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