in:

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  The standard deviation of the logarithmic return of stock i over the past K months, measuring the volatility of stock returns. Higher values ​​indicate more volatile stocks and higher risk. Data from the past 12 months is usually used.

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  The standard deviation of the logarithmic return of the market benchmark over the past K months, measuring the volatility of market returns. Higher values ​​indicate greater market volatility and higher systematic risk. Data from the past 12 months is usually used.

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  The correlation coefficient between the daily returns of stock i and the market benchmark over the past Y years. It is used to measure the linear correlation between the stock return and the market return. Positive values ​​indicate changes in the same direction, and negative values ​​indicate changes in the opposite direction. The daily return is calculated using three days of overlapping returns, $\hat{r}{it} = \frac{1}{3} \sum{k=0}^{2} \log(1+R_{t+k})$, where R is the daily return. Using overlapping returns can improve the stability of correlation estimates and reduce the noise impact of single-day returns. In general, Y is taken as 5 years to ensure that there are at least 750 valid daily returns, so as to obtain a more reliable correlation estimate.

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  The length of the time window (in months) used to calculate the standard deviation of stock and market returns. Generally, K is taken as 12 months to ensure that at least 120 valid daily returns are included, so as to obtain a relatively stable volatility estimate.

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  The length of the time window (in years) used to calculate the correlation coefficient between stock and market returns. Generally, Y is taken as 5 years to ensure that there are at least 750 valid daily returns.