So why don't we get started? Hi, good morning, good afternoon, good evening. Welcome to this Felix Live refresher session on equity index futures. And what I should mention is that, of course a lot of the concepts that we're gonna discuss here today apply to a range of products, right? We will start actually with a refresher on thoughts just to understand the general mechanicals that apply on almost one-to-one basis to futures as well, not just stocks but also other asset classes as an underlying. And then of course, not just single stocks, or equity indices either, but also, on the single stock futures front.

But, futures on equity indices are definitely, more liquid and closely monitored by a very broad range of market participants.

Hence the decision to focus on these products than towards the second half of this session.

But allow me to quickly introduce myself. My name is Thomas Krause. I'm head of financial products, here at Financial Edge.

I started my career in fixed income, mostly trading rates and FX in cash and derivatives, but then also had the opportunity to work in a cross asset mandate, which then gave me some good amount of insights into equity and credit markets as well.

Quick look on the agenda.

As I said, it's a refresher on forwards and equity index futures, and this in general means that it's gonna be relatively fast paced because we really wanna make sure that we have the time to refresh your knowledge on a couple of important items.

What this includes, for example, is that we'll start with a general recap on forward prices, and then we look at the drivers of equity forward and futures prices in a little bit more detail.

We then have a look at the actual equity index futures mechanics, we're gonna see an example, contract details, et cetera, et cetera.

And we will have a look at the application, of these products as well, at least give you, one or two examples for that.

Before we start though, a couple of general reminders.

First of all, you can access the course materials that should have been shared, or a link should have been shared, via the chat.

But you can also find the materials in the resource section here on Zoom.

Or you can also find them on the Felix Live website. That's number one. Number two, you can ask questions during the session, which means when there's something you would like to have more information on, just let me know.

The important thing to remember is you have to use the Q&A function for that as I won't monitor the chat.

And then last but not least, after the session, you will be directed to a feedback form. And I would personally appreciate it very much if you could use one or two minutes of your time to just answer.

I think it's three questions. So that shouldn't really be, uh, too time consuming.

And also, what you can do via these forms, of course, to let us know which kind of topics you would like to see covered in this format in the future.

And if you have and want to ask any follow-up questions, this would be the perfect way to do that, as well.

But without further ado, let's dive right into the topic of today. And as I mentioned, we're gonna start as the Very basics right on the front and front of you. What you can see is a general definition of a forward that is nothing else in the agreement to buy or sell the underlying add a price agreed upon today, but for settlement at a specified date that is in the future.

And that means after this spot date.

Now the settlement date is often referred to as a forward date and agreed upon price, as the forward price.

And let's have a look at a concrete example here, and we're looking at an FX forward here, right? But the mechanics, as I said, would apply in almost the exact same way for all other types of under like, and in this example here we have a trader that agreed to buy a hundred million dollars against euros at an agreed upon price of 10 no, sorry, 1.1029.

And the agreed upon settlement or forward period is three months.

Now, as you can see on the timeline, when you actually look at it, this three months period actually doesn't start to count from the transaction date that would be today, but actually on the spot date, right? And from there, then it's a three months forward start.

So that's one general rule.

The forward period starts to count in most cases, at least at the spot date.

So that is three months forward means three months after spot, not after the transaction date.

So what do we do at the transaction date? We agree the trade details, right? That includes size.

That includes when, uh, you know, the settlement actually takes place, either forward date that includes also the price of course.

And at the forward date then, or we can call it settlement date if you wish.

We settled the agreed upon transaction.

In this case, the trader will receive a hundred million dollars and in exchange will pay 90.67 million euros. That's just a result of the exchange rate that had been agreed upon, right? And if the dollar strengthened, then over this three months forward period, for example, following the move that we've seen over the last couple of weeks, this trade would've been potentially at least very profitable.

Now, what I should mention here as well is that there in general are two types of settlement that can be agreed, right? There's physical settlement and cash settlement quickly to distinguish these two from each other.

In case of physical settlement, the settlement involves the actual delivery of the underlying.

That means the buyer is obligated to pay the agreed upon price and the seller must deliver the asset, whichever the underlying is in case of cash settlement. On the other hand, the contract is settled by paying or receiving the difference between the contract price that originally has been agreed upon and the market price of the underlying at the time of settlement.

That means that no physical delivery of any asset occurs. It's really just a cash transfer that reflects the economic value of this contract.

And that's why this method is commonly used when underlyings are, should we say, difficult or maybe even impractical to deliver physically. Like it's the example, the, like, it's for example, the case for indices like the ones we're talking about here today but also commodities to some degree.

Alright? So, now as we've seen the, um, mechanics of forward contracts are relatively straightforward.

And I think I said it already, it's quite obvious that the forward price is an important component in a forward transaction, right? That's the price we agreed upon at the transaction date.

The question is, of course, where does this forward price actually come from? And I want you to think about the question on the slide here for a minute, right? Assume that you work as a market maker and you have been asked to quote at 12 months forward price on an asset.

Now, based on the information that you have been given, what would be the fair forward price? And made me think of the fair forward price more as a mid price, mid-market price that you would quote.

So which mid price would you use to base your bid and ask prices on? Now, the information that has been given to you is a following.

First, the spot price of the asset is a hundred dollars.

Second, the analyst community has a 12 months price target out of 107.

We expect the asset to go to all the way up to 109 over the next 12 months period.

The client is even more aggressive. They believe that the asset is gonna go all the way up to 115, and we have been given the 12 months interest rates and we also have been given the information that the asset pays no dividend.

So how can we approach this? Well, in general, right? Affords can be seen just as delayed spot transaction with delayed settlement.

So to price a forward fairly, what we have to do is, is to determine the economic impact of this delay in settlement for both parties, and then we should really adjust the spot price by this net impact.

Then the question of course becomes, okay, so what are those impacts right? Now, let's look at the forward seller first, right? They receive the money 12 months later then in comparison to a spot transaction if they sell on a 12 months forward basis, right? That means because 12 months interest are, or interest rates are at 5%, they face an opportunity cost of 5% per annum. Because if they would've gone for a spot settlement, they would've received the a hundred dollars in two days from now, which they then could have invested for a hole here at 5% ignoring account conventions, that would've been about $5 in return terms, right? And, uh, that then basically means that the forward price here from the perspective of the forward seller should really be $5 higher to compensate them for this sort of disadvantage by delaying the settlement by 12 months.

And in case you're wondering why we're not including dividends here. Well, it said at the bottom of the slide that this asset does not pay dividends.

So, let's take the side of the buyer. What would be the impact here? Well, the buyer through the delay in settlement doesn't have to pay the purchase price at spot, but 12 months later, which means they experience a benefit of 5% per annum because they can use this money, for example, in the 12 month investment at 5%, and that means they should pay a higher forward price again, because there's no dividend paying asset. We're looking at, there is no inclusion of dividends here.

So in both sort of, you know, it doesn't matter which perspective you take, in both cases, it's clear that the forward price really should be $5 higher.

Now, an alternative way to explain the fair level of the forward price is also to look at the hedging cost of the market maker.

So remember, a market maker is not there to take directional views and turn this into profits, but it's sort of more about providing liquidity.

And that means that if a client asks us to sell them something on a forward basis here, we might want to think about how we can hedge this position, in the most efficient way.

Now to eliminate the market risk of a short forward position, IE the client buys something from a forward basis from us.

One potential hatch approach, just one of many could be to buy the asset right now, right? Because right now is the only point in time where we exactly know where the spot price is.

But this then means if we're buying the asset right now in the spot market, that we must pay for the settlement at spot, which then means we are settling or we have to pay a hundred dollars in two business days from now and we get our money in 12 months and two business days from now from the client through the transaction, which then basically in essence means we have to borrow the a hundred dollars for the interim period of 12 months and we need the money on the spot date as uh, we have set, right? So that means we as a market maker would have to borrow the money, we pay 5% interest, and that means that the borrowing that we need to repay in 12 months from now is, well, the total payment that we have to make in 12 months from now is not a hundred, but it's 105 because we have to pay the money back plus we have to pay the 5% interest.

And so if we have to pay $105 to whoever we borrowed the money from, then that's of course the amount of money that the client per minimum has to pay to us on the full transaction so that we're breaking even now in reality, of course we're gonna put bid offers around it, but you're, we're thinking about the fair forward price here in this case, okay? So far we have excluded, dividends in the equity space though what you know frequently has happening that the stock that you might have as an underlying year in a forward transaction does actually pay dividends. So let's quickly think through how the forward price should change if the asset actually would pay dividends.

And let's just assume here that we're, now including a total dividend of the six, sorry, 12 months forward period of $6.

And let's assume this is the future value of all dividends received over the 12 months period at the end of this 12 month period.

This gets us nicely around time, value of money issues, et cetera, et cetera.

So how does that impact the economic impact of delaying the settlement? Right? Well, the seller on a forward basis still has the opportunity cost of 5%, right? Because they still get their money later by 12 months. They still cannot invest it and not generate this 5% income.

On the other hand though, by not selling the stock in the spot market, but actually selling it forward on a 12 month basis, that also means that they will physically own the stock over the next 12 months.

And that means that they will receive the dividend payments that are gonna be made over the next six months sorry, 12 months period.

And that, as we said, is in dollar terms $6.

So by pushing the settlement out by 12 months, the net impact from a forward buyer's perspective would be, a $1 a $1 disadvantage simply because yes, they don't have to pay the 5% funding, but they also don't receive the $6 dividend. And that basically means if there was a dividend payment of $6, apologies, I'm going back then the forward price actually wouldn't be 105, but it would be instead $99.

So what we can see here is that the forward price interestingly enough, has nothing to do with any of these expectations that I outlined here, right? So the forward price simply is the result of the spot price plus the borrow costs minus the dividend yield.

And that is something we can then basically turn into a general observation. Everything we have just intuitively covered here can be condensed into a relatively simple numerical approach.

And when you sort of look out forward pricing, you know, then very often you get a formula that's very similar to the one that you can see here on the slide saying, fair forward price is a spot price adjusted by the cost of carry and the cost of carry, is pretty much what we mentioned on the previous slide, right? Because the cost of carry can really be taken literally it's a cost of taking a spot position and then carrying this spot position all the way through to the forward date.

So that hopefully is intuitive.

One question you might ask yourself though is why forward prices should be fair, right? Why do we, or would we expect that without dividend? The forward price would be somewhere around 105.

What stops them from deviating from their fair value? And now this all comes down to one of the most important principles in financial markets.

That's the no arbitrage principle, or if you want to call it differently also can use a law of one price, right? And this principle generally says that identical financial instruments or assets must have the same price across all markets in a frictionless market, which means that's a market without transaction costs, without taxes, without restrictions to trade.

So long and short positions are possible, et cetera. Because if this wasn't the case, then arbitrage opportunities, IE the opportunity to generate a risk-free profit by simultaneously buying and selling the asset at different prices would be given, right? And that's, I think, quite intuitive when you're looking at a concrete example.

So let's assume that the same stock trades at two venues at different prices on the one venue, it trades at a price of 100, and on the other venue it trades at 102.

Now under there's all circumstances, what we all would do of course, is we would buy the stock at venue one, for a hundred dollars and then simultaneously sell it at 102 at venue two, right? And that would allow us to realize the risk-free profit of $2 if we ignore our transaction cost.

Now, what this would do, of course, is it increases the price on menu one and it decreases the price on venue two.

And this will continue to happen until this arbitrage opportunity is gone.

So that's for this very simple example of two different prices in two different venues.

But how does it apply in case of a forward is the question? Well, let's go back to the previous example here where we calculated the fair forward price to be at 105, right? So we're ignoring dividends here now again, and let's assume that we calculated the fair forward price at a level of 105 and we called a market maker and the quote was 102, what would you do under those circumstances? Now, what we can very easily conclude is that in comparison to where we believe the fair price is, the forward is too cheap, right? And whenever something is too cheap, then the good idea is to start with buying whatever you feel is cheap.

However, just buying this forward, even at a low price at too low price is not arbitrage yet because we would still have exposure on the future development of the price of the underlying, right? So if you go longer forward, even if it's cheap forward and the underlying tanks, now that still is gonna lose your money.

So we need to sort of close that hatch or the, that arbitrage we need to get rid of the directional risk that we're having.

So as we're long the forward, what we have to do is sell the asset short in the spot market, for example.

So what we're gonna do is we're gonna sell the asset at the current spot price of a hundred dollars, and then we get a hundred dollars at the spot, and we take these a hundred dollars and invest them at an interest rate that was given to us at 5%.

This means in 12 months we would receive $105 from our investment, but we only have to pay $102 for the stocks that we will then use to deliver, uh, it back to where we borrow the stocks from and close our short position.

And this means that we would basically have a risk-free profit of $3, which you know, of course actually needs to be present valued because it's gonna be realized in 12 months time. But you get the idea right.

Now, in addition, what I should mention, of course here as well, we, we really simplified this example because we're not considering stock lending fees, et cetera, et cetera.

But you know, we wanted to keep things simple here.

Now that's the general idea.

So this is why forward prices should be around their, um, fair levels.

And the good news is that these principles that we discussed, right, the formula, the no arbitrage principle, et cetera, et cetera, apply to forwards on all underlines, right? The only thing really, and you can see this here, the at the box at the bottom, uh, that differs dependent on what the actual underlying is, are those cost of carry components now funding costs you see on forwards on all assets. Because the first thing that at least in our conceptual hedging, program we have to do is borrow the money and buy the underlying spot.

Now, as I said before, right, that's not necessarily what is actually happening, but that's sort of like the theoretical construct we're using to develop this pricing form this year, borrow the money and buy the asset spot, then you're holding that asset over the forward period.

And if the asset pays any kind of dividends or coupons in case of a bond where if you get another currency and you can invest it for a different interest rate as well, then of course these are components that are, considered to decrease, the forward price.

So basically are counteracting the funding cost, assuming interest rates are of course positive.

So, we are here though to talk about the equity side.

So let's have a closer look at this product.

And, here's a concrete formula that can be used to calculate the fair forward price. And as we intuitively derived earlier, right, the fair forward is equal to the spot price.

Here you go.

This is a spot price plus a spot price times the interest times stays over basis, which is basically the financing costs.

And then we subtract the dividends as discussed intuitively as well.

We can rearrange this a little bit and then we get to the formula that you can see at the bottom here. Spot price times one plus interest times stays over basis minus dividends.

Be aware that this formula, strictly speaking only applies for forwards with a forward period of up to 12 months.

But you know, that's a general approach.

Now, what you often find in literature is that the formula is given slightly different, like one plus interest minus dividend yield.

And while there's nothing wrong with this approach, I personally find it better to use the actual expected dividend payments as these amounts will remain relatively constant because a dividend yield is a function of the dividends that we expect to receive, but also of the spot price, right? Because when the spot price changes, but the expected amount of dividend stays the same, the yield will have to change and therefore dividend yields change more frequently.

But then on the other hand, I think the main challenge here is not to calculate a dividend yield out of a given set of dividends, but to forecast these actual dividend payments over the forward period correctly.

And as a general rule, just to pointing that out all dividends for which the x diff date falls between the transaction date and the forward date should be included because that all the dividends that will strictly speaking fall onto the forward seller, right? However, the problem with dividends, even when, you know, companies try to generally maintain them on relatively stable uh, levels, they are at the end of the day paid out at discretion of the company board and they are really only announced in detail a few weeks in advance of the actual payment.

And so what happens is that even companies with historically steady dividends can increase, decrease, or even suspend dividend payments when it seems to be necessary.

And therefore it can be actually quite challenging to forecast actual dividend payments accurately. And that's of course, especially the case for longer term, contracts.

Okay? That's, I think a reasonable generic introduction.

Now, let's go back to the formula and just kind of derive a couple of, very basic rules here, right? So as we can see here that if interest rates are higher than dividend yields, then the forward trades add a premium to spot because the funding advantage that's achieved by delaying the settlement is gonna be higher from the forwards buyer perspective, than the actual dividend that they will forego.

If interest rates on the other hand are lower than the dividend yield than the forward trades at a discount to spot, and if interest rates and dividend yields happen to be identical, then spot and forward price are gonna be the same.

So a nice reminder of what we said already, and that is the forward price does not reflect expectations of rising or falling prices in the future, but instead it's just based on the difference between funding costs and, asset yield, right? So formula really simple and intuitive but it's important to remember that in many cases the actual forward price is driven by supply and demand dynamics.

So pricing in a narrow sense is very often not required.

But knowing this formula, having seen it, is still very useful simply because many market participants will calculate the fair value of futures and compare to the actual price to see if forwards or future prices are actually underpriced or overpriced. And should they find a substantial difference between the two, then they're gonna act accordingly, like we've discussed in the concept of arbitrage.

What is important though, as well to remember is that we said earlier when introducing the new arbitrage principle, it's based on the assumption of a frictionless market, which in practice of course isn't given, right? There are transaction costs, we have maybe different interest rates that apply for borrowing and investing.

We have different funding costs for different investors, et cetera.

And what this all leads to is that inevitably different market participants will see the fair price of a forward or future than at different levels.

But of course the difference won't be necessarily enormous, but it's important to just keep that in mind for further, for our further discussions, right? So now we know the components included in the equities forward or futures price and now we want to have a quick look at sensitivities of future and forward prices because it's not only the settlement date and potentially the price that changes when you move from spot market to forward instruments.

It's also the risk factors that you are exposing yourself to.

And I hope this is intuitive, right? Because we discussed at great lengths now why the forward price is basically the spot price adjusted by the cost of carry and the cost of carry.

We identified inequities as interest rates and dividends at these was these were the two components driving the cost of carry, right? And so as a rule, as a general consequence of that, the forward price were the futures price should change when either the spot changes, the interest rate changes or the expected dividends change.

And what we're showing on this slide here is how the forward price changes when these different drivers change, right? And the first thing that we do here, and this is done on the left hand side, is basically calculate what goes through this original example.

This time we're including the dividend of $6, right? So that means spot is at a hundred, there's a 12 month interest rate of 5%, and there's a 12 month future value of dividends expected to be paid, and that is $6.

So basically to calculate the fair forward price, it's a hundred, that's a spot plus the funding costs of 5% on a hundred, that's $5 minus the dividends, that's six.

And the fair forward price in this kind of, environment is then $99.

Now, in the second box from the left, the, we assume that the spot price increases from a hundred to 101, and in this case, the fair value of the future actually increases to a hundred 0.05.

The reason for that is that the interest rate of 5% now applies not to the amount of 100 anymore, but on the amount of 101, because that's the amount of dollars that has to be borrowed.

Now in order to be able to buy that asset here in the spot market, and that means that interest rates are now 5% on 101, which means $5 and 5 cents, the dividend amount has not changed at all.

So it's basically still $6.

And then what we have is effectively we have 101 as a spot price plus five minus six, and that leaves us sorry, plus 5 0 5 minus six. And that leaves ascend with the a hundred 0.05, right? So rule, to take away then from this observation, an increase in spot price leads to an increase in forward prices, all else being equal.

Next thing that we're gonna do, and we're now using, moving into the slight red-ish box, we're assuming that interest rates change, right? And we're also assuming that the spot remains unchanged.

That may be a bit of an unrealistic scenario because if short-term rates increase by a full percentage point, it's sort of, you know, maybe unrealistic to assume that spot prices haven't changed one bit, but it's just, to show the isolated impact, right? So after the increase in interest rates, the third forward price would also be higher simply because the borrowing rate now is no longer 5%, but it's assumed to be 6%.

So we're applying this to the spot of a hundred, and this then will increase our funding cost to $6, which then equalizes the $6 dividend that we expect to receive.

And the fair forward price has changed to a hundred.

So increase in interest rates leads to an increase in forward prices, right? Last thing or last factor that we have identified as a risk parameter is the dividend.

You know, what we we're gonna see what happens when they increase? So let's say the stock is now expected to pay a total dividend of $7 over the period.

In this case, interest amount will remain at $5 a spot price is the same.

The buy off the forward, however, will forego a total dividend of seven.

Consequently, the spot price falls to 98.

So here this thing changes a little bit, and that means that an increase in dividends actually leads to a decrease in forward price.

And then the last thing that we're doing on this slide here is we're looking at the passage of time, right? And here you have to make a couple of assumptions because, what you can do is just like, okay, we have a 12 month forward, let's look at this three months later, and this means it's now become a nine months forward contract, right? But then we have to make an assumption about where nine months interest rates are and also what's the expected dividend payment over the next nine months period.

And we wanted to keep this really deliberately simple here. So what I'm doing here is I assume there's a perfectly flat yield curve that means 12 months and nine months, interest rates are the same level, we're assuming interest rates have not changed at all. So it's basically still a yield or an interest rate of 5%.

And we also assume that dividends are paid in equal amounts regularly once a quarter, so around $1 50 per quarter. And we're ignoring the time value of money here for simplicity right now. What this means then basically is that three months later, one of the dividend payments actually has fallen out of the equation.

It has already been paid, and the total value of dividends is now down to, uh, $4 50 in that case, right? If we're applying 5% interest and four and a half dollars dividends, the fair value of the forward is gonna be 99.

Um, and, um, and a quarter.

And the reason for that is that yes, interest rates are still 5%, but this 5% now only applies for three quarters of a year, IE in nine months period.

So that means the interest amount is gonna be $3 75 cents.

We then also expect to get dividends of only in four and a half dollars.

So basically a hundred plus 3, 7, 5 minus four, uh, more four and a half.

That gives us the 99 25 year.

Why I've chosen to put this on here is just simply to show that, um, as time goes by, forward futures prices have the tendency to converge, uh, to spot. That doesn't necessarily have to happen because there's other factors.

It depends really when our dividend paid and how they are distributed across a period, uh, what happens to interest rates, et cetera. But under this scenario that we have sort of assumed here IE stable or, you know, equally distributed dividend payments and stable interest rates, the forward price actually converges to spot as time goes by.

Okay, enough about forwards because we're here to, uh, talk futures.

And this slide just is a quick reminder on the main difference between forwards and futures, right? So forwards are OTC contracts, which means terms of these contracts like price, quantity of the asset, uh, absolutely privately negotiated between the parties that are involved in the deal, right? No exchange involved that sets, uh, fixed contract terms, anything like that.

The advantage of that clearly is high level of flexibility.

Contracts can be really tailored to the individual needs, but then of course there's something to consider and that is these products are not centrally traded, which means prices are not that transparent as there's no central market price and you need a valuation model, similar to the simple one that we've put together.

That's, you know, because this is needed to figure out where the fair price roughly should be, right? So then let's turn to futures. And they are very similar to forwards in the sense that they are contracts to buy or sell an asset at a predetermined price, at a specified time, et cetera.

The difference is that futures are traded on an exchange, and that means the terms of future contracts, something like size, settlement procedures, its expiry dates, et cetera.

That's standardized by the futures exchange.

And this standardization then contributes to greater liquidity because there's just a small number of contracts that investors can choose from available.

And so trading activity really concentrated over a smaller number of contracts that increases liquidity and that makes it easier to buy and sell these contracts reasonably quickly.

It pon, you know, positively influences speed of spread, et cetera, et cetera.

Something that's less obvious, but that is still worth mentioning I think is that futures or exchanges where futures are traded offer valuable data on, for example, trading volumes and open interest.

And that can be quite useful information, where you can find some details about market sentiment, liquidity, et cetera, et cetera.

And while this information is reasonably important, very often I found it's not necessarily that well understood, I don't necessarily mean the trading volume was that, because that's very straightforward.

It measures the trading activity of a specific futures contract for a particular trading day, let's say, right? It starts at zero in the morning when trading begins, and then we count basically how many contracts are changing hands over the trading day.

And we stop counting then basically when trading finishes at the end of the day, and then we reset this number back to zero to be prepared for the next day, right? So what's the purpose of trading volume? Well, it tells you how many contracts are changing hands on a day, and you can look at this number, over a longer period of time that gives you a good idea about the average of how many contracts are trading and that you can use as an indicator for liquidity in this contract.

And that helps you to understand if a certain transaction that you're planning is gonna go through the market relatively seamlessly or if it's gonna have a larger impact.

So example, you're planning to trade 5,000 contracts in a particular futures and the daily trading volume is 5 million.

I think it's fair to say that 5,000 contracts volume shouldn't really have a very, very significant market impact if you are not sort of placing the order at the worst possible point in time. However, if the whole daily average trading volume is let's say 20,000, then basically you're trying to trade a quarter of daily volume, you should be really kind of consider how it's best to place the order to avoid significant market impact. That's just a very, very simple way to look at liquidity right now. What's open interest then on the other hand, well, you see here the definition, right? And what open interest really provides is information on how many open futures positions are outstanding.

So it's basically a sum of all positions that people have built.

IE they went long, they went short but that have not been closed or settled yet.

So it's basically, and that's what it says on the slide here, an indicator for the risk that participants are holding via these contracts.

That's maybe a little bit abstract.

So I think using an example to clarify how these numbers behave, will serve as well.

So we assume here that a new futures contract is launched today.

And because it is a brand new contract volume and open interest per definition are zero because it was just impossible to trade this contract before as it didn't exist, right? And now let's say that the first trade ever in this contract is made by trade IA who buys a hundred contracts opening a new long position.

So establishing a loan of a hundred contracts and counterparty in this transaction is trader B, well, basically the exchange, but because Trader B had an opposite order, and that is to sell a hundred futures contracts opening a new short position of 100.

So net result a hundred futures contract has changed.

Hands volume is a hundred and also a is long, 100 contracts, B is short, 100 contracts, and the total amount of open positions is a hundred, right? A hundred long, hundred or short, that's it.

So open interest is at a hundred as well.

Now, let's assume that the second trade of the day is B, buying back 50 contracts, i.e. closing half of their short position.

Now the counterparty in this transaction is effectively trader C who sells 50 contracts to establish a new short position.

In this case, 50 contracts have changed hands.

So the volume increases from 50 sorry, from a hundred to 150 just to reflect that additional transaction.

But as you can see here, the open interest actually remains unchanged as a is still long, 100 contracts while B has reduced reduced their shorts to 50.

The gap was filled by trader C, right? So now we have a hundred long position held by trader A and the opposite is held by trader B and trader C who are both short 50, and therefore we still have an open interest of altogether 100.

And now let's go and have a look at the search trade of the day where Trader C buys back their shorts closing their position.

And counterparty in this transaction is actually now trader A who decided to cause half their long position, right? Again, 50 contracts have changed hands and consequently the volume has increased by another 50 and it's now standing at 200 for the day.

But the open interest now has actually fallen because both counterparties that were involved in the third trade are using the trade to close their positions.

And so after this trade has occurred, a only long 50 B is still short 50, so the open interest is 50.

So hopefully that gives you a better understanding of those numbers.

And with that, let's finally have a look at equity index future contracts. And of course there are many of different index contracts out there, but I think it's safe to say that the one that we're showing here, the E-Mini S&P 500 contract tends to be the most liquid, of them all, at least, on a normal day, right? So let's look at it in a little bit more detail.

And as I mentioned earlier, future contracts are standardized, which means the exchange sets the contract specifications, right? And on the left hand side, what you see here is the contract specifications that the CME has set for those E-Mini S&P 500 future contracts.

Now, the underlying is obviously the S&P 500, but the question is what exactly do I buy when I go long one of these contracts? Well, basically you are going long the S&P 500 index on a forward basis, but the question then is, well, how long am I, i.e.

how much money am I practically synthetically investing through this derivative right? Now? The answer to this question is given by the contract size, which is here on this slide given as $50 per index point, right? So $50 times the number of index points that gives you the effective contract size of one of these future contracts, which means the actual size of the position does not only depend on the number of futures you are buying, but it also depends on the level of this index level at which you're buying the futures, right? And that's very consistent with how stocks work, right? Because the amount of money invested in example, and for example, Microsoft does not only depend on the number of shares you buy, but also on the level at which you buy them, right? Then the next point here on the specification side is that's listed is the tick size, right? And the tick can be understood as the smallest possible price change of the futures contract.

We see here it's defined to be a quarter of index points.

So that means if the current price of the index was 5,000 points, this price can move up to 50, 35000.25, or it can move down to 4999.75.

And of course it can move in multiples of 0.25, but a price of, for example, I don't know, 5,000 point 13, that would technically be impossible.

So the smallest move in price and coming back to that point is a quarter of an index point.

And as each index point is worth $50, the value of a tick must then be a quarter of that, which means $12 and 50 cents, right? Contract size and tick size and tick value, however, are not the only things that are standardized.

The expiry date, which basically is the future term for forward date is also standardized.

And in general, the E-Mini S&P 500 future contracts all expire on the third Friday of the contract months.

And, as contract months or contract months in general, follow this quarterly cycle of March, June, September and December.

So at the moment, given that we're early February, the nearest contract months, which is also referred to as a front month contract is March, and the actual expiry day would be the third Friday in March, 2024, which I believe is the 15th of March this year.

But that's not the only contract that is theoretically available, as you can see here on the slide, because I'm not mistaken at the moment, they are, always 21 consecutive quarterly contracts listed.

So we have the March future 24, the June, future 24, September 24, December 24, and a whole bunch of contracts at 25, 26, et cetera.

Question is, however, if they are all equally liquid and we're gonna, have a look at that towards the end of the session.

So what about the settlement? Because earlier I said there can be physical settlement that can be cash settlement. The CME says for these contracts, cash settlement is what's gonna happen.

Okay? So now we wanna put this actually into real life context.

So we're gonna go over to the right hand side where we look at a concrete example.

And what we're looking at here is actually, the December, 2023 futures contract.

And the data was taken on the 23rd of November, 2023.

And when we collected the data, futures price for this contract was 4565.75 index points.

If we apply this formula then to the actual, to the actual last price, then what we get is a contract size of 228,000 and a bit, right? And, um, that's just the size.

Now, as a contract expires on the 15th of December, 2023 at the time i.e. in November 23, buying one contract would have practically meant agreeing to buy the S&P 500 index with forward settlement on the 15th of December, 2023 for total volume of 228,000 and a bit, right? And just to give you a little bit of a flavor, how much risk was being held in these contracts on that day, I've given you the open interest, as well.

And that was just a bit below 2.2 million contracts.

And so if you then multiply this 2.2 million with the contract value, you end up with a number that adds to around, I believe $500 billion.

That's clearly an oppressive amount of money, okay? So one thing that I should have mentioned earlier when discussing forwards and futures was that, you know, for futures, given that there's a central market price, it's actually fairly simple to calculate the p and l, for future trade.

So to see this how this works in practice, let's have a look at the question here at the bottom right corner.

So here it is that we should assume that we bought a hundred of these December 23 contracts at the last price, which you remember is 4565.75.

And then we were able to sell these contracts at 10 index points higher right now.

Question then was ignoring the transaction cost.

What is our profit? Now, the information we've been given is simply that we have made 10 index points for a hundred contracts, and each index point gives us a value of $50 per contract.

And that means we have a, in total a $50,000 profit ignoring transaction costs, et cetera.

So it doesn't really get much simpler than that, right? But of course, index futures are not only used to build speculative long or short positions, a great deal of equity index, future tradings actually as a result of hedging transactions for other equity products. So like, for example, selling index futures to hedge an equity portfolio.

And we wanna have a look at a simple example here.

We have an investor who's currently long S&P 500 company companies and let's say that the combined value of the portfolio at the moment is a hundred million dollars.

And this investor is looking to temporarily hedge this market exposure, for example, because they are expecting a short lived correction, stock prices, whatever, right now the front men's front month's contract trades at 4565.75, and this means that the contract size is 200 a 28,000 and a bit as we discussed on the previously.

Now, the total long position to be hedged, as we said, is a hundred million dollars, right? And we also know that selling one futures contract generates a short position of 228,000 and a bit.

So a very simple method to calculate the hedge ratio, i.e. the amount of futures that we need to sell to have our portfolio hatched perfectly, at least, using make some assumptions, is to divide the current portfolio value.

So the amount that we want to hedge a hundred million in this case by the contract size, which is the size of hatch per contract. So we're doing this here, a hundred million divided by 228,000 contract size as we said.

And that means the investor should sell 438.04 contracts. And of course, for practical reasons, it seems likely that 438 contracts will be traded.

So now let's assume that this has been done and the investor actually sold 438 contracts at this last price or at the price that we've been given here.

And now let's also assume that over the next few sessions, the equity index as well as future prices and also the cash portfolio all fall 10% in value.

So what does it mean now from a P&L perspective? And let's split this up.

So first we're looking at the cash portfolio, and that's relatively simple to calculate, right? Because we had a hundred million that loses 10%.

So the performance of that will be 10 million dollar loss, right? That's a cash portfolio.

Now, let's think about the futures hedge, right? Because we sold those 438 futures.

Now what we've been given is that futures have fallen 10%.

So 10% of 4,565 is about 456.5, index points, which we gained because we sold futures, future prices have fallen, we can buy them back cheaper.

That's 456.5 index points.

We have sold 438 contracts and each contract, or sorry, each index point is worth $50.

And if you do that, and I've done that before, obviously, then sorry, it's 9,997,350.

So from a total P&L perspective, that is now a loss of a little bit more than two and a half thousand dollars.

Why is it not perfect? Well, remember we have rounded down the number of contracts that we're selling, so we slightly unhatched here a little bit, but I guess in comparison to losing $10 million on an unhatched position, a loss of two and a half thousand dollars or a bit more than that, that definitely feels to be okay.

So that methodology that hedge really is very simple to calculate and also quite intuitive.

The only thing I guess that's, worth pointing out here then as a consideration is it does have a somewhat of a limitation because this hedge will only work as good as we've just seen when the correlation between the cash equity position.

So the a hundred million portfolio and the equity futures contract is perfectly negative, so basically minus one.

But what if the portfolio consists of stocks that have the tendency to yes, move in the same direction than the broader market, but they move a little bit more aggressive.

So that might be the case for a portfolio that's tilted towards growth, right? So in such a case, it should also be expected that if the index futures fall 10%, that the portfolio will actually fall a little bit more. Because what we tend to see on this growth stocks is yes, they go up faster than the index on the way up, but they also fall, might potentially fall faster than the index on the way down.

And so in order to consider this individual risk of a portfolio in comparison to the index futures we might wanna adjust our hedge, uh, slightly, and we can use what's called a beta adjusted hedge.

Now, beta in general is a measure of the equities, or of stock where equities portfolio sensitivity to market movements, right? It's measured by comparing the returns of the cash portfolio with the underlying index.

And then it indicates somewhat the relative volatility of the portfolio compared to the actual index.

Now, a beta of greater than one then indicates that, you know, this portfolio has a higher sensitivity in the market.

So it moves the same way, but it moves at a larger speed.

And the beta of less than one indicates a lower sensitivity, right? So if we're using a concrete example of beta of two, for example here, that means the portfolio moves in the same direction than the market, but it moves at twice a speed.

And that is, as I said, not just happening when the market goes up, but also the portfolio's expected to fall twice as fast when the market moves down.

And now let's have a look at a concrete example here to see how this beta adjusted hedge would work in our portfolio context.

And this time we're going back to the example we've looked at previously, right? So we again have our investor with a hundred million dollars invested in this, portfolio of S&P 500 companies.

The index level is unchanged, but we have now the information that the portfolio beta has 1.2, and this indicates that portfolio moves the same direction as I said, but it tends to move 1.2 times faster.

So that translates into the fact that we would expect if the index rises 1%, the portfolio is expected to increase in value by 1.2% and then of course we'll fall for by 1.2% in case of a 1% downward move of the index.

Now what does that mean for our future hedge? Well, the investors looking to hedge against an expected correction, right? And that means they might want to adjust a simple hedge ratio for their portfolio beta.

So instead of selling 438 contracts, they should now sell 525 contracts. How did we get there? Was basically multiplying the number of features that we've initially suggested using our simple, hedge ratio here.

Buy 1.2. Why buy 1.2? What is the rationale behind? Well, basically what this effectively means is that the investor is now selling futures, which the total position size of around $120 million. So that's 228,000, times 526.

So the idea is the following, right? As the investor portfolio moves 1.2 times faster than the index, the investor needs to over hedge from a contract size perspective.

So a portfolio of a hundred million dollars was a beta of 1.2 is hedged by selling $120 million worth in equity in next futures.

And if the index then declines by say 1%, and the cash portfolio declines 1.2% as predicted by beta, the investor loses 1.2% on the cash portfolio, but gains 1% on the futures hedge.

But the futures hedge is 1.2 times the size of the cash portfolio, and then the net effect would basically add up to net zero.

I think this doesn't sound too complicated.

In fact, the master we're showing here also really is not right.

Where the real challenge in this approach lies, however, is to determine the right beta.

Right now beta is basically calculated using, uh, regression analysis on historical returns of the single stock or stock portfolio that we're looking at here, and the benchmark index, right? And it may vary depending on the period over which is calculated.

So you can say that beta to some degree is data history dependent, right? So if it's calculated over one period, like let's say three months, it may actually significantly differ from the beta that's calculated over a longer period of let's say, uh, 12 months, right? And even if that wouldn't be the case, even if those three and 12 months beta would be exactly the same, um, then we wouldn't have that challenge here. But we still have to consider the fact that past beta and the realized beta over the hedging period are not guaranteed to be the same because past beta is a historical measure, right? And while it can provide insights into how this stock portfolio has reacted to market movements in the past, there's really no guarantee that it will accurately predict the future sensitivity.

Because that might change, because if market conditions change, economic factors, market narrative, et cetera, et cetera, we might even alter the portfolio so that all might have an impact.

Now, what this means is that I think even if the beta adjusted approach generally makes a lot of sense.

Invest as much must approaches with a degree of caution and feels like good practice that one should regularly update these beta calculations to reflect current data, to reflect changed market conditions.

And also probably is worth calculating a range of betas over different time periods or different length, et cetera, et cetera, to understand how the beta of this portfolio has you know, behaved in the past.

Is it very comparatively stable? Is it, is it unstable? Et cetera, et cetera.

So, is the hatch then going to be as good as in our previous example? Well, that obviously depends on the realized data of the portfolio, and that comes back to the point raised earlier.

We're using historical gator.

So there's no guarantee that it will actually, um, be the perfect hatch that we have envisioned.

Okay. Now, let's quickly wrap this up with a, you know, very brief look at advantages, disadvantages, a lot of these things we have already said, right? We said clear advantages of equity index futures are that they are very liquid.

So that means that we can enter and exit positions with minimal market impact. They're also very narrow bit of the spreads, and that's of course good from the perspective of transaction costs.

We have also said that market transparency is a significant advantage.

You see where the prices are. If you have level two access, you see even the debts of the market, et cetera.

And then one thing that we haven't talked about at all, but that, I'm sure most of you will be familiar with already at some level is that because these contracts are centrally clear, they basically is no or hardly any counterparty risk involved, which clearly is a good thing.

And then last but not least, these products, um, provide significant leverage. It's only a fraction of the contract size will have to be deposited as emission margin, maintenance margin, whatever.

And I think somewhere, you know, right now it's probably in the ballpark of $12,000.

Don't quote me on that, but if you think about it, assuming 5,000 index level roughly that gives us $250,000 contract size, $12,000 is a reasonable high leverage.

But of course, we need to also be aware of the potential considerations right now, the main thing I think we have already discussed, you know, not I think, but we have just discussed that, is that we need to be aware of the difference between the constituents of the index.

That's basically the underlying here for that future contract and the constituents of our portfolio. And what this needs, and as I said beta might help, but the question of course is how stable, uh, beta will be.

And then going back all the way to the beginning of the session where we talked about cost of carry and what drives it, we have learned that future prices will not just be driven by the level of the equity index itself, but they also have an element of interest rate and dividend risk in them.

And especially for a future contracts on indices, the dividend is extremely difficult to forecast because not only do we have to think about how are, what, which dividend amounts are the companies in the index gonna pay, but you also know that indi index constituents are changing over time.

So if you're thinking about longer date equity futures, not only do you have to forecast dividends, but you also might have to think how is the composition of index actually changing? Are there new companies coming in, other companies being kicked out? And then how is that gonna impact the, uh, the dividend, dynamics? And then there's two other elements to consider, which are, sort of here at the bottom of the slide and there's a future basis and the role risk.

Now, we don't have time to discuss all of that in great amount of detail, but I at least wanted to introduce you to the idea of the future role, right? And this is basically what this slide is for.

And, to understand the future role or the concept of future role, I think it's useful to have a look at the liquidity situation.

Right now, as mentioned earlier, there are more than one E-Mini future contracts that are in theory available for trading at the same point in time question that I sort of raised back then is are they all equally liquid? Now, let's have a look at open interest and trading volume of two contracts here as an example over time, right? I'm and what you can see here are open interest on the left hand side and daily trading volume on the right hand side of two contracts.

The September 23 and December 23 contract, both E-Mini, 500 contracts. And we're obs starting our observations in May, 2023 when literally both the September and December contract were not the front month's contract, because in May the front month's contract was the June contract.

So let's see what has happened or what was going on back then.

Now, as you can see, open interest and daily trading volume for both these contractor were observing here.

Basically were pretty close, if not equal to zero in May, 2023 and this state like that for a reasonable amount of time.

But as we approached June, 2003, there was something changing.

And that is that the open interest in the September contract started to increase rapidly.

And at the same time, the trading volume of this contract started to increase rapidly.

Now the, then we saw a almost leveling out, um, of the open interest and the open interest was relatively steady for a couple of months.

And then the open interest really starts of the September contract starts to fall rapidly as we're approaching, sorry, September contract as we're approaching the months of September.

And at the same time when September open interest drops, we see that the open interest in the December contract starts to rise rapidly.

And again, we see here the same, were being reflected in daily trading volumes.

So just by looking at the data, the key takeaways, the following, in case of equity index futures, the liquidity is highest in the front months contract until this approach is it's expiry, right? And a few days prior to the actual expiry of the contract, what we see is that the risk held by future contracts is transitioned from the front months to the then next contract.

And by the contract that the by the time the contract actually expires, almost all of the open interest has shifted, which means that actually very few contracts are settled, most positions are closed out before expiring.

But of course, if you think about our investor example that sold futures to hatch their position, if now they buy back their short position in the front month contract shortly before expiry because they don't want to go into settlement then you know what this means is they no longer hedge, right? If they want to remain their hedge in place, they would have to do something in addition to that. And that of course would be to open a new short position in the next contract.

And this is then what most market participants do, and that's what's called the future's role.

And this means nothing else than rolling your position from one contract to the next contract prior to the current contracts expired. So that's the general idea of a future's role. Ladies and gentlemen, that's all I wanted to share with you here today.

I thank you so much for your participation.

Hope you found this beneficial.

Any questions, please let us know.

But I hope you found this useful and I will see you in one of these sessions, again very, very soon.

Have a great rest of your day and a great weekend.

Thank you and goodbye.