802 Part VI: Measuring and Trading Volatility 
Using 1,000 days of data: 
Median 100-day historical volatility: 48% 
Median 50-day historical volatility: 49% 
Median 20-day historical volatility: 52% 
Median 10-day historical volatility: 49% 
If these were all the data that one had, then he would probably use a volatility esti­
mate of 48% or so in his option models or probability calculators. Of course, this is 
starkly different from the current levels of historical volatility (shown at the begin­
ning of this example). So, one must be careful in assessing whether he expects the 
stock to perform more in line with its longer-term (1,000 trading days) characteristics 
or if there is some reason to think that the stock's behavior patterns have changed and 
the higher, more recent volatilities should be used. 
The pertinent volatilities to consider, then, in a strategy analysis are the medi­
ans as well as the current figures. If the trader were going to be buying options in his 
strategy, should he use the minimum of the volatilities shown, 48%? Probably. 
However, if he's a seller of options, should he use the maximum, 130%? That might 
be a little too much of a penalty, but at least he would feel safe that if his volatility 
selling position had a positive expected return with that high a volatility projection, 
then it must truly be an attractive position. 
In an analysis like that shown in this example, there is nothing magical about 
using 1,000 trading days. Perhaps something like 600 trading days would be better. 
The idea is to use enough trading days to bring in some historic data to counterbal­
ance the recent, erratic behavior of the stock. 
Among other things, this example also shows that volatilities are unstable, no 
matter how much work and mathematics one puts into calculating them. Therefore, 
they are at best a fragile estimate of what might happen in the future. Still, it's the 
best guess that one can make. The trader should realize, though, that when volatili­
ties are this disparate when comparing recent and more distant activity, the results of 
any mathematical projections using those volatilities should not be relied upon too 
heavily. Those results will be just as tenuous as the volatility projections themselves. 
Of course, in any case, the actual volatility that occurs while the position is in place 
may be even more unfavorable than the one the trader used in his initial analysis. There 
is nothing that one can do about that. But if you choose what appears to be a somewhat 
unfavorable volatility, and the position still looks good under those assumptions, then it 
is likely that the trader will be pleasantly surprised more often than not - that actual 
volatility during the life of the position will tend to be more in his favor than not.