1) In classical buy-and-hold investments the utilization of a portfolio of investments is as it is know to reduce the variance-risk of the account equities. The problem of defining the percentages of the participation of each asset or instruments in the portfolio is an interesting challenge. A classical solution, after the Nobel prize of Markovitz, can be found e.g. in the book:
ELTON E.J.-GRUBER M.J. (1991) Modern portfolio theory and investment analysis Wiley.
From this book I personally utilize the cut-off-rate algorithm that is based on the assumption of the single index market model, the forecasted for the future horizon of the portfolio of the average rates Ri , they standard deviations Si , and their beta coefficients bi relative to the overall index of the market (that can be a weighted average of all traded instruments). The beta coefficients have a direct relation and simple derivation from the matrix of correlations of all instruments. I have coded this algorithm to run and create and update portfolios for more than 300 instruments even in a minute to minute frequency.
Assuming that all n in number instruments are uncorrelated between them , of equal standard deviation and all beta are equal, then the algorithm gives a simple practical formula: If the forecasted return for an instruments is Ri, then is percentage in the portfolio must be ai=Ri/(R1+R2+...+Rn). In other words as its return contributes to the sum of all returns
Nevertheless this algorithm is not a trading system in its own as it depends heavily on the forecast returns Ri, therefore it is only a part of a trading system. Assuming that we have a good forecasting system and after application of the cut-off-rate procedure, the adjustment of the size of the positions on the instruments so that the portfolio percentages are kept constant during the forward horizon, is a trading by itself. It is a trading that the fluctuations of the prices during the horizon are assumed unpredictable, and still their occurrence has a favorable effect on the profit, compared to the non-existence of fluctuations. See also on the category "speculators" in the post no 3.
2) An experienced modern trader on instruments of high leverage (commodities, forex etc) has already understood that the real goal of the tradings (e.g. in forex) is not to maximize profits, but to minimize the final variance of the equities curve in the account. Once this is done then by the utilization of the leverage and reinvestment this can lead to very high profits. The effect of a portfolio is that it decreases the variance of the average return by an order of n^(1/2) where n is the number of instruments in the portfolio, Therefore the effect of using a portfolio (e.g. in commodities) is eventually the increase of the profits.
3) But again in modern trading there is another very strong reason that the use of portfolio increases dramatically profits. Most good trading systems do not have continuously open positions. They carefully observe the market, and open positions for small time intervals (e.g. 20% of the time), while most of the time (e.g. 80%) have not open positions. We may call this trading systems with high intermittency. Then while the use of portfolio for systems that are continuously in the market has as a first effect that the portfolio averages their returns and decreases the variance, the use of portfolio for systems of high intermittency is that it almost adds-up the rates of return of each system. To give a simplistic example, let as say that the system A trades Monday-Wednesday-Friday and has return Ra, while the system B trades Tuesday-Thursday and has return Rb. Then the superposition or simultaneous run of the two systems will have return Ra+Rb and not (Ra+Rb)/2 . We may call this phenomenon "the packing effect of systems of high intermittency".
Summarizing we say that while for buy-and-holders the use of a portfolio reduces the variance risk, for traders the use of a portfolio increases in a fantastic way the profits.
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