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.