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➡️ Quant Finance from scratch part 14: market beta Step 1, a simulated market and three stocks: the market moves about 1 % on a typical day (15.9 % a year). Three stocks follow it with betas of 0.5, 1 and 2, each with its own random push of 0.7 % a day. Step 2, beta in plain words: beta is a stock's sensitivity, or exposure, to the market factor, and a measure of risk, because it shows how strongly the stock swings relative to the market, in step with it. On the 122,149 simulated days when the market fell about 1 %, the three stocks fell 0.5 %, 1.0 % and 2.0 % on average, and on the days it rose about 1 % they rose as much. Step 3, the slope: put every day on a map with the market's move across and the stock's move up. Beta is the slope of the line that fits the cloud best, computed as Cov(stock, market) / Var(market). Over 10,000 simulated years it measures 0.50, 1.00 and 2.00, exactly the built-in betas. Real betas have to be estimated like this from past returns. Step 4, many betas: a factor model gives a stock one beta per factor. The three-factor model of Fama and French (Journal of Financial Economics, 1993) adds firm size and book-to-market (value) to the market factor, and later videos cover them. In everyday use,
➡️ Quant Finance from scratch part 14: market beta Step 1, a simulated market and three stocks: the market moves about 1 % on a typical day (15.9 % a year). Three stocks follow it with betas of 0.5, 1 and 2, each with its own random push of 0.7 % a day. Step 2, beta in plain words: beta is a stock's sensitivity, or exposure, to the market factor, and a measure of risk, because it shows how strongly the stock swings relative to the market, in step with it. On the 122,149 simulated days when the market fell about 1 %, the three stocks fell 0.5 %, 1.0 % and 2.0 % on average, and on the days it rose about 1 % they rose as much. Step 3, the slope: put every day on a map with the market's move across and the stock's move up. Beta is the slope of the line that fits the cloud best, computed as Cov(stock, market) / Var(market). Over 10,000 simulated years it measures 0.50, 1.00 and 2.00, exactly the built-in betas. Real betas have to be estimated like this from past returns. Step 4, many betas: a factor model gives a stock one beta per factor. The three-factor model of Fama and French (Journal of Financial Economics, 1993) adds firm size and book-to-market (value) to the market factor, and later videos cover them. In everyday use, "beta" almost always means the market beta. Why it matters: in Part 11, mixing many assets averaged their own pushes away, while the shared market swing stayed. Beta measures how much of this systematic risk a stock carries, so a big equal mix of beta-2 stocks still swings about twice as much as the market. In the CAPM (William Sharpe, Journal of Finance, 1964), a higher beta means a higher expected return, and that is the next episode. This video is for education only, and nothing in it is financial advice. #quantfinance #beta #capm #finance #python

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