For those who have (are) seriously engaged in co-movement analysis of financial instruments (> 2) - page 15

 
hrenfx:

EURUSD^Koef1 * GBPUSD^Koef2 * EURGBP^Koef3 must be cointegrated. Obviously, this would be if all coefficients were equal to 1/3.

Wrong.

Theoretical cointegration will be when the volume vector of EURUSD, GBPUSD, EURGBP respectively equals (1, -EURGBP_0, -1) (or is proportional to it). You don't take into account the exchange rate translation to the account currency (say, USD). You need to "cointegrate" the equity of the account, not just the exchange rate numbers.

The second component of the vector is the EURGBP exchange rate at the time of opening all three. I checked it on Xupypr' s script.

Maybe the same error is in Recycle as well?

P.S. I can provide the calculation, it's simple.

P.P.S. I don't work with products. I work with sums, i.e. what we can actually trade. Only now I noticed that you have a product, i.e. something like an index :)

 
costy_:
I think it is necessary to see indices of currencies which are used for trading.

Cross is an elementary synthetic of two majors.

An index is a synthetic of majors with almost hard-coded weights.

If you add such a synthetic to a set of majors, you get a "ring". I.e. indexes (as well as crosses) do not contain any additional information in comparison with majors.

 

hmmm... 0.3EurUsd 0.3GbpUsd <> 0.3EurGbp....... your indicator is bullshitting ....

 
hrenfx:

The index is a synthetic of majors with almost hard-coded weighting coefficients.

I do not use weighting coefficients of "majors",


 
Mathemat:

In fact, I'd have to turn my brain somewhere drastically to find something.

Turning:

You have $1000. You know that some FI has gone up 1%. This means that if you had invested your $1000 in that FI (bought) at the start of the rise, the return would have been 1% - $10.

What does it mean to invest $1000 in an FI? It means that you buy or sell $1000 worth of FI.

Examples:

  1. You buy $1000 worth of potatoes.
  2. Bought $1000 worth of stocks.
  3. Bought EURUSD for $1000.
  4. ...

So, if you suddenly want to buy EURUSD at $333, sell GBPUSD at $333 and sell EURGBP at $333, you will not make any profit, you will get a minus for trading costs.

The $333 is the margin (collateral) you will pay when you buy/sell the FI.

Get those pipsdollars and other bullshit out of your head. Why complicate things? How will you trade if one FI has USD as its base currency and another one has EUR? And if there is a bunch of base currencies?

All this nonsense about pips and lots should be forgotten like a bad dream. There is a concept of investing through buying and selling FIs, buying and selling a portfolio, buying and selling TCs...

Recycle in particular and from these considerations is universal.

 
Then we are not talking about cointegration, but something else. So, do you want to show the calculation or not? I'm talking about a calculation that proves that at a certain lot ratio and with EURUSD, GBPUSD and EURGBP open at the same time, equity is stationary? Well, not counting the costs (spreads, commissions, swaps) of course.
 
Mathemat:
Then we are not talking about cointegration but something else. So, do you want to show the calculation or not? I'm talking about a calculation that proves that at a certain ratio of lots with EURUSD, GBPUSD and EURGBP open at the same time the equity is stationary? Well, not counting the costs of course (spreads, commissions, swaps).

show me, of course...

---

I in turn show for Sell GbpJpy Buy GbpChf = Buy ChfJpy

Sell GbpJpy - Lot = 1

Buy GbpChf - Lot = 1

Buy ChfJpy - Lot equal to the Opening Price of Buy GbpChf :)

 
hrenfx:

So, if you suddenly want to buy EURUSD at $333, sell GBPUSD at $333 and sell EURGBP at $333, you will not make any profit but get minus for trading costs.

$333 is the margin (collateral) you will pay when you buy/sell FI.


In red - when you sell EURGBP at $333 then yes EUR is sold at $333, but GBP is sold lower and you do not get a lock

blue - it all depends on where the price will go, the coefficients are not equal.

 
Mathemat:
Then we are not talking about cointegration, but something else. So, do you want to show the calculation or not? I'm talking about a calculation that proves that at a certain lot ratio and with EURUSD, GBPUSD and EURGBP open at the same time, equity is stationary? Well, not counting the costs (spreads, commissions, swaps) of course.
Of course, show me.
 
Aleksander:

show me, of course...

---

I in turn show for Sell GbpJpy Buy GbpChf = Buy ChfJpy

Sell GbpJpy - Lot = 1

Buy GbpChf - Lot = 1

Buy ChfJpy - Lot equal to the Opening Price of Buy GbpChf :)

Seems to be true.

What is there to show, everything is clear. There are three currencies - EUR, GBP, USD. They say that it can be simpler, but it is very simple for me:

_0 - exchange rate at opening, without zero - closing (at any given time)
Deposit currency - usd
Triple EUR/GBP/USD, we open all three pairs. Here are formulas to change the equity (L, M, N - volumes in lots):

1. eurusd: L * 10^5 * (eurusd - eurusd_0)
2. gbpusd: M * 10^5 * (gbpusd - gbpusd_0)
3. eurgbp: N * 10^5 * (eurgbp - eurgbp_0) * gbpusd

(10^5 removed, unnecessary)

Paper profit (equity) = L * (eurusd - eurusd_0) + M * (gbpusd - gbpusd_0) + N * (eurusd - eurgbp_0 * gbpusd ) =
= (L + N) * eurusd
- (L * eurusd_0 + M * gbpusd_0)
+ (M - N * eurgbp_0 ) * gbpusd


We have three brackets.
The first one can be zeroed out when L + N = 0.
The second one remains constant and depends only on conditions at position opening.
The third one can be zeroed out when M = N * eurgbp_0.

This means that under these conditions, the profit does not depend on further behavior of all pairs and is equal to -(L * eurusd_0 + M * gbpusd_0).

Let L = 1 for convenience, then N = -1, M = -eurgbp_0.

Consequently, the profit is equal to -(eurusd_0 - eurgbp_0 * gbpusd_0), i.e. it is equal to zero. Pair spreads are neglected here. In fact, this result could have been expected: if a fixed profit is equal to something, it is equal to zero :).