To calculate the rolling beta of a stock, you need to follow these steps:
- Determine the time period you want to use for the rolling beta calculation. This could be a specific number of trading days, weeks, months, or any other time frame.
- Collect historical price data for both the stock you are interested in and a benchmark index. The benchmark index should represent the overall market or the specific sector in which the stock operates.
- Calculate the returns of both the stock and the benchmark index over the selected time period. The return is calculated as the percentage change in price from one period to another.
- Calculate the covariance between the stock's returns and the benchmark index's returns using the following formula:
Covariance = SUM((Stock Return - Average Stock Return) * (Benchmark Return - Average Benchmark Return)) / (Number of Observations - 1)
- Calculate the variance of the benchmark index's returns using the formula:
Variance = SUM((Benchmark Return - Average Benchmark Return)^2) / (Number of Observations - 1)
- Calculate the rolling beta by dividing the covariance by the variance of the benchmark index:
Rolling Beta = Covariance / Variance
- Repeat this calculation for each subsequent period, one period at a time, as you move forward in time.
By using a rolling window of data, you can track the beta of a stock over time, which provides a more dynamic measure of the stock's sensitivity to market movements compared to a static beta calculation.