By contrast, most other position traders usually have a directional bias in the marketplace. They establish a trade because they expect the stock to move either up or down. They are willing to establish a position where they will make money ifthe stock behaves as they expect, but they do not wish to assume significant risk that the stock will make a large move in the opposite direction. They are making a directional play and want to limit their potential loss if the stock goes dramatically against them. They are not concerned about their position delta. In fact, they have likely constructed the position with a definite directional bias. What they want to do is protect their down-side risk share for share if the stock should move strongly against them. This process involves purchasing or selling enough option contracts that their position would be neutral beyond some point if the stock should move against them. Covering your risk on a share-by-share basis is known as contract-neutral hedging.
We have already seen these approaches in action. Returning to our earlier example once again, the trader purchased 1, 000 shares of stock at $48 and 10 July 45 puts. After purchasing the stock and put combination, although the trader was long 700 deltas, the 10 puts would fully protect the 1, 000 shares in the event that the stock would drop lower than $45 per share. The purchase of the stock was therefore hedged on a contractneutral basis. In contrast, the market maker hedged his sale of 10 July 45 puts by selling 300 shares of stock. Although this procedure reduced his position delta to zero, if the stock plunged below $45, his position would continue to lose money as the stock continued to decline. The short sale of 300 shares would only partially offset the continuing losses from the 10 puts, representing 1, 000 shares of stock. The market maker used a deltaneutral hedge. Note that the decision of how to hedge directional risk in each case resulted from their respective profit expectations. The trader was willing to accept directional risk on the up side, but with only limited risk on the down side. Therefore, a contract-neutral hedge was the appropriate choice. The market maker wanted to protect the projected profit from the bid-ask spread differential and therefore chose a delta-neutral hedge. As we will see shortly; the market maker's preferred hedge would have been to purchase other puts on a delta-neutral basis. This action would provide three benefits. One, the position would be delta neutral in order to protect the anticipated profit from repurchasing the July 45 puts.
Two, the purchase of the other puts created another anticipated profit from their eventual resale. Three, the purchased puts would provide more down-side protection than the stock in the event of a major downward move in the price of the stock.
You must keep in mind that as option deltas are affected by both the passage of time and changes in the price of stock, the position delta will fluctuate as these factors come into play: For delta-conscious traders, position delta should be monitored on a regular basis. This advice is emphasized by the following situation.
Stock ABC is currently trading at 62. There are 30 days until March expiration. The investor has the following position. Long 2, 500 shares of stock = long 2, 500 Long 25 March 55 puts with a - 22 each (25 X - 22) = short 550 Short 25 March 70 calls with a -18 each (25 X -18) = short 450 The total net position delta (P) is long 1,500 (2, 500 - (550 + 450) =1,500).
In other words, the position is the equivalent of being long 1,500 shares of stock while stock ABC is trading at or near $62 at this particular time. This situation translates to an anticipated increase in the value of the position of $1, 500 ifABC increases to $63. You must note that this situation does not translate to the position increasing $1,500 for each $1 increase in the price ofABC. Let's look at the situation after a significant change in stock price. StockABC is currently trading at $87. There are 30 days until March expiration. The investor has the following position: Long 2, 500 shares of stock = long 2, 500 Long 25 March 55 puts with a 5 delta each (25 X -5) = short 125 Short 25 March 70 calls with an 85 delta each (25 X -85) = short 2,125 The net delta position (P) is long 250 (2,500 - (125 + 2,125) = 250).
As the stock increased in price, the deltas of the March 55 puts decreased-and those ofthe March 70 calls increased. The March 70 calls are now $17 ITM with a delta of almost 100.
Let's look at this example again, this time moving forward to the day of expiration (where the stock price remains at the original price). Stock ABC is currently trading at $62. There is one day until March expiration, and the investor has the following position:
Long 2, 500 shares of stock = long 2,500
Long 25 March 55 puts (0 each) = 0
Short 25 March 70 calls (0 each) = 0
The net delta position (P) is long 2,500 (2,500 - (0 + 0) = 2,500).
We have the same position in each case. Depending on the time until expiration and/or changes in the price of the stock, the position delta can be dramatically different. This example is designed to impress upon you that the position delta (P) is time and price sensitive, just like individual
option deltas. Although not highlighted in this example, position delta might also be sensitive to changes in implied volatility.
We offer one final point concerning position deltas and option-price changes in the real world. We must point out that far OTM options, whether they are calls or puts, consistently behave differently than the pricing models would suggest. In the case of puts, they tend to retain a higher value than the models would indicate (based on the implied volatility of the other options with the same expiration). This situation results from a bias towards the demand for these options, reflecting the facts that (1) there is little incentive to assume risk by selling these cheap options, and (2) they retain an attraction to be purchased as disaster protection in case of a crash in a stock. By contrast, people who have long positions in a stock become additional sellers of OTM options, because their positions are already gaining value as the stock increases towards the OTM strikes. It is not uncommon to have a situation where the pricing model assigns an OTM call option a 10 delta, the option is trading for .50, the stock increases in value by $2, and the option price remains unchanged. Many experienced traders ignore or substantially discount farther-out OTM call deltas when calculating their position delta.
Read More: Delta Neutral versus Contract Neutral
