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Wednesday 21 October 2026 18:28:52 GMT
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➡️Quant Finance from scratch Part 10: Correlation Step 1, two assets and one hidden market. Every day the simulated market gives both assets the same push, and each gets its own push, typically half as big. Each asset is built to swing 20 % a year. Step 2, the cloud. Put each day on a map, A's move across and B's move up. Their own pushes alone would make a round cloud, and the shared market stretches it along a rising line. Step 3, what it measures. Put every move in typical swings (distance from its average divided by its standard deviation), multiply the two moves of each day and take the average. Moving the same way counts plus, moving apart counts minus. Over 10,000 simulated years this pair scores +0.80. Step 4, the scale. The average always lands between −1 and +1. At +1 every point sits on a rising line, at −1 on a falling line, and at 0 the cloud is round. Step 5, cause. Correlation never tells you which one causes the other. Here neither does, because the hidden market moves both. Step 6, risk. Put half your money in each. Each asset alone swings 20.0 % a year, and the 50/50 mix swings 19.0 % at a correlation of +0.80, 14.1 % at 0 and 10.0 % at −0.50. The code builds every pair from the same market and the same noise, weighted with the square roots of |c| and 1 − |c|, so each asset keeps its 20 % (variances add, Part 3). The average of the products is exactly the Pearson correlation. Why it matters: portfolio risk depends on how assets move together, the core of Harry Markowitz's
➡️Quant Finance from scratch Part 10: Correlation Step 1, two assets and one hidden market. Every day the simulated market gives both assets the same push, and each gets its own push, typically half as big. Each asset is built to swing 20 % a year. Step 2, the cloud. Put each day on a map, A's move across and B's move up. Their own pushes alone would make a round cloud, and the shared market stretches it along a rising line. Step 3, what it measures. Put every move in typical swings (distance from its average divided by its standard deviation), multiply the two moves of each day and take the average. Moving the same way counts plus, moving apart counts minus. Over 10,000 simulated years this pair scores +0.80. Step 4, the scale. The average always lands between −1 and +1. At +1 every point sits on a rising line, at −1 on a falling line, and at 0 the cloud is round. Step 5, cause. Correlation never tells you which one causes the other. Here neither does, because the hidden market moves both. Step 6, risk. Put half your money in each. Each asset alone swings 20.0 % a year, and the 50/50 mix swings 19.0 % at a correlation of +0.80, 14.1 % at 0 and 10.0 % at −0.50. The code builds every pair from the same market and the same noise, weighted with the square roots of |c| and 1 − |c|, so each asset keeps its 20 % (variances add, Part 3). The average of the products is exactly the Pearson correlation. Why it matters: portfolio risk depends on how assets move together, the core of Harry Markowitz's "Portfolio Selection" (Journal of Finance, 1952; Nobel prize 1990). One catch: correlations measured in calm times can rise when markets fall. Longin and Solnik (Journal of Finance, 2001) found that the correlation between the largest stock markets increases in bear markets. This video is for education only, and nothing in it is financial advice. #quantfinance #correlation #portfolio #risk #python

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