# compare delta value in the long call option for profit gain

I have a question about delta and its relation with the long call option. If I plan to buy a long call option to bet the stock price will go up. Is larger delta value better or smaller delta value better in terms of profit gain? For example, a stock is at 100 dollars right now. I decide to buy a call option with an expiration date 6 months later. The option with strike price 110 dollars has delta 0.45 and the option with strike price 120 dollars has delta 0.40. So, which option is better? Moreover, if we also consider in the money options (options with strike price lower than 100 dollars), does the answer change? Thanks

• I think it's important to remember that delta is just what you would expect it to move. It is "a guess" based on some logic; it is not set in stone. Note that mathematicians have fancy words for "guess", such as "probability calculation", "high sigma outcome" etc etc. It's a "guess". Oct 2, 2020 at 13:44
• @Fattie - Delta has two components. It's primary function is telling you approximately how much your option is going to move if the underlying moves one dollar. This aspect is purely mathematical, based on option pricing formulas rather than some sort of guess. The secondary aspect is that many people use delta as the probability that the option will end up in-the-money at expiration (or as you said, a 'guess'). I have issues with this because delta will change as implied volatility changes so it can be a moving target. Oct 2, 2020 at 14:08
• BB, re "A" well yes, but it doesn't "help you decide which trade will be more profitable". (Perhaps I misunderstand the question, or you and I are interpreting it differently.) re "B", huh, I did not know that "many people use that as a guideline" - that just seems, well, incorrect to me. {ie, I agree with, if I understand you, your final sentence there!} Oct 2, 2020 at 15:46
• You are omitting consideration the actual price of each option - all else being equal, the lower the strike price the better the call option, but of course the price will increase as well. Oct 2, 2020 at 18:08
• That should be an answer on this confusing QA. Oct 4, 2020 at 12:53

You really need to model some numbers to get a big picture view of what the possibilities are. Here are some current bid quotes for IBM's 11/20 calls:

IBM = \$120

120c = \$5.60

125c = \$3.35

130c = \$2.00

135c = \$1.00

Assume that you buy one call. What will the above calls be worth at expiration at \$125, at \$130, at \$135 and so on?

Plan B: Pick an arbitrary amount, say \$2,500. Buy as many of each call as you can with \$2,500.

Again, what will these positions be worth at expiration at \$125, at \$130, at \$135 and so on?

The above ignores delta.

Download an Excel spreadsheet for option pricing or get some pricing software or use your broker's option analytics and repeat the above exercises and then vary the time between now and expiration.

By now, you show be realizing that asking whether a 45 delta call is a better choice than a 40 delta call isn't going to help you understand the big picture.

• Yes. I agree that the absolute number of delta is not very useful. I think the changing ratio in the option value vs the changing ratio in the stock price is very important. Oct 2, 2020 at 16:37
• I just did my calculation. Basically, buying an option with six months expiration date is better than buying an option with one year expiration date. Assume always choose a strike price higher than the current price for the long-term call. Buying an option with higher striker is better than buying an option with lower strike price. Is this true? Oct 2, 2020 at 18:28
• What option to buy depends on the strategy being used and to some extent, IV and cost. To simulate longer term investing, for something like the Stock Replacement Strategy (buying a high delta call), you should go out 6-12 months. The Poor Man's Covered Call (a diagonal spread) would be similar. That doesn't mean that you can't utilize closer expirations. It depends on what you're trying to achieve. Oct 2, 2020 at 19:04
• Do yourself a favor and pick up a copy of "Options as a Strategic Investment" by Lawrence G. McMillan. Read it. Then read it again. Well written with many clear examples. Under 100 pages or so will give you a fundamental understanding of basic strategies. Occasionally you can get a used copy of an older 3rd edition for under \$10. There's no need to spend \$75+ for the latest edition (1,000+ pages) since it involves more complex products and strategies which will most likely not be of interest to you for awhile and might take you years before being competent enough to utilize them. Oct 2, 2020 at 19:04

If calls are out of the money, the "delta" gets closer and closer to zero as you get nearer expiration.

If calls are in the money, the "delta" gets closer and closer to one as you get nearer expiration.

You question,

Is larger or smaller delta value better in terms of profit?

Delta has nothing to do with profit.

You can have a high or low profit (or indeed high or low loss) with either a high or low delta.

Moreover, the delta would have changed (drastically) throughout the trade. Delta "when you first begin the trade", again, is sort of meaningless in terms of "how much profit will you make".

Say you asked: "how does the sell price affect profits?" ... the question is off-track. Sure, obviously a higher selling price "affects" profits but it's kind of a misguided question. (You can't - obviously - anyway know what the selling price will be when you enter.)