Portfolio Correlation coefficient

You can never have a proper portfolio or you can never build a proper portfolio if you ignore the idea of correlation. Because whether and to which degree assets move in sync, or in completely different cycles, is what is going to determine how much you can diversify your portfolio and again, we have not quite defined this concept of diversification just yet. The important thing is that you cannot have a proper portfolio if you ignore this concept of correlation. Now, correlation sometimes, you know, many of the things in finance are referred to with Greek letters. We have already seen Beta and correlation is one of those and the typical letter used to describe correlations is basically Rho (ρ).

Importance of Correlation

What is Correlations?

Correlation are always measured between pairs of variables. It could be two assets, it could be height and weight, and it could be anything. Any two variables can have a correlation and that correlation can actually be estimated.

What is the correlation and why that correlation is important?

What does correlation measure?

Correlation measures the strength of the relationship. I can have two variables, which again, could be the return of an asset and the return of another asset or it could be the height and the weight of all the people taking this course, right? In which case you more or less would expect a positive relationship, but that says something. It says that there are two things about correlation that are important.

• One, is the sign of the correlation, and the sign could be positive or it could be negative. If it is positive, it means that the two variables tend to move together. So where you would expect taller people to be a little bit, heavier and shorter people to be. A little bit lighter so in general if you actually look at it over a, a large number of people. You would expect a positive correlation between height and, weight. In the same way that you would expect a positive correlation in finance between risk and return. So one thing that is important. About those correlations is the sign. Is the correlation positive or is the correlation negative. If you were selling ice cream for example. In the end then you actually looked at sales of ice cream and temperature. Well more likely than not there is going to be a negative correlation because the colder is the temperature the less the ice cream you are going to sell. So a correlation could be positive or a correlations could actually be negative. Now that is not the only thing that matters.
• The other thing that matters in terms correlations are basically the strength of the relationship. Because its strength relationship can be very loose and by that, I mean that if you know the value of one of the two variables there is not much that you can say about the value of the other or it could be very strong and by very strong I mean that if you know the value of one variable. You can make a fairly accurate prediction in terms of what would be the value of the other variable. And so it’s important that you keep in mind these two dimensions of correlations.
• Correlations measure the sign. Positive or negative?
• Do they move together? Do they tend to move together, or do they tend to move in opposite directions?
• And the strength of that relation. Is there a clear relationship between the two?
• By knowing the value of one variable, can I make an accurate prediction or a very loose prediction about the value of the other variable?

So this correlation coefficient that we’re looking at. This row that we are looking at, measures the sign and the strength of the relationship between these two variables. And by measuring the sign and the strength obviously the sign can only be two. Could be positive or could be negative. Of course it could be zero, too, but that would be a very. Special case, and in terms of the strength, it could be weak or it could be strong. We’re going to get a little bit more technical in just a second. But for now let’s say strong relationship, basically tells me if I know the value of one variable. Gives me a very accurate prediction of the other. And the weak, if I know the value of one variable, it doesn’t tell me a whole lot. About the variable of the other. Now let us do a little bit of theory, just a tiny bit of theory. And, but this, this is important. The range in which correlations fall can go between one on the positive end and minus one on the negative end. Now, on the positive end, the meaning of a correlation equal to one. There is two important things. Remember that we’re looking at the sign. And we’re looking at the strength. Well, in terms of strength, it does not get any stronger than that. That is, if I can, if I could tell you. If you give me the value of one of the two variables. And I could tell you exactly what the value of the other is going to be. Then that is basically a correlation equal to one. That is what sometimes we call it deterministic relationship if you know the value of one. You can tell exactly, not approximately, not pretty accurately, but exactly what would be the value of the other. In other words, if you have X on one axis and Y on the other axis. The relationship between X and Y is given by a straight line, and all the points would actually fall along the line. So that if I give you the value of one, you could tell me exactly what is the value of the other. That would be a positive relationship, and a relationship equal to one. It does not get any stronger than that. It gives you total accuracy, total predictability. Know the value of one variable; you will know exactly the value of the other. Let us jump on the other end, and let us go to the range, to the value of minus one. Well, minus one means more or less the same, the only difference is that now, the relationship is negative. And so basically we have, if we have X here and Y here, we have a line with a negative slope. And all the points along that line would actually fall exactly along that line with a negative slope. And again it remains the case that if I give you the value of one variable. Then you can tell me exactly what will be the value of the other. In terms of the strength, it doesn’t get any stronger than that. So the two extremes plus one and minus one is as strong as a relationship can be. And it is as strong as it can be because then the relationship becomes deterministic. You do not predict more or less what the other variable will be. You actually predict exactly what the other variable would be. Now with the way I am expressing this, you can safely guess that in finance we do not have any relationship with values of one or values of minus one. There are no deterministic relationships in finance. So what matters, is whether we’re getting close to one extreme or close to the other. Because that would actually indicate a very strong correlation between the two. But in finance, you know, finance is not physics. In physics you, you have. And in mathematics, you have a lot of deterministic relationships. In finance, we do not have those. But it’s still important. Although we do not find in practice, variables, financial variables that are correlated equal to one. Or correlating equal to minus one. It is important that you know, that this is the highest possible value. And the lowest possible value because the closer we get to those extremes, then the stronger the relationship actually is. So, again, it is important to keep in mind that although in financial markets. We do not expect to find valuables that have a correlation equal to one or equal to minus one. The extreme values of the correlation coefficient, it is important to know the theoretical streams. Because what we really want to know is that the closer, the correlation coefficient gets to one. Or the closer it gets to minus one, then the stronger. Is the, the relationship between the two variables that we are looking at, and the more predictability there’s going to be between these two variables. Now, on the same token, as we get away from the streams and we are getting closer to zero. Then the relationship becomes weaker and weaker and weaker. And, and actually becomes weaker. Well, remember what that means. It basically means that if I give you the value of one variable there’s very little that you can tell me about the volume of the other. When we are getting, approaching zero on both from the positive side and from the negative side. Then we have more than certainty. Basically our model doesn’t work if I tell you one variable, there’s very little you can tell me about the value of the other variable. Now, here is one important thing. Although in theory, a correlation could be positive or could be negative, it could be all the way or all the way to minus one. For example if you look across world equity markets, or if you look at individual stocks within a market. If you look at long enough period of time, you’re going to find that all these correlations are positive. And the reason they’re positive, let us back to some of the issues we discussed,. In the first session that is something tends to pull all the returns in the same direction and that is what we call the market factor. That is each company will be affected by the lot of individual factors and in the portfolio sort of diversify way. But, there’s going to be someone pulling or something pulling the return. Those global factors, macro factors, pulling the return of all the companies in the same direction or all the market in the same direction. Remember, this is on average and over time. On any given year, some stocks will go up and some stocks will go down within the market. And some markets will go up and some markets will go down within the world market. But, what really matters is that you know, that degree of diversification that we obtain when we put all these assets together. Now, why is it that it is positive? Well it depends on that market factor but let me go back one. Final time to the to the markets we were working with in Session One. And if you actually look at last line now, that give you the correlation between each individual market and the world market. And so if you look at the 1.00 for the world market. Well that basically tells you that the correlation between a variable and itself is going to be one. It’s like plotting the same variable twice. And so by definition, the correlation between a variable and itself is always going to be one, but look at the other numbers. The US market, very high correlated with the world market. The Spanish market, pretty highly correlated with the world market. And the Egyptian market, much lower correlation with the world market. And this should not be surprising. The reason it should not be surprising is because Egypt is an emerging market. Emerging markets tend to be a little bit more isolated from large world capital markets and large world equity markets. And so you would expect that small more isolated markets. Almost by definition would have a lower correlation that large and more integrated market. But what I wanted to highlight with this. Look at the data that we’ve been looking at so far. Is that all these three correlations are positive. The correlation between the U.S. and the world market. Spain and the world market. And Egypt and the world market. All of them are positive. In different degrees. The U.S. is the most highly correlated. Egypt is the least highly correlated. But all of them tend to move in the same direction. That basically means remember. The fact that all the correlations are positive, that means that when the world market goes up, these three markets tend to go up too. It does not really, we’re not talking about causality here. We are not saying that because the world market goes up. The Spanish or the Egyptian market go up or the other way around. What we are saying is simply that they tend to move together. And just in passing let me mention that, that is an important thing. Correlation does not measure causation. And, and what basically that says. Is that when you say that two variables have a very large positive correlation, or a very large negative correlation. You are not implying anything about which one the determines the other. What you are saying is that they tend to move together. In the same direction or the opposite direction and that, they are very strongly related. However, you are not saying anything when you calculate a correlation in terms of which one is affecting the other. It does not matter whether x affects y or affects x, the only matter is. The only thing that matters is whether they tend to move together in the opposite directions. Whether their relationship is strong or their relationship is actually much weaker.

Portfolio Correlation coefficientCapital Budgeting TechniquesPortfolio Correlation coefficient You can never have a proper portfolio or you can never build a proper portfolio if you ignore the idea of correlation. Because whether and to which degree assets move in sync, or in completely different cycles, is what is going to determine how much you can diversify your...