Correct calculation of currency indices. - page 18
You are missing trading opportunities:
- Free trading apps
- Over 8,000 signals for copying
- Economic news for exploring financial markets
Registration
Log in
You agree to website policy and terms of use
If you do not have an account, please register
Let's just get this over with.
--
I divide currency (and other asset) indices into "clean" and "dirty" (; unclean ;).
"Unclean" ones most often claim to bemore useful for trading (which I highly doubt, because the authors most often just don't know how to count clean indices). ;-)
So net indices.
The problem statement is simple: to derive formulas to calculate some floating values (called indexes of the asset), that satisfy the condition of complete consistency with the other indexes of the basket and their traded relations (trading instruments) at any point of time. In other words (in terms of currencies): the ratio of one index (say USDx) to another (say EURx) must match the rate of their traded relation (i.e. EURUSD) at any time. Ah yes, the basket. We cannot derive such formulas unless we first fix a set of instruments (currencies and pairs). Such a fixed set is called a basket.
For example, let's derive formulas for a set of instruments that includes all currency pairs between [USD, EUR, GBP, JPY and CHF]. Five currencies (in this case), but there may be any number of them, as long as there is enough information for their construction (i.e. all rates of corresponding currency pairs are known or can be derived from known ones).
To do this let's build the following matrix:
Consider the rows of this matrix. In each row we have a set of currency pairs (or their inverse values easily obtained from pairs) and one unit (like CHFCHF or EUREUR).
If we multiply all elements of each line, the result will be fractions of the form XXX^5 / (USD*EUR*GBP*JPY*CHF). It is principally important for us that all these fractions have the same denominator (I call it the basket denominator). In the numerator of all these fractions, the same currency is multiplied by itself five times (the number of currencies in the basket). If we calculate the fifth (for a given basket) power from these values, the currency in the numerator will return to the first power, and the geometric mean of all currencies in the basket will appear in the denominator. As it was mentioned above, this value is the same for all the fractions, and that is why the obtained values have the property that when divided by one, after the reduction of denominators they guarantee the equality of the obtained ratio to the corresponding currency pair at any moment of time.
The problem is solved. The formula is derived and justified.
--
Whoever understands the reasoning can easily understand the simple mathematical fact that the calculation of the net indexes cannot be done differently (the variation-optimization method is not another way) and cannot lead to other values (to the exact multiplier of the denominator).
Amen.
I hope the topic can finally be closed.
Although it is possible of course to wallow in some "dirt". :) It would only be a reasonable justification.
Igor's right. The first derivative, from the index spectrum alone, gives everything you need to trade. But it is also desirable to calculate the indexes correctly to have an advantage over the market. I.e. for trading.
What's the beast?
Here we go. Is there going to be a rationale for your uncleanness?
;)
No specifics there - I've been reading from the first page, I thought at last someone had seriously decided to "pick apart" the market because the article was published and a discussion was about to take place, but I guess I was wrong...
OK, so it's like this - I'm sad, I wrote it ))))
As for the subject: the indexes have a point - "you just do not know how to cook them" (c), sorry for being banal, I do not understand who promised that the indexes should correspond to a similar movement in currency (major currencies), the same Zhunko and hrenfx show the same thing with different methods - if there is an imbalance between the indexes and the major, then this imbalance will be settled by the market: either the crosses will move or the majors will move, and if the majors move, there will be a trend that often starts pulling the so-called "allied currencies" - apparently the market has such rules and no one wants to break those rules. In principle what I have written is just another "water", but I can say with certainty that "spectral analysis by Zhunko" and analysis of correlation and a basket of currency pairs by hrenfx, can be replaced by changes in price increments - if the price increment per unit time is constant for all currencies, but the sign of increment changes periodically - then there is no imbalance, and if any currency has not changed its sign in the same way as the others, then there is imbalance.
ZS: hrenfx raised the issues correctly in his threads - the price is not always driven by the volume of supply and demand, often the inside drives the price more effectively than the demand
You can calculate indices, take derivatives from them, or whatever you need, but if it is an inside information, you will not get it from what you have now (only after the fact). No matter how much you change the basis (for example, Athenian transformations) no new information will appear.
On the highlighted: if the indices are calculated using quotients, there will never be an imbalance (only discreteness errors are excepted).
You can calculate indices, take derivatives from them, or whatever else you need, but if it is insider information (hidden from the market), you will not get it from what you have now (only after the fact). No matter how much you change the basis (the Athenian conversion is an example), no new information will appear.
On the selected: if indexes are calculated by quotients then there will never be an imbalance (exceptions are only discreteness errors).
At the risk of being rude (so the thought has slipped) - any reversible lossless transformation does not carry any new information.
The moral is: to beat the market one should look for irreversible transformation, or as they say, lossy compression.
Let's not generalise. We are talking about the dollar index. Your opinion and justification in the studio. By the way, right on topic.
At the risk of being rude (it's just a thought), any reversible lossless transformation does not bring any new information.
Hence the moral: in order to beat the market one should look for irreversible transformation, or as they say, compression with loss of information.
At the risk of being rude (it was a thought), any reversible lossless transformation does not carry any new information.
Hence the moral: in order to beat the market we need to look for irreversible transformation, or as they say, compression with loss of information.
We do not need to lose information. We need to concentrate it. ;)
// almost a jokeAt the risk of being crude (so the thought has slipped in) - any reversible lossless transformation does not carry any new information.
Hence the moral: in order to beat the market, one must look for an irreversible transformation, or as they say, a compression with loss of information.
Metamathematics proves that any non-contradictory mathematical theory is a tautology (formally carries no new information). Nevertheless mathematics is a very useful discipline, although it is a servant of sciences :)
Your reasoning is pure sophistry, the proof of which is only in your head (if any).
It's kind of like filtering.
Yeah, well, it's just important to filter out the useless information. I just wish I knew more about it...
:)