@quantfinancetogo: ➡️ Quant Finance From Scratch, part 3: why risk grows with the square root of time, in 16 lines of Python you can follow line by line. Two questions guide the video: why is this rule so important in quantitative finance, and what does it mean for a stock? Step 1, a thousand prices. Each one moves $1 up or down per step, like a coin flip, for 400 steps. A few end up far away, and most stay surprisingly close to the start. Step 2, the spread. The standard deviation is the typical distance from the middle: about $5 after 25 steps, $10 after 100 and $20 after 400. Four times the steps give twice the spread. Step 3, why a square root. Ups and downs cancel each other out, while their squares only add up. That sum is the variance: 100 after 100 steps (99.6 in our run), and its square root is 10. That is the ten from the start: 73 % of the prices end within $10. Step 4, the drift from part 2. It grows in a straight line, the randomness only with the square root. From 25 to 4,000 steps the drift grew 160 times and the randomness about 13 times, so the share of prices below their start fell from 43 % to 4 %. Step 5, a stock. Say it moves 1 % up or down a day. A year of 252 trading days gives 1 % × √252 = 15.9 %, and 66 % of 20,000 simulated years ended inside that range. With a drift of 6.8 % a year, the chance to end above the start grows from 64 % after one year to 91 % after ten, in this simple model. Why quants care: the rule turns daily risk into yearly risk, and it sits inside every option price, because a later deadline leaves the price more room to move. This video is for education only, and nothing in it is financial advice. #quantfinance #finance #volatility #python #probability

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Wednesday 30 September 2026 07:53:10 GMT