Posted:
edited January 2014
Okay, I want to calculate for a particular pair of numbers, how much, in a simple %, the "range"/variance? is.

Lets say for x and y:

((x-y)/((x+y)/2))*100

1. What is this formula called?

2. Is it applied in basic finance?

3. Can it be simplified further?

I think it can be simplified futher as

[200(x-y)]/(x+y)

I cant remember sh1t from my high school maths so... any help appreciated as to what I am doing here. Thanks.

So, for example, x = 1.33 and x = 0.99, I get 29.31%

The practical application is as follows:

For a particular currency pair, a quick calculation of this "range/variance" within a time period, say 2 years, where you only know the maximum and minimum.

1.33 and 0.99 is the maximum and minimum of a 2 year period of the currency pair AUDSGD. So applying the formula this "range/variance" is 29.31%.

Kind of a measure of volatility... but not sure what the proper technical term is.

Is this something like a very simplified "percentage band" that the currency pair trades in within a certain time period, sampling only the maximum and minimum?

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Oh, how do I write it above so when using 200*(x-y) the result of x-y should only be a positive number.

Something like 200*|x-y|

Is that it?

If you think this is basic Math homework far beneath your skillz feel free to ignore but if you are feeling nostalgic you can share your thoughts here...

Yes, there is Google, but I am more interested in if this simple percentage band calculation is used in rough estimates in finance/forex/etc.
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I don't know what the formula is, but statistically it's worthless. Variance needs all the data points, not just the high and low.

All that doesn't mean some group doesn't use it, but if that is the financial industry it's no wonder they screwed up risk assessment so badly.
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It might help of you set it equal to something. It's a polynomial BTW.

Often times these are set equal to one.
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The formula is calculating a percentage with known numbers, not solving for them. Setting that equation equal to anything is incorrect and even less meaningful than the percentage is.
Posts: 9,262member
Quote:
Originally Posted by FloorJack

It might help of you set it equal to something. It's a polynomial BTW.

Often times these are set equal to one.

Ah... But I think here I'm setting it to be equal to the result. The result (let's call it Simplified Percentage Band) being unknown, x and y being known.

For example,

Simplified Percentage Band = [200(x-y)]/(x+y)

Polynomial. That brings back some memories, I've totally forgotten what that even means.
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Quote:
Originally Posted by Hiro

I don't know what the formula is, but statistically it's worthless. Variance needs all the data points, not just the high and low.

All that doesn't mean some group doesn't use it, but if that is the financial industry it's no wonder they screwed up risk assessment so badly.

You are right, in that the data points are perhaps variance across many days or many weeks. You'd measure this simple formula for a day, then do standard deviation or something etc.

Which brings us ultimately to the point that if I was interested in Forex I'd look up all the technical calculations they do.

Which forex and stock traders use, all sorts of fancy-pants technical, statistical analysis.

WHICH SEEMS TO MEAN BOLLOCKS IN REAL LIFE. And yes, Maths either doesn't help run a sustainable financial industry, or that they don't know how to apply it properly.

For example, Bell Curve analysis discounts the possibility of very far outliers, which if used in risk management, masks some investments which are very risky, and these very investments make the Bell Curve a meaningless analysis.

On iTunes U there's a "town hall meeting on financial crisis" podcast from Duke University. Very good stuff.

In my view, the financial industries use of mathematical models needs a total overhaul. Period.

As for my little formula, maybe if these were combined with other data points over time or over other currencies, there may be hope for it!
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No. You are misapplying what the math of statistics means and does. The screw-ups most folks see in situations which cite statistics is almost entirely due to fatal oversimplification of those computing and/or interpreting the results.

If you aren't interested in actually getting the subtleties of the calculations correct it is best to run away from any form of mathematical analysis and just guess. At least you will be honest with yourself that way. In a way I think none of the financial houses were.

See those statistics do mean more than bollocks. When an idiot uses the information utterly incorrectly it has no reflection on the statistical analysis. You are even showing serious ignorance in your statements about bell curves, properly called normal distributions. See anyone who actually respects their ability to do analysis knows the tails of those curves go out to infinity entailing all possible outliers. They also understand that there are an infinite number of ridiculous far outliers out there.

I agree that the financial models need an overhaul. Unfortunately nobody knows enough about the specifics of human nature to make those models. It was the hubris of a few programmers, fed by a few years of up market momentum, saying they had a good model because they refused to acknowledge they didn't have the first clue about many critical variables. Or even worse, they didn't have a clue that they didn't have a clue.

If you want a formula for variance, just go for the basics: Discrete_case
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Ah...

I mentioned "And yes, Maths either doesn't help run a sustainable financial industry, or that they don't know how to apply it properly."

The latter, then.

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Quote:
Originally Posted by Hiro

... It was the hubris of a few programmers, fed by a few years of up market momentum, saying they had a good model...

Especially with so much online trading, and so much "automated trading programs" available, what do you think of all these?
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Quote:
Originally Posted by Hiro

The formula is calculating a percentage with known numbers, not solving for them. Setting that equation equal to anything is incorrect and even less meaningful than the percentage is.

Well then do this

((x-y)/((x+y)/2))*100=p

or even this

((x-y)/((x+y)/2))*100=f(x,y)
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Interestingly enough, the same formula is used for "modulation", which describes the relationship between resolution and sharpness of an image. It is approximately the same as "contrast".

Which makes sense somehow, because nvidia2008 wants to know the "contrast" of the exchange rates.

Unrelated to this thread, this morning I found a paper from ARRI (those guys who build expensive cinema camera equipment) where this formula and its relevance is explained on page 7:

Theory Basics for Motion Picture Imaging
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NVidia, you keep saying "maths" instead of "math". Would I be right in assuming you have a non-North-American background? The rest of the world abbreviates mathematics as maths.

Cheers
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Quote:
Originally Posted by nvidia2008

Especially with so much online trading, and so much "automated trading programs" available, what do you think of all these?

I think they are part of the root cause and responsible for much of the volatility.
Posts: 9,262member
Quote:
Originally Posted by tilt

NVidia, you keep saying "maths" instead of "math". Would I be right in assuming you have a non-North-American background? The rest of the world abbreviates mathematics as maths.

Cheers

Yes. I was brought up with the Queen's English, living most of my life in Her colonies (well, ex-colonies)...
Posts: 9,262member
Very, very cool. Thanks.

I've been somewhat interested in the whole 4K digital video phenomenon.

The author stresses you should shoot in Super 35mm, scan at 6K, to get quality 4K.

As opposed to shooting in 4K which actually gives you less than 4K.

Just the process of dealing with film, which I still believe gives some amazing visual and emotional quality when done right, is much more involved compared to the industry charging ahead to all-digital workflows.

Quote:
Originally Posted by durin oakenskin

Interestingly enough, the same formula is used for "modulation", which describes the relationship between resolution and sharpness of an image. It is approximately the same as "contrast".

Which makes sense somehow, because nvidia2008 wants to know the "contrast" of the exchange rates.

Unrelated to this thread, this morning I found a paper from ARRI (those guys who build expensive cinema camera equipment) where this formula and its relevance is explained on page 7:

Theory Basics for Motion Picture Imaging

Posts: 9,262member
Now that said, the ARRI paper also shows that the formula I presented right at the very start of this thread has some use.

As Hiro and Floorjack* mention, it's about capturing a lot more data points and graphing in various ways to get meaningful information.

Hiro is suggesting more of a variance and standard deviation approach.

Floorjack's suggestion of f(x) is more related to something like the modulation graph in the ARRI paper.

Food for thought, appreciate everyone's contribution.

Now back to my day job...
Posts: 202member
Quote:
Originally Posted by nvidia2008

Very, very cool. Thanks.

I've been somewhat interested in the whole 4K digital video phenomenon.

The author stresses you should shoot in Super 35mm, scan at 6K, to get quality 4K.

As opposed to shooting in 4K which actually gives you less than 4K.

Just the process of dealing with film, which I still believe gives some amazing visual and emotional quality when done right, is much more involved compared to the industry charging ahead to all-digital workflows.

You're welcome.

Of course the ARRI guys recommend using 35mm, they make the cameras... Film may still be the better way for the next couple of years or so, but prohibitively expensive (for my work, anyway). We will see a few quite interesting things in the next year, i. e. Red Epic/Scarlet...
Posts: 2,663member
OK we have a name for the function, modulation transfer function. It describes a rule of how to interpret data so I guess I was a bit strong saying it is statistically worthless.

But, from a predictive statistics standpoint it is still quite worthless.

That paper, which I don't dispute in the least, is doing fixed mathematics on fixed data to find a closed form solution in a closed system. That is the right approach for what the whitepaper is discussing. We have a simple comparison which is very useful for comparing discrete points in a fixed image (the modulation transfer function) which helps determine the point at which the data resolution is too small to discern any remaining differences in the data.

Taking an approach out of it's domain takes the mathematics out of context and can lead to all kinds of badness because the baked in assumptions which are necessary for correctness no longer apply. Sometimes creative folks come up with ways to address the issues and show that the equations are more general and that drives the overall understanding of the world forward, but this isn't what we have here. This says nothing predictive about the trajectory motion of the data through time.
Posts: 9,262member
LOL Yeah it was pretty obvious they were saying, Buy our cameras! Use Super 35mm film!

Show us some samples when you get 'round to shooting on Red...

Quote:
Originally Posted by durin oakenskin

You're welcome.

Of course the ARRI guys recommend using 35mm, they make the cameras... Film may still be the better way for the next couple of years or so, but prohibitively expensive (for my work, anyway). We will see a few quite interesting things in the next year, i. e. Red Epic/Scarlet...