Hi. I want to briefly recap because we are changing gears a little bit. And I spent lot of time on diversification, but I now want to just kindly, quickly not kindly, kindly, to reacpulate. So, we are risk. Averse. Hold portfolios. Better diversified. Right? As a result. A project. Well, by the way when I say project I mean, small, big, anything. The whole company's like a project too. Projects, risks. Is largerly. What is common? Across. Assets. Why? Because everything unique to the project is gone. It's gotten diversified, not because of the manager. This is very, but it's really important to think of, the manager think like the investor. The investor is not worried about your project. If they were worried about your project, that would be exactly when all the money is in your project. That's not the case. They're worried about the project to the extent that it's related to the market. And look 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, look, what's cool about it. Let's measure this by a S and P 500 and let's measure this by Apple. All I need to do is run the 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, regression, I think, was created for finance. You know it was 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 easy? How easily measured, just a regression. I must emphasize though that as soon as you run just a regression, you have to worry about how many months of data? Typically 60. That the animal you are trying to measure, in this case apple, has not changed dramatically, still looks similar in the past what your business is, which was orange. Right. So things like that and I am 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 biosis that you have to worry about and so on. If I want to measure beta properly, I need to know statistics. Okay, and I am 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 very interested in risk to figure out the return. Because risk drives return, which then I will use to evaluate. Orange. And why apple is a return? For two reasons. One again, apple is a comparable. And second, at this point we have seen, that debt is equal to zero. So, apple's return on equity which is in this regression will also... 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 is no debt, RA and RE for apple are the same and I am 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 capping. The short form for Capin. If you say that everybody knows what you did. But it is capitol. Asset. Pricing. Model. I want you to stare in 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's turned out it's not been defined yet, so let me define it. There's the risk, free. Return. As you'll see in a second, do you know how measure it? [laugh]. We talked about it right in the beginning. What kind of bond is considered risk free? The Government Bond. When you analyzing something that's living for a long time like a [inaudible] idea, as opposed to daily trading what people do. What kind of [inaudible], security will you look at? Long term or short term? 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 would, is the market give over and above the risk free rate? Remember the table that 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 seven%. I'm very wary of this. Because remember you are going to use this. There's a lot of data backing it, 80 years. But what did I tell you? One of the biggest questions is, why has this been so high? So, this is a little bit questionable, but used very commonly. Many people do surveys of what it's likely to be in the future. If you put all data together this has to be a lower number. And it's a very powerful number. Because even if you change it to say five%, which some people propose, does a dramatic impact. Because a two percent rate of return, is a huge amount. So you start of 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 of your project? It's your beta relative to the market. So, this, these two things multiplied together tells you the risk premium for Apple. So, let me give you some, let's move on and get some intuitions for this. Because I think this is, probably the most used equation, other than discounted value of, It's the, the stock prices. The discounted value of dividends. Look at this equation leniently. What is it showing? First of all, a graph. Well what is the risk free asset here? Measured as a long-term treasury. Bond. We'll, and the reason, 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 a government bond pay. And why do I feel confident? Because I believe that the government will pay. What is this? This is the risk premium which I will say should be somewhere between five percent and seven percent and this is where it's very important to recognize which number you want to use here and textbooks tend to use seven%. I believe it is a good idea to use five percent as well at a minimum because remember all the answers are not perfectly precise and what is this. This is the risk. Of comparable. 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 countries debt, most countries debt is private contract between the company and the bank. So it doesn't trade. In America, you can get some information on debt as well. But typically if you see a beta anywhere and we will some soon, it's about the equity because of the equity trades are easy to calculate. Now, hither held this ironic which is more difficult an instrument to think about, debt or equity. Debt is a contract, simple. To understand equity, love and fresh air, [laugh]. Very tough, but on the other hand, risk is easy to capture because of trading. You don't forget the importance of markets, okay? So what does this say? That the return that is expected, and please recognize, all r's in this are expected, because it's about the future. You're going to, use. Then from the past data except for RF, because you know it about the future, and it showed the government will pay. Please remember the expectant is very important. You're trying to predict to the future what may happen. That's why I gave you an emphasis on, don't use seven percent for RM-RF so easily, because. It's questionable. Okay. So this is a graph. And let me just, mm 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? Two. So very easy to draw this straight line. Let me ask you this what is the risk of risk free asset, right. What is the risk of risk free asset. So RF. Its Beta F has to be zero by definition. Why because the government bond remember I told you what the risk was... Was zero simply because I believe that I would get 1000 regardless of the state of the word, the face value of [inaudible]. The BF is zero. So I pick up the treasury bill rate - suppose its four%. Tell me which point have I identified on the graph. Four%. I blotched here. And I know beta is zero. There's another guy who's better I know. And what is that? The market itself. You see the intuition of [inaudible]? So important. So simple. Why? Because how does the market vary with itself? One on one. So this is the beta of... Market. 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 believe had no risk, unlikely, but let's find it. What should be it's return be? Well, if risk is zero, I plug in zero here, this whole thing cancels and left with the risk-free rate. Does that makes sense. Absolute sense. Let me give you one more intuition. Let me ask you what is the risk of a portfolio. Or, sorry. Lets not talk about a portfolio. Sup. What is the risk of a project whose riskyness is the same as the market? That is the project most one on one with the market. One percent up. One percent down. [inaudible]. So beta is one. Its beta turns out to be, beta 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? Rf and RF cancel. Isn't this cool? What is it saying? It's saying you, you can predict what's going to happen for two points. And they all, both make sense. If your project is almost risk free, your discount rate should be risk free rate. Think about this. If your project is bananas, your discount rate should reflect banana. If your discount rate is oranges, you would reflect oranges, right? Very intuitive, some intuition components. Okay. So, I'm going to just quickly re-emphasize one. What are the components? Risk free rate. Measurable. Beta F equals zero. Market return. Measurable. Not as well as RF, as RF is we believe is, yes that's exactly what it is. Why not it is perfect because may be a simply 500 options doesn't pick up all the kind of possible investments, right. So, its kind of faith but not quiet. Okay? But what is its beta be. Beta market has to be one. Look how simple it is. Right, but now let me ask you this: what is RM minus RF. That's the premium in the marketplace that you earn. Is this measurable, sure. If the first two are measurable I can go historically and look at the difference over eight years or over earlier markets and so on. And this could be seven percent or five percent or many people believe it may be even less. And this is, the biggest, research area. One of the biggest research areas in finances. Why has the risk premium been 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 Kapin so powerful, [inaudible] 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 averse. They therefore hold portfolios, if they hold portfolios, the risk of one thing will depends on its relationship with a bunch of other things. That one thing in our case is apple because we're trying to evaluate orange, comparable and what is everything else, the whole market place. Simple measure of risk. Why? Because not only is the idea simple, the measure of risk is very simple. How do we measure it? We've done it right. I'm just highlighting everything. We measure it by taking returns on Apple. A comparable for us. And running at a regression on markets. Can you measure those? Yeah. S and P 500 will do okay, just fine. Simple relationship between risk and return. I think this is, even so, so the idea is simple, the measure of risk is simple, but the relationship between risk and return is just so simple and intuitive that's what we talked about in Capen. It's linear. And easy to measure. Very easy to measure. I mean I'm, I'm getting a little carried away here, but I understand why. Because I can't think of, anything that could have been simpler than that. And easily measurable of course. Is it perfect? Answer is no. 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 betas does't capture in all the riskiness. And that's not surprising. Is it? [laugh]. For example, If I told you, you can measure love. Would you find one simple linear relationship. If you did, there is something missing, right. But the awesomeness of this is, conceptually it is so clean. And practically measuring is so clean too, but don't expect it to do wonders every time, okay. In a more detailed class we measure different ways of measuring risk and return but the profound simple fact is this - if you hold the diversified portfolio you just be looking at common elements across securities not specific and that basic idea carries through all future developments. I wanted to highlight them, don't expect it to be perfect but its 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, I'll show you how simple it can be. Let's take a break.
