 50 pct needs 100. You do not lose what you swing through. You lose what you stay below. Every deeper hole carries a non-linear bill on the way back, and the variance drag is just that bill aggregated across years.

The brochure prints the arithmetic mean because it is the bigger number. The bank account prints the geometric mean because that is the one that actually compounded. The wedge between them is the price of vol, paid in rupees you never see on a factsheet.

A return without its volatility is half a sentence. Read the other half before you sign the cheque.

How variance, drawdown asymmetry and the geometric mean sit underneath every honest return number