Hi, in this lecture I want to talk about something called the normal random Lock model. And the idea here, is that we've got a normal random lock, just like we had previously, except for now instead of the steps being plus one or minus one they can be any value. And those values are going to come from a normal distribution. What I'm going to do, is I'm going to use this model to talk about something about the efficient market hypothesis. And the idea behind the efficient market hypothesis is that market prices capture all available information. And if that's true any fluctuations in the price would be random. And so therefore stock prices will be just a random walk. Now of course if stock market prices should be going up at some rate that's proportional to growth of the economy but after we de trend it. What's left should basically just be random a random walk so first let's talk about random walks and then let?s think about the sufficient marketing hypothesis so here's how a normal random walk works you basically again just like before you said X equals zero and then each period you change the value by some random amount but that random amount comes from a normal distribution so instead of [inaudible] to plus one or minus one next period it might go to plus three and then next period it might go to minus one if I get a really bad shock so you [inaudible] those are shocks that drive it up and down and those shocks come from a normal distribution. So if I look at a bunch of normal random walks, I get a picture that looks something like this. Some of them end up really high, some look really low. But on average since the mean is a normal distribution of zero, we'd expect them, if I added all these things up to be right about zero. So there would be big winners, big losers, but things will come up right about zero. Now those step sizes, and this is the important part. I'm going to assume. Come from a normal distribution. And when we think the idea of that prices in the stock market are random walk, you could also u se a normal distribution. But that's not quite accurate. In fact, if you look returns on the DOW Jones industrial average, you'll see that it's not quite normal. There's more days where nothing really happens. There's also more days where there's really big events. So there's sorta fewer moderate days. So you get. Surprising large events, surprising small events and you get a lot of zeros. But it's not a bad first approximation think of it as a normal random walk. But we could fix it to approximate to normal exact excursion if we want it. There's a famous book by Burton L keel call, A Random Walk Down Wall Street. And what he argues is that prices in the stock market Are random walks. Now you might say, that's crazy, you know, there are trends, there's things that go up, there's things that go down. Well, let's look at some data on that. So, suppose the Dow Jones Industrial Average posted a gain the previous day. If there really were trends you'd expect there to be a gain the next day. Well here's a graph that shows whether or not that's true. Now if you look, here's the 50 percent mark, so if [inaudible] is right, you'd expect to see no trend. That if it's high yesterday, it's not necessarily gonna be high today. And if you draw a line, like in 1975 and look past there, it's pretty much true. Now, prior to 1975, it wasn't true. So we could argue. Market maybe have become more efficient. There really is no advantage there. But this makes sense, just think about it. Suppose it were the case that if prices went up today, they're going to go up tomorrow. Well what should you do. You should get even more today, because you're going to make money tomorrow. But if you get even more today, that's going to drive prices up today which means that they won't go up tomorrow, Which means that [inaudible] right, they're probably going to be random tomorrow. So any trend, people should anticipate. So here's the market hypothesis in short form. Prices reflect all available information, therefore any fluctuations should just be random. Because it's impossible, then, to beat the market. Here's the real long, version that the efficient market [inaudible] is associated with a random [inaudible]. And this is a term loosely used in the finance literature to character a price surge where all subsequent price changes represent random departures from previous prices. The logic of the random lock idea is that the flow of information is unimpeded and information is immediately available in stock prices then tomorrow?s price change will effect only tomorrow?s news and will be independent of the price changes today. But news is by define unpredictable. And thus resulting price changes must be unpredictable and random. So what does this mean this means that the stock market's containing all relevant information so if there was any information that you could use to make money somebody else could use it to make money and would already be in the price so for example suppose somebody invents a new drink that uses oranges and you know this is going to be wildly popular so therefore the price of oranges should go up that means if the price of oranges is here and you know it's going to go here you should buy oranges and you're going to make money. However, other people know that if, as well. If all information is out there and it's unimpeded, everyone will know that the price of oranges [inaudible] up and so the price of oranges will immediately be driven up. So therefore any changes in the price of oranges tomorrow are gonna be random. There will be no trend towards oranges reaching its price. They'll immediately jump to what their full information value will be. So what we get is, is that stock market prices should be random. Now, you could say, is that true? [inaudible]. I mean, we saw the one graph, but I mean, let's, let's look more deeply. Well, one thing that people noticed was something called the January effect. And if you looked at what happened to stock prices from 1927 to 2001, you see, wow. In January, stock prices went up four%, whereas, in the other months, they went up less. What does this mean? It means [inaudible] it's really good to invest in December, invest in late December, you'll make more money. Well, if everybody knows this, then what should happen? They should all invest in December. Prices will go up in December, which means that prices in January. [inaudible] will go down. So let's look in 2009. And let's look at what happened in the month of January. Well, what do you know? It went down. Let's look at 2010-2011. Now here is January right here. [laugh], and all we see is again it went down in both cases. So, if you think about. Any trend that might exist, any inefficiency in the market, once you identify it, other people should identify it, and therefore, you're not going to be able to make any money. Now, if you're the first mover, you can make some money. If you're the first person that if you know, if you're the first person to learn about orange prices gonna be any higher yes, then you'll make some money. But in general if you just look at the market, you shouldn't expect any systematic trends. You should see what's a random walk. Now of course people are critical of this. There has to be something wrong with it. Let's look at some of the criticisms of the efficient market hypothesis. Here's the first. There's way too much fluctuation. So this is just the price of Starbucks stock, and this is just, you know, year by year. And if you look at the fluctuation in any stock's price, it just goes up and down so much it's really hard to believe that the prices are really efficient. There must be other stuff going on. Here's another assumption, problem. There's consistent winners. If it were the case, that things were efficient, then we'd have, we wouldn't have anybody win. 30, 40 years in a row. Some of you might win ten years in a row but people wouldn't win 30, 40 years in a row. And you wouldn't see people who systematically outperformed the market at the level which you see real data. So this is Richard Hathaway, Warren Buffet's comp any, what you see is they've so consistently outperformed the market that it's hard to believe that that's luck. Okay. So what have we got. We've learned that we can write down a very simple. Normal random walk model. And with that model we can engage something known as the efficient market hypothesis. Maybe you believe it, maybe you don't. But it's a reasonable model to think about what stock prices look like. And if you fit it to the data you see in some cases it seems to work pretty well and in other cases maybe there are some consistent winners when there isn't too much volatility, it doesn't quite work. But it's still the case that the model helps explain a little bit what stock market prices look like. And it's also a reasonable model to apply to a whole bunch of other situations as well. Thank you.