794 Part VI: Measuring and Trading Volatility 
FIGURE 38-3. 
Stock price distribution, IBM, 7-year. 
7 
6 
5 
~ 4 :;:, 
C: :::, 
8 3 
2 
o----------------+---,.._,._""-¥-+-
-4.o -3.o -2.0 -1.0 o.o +1.0 +2.0 +3.o +4.o 
Sigmas 
dangerous naked puts and long stock on margin can be on days like this. No proba­
bility calculator is going to give much likelihood to a day like this occurring, but it did 
occur and it benefited those holding long puts greatly, while it seriously hurt others. 
In addition to distributions for individual dates, distributions for individual stocks 
were created for the time period in question. The graph for IBM, using data from the 
same study as above (September 1993 to April 2000) is shown in Figure 38-3. In the 
next graph, Figure 38-4, a longer price history of IBM is used to draw the distribution: 
1987 to 2000. Both graphs depict 30-day movements in IBM. 
FIGURE 38-4. 
Actual stock price distribution, IBM, 13-year. 
13 
12 
11 
10 
9 
o a ,-
E 7 
g 6 
(.) 5 
4 
3 
2 
o -4.0 -3.0 -2.0 -1.0 0.0 + 1.0 +2.0 +3.0 +4.0 
Sigmas