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<I>TSC</I> Options Forum: Facts About Delta, Part 2

This week, applying what you know about delta to multistrike or hedging strategies.

In last week's Options Forum, I wrote about an option's delta and provided some quick rules for calculating changes in an option's price. This week I'll address why knowing an option's delta is important and how it applies to hedging strategies. I received a few reader questions and comments about last week's column. Here's one: Steve, I really don't understand why I have to worry about the delta. Suppose I buy a call at $1 with a strike price at $30. If the stock goes to $35, I expect the call price with the $30 strike to go to $6. If it doesn't, I exercise the call option, then sell the stock. My trade is more profitable that way, and because it's an American-style option, I can exercise it at any time.

While our reader might not realize it, he is using delta to make a trading decision. He has also (maybe inadvertently) supplied us with a great layman's definition of what delta is all about. He expects the call to go to $6. That's the essence of knowing why delta is important, even if you're just using options as a single-strike trading vehicle.

This reader buys that call with the expectation it will behave a certain way relative to a change in the price of the underlying security.

That knowledge helps him choose which strike to buy, and if he doesn't get the expected result, it forces an alternative action. So in fact, this reader is intuitively employing delta in the decision-making process.

Another way to look at the table presented in last week's column is in terms of the likelihood of an option being in the money. For example, an option with a delta of 0.80 has an 80% chance of expiring in the money and a 20% chance of expiring worthless. A delta of 0.50 indicates even odds of being in the money or out of the money, and so on. These statistics are helpful when deciding what strike to buy or sell.

Also keep this in mind when buying cheap out-of-the-money options in hopes of a big payoff. An option that's three to four strikes out of the money has only around a 15% chance of coming into the money.

Knowing an option's delta, or the expected change in value relative to a change in price of the underlying, becomes even more important when using multistrike strategies or hedging techniques. The most important thing to know is that a position's total delta is calculated as the cumulative sum of its parts.

If you bought five at-the-money calls that have a delta of 0.50 each, your total long position will be equivalent to owning 250 shares of the underlying stock (5 x 0.50 = 2.50). If you shorted those five calls, you would have the equivalent of being short 250 shares. In both cases, the delta -- positive and negative -- will increase as the stock price rises.

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Take a look at a basic hedging example. Assume you own 100 shares of XYZ currently trading at $50. To fully hedge that position could be accomplished in several ways. The sale of two at-the-money calls with a delta of -0.50 each, the purchase of two at-the-money puts with a delta of -0.50 each or the sale of one at-the-money call coupled with the purchase of one at-the-money put (otherwise known as a collar, which I discussed

in a column last December).

Each of these approaches provides a delta-neutral position at a given moment in time, but they'll each react in different ways to a move in the underlying stock.

Now let's look at how the delta of a more complex option position, such as

a ratio put spread, would be calculated. Assume I'm long two XYZ $50 puts with a delta of -0.50 each and short three XYZ $40 puts with a delta of 0.25 each. My net delta would be -0.25. Meaning I'm net short approximately 25 shares of XYZ.

While delta might not seem that important when looked at as a static snapshot in time, it's a valuable and crucial tool in the real-time dynamic trading world. For practice, your homework assignment is to calculate and find two ways to bring the above-mentioned position to delta neutral, should XYZ stock decline to $35. Let me know what you find out.

Steven Smith writes regularly for In keeping with TSC's editorial policy, he doesn't own or short individual stocks. He also doesn't invest in hedge funds or other private investment partnerships. He was a seatholding member of the Chicago Board of Trade (CBOT) and the Chicago Board Options Exchange (CBOE) from May 1989 to August 1995. During that six-year period, he traded multiple markets for his own personal account and acted as an executing broker for third-party accounts. He invites you to send your feedback to

Steve Smith.