This is the S&P, Standard & Poor's 500 stock price index and it's used as a benchmark for returns. So this is what you did if you just invested in the whole market monthly from 2000 to 2016. And what it shows is quite a roller coaster ride of value, right? So, actually, I should have maybe plotted it longer. It was rising for a long time before that and then it had a huge drop from 100 it fell about in half. And then starting in 2003 it started a long increase again. And then here is the great financial crisis, 2007 to 2009. And then since then, has been going up a lot here. You know, from here to here, this is 2009. From here to here it tripled in value. It's amazingly unstable, the stock market. To think that the risk of any other comp, the Law of Large Numbers is not working here because this is the Standard & Poor's 500 Index. It's an average of 500 stocks. So if they were all independent of each other, the Law of Large Numbers would make the stock market as a whole almost constant. But, in fact, it's actually gone up hugely. So there's definite dependence across stocks. But I'm not going to be focusing on forecasting the stock market here. We're going to make the assumption that it's very hard to forecast. So we're going to look at risk as something that we can quantify by looking at the standard deviation of past risks and not focus on what's new right now. Now what I want to do next is to look at one firm within the S&P 500. What do you think it looks like if I were to plot Apple on the same chart here? Did you ever heard anything about how they performed? With that? Does anyone know how Apple has performed since 2000? I guess we're not an eager class of stock market devotees. Yes you did, yeah. Pretty well since the release of the iPhone, that's around 2007. You said pretty well, since the release of the iPhone. And, was it 2007? They did a series of releases of new different models. You're right. They did pretty well. So I'll show you what pretty well mean. I'm going to superimpose on the same plot, Apple OK. That's Apple. It looks different because I had to scale down to fit Apple onto it. So this is quite a good performance because I started both, re-scaled both of them, they started at 100 and it's now, what is that? 3,500, 3,600, something like that. So that means a 30, say a 40 fold increase in value in 15 years. So imagine that you were taking this class in 2000. I was teaching this class, maybe 15 years ago. But imagine that you were taking this class then. And, you came home to your parents and said, "You know, I think Apple's stock is a great investment. I just have a quick request of you. Could you take out a second mortgage on the House, borrow $400,000 and put it into Apple's stock?" Well, if you did that in 2000, your parents would now own over $15 million. The problem is, what's the problem with that? The problem is nobody knows the future. If you knew that Apple was going to do that, you would have obviously done that. But nobody knew that Apple was going to do that. So you had also faced some problems with your parents if you did that, because starting in 2000, Apple dropped quite a bit and you lost it's like three quarters of your money. It's hard to tell here right. It was really limping along for four years. So you come back four years later and your parents say, "Do you realize what you did? You've made us borrow $400,000. And now it's just, we're down to $100,000." But then you have to be convincing again. No. Just hang in there. This is the problem with investing. Hang in there please. And then it start recovering slowly. Yeah I think back then, this is before the iPhone. Here back in 2000. One, two, and three. It looks like Apple was washed up. When did they bring Steve Jobs back? Anyone know that? Anyone read about? I'm assuming you know who Steve Jobs is. Steve Jobs was the founder of Apple Corporation. And he was kind of a difficult guy and kind of quirky. So they fired him. It was his own company, but you can get fired from your own company. And they put in some professional management, whereas he was kind of a little bit strange. The professional management did this. They brought it down to a low value. And then they invited Steve Jobs back. They thought maybe he does have some kind of genius. But they're still doing well after his death. So maybe it's, you know, the company develops a sort of culture and a spirit that allows them to keep doing. I really think that's true about organizations. They go on for so long. Sometimes it's a great success. So for example, the Economist magazine was founded in London in the early 19th century and it was, it's still a great magazine. How can they last so long? I went and visited them once and I discovered that they don't even put by lines. They have a different culture. They usually don't put by lines on articles. In other words, if you were to work for the Economist as a writer, you will not become known. They will not put your name, print your name on the articles you write. So how can they do that? Because young people want to establish themselves somehow. But they do. And It's a different culture at the Economist magazine as a result. So every company has its own culture and it produces a strange outlier effect. This is the return on Apple's stock, in red, the red dash line and the return on the S&P, Standard & Poor's 500 stock price index. So you can see that the returns on Apple have been very variable. Much more variable than the return on the S&P 500. In fact, when you look at this it's hard to judge from this picture which one did better, right? It looks like Apple is going up and down all the time. It's this noisy, really noisy. And the aggregate stock market looks tanned by comparison. It's hard for you to judge which one did better. But you see maybe, if you look you can sort of tell that there are more ups and downs. But it's so noisy from month to month. These are monthly returns. So here last time Apple lost almost 60 percent in one month. So it was horrible. The other thing is I don't know if you can tell that it's correlated with the S&P 500. That when the S&P 500 moves up, it moves up and when the S&P 500 is down, for example. But, see, this is the experience of investing is puzzling because the noise dominates. It is so scary watching these things go up and, if you take an interesting investment like Apple, it just goes up and down so much from month to month. And, it could be under for years and you can really lose faith in your acumen after it's going badly for years. So, this is just the variance of Apple versus the variance of S&P 500. The standard deviation of Apple capital gain was 12.8 cents a month. That's not annualized. Annualizing means multiplying it by 12. This is a scatter diagram showing the returns on the S&P 500 on the horizontal axis and the returns on Apple on the vertical axis. And you can see that the scatter has an upward slope to it which means they're correlated. It's not that strong an upward slope, but when S&P is high, Apple tends to be high in return and when the S&P is low, Apple tends to be low. But it's more variable. But this goes from +60 to -80. And on this axis I have -50 to +50. So Apple is more variable than S&P 500. But you can see that there is a correlation. Actually it's better if I put a regression line in. This is a line fitted through the scatter points. And it shows it has a slope of 1.45 which is greater than one, which means that Apple overreacts to what happens in the aggregate stock market. And then it has noise on top of that. Apple noise, like Steve Jobs death noise that doesn't affect the overall stock market. So Apple actually, this is going to be a fundamental concept and as far as the beta of a stock is a measure of how it relates to the stock market. If the beta is one, then the asset tends to go up and down one for one in terms of returns with the aggregate market. If the beta is two, well, they're kind of rare to see beta two stocks. Beta 1.45 is getting high. So the Apple reacts more than directly to the stock market. So when times are good, people think they are really good for Apple. And when times are bad they think it's really bad for Apple. The concept here is market risk versus idiosyncratic risk. So market risk is the risk of the whole stock market. And for an Apple investment, the market risk of that investment is the risk that Apple will do something in reaction to the aggregate stock market. But idiosyncratic risk is Apple only risk. So that would be the death of Steve Jobs, or the iFlop the iPhone that nobody liked. That occurred. So they make mistakes and they take risk. The people at Apple have a history of taking risks. They'll try something that might not work out. They don't always work out, but on an average, they do. So the variance of the return on a stock is equal to it's beta squared times the variance of the market return and that's called systematic risk. Plus the variance of the residual and the regression, the residual in this regression. I think some of this might be, new, our graduate students can clarify some of these concepts for you. A regression line is a single line that best fits the data in your scatter plot. So how is this calculated? Imagine you have a scatter plot with 50 dots and you start by drawing a line through them. The vertical distance between a given dot and the regression line is that dot's residual. Also known as the error of your proposed line with regard to that single dot. So, to get a better fit I can try changing the slope or a constant parameter to force the line to go perfectly through dots one and two, but that will make the residual associated with dot three really big. So what do we do? We want to minimize some combination of all 50 residuals. So statistics proposes the least squares method. What do the different slopes mean? Remember the equation for a line in algebra class. y = mx+ B. The slope m is how much y changes for a 1 unit increase in x. In finance we call y as the return on Apple stock, x as the return on the market, slope m as beta, and the constant B is Alpha. Slope beta tells how much a particular stock co-moves with the market and thus as a measure of the stock systematic risk. So the idiosyncratic risk is the risk that the point will lie above or below that line. And you can see, there's a lot of idiosyncratic risk for Apple.