886 Part VI: Measuring and Trading Volatility 
that is somewhat variable. But, for the purposes of such a projection, it is acceptable 
to use the current volatility. The results of as many as 9 stock prices might be dis­
played: every one-half standard deviation from -2 through + 2 (-2.0, -1.5, -1.0, 
-0.5, 0, 0.5, 1.0, 1.5, 2.0). 
Example: XYZ is at 60 and has a volatility of 35%. A distribution of stock prices 7 
days into the future would be determined using the equation: 
Future Price = Current Price x eav-ft 
where 
a corresponds to the constants in the following table: (-2.0 ... 2.0): 
# Standard Deviations 
-2.0 
- 1.5 
- 1.0 
-0.5 
0 
0.5 
1.0 
1.5 
2.0 
Projected Stack Price 
54.46 
55.79 
57.16 
58.56 
60.00 
61.47 
62.98 
64.52 
66.11 
Again, refer to Chapter 28 on mathematical applications for a more in-depth 
discussion of this price determination equation. 
Note that the formula used to project prices has time as one of its components. 
This means that as we look further out in time, the range of possible stock prices will 
expand - a necessary and logical component of this analysis. For example, if the 
prices were being determined 14 days into the future, the range of prices would be 
from 52.31 to 68.82. That is, XYZ has the same probability of being at 54.46 in 7 days 
that it has of being at 52.31 in 14 days. At expiration, some 90 days hence, the range 
would be quite a bit wider still. Do not make the mistake of trying to evaluate the 
position at the same prices for each time period (7 days, 14 days, 1 rnonth, expiration, 
etc.). Such an analysis would be wrong. 
Once the appropriate stock prices have been determined, the following quanti­
ties would be calculated for each stock price: profit or loss, position delta, position 
gamma, position theta, and position vega. (Position rho is generally a less important 
risk measure for stock and futures short-term options.) Armed with this information, 
the strategist can be prepared to face the future. An important item to note: A model