Dimson Adjusted Beta
factor.formula
Step 1: Estimate the beta coefficients of individual stocks using a multiple regression model that includes leading and lagging market returns.
Step 2: Sum the estimated leading, current, and lagged beta coefficients to obtain the Dimson adjusted beta.
in:
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The return of stock i on day d within a specific time window (e.g., K months).
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The return of a market portfolio (such as an index) on day d within a specific time window (such as K months).
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The risk-free interest rate on day d within a specific time window (such as K months). Usually the yield of government bonds or other low-risk assets is used.
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The return of the market portfolio (such as an index) on day d-1 within a specific time window (such as K months). Represents the market return lagged by one period.
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The risk-free rate on day d-1 within a specific time window (e.g., K months). represents the risk-free rate lagged by one period.
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The return rate of the market portfolio (such as index) on day d+1 within a specific time window (such as K months). It represents the market return rate of the leading period.
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The risk-free rate on day d+1 within a specific time window (e.g., K months). Represents the risk-free rate for the leading period.
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The regression intercept term of stock i represents the expected excess return of stock i when the market return is zero.
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The sensitivity of stock i's return to the market return lagged by one period (beta coefficient).
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The sensitivity of stock i's return to the current market return (beta coefficient).
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The sensitivity of stock i's return to the one-period leading market return (beta coefficient).
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The residual term of the regression model represents the volatility of stock i's return that is not explained by the model.
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The length of the time window for calculating the regression is usually in months (such as 1 month, 6 months, 12 months). The window must contain at least 15 trading days of data to ensure the reliability of the regression results.
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The estimated value of the beta coefficient of stock i's return on the market return lagged one period, estimated by regression.
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The estimated value of the beta coefficient of stock i's return on the current market return estimated by regression.
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The estimated value of the beta coefficient of stock i's return on the market return one period ahead, estimated by regression.
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The Dimson adjusted beta coefficient represents the sensitivity of stock i to market risk after taking into account the impact of asynchronous trading.
factor.explanation
Dimson adjusted beta corrects the bias in beta estimates caused by infrequent stock trading by incorporating leading and lagging market returns into the regression model. Traditional beta calculations often assume that all stock transactions occur synchronously, which is not true in the actual market. For inactive stocks, traditional beta may underestimate their sensitivity to market risk due to the lag in price information updates. The Dimson method provides a more accurate risk assessment by capturing the impact of this asynchronous trading. This factor is suitable for quantitative strategies that need to consider the impact of liquidity, especially in inactive or illiquid stocks.