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This is the S&P, Standard & Poor's 500 stock price

Â index and it's used as a benchmark for returns.

Â So this is what you did if you just invested in the whole market

Â monthly from 2000 to 2016.

Â And what it shows is quite a roller coaster ride of value, right?

Â So, actually, I should have maybe plotted it longer.

Â It was rising for a long time before that and then it had

Â a huge drop from 100 it fell about in half.

Â And then starting in 2003 it started a long increase again.

Â And then here is the great financial crisis, 2007 to 2009.

Â And then since then, has been going up a lot here.

Â You know, from here to here, this is 2009.

Â From here to here it tripled in value.

Â It's amazingly unstable, the stock market.

Â To think that the risk of any other comp,

Â the Law of Large Numbers is not working here because

Â this is the Standard & Poor's 500 Index.

Â It's an average of 500 stocks.

Â So if they were all independent of each other,

Â the Law of Large Numbers would make the stock market as a whole almost constant.

Â But, in fact, it's actually gone up hugely.

Â So there's definite dependence across stocks.

Â But I'm not going to be focusing on forecasting the stock market here.

Â We're going to make the assumption that it's very hard to forecast.

Â So we're going to look at risk as something that we can

Â quantify by looking at the standard deviation of

Â past risks and not focus on what's new right now.

Â Now what I want to do next is to look at one firm within the S&P 500.

Â What do you think it looks like if I were to plot Apple on the same chart here?

Â Did you ever heard anything about how they performed?

Â With that?

Â Does anyone know how Apple has performed since 2000?

Â I guess we're not an eager class of stock market devotees. Yes you did, yeah.

Â Pretty well since the release of the iPhone, that's around 2007.

Â 2:25

You said pretty well, since the release of the iPhone.

Â And, was it 2007?

Â They did a series of releases of new different models.

Â You're right. They did pretty well.

Â So I'll show you what pretty well mean.

Â I'm going to superimpose on the same plot,

Â Apple OK. That's Apple.

Â It looks different because I had to scale down to fit Apple onto it.

Â So this is quite a good performance because I started both,

Â re-scaled both of them, they started at 100 and it's now, what is that?

Â 3,500, 3,600, something like that.

Â So that means a 30,

Â say a 40 fold increase in value in 15 years.

Â So imagine that you were taking this class in 2000.

Â I was teaching this class,

Â maybe 15 years ago.

Â But imagine that you were taking this class then.

Â And, you came home to your parents and said,

Â "You know, I think Apple's stock is a great investment.

Â I just have a quick request of you.

Â Could you take out a second mortgage on the House,

Â borrow $400,000 and put it into Apple's stock?"

Â Well, if you did that in 2000,

Â your parents would now own over $15 million.

Â The problem is, what's the problem with that?

Â The problem is nobody knows the future.

Â If you knew that Apple was going to do that,

Â you would have obviously done that.

Â But nobody knew that Apple was going to do that.

Â So you had also faced some problems with your parents if you did that,

Â because starting in 2000,

Â Apple dropped quite a bit and you lost it's like three quarters of your money.

Â It's hard to tell here right.

Â It was really limping along for four years.

Â So you come back four years later and your parents say,

Â "Do you realize what you did?

Â You've made us borrow $400,000.

Â And now it's just, we're down to $100,000."

Â But then you have to be convincing again.

Â No. Just hang in there.

Â This is the problem with investing.

Â Hang in there please.

Â And then it start recovering slowly.

Â Yeah I think back then,

Â this is before the iPhone.

Â Here back in 2000.

Â One, two, and three. It looks like Apple was washed up.

Â When did they bring Steve Jobs back?

Â Anyone know that? Anyone read about?

Â I'm assuming you know who Steve Jobs is.

Â Steve Jobs was the founder of Apple Corporation.

Â And he was kind of a difficult guy and kind of quirky. So they fired him.

Â It was his own company, but you can get fired from your own company.

Â And they put in some professional management,

Â whereas he was kind of a little bit strange.

Â The professional management did this.

Â They brought it down to a low value.

Â And then they invited Steve Jobs back.

Â They thought maybe he does have some kind of genius.

Â But they're still doing well after his death.

Â So maybe it's, you know, the company develops a sort of culture

Â and a spirit that allows them to keep doing.

Â I really think that's true about organizations.

Â They go on for so long.

Â Sometimes it's a great success.

Â So for example, the Economist magazine was founded in

Â London in the early 19th century and it was,

Â it's still a great magazine.

Â How can they last so long?

Â I went and visited them once and I discovered that they don't even put by lines.

Â They have a different culture.

Â They usually don't put by lines on articles.

Â In other words, if you were to work for the Economist as a writer,

Â you will not become known.

Â They will not put your name,

Â print your name on the articles you write. So how can they do that?

Â Because young people want to establish themselves somehow.

Â But they do. And It's a different culture at the Economist magazine as a result.

Â So every company has its own culture and it produces a strange outlier effect.

Â This is the return on Apple's stock, in red,

Â the red dash line and the return on the S&P,

Â Standard & Poor's 500 stock price index.

Â So you can see that the returns on Apple have been very variable.

Â Much more variable than the return on the S&P 500.

Â In fact, when you look at this it's hard to

Â judge from this picture which one did better, right?

Â It looks like Apple is going up and down all the time.

Â It's this noisy, really noisy.

Â And the aggregate stock market looks tanned by comparison.

Â It's hard for you to judge which one did better.

Â But you see maybe, if you look you can sort of tell that there are more ups and downs.

Â But it's so noisy from month to month.

Â These are monthly returns.

Â So here last time Apple lost almost 60 percent in one month.

Â So it was horrible.

Â The other thing is I don't know if you can tell that it's correlated with the S&P 500.

Â That when the S&P 500 moves up,

Â it moves up and when the S&P 500 is down, for example.

Â But, see, this is the experience of investing is puzzling because the noise dominates.

Â It is so scary watching these things go up and,

Â if you take an interesting investment like Apple,

Â it just goes up and down so much from month to month.

Â And, it could be under for years and you can really lose faith

Â in your acumen after it's going badly for years.

Â So, this is just the variance of Apple versus the variance of S&P 500.

Â The standard deviation of Apple capital gain was 12.8 cents a month.

Â That's not annualized.

Â Annualizing means multiplying it by 12.

Â This is a scatter diagram showing the returns on

Â the S&P 500 on the horizontal axis and the returns on Apple on the vertical axis.

Â And you can see that the scatter has

Â an upward slope to it which means they're correlated.

Â It's not that strong an upward slope,

Â but when S&P is high,

Â Apple tends to be high in return and when the S&P is low,

Â Apple tends to be low.

Â But it's more variable.

Â But this goes from +60 to -80.

Â And on this axis I have -50 to +50.

Â So Apple is more variable than S&P 500.

Â But you can see that there is a correlation.

Â Actually it's better if I put a regression line in.

Â This is a line fitted through the scatter points.

Â And it shows it has a slope of 1.45 which is greater than one,

Â which means that Apple overreacts to what happens in the aggregate stock market.

Â And then it has noise on top of that.

Â Apple noise, like Steve Jobs death noise that doesn't affect the overall stock market.

Â So Apple actually, this is going to be a fundamental concept and as far as

Â the beta of a stock is a measure of how it relates to the stock market.

Â If the beta is one,

Â then the asset tends to go up and down one for one in

Â terms of returns with the aggregate market.

Â If the beta is two,

Â well, they're kind of rare to see beta two stocks.

Â Beta 1.45 is getting high.

Â So the Apple reacts more than directly to the stock market.

Â So when times are good,

Â people think they are really good for Apple.

Â And when times are bad they think it's really bad for Apple.

Â The concept here is market risk versus idiosyncratic risk.

Â So market risk is the risk of the whole stock market.

Â And for an Apple investment,

Â the market risk of that investment is the risk that

Â Apple will do something in reaction to the aggregate stock market.

Â But idiosyncratic risk is Apple only risk.

Â So that would be the death of Steve Jobs,

Â or the iFlop the iPhone that nobody liked.

Â That occurred. So they make mistakes and they take risk.

Â The people at Apple have a history of taking risks.

Â They'll try something that might not work out.

Â They don't always work out,

Â but on an average, they do.

Â So the variance of the return on a stock is equal to it's beta

Â squared times the variance of the market return and that's called systematic risk.

Â Plus the variance of the residual and the regression,

Â the residual in this regression.

Â I think some of this might be, new,

Â our graduate students can clarify some of these concepts for you.

Â A regression line is a single line that best fits the data in your scatter plot.

Â So how is this calculated?

Â Imagine you have a scatter plot with

Â 50 dots and you start by drawing a line through them.

Â The vertical distance between a given dot and the regression line is that dot's residual.

Â Also known as the error of your proposed line with regard to that single dot.

Â So, to get a better fit I can try changing the slope or

Â a constant parameter to force the line to go perfectly through dots one and two,

Â but that will make the residual associated with dot three really big.

Â So what do we do? We want to minimize some combination of all 50 residuals.

Â So statistics proposes the least squares method.

Â What do the different slopes mean?

Â Remember the equation for a line in algebra class.

Â y = mx+ B.

Â The slope m is how much y changes for a 1 unit increase in x.

Â In finance we call y as the return on Apple stock,

Â x as the return on the market,

Â slope m as beta,

Â and the constant B is Alpha.

Â Slope beta tells how much a particular stock co-moves with

Â the market and thus as a measure of the stock systematic risk.

Â So the idiosyncratic risk is the risk that the point will lie above or below that line.

Â And you can see, there's a lot of idiosyncratic risk for Apple.

Â