Range vs. Standard deviation

[tradingjournals]

Did anyone do work (or know of work that was done) on trading range vs. standard deviation of price.? If you need notation, let us denote by R the range (Max-Min), and by S the standard deviation. Of interest is the behavior of R/S. (not to be confused by Resistance/Support).

Thank you!

 

[aqtrader]

Did anyone do work (or know of work that was done) on trading range vs. standard deviation of price.? If you need notation, let us denote by R the range (Max-Min), and by S the standard deviation. Of interest is the behavior of R/S. (not to be confused by Resistance/Support).

Thank you!

One of the applications to use sd is to set the width of Bollinger Bands. But it seems using average range +- sd is more interesting to define price band.

 

[Martinghoul]

Did anyone do work (or know of work that was done) on trading range vs. standard deviation of price.? If you need notation, let us denote by R the range (Max-Min), and by S the standard deviation. Of interest is the behavior of R/S. (not to be confused by Resistance/Support).

Thank you!

http://www.ivolatility.com/help/2.html

 

[tradingjournals]

http://www.ivolatility.com/help/2.html

I did not ask about how to compute S (standard deviation), but about the behavior of R/S (where R is the range).

 

[tradingjournals]

One of the applications to use sd is to set the width of Bollinger Bands. But it seems using average range +- sd is more interesting to define price band.

Thanks. Any fundamental reasons behind it? How do incorporate it in a chart as BB are usually in multiples of S (S, 2S, etc).

 

[Martinghoul]

I did not ask about how to compute S (standard deviation), but about the behavior of R/S (where R is the range).

Yes, I know what you asked for... If you look at the link I mentioned, you would have seen that it's a discussion of the various different measures of volatility. Specifically, you might wanna look at the Parkinson estimator.

 

[aqtrader]

Thanks. Any fundamental reasons behind it? How do incorporate it in a chart as BB are usually in multiples of S (S, 2S, etc).

I think the nature of S, that is, standard deviation, or called sigma, σ in math, is that statistically S is not just to show the degree of variation, but also a measure for the probability distribution. For example, the probability for the price to be in range of average R+S is 75.9%, and 97.9% to be in average R + 2S, and so on.
Thanks,

 

[tradingjournals]

Yes, I know what you asked for... If you look at the link I mentioned, you would have seen that it's a discussion of the various different measures of volatility. Specifically, you might wanna look at the Parkinson estimator.

Before I explain the difference, thank you for the link. In the first reading, I did not even notice that there are multiple pages (I think the navigation could be made clearer). My definition of R is different from the Parkinson's definition, but I find Parkinson very interesting and I could understand why you have thought about the R the way you thought about it earlier in this thread.

Suppose one wants to look at 2 years using 1-month bars. The usual estimation looks at end of year closes (24 observations in total). Parkinson's look at the ratios of a given year's high to same year's low. The use of logs in both is omitted here to simplify my writing of this post. My definition of R measures the distance between the highest close and the lowest close, among the 24 yearly closes (Not the R of a given year as Parkinson does). I could do the same for the 24 data points that would be generated by Parkinson's definition.

The range I am interested in is then the range of the 24 observations, not the range of prices within each observation. I hope it is now a clearer definition. Maybe Parkinson's can still help. If so how? My interest is not to search for an estimator, but rather to study the range of all possible sets of observations that has a given STD.

 

[tradingjournals]

I think the nature of S, that is, standard deviation, or called sigma, σ in math, is that statistically S is not just to show the degree of variation, but also a measure for the probability distribution. For example, the probability for the price to be in range of average R+S is 75.9%, and 97.9% to be in average R + 2S, and so on.
Thanks,

Thanks for sharing!

 

[Sergio77]

I think the nature of S, that is, standard deviation, or called sigma, σ in math, is that statistically S is not just to show the degree of variation, but also a measure for the probability distribution. For example, the probability for the price to be in range of average R+S is 75.9%, and 97.9% to be in average R + 2S, and so on.
Thanks,

This should hold only for normal returns, not for price. Price is not normally distributed. Returns also are not in most cases. Maybe for bonds and high cap stocks only.