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it's mood 🔥
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➡️ Quantitative Finance From Scratch, Part 23: Mean Reversion. Mean reversion means that a quantity which moves far from its long run average tends to drift back toward it. A single stock price behaves much like a random walk, but spreads, ratios and rates (the gap between two related stocks, interest rates, volatility) often show a pull back. The simplest model: every day the distance from the average shrinks by a fixed share, plus a random shock. The half life is the time it takes for half of that distance to disappear, so a short half life means a strong pull back. To test for the pull, you regress today's change on yesterday's distance from the average. A negative slope means a pull back. But even pure chance often looks like a pull here: in our test, 34% of pure random walks passed the usual limit of -2. So quants use a stricter limit for the t statistic of about -3 (the Dickey-Fuller limit, about -2.9). In this video we simulate one spread with a built-in half life of 10 days for four years. The regression finds a slope of -0.070, a t statistic of -6.05 and a half life of 9.5 days, far beyond that limit. The z score measures how many standard deviations the spread is from its average. Is it profitable? Only if the pull is real, strong enough to beat trading costs and still there in data you did not use for testing. A 2016 study of 97 published return signals found that their returns were on average 58% lower after publication. The average can shift, the pull can vanish, and a spread can keep widening before it comes back. Short samples can even make a pure random walk look mean reverting: in our test, three months of a pure random walk typically showed a half life of about 10 days. Education only, not financial advice. #quantitativefinance #trading #meanreversion #statisticalarbitrage #finance
➡️ Quantitative Finance From Scratch, Part 23: Mean Reversion. Mean reversion means that a quantity which moves far from its long run average tends to drift back toward it. A single stock price behaves much like a random walk, but spreads, ratios and rates (the gap between two related stocks, interest rates, volatility) often show a pull back. The simplest model: every day the distance from the average shrinks by a fixed share, plus a random shock. The half life is the time it takes for half of that distance to disappear, so a short half life means a strong pull back. To test for the pull, you regress today's change on yesterday's distance from the average. A negative slope means a pull back. But even pure chance often looks like a pull here: in our test, 34% of pure random walks passed the usual limit of -2. So quants use a stricter limit for the t statistic of about -3 (the Dickey-Fuller limit, about -2.9). In this video we simulate one spread with a built-in half life of 10 days for four years. The regression finds a slope of -0.070, a t statistic of -6.05 and a half life of 9.5 days, far beyond that limit. The z score measures how many standard deviations the spread is from its average. Is it profitable? Only if the pull is real, strong enough to beat trading costs and still there in data you did not use for testing. A 2016 study of 97 published return signals found that their returns were on average 58% lower after publication. The average can shift, the pull can vanish, and a spread can keep widening before it comes back. Short samples can even make a pure random walk look mean reverting: in our test, three months of a pure random walk typically showed a half life of about 10 days. Education only, not financial advice. #quantitativefinance #trading #meanreversion #statisticalarbitrage #finance

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