The Hidden Logic of Options | Put-Call Parity Explained with Legos

[00:00:00] We're excited to announce the launch of a new podcast, Teach Me Like I'm Five. In each episode, we will take a complicated investing topic and make it simple with the help of some of our favorite teachers in the world of finance. In this episode, Matt Ziegler sits down with Chris Abdel-Masia to explain why Legos can teach us all we need to know about options. If you want to keep receiving new episodes, you can subscribe to Teach Me Like I'm Five on all major podcast platforms or our YouTube channel. Thank you for listening. We hope you enjoy the new show.

[00:00:23] I even brought up my favorite Legos. We're going to learn that calls and puts are actually the same thing, and we're going to learn why they're Legos. You can create any payoff you want out of the options, including the stock. You can build the stock. You can build Dom's Charger out of the options.

[00:00:45] You're watching Excess Returns. I'm Matt Ziegler, joined today by Chris Abdel-Masia. You know Chris as the former super duper extravagant options trader, as the founder of Moontower AI, and the writer at Moontower.substack. Make sure you subscribe. I love getting those emails. Chris, thanks for coming on Excess Returns. Matt, thanks for having me. I'm looking forward to today.

[00:01:06] You know the show, Teach Me Like I'm Five, because I am a five-year-old at heart and by logic in so many cases. What do you want to teach me today? I'm excited to learn. Yeah, so I was stoked when you asked me to do this, because I'm in the middle right now. I have a sixth grader, and I'm in the middle right now of teaching him options.

[00:01:29] And we're starting from the most basic places. What's a call? What's a put? And what are they worth at expiration when they expire? And the lesson I kind of want to do today is it really has two parts. It's one, to kind of help you think about options as I kind of explained it to him, is they're like Legos, actually. So I even brought up my favorite Lego.

[00:01:58] I love props for this. This might be the best part about this show. What kind of car is that, that we have a Lego car on? That is Dom's Charger from Fast and Furious. Dom's Charger, Fast and Furious, about to teach me about puts, calls, and some other magic. I love it. And this thing could be like, you could kind of think of that as like, that's something you build with Legos, right? That's the finished product. That's the stock. And that's where this gets kind of interesting, because what we'll do is we'll see.

[00:02:27] So most of us, when we learn about what a stock is, we learn what a stock is, and then we learn what options are. Our options are derivatives. Their value is derived from the price of a stock. But the stock is usually the first thing we learn. And what we're going to see today is that we're going to learn some crazy stuff. We're going to learn that calls and puts are actually the same thing. And we're going to learn that, and we're going to learn how, why they're Legos.

[00:02:56] It's because you can create any payoff you want out of the options, including the stock. You can build the stock. You can build Dom's Charger out of the options. So that's the first thing I wanted to show you here. So just as a refresher, like, I know this is super basic, but we're just going to pretend, like, if you bought 1,000 shares. So, by the way, my son – What are you looking at here? What is this spreadsheet?

[00:03:25] And I'm assuming this isn't modeling out Fast and Furious movie actor contracts where I can't lose a fight, so this is my return. This is the spreadsheet. This spreadsheet is the spreadsheet that my son made, and I told him today. You can actually see here. It's called Options with Dad. He wrote that. This is not me. It's called Options with Dad, and he started with buying a call. Then Stuff is his main tab, and what I did is I just duplicated it and made this presentation tab for today.

[00:03:54] Unlike me in sixth grade, no one is stealing my homework. I'm stealing someone else's homework today. This is incredible. All right. Keep going. So, what we're going to do here is see – so, what his tool does is you put in Option and Stock Position, and it shows you what the P&L would be for a given stock price.

[00:04:16] So, what we're going to do here is we say if I buy 1,000 shares of the stock at $50, and this shows me what my P&L would be for a given stock price. You have stock price down here on the x-axis, and you have your y-axis, which is your P&L. So, if you buy the stock for 50, your P&L would be 0 at 50, and if you bought 1,000 shares and it went up $50 to 100, you would make 50,000. Likewise, if it went to 0, you would lose the 50,000.

[00:04:46] So, the thing to notice here is you have this completely linear return. So, for every dollar the stock goes up, if you have 1,000 shares, you make $1,000 and vice versa. So, that's the payoff of a stock. And this is generally the first thing we learn about stocks is really how they work, which is that if it goes up a dollar, you make however many shares worth for that dollar.

[00:05:10] Now, what I want to show is, first of all, let's talk about what a call option is and what a put option is. So, the first thing, I'm going to delete these, and what we'll do is say, if you have a call option, what a call option does is it gives you the right to buy the stock for a given strike price up into a certain expiration date. We don't have to worry about expiration dates at all today.

[00:05:37] We're just going to remember that if I buy a call option struck at $50, I have the right to buy the stock for $50. So, now, just conceptually, it would make sense that this value of this option would be higher if the stock price is higher.

[00:05:59] So, if the stock price is $75 and I have this option to buy the stock for $50, what I would do at expiration is I would exercise that call option. That would give me to I'm allowed to buy the stock for $50, and then I can go out into the open market and sell it for $75. Because I can do that, that's a $25 profit. That means that the option must be worth $25.

[00:06:26] So, likewise, if the stock had went down to only $40, I would not want to exercise that option. Because why would I want to buy the stock for $50 when I could just buy it in the open market for $40? So, just conceptually, we can understand that at expiration, if the stock price is below the strike price, the strike price being $50, if the stock price is below the strike price, the option has no value. We would not exercise it.

[00:06:56] If the stock price is above the strike price at expiration, its value will be the difference between the strike price and the stock price. And the way we can see this visually is we can pretend that we buy one option. We can say that we bought it. We can just say we bought it for $0. Somebody gifted it to us for nothing. And the strike price is $50.

[00:07:22] And we can see here that for $50 and below, our P&L is $0. We didn't pay anything for the option, but there's no profit at all. And from $50 and above, it's this linear looking payoff where I make a dollar for every dollar. It's above the strike price. So, we like to call these hockey stick diagrams for sort of obvious reasons.

[00:07:51] So, it's got this kink in it. And it just kind of starts to tell you a little bit about how interesting an option is. It's this thing that can, if you own it, you can make money. And you cannot lose more than what you would have paid for the option. Because you could just choose to not exercise the option. You could abandon it. So, if I had paid $5 for this option, now I have a break even.

[00:08:18] So, I need the stock to be at least $55, which is... I don't know if the hover over will kind of work here. But, yeah. At $55, my P&L is $0. Because I've covered my option premium at that point. And then I make $1 above $0 for every dollar that the stock is higher than $55. Likewise, if the stock is at $50 or lower, I have just wasted my entire $5 premium.

[00:08:45] So, my P&L is losing $5 in every case. It says $500 here because the multiplier on an options contract is 100 shares. A lot of lunch money. A lot of lunch money. Exactly. So, that's how a call option would work. Now, what we can do is we can also say, how does a put option work? So, we just go down here and we switch this to a put. And the put option is going to work the same way.

[00:09:14] Except for that a put option is the right to sell the stock at $50. So, we still have a concept of a strike price. We have the right to sell the stock at $50. And what we see is we just invert our logic. If the stock is at $40, the right to sell the stock at $50 is valuable. Because you can sell the stock at $50 and then you can cover your short shares at $40.

[00:09:41] Likewise, if the stock was trading for $75, the put is worthless. Because why would you want to sell the stock at $50 when you could sell it at $75? So, we get the exact opposite picture. The hockey stick diagram with the payoff leg going up and to the left. Okay. So, this is a – the thing that happens here is we can combine options. Like I said, they're Legos.

[00:10:09] So, we can combine options to create the payoff of a stock. If you remember, the stock price was that picture. Just that vertical – just we'll keep that picture in mind. Just lower left, upper right. Let's create the same exact thing just using options. So, what we're going to do is we're going to buy $150 call, which will give us the right to buy the stock $450.

[00:10:38] If we buy $150 call, and we're going to say we'll pay $5 for it. And the strike price is $50. And we're going to call – and that's going to be the call. Okay. So, right now, I've got this leg right here of this – of that former picture that up and to the right. But then I've got this guy here. We don't want him.

[00:11:04] So, let's go here and we're going to say, you know what, I'm going to buy a call for 50 – a 50 strike call for $5. I'm going to sell the 50 strike put. I'm going to sell the put. So, that's a minus one for sell. And I'm going to sell that for $5. And the strike price is going to be 50. And by the way, if you notice here, I'm long a call and short a call. The P&L is zero. So, good job, son.

[00:11:33] Your machine works. Yeah. Okay. Your machine works and you're making no money with the rest of us. That's exactly right. So, we're going to go here and we put selling one 50 put for $5. And what we've done is we have replicated a long stock exactly. Now, why does this make sense? We have to think about the scenarios. I own the 50 call and I'm short the 50 put.

[00:12:01] What that collapses to is no matter what happens at expiration, I am going to buy the stock for 50. Because if the stock is 50 above 50, I'm going to exercise my call. If the stock is below 50, remember, I'm short the put. So, the person who owns the put is going to force me to buy the stock for 50. In other words, I'm going to be assigned. That's called assignment.

[00:12:26] So, I'll be forced to buy the stock for 50 at expiration. Either it's going to be put to me or I am going to exercise the right to buy it there. So, no matter what happens, I'm buying the stock for 50. Well, if I know that I'm buying the stock for 50, no matter what happens at expiration, and I have that obligation now or I have that structure right now, then I own the stock now for 50.

[00:12:53] So, I have just replicated a long stock position using a long call and a short put on the same strike. Like, this is option people call this a synthetic. This is a synthetic future on the stock. So, it works exactly the same as if you had bought sort of an S&P future instead of buying the SPY ETF, for example.

[00:13:20] I kind of love this in the sense of it's just a reminder. It's like Superman on Earth has all these magical, mystical powers. But Superman on Krypton is just a regular guy. You can build this synthetic reality of being like, no, here's how we neutralize Superman. We just put him on the right planet. You got to think of it about all these ways and that all these variables actually exist. This is really cool to see visually. Yeah. So, okay.

[00:13:48] Now, this was like creating the idea of a synthetic. I really just tried to prove to you here only that options are Legos. But there is a bigger lesson here, probably one of the biggest lessons you can learn about in options. It has a fancy term. They call it put-call parity, which is another way of saying that on the same strike, a call is a put and a put is a call.

[00:14:17] Which sounds crazy until I have to prove it to you. So, what we can do here is we're going to go back to this long call position. We're going to delete this put and we have this diagram. So, if I buy, again, I own this call for $5. And I'm going to exercise it at expiration if the stock is above $50. And I will just abandon it if the stock is below $50. I would not exercise it.

[00:14:47] But what I'm going to do is I'm going to go and remember, we'll keep in mind here that, again, that options refer to 100 shares of underlying. So, let me do this. I own the call. I'm going to short 100 shares at $50. And we get this picture. Now, that picture probably looks familiar.

[00:15:16] We've seen this before. We've seen this before. We've seen this before. So, to narrate the picture, the picture is saying, I make money dollar for dollar with the stock price going down when the stock goes below $50. And above $50, I've basically lost my premium. And there's no change in my P&L for any amount above $50. It's all the same. What does that sound like?

[00:15:45] Well, this sounds like a put structure. Exactly. This is exactly the same. This is exactly the same as owning the $50 put. What do you call this? What's the name for this? This is kind of annoying. It's called a synthetic as well. Okay. I thought so. I just wanted to make sure there wasn't a new word that I was missing. Yeah. It's a synthetic. This is a synthetic put. There is – as we – so, this is long call short stock.

[00:16:12] So, anytime I hear the word synthetic, really what that's telling me is that something is being created out of two other things. Like there's Legos creating this thing and I should look for the variables. That's what synthetic is the clue for. That's correct. And we're going to – there's one synthetic in particular, kind of synthetic position that we are going to look at a little bit more closely. But what I wanted to do real quick with this is I'm telling – I'm showing you that this is exactly the way a put works.

[00:16:41] That – and this is a pretty deep insight here. It's like you could have went and bought the put. But if you had just bought the call instead and shorted the stock on a one-to-one basis, meaning that for every call you bought, you shorted 100 shares. So, one-to-one basis. You – if you buy call short stock one-to-one, you've created a put.

[00:17:08] Likewise, if I had sold the call and bought the stock, I've sold the put. That's exactly what a short put payoff looks like. So, call with an opposing position in the stock is a put. And likewise, a put – and we can do the same thing here. We'll say let's buy a put instead.

[00:17:37] Now, if I buy a put, the proper hedge for a put is if I buy a put, I need to buy the stock, right? Instead of doing the opposite in the underlying, I'm going to do the same, right? Because I'm going to buy the put, which is a bearish position, and I'm going to buy the stock, which is an offsetting position. And if I do both of that, I have created a – we're going to call this a fake call, like a synthetic call. They don't – see, in the marketplace, you wouldn't typically call this a synthetic, but it's a synthetic position.

[00:18:07] They will generally – they call it puts in stock. I mean it's very creative. So, I think there – maybe back in the day, they might have called this bullets. I don't know. But in any case, it is the synthetic equivalent to a call option. And here we did it by just buying a put and buying the stock. Well, I'm going to do something here where I'm going to actually just prove it to you that this is truly the synthetic position,

[00:18:35] and I'm not just like playing games here with this chart. We're just going to put – let's – I'm long a put and I'm long the stock. I think I'm long the 50-strike call for $5. Let's do this. Why don't we see what happens if I sell an actual call for $5? The 50-strike call, we're going to say I'm selling that for $5. And I'm just long the stock again. Or no. No, no, no. No, I'm flat. Okay. I'm flat.

[00:19:05] Because I'm long this – between this column and this stock here, I'm long a synthetic call. And here, I'm short an actual call. I have no position. So this is – the point of this is – so let's actually bridge this real quick to something that people tend to be very familiar with. A lot of people will do something like they will buy a stock. Let's say they bought the stock for $50.

[00:19:34] And then they go and they sell an out-of-the-money call. An over – like they used to call this a buy right. Now I think they just call it covered calls. So they sell a call for – sometimes they say words like income. We're not going to get me started on that. But the – if you sell a call and we're going to sell the $60 call, let's say. So you sell a 20% out-of-the-money call and you buy the stock for $50. We are going to sell the $60 call and we're going to sell that call for let's say $2.

[00:20:05] And we're going to delete this guy here. And we're going to be short that call, right? Okay. And short here. I'm going back. I know we've jumped into like the mid-career. You've got some experience. But back on kid terms, like I sold the call. It was the same. I'm short the call. These words all mean the same thing. Short, yes. Sell and short. So if we sell the call for $2. So we're selling a 20% out-of-the-money call.

[00:20:35] Let's make that the $60 call. There we go. And now we can see that this is the payoff that people who sell covered calls accept. They are long a stock and they're short a call. So what they've done is they will make money. I hover over here. At $60.

[00:21:01] So if you bought 100 shares, you will make at $60, you will make $1,200. Because you'll have made $10 on the stock that you bought. And you will have collected $200 on the call that you sold for $2. But that's the most you're ever going to make. This is our best case scenario. Best case scenario. Above $60, your stock is going to be called away. And you own all the downside.

[00:21:29] Except for if the stock goes to zero, you still have collected your option premium. So yes, you have collected that $2. So this is... Now what's interesting to me always is that a covered call is exactly equivalent. This is exactly equivalent to me having sold the 60 strike put. However, nobody goes out and tells people go sell the 60 put. They are... Go sell in the money puts.

[00:21:58] But that is exactly what they're doing. And again, once again, just to be thorough, I will prove this by showing you that if I bought the 60 put, I have no position. There you go. Zeroed out again. Zeroed out. So this put call parity concept, the reason it's important is besides for...

[00:22:26] I would call it more remedial reasons like understanding that when you sell a covered call, it is the same thing as selling it in the money put. But it's important because what it does is it collapses the space of what's actually happening. It turns out that if you buy... I won't prove it here, but if you buy a call spread, like a $5 wide call spread for people that... This is for a little bit more advanced users.

[00:22:54] If you buy a call spread for $5 where the strikes are $15 between them, it is exactly equivalent to selling a put spread of the same strikes at $10. It is exactly equivalent. So what happens is when you look at this zoo of option words, straddles and strangles and butterflies and call spreads and Christmas trees and condors and all the things,

[00:23:22] they are all just things that were made out of Legos. And if you know how the Legos interact, you realize that there's really only a couple of things. And everything is just a permutation of a couple of things. As a music guy, there's 12 notes. And there's a bazillion songs. Yeah. So as a Lego bucket kid, I'm thinking about mom and dad might not buy me the Batmobile, but I can make the Batmobile out of my generic bucket too. That's right.

[00:23:49] It might not be quite as cool, but I can still do it. But that's what you're showing me here with options. Yeah. And it's interesting on a lot of levels from retail to professionals. For a retail person, it's kind of this reminder that anytime you ever see some kind of a payoff which says in this state of the world, you don't lose, or in this state of the world, you win extra, there is an option underneath happening.

[00:24:19] You could replicate pretty much anything, any kind of structured product or fancy ETF. I'm not saying that you should. It's that, but you could do it. A lot of times a good product, the definition of a good financial product would be like one that had some economies of scale that allowed you to get these exposures without you having to do this yourself and possibly impale yourself. But the point is that you can understand what's happening

[00:24:47] when you realize that these are just Legos that everything is built from. For the more professional trader, this is very important because it's the foundation of so much of the analytics. For example, people will talk about what is an option surface.

[00:25:14] Well, on an option surface, the call price, what we actually do is we have a call price and we have a put price. And we actually start with the assumption that put-call parity must be true. And that allows us to back out the implied interest rate on the stock. So what we end up with is stocks themselves have the equivalent of a futures term structure. There is, you could have a one-year future on a stock. You could have a six-month future on a stock.

[00:25:44] And they might vary based upon not just the yield curve, but they also vary based upon how easy or hard to borrow the stock is. And so looking at the yield curve of the stock, you can kind of get a sense for, oh, is there a lockup coming up in six months? Because it looks like the stock is going to become easier to borrow six months from now. And that is actually reflected in the options term structure. Or you can have...

[00:26:11] So anybody building option surfaces has to be very aware of this formula, of the put-call parity equivalence, because that is how we're getting the interest rates. And it's also the basis for financial products like Box, where somebody is investing in an option structure to get a bond-like return. What's actually happening there is that we saw how the synthetic worked,

[00:26:38] where I buy this call, I sell this put, and I got the synthetic. Well, if I do that on the 60 strike, so no matter what happens here at $60, I'm buying the stock. Well, watch this. If I sell the 70 call... I got to change that to call. And I buy the...

[00:27:10] It's not going to make sense in terms of prices, but it doesn't matter. It's more of the payoff diagram that I want. What I end up with is long call, short put, short call, long put. So what's going to happen is no matter what at expiration... I should actually zero out all the prices. No matter what, I'm buying the stock at $60 at expiration.

[00:27:39] I'm going to buy the stock at $60 at expiration. And no matter what, I'm going to sell it at $70. So what happens is, I know at expiration, I'm going to end up with $10. No matter what happens, I end up with $10. Well, if I pay $9.80 for that payoff by expiration, I've done the same thing as buy a zero coupon bond, right? I have bought something for $9.80 that I know is going to be worth $10 at expiration

[00:28:08] no matter what happens. So all the boxes is long one synthetic and short and adjacent synthetic. And then the discount to the difference between the strikes is basically implies the interest rate, just like a zero coupon bond does. So that's like more advanced applications of this, but that is the... I guess this is why from beginner to advanced, you want to learn why options are the Legos.

[00:28:37] And this is fantastic because you just showed me how put call parity in stock land ends up being a way to reverse engineer a risk-free rate in something like the box product, which is a fantastic link between all this. That's right. Chris Ademasiya, thank you so much for teaching me this lesson. This is fascinating. We're going to have you back. What do you think? Any ideas? What can we talk about next? Oh, I got a million ideas. This is easy. Fantastic. Shooting fifth graders and fish in barrels. We'll be back. Thanks, Chris. You got it.

[00:29:06] Thanks so much for tuning into this episode. If you found this discussion interesting and valuable, please subscribe on YouTube or your favorite podcast platform or leave a review or a comment. We appreciate it. No information on this podcast should be construed as investment advice. Securities discussed in the podcast may be holdings of the participants or their clients.