Tom Sosnoff and Tony Battista are joined by Jacob Perlman for the Skinny on Options Math! Today, the guys are discussing Convenience Yield. Convenience Yield represents the value of having access to an asset during the duration of the contract. When an asset is widely available, this access doesn't mean very much and the convenience yield will be quite low. However, if the underlying is for some reason temporarily scarce, the convenience yield will be much higher. In this case, a seller in a futures contract would be better off liquidating their asset now and then repurchasing it at expiration to complete the contract. Tune in to the segment to find out all the ins and outs of Convenience Yield and how you can use it when placing trades!

Tony Battista: Thomas we're back my friend. The skinny On option math. We've got Jacob in the house, Jacob, what's up my man?
Jacob P: Not that much, winding down at the end of the year.
Tony Battista: Looking for a little market correction.
Tom Sosnoff: Are you done?
Jacob P: I have to give my final tomorrow and then spend the weekend grading it, and then I'm done.
Tom Sosnoff: Give your final tomorrow and spend the weekend grading it. Do they still curve these things? Hundred Percent.
Jacob P: Curve is an interesting word. That all of my students ask, what's the curve going to be? What's the curve going to be?
Tom Sosnoff: What do they use now? I don't know.
Jacob P: And, I don't curve things.
Tom Sosnoff: Okay.
Tony Battista: Good for you Jacob. There shouldn't be any curve on any of this. You should teach the curriculum the way they should understand it and then there should be no need for curve.
Tom Sosnoff: I like a curve.
Tony Battista: You should make the test fair enough that you can get that distribution curve that you live by.
Jacob P: The thing that they don't get is that like a seventy percent isn't necessarily a like C. A seventy percent might be an A if the exam is hard.
Tony Battista: Fine, Fine.
Jacob P: That's not cause it's curved, it's because getting a seventy percent on this exam showed me that you know the material very well, cause there were a bunch of hard questions.
Tom Sosnoff: Don't you hate it when professors would say that? I always hated when they would say you know-
Tony Battista: You should get a ninety, ninety-five or a hundred if you're going to get an A. You're making the test too hard.
Tom Sosnoff: A seventy percent is like an A, but it's still seventy percent.
Tony Battista: Right.
Tom Sosnoff: Is it possible to get a hundred percent.
Jacob P: I've never had a student get a hundred percent. I mean, in theory … If I gave it to one of my fellow grad students, they'd get hundred percent on it.
Tom Sosnoff: Yeah.
Jacob P: Probably.
Tom Sosnoff: Do you use the same tests or do you change them every time?
Jacob P: No you can't keep using the same one. They'll have found your old ones.
Tom Sosnoff: Yeah, okay cool. What are we covering today?
Jacob P: I wanted to talk about convenience yield.
Tom Sosnoff: Convenience yield. Is that something you can buy in a convenience store?
Jacob P: No.
Tom Sosnoff: Okay.
Jacob P: It's like a weird concept, but I was going through some of the backlogs in the market measures and there's one where you're comparing the cost of carry. You're talking about the cost of carry and you're comparing a synthetic option, a synthetic stock to just buying a stock. And after you do the risk-free rate adjustment and the dividend adjustment it comes out really close. In the example you did it was like down to a penny.
Tom Sosnoff: Okay.
Jacob P: That penny would still be like a perfect arbitrage.
Tom Sosnoff: Perfect, yes.
Jacob P: Right and so that can't be. There shouldn't be any perfect arbitrages in the market.
Tom Sosnoff: Okay.
Jacob P: And the missing ingredient there is what's called convenience yield.
Tom Sosnoff: Wouldn't the missing ingredient be something to the effect of bid-ask differential? Or …
Jacob P: Convenience yield is like this sort of general concept that sort of wraps up all the reasons. It wraps up all the advantages to just why is the stock a better thing to have than the synthetic.
Tom Sosnoff: Have you heard the term convenience yield?
Tony Battista: Never.
Tom Sosnoff: Okay, cause I just wasn't familiar with the term.
Jacob P: I was bothered by this arbitrage and I did a little digging, and this is the explanation I found.
Tom Sosnoff: Oh, I got it. Okay, so you're bothered by the arbitrage.
Jacob P: Yeah.
Tom Sosnoff: So we've done a lot of what's considered to be program trading, or what some would argue this is risk free arbitrage, but in reality it's not risk free arbitrage.
Jacob P: Right.
Tom Sosnoff: It's risk free arbitrage to the first person, but not number 2 through 2000.
Jacob P: Right. The first person in the game does get to win. That's what that means. But the point is that arbitrage then disappears and becomes risk, right? You can still do statistical arbitrage or volatility arbitrage. So these aren't actually arbitrage, these are just good bets.
Tom Sosnoff: That's basis trading we call it.
Jacob P: Right.
Tom Sosnoff: The difference is a basis trade is a bet on the spread as opposed to a pure arbitrage which years ago a lot of you had heard, people would have said buy New York, sell Chicago.
Jacob P: Right
Tom Sosnoff: That's a pure arbitrage.
Jacob P: Right.
Tom Sosnoff: Buy something here, buy something on Amazon, and sell it on Ebay for more.
Jacob P: Just free money, actual pure arbitrage is free money and shouldn't be there.
Tom Sosnoff: The reason that doesn't exist on the lists and exchanges anymore is, remember, years and years ago nobody had access to multiple exchanges, electronically, now everybody does. The other reason it doesn't exist is because there's so much money, that if there was something that was off they would figure it out in two seconds.
Jacob P: Right. It's essentially one of those times where the free market economic theory actually does sort of work out in its perfectness.
Tom Sosnoff: Of course, of course.
Jacob P: Where, yeah, anytime there is a little room for arbitrage it gets gobbled up almost immediately by … someone finds it, makes that money and then they run out however much of it they can.
Tom Sosnoff: Of course, so in Las Vegas every time they create a new table game, people are creating new table games all the time because it's trying to get people in the casino, get excited about it, whatever it is. Every time they create a new table game the casino basically has their own quants and their experts, their math experts, and their X traders, and everybody else. They sit down and they try to basically beat the game. When they can't then they release the game.
Well what happens, and I was talking to somebody that does risk management for casinos once because we played golf with him. He said about 50% of the games we release, the new games we release, there's a flaw.
Jacob P: They get broken?
Tom Sosnoff: They get broken. And we couldn't find the flaw in our research, but there's so much money out there seeking risk-free returns that usually within 48 to 72 hours
Tony Battista: That's how quick it is?
Tom Sosnoff: That's how quick it is.
Jacob P: Wow.
Tom Sosnoff: That somebody figures it out, beats us, and then we close the game down, change the rules, and then re-release it.
Jacob P: That's great.
Tony Battista: That's amazing. It's amazing it's that efficient.
Tom Sosnoff: Forty-eight to seventy-two hours. He goes, sometimes, it happens in 15 minutes we can figure it out. We once had a game, I forget what game it was, it was some version of one of those three card.
Tony Battista: Monte type things?
Tom Sosnoff: No, not Three-card Monte, but it was like-
Jacob P: Three card poker, hold'em, yeah.
Tom Sosnoff: I forget what they call it, Caribbean poker.
Jacob P: Yeah.
Tom Sosnoff: Some three card version of Caribbean poker. It was some version of it, and he goes, we shut it down in an hour. We shut it down in an hour.
Tony Battista: Cause the numbers just didn't look right anymore, right?
Tom Sosnoff: Because when you issue a new game in Vegas and within an hour there's five or six locals there with stacks of cash.
Jacob P: That are growing.
Tom Sosnoff: With stacks of cash. They come with ten, fifteen thousand dollars. No one goes to a new game with ten- with a five dollar minimum. So that's when we realized, oh boy, we're dead. They figured this out before we did.
Jacob P: They'll be okay. I think they can take the loss.
Tom Sosnoff: He was just talking about how efficient the markets are.
Jacob P: Right.
Tom Sosnoff: So people that think there's this inefficiency and they can play the inefficiency. It's just it does not exist. So, you ready? So we're going to talk about convenience yield and the missing penny.
Jacob P: Right.
Tom Sosnoff: This sounds like Harold and the Purple Crayon.
Tony Battista: That's correct.
Tom Sosnoff: What is convenience yield? So I think you kind of alluded to it.
Jacob P: So I gave like a rough intuition for what it is, but it does have sort of a formal definition as well. But the formal definition is sort of a lot like an implied volatility. It's the number it would need to be in order to make the value of a futures contract correct.
Tom Sosnoff: Okay, beautiful. So, the arbitrage-free value for a futures contract to exchange an asset with current price S at at time…
Jacob P: Tau, Greek T, if you say T it will be fine.
Tony Battista: I'm not going to make fun of you.
Tom Sosnoff: I do this every single time. In the future ought to be. And explain this for me cause …
Jacob P: So, this is just the usual risk-free rate. This is just the risk-neutral measure [inaudible 00:00:00] It's just money tomorrow is worth less than money today. How much less, either the risk-free rate times how long it is. That's how compounded interest works.
Tom Sosnoff: So people get all freaked out sometimes over understanding what this risk free rate is. If you're going to put money essentially somewhere and collect zero or just over zero on it right now, you're not going to take any risk. Somebody's going to make maybe one basis point on you for holding your money. And we consider that, what we say the risk free rate.
Jacob P: Well, I mean there in that case you're actually losing money because you're probably not getting the full risk free rate. The risk free rate is like whatever the T-bill rate is.
Tom Sosnoff: Right, but at some point there's some minuscule, even if you go direct, Treasury Direct and buy at the auction yourself.
Jacob P: Buy the thirty years.
Tom Sosnoff: There may be some little whatever it is. But when you take risk in the stock market, you're entitled to a long term rate that would be higher than the risk-free rate.
Tony Battista: Otherwise you wouldn't take it.
Tom Sosnoff: Why would anybody?
Jacob P: Why do people go to Vegas? They love gambling.
Tom Sosnoff: It's different in Vegas because there's an embedded loss.
Tony Battista: Free drinks.
Tom Sosnoff: But there's free drinks. The risk-free rate, we call it a positive drift. Okay and it's what you get paid for taking risk.
Jacob P: Right, the risk-free rate is the drift of the market. But it's also it in theory is sort of set by monetary policy. It's just how much money will there be. There will be more money tomorrow then there is now. That's just how Keynesian economics works. And how much more, E to the R, one day.
Tom Sosnoff: Okay, so however in reality the difference between owning something today and tomorrow, which is what you just said, beyond the changing value of the dollar. And the observed …
Jacob P: Futures price.
Tom Sosnoff: Futures price, okay, may be different from this.
Jacob P: Right. In principal that would be the futures price if there was no arbitrage and everything behaved perfectly.
Tom Sosnoff: So this is how you, so you've created a formula, or there's a formula that's been created. Which is the convenience yield.
Jacob P: There's a typo on the bottom line.
Tom Sosnoff: Okay so explain this.
Tony Battista: I was going to mention that.
Jacob P: So the real thing is the bottom line which is if there weren't anything else going on the future price would just be S, E to the R Tau, but it's not. That's just not the case all the time. The futures price is on you observe, what is it being trading at? That's it's price. There needs to be some adjustment on the right-hand side. Where they put the adjustment is next to the R. That's where the convenience yield gets it's definition. It's the thing that adjusts the risk free rate so that comes out as the right futures price. It'll vary asset to asset, expiration to expiration, cause it depends on all these things. In any case the top line there is just exactly what it needs to be so the thing on the bottom solves, is a true equation. Except it should be R minus C, not R minus E on the bottom line. We'll fix that later.
Tom Sosnoff: So, one thing you have to recognize here is that although it should be perfect, intraday it moves just off of perfect all the time. So perfect is … you almost never see perfect. So it gets a little bit cheap and it gets a little bit expensive, verse perfect which is when the arbiters step in and the corresponding other side either gets bought up or sold down to bring everything back into line almost instantaneously.
Jacob P: Right, and the other thing is that the arbiters are there sort of trading on convenience yield. That's what they're doing. The fact that it's a little off from perfect, has to do with this convenience yield.
Tom Sosnoff: So, why is there a convenience yield and why doesn't this qualify as an arbitrage opportunity?
Jacob P: So why is there a convenience yield, why don't these prices all line up perfectly? There's two other quantities that I ignored there, which would be, if you had a dividend paying instrument. In the case of actual physical assets futures, sometimes there's storage costs, where in both of those cases they affect how useful it is to own this thing now versus how useful it is to own it in a month right?
Tom Sosnoff: Well there's always interest cost.
Jacob P: Maybe you miss a dividend, maybe you miss, well the interest cost are in the R, those are the R. Maybe you miss a dividend payment, so that effects it, or maybe you own a hundred pounds of steel and you're going to need to sell it to someone in a month because of the futures contract you have to keep those hundred pounds of steel somewhere, and that cost you something.
Tony Battista: Storage cost.
Tom Sosnoff: One other thing, with respect to dividends, is especially for stock industry issues. You don't always know what the dividend yields. In other words, when most people do index arbitrage they guess.
Tony Battista: They come up with an arbitrary number.
Tom Sosnoff: The future dividend is going to be based on what the dividend yield increase has been and they amortize it over every single day, it's actually quite a complicated process and if there's no dividend, you know a lot of times people will buy something for fair value and bet on a dividend increase. If you don't get the dividend increase the whole-
Tony Battista: Or rate declining, right?
Tom Sosnoff: Yeah the whole trade is a lost.
Jacob P: Yeah.
Tom Sosnoff: Yeah it's ugly.
Jacob P: Yes it is.
Tom Sosnoff: It's not free money, I promise you. Oops, hold on. It's not free money. The convenience yield represents having access to the asset during the duration of the contract. When the asset is widely available, this access doesn't mean very much and the convenience yield will be quite low. In particular the futures will be greater than-
Jacob P: The current price.
Tom Sosnoff: Than the current price, unless the dividends interfere.
Jacob P: The only reason that you would want a good, that you would want to have the asset, if the convenience yield is low, because whatever asset it is generally freely available, then really the only reason you would want to own the thing now, rather than in a month from now, would be a dividend payment.
Tom Sosnoff: But why would an asset, why would the asset ever be cheap? Why would the convenience yield ever be high? I'm sorry.
Jacob P: The convenience yield if you have a particular time like short term scarcity right? So this happens with like seasonal goods will have a convenience yield. If briefly you know that the oil supply is low but will return, or the corn supply is low but will return, but here's more value to this thing now than there will be in a month and if that difference out strips the risk-free rate then the whole thing flips and the futures become cheaper than the spot price.
Tom Sosnoff: So you almost always see the convenience yield higher if we're in backwardation then.
Jacob P: Yeah the convenience yield is a measure of backwardation, that's it.
Tom Sosnoff: Okay, alright that makes sense because I was going to say you would never see it in Contango.
Jacob P: Right.
Tom Sosnoff: Okay.
Jacob P: Perfect.
Tom Sosnoff: Okay, so it's a measure of backwardation, I got it. Basically it's the risk free premium in backwardation? I'm sorry, it's not risk free, it's the risk premium in backwardation.
Jacob P: The risk premium rate, but yeah.
Tom Sosnoff: Risk premium rate, okay. Yeah I don't-
Jacob P: It has a time factor.
Tom Sosnoff: Okay. All right the risk premium rate. Okay then, actually I understand that now, that's scary. If the underlying is for some reason temporarily scarce, the convenience yield, cause we actually did this yesterday, when we did our segment on … We did the seasonality on natural gas. We talked about the predictability of the natural gas contract in the winters months as opposed to when it makes the most high, and it turns out the spread makes the most high in the winter, when it's in backwardation, and basically you can see all of this unfolding and that's a particular, that's a product that has, that would fit this-
Jacob P: That would have a high convenience yield during the winter.
Tom Sosnoff: We didn't use the term convenience yield so we've confused everybody.
Jacob P: A lot of things in this business are many words for the same thing.
Tom Sosnoff: The convenience yield may actually exceed the risk free rate, so that the futures is less than-
Jacob P: The current price.
Tom Sosnoff: The spot.
Jacob P: The spot, yeah. Usually that's opposite right, cause usually the futures are more expensive in this spot because they have a risk free rate adjustment.
Tom Sosnoff: Got it. So in this case a seller in a futures contract will be better off liquidating their assets now than repurchasing at expiration, to complete the contract. Yeah I actually get this, I've just never heard it discussed this way. As an application of this concept to a slightly different setting, a previous market measure found that while the cost of synthetic stock may both match the actual spot price, once cost of carry, which the synthetic won't have, and dividends, which the synthetic won't pay, are accounted for, it becomes extremely close. I think that we all recognize is, that's why we're indifferent to product. That's why we're indifferent to [SMP 00:00:00] five hundred, versus SMP options for spiders because when it's all said and done it all is going to …
Jacob P: It should all come out almost exactly the same.
Tom Sosnoff: Yeah.
Jacob P: Y=The only difference that's left, sort of by definition, is the convenience yield. What ever difference that's left in there is the convenience yield, it's sort of the abstract of the artificial, why would you want one of these more than the other if they have the same payouts at the end? The answer is because maybe one of them gives you more options during the interim.
Tom Sosnoff: Yeah the perfect example of this yesterday would have been like the [vics 00:17:00] because it had this, it doesn't have seasonality but it has that backwardated … It has that non-escape clause, so that you can essentially, so that you're stuck betting on a future date.
Jacob P: Right, you can't trade now.
Tom Sosnoff: You can't trade now. You can't get out. We saw that yesterday, so there was a huge, as we can now say, a convenience yield in vics yesterday. Pretty interesting, that would have been the perfect example to show for it and then lastly. However you can still expect synthetic stock to be very slightly cheaper after accounting due to convenience yield. If you want to continue to hold your position past expiration for stock you would just do that, but for the synthetic you would need to roll the position which would incur small additional costs.
Jacob P: Right that's essentially where a convenience yield and like a synthetic stock come from, it's from right when the synthetic reaches expiration. If you wanted to keep holding that position you need to put it on again, and you're going to have a little bit ask differential in there and a little bit of …
Tom Sosnoff: Yeah. Let me give you an example, we talked about this Toni, actually I talked about this in email this morning somebody had said they have some short in the money crude oil puts. I talked about, hey listen you're almost better off from a convenience side, we didn't call it convenience yield, from a convenience side letting the puts get assigned because the calls aren't worth anything. Let the puts turn into futures and then roll the futures because the roll mark of the futures is way cheaper and essentially, as convenience thing you're rolling a very simple product which is a one penny wide markup.
Tony Battista: Sure, you keep yourself exposed to market action though.
Tom Sosnoff: Yeah, right. From this discussion what's the takeaway for an individual investor?
Jacob P: I think the takeaway is that if you wanted to talk about backwardation and you want to have these things, it gives you like a very specific number for it, right? You can go back to slide two or whatever, where it had the formula. Which give you a … You want to know how backwardated this is, how far it is off of what it should be, you could just look at, you need to know the futures price, you need to know the stock, you need to know the [time tell 00:19:12] expiration, you need to know the risk free rate. Those are the only things you need to know, in order to get like this very specific quantifier, quantity for how much it's off.
Tom Sosnoff: How do you get the risk free rate?
Jacob P: Generally you the T bill rate.
Tom Sosnoff: Okay, so you're using the T bill rate of whatever it is, but I'm not sure, I'm think it's nice for somebody to know in case they need to articulate where some of the risk are and why there is opportunity in backwardation. I also think this is a temporary phenomena.
Jacob P: So yeah the convenience yield is like a very, it is what it is right now, right now and it will be something else in a month.
Tom Sosnoff: Right, right. It's not something that hangs around?
Jacob P: No.
Tom Sosnoff: Okay.
Tony Battista: Good job out of you two. I got my work done while you guys were talking, so that was pretty cool. Bootstrapping is next! Nice job Jacob, it was interesting listening to you live.
Tom Sosnoff: It was interesting, it really is.