We're back. I have encouraged you to stare this equation because it's very important, even though they're only two assets and answer the following. First understand what's going on. You've gone from investment in one Google alone into investment into Google and Yahoo but I've asked your specific two sets of things. One a realization that we talked about is that as soon as you go from one asset portfolio to two, you create a dynamic with variances of both in there or standard deviations. Plus, you create relationship makes a lot of sense, right? Okay. So the question I left with you, which was more 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 there too? Then will that happen? In other words, there's no point diversifying. Tell me the intuition and then we'll be done. The math I'll let you do [LAUGH]. The intuition is very straightforward. If row AB is equal to 1, what does that mean? That if Yahoo and Google moved perfectly together all the time, Yahoo goes up by 1%, Google goes up by 1%. Yahoo goes down by 1% Google goes down by 1%, 2%, 2% sign and magnitude are all going together. That will be make sense. Why divide up your money between two things which have a different name but essentially the same? How likely is this to happen? Low, right? There's no such thing as too 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 recognize that given a broad two definitions of risk, one which affect everything and one which is specific, which one will it 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 I keep saying this, it's the most fascinating subject. You don't need data almost to convince yourself for what's going on, right? Okay, so let me show you some graphs similar to the regressions. Remember, I show you some dots in regression and look what's on the various axis. If we look at any specific graph and 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 your portfolio or the relationship between two and it's good to visually show two relationships, right? Because if you have three things going on and becomes a little bit difficult. So that's why I'm spending a 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 r, my question to you is I'm going to have some fun with. 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 are lying on the straight line, yes? This is called a perfect positive correlation and within our context, when will it happen? When the things common to both are the only thing driving and that we call the market risk, okay? 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, life said it's negative perfect. Perfect is on, all dots are on the 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. And although another way to think about it is I can draw any line through this. It'll seem to make sense. Okay, Good news is you can estimate this. You could go in tow, Excel as we have put up the North and say what correlation equals correlation and then show you can do this equals correlation and then show array 1, array 2. 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 column or whatever, and depending on the data, if you're 60 we'll 01 through 60. If you have 50 0, 1 to 50 the only thing you have to worry about it, they should be matched with each other. So you can't have Google's return 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 one of these graphs? On average, if you pick two stocks, which is the most likely graph you'll see, chances are this is almost impossible. 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 in a positive perhaps, but you could see scenarios in that this is possible. So what I'm saying is perfect relationships, I'm ruling out, I'm just saying probabilistically finding this is much lower, then right top. And the reason for the right top is things are not perfectly related, but that 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 with? Think about the person you love the most, and you are a, they're b. He or she fit 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 is no such thing. And in fact, it's the wrong thing to look for, your looking for yourself in the other person. 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 will 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're 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 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're doing some exercises and so on, which is fine. But I expect you to think about this as we go along.