Systematic Risk Exposure (Market Beta)
factor.formula
Beta coefficient calculation formula:
CAPM Model:
in:
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The monthly return of stock i in the past K months is calculated as follows: $r_{i,t} = (P_{i,t} - P_{i,t-1})/P_{i,t-1}$, where $P_{i,t}$ is the closing price of stock i at the end of month t.
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The monthly return of the market in the past K months is usually represented by the return of the market index (such as the CSI 300 Index, the S&P 500 Index, etc.). The calculation formula is: $r_{m,t} = (I_{t} - I_{t-1})/I_{t-1}$, where $I_{t}$ is the closing price of the market index at the end of month t.
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The expected return on stock i.
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The expected return on the market portfolio.
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The risk-free interest rate is usually represented by the short-term Treasury bond yield. For example, the annualized yield to maturity of the Treasury bond of the same period can be used and then converted into a monthly yield.
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The covariance between the monthly return $r_i$ of stock i and the monthly market return $r_m$ measures the strength of their relationship in the same direction.
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The variance of the market monthly return $r_m$ measures the volatility of the market return.
factor.explanation
Systematic risk exposure (market Beta) reflects the sensitivity of individual stock returns to the fluctuations in the overall market return rate and is an important indicator for measuring stock systematic risk. Stocks with a Beta value greater than 1 usually have a return volatility greater than the market average, and are high-risk and high-return types; stocks with a Beta value less than 1 usually have a return volatility less than the market average, and are low-risk and low-return types; stocks with a Beta value equal to 1 have a return volatility consistent with the market average. The CAPM model assumes that market Beta is positively correlated with the expected return of a stock, that is, the higher the Beta value, the higher the expected return of the stock, and vice versa. In practical applications, the Beta value changes of stocks can be dynamically tracked by rolling calculation. It should be noted that the CAPM model is a theoretical model, and there may be various factors in the actual market, such as the idiosyncratic risk of individual stocks, investor sentiment, etc., which may cause deviations between the actual return and the predicted value of the CAPM model.