Monthly Weighted Idiosyncratic Volatility
factor.formula
Monthly weighted idiosyncratic volatility calculation formula:
in:
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The weight factor represents the weight of the residual term from the kth month to the current time, which is calculated as 0.9 to the kth power, that is, $\omega_k = 0.9^k$. The weight decays exponentially over time, giving a higher weight to recent residuals, reflecting the persistence and time-varying nature of volatility.
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The residual of the Fama-French three-factor regression of the i-th stock in the t+1-kth month. This residual represents the part of the stock's return that cannot be explained by the market risk premium, size premium, and value premium, reflecting the unique risk of the stock. The residual volatility obtained after eliminating systematic risk through the regression model more accurately reflects the degree of speculation of the stock.
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The length of the lookback period, which ranges from 24 to 60 months, is the number of historical months used in calculating the idiosyncratic volatility.
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The stock number representing the stock.
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Represents the current time (month).
factor.explanation
The monthly weighted idiosyncratic volatility measures the idiosyncratic risk exposure of stocks over a period of time after removing systematic risks. A higher idiosyncratic volatility usually means that stock prices are more volatile, and the volatility is not easily explained by market factors, reflecting the strong speculation of individual stocks. Empirical studies have shown that this factor is usually significantly negatively correlated with the future returns of stocks, that is, stocks with high idiosyncratic volatility tend to perform poorly in the future. This may be because high idiosyncratic volatility means high risk, and investors will demand higher expected returns, resulting in low returns for stocks with high volatility.