832 Part VI: Measuring and Trading Volatility 
moved two or three times that far with great frequency. Finally, there is a continu­
ity to the points on the histogram: There are some y-axis data points at almost all 
points on the x-axis (between the minimum and maximum x-axis points). That is 
good, because it shows that there has not been a clustering of movements by XYZ 
that might have dominated past activity. 
As for what is not a "good" histogram, we would not be so enamored of a his­
togram that showed a huge cluster of points near and between the "-1" and 'T' points 
on the X-axis. We want the stock to have shown an ability to move farther than just the 
break-even distance, if possible. As an example, see Figure 39-5, which shows a stock 
whose movements rarely exceed the "-1" or "+l" points, and even when they do, they 
don't exceed it by much. Most of these would be losing trades because, even though 
the stock might have moved the required percentage, that was its maximum move 
during the 10-month period, and there is no way that a trader would know to take 
profits exactly at that time. The straddles described by the histogram in Figure 39-5 
should not be bought, regardless of what the previous analyses might have shown. 
Nor would it be desirable for the histogram to show a large number of move­
ments above the "+3" level on the histogram, with virtually nothing below that. Such 
a histogram would most likely be reflective of the spiky, Internet-type stock activity 
that was referred to earlier as being unreasonable to expect that it might repeat itself. 
In a general sense, one doesn't want to see too many open spaces on the histogram's 
X-axis; continuity is desired. 
If the histogram is a favorable one, then the volatility analysis is complete. One 
would have found mispriced options, with a good theoretical probability of profit, 
whose past stock movements verify that such movements are feasible in the future. 
ANOTHER APPROACH? 
After having considered the descriptions of all of these analyses, one other approach 
comes to mind: Use the past movements exclusively and ignore the other analyses 
altogether. This sounds somewhat radical, but it is certainly a valid approach. It's 
more like giving some rigor to the person who "knows" IBM can move 18 points and 
who therefore wants to buy the straddle. If the histogram (study of past movements) 
tells us that IBM does, indeed, have a good chance of moving 18 points, what do we 
really care about the relationship of implied and historical volatility, or about the cur­
rent percentiles of either type of volatility, or what a theoretical probability calcula­
tor might say? In some sense, this is like comparing implied volatility (the price of the 
straddle) with historical volatility (the history of stock price movements) in a strictly 
practical sense, not using statistics.