It Took Us 15,000 Trades To Find Our Preferred Delta

we we're calling this one exploring the probability of touch across various deltas and just remember what probability of a touch is it's the chance that between now and whenever expiration is that the option that you are trading touches the strike price and the back of the envelope way to to look at this is it's two times the Delta okay so this is we don't have to make this more complicated than it than it is it's essentially probability of a touch is two times the Delta but we decided to take a look at probability of a

touch as it applies to calls and puts because in Bull markets you know the the the calls don't the the calls get touched more often than the puts let's take a look as we discussed that the realized probabilities of touching strikes in short option strategies is much lower than the theoretical probabilities this drops significantly when exiting positions at 21 days this is a piece that we did in the past so looking at 20 Delta options here theoretical chance of a 20 Delta option touching puts and calls is two times the Delta so the Delta is

20 the theoretical chance of touching is 40 on the calls 40 on the puts if you hold it to expiration in the last 10 years because we've been in a bull market the puts actually only have a 20% chance of touching the calls right at 40 but if you manage early both sides where you think the theoretical is 40% it's really only 10 and 14 that's the whole concept the whole reason we manag early okay that's cool let's go to next slide but to understand the effectiveness of the realized probability touch we can examine the

ratio between the realized probability Touch of 21 days and the Delta which is half of the theoretical probability touch I know these a lot of numbers but the reality is for options with a Delta of 20 the ratio is about3 on average so that's the coolest thing that when you manage early the ratio probability of a touch to it actually happening to whatever the theoretical is it's only about you know it's less than a third of the time and that's cool because remember the theoretical is 40% it's only 11 and 14 so what happens here

average is about three 310 of a percent essentially saying you know like there's no Edge in trading but there are these mechanical there's these things that you could understand about the mechanics of trading that are really interesting like if I said to you the chances of the market going down and touching a stock at a certain level is 40% if you sell the 20 Delta option but in reality okay if you manage early it's only 11% You' be like oh that's cool I'll do that AG that's all it is so let's go to the next

slide um however focusing only on the 20 Delta might not provide the full picture so this time we analyzed spy out of- the money puts and calls across various ranges from 10 to 45 which are the most commonly used out of the money Deltas all options were initiated 45 days and exited 21 days let's take a look at the put side first next slide please John so when we start to break it down um the probability of touch at expiration for all the Deltas are lower than the theoretical values two times the Delta but when

the positions are managed at 21 days the results improve significantly across all Deltas so did it really matter what Delta that we used and the answer is no it actually didn't and if you look at the actual probability of a touch uh 21 days divided by the Delta I mean these are in incredibly interesting numbers because essentially all of them are you know significantly below what the expectations are and and by the way we don't do 40 and 45 day options so so really looking at the further out of the money 10 yeah you know

obviously the at the money options are going to touch no matter what there's a 99% chance um unless you get the price action movement you know yeah right right right off the bat 100% yeah you're not going to sell a 50 Delta option expect it to only hit you know it's it's going to 100% it's almost like when you put on a position you know your p&l is typically zero or negative a few pennies per contract you know rarely is it you know POS the value of this study the value of this study is for

out of the money options it's not for 40 and 45 and 50 Deltas it's only for out of the money options y a graph makes it easier to see the Improvement that expiring that exiting positions early can bring to our short putut strategy the trend also shows that the gap between theoretical and realized pot pot Narrows as the Delta increases indicating a higher risk of touching with larger Delta options of course and that just you know common sense but really where we are in that 15 20 25 area you can see the actual vers the

um the theoretical in purple the actual at expiration in blue and then the and then green which is when you manage early so now we look at the call side which is going to be a little bit different it's higher than the puts but it also is surprisingly low if you manage early so again what we're seeing here is results that are very similar and um you can see a 10 15 20 and 25 Deltas the the actual probability of touch at 21 days to expiration is still a very small percentage of what the theoretical

would be you know 3% 7% 14 24 let's go to the next slide so we found a similar pattern in the graph and again positions become less effective when you have the higher Deltas but the lower Delta positions you can see how effective they are just look at the green compared to the theoretical and the actual it's very impressive very much got to manage early we've been talking about this and you know uh you you always remember when you don't manage early you never remember uh when you manage early and it works out it would

have worked out perfectly for you so manage early I think managing early 45 days we've said it numerous times that's putting on trades that's been two keys to flatten out my p&l curve 100% s I'm going to take a quick 90c break when come back we got wait one second oh I'm sorry I did the takeway I apologize yeah so for index options puts have a lower actual pop not pop pot probability to touch than calls across all Deltas managing the positions at 21dt significantly reduces the chances of being tested strikes compared to doing nothing

on average the realized probability to touch on the put side is slightly smaller than the Delta while it is almost the same on the call side and the difference between put and call sides become marginal when the positions are managed so manager