Talk:Mean reversion (finance)

Inconsistent

The Wikipedia article on "Regression toward the Mean" gives a different definition of mean reversion in finance:

"In finance, the term mean reversion has a different meaning. Jeremy Siegel uses it to describe a financial time series in which "returns can be very unstable in the short run but very stable in the long run." More quantitatively, it is one in which the standard deviation of average annual returns declines faster than the inverse of the holding period, implying that the process is not a random walk, but that periods of lower returns are systematically followed by compensating periods of higher returns."

http://en.wikipedia.org/wiki/Regression_toward_the_mean

Prices vs Returns

Returns should evidence regression toward the mean if they are a random variable. But this article claims that prices (the integral of returns) evidence mean reversion. If you look at the disambiguation page, Mean reversion in finance and regression toward the mean are conflated with each other, thereby conflating returns with the integral of returns.

What is the test of mean reversion?

Is mean reversion falsifiable, and in what sense? It seems clear to me that, given a measurement at time 0, another measurement at time 1, and a mean, we should be able to determine if mean reversion has occurred.

For example, let's take the numbers 0-99. The mean is 49.5. If we get a measurement of 39 at time 0 and 87 at time 1, then has mean reversion occurred?

I imagine so, because 39 is below the mean, and we expect the next measurement to be higher. But then 87 is further from the mean than 39 is, so I could just as easily say no.

Perhaps it is just my own fuzzy thinking, but in the absence of a definition to the above method signature (or a reasonable analog), it seems to me that "Mean reversion" is more akin to myth or tautology than insight.

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Ok, New info, from here: http://www.lmcm.com/pdf/UntanglingSkillandLuck.pdf

This says that reversion to the mean has occurred when t1's radius (distance from mean) is less than t0's radius. For my earlier example with 39, 87, 49.5, mean reversion *HAS NOT OCCURRED*. It seems clear that "mean reversion" does not hold for a uniform distribution. Any previous outcomes regarding radii do not affect the next outcome. No matter which direction nor which magnitude on the scale, all outcomes are equally likely.

Now, for a normally distributed random variable, mean reversion seems so obvious as to question its very observation.

But ok. The critical thing is that the phenomenon of mean reversion depends on the random variable's distribution. Jumping to the guideline of "mean reversion" without having an understanding of the underlying distribution is a mistake.

Nwallins (talk) 02:22, 4 December 2010 (UTC)

One intuitive test for mean reversion is whether the value can go to infinity or zero, given enough time. Stock prices can go very high and at least as often go to zero, so aren't very MR, ditto exchange rates where occasionally the rate between two currencies does go extremely high (typically whn a country goes bad, is conquered, changes government by force etc.) Intrest rates are seen as MR. FX does seem to go through periods of MR as do some equities, and even for a MR item like interest rates the mean itself is seen to change.

MR is used in several different ways in finance... 1) One is regression towards the mean, where if you sample noisy data enough times you, the average you get moves towards th 'real' value.

2) The other is where there is believed to be some process that pulls the price towards some avereage, as if it were on a rubber band, and as with a piece of rubber, the further you stretch it, the harder it is pulled back.

The article only talks of stock prices, but there is a lot of evidence that interest rates are mean reverting, and as above other instruments follow MR sometimes for a while. DominicConnor (talk) 21:34, 14 March 2011 (UTC)

(Mis)usage of term "standard deviation"

Standard deviation is not simply the square root of the sample range. If the term is being used with a different meaning in this context, it should state this clearly and preferably cite some references for the alternative meaning. Alternatively, the use of the term "standard deviation" here may be completely wrong. —Preceding unsigned comment added by Raouul (talk • contribs) 10:59, 4 April 2009 (UTC)

use of *SD* seems correct, but maybe second hand information? that the parenthetical statement is ridiculous. NOT square root, NOR range.

the actual Standard Deviation is taken over a population of price data: current datum and N previous.

eg. most recent 20 days closing price: each day the most recent 20 data are used to calculate SD. this is plotted on the graph as:

• a mid-point – the 20-day moving average, and
• plus & minus, double the standard deviation (upper/lower bound)

this produces "Bollinger Bands," which *ARE* used with something of the strategy described. presumably there are articles which could be used to clarify the main article?

• Standard Deviation
• Moving Averages
• Bollinger Bands

the main post makes somewhat more sense if you know that

the Moving Average of 20 is an example here of the MEAN, and the bounds defined by 2 SD indicate where the price movement *may* reverse, crossing outside the line may indicate a reversal in the immediate short term.

(variables in the equation here are: "20" - number of periods, "2.0" SD, whatever works best for the trader, and for the market being traded. "days" timeframe is whatever matches the data-set being graphed.)

theoretically: in a rally the price will trend between the MEAN, and the upper 2-SD. in a fall price will trend between the MEAN, and the lower 2-SD.

(except when it doesn't)

the breakaway falls, and spectacular rallies, -- the ones that do not reverse when they hit the boundary -- often closely follow the movement of the 2-SD-band! ...which rapidly becomes wider as the price deviates further from the mean. so the 2-SD is useful at predicting where a rising price will reverse -OR- it is useful at predicting how fast a rising price will continue to rise. every time a bound is hit the trader must determine if the price will continue to break the [moving] bound, or expect a reversal.

highly useful to the technical trader to know either of these pieces of information, but intimate knowledge of the current situation of the stock: of the company itself, the environment the company is in, and of the mindset of the market that owns it, are all needed to assess which it is most likely to actually be.

no one said trading was easy. —Preceding unsigned comment added by 70.67.179.130 (talk) 04:40, 8 July 2009 (UTC)