All right, so let's get started.

Hi, good morning, good afternoon, and of course, everyone, welcome to this physics live session.

I'm on bond market fundamentals. Excuse me.

My name is Thomas Krause.

I'm the head of financial products here at Financial Edge.

And it's my honor to guide you through this session today, which is gonna be introductory as I think the title just implies.

But what exactly are we going to talk about? What's on the agenda today? Let's have a very, very brief look at that.

So, we're going to start with an overall introduction to bonds. That means we're gonna clarify some of the key terminology that gets thrown around the bond markets et cetera.

And then we're going to have a look at the key coupon types.

So the format in which coupons, um, typically are paid.

We're gonna take an intuitive look at bond pricing, and we will also discuss the yield to maturity, and then wrap this up with the inverse price yield relationships that we see in fixed coupon bonds. Without further ado, let's get started with today's content.

And as I said, we're gonna begin with an introduction to the bond market or to bonds more specifically. And the first question that we are gonna ask, of course, is what is a bond? Actually, and you wouldn't be too surprised to hear that bonds are a specific type of debt instruments.

That means when we're talking about bonds, we're talking about debt.

We're talking about the concept of borrowed money.

And of course, whenever money is borrowed, it generally has to be repaid.

And in bond world, that typically happens at a fixed maturity, meaning when the bond is issued, i.e. when the issue of the bond raises the financing, borrows the money through selling this bond to institutional or to investors, I should say via a primary market transaction, the maturity date is already known. That means people that are buying this bond at the issues know at which point they will receive their money back, the latest.

That is typically the case.

There are of course, exceptions to this rule, but the vast, vast, vast majority of bonds out there works in this format.

Then in between the issu state of the bond and the date on which the bond is then finally repaid.

I.e. the investors or the lenders get their money back.

Typically, regular interest rate payments happen that is basically can be interpreted as the running rent that the borrower has to pay for having access to this capital.

And that could be it coming in different formats. We're gonna talk about this when we're looking at the different coupon types, but generally, what most bonds have in common, that there are some regular interest rate payments in regular intervals. That could be annually, that could be semi-annually, quarterly.

That obviously depends a little bit on the jurisdiction. That depends on the currency in which we're looking at type of bond, et cetera, et cetera.

So those are certainly three important things to be aware of which are obviously something that is not necessarily bond specific, because when I talked you through those three um, points, you might've said, well, yeah, that's fine, but this is exactly how a loan would be described. Where now is the significant difference between a loan and a bond? Well, the significant difference in most cases is basically, appearing in the last point here on the on the top of the slide. That's a tradability i.e. the ability for bond investors to relatively easily, in most circumstances, at least sell the bond to another investor on the secondary market before the maturity date.

So what that means is, if you bought a 10 year bond that has been issued today, let's assume this, and for some reason next Wednesday, you decide you don't want to have this bond anymore.

Most cases, especially when we're looking at fairly liquid bond types like government bonds, for example, it's relatively easy to sell this bond into the secondary market.

I.e. get your money back way before the actual maturity date.

And by do, do you do that by finding another investor that's willing to take this bond off your hands? Now, that doesn't of course mean that loans cannot be traded, but because of the specific nature of loans, usually they are a bilateral contract between the borrower and the lender, and not necessarily very open, and transparent terms, et cetera, et cetera.

Trading loans is possible, but of course, generally that comes at a much more. That happens at a much, much lower liquidity.

I.e. it's less easy, it's less simple as it's also takes usuall a bit of you know, time in addition to the time that it takes to sell a bond.

So liquidity typically tends to be higher in bonds, and then in otherwise maybe identical loan contract.

So there we have it. Bonds are securities, that means they're fungible. They can be bought and sold in the secondary market in most cases with relative eats.

Let's have a look at some of the key terms.

As I said, we would do some of them I've listed here on the slide.

The first important point to note here is of course, the issuer.

Who do we talk about when we're talking about the issuer? That is nothing else in the entity that's actually borrow the money, and that of, of course, is responsible to repay you as well.

So when you're actually thinking about corporate bonds, so you're moving away from the government bond world. Now for a second, it's really important to precisely identify who exactly is the issuer, because that means you identify who exactly do I have credit exposure against.

And that is, of course, a very, very important point to think about because for debt investors, it is of course, of utmost important to make sure that they're gonna get their money back.

The second point here, the maturity date, I think we already talked about that earlier on. That is the date at which the bond will be redeemed. Typically, as I said, this is known at the point in time the bond is issued, then the coupon and the coupon means nothing else.

Then this regular interest rate payments that we have already referred to here in this instance.

And that's basically what can be given in, in many, many different forms. We're gonna see some of them later on.

But when they are given as an interest rate, which is typically the case for fixed coupon bonds, what's important to remember here is that those interest rates are always referred or given to us in a per annum style.

That means if you hear someone saying that there is a bond that pays a 4% coupon semi-annually, that usually doesn't mean that every six months you will receive the four, 4% of your invested amount, but you will get 4% over the whole year.

That means every six months you will get roughly half of that.

Interest rates, as I said, per annum were expressed on a per annum basis.

Then let's talk a little bit about the par value, face value sometimes called the notional amount, et cetera. That's nothing else in the amount of money that the investor will receive back at maturity.

That's not necessarily the price you need to pay for the bond today, because the price of the bond is obviously determined by current demand and supply balances.

And it's expressed as it says here on the slide, usually as a percentage of base value.

So that's just all fair and square.

But, you know, let's put a concrete example to just sort of identify what these different points actually mean.

And let's say you have overheard someone saying that the four and a quarter November, 2030 for US treasury currently trades at 96.7%.

Now, what exactly does that mean? Well, let's identify the key terms that we've seen here. First of all, the, starting with the coupon here, the coupon is 4.25% per annum. That means if you buy this bond, you will receive in total an interest amount of 4.25%.

By the way, that's calculated on the notional amount that you bought per annum.

But you might know already that US treasuries have the convention of paying coupons on a semi-annual basis.

That means you won't get 4 25, but you will get two at 2.125 approximately, every six months.

Maturity date of this bond is November, 2034.

We don't know the date, the specific day here, but we know it's gonna be in November, 2034. If we wanna know the date, we will have to look up this security on one of the databases.

We know the issuer is the US Treasury, and we know that the bond price at the time was 96.7%.

Now, what does it mean if I was an investor looking to invest a hundred million or to buy 100 million notion of this bond, what would that transaction look like? Well, first of all, I know the price, and let's assume here there's no accrued interest involved.

So then this would be in fact, the price I have to pay for the bond.

So to get 100 million notional, we would have to pay 96.7% of the notional amount, and that means in total, we're spending $96,700,000 to get the bond at spot.

Okay? Then over the next almost 10 years, we're gonna receive 4.25% per annum you know, paid every six months.

So in November and may to be precise, and then add maturity at some point in November, 2034, we will get 100 million back because bonds typically are repaid at par.

More on that in a couple of minutes, right? So that's what a transaction on fixed coupon bonds could look like.

Okay. Now let's focus on a couple oil. Let's have a quick look at the, at the couple of additional points here, referring to maturity and coupon payments.

First of all is how exactly are bonds typically redeemed? I already said one important thing, and that is that the vast, vast, vast majority of bonds is issued with a fixed maturity.

That means, as I said, the moment the bond is issued, we know at which the bond will be redeemed, at which point investors will receive their money back.

That's what we mean by fixed maturity.

Then also important to note that most bonds when they are repaid are repaid in what we call a bullet payment.

So that means there's a one-off payment at the maturity date.

We're not typically seeing some sort of amortization features like we might sort of be accustomed to in, you know, in the connection or the context of mortgages or anything like that.

Typically, bonds are repaid in one full payment at the maturity debt. Going back to our US treasury that we've just seen, or that we just used as an example, what that means is the US Treasury will have to repay our a hundred million notional in one single payment in November, 2034.

There won't be any amortization like 5% every year or anything like that.

That is the vast majority of bonds. But of course, there are always exceptions to all these rules.

And here on the right you see a couple of ways in which bonds can deviate from those.

You know, generally applicable concepts that we've just described.

There are, for example, bonds that don't have a bullet repayment, but that might have some sort of amortizing feature.

This could either be predetermined where the issue of for some reason has decided that they want to pay down the notional amount in, let's say 10 equal amounts over the next decade, meaning that at the end of every year, for example, 10% of the notional will be repaid.

That is possible can be done.

It's not a very typical thing to see, though.

Sometimes there are bonds if you're thinking about mortgage-backed securities, for example, where there is an amortizing feature.

So you will get some of your money back before the actual final maturity date of the bond.

But very often then these payments will not be known with absolute certainty when the bond is issued because it depends, for example, on the prepayment prepayment behavior of the mortgage clients, et cetera, et cetera. But just a couple of examples to showcase that. Obviously, not all bonds have a a bullet repayment, and neither do all bonds have this fixed maturity date that's guaranteed, right? So we can have exceptions here as well.

And two common examples that you see are callable bonds and extendable bonds.

Now, let's go through them one by one starting with the callable bond.

Now, callable bond is a bond where the issue of the bond either party borrowing the money actually has the right, of course, not the obligation.

This is why that's an optionality in here to repay this bond before the actual maturity date.

So that could work, for example, a 10 year bond callable after five years.

And what that would mean is that this is a 10 year bond.

So that means, generally speaking, the issuer has the obligation to repay the borrowed money at par in 10 years time, but after five years, they can look at the bond and decide whether or not they want to return the money, and then obviously stop making interest rate payments to the investors.

And one reason why they would probably choose to do that is if interest rates had declined quite meaningfully.

So let's say they're currently paying an interest rate of 4% on that bond, now five years later, they realize that they could refinance this bond, if they would call it for the next five years at a much lower interest rate, then it probably would make sense to call the bond, give the investors their money back issue a new bond at much lower interest rates, and then obviously reduce their funding costs through that.

That's obviously great for the issuer, but if you think about the investor, they probably wouldn't like to have their bond called away, simply because in the case they get their money back early because interest rates have declined. They would have to reinvest this money at now. Much lower interest rates, not an attractive position to be in.

So you're taking a bit of a risk here on the investor side. And why would you ever do this? Why would you buy a callable bond over a normal you know, bullet bond with a fixed maturity? Well, of course, for taking this extra risk, you would expect to receive extra comp where additional compensation, and usually cold bonds do pay a slightly higher return rate from the start. They might have a higher coupon, they might come at a lower price.

We're gonna talk about those characteristics later on. So that's a concept of a callable bond. An extendable bond is basically just the opposite.

That would be a bond, let's say that is 10 years, and then after 10 years, the issuer has the right to extend this bond by another two years for, you know, something like that.

And that, of course, could be done for the same reasons, just that now interest rates might have increased quite significantly.

It could also be because maybe there's some financial difficulties in coming up with that money, et cetera, et cetera. But, you know, in both cases you would agree that, again, for the investor, it's probably not an attractive position to be in. They are taking a risk here because the issuer can decide when it's better for them to extend the maturity of the bond.

And again, for that, or giving that, providing that optionality to the issuer, the bond investors would typically ask for some higher return in compensation.

So these are just a couple of variations around the bond redemption.

Obviously, more of those types exist, but I think this we captured the most important variations here for sure.

Now, let's talk a little bit more about the way in which coupons or the coupon mechanics, because we said earlier what bonds typically have in common, they pay or they make regular interest rate payments. However, the mechanics in which these coupons can be determined can differ actually quite significantly.

The first and foremost and the most important, uh, structure I think you find in, in bond world by far, is the concept of the fixed coupon bond.

And those bonds work actually quite straightforward in the sense that when the bond is issued, the coupon i.e. the size of the regular interest rate payment is set at bond issuance.

Remember, our treasury bond here, we said the coupon was 4.25%.

That was determined the day the treasury bond was issued.

And that means now that over the next decade, US treasury is gonna make this payment of 4.25% semi-annually.

But you know, we talked about that and that coupon, and it says that in the second box here remains unchanged over the life of the bond.

Now, of course, if this was a corporate bond and the issuer would sort of run into some financial difficulties, there might be a voluntary agreement between the issuer and the investors in that bond to reduce the coupon payment, maybe to ease the financial burden. That would be sort of like a restructuring event.

But generally speaking, the coupon is set when the bond is issued and then doesn't change over the life of the bond until the bond is repaid. The coupon remains at its fixed level, right? Question then, of course, is what determines this the size of the coupon or the level of coupon. And that usually is two factors here. First of all, the general level of interest rates when the bond or at the point in time the bond is issued, and then of course, the credit worthiness of the bond issuer.

So of course you would agree with the idea that the US Treasury will pay a low interest rate just because US no government bonds in, in most cases are still considered SV credit risk free.

And so the US Treasury government bonds coupon should be lower than for example, the coupon of a, you know, triple B plus rated corporate issue.

Okay? But that's just the general specifics.

Now, let's have a look at the actual cashflow mechanics.

Not that it's super difficult, but you know, let's run through this because we need this later on. And we're thinking a little bit about bond pricing.

The example here, and we're moving away from US treasuries because to simplify things, I'm assuming annual payments. Here we have a 10 year bond, which pays a 3% fixed coupon annually.

That means if the bond was issued today, one year from now, we are gonna receive 3%. We're ignoring day count conventions, et cetera, here.

Now just for simplicity, but it also means two years from now we get the same 3% three years from now again, and then 4, 5, 6, 7, 8, 9, 10 years, we get the same 3% interest.

What is different at the 10 year point is that not only do we receive the final coupon of 3%, but we also get our notional amount back.

And that is 100 percent because the bond price, remember, is always expressed in percentage points of the notional.

And the vast, vast, vast majority of fixed coupon bonds are repaid at par, which means they are repaid at a hundred percent.

And then we add the 3% coupon on top, and that gives us, of course, the 103% final payment repay at par, issued at a price relatively close to par. We're gonna, or even at par, we're going to see this in examples later on.

And then in between the issuance date and the maturity date, fixed coupon payments all equally sized typically at least that's a fixed coupon format.

Let's move to the second coupon type that's of great interest. And those are what we call zero coupons, and then we call those instruments zero coupon bot.

And in a way, I would argue that this is nothing else than a special type of fixed coupon bot, okay? Because what the coupon is, you know, what you could argue is that when a zero coupon bond is issued, the coupon is fixed and it's fixed at a level of exactly 0%.

So the concept of a zero coupon bond means nothing else, that you buy the bond today, and let's say it is a 10 year bond, you get nothing over the next decade, no interim interest rate payments, and then you get your money back after 10 years. And of course, we all agree that only makes sense as an investment.

If there was some sort of a different source of return, then regular interest rate payments because they have been determined to be zero.

Now, of course, if interest rates are exactly zero, then maybe that's what we just have to accept. And remember, not too long ago, that's where interest rates were, right? But, um, in a normal market environment like today, for example, where, you know, 10 year yields are sort of in the US approaching 5% or no, not approaching, but you know, getting, moving maybe towards that direction, then of course just investing in a bonded pace is zero coupon and, and comes at a price at par. That doesn't really seem to make a lot of sense.

So where's the return in a zero coupon one coming from? You would've guessed it, right? Usually these bonds are issued at a price significantly below par.

What the example says here on the slide is, we have a 10 year zero bond that is issued at a price of 74.51%, and then 10 years later is repaid at par.

Yes, in between there is zero payment, right? And that means you don't get any interest rate payment over the next 10 years.

However, you see that there's a return because you would invest 70, let's round it up a bit, 75 million today to get 100 million notional, and then in 10 years you will receive 100 million back.

So we're basically back loading all the interest rate payments rather than paying regular amounts.

You get all the money back at maturity.

Now, where are the pros and where are the cons of such a structure? I what might make people choose to invest in zero coupon bonds if you don't get regular interest rate payments? Now, of course, if you are looking to invest money and you are looking for this regular cash flow, this regular interest rate payments, zero coupon bonds simply won't be for you.

But if you are an investor that is not looking for regular payouts, but rather than having maybe some higher degree of certainty about what your actual return is going to be over the next 10 year period, then zero coupon ones might actually be quite interesting, right? And so let's go back to the fixed coupon one and sort of elaborate a little bit on this phenomenon here, because it's about returns, about certainty in many cases.

So remember, we've, let's say we've bought this 10 year, 3% fixed coupon bond that pays coupons annually. And let's say the reason why we did this is we had a certain amount of money that we know we won't need for the next decade.

In fact, we want to make sure that our capital grows to a certain amount of the next decade, because in the, then at the end of this 10 year period, we have a certain payment that we need to make.

Just, you know, it doesn't really matter what this payment is, you were just creating an example here.

So then obviously buying a 10 year, 3% coupon bond is certainly not the worst option, but you can see as to why there's some sort of question mark around how much money we'll actually gonna have at the end of this 10 year period.

Where does it come from? Well, simply from the fact that remember, we don't need the money for the next 10 years.

However, if we buy this 3% coupon bond after year one, so 365 days from now, we will get the first 3% of our notional back.

So if we invested 100 million dollars today in three months sorry, in 12 months, we're gonna get $3 million, which we don't need at that point.

So we are here, we have 3 million USD, but when do we need that money? We need it at the originally 10 year point, which now, of course, because one year has passed is nine years in the future, we have 3 million.

Now, what is the rational investor gonna do with that money? Gonna reinvest this for nine years, right? Because we need the money at that particular point in time for nine years.

Question then, of course, is which interest rate does apply? Well, the simple answer is, well, the nine year interest rate that can be observed in one year's time, and that's accurate problem is today.

We don't know where this rate is going to be.

Yes, of course we can use sort of derivatives and hedges, et cetera, to to lock in a rate, but if we don't do this, we are taking something called reinvestment risk because we simply don't know where the 90 interest rate in one year is going to be.

And it's not only the first coupon payment that is having this reinvestment risk, but how about the second that needs to be, or we get money in two years time as well, that needs to be reinvested for eight years, but in two years time, so eight year rates in two years time, who has a view on that? And 3, sorry, 70 year rates and 3 and 6 and 4 and all those sort of different types of interest ads.

You know, we won't know with 100 percent certainty from today's perspective.

So there is naturally some degree of uncertainty that we're taking when we're buying a fixed coupon bond, at least if we're not planning to just draw down the money and consume with with the regular coupon payments. But if you're just thinking about an investment, then you will have some question mark about the actual final return. Granted, this reinvestment risk if impacts a relative small portion.

In this example here, it's just invert comma 3% of your notional.

So after one year you need to reinvest 3%.

That's not the majority of money.

However, if coupons are 5%, 7%, 10%, then you see that this reinvestment risk is impacts much higher proportions. And so it might be worse thinking about it.

So that's the situation.

If you buy a fixed coupon bot, how does it change if you buy a zero? Well, you know, remember how we define a zero coupon bot? We said it basically is a bond that pays absolutely no interest between the issuance date and the maturity of the bond.

We have even written it just zero payments at the one year 0.0 payment at 2, 3, 4, 5, 6, 7, 8, 9, and then all the money is received in 10 years.

So here, in this case of a zero coupon bond, we know exactly how much money we have to put down today.

That's 74.51%, and we know exactly that we're gonna get 100 million at maturity.

Now we can say, okay, if I have 75 million growing into a hundred million over a decade, what is the implied rate of return of that? We can calculate that, and then we have calculated the implied return on a zero coupon one. And there are no question marks around this, assuming of course, no credit risk here, because we know that our 74.51% is gonna grow to 100 percent, and it doesn't really matter where interest rates go in between.

We don't have that reinvestment risk that might be of interest for some investors.

I'm not saying it's something that we all should do or anything like that.

It's just, you know, you see the difference in risk profiles.

So another point though to consider, and you heard me saying this is true when we're not looking at credit risk is of course a credit risk because from a credit risk profile, zero coupon bonds differ as well, not just from a payment profile, right? So now we split our group here in two parts.

And let's say all of us have bought a 10 year bond from a specific issuer, but half of us bought this 10 year, 3% annual coupon bond, and the other half of us bought the 10 year zero coupon bond. We all invested exactly a hundred million dollars.

Now, we didn't buy the notional, we just bought whatever we can buy with a hundred million dollars.

So all of us are on the hook for 100 million dollars maximum loss, okay? That's 10 year bonds in both cases.

Now, let's fast forward nine years, 11 months and three weeks.

I.e. one week left until the bonds both bonds because let's say they have the same maturity dates will be redeemed.

At least that's the plan. But they're corporate bonds.

And let's say one week before maturity, the corporate declares bankruptcy and the market quickly realizes that this is a company that has way, way, way, way, way too much debt.

And therefore we expect recovery to be zero.

In this particular case, we're, you know, obviously making it pretty dramatic here just for simplicity.

But you know, let's just assume that, so another question is, is everybody of us equally unhappy because we all are unhappy, right? We're not gonna get our a hundred million back that we assumed we would one week from now. However, I would argue it's relative intuitive to say that one part of the group is even is, is slightly less unhappy.

And those are the ones that invested into this coupon paying bond. Because remember, this was a 10 year bond, paying 3% every single year.

So nine years have already been completed.

That means those of us who bought this coupon bond would've received nine times 3%, roughly speaking with ignoring time value of money, they would've received 27% of their capital back already.

Whereas those of us who bought these zero coupon bonds have been one week away from this massive payout, which now unfortunately will never occur.

So that's a point to remember that zero coupon bonds potentially have a different credit risk profile.

Now, of course, if you are investing in government issued, zero coupon structures, then that's not your primary concern.

But if you're thinking about private issuance, then of course that's something to at least, think about.

Okay? But, that should be enough for those fixed coupon bonds.

Now let's have a look at one other type of coupon structure.

It's fundamentally different in the sense that the coupon isn't fixed, but it is actually floating i.e. it's variable.

That means nothing else that the interest that investors will receive on their investment will vary dependent on some underlying market interest rate.

That is the concept of floating rate no, where rates or coupons are basically adjusted to market interest rate levels in regular intervals.

Now, what they have in common is that when we issue a floating rate note, we don't fix a coupon.

It's not saying 4.25% or 3% or anything like that, but what we're doing is we're fixing a, or we're setting a or determining a fit or a coupon formula.

And this coupon formula then generally has two parts.

The first part is we're linking coupon payments to and generally observable reference rate.

Those are typically the money market benchmark rates, like for example, IBOR, that obviously LIBOR was the most important component of this very well known, but we also know it doesn't exist anymore.

But there are I os that are still around EURIBOR, for example, right? Six months EURIBOR still is very much alive and, is used in the concept of floating rate notes in most currencies. However, especially on the developed market side those eyeball rates, those term deposit rates have been replaced with now the near risk rates, things like SOFR, SONIA, ESTR, TONA et cetera, et cetera.

And then depending on which reference rate is being used here, there are some mechanical differences that go a little bit about, you know, beyond the purpose of today's tutorial, just be aware that the fixing mechanism works ever so slightly different. But that's the first component, a money market benchmark rate that we can observe in regular intervals.

And they are because they're published in, you know, the financial papers and on Bloomberg, Reuters, et cetera, et cetera, or ative.

Then there's no sort of ambiguity as to where the reference rate is and then makes coupon or agreement on the actual interest rate payment between issue and investor. Of course, a very, very straightforward process.

That's the first part. But then the second part is that usually we add a credit risk on, or sorry, a credit spread on top of the reference rate.

And why is that important? Well, remember that those money market benchmark rates are interest rates that are generally referring to relatively short lending period.

So six months EURIBOR is for six months you know, investment period, if you wish, SOFR, SONIA, and all those other near risk rates are overnight rates.

That means this is an interest rate from one day to the next. And that is almost credit risk free so far in particular because that's not just overnight lending, but it's backed by actually collateral.

So it's repo transaction that we're looking at here.

So these are effectively near risk free credit risk free rates, we should say to be precise, right? But now if we are using, or if we are lending money to some issuer here for let's say a 10 year period, and the reference rate that we're linking coupon payments to is risk free or has very, very low credit risk, we might wanna have a spread on top of those low credit risk rates because we are actually lending money to this corporate for a 10 year period, and that is 10 year credit risk we're taking, right? So that's why there's two parts reference rate plus a credit spread.

And let's go through one example here only because to save some, some valuable time in the session.

Let's look at the way how these floating rate nodes worked all around the world for many, many years.

Now, of course in the absence of LIBOR, we have different mechanisms. But let's stick with the EURIBOR example here and let's say there was a 10 year floating rate node that had been issued and the coupon formula that was determined at issuance is six months arrival plus 0.5%, and we're have also agreed on a semi-annual payment.

So let's say this bond was issued today, although EURIBOR is not at these levels anymore, but let's say it was issued today, and let's say that today six months EURIBOR is actually, was set today at 3.96%.

What does that now mean? Well, that means that we now know six months EURIBOR for the first coupon period, that's 3.96.

We also know we have to add the credit spread because that's saying in the coupon formula, six months, you arrival plus 0.5% or 50 basis points.

That means the first coupon is effectively determined to be 4.46%. That's nothing else but 396 plus 50 basis points that is payable six months from now.

And it doesn't matter that this is a floating rate note here, the interest is still expressed on a per on basis.

And because we're getting paid after six months, we shouldn't get the whole amount.

So we get 4.46 times roughly 0.5, assuming here for simplicity that a six months period is exactly half a year, which in reality it isn't. But let's make our life easier here. Okay? So then we get the first interest rate payment six months from now based on 4.46% times notional times 0.5 ish.

And that's gonna be the amount of money we're gonna get in six months. And what happens then? Well, now we're looking at where six months EURIBOR at that point in time.

So now we say let's, what's the six months EURIBOR level? And let's say EURIBOR has increased, and is now at 4.5%.

Then what do we know is from here to there, the total interest that's gonna be paid is 4.5 plus a credit spread of 50 basis points.

That makes 5% here in total, that again, is cut in half because we're paying semi-annually and so on and so forth.

So what you see here is that depending on where your arrival goes over the next decade, the coupon payments on this investment will vary potentially quite significantly.

If your rib goes to 10%, you get 10.5%. If it goes down to zero, you get zero and a half percent.

If it goes down negative, you probably wouldn't have to pay because usually in floating rate notes, there is a passage in the perspective saying that the coupon is actually floored at zero.

And that is not because we want to protect investors necessarily, but of course it would be weird if there's negative coupon payments because then the issue would have to collect money from the investors, which of course could be a fairly difficult thing to do.

So that's a concept of a floating rate note. And now if you think about it, okay, when would I buy or when would I prefer fixed coupon bonds? When would I prefer floating rate notes? And we're really simplifying here, but the first way of looking at this is, well, what do you think is gonna happen to interest rates, right? If you think today's level of interest rates is relatively high, and we're gonna go down from here, then ask yourself very quickly, what would I do floating or fixed? I give you two seconds to think about it past.

And so I think you would've answered correctly saying, okay, I wanna buy fixed because I wanna lock in the current interest rate level that I think is higher for the next 10 years.

If you think on the other hand that interest rates are about to rise dramatically, then you probably wouldn't want to buy a fixed coupon one for let's say a 10 year fixed coupon one today locking in a fixed interest rate for the next decade. Because if you think that interest rates will go up, why would you buy a 3% coupon one today if maybe two months from now? Yields have more interest, rates have gone a lot higher, and you could buy much higher coupon ones at a lot lower prices, right? Then what you could do though, however, is to invest in a floating rate note, and then if you write an interest rates do go up, you will see your coupon rates increasing as well. However, of course, you know, just a bit of a disclaimer here, that is a significant simplification because what we're need to think about is that we're looking at a six months or even one day rate if you were thinking about fr linked floating rate notes, et cetera here in case of ens, and when we're buying a 10 year fixed coupon one, we're of course looking at 10 year interest rates. They're not directly comparable, but you get the idea. Okay? So those are the different coupon types.

And now let's spend the remainder of the session thinking a little bit about the price of a bond.

And we're looking at fixed coupon bonds only here, by the way.

And also we want to discuss what the yield basically means, and we wanna look at the inverse price yield relationship.

Now let's start with the theoretical foundation of pricing.

And I think, you know, that's obviously not specific to bonds, but there's of course a general concept saying that the price or the fair price of security is really nothing else in the present value of all this cash flows. And that's pretty much what a bondage, right? If we're thinking about a fixed coupon bond, remember the 10%, 3 sorry, 10 years, 3% bond we talked about earlier, that's nothing else than a series of cash flows that you buy, right? So you buy a 3% payment of the one year, 3% after two, 3 after 3, et cetera, et cetera.

And now what is the rational investor gonna pay for a series of future cash flows? And the answer is the present value or the sum of the present values of all these cash flows.

So bond pricing in a way is a three step approach.

First step is you want to roll out cash flows, right? So you want to determine how much money do I receive from that bond, at which point in time that's just working out the cash flow stream.

Then the second step is to, well, basically you need to present value the cash flows, right? And there we use this general time bill of money formula here that I'm sure you've all have seen.

The present value is nothing else but the future value of the cash flow.

So the actual payment divided by one plus ir you know, whatever you want to use here, it's for consistency we're using r to the power of time. Okay? So that's fine. First roll out the cash flows and then discount them.

The fundamental question is, what should we use as r What's the appropriate interest rate to use, right? And that's not necessarily that straightforward to answer. However, what I would argue is that in most cases we don't actually need to find r, right? And here's as to why this is because this formula that's shown here as the bond pricing formula in most cases isn't used to actually price the bond. Because technically speaking, a bond only really needs to be priced at one particular point in its life, and that's when it's issued after the bond has been issued because people buying and selling this bond in the secondary market means supply and demand dynamics will drive the price.

And then we have the price we see where the market is trading this particular security.

We don't have to price the bond necessarily.

What we obviously do wanna do is figure out, okay, where should the theoretical price of this bond be? And then we can compare the price that we feel is the fair price to the actual market price.

And that gives us then an idea whether the bond is trading cheap or it's trading expensive, but that's more a valuation type of approach rather than pricing, right? And we come to that a little bit later, but let's stick with this issuance pricing because that's something that actually needs to happen.

And there's then the question, how do we get this? R which we denote here as the required rate of return at the point the bond is priced.

Now I skip this slide because we can come back to that in a minute, but generally speaking, let's have a look at how bond issuance works.

And we're using the example of government bonds here.

We could do that for corporates as well, but government bonds is what I've chosen.

And what is true for many, many government bonds is that they are often issued via public auctions.

That means the issuer i.e. the government issues or places the securities directly with investors.

Yes, there are maybe banks involved in the process.

So the primer dealers come to mind here in the US but generally the US Treasury announces we want to issue a five year bond.

We want to issue 10 billion US dollars.

That is then made available via statement on the relevant websites. And then the auction process will start at the particular day and time that's been determined. And then basically what happens is that investors read this announcement, they know when they can bid for this particular bond, and when the time has come, they log into the auction platform and then they can bid for the bond.

And the way they have to place their bids in most cases will be the yield.

And the yield in this case means nothing else in the return that the investor is expecting to receive.

And in a way we can describe that as a required return because as an investor, what I would think about is if I'm not having for any reason to the obligation to buy this particular bond, I would think about, okay, what is the return this bond should pay for me under current market circumstances, et cetera, so that I will find this to be an attractive investment.

What's my personal required rate of return? And investors will go through this process and come up with answers, and then that's the return that they would put in on the bidding platform.

And now let's say we have received a couple of bids here.

Add a yield i.e. return required rate of return of 4.522%.

There's a total amount of 3.4 billion US dollars.

So investors have said we're willing to buy $3.4 billion when the return is 4.522.

That is of course not enough because remember, the total amount that should be issued is $10 billion.

So 4.522 is not gonna be the return.

Let's go to the next level and see what happened at 4.523.

Let's say there have been a different group of people that said, yeah, my required return is 4.523% and they are a little bit larger than the previous group.

They are willing to buy $4.9 billion of that bond at this level of return.

Now we're simplifying here once again to say, okay, that these are separate bids, they are completely independent from each other, which means there's this 3.4 billion where people are happy to buy at 4.522, and then there's another 4.9 billion independent at 4.523.

So we can say that the aggregated demand at this level of return is actually 8.3 billion.

That hopefully makes sense because that someone that's willing to buy a bond at a return level 4.522 is also gonna be happy to get the same bond at a slightly higher level of return.

So they won't just turn around and say, no, we wanted 4.522, they will be happy to get a slightly higher return.

Still not enough though, because remember we wanna place 10 billion, so we have to kind of go to the next level, and that was 4.524. There's gonna be another 2.5. Well, there was another 2.5 billion demand that brings us in total to 10.8 billion.

That's fairly close to the amount that actually exceeds the amount that we're issuing.

And so that would be the level of yield or return that is going to be or that this bond is going to be issued at.

Now the question is why do we have to price at all? Why don't we not just put a coupon of 4.524% and then it's a 10 year bond with that coupon? And, you know, possibly many, many reasons for that.

But you know, I think market con or general convention is that we're using coupons that are, easy to memorize.

So for example, we would use a coupon of let's say 4.5% here in this particular case, much easier to remember than 4.524, right? And now with that, what we can do is saying, okay, we're we're issuing a 10 year, or sorry, five year bond that pays a 4.5 percent coupon semi-annually.

But then of course investors would say, yeah, that's all fine.

But remember we ask for a yield of 4.524%, how are we going to get 5.4 to 5 to 4% if the coupon is only 4.5? And the answer is, we're gonna sell this bond at a slide discount.

So we now need to calculate the price of the bond.

And this is where we're going back to this one here.

We now know the coupon, right? So that's been determined to be 4.5 percent paid semi-annually, but forget about this now for simplicity.

So every six months, we get half of 4.5%.

We now know, we also know that the bond is redeemed at par.

So we know all those bond cash flows, and we have basically the required rate of return from our bond investors because that was determined to be 5.42, 5.524% in the auction process.

So this is our, and now basic one, not quite, because now this is a semi-annual bond. So the mask changes slightly, but that's not the most important point.

But I want to demonstrate here is how we can price the bond based on the required rate of return that has been determined through the auction process.

Then we can just do the mass, we can do the discounting with the relevant required rate of return.

We get the price, and that's gonna be the issuance price of that bot for those who want to know the math in a little bit more detail.

Here's an example that goes through this in with slightly different numbers, but I leave that for you to read up on this.

In your own time, now the bond has been issued and now investors that bought the bond through the issuance process and now decide they don't want it anymore, for whatever reason, they're going to go to the secondary market, start selling the bond, then other investors that didn't get the bond on the issuance process want to buy it. And so there's a secondary market activity.

And then of course, depending on, you know, how much buying and selling interest there is, the market price of the bond is going to move away from the issuance price could go up, could go down.

And that's the point when we will actually stop using this formula that we're seeing in the context of pricing, because pricing is now done by demand and supply forces.

But we're still gonna use this formula, not just, but not for pricing, but actually we want to calculate what we call the yield to maturity.

'cause what's important for investors, uh, when they now thinking about bond investments is not so much only the price of the bond or only the coupon that they're gonna receive, but actually how this translates into a total return, right? And we've briefly touched upon it intuitively.

We said, well, look, if you get a bond, um, that pays a 4.25% coupon, but you buy it at 96% or 96.7% of the treasury example, uh, of its value, and they hold it for 10 years, not only do you get the 4.25% coupon, but you also have capital gains. And that both are important factors, uh, of your, uh, total return.

So what is important for investors is have like a comparison tool, um, to that allows them to look at two bonds that trade at different prices, but also pay different coupons to figure out, okay, which of these two bonds pays me a higher return? And that's the concept of the, uh, yield to maturity.

And the idea here is that now we know the price of the bond.

We know the cash flows of the bond.

We're simply rearranging this bond pricing formula and solve it for our IE the required rate of return that's implied in the bond price.

That's a yield to maturity.

That's what people usually talk about when they're referring to yields. When you hear people bond yields have gone up, they, this refers to the yield to, uh, maturity.

Now, how is this calculated? We have said, okay, we're just taking the bond price.

We're putting it into the formula that we've seen earlier.

We're rearranging to solving for, well not rearranging as no closed form solution, but we actually, uh, need to goal seek, if you wish, for, uh, the, the yield here or are, um, using this synonymously now.

Uh, and then we have the yield to maturity. What this means is, uh, it's based on a couple of assumptions, right? And the first assumption is that the investor that is, um, you know, or that is buying the bond at its current market price, that's a fair assumption.

'cause where else would you buy? Second assumption is that the bond is held to maturity.

That may or may not be the case.

Um, but of course, you know, um, it's relatively intuitive, I think to to say that if the investor doesn't, um, uh, hold this bond to maturity, then the return will depend largely on the coupon payments, but of course also on the sale price that they will be able to, uh, achieve whenever they decide to sell the bot.

So that's, uh, another assumption here that is still, I think, relatively unproblematic.

The third one is then that we have to think about, um, you know, when we're, when we, when we're looking to determine the hold return of the bond investment, not only can we think about the coupon payment and the price, but we also have to think about this reinvestment that we have already, uh, talked about. Because remember, if you bought that 10 per 10 year, 3% bond, after one year, you get 3 million of your notional back and that you will now have to reinvest. And that is part of your total return of the investment, so to speak.

We don't necessarily know, uh, where this reinvestment rate will be.

So to calculate, uh, a number that we can use to comparison in a straightforward and easy way, we're making assumptions on the reinvestment rate.

And that is basically that all coupon payments can be reinvested, all future, um, coupon payments will be reinvested for the remaining time to maturity at an interest rate that's equal to the yield term maturity.

So it's an internal rate of return calculation evaluation. Of course, that assumption is ignoring reinvestment risk because we're just basically saying, okay, assumption is we can reinvest every payment over the next 10 years at the rate of let's say three and a half percent. What this effectively means is we're assuming that interest rates for all different types to maturity are the same and they will never change. And then of course, there's a bit of a stretch.

We could argue though that it's not, you know, extremely problematic because it only impacts reinvestment.

Um, I think the more corporate point to make though is everybody knows that this is an assumption of the yield to maturity calculation. So everybody knows that the yield to maturity is not a guaranteed rate of return, but it is an approximation of the total return that an investor will make over the next, uh, couple of years IE between now and maturity of the bond under the assumption that reinvestment rates will be x.

And that's, remember that's what investors want. They want a quick and dirty comparison tool to say, this bond at that price, but was that coupon.

And this bond was a lower price, but a higher, uh, but a, um, uh, a lower coupon as well, which one pays a higher return? And then the first point to look at will indeed be the yield two maturity that as we have set couple of times now, has generally three components.

First one is, of course, the coupon. That's an important part of your return, assuming we're not talking about zero coupon one here, right? Then the coupon is an important driver of your return. You get, for example, 3% every year.

That's part of your return reinvestment returns we already said. But we're going to now, um, just for simplicity, ignore those, um, from now on, um, which is, um, important in a nice, uh, way of simplifying the understanding of the price yield, uh, relationship.

Um, but the one thing that we definitely need to consider are capital gains and capital losses, which is basically nothing else than saying do we buy this bond at par, above par or below par? So let's, um, just develop this, uh, conceptually here for our, uh, 3% annual fixed coupon bond we've seen earlier.

Okay, so let's say we bought this bond and it pays us 3% annually here.

Um, we're not considering reinvestment recurrence for simplicity, but let's say we bought this bond at a price of 95% and this was a 10 year bond.

Now, if we're holding this bond to maturity and we're getting our 3% annually, and we wait, uh, for the redemption to happen, what's gonna happen is that we're gonna get repaid par IE we have put 95 million uh, dollars of our money in.

Then we get 3% on a hundred million over the next decade, every single year.

And at the end we will get a hundred million out. So not only do we get 3 million coupon every year, but we also see our capital to appreciate by 5 million in total.

Those are the two return components.

Hopefully it is, uh, straightforward to see that the yield to maturity in this particular case will be larger than 3% because 3% is the annual return from the coupon, and then we get the capital appreciation on top of that.

That will work out to be more than 3%.

You could approximate this, but for now, it's fair enough to just say, okay, yeah, it makes sense that the yield will be higher than three.

Now, if we didn't buy the bond at 95, but let's say we bought the bond at 105, then this changes simply because yes, we're still getting the same 3% annually, but now we have paid 105 million upfront and we're gonna get back only in the verta commas a hundred million.

That means the yield to maturity of this particular, uh, transaction of this particular bond purchase should be below 3% because we're losing some of that, uh, coupon income here through the capital depreciation or the capital loss that we face simply because we bought the bond above par and it will be redeemed, uh, at par. And by the way, I said again, um, we're ignoring accrued interest here, uh, for simplicity.

So what that means is, and now we can see where, um, you know, if the price would continue to go up now to 110, yes, yield to maturity would still be below 3%, but it would now be, uh, even lower than the previous one, simply because we have higher capital losses.

And that leads us right into the last point that I wanted to mention that sort like a nice wrap up here. And that is that the relationship between the bond price and the yield in specific ways, the yield to maturity, that's what we call an inverse price, yield relationship. Meaning if the bond price goes up, the bond yield goes down. What does it mean if people now for some reason decide to all go out and buy bonds, they are bidding up the bond price.

That means someone that now buys the bond at the now higher price will pay a higher price for getting the exact same cash flows than the person that bought the bond at a lower price.

And that means, in comparison, the yield of this investor that was late to the party and bought at a higher price is gonna be lower than the one of the person who bought first at the lower price.

So if people buy bonds, bond prices go up, yields consequently go down, it doesn't impact the investor that already bought it.

But everybody that buys a bond at a higher price will face a lower yield than the, uh, one before.

If the opposite happens and people sell bonds, bond prices consequently drops.

That means yields are going up. And that means having, not having bought the bond is actually giving you an advantage now because you can have a higher yield, uh, locked in.

Okay. So that, ladies and gentlemen, that's pretty much all I wanted to um, share with you today.

I just got a question, um, I'm reading through now.

See if I can answer that.

Yeah. Okay. So, uh, I think the question is around, um, how does it work in a re sort of restructuring event, um, when, when we have all those different bond holders? 'cause that will be, uh, quite difficult obviously to get them to agree on something. And that is a very, very, um, typical issue that you absolutely see.

Um, because in a way when there is a restructuring necessity, so if the, if the bond issuer, um, basically, um, has to face reality that they won't be able to meet these financial obligations, then of course the best, theoretically the best case would be to get all, um, creditors on the table and then sort of find the best way out. And that means, for example, reducing coupon payments, extending bond maturity, et cetera, et cetera.

The problem with those sort of things often is that while there might be a solution that's in the best interest of everyone, it's actually hard to agree amongst all those different parties here that all have sometimes conflicting interest.

So, you know, voluntary restructuring very often is actually quite hard to achieve.

And that's why you would still probably go through in many, many cases through sort of like a court driven, um, insolvency and restructuring process.

And then there would be decision made because that's the sort of like collective action problem really that we see many, many times that a group of, um, parties will probably not be able to agree on a solution that's in the best interest of everyone, but they will str well fail to agree on something just because they have conflicting interest. That is my general answer.

I know it's not, uh, very precise, but that's indeed a, a, a fairly, fairly specific question that will be what the answer depends a lot on the circumstances.

Um, how do investors base their bid for government bonds? IE how do they decide whether to receive a yield of, uh, 4 35 versus 4 35 3? Well, that is an interesting question. Generally, I would say, uh, the starting point is obviously looking at where are, you know, uh, bonds currently trading, right? So, uh, the good thing about governments is that they have a fairly regulation schedule.

So they don't issue a 10 year bond or a five year bond, as now example every, uh, you know, couple of years.

But there's a pretty regulations calendar.

So even let's say they, they issue a new five year bond today, there's probably a relative, uh, recently issued, uh, bond that has a maturity of around five years, maybe 4.75 or four and a half or five and a half even.

Um, that will obviously give you a fair, good indication as to what yield would be appropriate.

So let's just say we have a 4.9 year, um, government bond here that trades at a yield level of 4.35.

Now it's about four, uh, 10 years at sli, uh, sorry, five years.

So that's a slightly higher maturity.

Then you would sort of factor in, okay, maybe there's a normal upward sloping yield curve.

We're taking a little bit longer, uh, time to maturity.

So we would, uh, basically expect, uh, yields to be slightly higher.

Uh, but also what you have to do then is, is to consider, okay, what is the current, um, sort of market appetite for those securities? Are there any concerns maybe around increasing debt levels, et cetera, et cetera.

So all those things will find their way into the actual decision, uh, of the, of the individual investor.

And last but not least, what's also important is to think about how important is it for me as an investor that I get part of this bond.

If I have sort of a necessity to invest money in government bonds today, I would probably make a bit of a concession on the yields, um, that I'm, that I'm bidding for just to make sure I wanna be one of those people that gets the bond.

And the problem is in our, uh, previous example, and maybe we'll just go back to this, uh, very briefly because it fits with that question.

Um, so if I was, um, a fairly, um, aggressive bidder and I said, okay, I want to have a yield of 4.527%, um, then in this particular case, I wouldn't have gotten anything, right? So because my bid was too high, uh, and only people that bid this rate the Highest accepted yield or lower will get the bonds that they have asked for, I will not get anything.

So I need to also, you know, in addition to all those sort of market related questions, I also need to think about do I really need this bond? If the answer to that question is yes, then maybe I should be a little bit more generous or be a little bit more defensive on the yield that I'm, that I'm asking for.

So hopefully that answers, uh, that question.

And with that, um, there are no unopened questions left.

So thank you so much for your participation. Hope you found this beneficial here today.

Uh, have a great rest of your Friday, a fantastic weekend ahead. For some of you, it's gonna be a long one.

Uh, so enjoy that very, very much.

Um, it was an absolute pleasure talking you through this topic, and I hope to see you again in the not too distant future on um, different one of these sessions.

Remember the feedback. Uh, take care guys, and I'll see you soon. Bye-bye.