Chapter 28: Mathematical Applications 485 
tively. Some later time, the stock falls to 27 and the trader needs to reevaluate his 
position. The hedge ratios may have become .42 for the January 30 and .14 for the 
January 35, indicating that a 3:1 ratio would be neutral (.42/.14 = 3). He now has a 
bullish position, because his 2:1 ratio is less than the neutral 3:1 ratio. It is not manda­
tory that the trader act on this information. He may actually be bullish on the stock 
at this point and decide to remain with his position. The usefulness of the hedge ratio 
is that it allows him to see that his position is bullish, so he can make a correct judg­
ment. Without this knowledge, he might still think his position to be neutral, a criti­
cal mistake if he indeed wants to be neutral. If the trader's ratio is greater than the 
neutral ratio (2:1 vs. 3:2, for example), he is bearishly positioned. 
As a final point, it should be noted that the ratio can be adjusted by buying or 
selling either option. 
Example: If the stock falls and it is desired that the ratio be increased to 3:1, one 
might sell more January 35's or might decide to sell out some of his January 30's. A 
bullish adjustment could be made by buying on either side of the spread in a similar 
manner. In general, one should adjust by selling time premium or buying intrinsic 
value. That is, out-of-the-moneys are usually sold and in-the-moneys are usually 
bought, when adjusting. 
AIDING IN FOLLOW-UP ACTION 
The computer can also be an invaluable aid to the strategist in that it can help him 
monitor his positions. It is generally necessary for the strategist to have some way of 
inputting his positions into an inventory database and also to have some way of iden­
tifying different securities that are grouped within the same trading position. Once 
this has been done, the computer can simultaneously read pricing data ( either real­
time or closing prices) and the inventory database to generate information concern­
ing the current status of any position. 
A current mark to market (profit and loss) statement is of obvious use in that 
the trader can see how he is doing each day. The computer can also easily generate 
a set of warning flags that may be of interest to the trader, and could produce a list 
summarizing possible positions that need action. In most of the strategies that were 
described, it was shown that the strategist should avoid early assignment if at all pos­
sible. It is a simple matter for the computer to calculate the remaining time value 
premium of any short options, and to warn the trader if there is only a small amount 
of time value premium remaining, perhaps ½ point or less. For similar reasons, the 
trader may want to have a daily list of positions that are nearing maturity, perhaps