It's all wrong, friends. - page 6

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The tail (red dots) seems to be similar to exp(-|x|), but there is certainly not much data. Not too thin, but not that thick either.

 
Avals писал (а) >>

..... I.e. apart from the formal correlation coefficient, the portfolio is based on systems that are essentially different from each other - "ideologically independent" :)

There are two types of diversification, one uses the uncorrelatedness of quotes. The second one uses "different ideas" of a trading system. In the first case it is clear, but the second one has always caused discomfort for me. Let me explain, if I have 2 different TS with different ideas, then I can set them on one pair. There is a situation, when one system is in Sell and another one is in Buy, but the Pontryagin's maximum principle, only one of these positions is correct.

Therefore it is not necessary to have a TS with a different idea put in it, for each currency has its own TS (optimized just for this pair, albeit parametrically), if there are such systems, then we select the most uncorrelated quotes.

Neutron I'm sorry, but usually the area under the curve equals 1, the probability density, and in your charts I don't see any NZR.)

Avals if we approximate balance curve by straight line(y(x)=a*x+b) by OLS, then difference between this curve y and balance curve just has to obey NZR if number of trades is big enough.

 
Prival писал (а) >>

Neutron I'm sorry, but usually you normalise so that the area under the curve equals 1, the probability density, and in your graphs, I don't see NZR anywhere )).

Hi Sergey.

It's me who screwed up the wrong term in my haste :-)

I was talking about splitting the capital into equal shares by instrument, in this case I needed to add up n BPs with an amplitude factor of 1/n each. On the first chart I forgot to do this, on the second I corrected it.

Now, I agree with Avals that it's not correct at all, because transactions don't occur simultaneously in real life and how to add them up is unclear to me. But, for the sake of fairness, it should be noted that this difficulty concerns only the graphical representation, it is not critical for the resulting estimates, since the non-simultaneous nature of the transactions does not violate their additivity.

 
Prival писал(а) >>

There are two types of diversification, one uses uncorrelated quotes. The second one uses "different ideas" embedded in the trading system. In the first case everything seems to be clear, but the second one has always caused discomfort for me. Let me explain, if I have 2 different TS with different ideas, then I can set them on one pair. There is a situation when one system is in Sell and another one is in Buy, but only one of these positions is correct.

If the task is to build a continuous control model, i.e. a forecast is given at any moment of time, then from these positions it will be so. Not for all tasks it is possible. In particular for the market. Why it may not be possible is described for example in the above references. A (probabilistic) prediction is possible only at some moments and for some time period. At the same time, taking into account fractality, opposite predictions are possible but with different time horizon. I.e. it is quite normal when a system on weekly charts buys, and on hourly charts sells, if these systems have different timeframes of position holding and accordingly different targets (not necessarily tp and sl). Time frame is not important here, the main thing is the expected holding period. Of course it is not defeated in many systems. But if systems enter and exit at the same time, i.e. the difference in position holding periods is very small, such systems are certainly inefficient. They either have to hold positions at different (non-intersecting) time periods or the holding horizons must differ considerably.

Prival wrote >>

If we approximate the balance curve by the straight line(y(x)=a*x+b) according to OLS, then the difference between this curve y and the balance curve must obey RBNT at large enough amount of trades.

It doesn't have to. What you are describing is a stretching of the historical NR series. Deviations from that curve are determined by the RMS. If we defer another 2 at a distance of 3 RMSEs from this line, the exit of equity beyond them is a very rare event that cannot be explained by normality. This is a characteristic of LR but if we continue the straight line into the future, it is very possible that the equities may exceed 3 RMSE. Even if we recalculate the coefficient a and RMS (respectively the boundaries of 3SCO), exit is still possible. In the last case, the Bollinger Bands will appear.

I.e. on history it is practically always possible to pick up MO and RMS that the data will be according to Gauss, we are talking about the situation with the "right wall", when the future has not yet come ;)

 
Neutron писал(а) >>

Now, I agree with Avals that this is not correct at all, because transactions do not occur simultaneously in real life and how to add them up is not clear to me. But, for the sake of fairness, it should be noted that this difficulty concerns only graphical representation, it is not critical for obtained estimations because non-simultaneous transactions do not violate their additivity.

Sergey, the non-simultaneousness of transactions violates the meaning of the time series correlation coefficient. When the calculation uses the values of two CB at the same points in time, even if there really is a dependence between them with some time lag (even a variable), then due to the fact that the time effect of this dependence is much larger than this lag, the correlation coefficient will still be significant, and the lag effect will simply be smoothed out. But in the case of two discrete systems the trades occur at different moments of time and they have different durations and that's why besides the lag mentioned above the shift lag of compared trades is added, the property of smoothing the time lag is also under a great question, etc. The significance of correlation under such conditions is not obvious. And the whole theory of portfolio investing is based on it.

Of course it is possible to return to fixed time intervals and smooth the above random influences: take not values of individual transactions, but their sum over certain time intervals (these intervals must include statistically significant number of transactions), synchronizing them between systems (for example the sum of returns per calendar month), but then there are problems with representativeness: until the required data volume is collected one of the systems will likely die or need its modification. I.e. lifetime of systems does not always allow to obtain statistically significant correlation coefficient in this way. Exactly almost never(( And even if we have calculated it, where is the guarantee that this value is still relevant?

 

I increased the number of diversification instruments to 100 and changed the parameters of the original distribution slightly. To my surprise, I do not observe a normalized distribution of the incremental balance curve for the portfolio as a whole (see the first figure, red dots), or it is weak:

There is, however, a marked narrowing of this distribution compared to the original distribution (blue dots), indicating a proportional reduction in risk. Of course, this is only true with all the comments and additions Avals has made in his posts.

The distribution shown above is built for correlation coefficient of balance curves a=+/-0.5 in equal quantities.

But a totally different picture can be observed for the case when most of the balance curves are equally correlated (Fig. right). In the previous case, I had 50% of balance curves positively correlated, the rest negatively correlated (I'm talking about the correlation between income increments of different TS occurring in the same time interval). This is very bad! Diversification is out of the question in this case. I.e. one has to watch closely that the results of the TS do not correlate with each other, or correlate with the same contribution, but with a different sign. Although it is clear.

Below is a comparison of equity obtained for one instrument - the red line, and for the portfolio consisting of 100 instruments - the blue one (fig. left) and 10 instruments - the right one:

It should be recognized that the initial non-Gaussian distribution of the TC balance curve increments does not impair the quality of portfolio diversification at all. A strict requirement is imposed only on the independence of transactions for instruments in the portfolio.

All we need is to invent and build TS, which would give positive and independent balance for each of 100 instruments!)

 
Neutron писал(а) >>

I increased the number of diversification instruments to 100 and changed the parameters of the original distribution slightly. To my surprise, I do not observe a normalized distribution of the incremental balance curve for the portfolio as a whole (see first figure, red dots), or it is weak:

There is, however, a marked narrowing of this distribution compared to the original distribution (blue dots), indicating a proportional reduction in risk. Of course, this is only true with all the comments and additions Avals has made in his posts.

The given distribution is built for correlation coefficient between balance curves a=+/-0.5 in equal quantities.

But a completely different picture is observed for the case when most of the balance curves are equally correlated (Fig. right). In the previous case, I had 50% of balance curves positively correlated, the rest negatively correlated (I'm talking about the correlation between income increments of different TS occurring in the same time interval). This is very bad! Diversification is out of the question in this case. I.e. one has to watch closely that the results of the TS do not correlate with each other, or correlate with the same contribution, but with a different sign. Although it is clear.

Below is a comparison of equity obtained for one instrument - the red line, and for the portfolio consisting of 100 instruments - the blue line (fig. left) and 10 instruments - the right one:

It should be recognized that the initial non-Gaussian distribution of the TC balance curve increments does not impair the quality of portfolio diversification at all. A strict requirement is imposed only on the independence of transactions for instruments in the portfolio.

All we need is to invent and build TS, which gives positive and independent balance for each of 100 instruments!)

After all this hard work - a stunning conclusion! :)

 
Avals писал(а) >>

If the objective is to build a continuous control model, i.e. a forecast is given at any point in time, then this is the case from this perspective. In particular for the market. Why it may not be possible is described for example in the above references. A (probabilistic) prediction is possible only at some moments and for some time period. At the same time, taking into account fractality, opposite predictions are possible but with different time horizon. I.e. it is quite normal when a system on weekly charts buys, and on hourly charts sells, if these systems have different timeframes of position holding and, correspondingly, different targets (not necessarily tp and sl). Time frame is not important here, the main thing is the expected holding period. Of course it is not defeated in many systems. But if systems enter and exit at the same time, i.e. the difference in position holding periods is very small, such systems are certainly inefficient. Either they must hold positions in different (non-intersecting) time periods, or the holding horizons must differ considerably.

They don't have to. What you describe is a stretching of the historical HP curve. Deviations from this curve are determined by the RMS. If you set aside another 2 at a distance of 3 RMSO from this line, then the exit of equity beyond them is a very rare event not explainable by normality. This is a characteristic of LR but if we continue the straight line into the future, it is very possible that the equities may exceed 3 RMSE. Even if we recalculate the coefficient a and RMS (respectively the boundaries of 3SCO), exit is still possible. In the last case, the Bollinger Bands will appear.

I.e. on history it is practically always possible to pick up MO and RMS that the data will be Gaussian, we are talking about the situation with the "right wall", when the future has not yet arrived ;)

1. Ok for the first point I completely agree, and I do not think the use of tp and sl at all is acceptable. TC should determine this herself.

2. On history it is obligatory (for me, as this to me is the main sign of a good TS), going outside the 3SCO is a sign of a bad system or a dying system if it appeared to the right.

 
Vita писал(а) >>

After all this hard work, a staggering conclusion! :)

What's more, the result could have been negative at all! But its value will not suffer in any way.

You know it very well6:-)

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