[MUSIC] So, point number one, the goal of diversification, the ultimate goal of diversification is to maximize, to get the highest possible risk adjusted returns. Point number two Point number two sort of follows from the first. And that is that when I do diversify a portfolio, would I obtain as a result is the possibility of choosing the combination that gives me the highest,. Risk adjusted return. So, not only the goal of diversification is obtaining the highest possible risk adjusted return. The result of diversification is obtaining that highest possible risk adjusted return. And I want to illustrate this by putting together an emerging market and a developed market. Spain as an example of a, a developed market. And China as an example of an emerging markets. And what we're going to do is we're going to look at this little picture. And this little picture actually is built on the behavior of the Spanish market and the Chinese market over the last ten years. Between 2004 and 2013. And so the numbers that you're seeing there, over the last ten years, the Spanish market generated a mean annual return of 11.9%. The Spanish market also generated a volatility of 28.1%. The Chinese market generated a mean annual return of 19.6% and the volatility of the market, over there, the Chinese market over that period was about 39% So, look at the poem that is actually label Spain. If I had put all my money in Spain, over the last ten years, then my mean annual return would have been 11.9%. And my volatility would have been 28%. If I had put all my money in the dot in the point labelled CHN China then my mean annual return would have been 19.6%, and my volatility would have been 39 percent. Now, we're talking about diversification. And therefore what really matters is combining the Spanish market and the Chinese market. And for that, we need to keep one thing in mind, which is what we talked before, correlation. And if you look at the correlation there you see it on, on the screen as .6. That is actually not an extremely high correlation. But as we said before. It's positive which means that in the long term Spanish market and the Chinese market tend to move more or less together. Not very closely. Related but more or less in the positive direction. And that means that both of them in the longterm they tend to go up. Now again what we're saying, look at the blue line there. That blue line is basically different combinations of the Spanish market and the Chinese market. So the first point to the left and above Spain is a combination in which you invest 90% of your money in Spain, and 10% of your money in China. That 90%, that 90 10% combination between Spain and China actually gives you a return and a risk of that portfolio, and that is identified by that dot. As we move, actually to the right and above, then we're basically decreasing the proportion of Spain in the portfolio and increasing the portfolio of China. So let's look now at the first point to the left and below the CHN point. That is a portfolio that is invested 90% in Chinese market and 10% in the Spanish market. So all those infinite points in fact Along the blue line are what we call feasible portfolios. Are portfolios that I could have built, that I could have had by combining the Spanish market and the Chinese market. All right. Now let's look at a couple of important points along that blue line. Point number one, that I want to highlight is that one. Now that one, as your eyes could tell you, is the point that goes furthest to the left. And if you look actually at the bottom line, what we're measuring on the horizontal axis is risk. And that means that the point that goes furthest to the left. Is of all the possible combinations between Spanish market and the Chinese market, we get the combination that gives me the lowest possible risk. And in our case, that is the lowest possible volatility. So for example, in that particular case that is 87% in Spain, and 13% in China. If I had invested over the previous ten years 87% of my money in Spain, and 13% of my money in China, that would have given me the combination between. These two markets that would have led to the lowest possible risk measured in terms, of volatility. And that actually would have enabled me to let's say, the Spanish investor, to reduce risk from 28.1% to 27.8%, a little bit. A tiny little bit, not much, but it's a reduction in risk, and notice that that reduction in risk came at the same time with an increasing return. If I had been solely invested in Spain, my mean annual return would have been 11.9%, but because I put 13% of my money in China, my mean annual return was actually higher 12.9%. So, if I'm a Spanish investor that diversified into the Chinese market, and decided to put 87% of my money in Spain, and 13% of my money in China. I won two ways. I won because my risk is a little bit lower, and I won because my return has actually been higher. So I win in, in two different dimensions, I have lower risk, but I also have a higher level of return. Now, you can always find people that say look, I've been investing in my own market forever, and I can take the volatility of that market. I'm kind of used to the volatility of that market. Well, that's not a reason for not diversifying. And the reason for that is, let's look at this other green point. That other green point is actually roughly 74% invested in Spain, and 26% invested in China. And by construction, that particular portfolio has the same volatility as the Spanish market. So that, what that means is that if I had had over the last ten years, 74% of my money invested in Spain, and 26% of my money invested in China, the volatility of that portfolio would have been 28.1%, which is exactly the same volatility that it would have had if I had been fully invested in Spain. But, you can see what the difference is. The difference is that my mean annual return would have been 2% points higher, 200 basis points higher by being properly diversified. So this is like a free lunch. In fact diversification is what sometimes we call in finance the last free lunch, that you can find in markets. Because in this case by going out of Spain and investing part of my money in China. About a quarter of my money in China, and three quarters of my money in Spain. I ended up with a portfolio that has, the same level of risk, but a higher level of return, than putting all my money in, in Spain. So this is a reason for diversifying. We can get a little bit of a free lunch, and it's easy to explain why the Spanish investor is always better off. Because in the first point, he reduces risk and increases return. And, in the second point he gets the same level of risk, and gets a, a higher, an even higher return. Now, it's a little bit more difficult if you look at that picture to sell diversification to the Chinese investor. And, the reason it's a little bit more difficult, it is because you cannot offer. The Chinese investor. A way to win in both directions. Notice that if we move from the point labeled CHN to the first point to the left and below. At that point what we're doing is yes we're reducing the risk of the portfolio, but we're also reducing the returns. And so now we face a trade off. The Chinese investor can get actually, a lower level of risk by diversifying into Spain, but it's the sacrifice of that the cost of that is expecting lower returns. That didn't happen to the two points that we had seen before in Spain, you know in, in the two points, in the two diversification strategies that we have seen before this Spanish investor in one. He won two ways, by reducing risk and increase in returns and in the other, he was not wore soft in one way, in terms of risk, but was much better off in terms of return, well unfortunately. We cannot offer that for the Chinese investor. Does that mean that there's no way to convince the Chinese investor that he should diversify in Spain? No, it doesn't mean that. And the reason is, let's look at these numbers here. Now, let me be clear about what we have here. The first two columns are proportions of our money invested in the Spanish market and in the Chinese market. And notice that if you go line-by-line, all those first two weights always add up to one. So in the first case, I have all my money invested in Spain and nothing in China. In the last case I have all my money invested in China, and nothing in Spain. And then in the second case, if I have 90% of my money invested in Spain then I have 10% of my money in China. Whatever I don't invest in one market, I invest in the other. So the sum of those two weights is always going to be equal 1. Which means my portfolio is always fully invested. The next two columns return and risk are the numbers that generated the blue line in the picture that we have seen before. So, that blue line that you're seeing now again has been generated from the two numbers, that we labelled return and risk in this particular picture. So that's another way of saying that is that, each portfolio each combination of the Spanish market, in the Chinese markets gives me a return and a risk that is consistent with that particular portfolio. Now, what's really important for us now, because remember how we got to these numbers and to this picture. We were thinking about ways of convincing the Chinese investor that he needs to diversify, too. Now, the last column. Is basically the third column divided by the fourth. So for example if I divide 11.9 by 28.1 than I get 0.424. If I divide, I'm going to the very end now, 19.6% by 39%. I get 0.503. So, if I divide the return column by the risk column, I get the last column which RAR. And that RAR is basically risk adjusted return. Very quick and very direct way of calculating risk adjusted return. Again there are much more technical and better ways of looking at risk adjusted return but by putting one divided by the other, we're basically, basically getting a measure again, quick and dirty, of risk adjusted return. And remember, what investors want at the end of the day is to get the highest possible risk adjusted return. Well, that's where you have it. In this particular case, if you put 40% of your money in the Spanish market, and 60% of your money in the Chinese market, then you actually will maximize. The combination between risk and return of the Spanish market and the Chinese market. Now here comes the interesting thing. I could show you mathematically that you will never find that maximum risk adjusted return, by putting all your money in Spain, or by putting all your money in China. In other words, if you try to find the highest possible risk adjusted return it's always going to be somewhere in between. And being somewhere in between, means that you're splitting your money between the two markets. And basically it means that you're diversifying. It's a very important result. If I'm combining two assets, and the correlation of those two assets is any number lower than one, and remember that in this case is .6, I will never get. The highest risk adjusted return by putting all my money in one market or by putting all my money in the other market. I will always find the highest risk adjusted return by putting my money somewhere in between and in this particular case, it happens to be, 40 60 in some other cases maybe 90, ten or 25, 75, it doesn't really matter. But it's never going to be all my money one market, and no money in the in the other market. [MUSIC]