@quantfinancetogo: ➡️ Quant finance from scratch Part 9: volatility drag Step 1, plus 50 %, then minus 50 %. Start with $100. Gain 50 % and you have $150, lose 50 % and you have $75. The average of the two returns is 0 %, yet you are down 25 %. Step 2, why. The gain added $50, but the loss took half of $150, which is $75. Percent moves multiply (Part 5), so the loss hits a bigger pile. Step 3, the square. Up and down by the same percent s leaves (1 + s) × (1 − s) = 1 − s² of your money: $99 for 10 %, $75 for 50 %. Step 4, the rule. Per step that is about half the swing squared. This is volatility drag: your money grows at about the average return minus half the volatility squared. Step 5, the test. Two simulated investments, both built for 10 % a year on average, with a volatility of 10 % and 50 %. Over 10,000 simulated years the calm one averaged 9.9 % with a growth rate of 9.4 %, while the wild one averaged 11.0 % and its money shrank by 1.5 % a year. Step 6, the rule predicted both. Half the volatility squared is 0.5 % for calm and 12.5 % for wild: five times the swing, 25 times the drag, more than its whole average. Average minus drag gives 9.4 % and minus 1.5 %, matching the simulation to one decimal. So is your average return lying? It leaves out the drag. The average return is the average daily return times 252. The growth rate is the average daily log return times 252 (Part 5), the rate the money compounds at. The rule is approximate: for plus and minus 50 % the exact loss per step is 13.4 % against its 12.5 %. Why quants care: in the classic stock price model, the typical path grows at the average minus half the variance. The same drag hits funds that reset their leverage daily. This video is for education only, and nothing in it is financial advice. #quantfinance #volatilitydrag #compounding #volatility #python

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Friday 02 October 2026 15:31:22 GMT