For many years, since 2000 I was working and experimenting on the details of the idea, that it is better an optimal portfolio (e.g. optimal in the sense that it maximizes the portfolio Sharpe ratio rate_of_return/standard_deviation_of_rate_of_return) of trading systems on the same pair or instrument but at different time frames (or rainbow frequencies see post 5 ) compared to single trading system on the pair or instrument , that is trading at a single optimal time-frame ( in the sense that all neighbouring time-frames give worse results in the Sharpe ratio). And the idea is valid, but it is not very practical in manual trading. It is easier in 100% automated trading due to the complexity of its conduction. It is not adequate that you put expert-advisors to run independently on different time frames. As there is intermittency in good trading systems, in other words time intervals that the trading does not occur, an algorithmic logic must allocate the portion of the funds that is appropriate for trading, among the different trades of different time-frames according to some evaluation metrics as if in a queuing system. Also the portfolio allocation percentages may vary slowly, and the funds must be allocated according to them, even for the same pair or instrument.
The years after 2009, I have concentrated almost entirely in forex due to the advantages that the brokers and trading platforms give to very small size accounts. As I have found that the "sessional gaps or spikes" at the beginning of the Asian, European, and American sessions are the single most important and strong consistent periodicity compared to neighbouring time-frame periodicities (even at periods of crisis), the above idea lost for me its attractiveness. I concentrate now on a single optimal rainbow frequency (that of sessional periodicity) so that the 100% manual, half-manual half-automated, or 100% automated trading, is equally simple as far as optimality of the time-frame is concerned.
Summarizing the ways that optimal portfolio theory can apply we find at least 3 perspectives
1) Optimal portfolio of instruments (see post 14)
2) Optimal portfolio of strategies on the 4 basic price patterns (see post 32)
3) Optimal portfolio of time scales or characteristic frequencies. (current post)
In the context of the present post we should include an important statistical principle relevant to time-scales and statistical success of the trading: If the indented duration of the trading is a time interval T (e.g. one day, or a month or 5 years etc), then in detections and assessing of the trend we should include a time scale greater or equal to T. (E. g.. If we intent to make many intraday trades for one day, (T=1 day) then in the trading we should include also detection the trend in a time interval >=T. It is not the duration of the individual trade that deternins the maximum scale of detecting the trend but the duration of all the trading). Therefore the intended duration of the trading itself, puts a constraint of large enough time scales, of assessing the trend.
Summarizing the ways that optimal portfolio theory can apply we find at least 3 perspectives
1) Optimal portfolio of instruments (see post 14)
2) Optimal portfolio of strategies on the 4 basic price patterns (see post 32)
3) Optimal portfolio of time scales or characteristic frequencies. (current post)
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