Option Investor
Trader's Corner


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I lied. In my last Trader's Corner article, I said that this week's article would discuss gamma. It doesn't. All week, I kept worrying about tidbits of information about delta that I hadn't been able to squeeze into the last article.

For those who didn't read last week's article, delta measures the amount of movement one might expect in an option's price for each point move in the underlying. It also measures the theoretical probability that the option will be in the money at option expiration. It can also measure the risk an options position has due to price movement.

One of those tidbits concerned buying options for an expected short-term move. One example last week pointed out the benefits of buying an option with a delta of at least 0.70 when you expect a quick, small move. Lawrence McMillan speaks to this on his tome on options. When you're trading a short-term move, he warns traders that the delta should be as high as possible. In fact, he would suggest buying or shorting the stock instead if you're day trading since stock has a delta of 1 or -1, depending on whether it's being bought or sold.

Not all of us are going to do buy stock. Not all traders day trading an expected quick move want to buy options with deltas that high, either, and they would have a point. Let's review. I mostly traded OEX options when I was day trading. Those options feature wide bid/ask spreads. For example, on October 24 with the OEX at 707.86, the NOV strikes from 695 to 715 had bid/ask spreads from $0.60-1.20. It's a pretty good guess that the $0.60 spread was narrowed by someone coming inside the market maker's price with a small order (5 contracts), so that as soon as that 5-contract order was snapped up, that bid/ask spread would have widened a bit. Even the narrowest $0.60 spread was probably only temporarily that narrow.

Some traders say they can consistently get fills in the middle of the bid/ask spread for most securities, but I often had to look to pay 60-70 percent of the bid/ask spread to buy an OEX option and give up 60-70 percent to sell it if I wanted to get quick fills. In my experience, that meant buying an option with a delta of at least 0.70 or 70 percent if I wanted to pay commissions and my part of the bid/ask spread on both sides and still consistently make a profit on a three-point move.

Not all options have such wide bid/ask spreads, however, and other considerations might be important. Without the need for options prices to leap across that wide bid/ask spread, traders might instead be concerned about getting the most bang for their bucks in the form of the highest percentage increase in option price. For example, with the QQQQ at $53.77 near the close on 10/24, two QQQQ calls were priced as follows:

NOV 53 Call
Bid/Ask 1.82/1.84
Delta 0.63

NOV 56 Call
Bid/Ask 0.38/0.41
Delta 0.24

Assume a purchase price of $1.83 for the 53 strike call and $0.40 for the 56 strike one. If we imagine that the delta stays constant across a three-point gain, something that wouldn't strictly be true, the 53 strike would theoretically gain $1.89 (3 x 0.63), a 103 percent appreciation in price. The 56 strike would theoretically gain only $0.72, but that's a 180 percent appreciation in price. If you're looking at percentage gains, the option with the lower delta is often the one that shows the greatest percentage appreciation.

As is true of so many aspects of options, tradeoffs always exist. Trading the OEX, I needed the bigger price appreciation that a higher delta option provided. Those trading options with tighter bid/ask spreads might prefer the higher percentage price appreciation that a lower delta option provides. I still liked the highest delta I could afford, but others will make different decision.

Be cautious, though, not to buy an option with a delta so low that it won't move much at all. I've heard from subscribers who have bought options with deltas of 0.05 (calls) or -0.05 (puts) and then couldn't figure out why their options didn't gain much when the underlying moved a point.

Another tidbit not covered in the previous article about delta was the concept of "up delta" and "down delta." McMillan mentions the concept in OPTIONS AS A STRATEGIC INVESTMENT. Theoretically, if a call's delta were 0.80, the call should gain $0.80 if the underlying moved up a point and lose $0.80 if the underlying moved down a point. Theory and practical results don't always match, however. Traders might notice that when the underlying moves higher by a point, the call gains more than it might lose if the underlying dropped a point. McMillan gives an example of an ATM call with a delta of 0.50. When the underlying moved up a point, the call might appreciate by 5/8 of a point (the book was written when options were still priced in eighth's), but when the underlying moved down, the call might lose only 3/8 of a point.

Let's look at a real-life example. Near the close of trading on October 24, Dupont (DD) closed at $47.54. DD had November 47.50 strike calls. They were set up as follows:

NOV 2007 47.50 Call
Bid/Ask: 1.00/1.15
Delta: 0.4886

On October 25, Dupont (DD) closed higher by $0.80, so the DDKW could be expected to have gained $0.39 ($0.80 x 0.4886). Instead, the DDKW showed a bid/ask spread of 1.5/1.65, showing gains of $0.50. If DD had dropped $0.80 instead and we were to see that "up delta/down delta" effect, it's possible that the call would have lost less than $0.39.

A last tidbit concerns a possible misconception caused by a blanket statement that at-the-money options tend to have deltas near 0.50. While that's true, some variation in delta exists across in the ATM options with differing expiration dates. A front-month at-the-money option, one that expires in 30 days or less, might have a lower delta than an option that expires in several months. A front-month out-of-the-money option might also have a lower delta than one that expires in several months. The opposite might be true for in-the-money options, however. Front-month in-the-money options tend to have higher deltas than the same strike option several months out.

For example, on October 25, with QQQQ closing at $53.05, November, December and January 53.00 ATM calls showed the following deltas:

QQQKA/NOV 2007 53 Call/Delta: 0.5368

QQQLA/DEC 2007 53 Call/Delta: 0.5548

QQQAA/JAN 2008 53 Call/Delta: 0.5643

As predicted for ATM options, the delta for the further-out JAN 2008 option was higher than the delta for the front-month NOV 2007 one.

November, December and January OTM calls showed the following deltas:

QUEKH/NOV 2007 60 Call/Delta: 0.02

QUELH/DEC 2007 60 Call/Delta: 0.08

QUEAH/JAN 2008 53 Call/Delta: 0.15

As predicted for OTM options, the delta for the further-out JAN 2008 option was higher than the delta for the front-month NOV 2007 one.

November, December and January ITM calls showed the following deltas:

QQQKS/NOV 2007 45 Call/Delta: 0.88

QQQLS/DEC 2007 45 Call/Delta: 0.86

QQQAS/JAN 2008 45 Call/Delta: 0.85

As predicted for ITM options, the delta for the further-out JAN 2008 option was lower than the delta for the front-month NOV 2007 one. This is the inverse of the time relationship shown for ATM and OTM options.

The different results for ITM options make sense if you think about delta's prediction that the option will be in the money at expiration. If an option is out of the money, allowing more time increases the possibility that it will be in the money at option expiration. If an option is already in the money, however, extra time is just extra time when the underlying might move enough so that the option is out of the money by expiration.

This tidbit of information can be important when choosing an option. How many times have you tried to decide whether you ought to buy a front-month option or one further out? Do you tend to buy cheap OTM options? Do you anticipate that the movement that you're expecting in the underlying might take a number of weeks to be fulfilled? If so, you should know that the delta of your option will be decreasing during those ensuing weeks while you're waiting for the movement.

So, I lied about moving on to gamma this weekend, instead spending another few pages talking about delta again. There's more to cover, including a discussion of how delta varies with the volatility of the underlying. However, the purpose of these articles has been to introduce some ideas about delta, not to exhaust the subject. Traders interested in learning more should consult McMillan's book. We're moving on next week.

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