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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Â numbers. Okay, Take care.

Â