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And that coefficient and first and foremost and

Â the far more important thing about the correlation coefficient.

Â I know statistics can be boring.

Â I used to teach statistics I know that nobody likes it.

Â And when you start talking about correlations and

Â things like that and co-variances.

Â People sort of disconnect this is not for me, this is not interesting.

Â You do have to pay attention here because and let me speak here from

Â a financial point of view from a portfolio management point of view.

Â You can never have a proper portfolio.

Â You can never build a proper portfolio if you ignore the idea of correlation.

Â Because whether and to which degree.

Â Assets move in sync, or in completely different cycles,

Â is what's going to determine how much you can diversify your portfolio.

Â And again, we haven't quite defined this concept of diversification just yet.

Â But what is important for

Â you to keep in mind is that you cannot have a proper portfolio.

Â If you ignore this concept of correlation.

Â Now, correlation sometimes, you know,

Â many of the things in finance are referred to with Greek letters.

Â We've already seen Beta and correlation is one of those.

Â And the, the typical letter used to describe correlations is basically Rho.

Â So, sometimes when you hear people talking about Rho they basically talking

Â about correlations.

Â And, what we're going to spend a few minutes now is,

Â is in trying to understand why these correlations are very important.

Â So first, let's, let's define it.

Â Correlations are always measured between pairs of variables.

Â It could be two assets.

Â It could be height and weight.

Â It could be anything.

Â Any two variables can have a correlation.

Â And that correlation can actually be estimated.

Â Now, how do we estimate the correlation for us, at this particular point,

Â it's not important.

Â The technical note is going to help you a little bit with that.

Â But what is important is that you understand the concept.

Â What is the correlation and why that correlation is important.

Â Now, first, what does it measure?

Â Well, it measures the strength of the relationship.

Â I can have two variables, which again, could be the return of an asset and

Â the return of another asset.

Â Or it could be the height and

Â the weight of all the people taking this course, right?

Â In which case you more or less would expect a positive.

Â Relationship, but that basically says something.

Â It says that there are two things about correlation that are important.

Â One, is the sign of the correlation, and the sign could be positive or

Â it could be negative.

Â If it's positive, it basically means that the two variables tend to move together.

Â So where you would expect taller people to be a little bit, heavier and

Â shorter people to be.

Â A little bit lighter so

Â in general if you actually look at it over a, a large number of people.

Â You would expect a positive correlation between height and, weight.

Â In the same way that you would expect a positive correlation in

Â finance between risk and return.

Â So one thing that is important.

Â About those correlations is the sign.

Â Is the correlation positive or is the correlation negative.

Â If you were selling ice cream for example.

Â In the, and then you actually looked at sales of ice cream and temperature.

Â Well more likely than not there's going to be a negative correlation because

Â the colder is the temperature.

Â The less ass, the less ice cream you're going to sell.

Â So a correlation could be positive.

Â Or a correlations could actually be negative.

Â Now that's not the only thing that matters.

Â The other thing that matters in terms correlations are basically the strength of

Â the relationship.

Â Because it's strength relationship can be very loose and by that I mean that.

Â If you know the value of one of

Â the two variables there's not much that you can say about the value of the other.

Â Or it could be very strong.

Â And by very strong I mean that if you know the value of one variable.

Â You can make a fairly accurate prediction in terms of what would be the value of

Â the other variable.

Â And so it's important that you keep in mind these two dimensions of correlations.

Â Correlations measure the sign.

Â Positive or negative?

Â Do they move together?

Â They tend to move together, or do they tend to move in opposite directions?

Â And the strength.

Â is, is there a clear relationship between the two?

Â By knowing the value of one variable, can I make an accurate prediction or

Â a very loose prediction about the value.

Â Of the other variable.

Â So this correlation coefficient that we're looking at.

Â This row that we're looking at, measures the sign and

Â the strength of the relationship between these two variables.

Â And by measuring the sign and the strength obviously the sign can only be two.

Â Could be positive or could be negative.

Â Of course it could be zero, too, but that would be a very.

Â Special case, and in terms of the strength, it could be weak or

Â it could be strong.

Â We're going to get a little bit more technical in just a second.

Â But for now let's say strong relationship,

Â basically tells me if I know the value of one variable.

Â Gives me a very accurate predication of the other.

Â And the weak, if I know the value of one variable, it doesn't tell me a whole lot.

Â About the variable of the other.

Â Now let's do a little bit of theory, just a tiny bit of theory.

Â And, but this, this is important.

Â The range in which correlations fall can go between one on the positive end and

Â minus one on the negative end.

Â Now, on the positive end, the meaning of a correlation equal to one.

Â There's two important things.

Â Remember that we're looking at the sign.

Â And we're looking at the strength.

Â Well, in terms of strength, it doesn't get any stronger than that.

Â That is, if I can, if I could tell you.

Â If you give me the value of one of the two variables.

Â And I could tell you exactly what the value of the other is going to be.

Â Then that is basically a correlation equal to one.

Â That is what sometimes we call it deterministic relationship if

Â you know the value of one.

Â You can tell exactly, not approximately, not pretty accurately, but

Â exactly what would be the value of the other.

Â In other words, if you have X on one axis and Y on the other axis.

Â The relationship between X and Y is given by a straight line, and

Â all the points would actually fall along the line.

Â So that if I give you the value of one,

Â you could tell me exactly what is the value of the other.

Â That would be a positive relationship, and a relationship equal to one.

Â It doesn't get any stronger than that.

Â It gives you total accuracy, total predictability.

Â Know the value of one variable, you will know exactly the value of the other.

Â Let's jump on the other end, and let's go to the range, to the value of minus one.

Â Well, minus one means more or

Â less the same, the only difference is that now, the relationship is negative.

Â And so basically we have, if we have X here and

Â Y here, we have a line with a negative slope.

Â And all the points along that line would actually fall exactly along that

Â line with a negative slope.

Â And again it remains the case that if I give you the value of one variable.

Â Then you can tell me exactly what will be the value of the other.

Â In terms of the strength it doesn't get any stronger than that.

Â So the two extremes plus one and minus one is as strong as a relationship can be.

Â And it's as strong as it

Â can be because then the relationship becomes deterministic.

Â You don't predict more or less what the other variable will be.

Â You actually predict exactly what the other variable would be.

Â Now with the way I'm expressing this, you can safely guess that in

Â finance we don't have any relationship with values of one or values of minus one.

Â There are no deterministic relationships in finance.

Â So what matters, is whether we're getting close to one extreme or

Â close to the other.

Â Because that would actually indicate a very strong correlation between the two.

Â But in finance, you know, finance is not physics.

Â In physics you, you have.

Â And in mathematics, you have a lot of deterministic relationships.

Â In finance, we don't have those.

Â But it's still important.

Â Although we do not find in practice,

Â variables, financial variables that are correlated equal to one.

Â Or correlating equal to minus one.

Â It's important that you know, that this is the highest possible value.

Â And the lowest possible value because the closer we get to those extremes,

Â then the stronger the relationship actually is.

Â So, again, it's important to keep in mind that although in financial markets.

Â We do not expect to find valuables that have a correlation equal to one or

Â equal to minus one.

Â The extreme values of the correlation coefficient,

Â it is important to know the theoretical streams.

Â Because what we really want to know is that the closer

Â the correlation coefficient gets to one.

Â Or the closer it gets to minus one, then the stronger.

Â Is the, the relationship between the two variables that we're looking at,

Â and the more predictability there's going to be between these two variables.

Â Now, on the same token, as we get away from the streams and

Â we're getting closer to zero.

Â Then the relationship becomes weaker and weaker and weaker.

Â And, and actually becomes weaker.

Â Well, remember what that means.

Â It basically means that if I give you the value of one variable there's very little

Â that you can tell me about the volume of the other.

Â When we are getting, approaching zero on both from the positive side and

Â from the negative side.

Â Then we have more than certainty.

Â Basically our model doesn't work if I tell you one variable,

Â there's very little you can tell me about the the value of the other variable.

Â Now, here's one important thing.

Â Although in theory, a correlation could be positive or

Â could be negative, it could be all the way or all the way to minus one.

Â For example if you look across world equity markets, or

Â if you look at individual stocks within a market.

Â If you look at long enough period of time,

Â you're going to find that all these correlations are positive.

Â And the reason they're positive, its back to some of the issues we discussed,.

Â In the first session that is something tends to pull all the returns in

Â the same direction and that is what we call the market factor.

Â That is each company will be affected by the lot of individual factors and

Â in the portfolio sort of diversify way,.

Â But, there's going to be someone pulling or something pulling the return.

Â Those global factors, macro factors, pulling the return of all the companies in

Â the same direction or all the market in the same direction.

Â Remember, this is on average and over time.

Â On any given year, some stocks will go up and

Â some stocks will go down within the market.

Â And some markets will go up and

Â some markets will go down within the world market.

Â But, what really matters is that you know, that degree of

Â diversification that we obtain when we put all these these assets together.

Â Now, why is it that it is positive?

Â Well it depends on that market factor but let me go back one,.

Â Final time to the to the the markets we were working with in Session One.

Â And if you actually look at last line now,

Â that give you the correlation between each individual market and the world market.

Â And so if you look at the 1.00 for the world market.

Â Well that basically tells you that the correlation between a variable and

Â itself is going to be one.

Â It's like plotting the same variable twice.

Â And so by definition, the correlation between a variable and

Â itself is always going to be one, but look at the other numbers.

Â The US market, very high correlated with the world market.

Â The Spanish market, pretty highly correlated with the world market.

Â And the Egyptian market, much lower correlation with the world market.

Â And this should not be surprising.

Â The reason it should not be surprising is because Egypt is an emerging market.

Â Emerging markets tend to be a little bit more isolated from large world

Â capital markets and large world equity markets.

Â And so you would expect that small more isolate markets.

Â Almost by definition would have a lower correlation that large and

Â more integrated market.

Â But what I wanted to highlight with this.

Â Look at the data that we've been looking at so far.

Â Is that all these three correlations are positive.

Â The correlation between the U.S. and the world market.

Â Spain and the world market.

Â And Egypt and the world market.

Â All of them are positive.

Â In different degrees.

Â The U.S. is the most highly correlated.

Â Egypt is the least highly correlated.

Â But all of them tend to move in the same direction.

Â That basically means remember.

Â The fact that all the correlations are positive,

Â that means that when the world market goes up, these three markets tend to go up too.

Â It doesn't really, we're not talking about causality here.

Â We're not saying that because the world market goes up.

Â The Spanish or the Egyptian market go up or the other way around.

Â What we're saying is simply that they tend to move together.

Â And just in passing let me mention that, that is an important thing.

Â Correlation does not measure causation.

Â And, and what basically that says.

Â Is that when you say that two variables have a very large positive correlation, or

Â a very large negative correlation.

Â You're, you're not implying anything about which one the determines the other.

Â What you're saying is that they tend to move together.

Â In the same direction or

Â the opposite direction and that they're very strongly related.

Â But you're not saying anything when you calculate a correlation in terms of

Â which one is affecting the other.

Â It doesn't matter whether x affects y or affects x, the only matter is.

Â The only thing that matters is whether they tend to move together in

Â the opposite directions.

Â Whether their relationship is strong or

Â their relationship is actually much weaker.

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