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# Dancing with Delta

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Whether option traders realize it or not, they're dancing with delta when they choose the option they'll trade. Delta measures the amount an option's price changes with each one-point move in the underlying. For example, an OEX call with a delta of 0.70 would move approximately \$0.70 for each one-point gain in the OEX. It would lose approximately \$0.70 for each one-point drop.

Delta values are positive for calls and negative for puts. The negative value for puts reflects the fact that puts will lose value when the underlying climbs and gain value when it drops. For example, an OEX put with a delta of -0.70 will lose about \$0.70 when the OEX gains a point and would gain about \$0.70 when it loses a point.

Why all those "approximately" and "about" statements? Two things happen as price moves. First, other inputs into the price of an option such as volatility measures may be changing at the same time. Secondly, delta changes a bit as the price of the underlying moves. Deltas of at-the-money options are near +0.50 for calls and -0.50 for puts. The further out of the money the options are, the closer their deltas are to zero. The deeper in the money they are, the closer their values are to 1.00 and -1.00, respectively, for the calls and puts.

Sometimes new options traders choose an option based only on its price. We've all done that, but it's important to have some basic understanding of the delta of an option. For example, an options trader who wants to day trade the OEX, hoping to capture an expected six-point climb before next likely resistance is hit, would expect that call to gain about \$3.00 if it was an at-the-money strike, but only about \$1.68 if the trader chooses a cheaper call about 30 points or 6 strikes out of the money. That call might have a delta of about 0.28, resulting in that prediction of a much smaller gain. Of course, by the time that the OEX rose 30 points, the delta of that call that was originally 6 strikes out of the money would have changed, so the comparison is not exact, but the point still holds: cheaper options aren't always better for the trade.

The higher the delta of your option, the more of an expected move you'll capture. This can be particularly important when considering short-term moves over an expected small range, especially when commissions are considered. An option trader who wants a more speculative trade might choose a cheap option with a smaller delta. If a big move does result, that trader's return on capital might be greater than that of the trader buying the more expensive higher-delta option, although the buyer of the higher-delta option gains more profit in dollars.

For example, on November 3, 2008, with the OEX at 462.01 at 3:38 pm ET, an options pricer quoted the 460 call at \$22.49 and the 490 one at \$10.92. If the OEX were to rise 30 points before the end of that day, an unlikely occurrence in previous times but perhaps not so odd a calculation recently, the pricer returned a theoretical price of \$42.01 for the 460 call and \$23.88 for the 490 one. The holder of that 460 call theoretically profited \$19.52 or 87 percent. The holder of that 490 call theoretically profited \$12.96 or 119 percent. While the holder of the call with the higher delta pocketed more dollars, the holder of the call with the lower delta received a higher percentage gain on the original investment.

When considering an expected smaller move than the theoretical thirty points in the previous example, however, that lower-dollar gain on the lower-delta option may mean that there's no profit captured even if the underlying does move in the right direction. The gain captured might not be enough to pay for commissions. This effect and the one noted in the previous paragraph illustrate the maxim that in options, there's often no single right way or wrong way to think about trades. Each options trade has its strengths and its shortcomings. Options traders are always faced with tradeoffs, but that's what makes options trades so flexible.

Delta becomes even more important when considering combination trades or high number of contracts as a high positive or negative delta for the position means that the options trader has accumulated much risk due to possible price movement. However, that's the topic for another and more advanced Options 101. For now, what the new options trader needs to know is that any options trade is a dance with delta.

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