[MUSIC] Okay, so first session on risk and return. We're basically going to first of all we're going to think a little bit about how we calculate a periodic return and a periodic return is basically the return on any given period. Now, in finance we never look at one period. Sometimes we may look for any specific purpose. But when want to evaluate the performance of assets, what we basically do is to aggregate performance over time. And in order to do that we need to aggregate information into statistics into measures that tell me something about the return characteristics and the risk characteristics of different assets. So we're going to look at two different ways of calculating mean returns, and two different ways of assessing risk. And importantly, in everything that follows in this session, we're not going to be looking at any formula, this session is complimented by two technical notes and all the formulas and expressions that you need are contained in those two technical notes. So what we're going to do here is to maximize the intuition, the understanding of each of these variables that are used to describe returns and risk. And then you're going to, go a little bit deeper, into the actual calculation of these managers. And then you're going to test yourself, with a little problem set in order to see whether you're understanding the concepts or not. So, we're going to start right away. And the first thing that we're going to do is to define a periodic return. And first thing about it, about this in the simplest possible way. If you buy an asset, if you buy a share of stock and you buy it at the beginning of the year and you sell it at the end of the year when you compare the price at which you buy and the price at which you sell that price might have gone up or it might of gone down. If the price goes up, then you obtained a gain, and we call that a capital gain. And if the price went down, then you obtained a loss and we call that a capital loss. So be, when you compare the price at the beginning of the period and the price at the end of the period, one of the two sources of return is what we call a capital gain, or a capital loss. Now on top of that, many assets actually pay you a cash flow. Some companies pay dividends. Some bonds pay coupons and that basically is the cash flow that you put into your pocket. And it will be part of your return. So again, if you buy a share at the beginning of the period and sell it at the end of the period, not only you can get that capital gain or loss, which is given by the change in price between the beginning and the end of the period, but you also can pocket the cash flow, which again. Could be a dividend, could be an interest payment if it's a bond, and on, and on, and on. Once you put together these two sources of returns, then that is what you actually get your return. Except for the fact that we need one more step. And the one more step that we need is typically we express everything, both the change in price and the cash flow that we get, relative to the price at the beginning of the period. And that basically means, well, that the reason for this is simple is, it's not the same thing to actually get a capital gain and a cash flow when you paid $2 for a share of the stock than when you paid $10 for a share of the stock. So suppose that between the beginning and the end of the period and there was a capital gain of $1. And you actually got a dividend of $1. Well that's a $2 gain that you actually got. One from the changing price and one from the cash that you put in your pocket. So if you paid$2 for that share of the stock then you actually got a very big return. That is, you got $2 in terms of gain compared to $2 that you paid at the beginning, but if you had paid 10 or 20, or $30 for that share, in proportional terms what you actually got in terms of return is much lower when you pay 10, 20, or $30. So what we typically do, in order to calculate that return, is to standardize, to divide everything by the price that we paid at the beginning of the period. So you can put now in the back of your head, and again I don't want to do any formulas at this point. But in order to calculate a return, you basically need two things. You need a change in price between the beginning and the end of the period. You need to know the cash flow that you're putting in your pocket, if any between the beginning and the end of the period, and once you have those two, components you add them up and you divide the whole thing by the price that you paid at the beginning of the period. All right, so those are the two sources of gains that you get when you buy your share of stock. And now we're going to look at a set of data. And, and let me clarify a few things about the data that you're seeing. You're seeing there three equity markets. And, it's important that we understand that this is equity. This is not debt. So, these are stock markets. These are broad diversified indices. This is not, for example, in the case of the US, the widely used S&P 500, all these are Morgan Stanley indices. And it doesn't really matter, Morgan Stanley, Financial Times, Dow Jones. There are many providers of data, this just happens to be Morgan Stanley data. And they are basically broad indicators of the performance of the equity market in each of the three countries that you are seeing there. Now, in the last column you have the world market, and that is basically an aggregation of all the equity markets, developed markets and emerging markets put together into one. So that world equity market is basically the composite of developed and emerging markets all together and all expressed in the same currency to which I would get to in just a minute. So. A couple of characteristics about those returns. Characteristic number one they are, all of them, what we call total returns. And total returns basically mean that we don't leave anything out. That means that we're putting together the change of price, between the beginning and the end of the period. But we're also putting together the cash flows, paid by the companies in the index. So when you look at, for example, that 10.7% for the year 2004. In the case of the US, that means that when you put together the change in the value of the index between the beginning and the end of the period, and you put together the cash flow, the dividends paid by all the companies in the index. When you aggregate those two things and put it relative to the value of the index at the beginning of the period you get that 10.7%. Okay. So characteristic number one of those returns is that they, they are again they are total returns and that means we're putting together all of the sources for which we can get a return and that means capital gains or losses and dividends paid by these companies. Characteristic number two. All of them are expressed in terms of dollars. If you're actually looking at those three first countries the, the local currency in each country's different and typically we would express the returns in that particular currency. Now because we want to make some comparisons, and we will make those comparisons a few minutes from now. We want to put everything in the same currency and that currency is the dollar. And we also do that because if you look at the last column, that world market portfolio we're aggregating many countries with many different currencies and that is like adding apples and oranges, it doesn't really make any sense. Unless you add the map in the same currency and that's why we're, again we're using the dollar as that particular currency. So keep in mind that the characteristics of those returns. Number one is that they're expressed in dollar, number two that they still have their total returns and that they're put together all the sources from where we can get gains. All right? Now, we're going to go back. And we're going to think a little bit in terms of the in terms of the following and that is suppose that I ask you to tell me something about the performance of the US Market or the Spanish Market or the Egyptian Market, well you're not going to be looking at one year you, you ideally would like to be looking at a relatively long period of times. Which means that you're going to have a series of many returns they could be annual returns, they could be monthly returns, they could be daily returns. What we have here are annual returns, the ones that were looking at, but ideally if I want to be able to tell you something about the relative performance of the U.S. market, the Spanish market or the Egyptian market or any other market then I would like to look at a longer period of time. And the problem is not a problem but what happens is that when I am looking at a long period of time you know, just looking at a series of returns is not going to help me. Maybe making a little graph might help me a little bit, but maybe not a whole lot. So what I need to do is to summarize information. And summarizing information basically brings im, implies bringing all the numbers together into one specific measure. And that measure could be something that describes returns, or something that describes risk, or something that describes, as we're going to discuss in the next session, risk adjusted returns. [MUSIC]