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We are back. I have encouraged you to stare at this equation because it's very

Â important even though there are only two assets and answer the following, but first

Â understand what's going on. You've gone from investment in one Google alone into

Â investment into Google anyhow. But I've asked you a specific, two sets of things.

Â One, a realization that we talked about, that as soon as you go from one asset in

Â your portfolio to two, you create a dynamic, where there are variances of both

Â in there or standard deviations plus you create two relationships. It makes a lot

Â of sense, right? Okay. So, the question I left with you, which was most specific, is

Â when do you think you will not benefit from diversification? Or another way to

Â say that is when will sigma P be equal to the average sigma i's. How many sigma i's

Â are there? Two . In other words, there is no point in diversifying. Tell me the

Â intuition, and then we'll be done, the math I'll let you do. The intuition is

Â very straightforward. If, a row AB = one, what does that mean? That if Yahoo and

Â Google move perfectly together, all the time Yahoo goes up by one%, Google goes up

Â by one%. Yahoo goes down by one%, Google goes down by one%. Two%, two%. Sign and

Â magnitude are all going together. That will be, make sense. Why divide up your

Â money between two things which have different names, but are essentially the

Â same? How likely is this to happen? No, right? There's no such thing as two

Â perfectly same companies, okay? So, put in one here, substitute one here. And try to

Â show that this is true, regardless of magnitude. So, I'm now pushing you to do

Â this, right? You should be able to show it. It's simple Algebra, and I'm not going

Â to use numbers because I want you to run with this and do it. But the second

Â question is the following, before we move on. If you were to find a perfect

Â correlation between two investments, Google and Yahoo, what would be the main

Â source of risk in both? Would it be the market? Or would it be specific? Mark is

Â standing for market. I hope you r e cognize that given a broad two definitions

Â of risk. One which effects everything and one which is specific, which one it'll be?

Â Has to be this. Because market is common to both and relationships happen because

Â of common things. Whereas, if you were totally different personalities, i.e.

Â Google is in a totally different industry, has no market effect, and so is Google, I

Â mean, so is Yahoo. It would be a different story. But that's unlikely to happen.

Â Doesn't this make sense? It makes a lot of sense, and that's why I think, you know, I

Â keep saying this, it's the most fascinating subject. You don't need data,

Â almost, to convince yourself of what's going on, okay? Okay. So, let me show you

Â some graphs, similar to the regressions. Remember, I showed you some dots, in

Â regression. And look what's on the various axes. If you look at any specific graph,

Â and let's, let, I'm going to, purposely look at the middle one, because it's most

Â transparent, and please go back and forth. What do I have? Ra, rb. So, think of ra,

Â rb as the two securities in a portfolio or the relationship between two. And its good

Â to visually show two relationships, right? Because if you have three things going on,

Â it becomes a little bit difficult. So, that's why I am spending lot of time on

Â the relationship between two things. And this, you will see repeatedly happening

Â in, as I make the formula more complex. Okay, so let's stare at this and Art, my

Â question to you is, I'm going to have some fun with you. So, my question to you is

Â the following. What is on the top left graph? What am I showing on the top left

Â graph? All the dots align on the straight line. Yes. This is called a perfect

Â positive correlation. And within that context, why will I, when will it happen?

Â When the things common to both are the only thing driving. And that, we call the

Â market risk. Okay? What is at, so this is perfect positive. What is on the right

Â bottom? Same thing. But now, the relationship is what? Negative. And how

Â can you tell that? First of all, I've said it's negativ e, perfect. Perfect is all

Â dots are in a straight line. But now, the straight line is shaped like this, instead

Â of shaped like that. So now, you've seen the two extremes. What's in the middle?

Â What's going on here? This is dot all over the place, and I cannot see any

Â relationship between A and B, which is measured by a relationship of zero.

Â Another, another way to think about it is I can draw any line through this. It will

Â seem to make sense, okay? Good news is you can estimate this. You know, you can go

Â into Excel, as we have put up the note and say, what? Correlation, equals correlation

Â and then show, you can do this, equals correlation and then show array one, array

Â two. That means show me the data on A, show me the data on B. Where is it? And A

Â will be in the A column, B will be in the B column, or whatever. And depending on

Â the data, if you're 60, you'll say row, one through 60. If you're 50, you'll say,

Â row one through 50. The only thing we have to worry about it, is, they should be

Â matched with each other. So, you can't have Google's return in, in 1975 match

Â with Yahoo's return in 1985, that's a silly thing to do, okay? Because if you do

Â that, you're likely to show up here. Okay. Now, what's happening here? A negative

Â relationship. And what is happening here? A positive relationship. But not perfect.

Â So, let me ask you, in reality, which is the most likely run of these graphs? On an

Â average, if you pick two stocks, which is the most likely graph you'll see? Chances

Â are, this is almost impossible and that's the beauty of diversification. Why?

Â Because two things cannot be identical in every respect. They have to have some

Â unique reasons for moving. Similarly, probably the right low part is unlikely to

Â happen. I would actually say that this is also unlikely to happen, simply because

Â almost everything that we see is affected by the common market and in a positive way

Â perhaps. But I am, you could see scenarios and this is possible. So, so, what I am

Â saying is prefect relationship, I'm ruling out, I am just sa ying probabilistically

Â finding this is much lower than right top. And the reason is, for the right top is,

Â things are not perfectly related, but they would have a common thing. And that common

Â thing is called? The market. And they have a positive relationship with the market

Â typically, most companies. So, this gives you a sense of what's going on in the real

Â world. I'm going to ask you one question which has nothing to do with Finance.

Â Where do you think love is? Think about the person you love the most. And you are

Â A, they are B, he or she. Which graph signifies love? And it is also, I believe,

Â the graph on the right top. Because if you're looking for a perfect relationship,

Â there's no such thing. And, in fact, it's the wrong thing to look for. You're

Â looking for yourself in that person, you know? That's probably not the right thing

Â to approach love. It's noisy. There's tension. But hopefully, the relationship

Â is positively inclined. Okay, so bless you. Let's take a break. I hope you

Â enjoyed these graphs. We'll come back and move on to three assets with the

Â following. This is a short piece, I wanted you to look at data visually and get a

Â sense of where we are headed. And we'll come back. While you are taking a break,

Â think about where is Yahoo and Google likely to be? Where are they likely to be

Â on this graph? And closer to which, which of these graphs? You have some hints and

Â you can intuitively think. That's the awesomeness of this. So, see you. Quickly,

Â take a quick break, unless you are doing some exercises and so on, which is fine.

Â But I expect you to think about this as we go along.

Â