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Â Which brings us to result number three.

Â And result number three is that when I get to gain the most by diversifying,

Â is when the correlation of the assets that I've been in the portfolio, is lower or

Â is relatively low, compared to what I already have.

Â In other words, the lower the correlation between the asset that I bring and

Â the portfolio I already have, the more I stand to gain in terms of diversification.

Â Now, let me make a very quick experiment here.

Â I've done this in many different courses and

Â in many different types of people, and they actually always tend to guess wrong.

Â Until you give them a little bit of time to think about it and

Â then they realize the right result.

Â Let's suppose we form two portfolios.

Â Portfolio number one.

Â Here we're going to put the US, and Canada, and

Â Germany, and the UK, and Japan.

Â All very large stable developed countries.

Â And portfolio number two, we're going to put emerging markets.

Â So we're going to put Mexico and Brazil, we're going to put Hungary and

Â the Czech Republic, and we're going to put Indonesia and Malaysia.

Â All right? So we have a portfolio of

Â developed markets, and a portfolio of emerging markets.

Â Which portfolio is going to be more volatile?

Â The vast majority of people,

Â just about I would say, everybody would guess that portfolio one will be,

Â the one of developed markets, would be far less volatile than portfolio two.

Â And that is the mistake of not thinking about correlations.

Â Because, the problem here is that each

Â individual asset in the develop market portfolio,

Â has less volatility than each individual asset in the emerging market portfolio.

Â But, and these two things matter from the portfolios point of view.

Â The correlations across the developed market are far

Â higher than the correlations across the emerging markets.

Â And that is a critical part of the risk of a portfolio.

Â So, if you just think of the average volatility,

Â then obviously the emerging market portfolio is going to be more volatile or

Â far more volatile, than the developed market portfolio.

Â If you take into account that these markets,

Â the emerging markets are far less synchronized than developed markets are.

Â That actually pulls the return of the portfolio quite a bit down.

Â To the point that, you know, if you actually look at properly diversified

Â developed markets' equities portfolio, and a properly diversified emerging markets'

Â equity portfolio, yes you might find that this one's a little bit more volatile, but

Â typically a lot, a lot, a lot less than most people would tend to think.

Â And let me illustrate this with the comparison between developed emerging and

Â frontier markets.

Â Developed markets I guess that most of you know,

Â we're not going to put any formal definition here.

Â Emerging markets are let's say one step below.

Â They're not as large or not as liquid.

Â As developed markets and frontier markets are even one step below.

Â For example, developed markets the US and Canada.

Â Emerging markets Brazil, and Mexico, and Hungary, and the Czech Republic.

Â Frontier markets, maybe Bulgaria, Romania.

Â Or some other Latin American countries.

Â Like could be Bolivia relatively smaller markets in Asia.

Â And so, you know, you would think, and, and

Â most people would tend to think that developed markets are less volatile than

Â emerging markets, and emerging markets are less volatile than frontier markets.

Â Well, guess what?

Â That is typically the case, but

Â here you have a recent article from the Wall Street Journal.

Â And it says Investors Rewarded for Trek Into Little Known Markets.

Â And the little known markets,

Â this is basically an article about Frontier markets.

Â But here comes the interesting thing.

Â Look at that picture.

Â That picture shows volatility over time of developed, emerging, and frontier markets.

Â And look at those numbers there.

Â Volatility of a diversified portfolio of emerging markets in the year 2013, 24%.

Â Developed market volatility in 2013, 23.7%.

Â That's what's the point that I was illustrating before.

Â Most people would tend to think that an emerging market portfolio would be

Â far more volatile than a developed market portfolio.

Â Well look at what the data shows.

Â In the year 2013, the emerging market's portfolio was

Â just a tiny bit more volatile than the developed market portfolio.

Â But look at the last number.

Â Those frontier markets that are even more volatile than individual emerging markets.

Â Well, they're more volatile than individual emerging markets, but they're

Â also less correlated than developed markets and that the emerging markets.

Â And therefore, look at that number 17.4.

Â They're actually less volatile than a portfolio of emerging markets, and

Â less volatile than a portfolio of developed markets.

Â Now of course you would not expect that to be the case all the time.

Â You would expect over time, over a long period of time,

Â if frontier markets to be a bit more volatile than emerging markets, which in

Â turn you would expect them to be a little bit more volatile than developed markets.

Â But at the end of the day, you know, because you need to think in terms of

Â individual correlations and also, individual volatilities when you bring

Â everything into a portfolio, sometimes the results may not be exactly what we expect.

Â This is a quote from that article.

Â It says individual frontier markets can be quite volatile, but

Â as a group there is a much lower correlation between them.

Â So when you blend them together in a portfolio, you get much lower volatility.

Â And not so much about frontier markets, but about emerging markets, pulling in

Â more or less in the same direction, this article from the Financial Times.

Â It says, if you look over the past ten years, taking this market individually,

Â you will find that their volatility has been quite high.

Â But if you put them together into an index or a portfolio,

Â then you find the standard deviation and the volatility tend to be very low,

Â because the correlation between the individual countries is also very low.

Â So that is the key.

Â And a critical point to understand.

Â That when you're thinking about the risk of the portfolio,

Â individual volatility is important, but

Â correlations within the assets of the portfolio is just as important.

Â And that is the critical result in terms of diversification.

Â So going back, keep in mind those three results that go to the heart of what

Â diversification is all about.

Â Result number one, that you have you know,

Â minimizing risk sounds okay, maximizing returns sounds okay, but

Â when you really think about it you neither want to do one nor want to do the other.

Â What you really want to do is to get the best possible combination between

Â risk and return.

Â So result number one, diversification's goal and

Â result is basically to get the possible, the maximum possible risk adjusted return.

Â Result number two, that is what we get when we diversify.

Â We'll never get the highest possible risk adjusted returns by putting all our

Â money in one asset, or by putting all our money in the other asset.

Â The maximum risk adjusted return will always be somewhere in between,

Â when we are diversified.

Â And result number three is that the correlation.

Â The lower the correlation, the better the risk of the portfolio,

Â the lower the risk of the portfolio is going to be.

Â So lower correlations help me diversify.

Â Help me lower the risk of the portfolio.

Â So in short,

Â in order to sort of conclude session two of this course remember two things.

Â One, the critical concept of correlation that measures the sign and

Â strength of two variables, which can be weak or strong, positive or negative.

Â Remember this is not a statistical, boring mandate.

Â It is absolutely essential from a practical point of view to understand and

Â to build a proper portfolio.

Â And concept number two, diversification with the three points that we

Â just highlighted, that it enables you to maximize risk adjust and return.

Â And whenever you're thinking of bringing more assets into

Â your portfolio from the point of view of reducing risk,

Â the lower the correlation, the more you'll be able to reduce that risk.

Â So in sessions three and four, we're going to talk about the cost of capital,

Â which in a way is somewhat unrelated to this, but

Â as you'll see we're going to find a way as we anticipated a little bit before.

Â The CAPM, the model that we're going to use to calculate the cost of equity, or

Â the required return on equity is based on beta.

Â Beta is a measure of risk when you're properly diversified, and

Â that's why all that is very much related to the topics that we just discussed.

Â So I she, I see soon in session three of this course.

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Â