Welcome back. As I said, I have set up your thinking hopefully for the next phase. We are going to talk about bonds and stocks. Bonds this week. Stocks next week. They are very important to integrating our knowledge and let's just see what a bond is. The good news with bonds is, you already know what they are, okay. But let's go slowly. Like the word suggests, bonds bind people. So the bond is like a contract between two people. One giving money, one getting money. We have seen these before. In fact, the most generic notion of a bond is a loan. And I want to make one thing very clear. A loan can be made, or is made usually between one institution, a bank and a person. So you take a mortgage loan. We did a loan for cars. We did a loan going to business school. You do a small loan to run your business. All of these are typically, typically contracts. Entity, that is wherever you are and another entity, usually a bank. So I want you to understand that that's also a bond. The bonds we'll talk about today are a little bit more and those are contracts that can then be traded on their own. And I think that's awesome, in some sense, right? Because I have money to borrow. I don't have to just have the possibility of just going to the bank. Why shouldn't I be able to borrow from the public at large? And then it be traded later. There are advantages to doing that. There are advantages to working with a bank too, so I'm not trying to say one is clearly dominant over the other. There's a lot of research on both. All I'm saying is, why not have both? Having said that, remember, this explicit IOU that's common to an entity versus an entity and common to what a bond is that we'll talk about which is issued by one entity to everybody who wants to lend money. It's an explicit IOU, both are explicit IOUs. But one is an IOU that's between two specific entities and one is an IOU between an entity and a population in general. Okay, so I will start off with the kind of entity that we all know about. And the reason is, unlike the peculiarities of corporate bonds which I'll spend very little time on right at the end. Common bonds are issued by everybody, every country. So when you have to borrow money, you being the government, you issue an IOU and it's called a bond, right. And usually in America it's called a government treasury bond. In your country, wherever you are, it'll have a name which will be very explicitly associated with the government. And by the way, it's not just the federal or the major central government that issues bonds. In the US for example, municipal, state governments, state entities also issue bonds, okay? And there are tax laws that are different across different bonds. What I'm going to do is, I want to stay away from the tax laws because you can Google it stuff like that. So whenever you can Google something, it's probably not reached that stage where thinking deeply involved, right? As I said though, once in a while I Google like who am I. Google kind of stares at me and says if you haven't figured it out, how do you expect me to, but one day I think we will know the answer to that. So lets keep moving, we are talking about common bonds. And my favorite bond is the Zero-Coupon Bond which we'll keep coming back to. And what does coupon mean? Remember, that coupon is something that's paid periodically, and we'll do that in a second. Whereas a bond pays coupon periodically. Remember the PMT? That's like a coupon. But a bond, typically issued by the government and corporations, pays in two ways. One is a coupon, like a PMT, and the other is face value or fixed amount at maturity. And luckily it's a round number. It's not like 22.232 makes you miserable thinking about decimals anyways, all right. So the bond that I'm talking about right now pays only once and at maturity. Maturity is when the bond contract is over. Okay, so we'll see in a second, timelines will come in again. An example of such a bond is a Treasury bill or strip in the United States. What I'm going to do today too is given that we are going to talk about publicly traded stocks and bonds today. And next week we will talk about what is happening in the market. I'll go on a website and show it to you. And then you can be on your own and kind of search around. I think it's pretty cool. Okay, so. Discount bonds are, Zero-Coupon bonds. Why are they discount? So let me just, let me ask you this, before we do this little formula. So, this is what the timeline looks like. Zero, and some period n, right? What does this point to? So one year passes, two year passes, three year passes, four year passes. It doesn't have to be years. It can be periods. Turns out, actually, in the US, the period is six months. That's how bonds are priced on a six month periodic basis because that's when coupons are paid. What does this bond do? It doesn't do anything here. Zero, zero, zero, zero and then gives face value F. So that's the timeline. And the nature of this beast is very simple, right? So you start off with things that are very straightforward. So what is this? This says give me some money today, which has not been indicated. Give me some P today. For a future value, in the future obviously. Remember this is the very first class, where we talked about single payments. So it is something very simple for you to understand. What is the face value? Typically, it's a round number. And in our examples, just for simplicity, we'll use 1000. It could be 100, 1000, it's not going to be a strange number. Okay, and so what is the question going to be? I have to give you this and n and it should be a very simple problem to solve. Everybody okay with this? So I want to be very clear on a Zero-Coupon bond. So knows coupons, it is also called discount. Why is that? For a very simple reason, R is greater than 0. If R is greater than 0, the price of a bond you know has to be less than face value of this kind of bond. Why? Because there's no coupons to compensate for the decrease in value of F when you discounted that. So please don't think it's on sale. Don't think you're making, creating somehow making money, no, no. Just compensating you for the time value of money, right, and in a fair way. So the reason why it's also called a discount bond, when you hear that word. As soon as you hear unqualified discount bond you should be able to think zero-coupon, okay. So let's do examples. First, a very simple example. Suppose a zero-coupon bond pays $1,000 exactly one year from now. What is the price of the bond today if the interest rate on similar bonds is 2%? And whenever I say interest rate unqualified, what does it mean? Monthly, quarterly, yearly? Always annual. So I'm going to give you a very simple example, and then do another one, and then we'll take a break, okay? This is very simple, right? I shouldn't have to do this on a calculator. I mean, video, that is. You have to obviously use a calculator because you're dividing. So face value is 1,000. What is n, 1. So what do you do? You take 1,000 and divide by 1.02 raised to power of 1. I'm just being a little painful here. Okay, so the answer is $980. How do you make sure your answer is right? Remember the beauty of finance? Make sure your answer is right take 980.39 multiplied by 1.02. What should you get? You should get exactly $1,000. And if I made a mistake, fix it, all right? Making mistakes is okay in life. In fact, I promise you one thing, during these classes, I have made mistakes. Hopefully they are small ones like typing in the wrong number and so on. I'm trying to focus on the fundamentals being right and not so much on calculations. This is too simple, right? Okay, let's do a more complicated problem. And by the way, as I said, I'll show you real data today. So another concept which I'll now give you, related to bonds, is something called yield-to-maturity. Pretty simple to explain right? What does yield mean? It is another word for kind of a return. To maturity means what? Till maturity. Maturity is the length of the bond. Remember, bond is a contract. It has to specify the length of time and it has to specify the amount of money, at various stages, before you're willing to enter that contract. Is that, yeah? So what is this bond? Remember we are still in zero-coupon bond world. What is the yield-to-maturity of a 10-year zero-coupon bond with a face value of a $1000 and a current market price of $744.09. You can literally open up the newspaper and look for this bond and you'll find it. Okay, the face value may not be 1000, it may be 100, but that's just a 0 or a 10 depending on how you look at it. So look at the formula. So what have I done? I have replaced the r, the little r by yield-to-maturity. And I'm asking the following question. If I take $1,000, how many periods from now, ten periods from now. And I'm here and I tell you this price. And I have 1 to 10 periods. I'm asking you, what is the rate of return built into this relationship? So you know the price has to be face value over one plus yield-to-maturity raised to power n. What is the number? I don't know. This, because I've told you this, and I've told you this. And how have I told you this? That IOU that you get from the government tells you this. Is says the face value is 1,000 and the coupon rate is 0. C over F, the coupon is a fraction of the, but it's not paying any. So notice what's going on. What's the problem here? If this was a one period problem, you could do it in your head. So what does the yield-to-maturity remind you of? In finance what we do, like in lot of stuff in life, we create new terminology so that you get confused. What is the yield-to-maturity in this context? Does it remind you of something? Yep, it should. It's the IRR of the bond. So, if you solve for IRR, what do you get? You just have to worry about the fact that ten years have passed, so remember, you have to do some little bit of math, and that's about it. Please do it. And the answer is 3%. I'll go and show you a simple way of doing this stuff on a calculator. You just have to hang on for a second. But let me just move on because this is not going to be a difficult thing, it's just a calculation thing. But let me ask you this, supposing you wanted to confirm whether 3% was right, what would you do? You would take $1,000 and do its PV at what rate, 3%. And how many periods left, 10. And what answer should you get? PV for 1,000, 3% is the rate of return built into the bond. If you hold it till maturity, the price has to be this. If it's not, there's something wrong, and you can trade on it. And trading happens when the pricing doesn't seem right. All right? So even if it's off by $0.01, you know these bonds trade more than anything else. And simply because they are viewed, as we will see in a second, as risk free, okay? And we'll see why. But right now, let's stay on the mechanics. Is this clear, yep, okay. Let's do one more twist of it and then we'll, I think it may be a good idea to just think about what we've been talking about. What comes first, price or yield-to-maturity? If you go back to the problem I gave you price and you figured out yield-to-maturity. What comes first? Many people think both happen simultaneously and I agree. Because if you know the price you know the yield-to-maturity. If you know the yield-to-maturity you know the price, all right? One and the same thing. But I like to think you know the price before yield-to-maturity. People don't go walking around saying, you know Thinking in terms of percentages. No, the government comes and does literally this. I am going to give you thousand dollars ten years from now, it's in an auction actually, how much will you pay me today? So you've got to figure out value in your head. You carry value in your head, not percentages. In some senses, the fact that I'm saying yield to maturity and price are determined together, I still believe that we think of price value first, right? Just like an auction. You want to buy an Apple? How much will you pay for it? Similarly, do you want to buy $1,000, 10 years from now, how much will you pay for it? And built into that exercise for that is the yield to maturity. What makes the yield to maturity of a zero coupon bond risk free? This will keep coming and the reason is, if you start now, buy it for 744.09 and hold it 'til this time, hold it for the entire time. What are you sure to get? You're sure to get the $1,000. So remember, there is, if you hold it, that's why it's called yield to maturity. If you hold it 'tll maturity, remember, there's nothing happening in between. You're just holding it. You will get the 1,000. Of course, what's the assumption there? The government is still there and these days that's quite become questionable too. So remember value in finance is not by what you state you're going to do, it's what people perceive what's going to happen. So the same government will for sure to pay 10 years from now. We are struggling. Many times I think would you rather buy a bond issued by Google or by the U.S. government? [LAUGH] I'm not sure which is risk free, but that's just part. Don't believe just because a government is issuing it, it's risk free. But we'll take that as a basic thinking right now, that the government will go after other things if it does. So let's do one more twist on that problem we just did, and let's just real world twist. Turns out, for government bonds, in the US at least, the compounding interval is six months. And if that's the case, what's the yield to maturity if the price is the same? So, suppose I fix the price at $744.09. What is the yield to maturity on a ten year bond? It turns out, what will it do? And we'll take a break after this. What do you do? You remember this, right? If every six months you're doing the best thing to do is what? Change your timeline. So make this 1, 20. How much are you getting at the end? Still 1,000. Just for the sake of argument I'm just fixing this price at 744 just to make you think a little bit, great question. What would you say about the yield to maturity compared to the last one? What was the last one? 3%, that's why I fixed the price. Face value is fixed, too. You would want to say half of it, right? You would want to say 1.5%. And that's where you might as well take a dagger and shove it right in my gut, because what are you ignoring? Always pause, you're ignoring compounding. So the number has to be less than 1.5, right? So please do this exercise. Make sure I got the number right. What will you do? You'll do the PV of $1,000, how much N? 20. And what is the interest rate? 1.489. And what should you get? Good old 744.09. Let's take a break. Think about this, it's the simplest part. See you soon.
