Chapter 40: Advanced Concepts 
XYZ:90 
Position 
Sold 100 July 90 calls 
Sold 1 00 July 90 puts 
Option 
Delto 
0.56 
0.43 
Position 
Delta 
-5,600 
+4,300 
873 
1,300 shares 
These examples demonstrate how quickly a large position, such as being short 
100 straddles, can acquire a large delta as the stock moves even a small distance. 
Extrapolating the moves is not completely correct, because the gamma changes as 
the stock price changes, but it can give the trader some feel for how much his delta 
will change. 
It is often useful to calculate this information in advance, to some point in the 
near future. Figure 40-10 depicts what the delta of this large short straddle position 
will be, two weeks after it was first sold. The points on the horizontal axis are stock 
prices. The quickness with which the neutrality of the position disappears is alarm­
ing. A small move up to 93 - only one standard deviation - in two weeks makes the 
overall position short the equivalent of about 3,300 shares of XYZ. Figure 40-10 real­
ly shows nothing more than the effect that gamma is having on the position, but it is 
presented in a form that may be preferable for some traders. 
What this means is that the position is "fighting" the market: As the market goes 
up, this position becomes shorter and shorter. That can be an unpleasant situation, 
both from the point of view of creating unrealized losses as well as from a psycho­
logical viewpoint. The position delta and gamma can be used to estimate the amount 
of unrealized loss that will occur: Just how much can this position be expected to lose 
if there is a quick move in the underlying stock? The answer is quickly obtained from 
the delta and gamma: With the first point that XYZ moves, from 88 to 89, the posi­
tion acts as if it is short 100 shares (the position delta), so it would lose $100. With 
the next point that XYZ rises, from 89 to 90, the position will act as if it is short the 
original 100 shares (the position delta), plus another 600 shares (the position 
gamma). Hence, during that second point of movement by XYZ, the entire position 
will act as if it is short 700 shares, and therefore lose another $700. Therefore, an 
immediate 2-point jump in XYZ will cause an unrealized loss of $800 in the position. 
Summarizing: 
Loss, first point of stock movement = position delta 
Loss, second point of stock movement = position delta + gamma 
Total loss for 2 points of stock movement 
= 2 x position delta + position gamma