Hi. Welcome back. Hopefully you've had time to think about two assets in a portfolio. What are the characteristics? Just quickly. You have to worry about the proportion of wealth put in both. [UNKNOWN] Very important. You have to worry about the individual risks measured by standard deviations of variances. But most importantly, some new animal has started appearing and that's the relationship between two things, Google and Yahoo. And remember whenever you measure relationships, a relationship will pick up something common. Not something different. And you see the awesomeness of finance to define risks into broad categories, Market and Specific. Let's see. Revisit our two asset choices and the move onto three. And more. Was combining Google and Yahoo a good choice? And I don't want you to do numbers, if you have the numbers great, great. If you can figure out the standard deviation of Google and Yahoo and the relationship between the two, just substitute them in that formula, take that opportunity. To try to see what's going on. So, I'm asking you intuitively, though. Do you think, "Was combining Google and Yahoo a good choice"? Of course, your answer should, first question should be, "Hey Bozo. What do you mean? Relative to what? Well, Mr. Bozo says the following. Just use your head Bozo and try to think about it. So, the thing I'm asking is quite straightforward obviously. And, but, but kind of hidden is, could you have made a better choice, given that you invested /g. And I think probably yes, and the reason is, Google and Yahoo are roughly in the same space. Yahoo is much smaller, but let me say that Yahoo is probably competing with Google in the same space. So what's likely to be the correlation? Pretty high positive. So what, are you likely to benefit from diversification much? Probably not. Would Google and Boeing be a better choice? Again, do the analysis. This is your week of running with all the examples you can. It's my week of showing you the beauty of what's going on. I'm not going to use too many examples. I'm going to use real data in the real context. But for now, and I've already assign with real data, try to do this. But intuitively, what do you think? It's a better choice? Chances are, yes. They are very different industries, they're doing very different things, and therefore chances are, they'll have a lot of things specific to each other, which is the first sign of diversification. Common things? No. Specific, yes. The risk of the portfolio is affected by how many factors? So I'm going to start writing on this. Is it a good choice? Mm, I don't know. Certainly better. Intuitively. Do the numbers if you The risk of the portfolio is affected by how many factors? Portfolio. It's gone from one to two assets. Factors have gone to four, why? Let's just wrap up. The four factors are sigma, a, b, 2 a b. So there are four factors. One standard deviation of a times division of b. Two standard deviations or two variances but two relationships. Why are these different than the average risk of the two assets held in isolation? So, if I held only one, it would be this risk. The second this risk. And what's the average of the 2? Weights average, very simple. Why is the average risk of the 2 held in isolation different? Because of this. Or, if you like to think about it differently because of sigma ab. Many people prefer to think about correlations rather than covariances. And I think you know the relationship between the two. One is standardized and easy, intuitive. No there's not. I love covariances as much as I love correlation because, which comes first? Correlation doesn't have a hope because covariance comes first, tells you the sine. It suffers from units and magnitude problems, so you scale it. By what? How do you go from here to here. One more time. You just scale this by sigma a, sigma b. Okay? So, we have a very good sense, hopefully, of two assets. Let's keep co, moving, and go on to three. Suppose you have three securities in your portfolio. Google, and you dropped Yahoo. No, nothing against Yahoo, just from a diversification st, st, st, eh, perspective. So Google is the internet domain. And to be honest with you, I sometimes wonder what it does, because [LAUGH] it's a river, but obviously it's not the way it used to think in the past. It's not a physical commodity like Boeing. What does Boeing do? Man/g, huge physical things, planes. Google? Huge! But I don't know what. That's what's fascinating and troublesome at the same time. And Merck, well, it's a very different animal. What does Merck do? Merck produces medicines for people. Is it the same business as flying or being all over the Internet? No. So I'm picking three very different securities. So what's happened? I've consciously started thinking about diversification, but I'm still small. Three, what did I say? You need to diversify as more important, but you want to be large, too. So, well, how large is a quick question. How do you measure the risk of each of the three stocks? Again, something for you to do, and put in the table where they were not. Remember the table we started off this morning and left off last, week, that table. Try to substitute stuff as you calculate it, okay. Go, you may find it on the web. [LAUGH] The standard deviation still, let me assure you can, if you look hard enough. But try to calculate too. It turns out, we'll see, that Yahoo Finance gives you historical data, in order to be measured as well as say, for example, Morning Star, but it's free and you can do calculations and you can do [INAUDIBLE] , [UNKNOWN] and so on. So how do you measure the risk of each? Sigma g. Let me call it [COUGH] sigma Google, sigma Boeing. I don't remember it's [INAUDIBLE] mark three separate entities. So that's easy. How do you measure the risk of your portfolio? Now this is a tough one, how many do I have? How many securities do I have now? Three? And still I'm not, sorry, I jumped ahead, I don't want to show you the answer, I want to talk about it before we go there. It's going to look nasty, and nastier than what the two-one was. Not as simple, clearly much more nasty than one asset, right? One asset is very simple. Standard deviation of Google, or Boeing, or Merck. Now we're combining the three. So, what are the first thing you have to think about when you have not only that I've chosen Google, Boeing, and Merck, but what do I have to think about right away? I have to think about Xa, Xb, Xc. What are these? These are the proportion of my investment going into the three. So, suppose you look at the importance of this. Suppose I am diversifying slowly, right? But, this is 0 and this is close to 0. Have I diversified? I haven't. So, the rates are very important, having three securities superficially, in your portfolio, this is close to zero. And suppose this is 90% of your rate. You haven't really diversified, so the proportion of relative putting in each is very important and it's not the case that you put equal every time. I'm just giving you a sense of what's going on. How would you measure the risk of your portfolio? Think intuitively. How many, and we'll revisit this issue over and over, what will matter? These three clearly will matter, but what will matter to? Sigma a, b which is what? Relationship between a and b in terms off in the data. It's also the relationship between b and a. So the measurement of the two are likely the same thing, within a certain set of assumptions we have made. What else? Sigma ac and sigma ca. Finally, what/g? Sigma b c, sigma c b. So, we have, I've shown you all the elements. The rates are extremely important. The personality is called standard deviation's are very important. But, what is more, what is also important is relationships. Okay, so see, you'll see a pattern in a second. So I'm going put up this genetic equations, every time I do equation, there will be a list of equations for risk and return like I did for time value of money, will be on the web site. But, just stare at this, I know it's a little bit intense, there're a lot of terms going on. Let's start off and let's just walk through this a little bit slowly. Is this any surprise, remember the squares are simply because variances are squared. No, when would I have only this as my risk when x is 1, all my relevant 1. This is the second personality, second variance. Third variance. I told you these will appear. But now, how many relationships are there? Two between a and and b, they are the same because sigma a, a b is equal to sigma b a. Two between a and c and two between. B and c. Whatever I've done going from [UNKNOWN] one to the next. The first term is the same, the second term is the same, the third term is the same. The, actually turns out all terms are the same except starting with covariances and replacing. Covariance by correlation. And remember again, what is Rho ab? Correlation is equal to sigma ab over sigma a times sigma b. And I'm using this to substitute. And that's simply because [CROSSTALK] let me circle everything I've done [BLANK_AUDIO] It's simply because people prefer to look at rhos rather than covalence Some do. I, I actually am so used to both. remember cake, care in this context. So, when you think about it, the important thing is, the important thing is the intuition we derive. We start off by the intuition, we end with the intuition. How many unique variances? We'll take a break again after this because we're going to jump to, after this specific, we'll jump to a lot of assets and then take a break because that's a good time to get a sense of what's been happening. How many unique variances? Since we have done this, I'm going to go a little bit faster. But I'll do a video. And this is a good thing to guess. Three, don't forget weights. Because if one of the weights is close to 0, it's two so it matters that you [INAUDIBLE] . How many relationships? Actually, 6 and I'll explain in a second. How many unique, 3. How many total factors affecting the portfolio? But that I mean how many terms going on? How many relationships, what did I say, 6. Think about this, AB BA, 2, AC CA, 4, BC CB, 6. In a room with 3 people, how many relationships. Just do this. A, b, column abc. You'll have six relationships. And turns out, in the data in between under our assumptions, what happens is there are three unique. Why? Because ab, sigma ab is equal to sigma ba. These are the first two. Then sigma ac is equal to Sigma ca. And Sigma bc equals cb but therefore the 6 and the 3. But this spot, if it confuses you, just ignore it for the time being. Everybody's okay with 3 plus 6 is 9? How did I get nine? And remember this 9 is 3 squared. So, it's very important to understand how the pattern is emerging. Why three squares? Three people in a thing squared is 9. Three of them are what? Variances, unique. Six are relationships. Okay? Let me go one step further before taking a break, and show you the most fascinating thing ever. Suppose [LAUGH] you have 500 assets. Who, which portfolio has 500 assets? S&P 500. Can you believe one day I really walked into class and said, how many things are in S&P 500? And, you know, I mean, rightly enough the class thought I was an idiot, which wasn't a surprise to me. But, anyway. So, so 500. Right? How many total factors? Remember, in what [LAUGH] ? You should ask, "In what?" in the variance. Total factors, 500 squared. I can, I mean, it's mind boggling how many, 250000. Right, there should be four 0s. And five times five is 25. 250,000 happening in a portfolio. Isn't it mind-boggling? Why did I pick 500? Because there's simply 500 hares /g. But why did I jump from three to five? Because it would take two years to finish this class if we went from three to four to five. But the other reason I did is because portfolios already exists. So why create their own? And that's something I want to talk about for a second. You buy mutual funds which already exist, and Vanguard is one of the companies which has taken portfolio theory to its literal, taking it literally by saying that if you buy existing portfolios, you're capturing the whole market. How much you put in the market and the risk free asset as it turns out will capture, pretty much, anything you can do. Finally, why buy individual securities and put them in a portfolio because you would incur huge amounts of transaction costs. Okay. How many unique variances? How many guys in the room? And gals? How many unique personalities? You should know the answer to that. It's linear, 500. Yes? You are Google, you are Moogle, you are Doogle, all of them in a room, 500, how many personalities? 500. You don't even need to do that math. Remember, weights are very important. But let's assume they're roughly equally rated. What is the weight going to be? One over 500. In other words, you're just buying a portfolio, let's assume it's equally rated, it may not be, right. Is equally rated, you don't have to worry about how much do I put in this asset or not, so you see, in some sense, now the in large portfolio, the weight is not that important. Right, what's more important, diversification. Every spread, so don't buy 500 in Technology, buy 500 across. How many relationships? And this is going to blow your mind, you should know the answer. 249,500. [BLANK_AUDIO] 249,500 relationships going on in your portfolio. Why? How did I get that? Very easy. Total relationships is squared, right here. Subtract the unique, what am I left with. And you can actually do this math separately, directly, but why do it when you know the answer in a simple fashion. But what will those be, 1 to 2, 2 to 1, 1,3,2,3 and all of those. Okay, so just think through this. But, what's the bottom line? How many unique relationships? That's, that's kind of a not a real [UNKNOWN] . Thats not the bottom-line issue. This unique relationship is roughly half of these. Why? Because they come in pairs. So the bottom line of, what we have learned right now before we take a break is very quickly the bottom line, and I'll repeat this after the break. Think about it. Variance of an asset, I'll quickly go through this, take a break. Variance of an asset determines risk faced by you. Only if you hold 1 or very few. Variance of any asset is not important when held in large, diversified portfolio. Specific risks get cancelled out. And assets contribution to the portfolio risk is determined largely by is relationships with other assets. All relationships between people, or assets [LAUGH] , is due to common rather than specific things. Let's take a break now. We'll pick up with this slide. I'll go through this very seriously and slowly. And we will think through each one to come up, to come up with the bottom line. Let's take a break. See you soon, bye.