Now, Initially, the Williams had sold $250,000 (= 2,500 × 100) call options with a delta of 0.4563 so that the delta of this position is:

$$\text{Delta} = 2500 \times 0.4563 \times 100 = 114,075$$

To delta-hedge against this position, Williams needs to buy 114,075 shares from Xerox Inc, which he did, and thus he is delta-hedged. However, in the following month, the prices of both the stock and the call option decrease, and, as a result, Delta decreases to 0.4168. Thus the delta of the new position is, therefore:

$$\text{Delta} = 2500 \times (0.4168) \times 100 = 104,200$$

Therefore, in this position, he only needs 104,200 shares to be delta-hedged. However, he already has 114,075 shares! Meaning he has excess shares. Therefore he needs to sell (the excess shares): $114,075 - 104,200 = 9,875$ shares