[MUSIC] So, we saw in a very lively way what duration is and how you may not confused it with maturity. Let's have a look in this third video on the merits in investing in government bonds on other key concepts, and the first of these is the yield to maturity. Now how is it defined? The yield to maturity is the return you get on a bond if you hold it until maturity and the coupons are paid as agreed. So I give you one example here. Suppose that you pay today $95 for a bond, a short term bond which will mature in one year and will be refunded at par as we say or a face value of a hundred and in the meantime you get a coupon of $5. So in one year's time, you will get $100 back as the principle and you remember that big bottle on the rule, $100 back plus the coupon of $5. So question to you now is what is the year to maturity of this bond? So now we've just seen how to compute the yield to maturity of this bond. It's basically all the returns you make on the bonds, i.e. coupon plus principle. In this instance, it's 105 divided by the price you paid for this bond, 95. And you see that it gives you a return a year to maturity of 10.53%. Okay, so now we're going to see another key aspect. And indeed one, when I talk about it, it raises many eyebrows. Not just within my students, but also people I talk to family and friends that have difficulty in grasping why the price of a bond is inversely related to the yield. For the misconception is here quite simple to explain. People think that when your yield increases then your better off, right? It's better for you if you own a bond that suddenly yields 2% and in one years time possibly yields 3 or 4%. So you say I'm better off, why should the price of the bond decrease when the yield increases. Well, we can see the relationship on this chart. The red line depicts the 10-year bond index, it's a price index of the bond of ten years' treasuries in the US starting in 1990. You see that it rises, it goes from 105 to roughly 150 at the end of the period. And you can see that it correlates very strongly with the blue line, and the blue line is depicted on the right-hand scale, inverted. So an actual increase of the blue line on the chart is actually a fall in the yield. You see that it starts at roughly 8%. And it ends at roughly 2.5% which is more or less the bond yield today in the U.S. Okay, so there's this inverse relationship between the yield of a bond and the price of that same Bond. Well, let's think of this for a minute. I mean, shouldn't it be the opposite? Shouldn't it be that when the yield rises, the value of my bond increases? Well there's going to be a quiz. The next quiz for you is to find out, what is the rationale for thinking that when the yield of a bond rises, the price of that bond falls. Now, before we go into the formula which gives you the exact definition, and explains you why, when the year to maturity rises, the price decreases, I want to explain that with you in words. Suppose that I own a bond, Which yields 2%. It's a bond issued by the US Treasury and it yields 2%. Now, I bought it two years ago and just maybe in two months' time, the US Treasury issue a new set of bonds, but in the meantime, the deficit has risen so investors are kind of a bit wary of buying the treasuries because they think maybe the government will have difficulty in paying back the bonds it issued. And we'll see in the next video that this is one of the risks, the default risks, that you may encounter when you invest in bonds. Okay, so the government comes with a set of new bonds, and to make it attractive to these reluctant investor, they have to raise the yield, they have to get off for more yields. So say the new bond comes with a yield to maturity of 3%. Now does this new bond at 3%, and I still own mine at 2%, and say I don't want to hold it until maturity because I. I need the cash to buy a new car, or a house. So I want to sell my bonds. I have, say, $100,000 put into this bond yielding 2%. And I come to you and I say, would you buy my bond? And you're given this choice of saying 3% if I buy a new bond. 2% if I buy it from Michelle. Surely you will tell me hey, man, you can keep your bond. I don't find it very interesting. I prefer to buy the new one at 3%. To which I will answer wait a minute, if I give you a discount on the price of the bond. You pay it less than you would pay the bond which is yielding 3%, would you buy it from me? And you might say, yes, well, what kind of discount will you offer? Well, I will offer you exact discount on the price of a bond so that it yields 3%. So the year to maturity would be equated between the two bonds and on the old bond would be equated, because you reduce the prize. Okay, so now we know in words why there's this inverse relationship between yield and prize and this we show with this formula here. And this formula is familiar, should be familiar to you by now, it's the Net Present Value. And we seen in the video that it can be used to evaluate a company, the value of a company. But we can also use it to evaluate the price of a bond. And indeed you see this formula here where the bond price is some kind of net present value of the future cash flow, the future coupon and the principle which you get at the end. And the discounting factor, the opposite of the compounding factor. Discounting factor is precise and is yield to maturity. It's at the denominator of the formula. So, quite mechanically, if it rises the price of your bond or the value of your bond decreases. Indeed we have one graphical example here, we see that when YTM, the year-to-maturity, goes from YTM sub 0 to YTM sub 1. The price of your bond falls from P0 to P1 and you see that exactly with the formula attached to this chart. Now, in conclusion, we see that bonds are traditionally considered as a safe investment. Why? Because they secure a given stream of income and you get your principal normally in the end. We'll see that In the next video there might actually be some risks and that is not always guaranteed. Look at Greece for instance. They serve government and firms. In this instance, we talk about corporate bonds who needs to finance their activities. So to cover basically for their expenditures which may exceed the tax incomes they receive from a population. And we saw, now very importantly, in this video, that the year to maturity and prices of a bond are inversely related. And finally, and we'll see more of this when we talk about risks in the next video and also in another video which analyzes the impact of interest rates on equity and bond portfolio that the maturity of a bond is important but the duration is key. [MUSIC]