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➡️ Quantitative Finance From Scratch, Part 21: Linear Regression in finance Linear regression finds the straight line that best describes how one quantity moves with another. In finance, that is often a stock's daily return against the market's daily return. Least squares: for every day, you measure how far the real return lies from the line, square that distance and add everything up. The best line makes this sum as small as possible. The line has two numbers. The slope is the beta from Part 14: how strongly the stock follows the market. The intercept is alpha: what the stock earns on average on a day when the market does not move. What the line cannot explain is the residual, and R² tells you which share of the swings (the variance) the line explains, from 0 for nothing to 1 for everything. In this video we simulate two years (504 trading days) of a market and a stock with a built-in beta of 1.2, a second factor with a beta of 0.6 and no alpha. The line finds a beta of 1.26 (the 1.2 lies within the range of chance for two years of data), an alpha of +0.05% a day and an R² of 52%. With two inputs, the line becomes a plane: betas 1.27 and 0.60, R² 63%. Quants use regression to estimate betas, to size hedges, to test whether a strategy earns more than its risk, and to check whether two assets really move together. The limits: a regression only finds a relationship in the data you give it. It does not prove that one thing causes the other, a few extreme days can pull the line (three invented extreme days move our slope from 1.26 to 1.10), and a relationship from the past can change. Education only, not financial advice. #quantitativefinance #quant #finance #regression #beta

➡️ Quantitative Finance From Scratch, Part 21: Linear Regression in finance Linear regression finds the straight line that best describes how one quantity moves with another. In finance, that is often a stock's daily return against the market's daily return. Least squares: for every day, you measure how far the real return lies from the line, square that distance and add everything up. The best line makes this sum as small as possible. The line has two numbers. The slope is the beta from Part 14: how strongly the stock follows the market. The intercept is alpha: what the stock earns on average on a day when the market does not move. What the line cannot explain is the residual, and R² tells you which share of the swings (the variance) the line explains, from 0 for nothing to 1 for everything. In this video we simulate two years (504 trading days) of a market and a stock with a built-in beta of 1.2, a second factor with a beta of 0.6 and no alpha. The line finds a beta of 1.26 (the 1.2 lies within the range of chance for two years of data), an alpha of +0.05% a day and an R² of 52%. With two inputs, the line becomes a plane: betas 1.27 and 0.60, R² 63%. Quants use regression to estimate betas, to size hedges, to test whether a strategy earns more than its risk, and to check whether two assets really move together. The limits: a regression only finds a relationship in the data you give it. It does not prove that one thing causes the other, a few extreme days can pull the line (three invented extreme days move our slope from 1.26 to 1.10), and a relationship from the past can change. Education only, not financial advice. #quantitativefinance #quant #finance #regression #beta

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