Transcription
Option prices are driven not just by, um, the probability of what will happen, but the, uh, the magnitude of what can happen. A stock price is just a two-dimensional representation of all the, the branching trees of probability that can happen for the company. But the options market specifically defines what that looks like.
I remember when I was at SIG, way back when, there were, uh, some bosses that took exception to the idea that the dot-com bubble was irrational and a bubble, because their attitude was, the options market told you, like, the options market told you exactly the way this thing was distributed. Amazon was going to lose something like 80, 90% of its value. That was like baked into the options, but its stock value was being driven by this long right tail. The options market understood this stuff.
You're watching Excess Returns. I'm Matt Ziggler, and down from the Moon Tower Chamber, it's Chris Abdelmsia. You're back teaching me like I'm five. How you doing today, Chris?
I'm good, man. How are you?
Happy summer.
Happy summer to you, sir. It's a lovely hat you're wearing. I was telling you right before I pressed record.
I just want to highlight this again. Yeah, you got what? What?
It's my wife got it for me. Yeah, she got a thing for birds. It says "Grow" on it. That's pretty fitting for me. So, yeah.
Fantastic. Yeah. Nice macaw on there, rocking some floral patterns. This is the perfect thing to set us up to talk about some options. And I think you were telling me before, we're talking about coin flips versus futures. We're talking over-unders versus these future-style options. I know nothing about this. You're my guide. Where do we start?
Yeah. So, well, we, we, uh, when when you put this in my calendar, you put the, uh, you put the subject line "Bar Bet." And so, I think bar bets is a good way to talk about this. It's, uh, the different kinds of bets that we, um, we're going to talk about different kinds of bets. Um, maybe how to think about them a little bit, and then we're going to relate it to options. So for people that want to go a little bit further and are more financially inclined, we can do that.
So, um, this is the first thing I'll talk about with bar bets. Is, uh, there's the first kind of bet I'll talk about is I call it an over-under style bet. So an over-under style bet, would you, well, from the sports world, an over-under is often times like, is a football game and it's like, hey, the combined score is going to be over or under 70, uh, points between the two teams, let's say. Uh, so an over-under bet is, there's some, uh, number of points and it's, you, I almost think of it like a strike price, and if it's a, uh, and the, it pays out, it's a 50/50 bet. So, um, it pays even money. And so the line is set, or the strike is set, as like what the, what the marketplace or what the odds makers think is the 50/50 point. So, uh, that's an over-under bet. That is a, uh, uh, a coin flip is like an over-under bet. Going to be heads or tails. It's 50/50, um, and pays even money. Uh, a point, point spreads in ball games are, uh, like over-under style bets where, um, it's going to pay even money, you know, minus the, the commission or whatever from the, from the, from the, uh, bookie. But the, uh, so all of those are over-under bets. And the, the key thing about over-under bets is that, um, like I said, they are set like the price is set so that it's a 50/50 proposition. That's a very common bet. If, if somebody says to you, hey, do you want to make a bet? It's usually assumed, do you want to make an even money bet, uh, where it's like, we're going to exchange the same amount of money with each other if, uh, we win or win or lose. So, uh, that, that style of bet is, um, what determines the value of that bet is just the probability of the thing happening. Is it, if it's going to be more or less than 50% chance of it happening will decide whether it's a good bet or not.
So this is like, this is the coin flip thing. The coin flip, the 50% the 50/50 odds become the variable. And then you're saying we can move that variable away from 50 above or below. We can
Oh, so we can move. Okay. So, in all the bets I was talking about, um, the line is set so that it's 50/50, so that it's even money. Like, uh, I can, I can only win as much as I bet, kind of thing, not more, not less. Um, there are variations of, I would still consider these over-under bets, but where the, where the price moves. So like anything where you're going to give odds, for example, so you say, um, you know, three to one that you can't make this half-court shot, that is still an over-under bet in the sense that the, the amount you could win and the amount that you can lose are known beforehand. They're fixed. In this case, uh, I can lose, if we, if we bet a dollar, I can lose $3, or I can make $1 if I lay three-to-one odds. So, these are these kinds of bets are everywhere. Uh, we see that everywhere, too. Like a money line is an over-under style bet where there's odds involved. So, that, that the money line could pay, you could bet $100, but you could win $300, for example. Um, prediction markets work like that, too.
So, I actually have Cali open right here and I'm looking at a couple of them. I just saw.
Give me a good one. I want to gamble on something. What do we got here?
So, "Will Musk tag Trump in a post on X this month?" is an open prediction market here. So, I don't know. You want to take a guess as to what probability that's trading for? It's, uh, between zero and 100.
Oh, man. That's a fantastic. Uh, 30%. Where are we at?
That's really, that was really, really good. So, 27%. The market is, okay. Yeah. I, I, I don't, I don't have the bid and offer open, but it, I got think it last traded 27%.
So, actually, we should talk about this for a second. The unpack this.
Yeah. So, let's just say, let's just say that that was trading for 33%. So if you were to buy 33% probability that's, which sounds weird. It's like you're buying a probability. What does that mean? So if you buy 33%, you can think about it as you're paying $33 for something that can be worth $100. So you're betting 33. If that event does not happen by the expiration date, um, you will lose all your money. So you will lose one bet size, which is your 33. If you win, you'll win, you know, 60, 67. So like two bet sizes. So you are getting two-to-one by paying 33 for something you're getting two-to-one. If you paid 50 for something that settles to 100 if it becomes true, um, that's an even money bet. You're betting 50 and you can win 50. You know, you'll, you'll give 50 and at the end, you'll get a 100. So you net make a profit of 50.
So, um, whenever you look, which is kind of neat, whenever you look at odds, um, so prediction markets are always set in terms of probabilities. So, uh, let me find one here that's kind of, um, a lot of these are all like 28%. Like, "Justin Bieber has a number one album this year," 28%. "When will the National Guard leave Los Angeles?" And it's before August 1st is the date, and that one's also trading for 28%.
So the, the, uh, uh, the, um, but the odds on things, um, let's say I'm offering you three to one odds on a bet. The way you can convert that into a probability, like the way the prediction markets look, is if you're getting three to one, you take the small side, the one, you stick that in the numerator, and then you take, and the denominator becomes both the sum of both numbers. So three, the three plus one, so you get one fourth. So the probability, if you're getting, uh, three to one, the probability, if you were to put it in prediction market, uh, terms, is 25%. Um, so if you are getting four to one, then that in the prediction market would be trading for 20%. Because you can pay 20 and you can win 80. So that's four to one. But we did that by taking the one and putting it over four plus one, one over five, and that's how we get the 20%. So you can always convert odds into probabilities. And you could always, if you wanted to, you could, you know, go in reverse and turn the probability into odds. So if some, if something was 25%, you could also say I'm getting three to one for that.
Is there a functional, this is maybe a naive question, is there a functional reason to do that conversion back and forth, or is it just a cool representation of these are two ways to say the same thing?
Um, I think just because if you're just translating from, if somebody, for example, if somebody offered you odds on something and then you wanted to like look up where it's trading in the prediction market, you could convert and be able to see it in the same terms would be a good way of seeing it. We'll also, we'll come back to this later when we talk about the options, uh, when we talk about the options part as well. Um, this will, this will show up again. Um, but generally speaking, I like to take, I have a habit of when I see odds to convert them into a probability. Um, so, but all of, everything we've discussed so far is this over-under style bet where, like I said, like the, the amount you can win and the amount you can lose are fixed beforehand. I'm either getting, I might, it might be even money, or I'm getting odds, but I know my max loss. I know my max gain. So that is an entire category of bet that is, um, an over-under. The value of that bet just depends on the probability of the proposition actually happening. Um, so, for example, "Will Musk tag Trump in a post on X this month?" It is either yes or no. It's, it's, it's a binary thing. So yes, you're getting almost two to one, you're getting a little bit more than two to one odds on that, it's trading for 27%. Um, it's either going to happen or it's not going to happen. If he tags him in 10 posts this month, it doesn't change the fact that you're getting, uh, that you're going to make 73 bucks for every 27 bucks that you, that you bet on that, you bet on this, right? So, the amount of times he tags him does not matter. The only thing that matters is binary probability. Yes or no, did it happen? That's over-under style bets.
There's another style bet which I call future style bet, and that is, um, this is sort of like the dollar-for-dollar bet that has an unbounded outcome. So in this example, if you said, um, "How many times will Musk tag Trump in a post on X this month?" and the market for that will be like a stock. So it might be, you know, in this case, it's probably zero bid at one, but if people thought it was, you know, that he might tag him a bunch of times, somebody might say, "Hey, I'm, I'm, I'm one, uh, I'm, I'm willing to pay two," and if he ends up, I'm willing to pay two, and if he tags him five times, I net win three units. So, um, just like a stock, I, if I buy a stock for $10, I'm not betting on like if it's going to be over or under $10. I mean, I literally make money dollar for dollar for every dollar it's above $10. That is like a, like that's how futures work. That's how stocks work. Um, this is a, um, when I was on the trading floor, there was a lot of futures style bets that happened. Um, you know, the, I remember a colleague, how many, how many, um, out of a hundred, um, well, out of a hundred shot, out of a hundred threes, how many do you think you could make? I kind of remember that market opening up in like the 40s and people would, you know, people had like significant money on it. It's like $1,000 a basket kind of stuff. Was like, it was major action on Wall Street on this. And, uh, I think it ended up settling like in the, like in the low 70s. He hit something like 72 shots or something like that. And he, you know, was a total ringer kind of situation. But the, uh, uh, the, my, the most fun one I've ever seen was, "How many beers in an hour can a guy drink?" And he did it up in the office with an NYX.
I'm only, I'm happy to hear that it was how many beers you can drink in an hour and not, can you do 100 shots and finish them.
Yeah. Do you remember the outcome of the bet? How many beers?
Yeah. 20. It was 20. Right on the nose. Wow. It was very impressive. It was, he was the most collected dude I had ever seen. Just, just one at a time, slowly, no rush. Like he was enjoying it. It was a little bizarre to see, but, um, anyway, I don't remember where that market ended up like closing before he had to go into the settlement period and actually do it. But, um, the point is, that's an over-under style bet where you know, if you sell tens, you're losing dollar for dollar above 10. It's not like, hey, I bet you 500 bucks he's not going to do that. And then he, you know, he does 15 or 18 and you still just lose 500 bucks either way. You're losing a dollar a point on there. A dollar a beer. So, uh, that's a future style bet. And so, the example I, I like to give with this is, future style bets and over-under style bets are very different because, like I said, with the over-under style bets, the only thing that matters is the probability. Um, but with a future style bet, what really matters is what does the underlying distribution look like? Like, does it have a long tail to it? So, the, an example that I like to give is, um, let's say you live in Brooklyn and you commute to Manhattan for work and you take the subway. And if I tell you, uh, what's your over-under, or what's your, uh, if we have to set an over-under line on how long your commute takes to the city, like what do you think? You know, let's just say you live in Brooklyn, you commute in Manhattan. Sure. So, what, like 40 minutes, 45 minutes, something like that?
45 minutes.
And you know, you do that every day and you, you have, you know, some data and you know, you don't get to work late, so you know that it takes you 45 minutes to get to work. So somebody says it's 45 minutes. That's the fair odd. That's the fair 50/50 odds, like whether it's going to be above or below. But if I told you, okay, let's trade it future style where I'll pay you $45. Uh, I'll bid 45. You sell me 45s and however long your commute takes, um, we settle it a dollar a point. Right now, from that point of view, what does your risk-reward look like?
Yeah. So, I mean, basically, anything goes wrong in my morning, like maybe I get there faster, but that probably isn't happening that often. And on the off chance that, like, uh, you know, there's a bum on the tracks or something, there's all sorts of things that like could add time to this and then I'm losing. So, like the, the only good outcome is like I'm occasionally earlier than average or I, I just barely skate through and I get some free money.
That's right. It feels like it sucks. This feels like.
Yeah, it's right. It feels like a bad bet, right? Like you're, it does, it's like, you know, you're, how quick I can get there, sort of bounded by physics. It's like, if, if I get to the platform just as the train arrives and everything, like maybe I do it in 38 minutes. Like the most I can win is sort of like seven bucks if I sell 45s. But what if I get sick on the way to work? What if I get in a fight on the way to work and like I don't even make, maybe I don't even make it to work that day? Like I'm, and I'm just unboundedly losing above 45 for the, for, you know, a day's worth of minutes.
Right. So the, I'm thinking of the "While You Were Sleeping" thing and like the guy, you know, goes to work and ends up on the tracks, then the whole movie plays out, and you know, maybe he made this bet and now Sandra Bullock is even further out of a guy than she thought in the beginning. This could, this could go horribly wrong. Could go really wrong. So you don't want to. So when you're dealing with something where the distribution is actually skewed, you would not sell the future at the same price where you might set the over-under strike or the over-under line. Right? So, uh, so the point there with a future style bet or a stock style bet, um, it's not just the probability of the thing happening, but it's the magnitude by which it can happen. How long, how long that tail sort of looks will determine the fair price. So in the traffic example, it might be the case that you say, "Hey, um, over-under style, um, I'll trade 45s with you, but if you want me to sell you it future style, um, maybe I won't sell anything less than like 60 minutes."
So like I'm making. Build that buffer in.
That's right. So I might, you know, 95% of the time maybe I feel like I'm making somewhere between 10 and 15 bucks and I sort of get like beat up on the other 5% of the time and however long that tail is kind of like sets the fair price of the bet. But like I might not sell anything less than 60 future style, but I'd be willing to trade 45s over-under style. So this is like, um, this is a very, uh, really good way to differentiate bets whether it's an over-under style or a future style and then recognizing that the future style isn't just about the probability but also sort of this, the skew or the volatility of the underlying, um, distribution.
Uh, which clarify this. What do we call if the over-under is binary, the future style is, I guess, continuous?
Okay. I think that makes sense to me. I was struggling to fill in that if-then SAT question that I just put you on the spot. So, yeah.
Yeah, I, I guess, yeah, I, I think it was continuous, but I, I've just always called it like over-under style or future style. And when I was, even when I was in training, because, you know, you, you sort of do like a lot, a fair amount of betting and propositions and stuff because it, like, sort of tunes your intuition about these kinds of things, but like, you, you might propose a bet and somebody's first question is always like, "Are we doing this over-under style or future style?" And it was the immediate recognition that the price would be different, right, um, depending which way you went. So, uh, so this is, I threw the word volatility in there. So, uh, the future style bet, um, you know, depends on the vol, uh, um, you know, how far away you would price the future style bet versus the over-under style bet will depend a lot on like the volatility and the skew in the underlying thing. Like, if the thing is very volatile, like the commute, um, where it's like pretty constrained most of the time and then it basically blows up a very small percent of the time, um, you're going to price that very differently. That's a very, that's a lot of skew in that one.
So option contracts, like an outright call option, for example, is, um, the value of the option is very sensitive to whether, not just the probability of the stock going above the strike price, but how far it can go above the strike price, which is the volatility part, like how, um, it's sensitive to both values. Um, and we can actually, the fact that it's sensitive to both values is interesting because it lets us, um, by looking at, uh, by looking at option prices, we can actually learn a lot more about a stock than just looking at stock price. Um, if you don't, I actually made a little something. I can show it if it, if it's helpful.
Break out the screen share.
This was a hit last time. We got to do this again.
Yeah, it's still my son's spreadsheet, but the method of adding stuff to it, he did not. This is where if you missed the last time Chris came on and taught me option math, we used this spreadsheet that his real-world son built. So, extra shout-outs to your son because this is freaking amazing that he built a spreadsheet and now you're teaching me with it.
Yeah, we're gonna. Well, yeah. And this is, this is, this is this is stuff I did, I'm, which I'll use to teach him, kind of, kind of fun. Uh, but the, Okay, so I wanted to talk about, we can pretend that, um, imagine we have two stocks. They're both $100. Stock A, Stock B. Maybe Stock A is A for average and Stock B is B for biotech. And we'll see why in a second. Okay, so Stock A is, uh, we got the average stock and then we got biotech stock. Okay, both stocks are $100, but both stocks are $100 for totally different reasons. So, Stock A is $100 cuz let's say it has a 50% chance of being worth $200 and a 50% chance of going to zero. These are volatile stocks. So, it's either going to double or it's going to get, uh, it's going to lose all of its value. So, it's its fair price is $100. 50% chance of being 200 plus the 50% chance of being zero is 100, $100 stock. Biotech. So, and I kind of represented that here where, um, this is like a histogram. So, there's, you know, 50 instances out of 100 of it going to zero and 50 instances of it going to 200 and that sets its price, its fair price at 100. B, Stock B, biotech, is also trading for 100 and it's fairly priced at 100. However, its $100 price is being driven by the fact that it has a 10% chance, in 10 instances, it's going to be worth $1,000. Um, you know, the FDA, there's a 10% chance the FDA is going to say, "You nailed it. This is a great drug. Let's go through with that." So, there's a 10% chance it's worth a thousand. And there's a 90% chance that they've just been wasting their time for the last 10 years. So, uh, 90% chance it goes to zero. Now, that stock is also worth $100. Um, 10% chance of it being worth a thousand and 90% of it being worth zero. Now, if you were just looking at both stocks, they're both $100. You, uh, could be fooled into thinking they were the same sort of thing. Like, they're both of these stocks are under, like the stock price itself doesn't hold a lot of information. Um, it doesn't tell you that this is what the underlying distribution of each stock looks like. This is where options become really cool because options will tell you exactly what that distribution looks like.
So, because I mentioned that the stock price, uh, the option prices are driven not just by, um, the probability of what will happen, but the, uh, the magnitude of what can happen. So, I'm going to switch here to the call values tab. So, I actually, before I do that, let's, let me, let me do one more thing. Actually, I hid this over here.
Ha, the reveal. The reveal.
Okay. Um, that I just wanted to point out. So, this, this example here, I gave a very, very stark example that we don't typically see in the markets where this is a bimodal distribution. There's two possible outcomes and that's it. But that is not really, most things don't work like that in the stock market. The, the distribution is more continuous. So, this is a little bit more of a, the same idea, but using continuous distributions where Stock A in this case is the bell curve. So, it's a $100 and the probability of it going up or down and the distances are, um, symmetrical around the center of the bell curve. Stock B, uh, if it wasn't such a stark bimodal distribution, could be a stock that looks a lot like this. Like, any, often times, like new technology stocks, like a lot of the.com stocks back in the late 90s, they were actually distributed like this, where the stock price could be 100, right? So, you know, you could have had, um, both Amazon and Pets.com, both could have been $100, but most stocks, most stocks were Pets.com back then, and the fact that they were going to go to zero, zero, or lose most of 90% of their value was actually fairly well understood by the options market, and the options market priced it as such. So, but the stock could still be worth a h, 100red because there was this long right tail that, hey, this could become Amazon. So that's, so this is like where you get this situation where you have a $100 stock, this orange lot in the, and the orange distribution governs how that stock's value is determined, where it says, you know, most of the time you're going to lose a lot of your money on this stock, but sometimes you're going to make 10x, 100x on on that company. So it looks like this distribution. So this one over here is pretty stark. I, it was a toy example. This is a real world look at a, there are stocks that absolutely look like this, and the options market can kind of show that. So, this is a, just a little bit more realistic, but I want to switch now to call value.
So, we're kind of going there. This is, this is really cool, too, because it's a good visual representation and reminder for people like, if you're a fundamentals guy, you don't, you might not necessarily look at where the options pricing, like where this is occurring. This is a really cool way to do a different version of scenario analysis and look at a financial instrument that either agrees, disagrees, confirms, or denies your view and why it's positive views.
Yeah, absolutely. Sometimes I take this, it, I, I say this in an extreme way, not because it's like perfectly true, but because it demon, it's helpful. It's that sometimes I like to say like the options market sort of like is the underlying market because it is a, you know, the, the options surface is a much fuller picture of what is actually going on with the stock. A stock price is just a two-dimensional representation of all the, the branching trees of probability that can happen for the company. But the options market is specifically defines what that looks like.
Yeah. It's, it's the difference in granularity of being like, I'm looking top down and I'm recognizing topographically, hey, that's an oak tree there, but this is like, okay, here's all the leaves, here's the branches, here's the one that the termites ate, here's the one that, you know, is about to blossom and bear fruit. This is really interesting.
Yeah. Yeah. So, this is, so we're going to go to the call values here because I wanted to, I wanted to, even though we, we just looked at those two stocks. But this is a look at what the call values on each stock would be worth. So, to figure out the call value, first I'll kind of step through that, um, which is, uh, fairly simple because the scenarios are, there's only two scenarios. So, in the case of, we're going to think about the 100 strike call. So, remember Stock A, it can either be worth zero or it can be worth $200. So, the 100 strike call, the most it can be worth is $100 itself because if the stock goes to 200, um, then the diff, that you would be able to exercise your call, buy the stock for 100 and sell it, the shares for 200, and you would make a $100 profit. And there's a 50% chance that that call is worth 100. So, the call value is $50, which we see here that the blue 100 strike call is worth $50. We notice that the 200 strike call, 300 strike call, they're all worthless because we already said that the stock cannot go below above 200. So, all the other strikes are worthless calls. Now, Stock B's call values, it's the same math, but the, the difference is, is the probability of any one of these calls. It's actually the same probability that any one of these calls goes in the money, and that's 10%. Because if this stock goes up, it goes to a thousand. And that happens 10% of the time. So, every one of these calls has a 10% chance of being in the money. But the 100 call would pay you $900 if it was in the money. Um, the 200 call will pay you $800 in the money. So, 10% times how much you could win on each one of these determines the value, the call. So, um, so the 100 call is worth 90, 200 calls worth 80, and so forth until you get to the 900 call, which is worth 10 bucks because a 10% chance it's worth 100. So, the point here is, Stock B's call options are worth more than Stock A's call options, even though, even though it's less likely to go up. It only has a 10% chance of going up, but all of its calls are worth way more than Stock A's calls because it can go up so much. So, higher V, more skew, higher call values. Hope it's a man. That's rough.
Yeah, it's, it's. So, well, what I'm going to do here is now we're going to flip it a little bit because we're going to. This is my point, my toing it back to the beginning. Point of this was showing that the call values are sensitive to both probability and magnitude, just like a future style bet and unlike an over-under bet. However, we can actually turn options into over-under bets where they're not going to be sensitive to how far the stock can go above some certain price. And the way we do that is we trade a call spread where we buy one call and then we sell another call of a higher strike. And, um, well, I'm going to show you the visual here for that. So, this is an example of some random stock, the 50-75 call spread. So, what that's saying is if I buy the 50 strike call and then I sell the 75 strike call. So, if I buy the 50 strike call, in theory, I can make infinite money. Uh, however, if I se, um, for, I make dollar for dollar for the stock being above 50. If I sell the 75 strike call, then I have given up the ability to make infinite money because I'm going to owe money to, to, to the owner of that call for every, uh, um, every dollar above 75 that the stock goes. So, what happens is if I buy the 50 and I sell the 75, what happens is I've basically bought a bar bet. So, the most this thing can be worth is at my short strike at 75, the most it can be worth is $25, and the least it can be worth is zero. So, if something can be at most worth 20, uh, 25, and the least it can be worth is zero, it sure looks like a prediction market where the most it can be worth is 100 and the least it can be worth is zero. So, if I pay 12.5 for something that can be worth 25, it's like saying there's an even money chance of the stock finishing below, sort of, the middle strike. So, what I've done is I've taken these calls, which are super sensitive to the magnitude, and I've truncated it and I've said, let's just turn it into a bar bet. I'll just spread the calls off. So, all of a sudden, like a call spread and a point spread are the same thing to me.
You've truncated it. You've turned it into a coin flip by truncating, by putting parameters on that upside.
That's right. Amazing. So, if I, if I, for, for example, if I, if a call spread can be worth $25 because there's $25 of difference between the strikes. And if I pay $5 for that call spread, I'm getting, um, I'm going to, I can make 20 or I can lose five, right? So, I'm getting four to one odds. So, what I'm saying is I think that there's like a 20% chance, four to one. Uh, there's a 20% chance that the stock, you know, is going to go up to, let's say, 75, and I'm going to get paid four to one in that scenario. And this is kind of why I talked before about turning, um, odds into probabilities, because if you think about a call spread, it's always presented to you in terms of odds because it's like, hey, what's the most I can make on this thing versus how much I'm going to outlay. So, in this case, I pay five for something that can be worth 25, which means I'm getting, uh, 20 to 5, or four to one. And then I want to convert that into a probability. So, that's why we sort of went through that earlier, uh, because I, I think it's very handy to turn call spreads into probabilities. If you think one step further, you will realize that if you were to look at all the call spreads, you would get a bunch of probabilities, and what would happen is you would actually have a histogram of the stock price. And that's what I meant before about the option prices will tell you the distribution of the stock, because all you need to do is look at all the call spreads, and suddenly you know if this stock looks like this, this blue one, or this orange one, the call spreads will tell you. So, uh, so that's a review on the call spreads.
So, now what I want to switch back to is we saw that Stock B biotech had way higher call values than, uh, than Stock A. B had much higher call values. In fact, I mean, you go get to all the way the 500 call and the 100 call are worth the same, even though this one is so far out of the money in Stock B. Okay. Now, if we look at the call spreads, the relationship flips because all that matters is the probability. Now, so Stock A's call spreads are worth more than Stock B's because Stock B only has a 10% chance of making a fixed amount of money. So, every one of these call spreads, the 100, 200, the 200, 300, they're all worth the same. They're all worth $10. There's a 10% chance of getting paid $100 on any one of those. But Stock, uh, Stock A, the 100-20 call spread is worth $50. There's a 50% chance it's going to be worth $100. So, Stock A's call, Stock A, which has a higher, much higher probability of going up, has way more valuable call spreads, but way less valuable calls. So, this is, this really sort of highlights the difference between, um, the over-under style bet and the, um, uh, the, the future style bet.
I'm fascinated by chopping it up into the pieces. And that last graphic really made that clear to me. This is the complete overarching connection. If you chop it up into all these little pieces, then there's just less pieces because they have to add back up to 100. It's just probability 101 stuff. But if you start to think about it that way, then you start to realize all the different ways you can parse out what are the pieces on the table, how far they spread apart, what am I trying to make this bet on. This is a really cool way to strategically visualize this.
Yeah, I think it, the importance, I think for investors is exactly, is really exactly what you're saying. You know, if you're thinking, if you're just thinking blindly about how much, like just thinking about how much of a stock you should put in your portfolio, it matters a lot to you whether its value is being driven by, like a really far right tail, or it's going, it's, but it's probably going to be a zero. You would probably size that trade very differently. You're not going to make that half your portfolio. Um, you know, you're going to think about that more as like maybe the way some people might think of a Bitcoin allocation or like a venture capital allocation. Um, and just looking at the stock price by itself just doesn't tell you enough. And so the options will, will kind of, uh, uh, will tell you, will tell you that. So, it's, it's, uh, you know, and then if you're trading the thing, uh, it allows people that have a very nuanced view about a stock because, you know, you, you might not have a view as to like why, how far can this stock go? In which case, you really shouldn't be trading the options because then you, you're not really, you don't have a great sense of what you think the volatility actually is. But you may have a pretty good sense about what's the chance of X or Y happening, in which case the right way to go about it is surgically with a spread.
I love that you've just connected this to us, to for me at the end here, between the portfolio theory approach and the individual idea or security or investment choice, the, in individual selection, right? Because if you can see this completely unpacked in both directions, in the complete composite portfolio and has the complete composite of probabilities inside of one position, if you can learn to think through those all the way through from both directions, and hey, apply it to life too, not just to like what Occupank or what your Bitcoin allocation is. That is a really powerful way to have a much deeper, nuanced, 360-degree view of what go, what's going on. Might not make you better, but it does help you think about it.
It does help you think about it, and it does help you, it absolutely helps you get context when you're looking at, um, all these things like prediction markets and the price of assets and, you know, what's driving the price of this? Is it the probability or is it the magnitude? And that's a very handy thing to think about when you're, um, whenever you're looking at prices because a lot of times prices don't make sense when you look at them from, uh, let me say this. I remember when I was at SIG, way back when, um, there were, uh, some bosses that took, uh, uh, that took exception to the idea that the dot-com bubble was irrational and a bubble because their attitude was, the options market told you, like, the options market told you exactly the way this thing was distributed and it was not, it was completely rational. And if you remember at one point, Amazon did lose, is 90% of its value. And if you, and I remember even in training when we were like, look, when we were learning to analyze this stuff, we would look at Amazon's stock price and we would look at the options distribution and we would notice that the, the modal outcome implied by the options was that Amazon was going to lose something like 80, 90% of its value. That was like baked into the options, but it's being, but its stock value was being driven by this long right tail. The options market understood this stuff. So, um, you know, I think people still call it a bubble, and I still do it as sort of like a habit, but when I stop and think about it, I'm like, new technologies are usually, it's rational for them to be bid that way. If you think it's going to be, uh, world-changing, you know, I'm just glad that I can be the dumb money now and not just, you know, the stock investors of the world. It's a good, good new lattice work angle.
Join the club to be Chris. It's crazy that people want to bug you on the internet. Ask you more questions, or should they look you up?
Uh, come to my Substack, Moontower.substack, or they can follow me on Twitter, X, whatever.
Fantastic. Go follow Chris in all the places. See the prior episode we did here. Just scroll back in the Excess Returns feed and we'll see you real soon. Thanks, Chris.
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