872 Part VI: Measuring and Trading Volatility shown in Table 40-9. However, since both options are sold, each sale places negative gamma in the position. The usefulness of calculating gamma is shown by this example. The initial posi­ tion is NET short only 100 shares of XYZ, a very small delta. In fact, a person who is a trader of small amounts of stock might actually be induced into believing that he could sell these 100 straddles, because that is equivalent to being short merely 100 shares of the stock. TABLE 40-9. Position delta and gamma of straddle sale. XYZ = 88. Option Position Option Position Position Delto Delta Gamma Gamma Sell l 00 July 90 calls 0.505 -5,050 0.03 -300 Sell 1 00 July 90 puts 0.495 +4,950 0.03 -300 Total shares - 100 -600 Calculating the gamma quickly dispels those notions. The gamma is large: 600 shares of negative gamma. Hence, if the stock moves only 2 points lower, this trad­ er's straddle position can be expected to behave as if it were now long 1,100 shares (the original 100 shares short plus 1,200 that the gamma tells us we can expect to get long)! The position might look like this after the stock drops 2 points: XYZ: 86 Position Sold 1 00 July 90 calls Sold 100 July 90 puts Option Delta 0.44 0.55 Position Delta -4,400 +5,500 + 1 , 100 shares Hence, a 2-point drop in the stock means that the position is already acquiring a "long" look. Further drops will cause the position to become even "longer." This is certainly not a position - being short 100 straddles - for a small trader to be in, even though it might have erroneously appeared that way when one observed only the delta of the position. Paying attention to gamma more fully discloses the real risks. In a similar manner, if the stock had risen 2 points to 90, the position would quickly have become delta short. In fact, one could expect it to be short 1,300 shares in that case: the original short 100 shares plus the 1,200 indicated by the negative gamma. A rise to 90, then, would make the position look like this: