I'll revisit what we did, not all the formulas. But basically what we did was conceptually showing that as you diversify into large portfolios, keeping in mind that you're not putting all your eggs in one basket still. Which is what diversification means is that you are not putting everything in technology, Google, Yahoo, Microsoft, all these companies, but instead you're spreading your wealth across, so that's diversification. What's the bottom line? Let's spend a few minutes in this relatively short piece, because I want to go here to become real, and then we will go into actually exciting stuff of going back and trying to evaluate orange, remember? It's been a long journey, but hopefully filled with data and a lot of intuition, so let's get started. Variance of an asset matters. Variance of Google matters only if you have put all your money in Google or most of your money in Google. Or most of your money or all of your money on very few things, because personalities do matter when the group is very small, and this also reflects about humanity. Most of what human being gets in life of all of us, we're social people and relationships matter much more than your personality though we are hung up on making superheroes out of all of us, and focusing on the person so much. Anyway, so variance of any asset is unimportant when held in large diversified portfolios. Remember the word large is a little bit misleading because what did I say here? As long as it's greater than 30, the more operative word is diversified. Let me show you little graph which you should be able to generate if you're really good at computing and you want to do analysis with a lot of data, this is what happens. Suppose this is the standard deviation of your portfolio and this is the number of securities in your portfolio. It around one, so on so forth. This is what happens. It starts off roughly here and you are randomly choosing, you're drawing this graph many times. This is what you see. Believe it or not, round about 30, what starts happening? Your ability to reduce risk starts becoming slow. Thirty is not a magical number, but it's [inaudible] , we telling you some following sense. By the way around 30, things start behaving normal too, so 30 may be a magical number or not. But anyway so as you progress, what are you doing? You start off with one, [inaudible] , and you start adding others. Those others have to be from different industries. Large, therefore is not that key, what's key is diversification. What happens? Risk keeps dropping till it levels off. Maybe what's going on is when you pick 30 things, they are randomly chosen rather than specifically. What you end up doing is you're creating a portfolio that's pretty diversified, so adding more doesn't help. However most of us invest in mutual funds or we invest in existing ones. So if you want to invest in S&P 500, you can do that. The costs is nothing, it already exists, but it's got 500 in it. That doesn't mean you're spending money for buying each one of them. The beauty of a mutual fund and a existing portfolios is, the work has already been done. Vanguard has pushed that envelope I think rightly so, where they are just charging you the minimal amount and telling you that creating your own portfolios could be costly for two reasons. One, you may not be diversified and you may be inclined to choose within one industry even though you are risk-averse. But more importantly, just from a transaction cost perspective, it doesn't make sense to create 30 of your own and spend money on each one of them and buying and/or selling. Why not buy the whole? That's the second thing which is practically a very important thing to know. Third, specific risks are diversified, only relations among the asset's matter, and let me just spend some time on this. The way you think of specific is like this and you'll see this. What was this? By the way, this tilde on top is to show that something's random. So what is this? This is called Epsilon and it's noise. Suppose things are bouncing around, on average the value is zero, but it's bouncing around without any relationship with anything. If you add another one of them, so let me call it one. You can add another to it. Keep adding what will happen? Law of large numbers will show. With about 30 of these what will happen to them? They will amount to zero. That's the math behind it. If I call the specific risks, and that makes sense, you see know [inaudible] Specific risk is something that's not related to something else. What happens when you add a bunch of unrelated things? The probability of canceling each other is one as soon as you have 30 or more. It's almost a perfect prediction, which is unbelievable to have in real life. What happens? Common things can't cancel, specific things cancel. Please remember that things specific you can diversify, and assets contribution to the risk of a portfolio, therefore cannot be specific thing. Cannot be for example, the thing to focus is not Google. What is the thing to focus on? Google's relationship with everything else. Everything. Supposing you're invested in the S&P 500, you don't want to worry about, you say, okay, let me just follow this sucker. We'll talk about what risks that means in a second as we go along. But basically, what you're doing is you're capturing Google's relationship. S&P 500 is how many other securities? 499. You're not worried about this. This doesn't matter. It's divided by 500. Who cares? But there are how many relationships? We just did it, 249,500 relationships going on in the whole. But between Google and the other 499, but they come in pairs. You have almost a thousand relationships going on. All relations are due to common or systematic. Let me just make sure I get rid of the writing. This is by the way, quite cool. All relations are due to common systematic. That's simply a reflection of this statement. Sorry. If you look at this, this statement and this statement are saying the same thing. You're canceling specific, what remains is common. But what is the common due to markets moving up and down as a whole? Basically, does this give you a notion of the riskiness of a particular business? The riskiness of a particular business shouldn't be viewed in isolation, it should always be viewed relative to the market. Why? Because we as risk averse people do not ever invest in one. This is the biggest danger of a manager within a company. When you are within a company, you're thinking like the manager of your projects and that's it for you. But you should think like an investor. An investor is not concerned about a specific project. They're concerned of a specific project only to the extent that that specific project has something to do with market movements. Why? Because if you're holding the S&P 500, what specific things are there? Nothing. Only 500 out of how many? 249,500. I mean, out of 250,000 and the rest are 249,500 relationships. You see how simple investment has become? You're focused largely on things that you can't diversify because it affects mostly everything. I'm now going to go before the next break and capture this. This is the first awesomeness, is this diversification concept. But see how finance tries to capture it. You'll recognize why we did regressions and relationships. What we're trying to do now is measuring the risk of a project idea keeping in mind what we just learned, and this is so cool. Look at what's going on here. The risk of an idea project analysis is always relative to other things. What were we trying to look at? We're trying to look at Mr. Orange. When we look at Mr. Orange, we first have to identify whom the comparable who was Mr. Apple. When we looked at Mr. Apple, what did we say? "Heck, good news, no debt." Debt was zero. The main thing we were worried about was identifying the risk and return of what? The equity of Apple. This is the backdrop, just reminding you so that you know the context. The context will be different for you when you're evaluating your own project. But how do you measure the relationship of the idea or the project or the comparable with the marketplace? The first model used in finance for measuring relationships is pretty much remained the same. It's called the market model. The market model says this, that the return on the equity of what? This is whose return? Apple's, why? Because that's who my comparable is, that's who I can measure. I'm new, I'm trying to evaluate me, but my benchmark is Apple. This seems a little bizarre here, but Apple. I'm going to take Apple's return, say for the last 60 months or so and run a regression with the return on the market. Why? Because I want to capture the relationships of Apple with a large portfolio because that's what people hold. The riskiness of Apple is only important to the extent that it moves with the market. You see the awesomeness of it? We can use S&P 500 or we can use just as an example, Russell 2000, and do what? We can measure it, the returns are available. This is Apple or this is on the other side, you either use S&P 500 or Russell 2000 to capture the whole marketplace. What does this remind you of? It's a regression, a regression between the return on the equity of Apple on the return on the whole marketplace. What is the slope measuring? The slope measures the sensitivity of apple to the entire marketplace. So how many relationship is Beta capturing? A lot of relationships in just one estimate. Let me just show you a little bit of something that we already saw. What is the Beta? If you stare at this equation, the Beta is, let me write it out. We did this before, but it's the covariance of return on Apple with return on market divided by variance of the return on the market. One is covariance and standardized by variance. How many relations does Beta capture? It depends on which one you use, right? But going to 2,000 may not be necessary as I said because even 500 are capturing most of what's going on, so let's stick with 500. How many relationships are you capturing with one Beta estimate? The Beta i is capturing relationship between Apple's return with 500 different things. But one of those things inside this 500 is what? Apple itself. It's capturing minus 1/499 relationships, right? But they come in pair, but they are the same. Look at the richness of this one regression. The one regression captures all the relationships that reasonably can be captured, and guess what the risk of Apple is called? Beta. Why? Because you like this. Why is it called beta? Because heck, look at this word Beta, where did it come from? Remember we did this regression, and we said it's a good idea to look at changes. First of all, returns are already changes, so we have taken care of that. What is y_i? Apple. What is xi? Market. It's called Beta. Think about this, think of regression having created centuries ago and is waiting for an application, we couldn't have been a better one. Why? Because the relationship between Apple and the market is capturing exactly what risk is all about. It already has a name. It's called Beta. It already had a name. Quickly, one last thought. What is this capturing? All the unique specific stuff that you don't need to worry about. What is it by definition? It's like noise bouncing around. Let's take a break now and I hope when you come back, you'll be excited about this because I'm going to now run with this, with data, and take this measure and show you another simple model that has gotten a Nobel Prize just by itself. Multi people worked on it and Bill Sharp got the Nobel Prize for profound work. Just stare at this, I have now taken the concept of diversification and converted into one simple number, which is the Beta or the sensitivity of Apple's return on equity on the whole marketplace. What's important is both should be measurable. See you soon. Bye.
