Tony: Thomas we're back my friend. The Skinny on Options Math. While you're watching this, if you want to take a look at where the Scott's Short and Trade is, it's on the upper left-hand side of the site. Easy for you to find. Trade of the week, the cross between the ETS Synthetic…
Jacob: That's not the left-hand side. (laughs)
Tony: I'm sorry. It's the left because it was on my left screen. It's on the right-hand side, where the arrows were.
Jacob: Yeah.
Tom: Thank God we've got our genius back.
Tony: Thank God Jacob is here. The Skinny on Options Math
Jacob: Minor errors. (laughs)
Tom: You would fail automatically bad.
Tony: 100%.
Tom: Jacob, how are you?
Jacob: I'm pretty good. How are you guys?
Tom: We're good.
Jacob: Yeah.
Tom: We're good, we're good, we're good. We were in a state of shock and despair yesterday with the market rallying, but since the selling off today you've brought us good luck, so now you get to…
Jacob: (laughs) Your emotions are way too vulnerable to, what the numbers are.
Tom: I guess.
Tony: For insensitive SOB, we really have a lot of emotions.
Tom: We are
Jacob: About these numbers. (laughs)
Tom: I guess we're like teenagers with emotions. Yes, absolutely. Yes. We're, Chicago is littered with people like us.
Jacob: Yeah.
Tom: Littered. You go around the world and you go down the street, and people are always happy and they're just, they kind of look at you. In some place, some countries they smile, some countries they look at you like they're gonna kill you. But for the most part, most people are just happy. We're happy idiots as a society. You don't think so?
Jacob: I don't know. I'm from New York, which maybe is just distinct, distinct different.
Tom: New York is not. Yeah.
Jacob: People are busy. It's different than happy.
Tom: People are busy. Yeah, I guess busy. In the mid-west people are happy. People are genuinely nice.
Jacob: All right. All right.
Tom: Even I had some Russian guys in last night, and they, as they walked down the street they were actually smiling. People don't smile in Russia. They don't smile in Eastern Europe, and it's rude.
Jacob: It's rude. It's bragging.
Tom: What?
Jacob: It's considered rude. It's bragging.
Tom: Yeah. It's something. You're not supposed to show whatever. But these guys are just, they're smiling out. It's nice. I like it.
Jacob: Right.
Tom: We're changing the world. But what do we got today?
Jacob: I want to talk about, if you… Right. If you just put a trade on, and you're waiting for 100% profit, it will take until expiration. But if you're going to manage it earlier, then you can expect to take it off sooner than that.
Tom: You're not challenging the tastylive research are you?
Jacob: No. No. I'm gonna go,
Tom: Because [crosstalk 00:02:31] we've been working on this.
Jacob: I was gonna put forward the theory and the research seem could run the number and see if the theory lines up with the research. But I'm going to show what the theory says.
Tom: This is the most beautiful thing about tastylive, if it works.
Jacob: Yeah.
Tom: If it doesn't work? Oh man, we're gonna have to hang Jacob by the… But, I'm going to give you a little piece of
Jacob: There's some wiggle room. The one that's we're going to have today is the one that's easy to check and implement for a person. It's not the fully correct solution. The fully correct solution is much longer and more obnoxious. If it doesn't quite line up with what the researcher said, there is that room for gap.
Tom: The researchers smoked a pork.
Jacob: Oh, no. I just had some of those. Delicious.
Tom: Oh, you've had them. Okay. I was just going to say so they're going above and beyond right here.
Jacob: I was very glad for the Scott sider's segment, because they gave me their taco.
Tom: You had one of their tacos?
Jacob: Yeah.
Tony: Pretty good, huh?
Jacob: Oh, it was delicious.
Tom: You have to be very careful about pushing too far. Another Jew eating pork had red shirts on.
Jacob: I got endorsed.
Tom: Tell you, it's…
Tony: Just weakening the race.
Tom: Irresistible meat. Let's start. Ready Jacob?
Jacob: Yeah.
Tom: Let's have some fun. How long do managed trades stay on? Now if you know the tastylive mantra. Jacob, one of the most important things we have stumbled across in the last couple of years is our ability to manage winners has changed our entire game plan with respect to trading. The number of occurrences, everything made sense to us, but as we're starting to get more aggressive and do more and more studies, we have multiple cheat sheets out there now. With respect to managing winners, the relationship between number of days going by and the percentage of max profit has changed the game for everybody.
Jacob: This is going to be the, what? If Black-Scholes were definitely true, this is what the results should be.
Tom: Okay.
Jacob: And as far as I know, data is not sufficient to say Black-Scholes is untrue. But probably this is very close to what's observed.
Tom: Yeah. Don't worry. We're not going to hold you to it. The entire world of theoretical pricing is not
Tony: Is not on your shoulders.
Tom: Is not on your shoulders for this 15 minutes segment.
Tony: Quite yet.
Jacob: Notice the entire theoretical pricing buy in strict fractals, and I'm just going to do computation with strict fractals because they are much easier computations.
Tony: Of course.
Tom: Okay. Here we go. He's going to torture me, this one today. In Black-Scholes, returns follow a Brownian motion with drift. Hang on, one second. If you fix a level of the underlying at which you take a position of. What is this again? S?
Jacob: Call that level where you take from going off S-star.
Tom: S-star is the lovely thing's going off. This will correspond to the return of the following formula. Where S, which is that lovely take something off is the Spot Price.
Jacob: That's S-zero, right? That's the initial price. Right? This is the usual way you can do, if you want to move between Brownian motion space in return and this log, this symmetric Brownian motion, and the prices is always this log of the fraction. That's just the definition for what returns are.
Tom: Of course. You always make me feel so stupid in the first line of, the first sentence.
Jacob: No, no, no. (laughs)
Tony: That's 22 of 9.
Tom: I mean, 15 minutes ago back I was walking on top of the world talking about
Tony: I was a genius.
Tom: I was a genius. 15 minutes later
Tony: Talking about a combo.
Tom: Talking about a combo. 15 minutes later, Jacob puts me in my place in the first sentence.
Tony: Jacob, can we get you full time?
Jacob: I need to finish my job.
Tony: If we are waiting with a Brownian motion with drift to reach a specific, another level, it follows what is known as an inverse Gaussian distribution shown on the next page, which gives a random positive number according to density. Explain please.
Jacob: This is the combination we've done a lot with the competing probability of being in-the-money expiration, competing probability of retouch. It's this, nicely in the finance theory almost all the distributions we used have what is called analytic density functions, which are these things that I can write down. And then if I want to know what the probability that my random number is in some range, I just integrate that density between over that range. Then it becomes like a first-year calculus exercise. Usually, and actually on [inaudible 00:06:32] exercises and it's well approximate by computers
Tom: Got this.
Tony: You don't got a take.
Jacob: All right here's a picture of inverse Gaussian
Tom: I'm working on inverse Gaussian theory right here, okay? Distribution.
Jacob: Yeah. Here are some pictures of some inverse Gaussian distributions. You seem to have an idea of where they sit. The important thing here is just to get an idea, because we're going to be having an easy way to compete with the meanest in a minute. We'll all know. And then you'll want to see, and then if I know the mean, what spread am I expecting around the mean? And you're expecting a spread with these shapes that are out there.
Tom: Our research guys will say, after 10 days, if you've reached x% of your profit, that's our little cheat sheet.
Jacob: Yeah.
Tom: You're making this much more complicated for me. At this point, okay. This Gaussian distribution. How long on average, when you say manage trades, what do you? What's a manage trade?
Jacob: A manage trade is…
Tom: Any trade?
Jacob: Any trade where you have a specific point where you're gonna take it off. You'll pre-decide yourself, I'll take this off at
Tom: 0.5
Jacob: It should be 50% profit. The actual communication I'm gonna do is a little bit simpler than that. I'm going to do it for. I'm going to take it off when the underlying hits some dollar.
Tom: Okay. Okay.
Jacob: The conversion between the 2 just makes the formula much worse.
Tom: The words manage trades here just so we know. This is, you're managing…
Jacob: Yeah.
Tom: It's just every trade you do.
Jacob: Right. Every trade. Any trade that you do and then don't go on vacation. (laughs)
Tom: That's okay. I got it. Any trade you don't have to wake up in a combo for a couple of years later
Jacob: Right.
Tom: They get hit by the bus whole thing.
Jacob: No. Right.
Tom: Okay. Take us to this. There's too many formulas in here for me.
Jacob: All right. The Brownian motion in which it appears in Black-Scholes, in probability we usually parameterize our Brownian motion by a drift
Tom: This is just the risk-free drift, right?
Jacob: Right. Well, it's shifted by the volatility squared over 2. This is the correction factor for the geometric parameter for geometric Brownian motions, but yeah, it's the risk-free rate minus volatility squared over 2.
Tom: Okay. That's probably true. We're basically, when he says drift, we're talking. That's why markets are generally up more than they're down 53, 47 what everyone is saying. Okay? I just want to confirm.
Jacob: Also that has to do with the fact that the median sits lower than the current price.
Tom: Yeah.
Jacob: The drift is different there. The drift is that over a long period of time you do expect it to not just go more often than it goes down, but to go up.
Tom: Right, okay. Because you should get paid for taking risks.
Jacob: Right. And then it's modern, Kingston economics. Economy is supposed to expand, we have an inflation rate.
Tom: Right.
Jacob: It's all these things. Numbers go up over time. It's part of, it's all part of the policy. And then the other parameter use is variance, and variance is thankfully very familiar to everyone, it's this volatility. Volatility is the square of the variance. That one is fine. The drift is a little bit funny looking. Those are the two parameters you would feed into a normal Brownian motion, and if you're doing an inverse Gaussian. Unfortunately inverse Gaussians aren't only used to invert Brownian, to find the hidden tense for Brownian motion. They have a lot of, they do a lot of things. The two parameters that they take aren't just the 2 parameters from the Brownian motion. There are modifications of it, and the modifications are the ones that you see there. If someone wants to do it, the inverse Gaussian function is an easy thing to use.
Excel knows about it, you can stick in the parameters. I should've wrote up what the parameters ought to be. But the takeaway is that the mean that you get for the inverse Gaussian is that if you have the underlying volatility sigma and you're in risk rater R, and you're waiting for something to get you from S-zero to S-star, it will take on average that long. And that's the formula.
Tom: Anybody who doesn't understand this the first time around, Tony will do an extra session after the close today.
Tony: What did Jacob say?
Jacob: [crosstalk 10:03:00]
Tony: Correct.
Tom: That would be the funniest statement ever. What did Jacob just say?
Jacob: You can go around the office ask everybody. (laughs)
Tony: Right. I would start off and say something like this, well Tom stumbled on slide 2 with S-star, and then I would go off of it.
Tom: My takeaway of this right here is that again, this makes the also, I mean ultimately we're making the mathematical… We're having the mathematical discussion to explain why you need a lot of occurrences, and why you need to manage those occurrences in order to come out ahead.
Jacob: There's 2 other things that's going on here that you can see from the signs involved. One of them has to do with comparing. There is a good reason to compare R to Sigma squared over 2 when considering things, and it's actually a very small number. That's sort of how they pick R, is to be close to Sigma squared over 2 standard volatilities. When that's negative, you expect a negative drift in your things. You, the formula, what you want to be doing is looking for trades you want to be short in the market. And then, if volatility squared over 2 is below the risk-free rate, then you're expecting a positive drift in everything, and that's the time where you maybe more inclined to go long.
Tom: Okay. Basically you're saying when things get oversold you might go long, when things go overbought you want to go short. Essentially yeah.
Jacob: And is the 2 numbers are really close to zero, then the expected time to manage a trade starts getting bad. That's really, I know that we all hate low volatility here, but actually really low volatility would be fine. The problem is when volatility squared is really close to R. That's where a lot of the techniques that we try to use, at least in theory, starts to break down.
Tom: I have this funny feeling. When Jacob gets married, okay? He's going to try to pull a mathematical argument the first time that they argue, and it's not going to work. (laughs)
Tony: No, it's not going to work.
Tom: When he gets hit.
Tony: I'm going to give you one line. We had a life changing experience there, burning man with the whole facial
Jacob: Oh, right. Listen, she's done on Monday. Well that's probably gone by then. (laughs)
Tony: Once you get married, you have to learn this sentence. Honey that's an excellent idea, let me look into it. (laughs) If you can master that, you can have a wonderful marriage.
Tom: I was just thinking that the math explanation is not going to fly. It wouldn't fly. It wouldn't fly in my house. Do, did you change the question? Did you change the question? I don't understand.
Jacob: Well, so this is what I was saying earlier, that what I answer here wasn't quite 50%. it's taking it off at 50% profit. It's taking it off at a specific level of the underlying. Those don't exactly correspond, because you can know what level of the underlying would correspond to that amount of profit if nothing else changed.
Tom: Got it.
Jacob: But, time is changing, volatility is changing. Right? Everything else is changing. Your actual percent profit, your actual profit you're making out of a trade is moving as you do these things. In the long term, those mostly cancel out, except for the Theta effect. I don't know. The next slide'll cover that.
Tom: Which in the end, by the way, this whole discussion makes sense except I don't understand all the little specifics to the formulas. In the end, really, what are we doing? In the end, the end of this whole mess, Tony, all we're hoping is that the Theta effects, our performance. The combination of the Theta effects and our ability to sell based on high IV rank. That all that is what ultimately ends up being our takeaway. That's what we get to take home with us. So yes, in two ways. First, this only asks how long for the underlying to reach the excise point without worrying if that is before expiration or not. This will over-estimate how long you have to leave a trade on, but only by a little provided that you are exercising significantly below 100.
Jacob: Right. That formula is going to come up pretty wrong if you're deciding to take your trade off at 90% correct max profit. It's going to be over-estimating how long you'll need to wait for that, because a lot of those will just write till expiration. And it assumes that
Tom: I completely understand.
Jacob: It assumes that you'll need to leave everything on until the profits.
Tom: It's the classic mistake that this seems to always make.
Jacob: Right.
Tom: It's the whole mentality of they took this, let your profits run from this old stock mentality into the drill's world, which can mean no sense at all.
Jacob: Right.
Tom: But we never can figure that out, but professional traders didn't care about figuring out because they were forced through precision managements or portfolio managements, do it anyway.
Tony: Correct.
Tom: It didn't make a difference. They did it by default, but not by understanding why they were doing it.
Tony: And it doesn't make a difference that Jacob makes me feel stupid once a week, because he can move, immediate some peace 20 points. And the Nasdaq 60 points.
Tom: He has powers.
Jacob: I really doubt I have much power over that.
Tom: Oh, yes you do. Yes, you do. Right now there's 50,000 people going, "Don't let that kid leave that space right there."
Tony: If you guys go to break, you're dead.
Tom: Secondly, this only covers managing in the specific spot price of the underlying, which does not correspond to a specific percent of max profit since there are other inputs to C. Since the other inputs are also changing, accounting for this makes the process messier, but on average the dominant factor comes from.
Tony: That's the Theta.
Tom: That's the Theta. Okay. This means that the estimate will be pessimistic for in-the-money trades over how long they need to be left on, and the reverse for out-of-the-money trade, which is exactly why we sell high IV rank out-of-the-money options. I mean everything that this thing so eloquently explains is what we do every single day. The one thing I want to say is it actually goes the other way on the curve, which a lot of people are starting to realize the reason you go to 45 days or whatever it is, is because Jacob says here. It's, it gets funky in the last couple of days. If you're going to 80%, 90%, 100%. But it also goes the other direction if you're early. You could get 20% or 30% potentially on the first day.
Jacob: Right.
Tom: Which means your way, which is again gets in their argument, should I take this stuff off right away, should I not? That's what we're trying to do, is to get default. If you concentrate on the
Jacob: If you get [served this 00:15:50] on the first day, that's an excellent return on capital per day. I'd do that.
Tom: You can see we can always reload, there's expenses whatever it is. But the point is be quicker then, take your profits off when you can.
Jacob: Okay.
Tom: There's no reason to wait. It's completely misleading.
Jacob: And a lot of the formulas have these similarity blow-ups right at expiration date. If you're going to have predictable smooth behavior in your trades, which probably you do. You don't really want these massive spikes up or down. Just stay away from them. Don't have things on right at expiration.
Tom: Tony, just so you know 2175 was some short Nasdaq futures that I had on for the last 5 weeks. I had sold them at 4022. I just was saying, I'm not covering those things just to get back to even on. I just cover them there, that's all that was, was a cover. Less than 1%. Jacob, that was amazing today, and helped by the fact that Tony said that the Nasdaq just dropped 60 handles, while you're sitting here with a mini crush. We actually just made up. We went down, and we made up yesterday,
Tony: Correct.
Tom: but that's something that never happened, so we considered that to be a mini crush.
Jacob: This is essentially uncorrelated, right? It is zero that we got up yesterday if they're going down today.
Tom: They're definitely uncorrelated, but that was an amazing piece today, and very complicated, but in theory that's backing up everything that we've been talking about in the show almost non-stop. And you're giving the math again. This is what's so cool. Giving the mathematical, having somebody on here that can explain the math behind what we talked about at a much simpler level is just. It's the bomb. That is.
Tony: Absolutely. And please come back everyday.
Jacob: Once a week.
Tom: Thank you so much for your time.
Tony: Thank you so much for your time, Jacob. We're going to take a break and we're going to come back with a bootstrapping next to tastylive street live.