[MUSIC] Which brings us to result number three. And result number three is that when I get to gain the most by diversifying, is when the correlation of the assets that I've been in the portfolio, is lower or is relatively low, compared to what I already have. In other words, the lower the correlation between the asset that I bring and the portfolio I already have, the more I stand to gain in terms of diversification. Now, let me make a very quick experiment here. I've done this in many different courses and in many different types of people, and they actually always tend to guess wrong. Until you give them a little bit of time to think about it and then they realize the right result. Let's suppose we form two portfolios. Portfolio number one. Here we're going to put the US, and Canada, and Germany, and the UK, and Japan. All very large stable developed countries. And portfolio number two, we're going to put emerging markets. So we're going to put Mexico and Brazil, we're going to put Hungary and the Czech Republic, and we're going to put Indonesia and Malaysia. All right? So we have a portfolio of developed markets, and a portfolio of emerging markets. Which portfolio is going to be more volatile? The vast majority of people, just about I would say, everybody would guess that portfolio one will be, the one of developed markets, would be far less volatile than portfolio two. And that is the mistake of not thinking about correlations. Because, the problem here is that each individual asset in the develop market portfolio, has less volatility than each individual asset in the emerging market portfolio. But, and these two things matter from the portfolios point of view. The correlations across the developed market are far higher than the correlations across the emerging markets. And that is a critical part of the risk of a portfolio. So, if you just think of the average volatility, then obviously the emerging market portfolio is going to be more volatile or far more volatile, than the developed market portfolio. If you take into account that these markets, the emerging markets are far less synchronized than developed markets are. That actually pulls the return of the portfolio quite a bit down. To the point that, you know, if you actually look at properly diversified developed markets' equities portfolio, and a properly diversified emerging markets' equity portfolio, yes you might find that this one's a little bit more volatile, but typically a lot, a lot, a lot less than most people would tend to think. And let me illustrate this with the comparison between developed emerging and frontier markets. Developed markets I guess that most of you know, we're not going to put any formal definition here. Emerging markets are let's say one step below. They're not as large or not as liquid. As developed markets and frontier markets are even one step below. For example, developed markets the US and Canada. Emerging markets Brazil, and Mexico, and Hungary, and the Czech Republic. Frontier markets, maybe Bulgaria, Romania. Or some other Latin American countries. Like could be Bolivia relatively smaller markets in Asia. And so, you know, you would think, and, and most people would tend to think that developed markets are less volatile than emerging markets, and emerging markets are less volatile than frontier markets. Well, guess what? That is typically the case, but here you have a recent article from the Wall Street Journal. And it says Investors Rewarded for Trek Into Little Known Markets. And the little known markets, this is basically an article about Frontier markets. But here comes the interesting thing. Look at that picture. That picture shows volatility over time of developed, emerging, and frontier markets. And look at those numbers there. Volatility of a diversified portfolio of emerging markets in the year 2013, 24%. Developed market volatility in 2013, 23.7%. That's what's the point that I was illustrating before. Most people would tend to think that an emerging market portfolio would be far more volatile than a developed market portfolio. Well look at what the data shows. In the year 2013, the emerging market's portfolio was just a tiny bit more volatile than the developed market portfolio. But look at the last number. Those frontier markets that are even more volatile than individual emerging markets. Well, they're more volatile than individual emerging markets, but they're also less correlated than developed markets and that the emerging markets. And therefore, look at that number 17.4. They're actually less volatile than a portfolio of emerging markets, and less volatile than a portfolio of developed markets. Now of course you would not expect that to be the case all the time. You would expect over time, over a long period of time, if frontier markets to be a bit more volatile than emerging markets, which in turn you would expect them to be a little bit more volatile than developed markets. But at the end of the day, you know, because you need to think in terms of individual correlations and also, individual volatilities when you bring everything into a portfolio, sometimes the results may not be exactly what we expect. This is a quote from that article. It says individual frontier markets can be quite volatile, but as a group there is a much lower correlation between them. So when you blend them together in a portfolio, you get much lower volatility. And not so much about frontier markets, but about emerging markets, pulling in more or less in the same direction, this article from the Financial Times. It says, if you look over the past ten years, taking this market individually, you will find that their volatility has been quite high. But if you put them together into an index or a portfolio, then you find the standard deviation and the volatility tend to be very low, because the correlation between the individual countries is also very low. So that is the key. And a critical point to understand. That when you're thinking about the risk of the portfolio, individual volatility is important, but correlations within the assets of the portfolio is just as important. And that is the critical result in terms of diversification. So going back, keep in mind those three results that go to the heart of what diversification is all about. Result number one, that you have you know, minimizing risk sounds okay, maximizing returns sounds okay, but when you really think about it you neither want to do one nor want to do the other. What you really want to do is to get the best possible combination between risk and return. So result number one, diversification's goal and result is basically to get the possible, the maximum possible risk adjusted return. Result number two, that is what we get when we diversify. We'll never get the highest possible risk adjusted returns by putting all our money in one asset, or by putting all our money in the other asset. The maximum risk adjusted return will always be somewhere in between, when we are diversified. And result number three is that the correlation. The lower the correlation, the better the risk of the portfolio, the lower the risk of the portfolio is going to be. So lower correlations help me diversify. Help me lower the risk of the portfolio. So in short, in order to sort of conclude session two of this course remember two things. One, the critical concept of correlation that measures the sign and strength of two variables, which can be weak or strong, positive or negative. Remember this is not a statistical, boring mandate. It is absolutely essential from a practical point of view to understand and to build a proper portfolio. And concept number two, diversification with the three points that we just highlighted, that it enables you to maximize risk adjust and return. And whenever you're thinking of bringing more assets into your portfolio from the point of view of reducing risk, the lower the correlation, the more you'll be able to reduce that risk. So in sessions three and four, we're going to talk about the cost of capital, which in a way is somewhat unrelated to this, but as you'll see we're going to find a way as we anticipated a little bit before. The CAPM, the model that we're going to use to calculate the cost of equity, or the required return on equity is based on beta. Beta is a measure of risk when you're properly diversified, and that's why all that is very much related to the topics that we just discussed. So I she, I see soon in session three of this course. [MUSIC]