The number of days is not the fundamental problem. There is no mathematical connection between BBs and HV. I needed to remind myself that volatility is all about the variation in the day to day changes, which is completely different from the deviations from the average over several days.
An astounding thing about volatility is that for a price that is ramping up or down at a constant fractional rate, the volatility is ZERO, regardless how large or small that rate is. To calculate HV, you calculate the series of % changes from one day to the next, take the average of those changes, and calculate the variance (the average of the squared deviations) of those % changes. The standard deviation of those % changes is the square root of the variance. The annualized volatility is found by multiplying the variance times the annual number of trading days and taking the square root. If it ever happened that the fractional price change over a period of time was constant, the variance would be zero and the HV would be zero. However, if the changes from day to day were not zero, the standard deviation of the prices averaged over the same period of time could be huge, and that would determine wide Bollinger Bands.
In the real world, price never increases or decreases at a constant rate. In regions where charts are relatively flat, the standard deviation related to Bollinger bands becomes dominated by day to day changes, and there is probably an approximate relationship between volatility and BB width, but only in flat regions, not in general. In regions where charts are not flat, BBs will always grow wider, but except in the transition areas from flat to sloped, HV may change very little. It all depends on how regular the changes are within the slopes.
The 50 day annualized HV for AGE.TO is just under 50%. I also calculated 10 20 and 30 day HVs that are in the ball park with the IVolatility numbers for AEM. I did not download the AEM data to calculated those exactly. |
