Correct calculation of currency indices. - page 2

 
Prival >> :

You account for currencies using, a constant coefficient. Which was once calculated by someone once. In order for it to work what you want it to work. Currency rates should not change since you calculated the coefficients. Then everything will add up. But exchange rates change, so everything floats.

I don't think currency weights change instantly because it depends on the amount of currency in circulation.

Why do the exchange rates converge, then diverge again?

 
Mathemat >> :

OK, I will repeat Prival's request to you: formulas, please. How do you calculate the euro and pound indices?

I join in.

Also, if anyone has weights for currencies or calculations with even the most sensible justification, please share.

 
Urain >> :

I don't think the weight of currencies changes instantly because it depends on the amount of currency in circulation (i.e. inflation)

And why "the routes meet and then they diverge again :)" see the picture above.

Maybe the weight does change instantaneously? With a difference of one point, for example.

Assume that the weight changes all the time.

When calculating indices for currencies, what matters is how they move apart from each other. Everything else is irrelevant. Among other things, it does not matter that synthetic pairs derived from those indices do not resemble real pairs.

Otherwise, why calculate them at all? Take the natural pairs and admire them.

 
Mathemat >> :

OK, I will repeat Prival's request to you: formulas, please. How do you calculate the euro and pound indices?

USDX = 50.14348112 *(GBPUSD, -0.133)*(EURUSD, -0.59 )*(USDCHF, 0.05 )*(USDJPY, 0.136)*(USDCAD, 0.091)

expression ( x,y ) means x to the power of y.

EURx=EURUSD/USDX

GBPx=GBPUSD/USDX

as a result EURGBP does not always equal EURx/GBPx ???

 
Zhunko >> :

Could it be that the weight changes instantly after all? With a difference of one point, for example.

Assume that the weight is changing all the time.

When calculating currency indices, what matters is the dynamics of the currencies from each other. Everything else is irrelevant. Including the fact that the synthetic pairs derived from these indices do not resemble real pairs is not important.

Otherwise, why calculate them at all? You may use real pairs and enjoy them.

Personally I need it for extrapolation purposes, as each pair contains the movement of 2 currencies, it is difficult to extrapolate correctly,

It requires hard calculations, and everything is quicker and more accurate when the currencies are separated.

 
TheXpert >> :

I join in.

Also, if anyone has weights for currencies or calculations of them with any kind of intelligible justification, please share.

The calculation of the Dollar Index (USDX) by a basket of six currencies is not accidental - it coincides with the data used by the Federal Reserve System to calculate the trade-weighted dollar index by the currencies of those countries that make up the principal U.S. foreign trade turnover. The Eurozone accounts for most of the US international trade (57.6%), followed by Japan with 13.6%, the UK with 11.9%, Canada with 9.1%, Sweden with 4.2% and Switzerland with 3.6%.

USDX = 50.14348112 *(GBPUSD, -0.133)*(EURUSD, -0.59)*(USDCHF, 0.05)*(USDJPY, 0.136)*(USDCAD, 0.091)
expression ( x,y ) means x to the power of y.

In the formula USDX on NYBOT USDSEK 4.2% weight is divided by 1.4% for Eurozone (as not all brokerage companies have quotes for Sweden, and Sweden turnover with Eurozone is over 80%, i.e. USDSEK is directly related to Eurozone)

 

Making up your own indices can play a cruel trick . Much more important is what all real market participants see . As with non-standard ETFs. The good thing about the standard one-hour bar

The good thing about the standard hour bar is that it is the same for everybody.

 

It is clear then, Urain. On forex AC / BC != AB (if A, B, C are currencies). The reason is not the "wrong" index formula, but the fact that EURUSD, GBPUSD and EURGBP are quoted independently and even at different points in time. Arbitrage opportunities arise, which are quickly levelled off.

 
Mathemat >> :

It is clear then, Urain. On forex AC / BC != AB (if A, B, C are currencies). The reason is not the "wrong" index formula, but the fact that EURUSD, GBPUSD and EURGBP are quoted independently and even at different points in time. Arbitrage opportunities arise, which are quickly levelled out.

I poked around in the code and found that if the cross rate is calculated wrong:
EURx/GBPx
but like this :
(EURx,0.59)/(GBPx,0.133)
it is better but not quite good
the degree is reversed from USDX
Does anybody know the right way?


 
Mischek >> :

Making up your own indices can play a cruel trick . Much more important is what all real market participants see . As with non-standard ETFs. The good thing about the standard one-hour bar

the fact that it is the same for all. What is good about a S&P breakout on the USDX chart - it will affect the Straight pairs.

I already wrote:
"Personally, I need it for extrapolation as each pair has a mixture of 2 currency movements, so it's hard to extrapolate correctly"

That's why you need an index calculation that, when checked, would give the values of
of currency pairs (at least approximately)

Reason: