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      Taking the long-term investor first, the adjusted gain factor of 8.57 over 18 years (936 weeks) will reduce down to an annual gain of the 18th root of 8.57, which is a gain factor of 1.126762 per annum. This is a gain in percentage terms of 12.67% per annum.

      Brought to a weekly basis, the weekly gain is the 936th root of 8.57, which is 1.002298 over one week. In percentage terms, this is equivalent to 0.2298% per week. This is the gain that, if reinvested each year, would compound to a gain factor of 8.57, or 757%, over 936 weeks.

      Carrying out the same calculation for the investor who buys and sells with the 13 trends with an average adjusted gain of 1.381 over 45 weeks, we have to raise 1.381 to the power (52/45) which gives an annual gain factor of 1.452. In percentage terms this is equivalent to 45.2% per annum. This is the gain that if reinvested each year for 18 years will give an ultimate gain of 1.381, i.e. 38.1%.

      Compared on an annual basis, therefore, and with dealing costs now being taken into account, the gain from taking advantage of 13 upward surges in the share price over the 18-year period rather than one such surge lasting 18 years improves the gain on an annual basis from 12.67% to 45.2%, i.e. by a factor of about three and a half.

      The clear message so far is that the theoretical annual rate of gain made from shorter-term transactions is vastly superior to the rate of gain made by buying and holding.

      The reason we use the word theoretical is because we have made the assumption that we buy at the exact beginning of a trend and sell at the exact end. We shall take a more realistic view of where an investor might have got on board a rising trend, and where he would get off it, later in this chapter. At the moment we are simply trying to evaluate the theoretical effect of increasing the number of transactions over a certain time period. The reason, of course, that these 13 transactions give a superior gain is because the perfect timing of our theoretical investor takes him out of the market while the price is falling, whereas the buy and hold investor has to cope with the ups and downs of the 18-year period.

      Figure 1.3 Short-term trends in the Grand Metropolitan share price since 1978. These are represented by a centred five-week moving average

      Looking at Figure 1.1 more clearly, we can see that as well as the medium-term trends we have been analysing so far, there are trends of a shorter timescale. These trends are isolated by means of a five-week average, shown in Figure 1.3. The share prices at the turning points can be extracted just as in Figure 1.2 in order to analyse the price changes caused by these short-term trends. There are 41 such short-term uptrends, and the price data for these are given in Table 1.4. These trends lasted for an average of 12 weeks, as opposed to the 45 weeks of the longer-term trends. The average rise of each of these 12-week trends was 22.7%.

      Table 1.4 Gains made in short-term trends in the Grand Metropolitan share price

      Table 1.5 Buying prices, selling prices and gains in short-term trends in the Grand Metropolitan share price adjusted for dealing costs

      Just as in the case of the 13 longer-term trends, we have to adjust the buying and selling points of the trends to allow for buying and selling costs. This is done in Table 1.5. We find that the average gain per transaction now falls to 17.94%. In order to compare this gain over a 12-week period with the previous values for 18 years and 45 weeks, we have to recalculate the gain as if it occurred over one year. We find that the gain factor of 1.1794 over 12 weeks is equivalent to a gain factor of 2.044 per annum, i.e. 104.4% per annum. This value supports our view that the rate of gain increases as we shorten the transaction time, even though of course the gain per transaction is less.

      Figure 1.4 Very short-term trends in the Grand Metropolitan share price between July 1984 and September 1987. These are represented by the share prices themselves

      Since we have this rate of gain moving so positively in our favour, the natural next step is to look for even shorter uptrends to take advantage of in this way. In Figure 1.4 we show an expanded portion of the Grand Met chart between July 1984 and September 1987. The very short-term movements which could not be seen clearly in Figure 1.1 can now be seen easily. In this time period there are 34 such trends. The actual price movements for these 34 trends are given in Table 1.6. Many of these trends last for only one week, and the longest for eight weeks. The average length of time for which these very short-term trends persist is 2.6 weeks. The average gain of these 34 transactions is 7.9% compared with the 22.7% in Table 1.4. We now appear to be coming to the shortest possible trends which will give us a profit, since we still have to adjust these for the dealing costs.

      Table 1.6 Gains made in very short-term trends in the Grand Metropolitan share price

      This is done in Table 1.7, once again by increasing the buying prices by 2.5% and decreasing the selling prices by 1.5%. Now we can see that the average gain per transaction has fallen to 3.7%. Once again, in order to compare with the previous calculations, we have to express this gain as if it occurred over one year.

      Table 1.7 Buying prices, selling prices and gains in very short-term trends in the Grand Metropolitan share price adjusted for dealing costs

      As before, we have to upgrade this gain to the equivalent gain over a one-year period, and this works out as a gain factor of 2.068, or 106.8% per annum. Since this is only marginally higher than the rate of 104.4% per annum obtained with the 41 short-term trends of Tables 1.4 and 1.5, it would appear that we are at about the optimum number of trades over the 18-year period in terms of rate of gain per week. However, bearing in mind the additional effort required for these very short-term transactions, we can consider that using the short-term trends rather than the very short-term trends represents the optimum, and its annual gain of 104.4% is a vast improvement over the annual gain of 12.67% made by the buy and hold investor.

      The four situations we have examined so far are summarised in Table 1.8. Dividends have been omitted from each of the transactions in order to simplify the comparison.

      Table 1.8 Length of trend, percentage gain and annual rate of gain for transactions in Grand Metropolitan shares

      Two

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