It's all wrong, friends. - page 5
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Well, balance sheet curves are something with, to put it mildly, different statistical characteristics than quotation curves.
So let it grow, who's stopping it, Vitaly. Yes, for us the primary reality is a stream of quotes with very nasty statistical properties. We apply all the power of our intellect to it (oops, no, not all of it) and get another reality - a stream of returns balance. I'm not saying it always happens that way, but quite often this second stream has much more convenient and observable statistical properties that sometimes allows to build an acceptable model of it.
In his explanation of the benefits of diversificationSergei has exactly studied the second flow, abstracting from the first. And I myself got hooked on this second reality in my article on sandwiches. And got a couple of conclusions concerning this second reality without referring to the first. And what's so bad about that?
Who says that the lack of independence between cable and eura charts must necessarily lead to the same result for the respective balance charts?
I've taken a closer look at Neutron's reasoning. In fact we are only operating with balance curves here - or am I wrong, Sergei? Well, balance curves are something which has, to put it mildly, other statistical characteristics than quote curves. So why are we talking about bar statistics referring to non Gaussian bars?
Ideally everyone wants returns to be Gaussian, which may be temporary. It would be desirable to have it longer, but unfortunately it is impossible to predict the duration of this period in advance. The individual system has its own criteria, that it has become bad. Besides useful features the portfolio brings additional non-stationarity to the results due to the fact that drawdowns of individual systems can occur with quite a different probability than it is theoretically possible. By reducing some risks, we bring in new ones. I'm not saying that portfolio is bad, but formally, we cannot do without correlation when selecting systems for a portfolio :)
As for MA, of course, it means that negativity disappears, because it is averaging.
Who says that the lack of independence between cable and eura charts must necessarily lead to the same result for the respective balance charts?
There just aren't that many fundamentally different ideas for TS, especially at the disposal of a single individual :) What technically seems different, when looked at in more detail has a common basis, uses the same property of the market. A significant change in this property can correlate the losses in a way that is not observed and not theoretically possible from a Gaussian perspective.
They can, of course. If you simply "sum up" the individual systems without multiplying the risk of each individual by the root of n, then in the worst case of complete correlation of individual drawdowns the total drawdown will be equal to the original drawdown. And the probability is still close to the theoretical one - if the model is correct and takes into account correlations between balance graphs.
In fact we are only operating with balance curves here - or am I wrong, Sergei? Well, balance curves are something which has, to put it mildly, different statistical characteristics than quote curves. So why are we talking about bar statistics referring to non Gaussian bars?
I absolutely agree with you, Alexey!
And also, to illustrate, let's take a dozen BPs with awfully non-Gaussian distribution in the series of the first difference (see fig. the blue dots) and strong correlation between them (see the table).
Now add up all ten BPs and plot the distribution of its increments (red dots).
It can be seen that this distribution can be called Gaussian only with caveats, large ones. For comparison, the black line shows the normal distribution...
So this fact should not bother us. I repeat that you can put a real non-Gaussian distribution of the increments of the balance curve into the model and the problem of deversification will be solved exactly. As Mathemat correctly pointed out , even this is not necessary, in the worst case we will get risks as good as the capitalisation of a single instrument.
So let it grow, who's stopping it, Vitaly. Yes, for us the primary reality is a stream of quotes with very nasty statistical properties. We apply all the power of our intellect to it (oops, no, not all of it) and get another reality - a stream of returns balance. I'm not saying it always happens that way, but quite often this second stream has much more convenient and observable statistical properties, which sometimes makes it possible to build an acceptable model.- I agree with the assumptions completely.
I forgot to pronormalise the resulting BP :-(.
After normalization the picture is as follows:
We can see that the obtained series (red dots) is normalized, but weakly, due to the small number of initial BPs included in it.
They can, of course. If you simply "sum up" the individual systems without multiplying the risk of each individual by the root of n, then in the worst case of complete correlation of individual drawdowns the total drawdown will be equal to the original drawdown. And the probability will not be far from the theoretical one anyway - if the model is correct and takes into account the correlations between balance graphs.
The correlation coefficient objectively reflects the dependence of the two CB only if each of them is stationary. If the returns of each system are stationary (or as long as they can be considered stationary), then it will be as you wrote. Roughly speaking, as long as the systems work as planned then all is well and good if they "break" out of sync. Since the markets are now all linked, then imho we can only hope for incoherence of ideas underlying the TS. I.e. besides formal correlation coefficient in the basis of portfolio there should be systems essentially different from each other - "ideologically independent" :)
I forgot to pronormalise the resulting BP :-(.
After normalization the picture is as follows:
You can see that the obtained series (red dots) is normalized, but weakly, because of the small number of initial BPs included in it.
It is not clear from your picture whether the series is normalized or not. There is not enough data, just in the tails. All the more it is difficult to visually estimate limits of e.g. 3 sigmas for each of them. Only RMS change is visible.
In general, if the correlation of two symbols is simple enough, then the correlation of returns of the two systems is not very simple. The trades are usually discrete, with different frequencies and only overlap in time. The classical correlation for two series with the same amount of data taken at the same moments