Hi, good morning, good afternoon, good evening, and very warm. Welcome to this Felix Live refresher session on FX Forwards and Saps.

My name is Thomas Krause. I'm head of financial products here at Financial Edge, and I have the honor to deliver the session to you today.

And maybe just a few words about my person.

I started my career in fixed income, mostly trading interest rates and fx and both cash and derivatives. And then towards the end of my practitioner career, I had the opportunity to work in a cross asset mandate, which then gave me some good amounts of insights into credit and the equity markets as well.

But let's have a look at the agenda today.

As I said, this is gonna be a refresher on FX forwards and swaps, and this in general means it's gonna be relatively fast paced because we wanna refresh your knowledge on a broad variety of products and concepts. And what we're gonna do here today specifically is that we're gonna discuss FX forwards. We're gonna look at the interest rate parity principle risk exposures in outright forward positions, and then we're also gonna look at FX swaps, terminology conventions.

And we will very briefly touch upon the FX basis as well before we start, a couple of terms, excuse me, general reminders.

You can of course access the course materials.

You can see the link in the chat of the session.

They can can also access the materials via the resource button here in your zoom window.

And you can of course also access the materials via the Felix Live website.

Second point to mention is that you can ask questions during the sessions. The only thing you need to be aware of, you have to use the q and a function because I won't monitor the chat at all.

And then after the session you will be directed to a feedback form. And of course your feedback is very important to you. So please take this extra few seconds to answer those couple of questions.

And of course, the feedback form is also a great way to ask any kind of follow-up questions or to let us know which other topic areas you would like to see covered in this format as well. But I think that's it in terms of general reminders.

And with that, let's dive right into today's content.

And the first thing we're gonna do is we're gonna start looking at the general rules around FX quotations.

And we're gonna start doing this with the spot market.

Now in currency trading, right, we always quote in pairs, right? One currency is bought and then of course the other one is sold. And while they sound very straightforward, it is a source of a lot of potential confusion when it comes to a price quote.

Because when you look at stock prices, for example, you just know that when someone says Microsoft is trading at 420, that this means you have to pay $420 for one Microsoft share.

Not that $1 buys you 420 shares of that company, right? When you move over to fx, then it's sometimes not quite that obvious because when someone says your dollar trades around 109 and you have not really looked at this currency pair ever before and you don't really have a lot of experience in FX, then you won't be that sure anymore because what this could mean is that one Euro buys you $1.09 but it could also mean that $1 buys you Euro 1.09.

So which one is it going to be? Well, there is a general convention and that is that in a currency quote or that the currency quote is always given as the number of units in what we call the quoted currency per one unit of the call base currency.

Now think of it as follows, the base currency is the currency you're trading.

The quoted currency really determines the price of the base currency.

And with that in mind, the only thing we have to know is which one is actually the base currency and which one is the quoted currency.

And the general rule here is that the currency that's quoted first in the pair is the base currency.

The second mention is then what we call the quoted currency.

So let's have a look at this numerical example here on the slide, and we're gonna start on the left hand side looking at Euro dollar, which is quoted at 1.0950 to 1.0953.

So we know that as per convention, I mentioned before euro is the base currency in this pair used dollar is the quoted currency.

So the price you can see here is basically the price of one Euro expressed in US dollars, right? And with that knowledge, we can now derive how to interpret the bit of a spread that's you can see here, right? Because if I'm looking to buy euros, I would have to pay the ask price, which is $1.0953 per Euro.

If I was looking to sell euro, I would only in a ver commas receive the current bid, and that at the time was 1.0950.

So really not different to any other bid ask bid of a spread that you have come across.

What we've also visualized on the screen, and we're using different colors to do that here, is that the, excuse me, the FX quote consists of actually two components.

In most cases, FX quotes are given with five digits.

And the general rule is that the first three digits are referred to as the big figure.

The last two digits are referred to as the pips.

Now, for the euro dollar pair that we've talked about before, one pip basically then represents one 10000th of the quoted currency.

It's a fourth decimal point.

However, the value of a PIP can generally differ from one currency pair to another.

And to illustrate this, let's take a quick look at dollar yen, which you can see on the right hand side on this slide here.

It's quoted at 149 or 149.04 to 1 49.05.

And as we define the pips as the last two digits in the quote, one pip in this currency pair is actually 100th of Japanese yen.

So be mindful of that.

But now back to Euro dollars and a, our specific FX language, let's assume that we sold euros at 1.0950 at the time when this quote was taken.

And today's euro dollar quote, let's say, is around 1.0890.

Now what does it mean has happened to this currency pair since trade inception? Now the price of Euro expressed in US dollars has declined, which then basically means that the Euro has lost some value against US dollars.

Now, we did enter a short euro position because as I said, we have sold euros.

This move should then result in a positive P&L off that trade because for selling one Euro, we got $1.0950 initially.

And at the moment, we would only need $1.0890 to buy back the same Euro.

So there should be a small profit there as we were sure euro and Euro went weakened against the US dollar.

So another rule that's worth remembering if the FX quote goes up, this means that the value of the base currency has increased versus a quoted currency and vice versa.

Now, what you cannot necessarily deduct from that move alone is whether this move was now a Euro weakening or a dollar strengthening move. For that, you would have to look at other currency pairs for more context, but at least relatively speaking, we know, what has happened.

But let's move away from spot and um, start looking at FX forwards. And the good news is that FX forwards basically work like forwards and any other underlying right, they are the agreement to buy or sell the underlying at a price agreed upon today.

But the settlement will happen at a specific date in the future.

That is after the spot date now, and the settlement date is often referred to as a forward date.

The agreed upon price is often referred to as the forward price.

Now let's have a look at this concrete example here.

On the slide, we're looking at a six months euro dollar forward at the transaction date, we agree that trade details like size, settlement, date, price, and then at the forward date we settled the agreed upon transaction.

And it's important to note that the forward period generally starts to run from the spot date.

So if we were to trade the six months forward today, and this is Friday the 15th of March, the settlement of this trade would actually not occur on the 15th of September, but on the 19th of September, why? Well, simply because today is Friday, that means spot date is Tuesday the 19th and six months on top Of that brings us to the 19th of September, assuming that this is a good, uh, business day.

Now, generally speaking, FX forwards are extremely liquid up to one or two years anyway, uh, especially this is the case for the so-called straight dates.

So like one months, 2, 3, 6, 9, 12.

And at the bottom here of the slide in the small print, you can actually see the April, 2022 average daily turnover in outright FX forwards. And that exceeded 1 trillion viewers dollars, at least according to the triennial central Bank survey that's published by the bank for international settlement.

And that is clearly a huge number.

Now intuitively this makes absolute sense because one of the standard textbook examples for, you know, application examples for FX forwards is this sort of, you know, transactional FX or to hedge transactional FX risk, right? So let's say we have a European exporter that has agreed with a company in the US to export machines or equipment or anything like that for a total contract value of a hundred million US dollars, right? The payment was agreed to be made in three months time.

And this agreement then of course, generates for an exchange risk for the Euro exporter because if USD was to weaken significantly over the next three months period, the amount received in euros will then be significantly reduced by that move.

Right? Now, one possible solution of course to this problem, um, for the European a exporter is to simply enter into a three months euro dollar forward.

And that means they agree the price on which they will sell the a hundred million dollars that they were receive in three months already today.

And that of course, is a very convenient and simple solution basically for everybody involved in this, in this transaction.

Okay, so let's now have a look at how these prices for FX forwards are quoted. Because in general what we can say is the market doesn't really quote the actual forward prices, but instead what we call the forward points and forward points are basically the amount by which the FX spot quote must be adjusted in order to get to the actual forward price.

Now, this might not feel super logical at the moment, but we will discuss the logic behind this in a minute.

So for now, let's just concentrate on how to interpret those numbers that we can see right in front of us, because what we are seeing here is something like a typical FX forward screen.

It shows three different currency pairs here we have euro dollar, we have cable, and we have dollar yen.

And then we see the quoted spot prices, and we recognize this one because we've seen it on the previous slide, right? Then we also see underneath, when we go through the rows here, there are forward points for different forward periods. So if we just pick up this here, what you can see is the six months forward points for euro dollar on the bid and on the task.

Now, let's pick this as an example and go through what these numbers actually mean.

So spot euro dollar quoted at 1.0950 to 1.0953 6 months forward points quoted at 89.10 to 89.6.

So hopefully just looking at these numbers makes it absolutely clear that this is not the forward price, because let's all hope that such a rapid decline in US dollar value against Europe is never ever going to happen, right? So what we see here, and I said it before, are the forward points i.e. the amount by which we have to adjust the spot code to get to the actual forward price.

Now, before we can do this, or in order to be able to do this properly though, we need to know two things, right? First thing that we need to know is how do we actually scale these points, these numbers here, because it seems rather obvious that this is not as simple as adding them to spot or subtracting them from spot.

So we have to scale these numbers somehow.

And this then actually brings us back to what we said on slide one.

And there we said that the last two digits of a currency quote were generally referred to as the pips or points.

Now, just didn't speak about points back then because in the context of spot transactions, I haven't heard points being used all that much.

It's usually pips, but you know, you could say points of course in the context of how, uh, FX forward. However it makes sense to bring up points because the numbers on this slide shown here on the screen shown here are actually called the forward points, right? And these forward points coded show us basically the pips or points for that matter by which the spot quote has to be adjusted to get to the actual forward price.

Now, in case of euro dollar, remember we said one pip equals one 10,000th of US dollars.

So in case of Euro dollars, what we have to do to get from forward points to, you know, to scale the forward points properly, we have to divide this number here by 10,000 before then adjusting this spot quote.

And again, care must be taken, right? Because for other currency pairs that might be different.

Again, if we're looking at dollar yen here on the right hand side this is where one pip, you remember, this represents one one hundredth of Yen.

So before adjusting or before adding, we were subtracting, we have to divide as well, but this time only by 100.

Okay? The second question then of course would be after we've made the right scaling, in which direction should the adjustment be made? In other words, do we have to add the forward points? Do we have to sub trick them to get to the actual forward rate? And as you can see on the screen, in most cases, this is pretty self-explanatory, right? Because if the forward points are given in negative numbers, then this means we have to subtract them, right? If they're given us positive numbers, then they have to be added.

And this then basically gives us all we need to know to answer the question that you see here and there, or the example or to, to understand the example that you see in the bottom left corner.

And this is, okay, what's a six months euro dollar outright forward on the bid right now? Spot quotedwas quoted at 1.0956 months, months forward points are quoted at 89.10.

So what would then be the six months forward price? Remember, we have to make the scaling that was divided this by 10,000 and then added to the spot simply because these are positive numbers here.

And the result we get when you do the mass is actually 1.103910, okay? So this is, as I said, really straightforward.

Once you are, um, familiar with the general conventions and rules.

Now every now and then, however you might come across some old legacy system that doesn't really show positive numbers, negative numbers, just, you know, everything is given at positives.

How can we in those cases then see if we have to add or subtract? Now, in such a case, what you'd simply have to remember is that the bid price should always be below the ask, right? And as a result, you can see whether you have to add or subtract those forward points by comparing the size of the forward points on the bid side and the ask side, right? Because if the left hand side is smaller than the right hand side in absolute terms, then you have to add the forward points.

If the left hand side is larger than the right hand side, in absolute terms, you have to subtract the forward points.

So let's have a very, very quick check here on the dollar hand side, because this is the pair with negative numbers here.

If those numbers were not negative, if the negative sign wasn't given, then what we would see here is left hand side would've been 426, the right hand side, 425, that means left hand side larger than right hand side, we would've subtracted here following this rule.

So there is a way around this later, we're gonna see how we can also, uh, basically use the idea or the concept of interest rate differentials to figure that out.

Okay, great. So with that, now let's go and have a look at the actual forward points.

And because this is sort of really leading us to the big question.

Now that we know how forward points are quoted, we of course wanna know where do these forward points actually come from, right? Well, of course, at the end of the day they are driven by supply and demand, right? But of course there is a theoretical basis for it as well.

And that's no different to any other forward contract in the sense that the starting point here will be the no arbitrage principle.

And as a quick reminder, this principle basically says if there are two or more ways to achieve the same risk profile or the same outcome, then the prices of all these different alternatives must be identical, right? And that's why we often refer to this principle as well as a law of one price, because if they were not the same, if the prices would differ, then what we would all do is sell them more expensive way and buy back the cheaper way and we will be left with no risk, but with guaranteed profits, which in efficient markets of course, um, shouldn't really be possible.

Now to take this generic statement and formulate this into a theoretical pricing formula, we then of course need to think about, okay, what are the different alternatives, right? And I think the easiest way to do this is just look at a concrete example.

So let's say we have an investor and this investor is looking to lock in the price for buying 100 million euros versus dollars six months forward, right? So what are the alternatives of doing this? There's of course more than two, but let's focus on on two here.

And the first one is, you know, clearly the most convenient one, and that's call the market maker and ask for six months euro dollar forward price, right? That is quickly done, super convenient et however, in theory, what the investor could also do is to buy the euros right now in the spot market, because right now is the only time we know exactly where the spot market trades, right? That means we have no uncertainty about the execution price.

The challenge if, if the investor would do this however, is that the investor must pay for those euros in dollars at spot, which is two business days from now.

And if we assume that the investor doesn't have those USD then they would have to be borrowed.

And then of course they would have to be repaid at the six months point.

And in addition, the investor will also receive the euros into business days and assuming that the investor has no need for euros over the next six months, because why else would they look to buy them on a forward basis? This money then would need to be invested, for six months.

And that clearly looks like a lot more hassle than the FX forward transaction. But of course, it's a possibility, right? So this is an alternative.

So now we have these two alternatives and ignoring this hassle and the transaction costs, the bid offer spreads, et cetera, et cetera, we can now say that both alternatives, one, trading the FX forward to buy euros, invest them, borrow dollars for six months each, that will, both or that both has to lead to the exact same result because otherwise there would be this arbitrage.

So what we can say, and we're doing this here on the right hand side, is that, you know, the six months euro dollar forward and the relationship between, or thefraction given by future value of the dollar borrowing, i.e. the amounts that needs to be repaid plus interest divided by the future value of our invested euros, i.e. the total to be received from the investment that must be identical.

And therefore we have a simple equation to start with.

So let's put some numbers into this, right? And just see how this works out.

Now what you see here in the gray box at the bottom is a couple or a bunch of market data, right? So we're given a euro dollar spot rate here, which is, you know, known because we've, we've seen that before.

We have a six months dollar interest, 5.395.

We have a six month zero interest of 3.7549.

And we have been given the fact that the six months for it forward period at the time was actually 182 days.

So with that, now we will go and look into our basic equation in the red circle and we're saying, okay, how can I calculate the future value of my US dollar borrow, right? And so I've just used nice round numbers and said, okay, let's assume we're buying 100 million, or we're sell, you know we're buying 100 million here, or we wanna buy 100 million euros, and that means we have to sell $109.5 million because that's the spot rate.

So that's where the 109.5 come from. But of course, any other amount would work in the same, in the same way.

So, now that's the present value. That's the amount of dollars we would have to borrow right now.

How do we get from there to the actual six months future value? Now, if you attended our session on money markets in general, you will remember hopefully that in case of money market interest rates with the exception of overnight rates, of course we use a simple interest approach to calculate future values and, and also to calculate present values.

Because the reason is that, for example, a for six months deposit, the interest will be paid at the end of the investment period which then means that means that there's no interest on interest.

So compounding doesn't really apply here.

And if we use the simple interest method, then the six months future value of the USD is calculated as you know, we see here in this circle is basically just the amount times one plus interest rate times, days over basis.

Days is a forward period here.

And we're using 360 because US dollar money market day count convention actually is actual over 360.

And then we can do the exact same approach for our future value of the Euro investment.

And you know, just using, obviously now the European interest rate, and then if we do the mass, then we actually get to the forward price that we already saw on the previous screen, or that we have worked out on the previous screen, and that was 1.1039 you know, and, and a bit.

So now that is the intuition behind the whole concept or that's the intuition behind the concept.

But if we rewrote this formula that we sort of intuitively developed on the previous slide, and we use placeholders instead of actual numbers, what we get is a formula that is very frequently referred to and also very frequently shown in the context of FX forwards. And that's the one that you see here in the white box at the top, and that's called the interest rate parity formula.

Now, according to this interest rate parity concept, the FX forward rate is really determined by the spot rate.

Here we have it, and then the interest rate differential between the two currencies involved.

Now, indeed, it can be shown that if in our example dollar and euro money market rates were identical, then spot and forward rate would be the same.

So let's assume here just for a second that by a weird coincidence both interest rates, so the one in dollars and also the one in euros were the exact same because both are using actual 360 as they count here, we have also the same number of days and the same basis.

And so what you easily can see is that basically in those circumstances, this fraction would lead to a result of exactly one.

And so what this formula simplifies to is that the FX forward is spot times one i.e. they are exactly the same.

However, if the two interest rates were different as in fact they are on our example, right? Then of course spot and forward rates will differ.

It's hopefully intuitive that the bigger the difference is between those two rates.

The bigger the difference between spot and forward rate would be, so if you dollar rates, for example, were not 5.395 but 6.395 the FX forward rate would even be higher than it is in the 5.395% case.

Okay? So this is a reasonably simple formula but it's very powerful because it allows us to draw a lot of conclusions, right? And we can really think about the relationship between the level of interest rates and the direction of the adjustment that we need to get to the forward price.

And what the general takeaway here is, is that the lower yielding currency appreciates on a forward basis and the higher yielding currency than does the opposite.

I.e. it depreciates on a forward basis.

So in this context of our eurodollar example, we had higher dollar interest rates and the US dollar moved then from 1.0950 to 1.1039 16 months forward.

And as recap on slide one, this means that on a six months forward basis, the US dollar is weaker to the Euro than at spot.

So USD was a higher yielding currency in our example, and it depreciates on a forward basis.

Euro is a lower yielding currency and it appreciates.

So that's exactly what you know, line was what we would've expected just by looking at the formula.

And that's obviously the mass, but what is the intuition behind all this? And that's basically what the green box here is, is all about, uh, which says there should not be a profit on an FX hedged carry trade.

So that probably needs some dissection, right? First we need to answer what is a carry trade? And in FX, a carry trade generally involves borrowing money in a low yielding currency, then exchanging it in the spot market into a higher yielding currency, and invested then at the higher yield.

Now, on first side, this looks like a pretty foolproof way to make money, but of course this strategy only works if there's no significant significant move in the exchange rate, at least in the wrong direction, because at some point, right, the borrowed money has to be repaid.

And in order to be able to do that, we must translate the higher yielding currency back into the lower yielding currency.

And if, for example, the lower yielding currency had strengthened significantly, we might actually lose a lot more on this final exchange then what we accrued because of the interest rate differential and the way leading up to the expired, right? So of course, you know, you can now say, well, there's a, a simple way to eliminate this FX risk, right? And the risk that would be to buy the lower yielding currency already back now on a forward basis.

But that would mean that you eliminate this foreign an exchange risk from the carry trade.

And as per the general rule, no risk, no return, an FX hedge carry trade should just not generate a profit because as we said in the beginning, risk for profits, i.e. arbitrage shouldn't really be possible in efficient markets.

And so for an FX hedged carry trade not to generate profits, the lower yielding currency must appreciate and the higher yielding currency must appreciate on a forward basis and the amount of appreciation or depreciation will then nullify or should nullify the interest rate differential.

Now this already, you know, super important and very, very strong points that we took away from just looking at this formula, but we can derive even a little bit more information from this formula.

And you can see that in this statement there at the bottom of the S slide.

And as we can see in the formula, there's basically three variables that drive the forward price, that's a spot price, and then the two interest rates involved.

And what this means at the end of the day is that when we enter into an FX forward contract, we're actually taking market risk on all these three factors, not just on the spot rate, but also on two interest rates.

And, um, before we look at these risks in a little bit more detail, let's, you know, just have a conceptional understanding of them and the sort of think about the direction of the risk.

So, let's assume we agreed to buy 100 million euros versus dollars.

So we're buying euros, we're selling dollars, and that will happen on a six months forward basis.

I.e. in six months time or six months after spot.

The rate we have agreed upon was 1.10391 right? Now the first question that stated here on this slide is what would have a negative P&L impact for us? A dollar strengthening or a dollar weakening? And for simplicity, we assume there's just no other positions here.

So what is it gonna be? Well, we have agreed to buy 100 million euros and sell dollars on a forward basis.

And while this is a forward trade, which only settles in six months time, we have already agreed the rate at which we're going to make the exchange.

In other words, we know the rate at which we buy the euros, and if dollar subsequently strengthens, this would mean a mark to market loss for us, all else being equal because we could have bought the same amount of euros for a smaller US dollar amount in most circumstances.

And hopefully this is intuitive because as soon as you bought anything in financial markets or, you know, generally probably regardless if that was on a spot or on a forward basis, you just really don't want to see the price of what you have board to go down i.e. you do not want to see euro to weaken or dollar to strengthen in case you have board euros on a four basis.

So that should be relatively intuitive. Understanding the interest rate exposure is maybe a little bit less intuitive, but I still believe there's an intuitive way of looking at it.

And that brings us back to the alternatives we talked about when we kind of built that concept of forward pricing.

Remember, we can think of an FX forward basically as a series of, you know, spot transactions, right? In this case here, what we could have done instead of trading the forward was buying Euro spot, invest them for six months and borrow the required USD.

So what this means is as soon as the forward trade has been agreed, we've basically fixed not just the spot, but we have also fixed the Euro investment rate as well as the dollar borrowing rate, right? And that basically means that we do not want to see Euro rates to go up and we do not want to see dollar rates to go down because we're technically through that effects forward having a long position in Euro rates and a short position in dollar rates because we have invested money in Euros, basically bought bonds in Euros, we sold bonds short in dollars, right? That's a way, uh, of thinking of it from an interest rate directional point of view.

But as we said in previous sessions here having the qualitative understanding of the risk is a great starting point.

It's just not sufficient because we need to quantify the risk in order to see, you know, how big is the risk that we're actually facing expressed in some workable, right? So what we've done here on this arguably quite busy slide is we've built a simple FX forward model or valuation model.

And that's based on the interest rate, power parity formula that, that we looked at a few months ago a few moments ago.

Now in the two columns on the left, you know, first of all at the top here you can see the trade data you can or the trade date, you can see the spot date for date, four days, euro, notional, et cetera, et cetera.

And then after you know, below that you can see all the relevant market data, euro, spot, euro, dollar spot, six months rates in dollars and euros. But everything as we have seen before.

Now, what we're doing then at the I wanna say in the bottom section, so here, that's basically where we are building this valuation model.

So we're basically calculating what is the value of this forward, the market value of this forward at this time.

And the first step what we're doing for this is we're looking at the future value of the dollar cash flow, right? So remember the trade was we buy 100 million euros and that means we're selling a dollars.

And because the exchange rate agreeable was 1.10391, that means we have to pay $110,391,000 at the settlement point. That's six months away.

Now if we're looking at this payment today, which is six months prior to the actual payment, we need to discount it by six months.

So to get the present value, and that's with 182 days forward period.

As we said, we use a six months dollar rate to do that, and that gives us a present value of 107,460,000 bid.

And that's, or because this is a payment we have to make, we put a negative sign in front of this number, right? And now we do the exact same for the Euro cash flow.

We will receive 100 million euros in six months out of the foot.

And then we calculate the pv i.e. we're using the discount rate in Euros, that's 3.7549.

This gives us an a PV of 98 million 137,000 in EBIT.

Now this is a positive number because that's an amount we are going to receive.

So what we want to do next is calculate the net present value, right? We cannot, however simply add those two numbers up here because they are given to us in different currencies. But what we can do, for example, is to translate the Euro payment or the present value of the Euro payment.

So this number into a US dollar amount. And that's nothing else than saying, okay, what is 98 million 137 euros in dollars? And because we're looking at it from a PV perspective, we now use the spot rate for translation i.e. 1,0950.

And that means we get a present value of our Euro payment in dollars of 107,460,000. That's the exact same number just with the opposite sign than what we have been given here in the present value or the present value of our dollar lag.

And so that means that the net present value of this forward apologies actually is zero, right? And that is basically telling us that the forward we have, well, the valuation model that we have calculated here seems to be fair.

Now what I should mention at this point is that we are ignoring something called the FX basis here for simplicity, but we will talk about that, uh, later.

So, now that we have our valuation model in place and it seems to work, what we can do is we can now use it to, you know, quantify the risks that we're exposed to here.

And what we can do is now we can start changing all those three risk factors we identified earlier around spot and the two involve interest rates, right? And that's exactly what we're gonna do.

And the first scenario we're looking at here is that the spot increases by one pip, which basically means dollar weakens ever so slight.

So when we do this, and I'm just gonna get rid of all those things here now to make us focus on, on this column or, yeah.

So what's the impact then of this on our valuation Now before rate has already been agreed upon, so there's no change in the future value of the dollar payment, no future value of the Euro payment, et cetera, et cetera.

And because dollar rates have not changed, there's also no change in present value of the dollar payment either.

So these numbers are completely unchanged.

The same applies for the Euro side, simply because Euro rates have not changed.

So there's no change in Euro present value either, right? The only thing though that happens now is that when we're translating the Euro present value into dollars, we're now using the change spot rate and this dollar has weakened by one pip.

We see that the Euro present value expressed in dollars is now a higher rate than before.

So it's not 107460 but it's a 107469 so about $9,000 higher.

Bottom line, the result that we can see here is if Euro dollar increases by one PIP for our 100 million transaction here at the market to market value of our forward gains by $9,813.

And this is in line what we said from the previous slide.

We said there a dollar strengthening would hurt us, but that also means that a US dollar weakening, is beneficial.

And now we do not only see the direction, but we also see the numerical impact of it.

Now what we can do next is we move to the next column here.

And instead of looking at the change of the spot, in terms of pip, we are now gonna look at what happens when dollar interest rates go up on basis points. So we're basically putting spot to where it was 1.0950 and now we're gonna ch start changing interest rates.

Now, again, the forward rate has already been agreed upon, so the cash flows on at settlement don't change at all, right? We still have 100 million euros and $110,391,000.

But now because we have changed the dollar rate, what this means is that the present value of our dollar payment is changing because we're now discounting with a slightly higher end.

And that means in absolute terms, the present value is now, going up the euro leg remains absolutely unchanged.

There's nothing that is because we're just looking at an isolated impact of US dollar rates.

And so basically what this then leads to is that a one basis point increase in dollar rates, changes the value of our forward here by 5,288 dollars.

So as we intuitively derived on the previous slide, we are short dollar rates and that means that an increase in US dollar interest rates will lead to a positive value chain.

Now, I'm not gonna go through the same thing here in, in Euros, but you can see what happens here. And as you would expect, the main impact is on the, um, present value on of the Euro payment, which now is different because we're assuming Euro rates have gone up one basis point.

And as we said previously, that would lead to a decline in forward value because we are long euro interest rates.

So that's a quick walkthrough through this valuation model and to just, you know, help us understand a little bit better the actual, risk drivers.

But let's now look at some practical applica implications of those exposures that we have.

Just mentioned now earlier, what I said was that FX forwards are frequently used for hedging purposes, right? But of course, not only by m and exporters, but also by investors.

And in fact, investors frequently use FX exports to hedge short-term investments in foreign currencies per.

So, um, the one thing to be aware of when you're using those instruments though, as on the investor side, is that, you know, in case the interest rate differential between the two involved currencies is substantial forward and FX spot rates might differ quite significantly.

And this is then of course, potentially having a significant impact on the return on your investment.

And this slide shows a concrete example on how significant exactly this could look.

So what we're having here is a USD based investor and they bought a German government bond six months left to maturity.

Now the dirty price of the bond, so the price they paid was 99, 695, and, you know, clean price so without accrued interest at the time was 98.94, but that's not really relevant here.

So that gave the bond a yield of 3.64%.

So if I'm putting this here that means the yield of to maturity of 3.64% in euros.

Alright? Now to avoid the FX exposure, the, because remember they're a dollar based investor and they are buying a European government bond. Now the investor hedges the redemption cash flow, right? So that is 101.5 whethers that come from, that's par redemption plus the coupon of 1.5% because that bond pays a 1.5% coupon and they use an FX forward to do so.

And let's assume the same rate we calculated earlier here, 1.1031.

So all cash flows on this trade will actually be known right at inception, the investor buys a bond and pays a dirty price in Euros 99.695.

Now the euros needed to do that are bought in the FX spot. Market spot rate is given at 1.095.

And this means the initial dollar payment is 109.166.

That's just 99.695 times the spot rate. Right now, the bond redemption payment, i.e. this one here is then as mentioned, hatched with an FX forward, which means the investor locks in the FX rate of 1.10391 right now for the bonds maturity date.

And this means 101.5 in euros will be sold at 1.10391, which gives the investor then these 112.0469%

in dollars, right? So effectively what the investor has done is invested $109.17 today and will receive $112.05 at maturity.

Okay? And what we can now do by simply looking at these two numbers, we can calculate the, you know, rate of return in US dollars because we have the present value, we have future value, we know the investment period is 182 days.

And so we can use this simple interest rate formula and calculate what is the implied rate of return.

Now I've done this for you already, and that result is 5.22%.

So remember the investor starts with buying a German government bond that has a yield of 3.64%.

Then they do this hedging thing with FX forwards and the implied annual rate of return is 5.22.

So where does this pick up come from? Well, the investor in this case gives up the higher yielding currency, which is US dollars and invests in the lower yielding currency.

And as we've learned earlier, the lower yielding currency appreciates on a forward basis according to interest rate parity.

And it does here because it starts at 1095 spot and then trade at 1.103914.

And this appreciation that basically leads to a pickup and return.

So it's basically a negative carry trade here if you wish, because the, you know, person has money in the higher yielding currency and then exchanges into the lower yield yielding currency.

And so they get basically this give up effect, uh, back through the FX quote.

Okay? So that also leads us very nicely to another product that we wanna look at here today.

And that is an FX one.

Now, the first thing we should say here is that one really needs to be a little bit careful with not mixing up languages here because there is sort of, you know, sometimes confusion between FX swaps and another type of FX derivative, which is called a cross currency swap. And while those have similar features, they are quite distinct instruments in terms of mechanics. So we make sure you use the right language here.

Now, what we're gonna look at here are FX swaps, not cross swaps.

And of course you know, we need to first of all establish what exactly is an FX swap and the textbook definition of an FX swap reads more or less as follows, FX swabs are a combination of an FX spot trade and an FX swap trade. So effectively in an FX wall, the counterparty agrees to buy a currency at spot and then simultaneously agrees to sell the same currency on a forward basis.

And then both prices, so the one for the spot trade as well as price for the forward trade are agreed at trade inception.

So all cash flows on this FX swap are no.

And just to introduce some relevant terminology here, the spot transaction is often referred to as the, and the four transaction is often referred to as the farm lack.

But let's have a look again at a concrete example.

And let's say we have an investor here that agrees to buy and sell. Let's terminally a hundred million dollars in a six months euro dollar FX swap.

We're using the same market data as before, spot 1.095 6 months forward points 89.10.

Now, what this basically means is that the investor agrees to buy 100 million dollars versus euros spot and then to sell.

And that happens at the same time, the same 100 million dollars against euros on a six months forward basis.

Because in most FX swaps the amount, or at least you know, the, the one of the two currency amounts usually remains unchanged.

Now the prices for both lags are based on the same spot rate, but then they differ by, you know, the, the price of the far lag because the forward lag differs by the forward points, which we have given you here, 89.1, and from a cashflow perspective, this means that at spot the investor receives a hundred million dollars and then pays 91,324 and a bit euros for it. That's just the spot rate.

And then six months later, the 100 million dollars are sold at the agreed upon forward rate at 1.10391.

And that means we're giving, we're getting 90,587,000.

Now, what feels strange for most people when they look at this instrument for the first time is that all these cash flows are known at trade inception.

And no matter where the FX rate is gonna move over the next six months, this won't impact these cash flows whatsoever.

So what we've basically done here is we took two FX transactions, one FX spot transaction, and one FX four transaction that both in isolation have exposure to spot, right? And then we combine them in this way and that leads to the fact that there's basically no, or at least only very little exposure to spot.

And that leads to the question why anyone would do such a trade, why trade FX products in a combination so that they don't really give you FX exposure, right? This might sound weird as I said, and you're completely forgiven if based on this sort, you think FX swaps are some sort of niche product don't trade in larger numbers or amounts.

But actually if you look at the market structure or reality, that looks quite differently because here what we can see is a breakdown of the OTC FX derivatives market.

This data has again been sourced from the triennial central bank survey of the BIS and represents sort of like the average values trading values observed in April, 2022. And as you can see, other than what might have expected from what we said on the previous slide, FX swaps actually dominate the OTC FX derivatives market, right? In terms of turnover, this type of instrument was behind a bit more than 50% of trading activity on the average trading day in April, 2022.

And that's not just 2022. If you look back at previous years, you find that this is not an outlier, but FX swaps have played a dominating role in, in many or in previous of these triennial surveys as well. So that of course then raises the question, what's behind this, right? 'cause it's clearly not hedging FX exposures that arise from an export contracts because that's sort of done with outright forwards, right? But what can these instruments, the combination of instruments of spot and forward really be used for? Now of course there are many different use cases but one that's particularly intuitive is the one that we introduce here on the slide, right? Because FX swaps can and are frequently used in the context of cash or liquidity, right? And the general aim here is for a company to ensure that it has enough cash on hand to meet short term obligations.

And then on the other hand companies are looking to avoid unnecessarily high cash balances, right? As well. Because cash doesn't really generate high returns and high amount of cash, therefore would be a drag on on the overall performance. Right? Now, if we combine this general strategy with the fact that many large companies operate globally and they therefore have multiple currency accounts, we can start to see that maybe, you know, they might wanna employ FX swaps. And, and let's again look at a concrete example, right? So let's say there's a company and the treasurer has just looked at the latest cash forecast across the different currency accounts. And what they've identified is that the corporate has a substantial euro surplus over the next six months and also has a substantial shortfall in US dollars over the next six months.

And that's basically the scenario he described in the, in the white box.

Now of course, this can be addressed in several ways right now, the first thing to do though that one could do do is sell the euro surplus, right? And, convert it into dollars, right? Simple FX export transaction.

However, that's maybe not the best because in six months this transaction will most likely have to be reversed because we are no longer have the euro surplus and we no longer have the USDshortfall.

So one could argue that this spot transaction and nothing else would basically expose the corporate for, you know, spot risk in Euro dollar over the next six months, which can be substantial.

So that's maybe not the best.

Now, what could the company do as well? They could invest the euro surplus and then borrow the dollar shortfall.

And that's certainly a viable option because it doesn't introduce this FX risk that we talked about.

And if we're assuming we have credit lines in place, which I think is you know, a realistic assumption here, then that could be arranged quite quickly.

However you think about it carefully, what you would probably start to expect is that the investment rates that the corporate gets for investing their money and the borrow rates they have to pay for boring money are will be quite different, right? Because you have to pay the credit spread and you know, things so forth.

So you can start thinking that maybe even this boring and landing is not the most efficient way, okay? Because it might come with relatively high transaction costs.

So maybe there's a more efficient way using a very liquid market without introducing FX risk. And of course there is, right? And you know what I'm talking about? This is using an FX swap and the idea really is to follow it.

The currency that has a surplus is sold at spot and then exchanged into the currency with a shortfall.

So that's basically just an FX spot trade, right? And that's kind of the first alternative we discussed. However, at the same time, what we do is we reverse or we, we enter into a forward trade that basically then reverses this initial exchange of the two currencies six months later.

And because the forward price is agreed as well, there is no FX spot risk.

So the corporate locks in the price for the reversal of the currency transaction as well.

And that then removes the FX risk mentioned earlier when we discussed just the spot transaction.

So what the company then has effectively done is to swap a surplus currency into a shortfall currency.

And that's temporarily, right? So basically what they've done is they have synthetically through the swap invested their euros over the next six months and they have synthetically borrowed dollars over the next six months.

Now the question then is why is it that this synthetic borrowing can be cheaper than the regular borrowing? Well, if you think about it and you just understand what we said in terms of effectively we're taking our surplus currency and give it up and in exchange for it, we get dollars.

What this can be understood is that basically is collateralized borrowing, right? The corporate has borrowed USD, but at the same time, effectively they put down the Euro amount as collateral, right? And this collateral then reduces a credit risk and therefore should lead to a reduction in borrowing costs.

Now, it's important to mention that of course this is an affect swap.

So it's just a combination of FX spot and forward transactions. So there is no explicit boring charges, credit spread, et cetera. But conceptually, this is why they might, or this might be the preferred option of this three alternatives that we have initially later. Okay? So I'm gonna skip the next two slides because it's a fairly technical information here.

But you know, of course feel free to have a look at them and reach out if you have any questions on them.

But, what I at least wanted to talk about before the session comes to an end is the FX basis.

And this starts with a confession, right? One of the reasons why the FX forward model that I shared with you earlier worked so perfectly, I.e. net present value zero is because I cheated and I used an implied Euro rate instead of the market rate for Euro interest rate.

So basically what I did is I used the FX forward rate that was given by the market together with FX bot and the observable dollar rate.

And then I calculated the implied rate or euro rate that was implied in the FX forward price, right? And of course, if you do that, the NPV of a forward will work, you know, swap for that matter as well will be zero.

Now, the reason I decided to do that was that I wanted to follow out to the general mechanics first.

And that's much easier if you ignore the FX market peculiarity, let's call it the FX basis.

But of course, in practice we cannot do that.

So let's have a look at the basis right now.

Now, as said in the previous calculations, we, we used the implied rate of 3.7549 euros.

However, when the example was created, six months Euro money market rates were actually at 3.885 which is 13 basis points higher than the implied rate.

Now, if it was just a, you know, one or two basis points, I might have said, okay, that may be rounding, that maybe day count bank, bank holidays, whatever.

But 13 basis points is a lot, and it's clearly too much to ignore this, so what's going on, right? Because according to the interest rate parity formula and no arbitrage considerations that we talked about earlier, the difference between the actual rate and the implied interest rate which is what we generally call the FX basis.

If you, if you look at the definition here on, on the slide, that should be in theory at least, exactly zero right now, of course could have been that this was just some strange combination of, you know, market data here, and that generally the basis was zero.

But, you know, to judge if that was the case, let's have a look at this basis over, history, right? And on this slide, what I'm showing you here is the six months euro dollar basis over time.

Now, on the right hand side here in this chart, you can see, that we, when we took this example, had a basis of minus 13, which means actually the, you know, implied rate and the actual money market rate had a negative, or the difference between them was a negative number of 13, right? But what this slide also shows that this was not just one day, it wasn't some weirdness that was there for one day, but the basis has actually been persistently negative in the euro dollar pair since the beginning of 2008, at least.

Now, if you go back to earlier dates, what you will see is that prior to 2007, the euro dollar basis would've oscillated around zero mark.

So slightly positive, slightly negative, but it would've been, you know, around zero, which is pretty much in line with the no arbitrage arguments that we, that we brought up earlier.

But then something changed and the basis went extremely negative a couple of times since.

So look at this here in, you know, in the 2008, 2009 area where we reached minus 200 basis points as most extreme level of the basis, right? So, now let's think about what drives the basis to such negative levels, right? And I think just by looking at the dates where, where these most negative levels were seen, so 2008, 2009, and then 2012 gives you a little bit of an idea as to, you know, what's been going on. Because what was going on in AUT in 2008, right? We were at the peak of the global financial crisis.

Now, the question, of course is what did that have to do with the ethics basis? And also, let's think about what does, what was 2012? Well, European sovereign debt crisis.

So both times we were talking about a crisis.

Now the question is, what's the link between crisis and the FX basis, right? Well, as explained before, FX swaps can be used to swap one currency into another currency.

And now you think back to what happened in, in autumn 2008, and we had a lot of banks that lost access to liquidity, right? There was a lot of loss of trust in the financial system. Short-term deposits were pulled out.

The assets of many banks turned out to be super liquid, so they couldn't sell them quickly enough to raise that liquidity.

And so we had a liquidity crisis in the banking system.

Some banks disappeared as a result of that.

And you know, central banks were obviously stepping in here to provide banks with a much needed liquidity.

So the Fed supplied the US banks with dollars, the ECB, supplied European banks with Euros and the Bank of Japan, et cetera, et cetera. So that was a, you know, the general situation.

Now, what needs to be said though is that the Fed obviously can only really supply you know, banks with US dollars that are under federal regulations. So that are basically, you know, having a banking license in the US and simplified, right? So that means we have had some European banks here that don't have that banking license, that are not having access to the US dollar liquidity, but they have dollar assets that might be illiquid, they cannot sell, so they need to finance them, right? Usually they were financed probably with by the issues of, well, you know, by, by taking some deposits from money market funds, et cetera.

But now these people are pulling their money out, which means you have to meet those dollar redemption requests. You can't because you don't have access to dollar liquidity.

But you know, you get a lot of euros from the ECB at very, you know very generous conditions, right? So how can we then combine FX swaps with that situation? So now the European banks would get euros.

What they need at least partially is dollars.

So what's due, you go into the FX market and trade on FX swap, right? Spot trade is you sell the euros and you buy the dollars that you, you need so much at the same time, because you don't wanna take that FX risk on, on the money that you borrowed from the ECB, you're gonna reverse that transaction three or six months forward by trading, uh, you know, on the in the FX forward market.

So this time round, you will sell the dollars on a forward basis and you will buy your Euros back. So what you're effectively doing there is you take euros and synthetically invest them in the forward market, and you borrow money or you borrow dollars synthetically in the fx, uh, swap market.

Now, of course, when, you know, under normal market circumstances when demand and supply for these transactions is balanced, that shouldn't really move the basis around.

But now, kind of consider those extreme scenarios where many banks were in the same situation.

They all needed dollar in liquidity, they couldn't get it directly from the Fed.

So they got it from VCB, from the Bank of Japan, bank of England, whatever, And then basically swapped it synthetically into US dollars.

And so there was a lot of money being synthetically invested via, you know, a lot of euros being synthetically invested in the FX swap market.

So really no surprise there that in response to that, the rate you get for the synthetic investment is getting lower and lower and lower and lower.

And that's basically just the demand and supply you know, reaction, response on, on the price, lot of demand for one particular side of the trade and the price will move.

And of course, in those days, nobody was really thinking about how to potentially arbitrage those things because it was really about, uh, you know, getting the much needed liquidity to avoid insolvency.

So that's a starting point. And now what you can see is that the FX basis is basically a good indicator to see how much demand is there for a specific currency to be borrowed, or, you know, in as if it's the case for used dollars.

You know, and, and how much are people willing to pay up to get access to the currency they are looking for? And dollar has been trading consistently at a negative basis against the Euro for years, and that shows that there is a demand for used dollars, at least synthetic, boring through those instruments. And that, ladies and gentlemen, is all I wanted to share with you today.

I hope you found this beneficial.

I thank you so much for your participation and hope to see you again on one of our sessions very, very soon.

Until then, take care of yourself and have a great weekend.

Thank you very much. Bye-bye.