Welcome back. So, we did some simple examples of the simplest security or bond

that is out there which is a bond which is based on a coupon and we try to calculate

the maturity. Let me tell you a little, simple way or doing this and let's take

thousand dollars and divide by 744. Bond 09. What is this telling me? This is

telling me future value, thousand, and present value, right? The only two things

I know. However, the key here is, the number of periods that , right? So, let me

return it, so that is 1.3439. Now, let me do this. Take A1. And I take the tenth

root of this, Remember we are doing compounding. So, if it's over ten years

without compounding, I do the tenth root of it. It's point, raised to .1. 1.03. So

remember the three%? You subtract one out of this calculation when you get to use to

maturity, right? Because its future value over present value. And you have to

subtract the one because that's the one back you put in is your investment, right?

The rate of return in our bind. Now, what's the difference between this and if

I make compounding happen every six months? I'm taking now one to the

twentieth. So take. A1. And now one to the twentieth is what?.05. Okay, there. I can

see what I did, my nervous ad put 2s equals . You see I make very silly

mistakes . So one point, O 1489. So you see how I did it. I am just showing you

that the fact of compounding is the only reason that calculations become a little

tricky and difficult. Okay. So let's move on. And I have got 1.489. I would

encourage you to be very familiar with this stuff. So something that you will see

all the time in the press. And toward the end, we will go to a website and you will

see all of this something called the yield curve. And it is in your face every

morning, if you pick up any newspaper to do with money or reporting about economy,

you will see this and I want it to get a flavor of what that means. It is the

relationship between the maturity of a bond and the yield, and it's for

government bon ds, and. Purely, should be zero coupon bonds, because it's trying to

show you the connection between the length of time and the interest rate on

government bond. So if it wasn't coupon it's not really picking up the

relationship kingly. Typical relationship and why, let me just show you the typical

relationship and why, so drawing a graph. If this is zero, right? And this is yield.

And suppose this one year, This is two years, this is 30 years. And the reason

I'm doing 30 is, believe it or not, you can buy a bond that promises to pay you

100 bucks 30 years from now. And it is traded, and it has a price, you know? So

that's why I kind of find it really cool. So the typical relationship is something

like this. It tends to go up and. I want to make sure that you get it. Before we do

coupon bonds, so the relationship is going up, why is that? The reason is very

straight forward. If you buy a one year bond versus a two year bond or compare a

one year bond with a ten year bond. Who's price is likely to be a lot. Always keep

risk at the back of your mind. But now I'm increasingly going to pull that concept

out and bring it to you because we are talking about real world investments. A

loan, not a stock. Risk has to be at the back of your mind. We will stay away from

it in an explicit manner, in explicit treatment but bring it forth as we go

along. So let me ask you this, very simple, let me draw a timeline. One bond,

one year from now gives 1000. And it's come in. The other government bond gives

you ten years from now, 1000. Which of these is perceived to be more risky? So

suppose you're just bought this bond and you are at some point beyond zero. And you

bought both of them. Whose price will fluctuate more? Think about it. Very

simple. Whose price will fluctuate more and because of what? You know the answer

to almost 99% of the questions, right? The answer is compounding. So this will

fluctuate less. And the reason is it's price is simply. One plus R. 1000 divided

by one plus R. This price is 1000. Divided by one plus R raised to power. Ten. So

imagine how R changes if for a common bond which doesn't have much risk, hopefully,

the main reason R is changing is because of inflation. Remember, I told you, R's

job is to keep up with inflation. So the main reason is inflation, and there's a

little bit of what we call real return built into it. So. If the interest rate

goes up per period. What happens to one plus R, versus one plus R raised to power

ten? One plus R raised to power ten is going to be much larger than one plus R.

So the price of a ten year bond fluctuates much more than the price of a one year

bond. And maybe, may have to sell these bonds at some point, right? So because of

that, what happens is, the interest rate built into a ten year bond has to

compensate me for risk, because I am risk averse. I don't like risk, right? I being

the average person. In fact, everybody wants to know, right? So what happens? The

interest rate is higher for ten year bonds and that's why the yield curve is going

up. Right. That doesn't always mean going up. There's a second component is how much

do we expect the interest rate in the future to be and stuff like that. But I

just wanted to give you a flavor of this and we'll talk about and see some data

later. Okay. Now let's move away from zero perform bonds to coupon paying bonds. And

the reason I'm going to coupon paying bonds is this is the nature of most loans.

That most loans don't just borrow, you don't just give money today and then pay

it back, one shot right at the end. Most loans, even corporate loans, have coupons

built into it. So let's start with government bonds. Most government bonds do

have coupons. So, and it's the most common type, type of bond out there. Okay? These

bonds pay periodic coupons and a larger face value at maturity. All payments are

explicitly stated in the IOU contract, okay? So this, we talked about the fact

that this is an IOU. So, the difference between a zero coupon and a coupon paying

bond is simply the coupon part, okay? And we'll just do some examples. I'm going to

spend a lot of time on this example. And I think you should stay with me. And the

reason is, we are not doing something profoundly different than what we have

just done. Having said that, the mechanics and the intuition of this is very

important. And I'll take a break when we think we've gotten over the, first few

steps of understanding this, okay? So does everybody, please pay attention to this

for a second. Suppose a government bond has a six percent coupon. A face value of

a $1000, and ten years to maturity. What is the price of this bond, given that

similar bonds yield an annual return of six%. What if the similar bonds yield four

percent and what if they. Yield eight%. So let's, before we take a break and you get

away for coffee or just go for a swim. . Just let's go through the mechanics of

this a little bit, and try to understand what it's talking about. So what I'm going

to do is, I'm going to develop the timeline and the formula. And then, we can

take a break, and then come back and do the number crunching. So. Let's draw the

timeline. The timeline is. If I remember right, how many years of this bond? Ten

years. However, what do you remember about bonds? The bonds of government bonds of

the US and I'm going to stick with those because that's what the data I'm showing

but you should be able to see this very clearly. Is. That they pay coupons every

six months and the nature of the pmt payment process determines the compounding

intervals, so zero through how much? Twenty. So that's the first thing. What

will happen at year point twenty which is year ten. What will happen here? You'll

get a 1000 bucks and this is called face-value. Very clear. Till now, what are

we talking about? A zero coupon bond. We just priced it. Here is a twist. It says

what? You will get a six percent coupon. And many times in the real world, the word

interest is used for coupon. I don't like that at all. To me, interest always

belongs to the market, doesn't belong to any entity. So, please I am going to be

painful and call it coupon. And the coupon rate of six percent is this, C over f, and

it's a percentage. So we know f is a 1000. So what is a coupon? Very simple. Six

percent of 1,000 is 60 bucks. However. Although this is all written in, on the

IOU, you know that the compounding interval is what? Every six months. So

what, what really is happening is you're getting 30 bucks and 30 bucks. And the

reason is over one year then you're getting 60 bucks. So 330 and the nature of

this bond is such that you also get 30 at the end. So how many 30s are you getting?

You're getting twenty 30s and how many thousands? One. Doesn't this remind you of

the loan? So 30 reminds you of what? The payment you pay on the loan. The only

difference between this, that the face value of a standard loan is. That the face

value of a standard loan is not there. You are just paying p.m.t., p.m.t., p.m.t.,

p.m.t.. Okay. So this the nature of the time line. Do I know end? Yes. Do I know

coupon? 30 bucks per six months. Remember I have to match end with the coupon. I

can't say 60 here. Okay. And what is R? R was six percent per year. Which is what?

Three percent per six months. In regard to details, so it's a very straight forward

problem to do and the two components of this. The price today will have a PMT

component. Right? 30 bucks. How many times? Twenty times, and the interest rate

is how much? How much is the interest rate? Interest rate is three%. Remember

half of six. And this is the PMT flow. And you'll do the pv of this. So this is the

nature of your PMT, and you'll do the PV of this. Plus you will do the PV of,

1,002. How many years from now? How many periods, Sorry? Ten years per periods.

Twenty. And then interest rate at three%. So the way to think of a coupon-paying

bond is it has two chunks. The first chunk. Is a PMT chunk. A present value of

a PMT chunk. The second is, present value of a one . So you remember, on the first

day of class, I broke up the introduction of PV and FV into two parts. First day, we

talked about single payments, the 1000 chunk. The next day, we talked about the

loans and so on, the PMT chunk. This is a combination of the two, just because the

nature of the beast is such that you have a final payment of $1000. So if you

understand the timeline, the formula and as I told you all of this is explicitly

stated in an IOU. Let's take a break and today, come back and crank through some

numbers. Okay, Take care.