## Fixed Initial Investments

10 December 2009

How much should be invested? The optimal amount is difficult to pinpoint because you would have to know what risks lie ahead, and of course, that’s not possible. However, based on a very small likelihood of losing 50% of the portfolio when 50% is invested, one might say that a portion under a 50% investment is best. To account for greater uncertainties in the future, you could increase your confidence by investing only 25% of the initial portfolio. This approach has negative effects, because a smaller relative investment reduces both risk and returns. When the investment becomes too small, the returns are no longer attractive.
The chance of a catastrophic risk is an important concern for any investor or portfolio manager. For practical purposes this is always figured on the historic profile of the data or trading results. This still leaves uncertainty in the final values. Nevertheless, the most extreme situation is often found by using the calculation for risk of ruin, most often applied to gambling situations in which the bet sizes, pay out, and odds are well defined. When there are enough test data and trades, this technique has been applied to trading systems.
Some analysts have tried to deal with the uncertainties of price movements by using a Monte Carlo technique in testing, which shifts the sequence of blocks of data, or profit and loss results, so that they occur in random order. The worst results are considered the greatest risk. This approach may be unrealistically severe, yet even the real performance is not likely to reflect the size of the risk in the future. For those traders applying a long-term trend-following technique to capture moves that are based on economic or government policy, sustained profits are most often followed by a reversal before the trade is ended. In fact, the ending change of direction is directly related to the sustained move. To move this data around so that the loss comes at a different time may create a large loss without the offsetting profit, which is a situation that is unfair to the trading strategy. Before applying a Monte Carlo analysis, it is first necessary to identify the dominant period of sequential correlation to avoid segmenting the series incorrectly.
For an initial investment, the optimal f is simply the maximum part of that portfolio that can safely be traded without any significant risk of ruin. For those investors who take out profits when they occur and continue to trade based on the same assumed initial investment, nothing need be changed unless exceptionally high risk causes a reassessment and decrease in the amount of leverage. However, it is more common and more complicated for the investor to vary the amount committed to the market by either increasing or decreasing leverage. This involves (1) determining the right time to change the leverage, (2) calculating the amount to increase the investment when there are profits, and (3) figuring the size of the reduction when there are losses exceeding some designated amount. These are issues that are addressed by optimal f.