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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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