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Re: Market Meanness Index
[Re: MatPed]
#449512
03/22/15 17:59
03/22/15 17:59
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Joined: Dec 2013
Posts: 568 Fuerth, DE
Sphin
User
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User
Joined: Dec 2013
Posts: 568
Fuerth, DE
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The theory behind it is that in a completely uncorrelated price series, the probability of a price to revert to the mean is exactly 75% Can someone please tell me where this statement comes from? A hint to its math. base might be also sufficient. Thanks, Sphin
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Re: Market Meanness Index
[Re: Sphin]
#449525
03/23/15 03:48
03/23/15 03:48
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Joined: Apr 2014
Posts: 482 Sydney, Australia
boatman
Senior Member
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Senior Member
Joined: Apr 2014
Posts: 482
Sydney, Australia
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The theory behind it is that in a completely uncorrelated price series, the probability of a price to revert to the mean is exactly 75% Uncorrelated with what? Or are you referring to a random walk process?
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Re: Market Meanness Index
[Re: boatman]
#449576
03/24/15 15:09
03/24/15 15:09
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Joined: Jul 2000
Posts: 27,986 Frankfurt
jcl
OP
Chief Engineer
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OP
Chief Engineer
Joined: Jul 2000
Posts: 27,986
Frankfurt
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Yes. Uncorrelated with itself, i.e. Price(today) has no correlation to Price(yesterday). Then you'll get the 75% mean reversion probability.
You can prove this with a simple geometrical consideration. Suppose you have a set of today's prices Pt, and a set of yesterday's price Py. By definition, half the prices from Pt are below the median and half are above the median; same for Py. Now combine the two sets to a 2 dimensional set of vectors with coordinates (Pt,Py). Every such vector represents a possible price change from Py yesterday to Pt today. This set of price changes can then be split by the median lines into 4 sub-sets:
1. (Pt < Median, Py < Median) 2. (Pt < Median, Py > Median) 3. (Pt > Median, Py < Median) 4. (Pt > Median, Py > Median)
The 4 subsets have exactly the same number of elements when Pt and Py are uncorrelated. The value of the median does not matter.
Now, mean reversion, or more precisely moving in direction to the median value means the following condition:
(Pt > Py and Py < Median) // yesterdays Price was below the median and rises, i.e. todays price is higher or (Pt < Py and Py > Median) // yesterdays Price was above the median and falls
The first condition is fulfilled in half of subset 1 (the other half had Pt < Py) and in the full subset 3 (because Pt > Py always in subset 3). So, this happens for 1/2*1/4 + 1/4 = 3/8 of all elements.
The second condition is fulfilled in half of subset 4 (the other half had Pt > Py) and in the full subset 2 (because Pt < Py always in subset 2). This is true for another 3/8 of all elements.
3/8 + 3/8 = 6/8 = 75%.
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Re: Market Meanness Index
[Re: jcl]
#449671
03/27/15 22:55
03/27/15 22:55
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Joined: Dec 2013
Posts: 568 Fuerth, DE
Sphin
User
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User
Joined: Dec 2013
Posts: 568
Fuerth, DE
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Sometimes I need a little longer, sorry for that. But mean reversion can be tricky and I'm interested in understanding your derivation. Suppose you have a set of today's prices Pt, and a set of yesterday's price Py. By definition, half the prices from Pt are below the median and half are above the median; same for Py. You are talking of 2 sets of prices Pt/Py like in bars of today/yesterday and there are 2 medians, one for the set Pt and one for the set Py? Now combine the two sets to a 2 dimensional set of vectors with coordinates (Pt,Py). Combining arbitrarily or each one of Pt with each one of Py? Thanks, Sphin
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