Continuation Probabilities

E

El Cazador

What are the odds of the market closing higher for 2 days in a row? How often historically has it happened? Not important questions at all but what about the odds of it not reversing for 8 days... or 11 days... or 23 days? When we have had the NAZ up for 7 days in a row is it safe to short the QQQ at the close of the 7th day? Are the odds increasingly smaller that the QQQ should close higher on the 8th, 9th, and 10th days?

Does anyone know what the longest string of days without a reversal is? I would imagine that someone at sometime must have done a college thesis on probability in the stock market.

Thanks
 
This is a rather easy study to perform using excel. It doesnt take a academic researcher to do it. ;)

I'm not the sharpest guy when it comes to programming and advanced excel usage... But I've used macro programming in VBA in excell to do studies similiar to what you are suggesting.

Just loop through the close field on the data you want, create a counter, increase it each time the close is greater than previous... Then when the close is less, print the value of the counter to a sheet in the workbook. Reset the counter and keep going until all the data is done.

Simple as that.

 
Just a little addition... Once you have the data, just use the "frequency" function in excell to sort the data so you can chart it. You most likely will see a bell curve type chart. So yes, I'm sure that after 7 days up, 8 days is less probable. But you should always remember to take other factors into consideration....
 
Sorry... Me again. :)

You probably wont see a bell curve, but rather the right half of a bell curve. (1 day will probably have the highest frequency)
 
I'm seeing some probability errors here. If I flip a two sided coin 5 times, and it lands on heads all five times, the odds of it landing heads the sixth time is still 50-50. The odds don't change simply because of past events. I believe this is called the gambler's fallacy? Similarly, if the Nasdaq were to close up 7 consecutive times, this doesn't change the odds of whether it will close up or down the next day.

Now, the stock market isn't a coin, and of course there are other factors. Some people might say that there is momentum and that it should continue. Others might argue that it's ripe for profit taking. But that's beside the point of what we're discussing here. Statistically, the 8th day after 7 consecutive up days has just as much possibility of going up(down) as any other.
 
It isn't a gambler's fallacy really. Any given day could probably be either up or down (though probably not exactly 50/50). But the odds of 7 straight up days is probably beyond the range of 2 standard deviations, and i'd deffinately short. Look at the bol bands I guess. I do the same thing a lot on individual stox in a pyramid when the hug the bol bands too long.
 
The problem here is we're trying to calculate probabilities of a certain event happening after most of the event has already occurred. Let me give an example. Let's say that we did a historical study and found that the market closed up just as many times as it closed down. I know that's not accurate, but it's probably not too far off. I'd be surprised if it closed up more than 55% of the time. Anyway, for the sake of argument, let's say the odds off getting an up day are 2:1.

Starting before day 1, the odds of getting 8 consecutive up days is 256:1 (2 to the 8th power.) However, if we are now past day 7, and have had 7 consecutive up days, the odds of getting an up day are 2:1. It's not 256:1. You don't base the odds on past behavior, whether it's flipping coins, rolling a die, or measuring the market.

Again, the stock market is a lot more complicated than dice or coins. And we may have our own reasons for believing the market will close up or down on day 8. But even if we could somehow factor in those variables, the odds would still be fairly close to 2:1 for getting an up day. Maybe it's 1.8:1, maybe it's 2.2:1; who knows?

I personally would bet that the market would close up that 8th day, given the strength that the market has been exhibiting.

One thing that's clear, though, this is the wrong way to figure out the odds: find out how many times 8 consecutive up days has occurred, seeing the relatively low occurrence, and concluding that the odds of getting an up day 8 are remote. If you wanted to do a historical test, you would find out how many 7 day streaks you had. Then find out how many times the following day was up. That would give you your historical probability, for whatever that's worth.
 
The gamblers fallacy is important to be aware of when considering your individual trades... (If your last 5 trades are losers, your next trade has the same odds of winning as the last 5, because each trade is statistically independent)

But, unlike coin flips or the results of a random game, market prices REPRESENT A VALUE that is considered by many people. If a stock is in an uptrend, and buying drys up, and the stock backs off 4 days in a row, but the trend is still in tact, the chances of buyers coming in on the 5th day are greater than the 4th, and on the 6th day are greater than the 5th.

People move market prices, not coin flips. Sometimes the behaviour of people can be as random as coin flips... But usually not.

 
Interesting question and series of posts. In my opinion, there is probably a slighly greater likelihood of a down day at this juncture than there would normally would be. The market isn't like a coin toss in one crucial respect ---- most of its individual participants do have memory of what has just occurred and many people also have open positions in that market. After seven up days, mass psychology will tend ----- it's a tendency, hardly a cerrtainly ---- to believe, just as El Cazador who started this thread believes ----- that the market is *due* for a down day. And such beliefs can easily become self-fulfilling prophesies, as some holders of long positions will be more inclined to take profits and some potential new longs will be more hestitant to buy, waiting for a pullback before entering. Of course, there's the opposite psychology ----- jump on the train while it's still moving ----- but probably on balance, the first perspective is likely to be a bit more prevalent than the second one.
 
Each day does increase the odds. But an easier way of looking at this is to bring it out of context.

With each game the Lakers win what is the probability that they will lose the next game?


Take a look at the odds now in Vegas for betting that the Lakers will lose the next game compared to winning the next game.

How many want to bet against them?

With trading we have an edge the reversal is shown early in the morning after the opening by a change in the price. If looking to go short it opens lower than yesterday's close-- it confirms what was thought about move and guess what we can still place trades, unlike in Sports where no more bets once game starts.


If we could still have the same odds that the Lakers would lose and make that bet when they are down 30 points after the first quarter. Talk about a trade.

Wait, I do this already in stock trading. Opps I've said too much

rtharp
 
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