The potential yield of the instrument. - page 2
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Nah. On historical data, optimal ZZ is when the average knee size is equal to double the spread. There is no greater Hypothetical Return in the World! A step sideways will give a lower return (proven rigorously).
Proof?
Suppose we have defined a BZ on the historical data, which is built using the following algorithm: If the price (Bid) has moved away from the previous maximum/maximum of the price by the amount equal to or greater than H-points, the top of WP is considered to be formed at that maximum/minimum. In this case, the average value of a WP knee tends to 2H (it is evident from the construction algorithm). At each step of building we take away to the profit value of 2H and give the spread - Sp. Then, after n-steps our capital will be equal:
Our task is to maximize this amount, provided that trading time is limited and the more we select a step - H, the less transactions for a certain time T will be performed by TC. Therefore, there is a golden mean when the number of transactions is sufficient and the profit in each transaction does not tend to zero.
The time needed for a price to cover a distance of H-points is proportional to the square of this distance (the law of one-dimensional Brownian motion):
We look for the maximum of the function in the right part of the equation in the standard way: we take its derivative over the parameter H, set it to zero and solve the resulting equation with respect to H:
It turns out that the optimal partitioning step on historical data, at which TC's income is maximal, is H=Sp!
The post above I ran it through - the step is not equal to the double spread. Apologies.
It is not much harder to prove that on the right edge of the quotient (when there is no way to peek into the future) this same split gives asymptotically maximum profitability in pips without reinvestment of funds. In this case, market entry is made at a price movement away from the extremum by H-points. This is the most profitable strategy that can be devised and it can be shown that its average return per trade tends to the mean value of ZZ minus 2H (the price at the right extremum) minus the spread. This measure is an adequate estimate of the return of an instrument on the chosen trading horizon - H.
Let it be on historical data...
If the knee value is equal to the spread, there will be trades with zero profit. Will the profit change if the knee value is increased to spread+1 point?
Yes, there will be such trades and yet, a +1 point increase in the knee will reduce the overall return of the strategy.
>> I don't believe it!
A picture of this World can be presented in different ways. Some comprehend it through Knowledge, others through Faith, and there are those for whom Love is enough. Personally, about something, I say "I know" or "I don't know".
On the subject: I know it is so(H=Sp->max) and not otherwise. You are free to believe me or not. It is your choice. We don't cross paths.
Yes, there will be such trades and yet a +1 point increase in a knee will reduce the overall return of the strategy.
>> It won't.
The proof of your corrected statement is obvious if we consider that when N (min knee) > n (another min knee), the set of eextremums for N is a subset of the set of extremums for n. Hence, it follows that the smaller the step, the higher the profit.
A picture of this World can be presented in different ways. Some comprehend it through Knowledge, others through Faith, and there are those for whom Love is enough. Personally, about something, I say "I know" or "I don't know".
On the subject: I know it is so(H=Sp->max) and not otherwise. You are free to believe me or not. It is your choice. We don't cross paths.
Sorry, forgot the link to the author, thought everyone knew this phrase - "I don't believe it", it's Stanislavsky's catchphrase, which has the meaning "not convincing".
We don't overlap.
Yes. In fact mathematics is a simpler and more straightforward science than the mathematics demonstrated by the multi-storey calculations above.
Well, I don't really have much more to say...
Do you look at the formula for finding an extremum and disagree with the result? Then point out the error.
Once again. If H is even one point larger or smaller than the spread, we will not make profit on a long enough portion of history! We can demonstrate the truth of this statement by testing the trading on historical data this way and that, and then look at the result.
Suppose we have an algorithm for creation of a phase in the above described (picture at the left). Then let us find the average return of a backward position for its different constructions. Let us take the EURUSD pair for approximately one year, set the spread equal to 20 points and plot a set of ZZ in the range H=10...30 points. Then let's sum up their shoulders by absolute value after deducting of the spread and plot the income graph for the whole trading interval that is the same for all H:
We can see that the result of "real trading" on the history, wonderfully coincides with the analytical solution and the maximum yield falls on the value of the step ZZ equal to the spread of the instrument. The step to the side by one point gives less profit (see picture on the right).
What was required to prove!