Are share prices random?

[yabz]

One test of randomness is the runs test (Bradley, (1968). Distribution-Free Statistical Tests, Chapter 12). A run is defined as a series of increasing values or a series of decreasing values. The number of increasing, or decreasing, values is the length of the run. For example UP DOWN is a run of 1. UP UP DOWN is a run of 2.

I have applied this test to the price of the S&P 100 (OEX) index from 16/4/02 to 1/1/97 (see below) which is a total of 1329 days. I then counted the runs that occurred in a list of 1329 random numbers normally distributed and with the same mean and standard deviation as OEX.

These are the results:

OEX
1 256
2 153
3 95
4 46
5 25
6 2

Random Numbers
1 250
2 116
3 80
4 47
5 26
6 11

(the runs are in the first column - its difficult to format a table on this board)

This is strong evidence, I would say, that prices are random

www.yabz.com

 

[EricP]

The fact that I've been profitable 9 out of 10 days all year long is only indicative that I'm VERY LUCKY! Same goes for other successful traders. Their day, and mine, is coming...

Or, perhaps we just trade randomly... in synch with the prices??

-Eric

 

[Lobster]

Originally posted by yabz
One test of randomness is the runs test (Bradley, (1968). Distribution-Free Statistical Tests, Chapter 12). A run is defined as a series of increasing values or a series of decreasing values. The number of increasing, or decreasing, values is the length of the run. For example UP DOWN is a run of 1. UP UP DOWN is a run of 2.

I have applied this test to the price of the S&P 100 (OEX) index from 16/4/02 to 1/1/97 (see below) which is a total of 1329 days. I then counted the runs that occurred in a list of 1329 random numbers normally distributed and with the same mean and standard deviation as OEX.

These are the results:

OEX
1 256
2 153
3 95
4 46
5 25
6 2

Random Numbers
1 250
2 116
3 80
4 47
5 26
6 11

(the runs are in the first column - its difficult to format a table on this board)

This is strong evidence, I would say, that prices are random

www.yabz.com

I did a similar test on 1-minute bars of the NDX a while ago and came to the same conclusion: If you just look at whether the next minute is up or down, prices appear to be totally random.

But obviously EricP has a point, and I knew that, so I started thinking, and the next step was pretty obvious: There are successful traders, therefore they must have some way of predicting something in the markets with a higher than random probability, but it is obviously not whether or not the next index bar will close higher or lower than the previous one. It must be something else.

As I understand it, there are two ways to deal with this situation and make a profit: You either rely on your gut / intuition and lead a long battle within yourself to separate it from your emotions, or you try harder and don't stop at your first experiment, until you eventually find and quantify an aspect of price development that is not equivalent to a random variable. I believe either way is viable, and I believe you might go the second route.

 

[silk]

While longer term prices appear random, short term prices are not random. Successful day traders can pull huge sums out of the market by learning the mechanism of the market.

Many traders have 9 up days for every down day. I'm up around 81% of the days for 2002. Thus clearly everything about the market is not random.

If i had to pick one stock today and guess where it would be in 6 months, higher or lower, i would have around a 50% chance.

But if i had to say whether i will make a few thousand dollars trading tomorrow morning, i would say yes, and be right around 81% of the time.

 

[Lobster]

Originally posted by silk

Many traders have 9 up days for every down day. I'm up around 81% of the days for 2002. Thus clearly everything about the market is not random.

That is not necessarily so. I can devise a system which will make you money 99% of all days just flipping a coin. But on the 1 out of 100 days you will lose 99 times more on average than you make on your average winning day.

And that's also where the mistake in our initial randomness tests lies: Just because there is a 50-50 chance that the next bar will close up does not mean you will have an expected gain of zero if you buy now.

Originally posted by silk

If i had to pick one stock today and guess where it would be in 6 months, higher or lower, i would have around a 50% chance.

That might be so, but if you had to guess a month ago whether or not the DJIA would be up three months from then you would have had a better than 50-50 chance. There are long-term patterns, too.

 

[JS11374]

Originally posted by EricP
The fact that I've been profitable 9 out of 10 days all year long is only indicative that I'm VERY LUCKY! Same goes for other successful traders. Their day, and mine, is coming...

Or, perhaps we just trade randomly... in synch with the prices??

-Eric

This has NOTHING to do with the randomness of price movement. Win/Lose ratio will explain this perfectly. Your profitablity ratio neither confirms, nor denies, the topic at hand. It is entirely irrelevant to the statistics presented, which I can confirm to be correct. I have done these tests myself some time ago.

 

[chasinfla]

fwiw. Speaking of the randomness of the change in prices (versus the absolute numbers themselves) my tests of randomness of prices (the presence or absence of trends) measured the number of consecutive closes in the same direction (plus or minus) over a given time period.

It was clear that trendiness was closely related to the time duration. The shorter the time frame, the less trendy the price changes. As time frames were extended, trendiness became more persistent.

What seems like randomness is, imho, simply a component of some larger trend. Even a 100 year chart of the Dow Jones, in the context of 1000 year time scale, is about as conclusive as a tick chart. Yet the existence of trends during that time -- actually, one persistent trend -- is clear.

 

[silk]

Let me add this to the quote, there are many successful traders who are up 9 out of every 10 days....And their largest up days are bigger than their worst down days.

 

[silk]

Where a stock price is headed in the long run is random. But how it will get there is not random.

I can't tell you where CTX homes will be trading in 12 months. But if i trade it every day for the next 12 months i will have made a ton of money.

 

[Kymar]

You think you're the first person to apply such tests to prices in the financial markets?

For many reasons, including some that have already been mentioned here, your evidence and approach are rather laughably insufficient to the conclusion you reach.

You might take a look at THE MATHEMATICS OF TECHNICAL ANALYSIS (Sherry and Sherry, 1992) for a much broader and deeper application of similar statistical methods to price data. A NON-RANDOM WALK DOWN WALL STREET (Lo and MacKinlay, 1999) offers a more difficult, more extensive, and arguably more sophisticated approach. And I wouldn't say that either book, or much work of this type that I've seen anywhere, addresses the key issues in a way that's very relevant to the practices of traders.

Along the way, you might also want to refine your language: The OEX represents a kind of average (i.e., an "index") of share prices, not share prices as such.