Chapter 38: The Distribution of Stock Prices 801 
back over the last 1,000 trading days for XYZ. A 100-day historical volatility can be 
computed, using 100 consecutive trading days of data, for 901 of those days (begin­
ning with the 100th day and continuing through the l,000th day, which is presumably 
the current trading day). Admittedly, these are not completely unique time periods; 
there would only be ten non-overlapping (independent) consecutive 100-day periods 
in 1,000 days of data. However, let's assume that the 901 periods are used. One can 
then arrive at a distribution of 100-day historical volatilities. Suppose it looks some­
thing like this: 
Percentile 100-Day Historical 
oth 34% 
10th 37% 
20th 43% 
30th 45% 
40th 46% 
50th 48% 
60th 51% 
70th 58% 
aoth 67% 
90th 75% 
1 ooth 81% 
In other words, the 901 historical volatilities (100 days in each) are sorted and then 
the percentiles are determined. The above table is just a snapshot of where the per­
centiles lie. The range of those 901 volatilities is from 34% on the low side to 81 % on 
the high side. Notice also that there is a very flat grouping from about the 20th per­
centile to the 60th percentile: The 100-day historical volatility was between 43% and 
51 % over that entire range. The median of the above figures is 48% - the 100-day 
volatility at the 50th percentile. 
Referring to the early part of this example, the current 100-day historical is 
80%, a very high reading in comparison to what the measures were over the past 
1,000 days, and certainly much higher than the median of 48%. 
One could perform similar analyses on the 1,000 days of historical data to deter­
mine where the 10-day, 20-day, and 50-day historical volatilities were over that time. 
Those, too, could be sorted and arranged in percentile format, using the 50% per­
centile (median) as a good estimate of volatility. After such computations, the trader 
might then have this information: