I promised you today that I would start showing you some ideas of risk coming in without having formulas, without having you to worry about it explicitly. But I think it's a good idea when you start talking about investments like you could buy a government bond and you think there's no risk but actually, there is. Things like that I have to deal with. Then I'll talk a little bit about corporate bonds. The only reason I'm talking about them today is not because corporate bonds are popular all over the world, but to show you that it's not very different from government bonds, except for additional sources of risk. We'll talk about risk and return later explicitly. But for now, in the context of loans and bonds, let's talk about interest rate risk. Think about this. Right now we're government bond, and what are we expecting? That if the government bond says coupon 30, 30, 30, and 1,000, we are expecting it to pay. We're expecting what is called no default. Let's keep that risk out of the picture. But the fact of the matter is that just because I buy a government bond and because I believe it'll pay for sure does not mean there's no risk. Let me just briefly cover the concept of risk. The uncertainty concerning bond values, prices due to interest rate fluctuations is known as the interest rate risk of bonds. In other words, given that I have the payments fixed and the government is expected to pay for sure, the only source of risk is price is changing because the discount rate or the interest rate, or the comparative cost of capital is changing. There are two types of this risk. One is called price risk and the other is called coupon reinvestment risk. I want to talk about both and I want to give you an intuition for both. I don't want you to be too worried about trying to do the math right now because as I said, the main focus of this class is to do value creation. This is something I believe you need to know at a gut level, you may not need to deal with. But if you have the patience for it, it'll also give you a sense of how risk works and I really like this stuff. So bear with me. It's cool stuff. Timeline once more and I'm going to be a little slow on this to give you a sense of what's going on. Suppose we start with zero-coupon and here's the bond, here's the 1,000, and for simplicity, let's assume it's 10 years, which actually I'll change to 20 periods. Why? Because six-monthly compounding is built into the pricing of all bonds. Everybody got it? Okay, let's start. You buy this bond here and let's assume its return built-in yield to maturity is about 1.489 percent. Why am I choosing this number? We just did this example right a while ago. This price today was about 74.09 if I remember right. Just confirm all of this, please. We have done it earlier. When will I surely get 1.489 percent? But how much in six months when if I hold this bond till maturity? This is called yield to maturity. I still have some risk. Even though I get $1,000, I want to emphasize one thing; you still have some risk built-in. The reason is the inflation built into the pricing of this bond reflected in this is at time zero, and the actual inflation is going to be a little bit different over time. That's the first one. But we're going to ignore inflation risk, we're talking about real stuff. Just talk about the $1,000 we will get for sure. 1.489 is the built-in return that I'll get per six month. First point, do I have to get exactly 1.489 every six months? Answer is no. That's one of the things about yield to maturity. It is an average I'll get over 20 periods. But it will go like this, like this, whichever way in the middle, and that's the key here, is that while time is passing, interest rates are changing. The reason I can immunize myself, and that's actually a word we use, immunize; like get a shot against changes, is by holding it till maturity. But meanwhile, things are bouncing around, and that's the point. Suppose after five years, which is about 10 periods from now, because of some financial need, I'm forced to sell this bond. Because of some financial need, I'm forced to sell this bond. You have become awesome at time traveling. Tell me, what will the bond's price be 10 years from now? Think again to your finance that the awesomeness of finance is you time travel. Quick question, will it be something that you know for sure? No. But that has never stopped us from valuing things. Imagine yourself first thing at this point, and then where should you look, past or forward? Forward. You know that the price at time 10, 10 periods from now, which is five 5 from now, has to be what? A $1,000 divided by what? One plus yield to maturity raised to power what? How many periods left? Ten. Question is this number you don't know today, which is this yield to maturity. At which point? At point 10. You know your yield to maturity today. It's the interest rate today. Ten years from now you don't. What is this going to do? Suppose yield to maturity fluctuates and becomes greater than 1.489 per period, what will happen to the price of the bond? It'll be lower than you expect. On the other hand, interest rates are bouncing around and it's gone below 1.489, because inflation has dropped or whatever in expectation. What will happen to the price of the bond? It'll go up. The point is not whether it'll go up or down, the point is, you do not know this standing today. You know P_20. Why? Because it's 1,000, and you expect the government to pay up. But you do not know P_10. That's called price risk. Just think about it. I'm going to come back to the other risk in a second. Think about it. What is price risk? I'm going to go back to the timeline in a second. Price risk we defined today as not knowing the price. Even if I have a zero-coupon bond, it has price risk at all points before 20, or all points before maturity. Because if I had forced to sell it in the future, I don't know what the price is. This is what happens. Price goes up if yield to maturity goes down, and the opposite is true. This is called price risk. It's in every bond. It doesn't matter what bond you have; coupon paying bond, not coupon paying bond. But suppose you now have coupon bonds and just give you some flavor of risk. Remember, it is so logical. I want you to follow the logic. Don't worry about the details here. Risk is very intuitive. Let me draw the same 20, 1,000. Now what's happening? Every period you're getting 30 bucks. Quick first question, and think very carefully before you answer. Suppose I hold this bond till maturity, and suppose the yield to maturity in this bond is two percent. Its pricing is such that the yield to maturity is two percent. Well, if I hold this bond till maturity, will I get the two percent per six months actually? It doesn't matter whether it's two or five. The question is very simple. Can you calculate the yield to maturity of this bond? What do I need to tell you? The price. Suppose price today is 1,000, what is the yield to maturity? Three percent. The price today is lower, it's higher, and higher it's lower. Just for simplicity, if you understand this problem better, let's make it three percent. We know that if the yield to maturity is three percent, which is exactly the coupon rate of three percent, we'll get exact face value. Let's make it very simple. You buy it for 1,000 and face value is 1,000. That's simply an artifact that the two things, coupon rate and yield-to-maturity, are the same. Which one of these are fixed? The 30 bucks is fixed. Yield to maturity changes. Quick question for you. What if I hold this bond till maturity and get the 1,000? Will I have a three percent yield to maturity? If you think about it, you want to say yes, but the answer is no. The reason is this number will change in the future, it's bound to. Markets change, inflation changes, the only thing fixed is the 30 bucks, so it's changing, the three percent is changing over time. Why is that risky? Because imagine at three percent, what are you going to do with this 30 bucks? When you get the first 30, what you're going to do? You're going to put it under your mattress. What will you do? You'll put it in the marketplace and you think, how much will it earn per period? Three percent, it's called coupon reinvestment risk. Why? Because built into your thinking is, when you get money and you keep it under the mattress, it's losing interest, so what are you going to invest every $30 at three percent? But the three percent is like little change. What's going to happen? Even if I hold bond till maturity which pays coupon, it has coupon reinvestment risk. Why is that? Because I do not know the future yields to maturity and therefore, I do not know how much the 30 bucks every time I get, it'll earn for me. Why is coupon reinvestment risk not in a zero-coupon bond? It sounds like a silly question. The answer is very straightforward. If it doesn't pay a coupon, you don't have to worry about what reinvestment you're going to do. There are two risks and let me just finalize everything one more time and it'll give you a sense. Remember again, be cool about this, don't worry about getting it perfectly right. Here's the thing. You're getting 30 bucks, 30 bucks, a 1,000 bucks. Suppose for some reason I have to sell this bond after year 10, I'll get two things, I have to worry about two things. What is the price 10? It'll be the PV of how many p means 30, payment 10, how many of them? Ten left and face value of a 1,000. You know this price will change depending on interest rates and if interest rates go up, if r goes up, price goes down. That's one simple rule. There are a few things in life that rarely work all the time, this is one of them. However, that was the only thing you would have to worry about if there was no payment. What you do have to worry about is though, what is the value of these at this point? Remember, you've been getting 30, 30, 30, so now you have to look at the value of these when you're selling them. These have risk too. Coupon reinvestment risk is the future value at time 10 of coupon of 30, n is equal to 10 times. This is also not known, so you have both risks. The good news is what? If r goes up, you benefit, if r goes up, you lose. The awesome thing about this is a coupon paying bond if interest rates go up in the future, that helps you for what? The part that you are reinvesting the coupons but when you sell it you know it's going to hurt you for the remaining value of the bond. They move in opposite directions and there is this notion of immunization which says, you can manage your portfolio that you perfectly balance the two risks. That's called being immunized. Now I'm going beyond the scope of the class but I wanted to just give you a flavor that even simple government bonds have risk built into them. One last time, what is the only strategy that is without risk? One, where you buy a zero-coupon bond and hold it till maturity. What I want to do now is spend about five minutes on corporate bonds and then we'll take a break and I'll come back and do some cool stuff, show you some data. One of the values of doing bond and stocks, as I said, is that you probably at a personal level, you start connecting with things and doesn't have to be that you're working in a company and so on, right? Corporate bonds almost always pay coupons. Corporate bonds are largely US phenomena and, as I said, there's no reason why we shouldn't have all kinds of opportunities to borrow and lend but they are largely a US phenomena. In most countries, "The bond" quote unquote is between an entity, you, the corporation, and a bank, just like individuals. Like government bonds, they are subject to interest rate risk. Why? Because they promise a coupon and the promise of face value and there's risk involved. But they also are subject to something called default risk. Default risk is the risk of not getting paid what you thought you would. People perceive that government bonds will pay for sure, or at least relative to companies, will pay for sure. However, corporate bonds may have problems and by the way the financial crisis has shown us tons of this. It turns out they're rating agencies that rate corporate bonds they say, AAA bond, is what? They rate bonds of sovereign countries too, but what they say is AAA is, for example, the best kind of rating you would get, and then AA and so on, so forth. I'm not going to go into too much detail but the notion of rating is an outside arm's-length party, is trying to tell you the investor as what exactly is the chances of default for this bond? Very tough to predict. Default risk, and models have been built and lot of effort goes into it but it's not an easy thing. One last thing, most bonds are contracts and loans. So corporate bonds are also contracts and loans. I do not want you to think that just because the word bond is used, it has to be coupon, coupon, coupon, face value. Bond inherently is any loan but most credit bonds issued by governments have coupon, coupon, coupon, face value. One last question for you. Suppose you have two identical bonds, same maturities, same coupon rates, one government, one corporate, okay? Sticking with our example, 30 bucks every six months issued by a government bond or a corporate bond and face value 1000, identical. Quick question for you, which will sell for less? I'm giving you, I'm saying come on guys. Corporation X 1000, face value 30 every six months for 20 times. Government of the US doing the same, which will sell for less. If you know the answer, you know risk. The one that will sell for less, because one that you perceive will have a chances of default. Why would you pay more for something that's likely to not pay you what it promises. So the thing that will sell for less typically is a corporate bond. Not because it's a corporate bond. The name doesn't mean anything. It's just your perception of actually what's going to happen in the future. Why? Because exactly what I just said. You perceive that all 30 plus thousand the government will pay but some of the 30 and maybe the 1000 will not be paid by the corporation. The thousand is likely to be more subject to default because it's so much larger but it also depends on what situation the company is when that payment is due. Okay? I will take a break. We have done a lot on bonds today, which was our plan but I do not want to leave this without introducing you to real-world data and how finance is just what we talked about is happening out there. I'm not pulling things out of a hat and that's what I love about it, is that it is everywhere, and it's only in the eye of the beholder that the difference is there. If you are an investor, you're looking at giving money to a company or to the government and vice versa. They're just borrowing from you. See you in a little bit, take a break and will go on the web.
