Hi, I want to briefly recap because we're changing gears a little bit, and I've spent a lot of time on diversification. But I now want to just kindly, quickly not kindly, but kindly to recap a little bit. So we are risk averse hold portfolio that are diversified, right? As a result a project where, by the way, when I say project, I mean small, big anything, the whole company is like a project too. Projects risk is largely what is common, Across assets. Why? Because everything unique to the project is gone, has gotten diversified, not because of the manager. This is where it's very important the manager thinks like the investor. The investor is not worried about your project. If they were worried about a project, that would be exactly when all their money is in your project, that's not the case. They're worried about the project to the extent that related to the market and looked at the beauty of this. How are all those relationships captured? Ri, which in our case was Apple Alpha plus beta i, market plus epsilon i. I have replaced in the typical regression y on the left-hand side by Ri, beta i, I am sorry. Rm was x in the typical relationship. Now, look what's cool about it. Let's measure this by a simply 500, and let's measure this by Apple. All I need do is run a regression to pick up the sensitivity beta, and this is the measure of risk. The good news is am I ignoring specific risk? No, it's in there. It's showing up here, but by definition, it's not related to the market. So that's why a regression I think was created for finance to just waiting for finance to happen. So quick thing I want to move on to now is given all this development, what does it mean? First risk is defined, I told you, defined but also measured. How is easy? How easily measured? Just a regression. I must emphasize, though, that as soon as you run just a regression here to worry about how many months of data typically 60. That the animal you're trying to measure, in this case Apple has not changed dramatically, still looks similar in the past to what your businesses, which was orange, right? So things like that, and I'm not going to talk too much about that because that falls in the domain of statistics. But you have to do this intelligently. There are statistical biases you have to worry about and so on. So if I want to measure beta properly, you need you need to know statistics, okay? And I'm skipping that part and moving on to something that's extremely important is how do I now use this risk measure to figure out what? I was interested in risk to figure out the return because risk drives return, which then I will use to evaluate Orange and why Apple's return? For two reasons, one again, Apple is a comparable. And second, at this point, we have seen that debt is a call to 0. So Apple's return on equity, the risk of this equation is telling me the risk of the equity of Apple, right, that will also determine the return on equity of Apple. But because there's no debt Ra and Re for Apple are the same, and I'm in business because I'm after Ra, okay? So let's see, how do I develop that relationship. And this is the only time I'm just going to show you the relationship. And this is called capital asset pricing model. The reason for CAPM, the short form for CAPM. If you say that, everybody knows what it is, but it is capital asset pricing model. I want you to stare at this equation. What is this equation saying? That any return can be broken up into two parts, the first one is what? The risk free return, as it turns out, it's not being defined here, so let me define it. There's the risk free return as you'll see in a second. You know how to measure it? [LAUGH] We talked about it right in the beginning, what kind of bond is considered risk free? The government bond, when you're analyzing something that's living for a long time like idea, as opposed to daily trading with people do. What kind of security we look at long term or short, long term. But which kind? Government bond, the second component is because of risk, but it has two parts. The first part is the average market risk premium. So what you want to figure out is how much does the market give over and about the risk-free rate? Remember the table we saw last week? In America, the rate of return on average of the last 70, 80 years, we in books tend to use about 7%. I am very worried of this because, remember, you're going to use this. There's a lot of data backing at 80 years, but what did I tell you? One of the biggest question is why has this been so high? So this is a little bit questionable, but used very commonly. Many people do surveys or what it's likely to be in the future. If you put all later together, this has to be a lower number, and it's a very powerful number. Because even if you change it to say 5% with some people propose, it has a dramatic impact because a 2% rate of return is a huge amount. So you start off with the risk-free rate you add to it the risk premium on the market. But the risk premium on the market is not what your project is, what is the risk off your project? It's your beta relative to the market. So these two things multiplied together tells you the risk premium for Apple. So let's move on and get some intuition for this. Because I think this is probably the most used equation other than the discounted value of dividends. Look at this equation linearly, what is it showing? First of all, a graph where what is the risk-free asset here? Measured as a long-term treasury bond. And the thing I like about it is very easy to measure, right? It's the one thing I know about the future is how much will the government won't pay And why do I feel confident? Because I believe the government will pay. What is this? This is the risk premium, which I will say should be somewhere between five and 7% Bill. And this is where it's very important to recognize which number you want to use here, and textbooks tend to you 7%. I believe it is a good idea to use 5% as well at a minimum, because remember, all the answers are not perfectly precise. And what is this? This is the risk off compatible equity. Why it's almost always the risk of the equity. Why? Because equity trades and even if there is debt in your business, most of the country's debt most in most countries. Debt is a private contract between the company and the bank, so it doesn't rate in America. You can get some information on that as well. But typically, if you see a beta anywhere and we'll see some soon, it's about the equity because equity trades and easy to calculate now here held this ironic, which is more difficult and instrument to think about debt or equity. That is a contract simple to understand equity, love and fresh air. Right? Very tough. But on the other hand, risk is used to capture because of trading. Don't forget the importance of market. Okay, so what does this say? That the return that is expected and please recognize all ours in this are expected because it's about the future you're going toe. Use them from the past data except for life because you know it about the future. And they showed the government will pay. Please remember, the expected is very important you're trying to project to the future. What may happen? That's why I gave you an emphasis on Don't use 7% for other minus out of so easily because it's questionable. Okay, so this is a graph. And let me just in talk about the intuition right here, because this graph lends itself to the intuition. Very well. Okay, quick question. How many points do I need to draw a straight line? Go. So very easy to draw the state line. Let me ask you this. What is the risk off the risk? Free asset? Mhm. Right. What's the risk of the risk free asset? So our f it's beta f has to be zero by definition. Why? Because the government bond. Remember I told you what the risk was. Zero. Simply because I believed I will get 1000 regardless of the state of the world, the face value of 1000. So b B F zero. So I pick up the treasury bill rates. Suppose it 4% tell me which point identified on the graph. 4% blotched here. And I know beta zero. There's another guy who's better. I know. And what is that? The market itself. You see the intuition off government so important, so simple. Why? Because how does the market vary with itself? One on one. So this is the bait off mark. So I have two points. One is this and one is this and I draw the straight line right through you see how simple this is. And that's the simplicity. I was talking about one little equation. So let me ask you this. What should be the return on a risk free asset? Suppose I found another project which I believed had no risk. Unlikely, But let's find it. What should it return be? Well, if the risk is zero, I plug in zero here. This whole thing cancels I'm left with the risk create. Does that make sense? Absolute sense. Let me give you one more intuition. Let me ask you, what is the risk off a portfolio? Our Sorry. Let's not talk about portfolio. What is the risk of a project whose riskiness is the same as the market that is? The project moves one on one with the market 1% up, 1% down. This it's beta is what Peter turns out to be exactly one Because that's the beta of the market. See what happens. The return on this should be the return on the market. Because what happens when you plug one R f and R F canceled? Isn't this school What is it saying is saying you you can predict what's going to happen for two points and they all both make sense. If your projects almost risk free your discounter, it should be the risk-free rate. Think about this. If your project is bananas, your this country should reflect banana. If you discount rate as oranges, you reflect oranges, right? Very intuitive. Some intuition components. Okay, so I'm going to just quickly the emphasized one. What are the components? Risk-free rate, measurable beta f equals zero market return measurable not as well as our F, because our f is we believe is yes, that's exactly what it is. Why not as perfect? Because maybe a simply $500 So doesn't pick up all the kind of possible right? So it's kind off perfect, but not quite okay, But what is its beta B? Better market has to be one. Look how simple it is. Right. But now let me ask you this. What is our M minus? R f? That's the premium in the marketplace that you were. Is this measurable? Sure. If the first two are measurable, I could go historically and look at the difference over 80 years or over earlier markets and so on. And this could be 7% are 5% are many people believe maybe even less. And this is the biggest research area, one of the biggest research areas in finances. Why is there screaming being so high in the U. S? More importantly, will it be the same in the future? Okay, so we have more or less captured everything. And why is Captain so powerful before we run into it? Based on a very intuitive and simple idea. And what is that? The intuitive and simple idea is that people are risk covers, therefore hold portfolios. If they hold portfolios, the risk off one thing will depend on its relationship with a bunch of other things. That one thing in our cases apple because we're trying to evaluate orange comparable. And what is everything else? The whole marketplace. Simple measure off risk. Why? Because not only is the idea simple. The measure of risk is very simple. How do we measure it? We have done it to length. I'm just highlighting everything. We measure it by taking returns on Apple A comparable for us and running it a regression on markets. Can you measure those? Yeah, it's simply 500. We'll do okay just fine. Simple relationship between risk and return. I think this is even so. The idea is simple. The measure of risk is simple, but the relationship between risk and return is just so simple and intuitive. And that is what we talked about in capital. It's linear and easy to measure, very easy to measure. I mean, I'm getting a little carried over here, but I understand by because I can't think off anything that could have been simpler than that. And easily measurable. Of course. Is it perfect answers? No. A lot of research has shown, not surprisingly, that not all assets fit this perfect relationship between when you measure the beta and you measure the return, the two beta doesn't capture all the riskiness. And that's not surprising, is it? For example, if I told you you can measure love, would you find one simple linear relationship. If you did, there's something missing in life, right? What's the awesomeness of this is conceptually, it's so clean and practically measuring. It's so clean, too. But don't expect it to do wonders every time. Okay, in a more detailed class, we measure different ways off measuring risk and return. But the profound, simple fact is this. If you hold a diversified portfolio, you should be looking at common elements across. Security is not specific, and that basic idea carries through all future developments. I wanted to highlight that. Don't expect it to be perfect, but it's profoundly close to perfect. So let's take a break here When we come back. I'm going to wrap it up with some fascinating data and in the context of valuing orange and show you how simple it can be. Let's take a break