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have you seen "dynamic synthetics" anywhere? I'd like to read...
I do dynamic synthetics.
For an example, consider a synthetic series at two points in time, 1 and 2:
S1 = w11*A1 + w12*B1
S2 = w21*A2 + w22*B2
-----------------------------
Let us subtract the second from the first:
S2 - S1 = w21*A2 - w11*A1 + w22*B2 - w12*B1;
dS = (w11+dw1)*(A1+dA) - w11*A1 + (w12+dw2)*(B1+dB) - w12*B1;
dS = w11*A1 + w11*dA + dw1*A1 + dw1*dA - w11*A1 + w12*B1 + w12*dB + dw2*B1 + dw2*dB - w12*B1;
dS = w11*dA + dw1*A1 + dw1*dA +w12*dB+ dw2*B1 + dw2*dB;
By "dynamic synthetic" I meant a multicurrency basket of orders (a synthetic trading instrument) that dynamically changes (some close, others enter) depending on the behaviour of their overall equity chart.
The summands in bold are "paid for" by the market and the other summands are "paid for" from your pocket to maintain stationarity of the synthetic. The coefficients should therefore change slowly.
It's a bit confusing. I understand you have two synthetics. The task is to get the total equiti and look at its properties after fitting the coefficients
Ikviti=k1*A1+k2*A2+k3*A3........ k1+k2+k3+...+kn=Const Although the latter is not necessary. Then you get k1<<Const; k2<Const....... I.e. the degree of influence of one instrument on the total equiti is insignificant. For the total equity to change its properties, we need most of the k-factors to change. So we need experiments and imho it is not only with currencies.
I do a dynamic synthetic.
For an example, consider a synthetic series at two points in time, 1 and 2:
S1 = w11*A1 + w12*B1
S2 = w21*A2 + w22*B2
-----------------------------
Let us subtract the second from the first:
S2 - S1 = w21*A2 - w11*A1 + w22*B2 - w12*B1;
dS = (w11+dw1)*(A1+dA) - w11*A1 + (w12+dw2)*(B1+dB) - w12*B1;
dS = w11*A1 + w11*dA + dw1*A1 + dw1*dA - w11*A1 + w12*B1 + w12*dB + dw2*B1 + dw2*dB - w12*B1;
dS = w11*dA + dw1*A1 + dw1*dA +w12*dB+ dw2*B1 + dw2*dB;
Have you looked at Vector Error Correction (VEC)?
No, but I use a recursive least squares filter in vector form (RLS) to select the weighting coefficients.
I have one question, why "IQUITY"?
There is a studied piece of history: Or1A1- the opening price of the leftmost bar on the instrument A1, then the Equity on this instrument is (Or2-Op1)*k1*St1, (Op3-Op1)*k1*St1, (Op4-Op1)*k1*St1... Where St1- value of one pip in the deposit currency
The same pictitivity for the second, third, etc. tools with the corresponding coefficients k2, k3, of course. Total equities will greatly depend on these coefficients and in principle they can be selected to meet certain criteria of equities at the studied segment. We can assume that for some time these coefficients will be actual to have time to take crumbs from table, but most likely this will be a usual bullshit after optimization period. In addition, the k1,k2,k3 coefficients... Will be proportional to open lots on real positions.