## Optimal Probability Level

Today we want to answer a question we get often which is "Is there an optimal probability level to sell options at?" Now remember that you can target any probability you want; 60%, 75%, 90% whatever. It's all based on what strikes you select.

That said there is an optimal probability level that we'll often use to sell options because of the highest ratio of return to capital usage. And honestly with all this talk of statistics and probability you shouldn't be surprised as to where this lands.

#### More Discussion

• Hey Jim, so when I talk about exiting early I mean taking profits early and not losses. This podcast show will help on the subject as well and I highly suggest listening to it this weekend: https://optionalpha.com/show-014-why-stop-loss-could-actually-be-creating-more-losing-trades-16985.html IF for some reason you never exited early or had a stop-loss then you would still make money long-term because IV still overstates the expected move and long-term option are always more expensive than they should be.

excellent explanation. fabulous.

• Just depends on the trade we are in and how high IV is really – generally speaking I do (nearly) everything around the 70% chance of success.

• Austin

What is the correct percentage for 1 standard deviation? 68% or 85% as stated in this video?

• 1 standard deviation is 68% – in the video when I talk about 85% prob of OTM, that is for each leg so that if you did each leg at 85% prob of OTM then your overall success rate is approx 68%.

• Austin

Got it. Thanks!

• Very welcome

Show Video Transcript +

In this video, I want to answer a question that we often get on the membership side of our website and the blog. And people always ask, and they want to know what the optimal probability of being in the money is or probability of being out of the money.

What’s the level at which we sell options at whatever probability level we want, whether it’s 60% or 80%? But is there an optimal level of return and risk or margin usage? What's the point of which we’re using our capital best for the best possible return that we can?

And one of the ways that we’re going to look at it is just through a quick little study we did with IWM naked puts. And the reason we chose naked puts is that they’re very easy to quantify as far as risk and return with the margin requirements that are in there.

Credit spreads are going to be a little bit different, same with iron condors. But with naked puts, it’s very easy black and white to see. On the chart here, you see we have the probability of being in the money running across the top.

We made some sample trades with IWM at a 60% probability of making money or being out of the money and at a 70% probability of being out of the money and 80% and a 90%, just blocking these four out.

Now, you can see the credit that we received for selling just one of these IWM naked puts is here. For the 60% level, you obviously got compensated a lot more because you took in more in credit.

At the 70% level, you got less, but you still took in \$166. 80%, you took in \$112. 90%, you took in \$47 of credit. And then down here below, just skip down with me, the margin requirement to hold just one of these for the 60% level because you’re trading closer to where the market is trading.

You have to put up a little bit more money in the margin, so you put up \$2,010 and then you can see it slowly starts to decrease after that because you’re going further out of the money so that brokers will adjust the risk.

Now, the return on capital or ROC down here is just simply the credit that you received divided by your initial margin requirement. You can see you get compensated obviously as you should in an efficient market for coming closer to the market’s current price.

If you reduce your probability of success, you will increase the potential return on capital that you have if you're right. Not to say that you will be right, but if you are right. With the 60% level, you’re at about a 12% return, at the 70% level, about 9.68%, at the 80% level, just under 8%, and at the 90% level, about 5% return on capital.

Now, where it starts to get really interesting with this study is the differential, so what we just put in here as the difference. The reduction in the credit that you received going from the 60% probability level to the 70% level was a 29.66% reduction in your credit, so about a 30% reduction.

Going from the 70% level to the 80% level, you had an even bigger reduction percentages of about 32%. And then going from the 80% level to the 90% level, it almost doubled as far as you're getting almost your reduction in credit was increasing exponentially almost as you went further and further out of the money.

You can see that as you go further and further out in selling premium, it's not this one lockstep that everything has. As you go 10% out, you get a 10% reduction.

It just doesn't work that way. You can see here with evidence that we’ve shown with IWM that you have an increasing differential and as you get out from 80% and 90%, it starts to accelerate.

The same thing happened with your return on capital. The reduction as a percentage of return on capital got reduced going from 60% probability level to 70% probability level.

There was a reduction in your return by 17%. That’s the differential percentages between 11.71% and 9.68%, and you can see it starts to accelerate. Had you go from the 70% level to the 80% level, it increased to a 19% reduction in return.

And then you can see it almost doubled as we went out to the 90% probability level with a 41% reduction in your return based on the return on capital between 80% and 90% probability.

You can see there's some clear line that's in between about 80% and 90% that encompasses the best use of capital, the best use of return on capital for the least reduction in credit and that’s what we’re looking for here.

We know that as you go further and further out, you get much less credit and much less return than coming back closer, so it's not worth going far out of the money, say the 90% or 95% probability of success level. And although that it has great returns, it may not be the best use of your capital.

Based on most of the pricing that we’ve seen and we’ve found, that somewhere around the one standard deviation probability level (as would probably come as no surprise because that’s based on everything that we have around option pricing and statistics) gives us probably the most optimal use of funds for the biggest credit received.

So the point at which our credit received is probably the most optimal for the money that we’re putting up in capital. This would be the 85% probability of being out of the money, and it’s probably somewhere between here where that yield curve starts to accelerate and have some optimal area, somewhere between 80% and 90%.

But we know that we can come in closer and take in more credit, we just have to realize that we’re not going to be as successful trading, so we’re not going to have the high number of wins that we would like to have.

If you want to have a high number of wins, you should probably be somewhere around the one standard deviation level which is about the 85% probability of success area.

Hopefully, this has been helpful. I know it was only a couple of sides, but it's got a lot of information in here and helps quantify why we do what we do as far as return and capital usage.

And if you have any comments or questions, please add them right below this video on the lesson page. I’ll make sure I get back to all of those questions and get you guys’ answers if we have them. Until next time, happy trading!