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Now we move to the other important aspect of investment in shorter-term trends compared with a buy and hold policy, and that is the question of the compounding effect on the gain of continually reinvesting the proceeds of each transaction into the next one. We will see that this compounding effect will totally transform the profit levels we have been discussing so far into rates of gain that will turn modest amounts of starting capital into fortunes.

One way of illustrating the effect of compounding is to take the case of an investor who, like the rest of us, would like to double his money, starting with say £1000. To double this from just one buying and selling operation would require a 100% gain in the share price (for simplicity we assume no dealing costs). If he is relaxed about making more than one successive investment, reinvesting the proceeds from each one into the next in order to achieve his aim, then the gain he has to make from each investment is shown in Table 1.9 and Figure 1.5.

Thus with just two investments with which to double his money, he needs not 50% from each, but 41.4% from each, since the total proceeds of £1414 from his first investment are put into the second (he requires a 50% gain from each investment only if he intends to withdraw the gain each time, reinvesting only £1000 on each occasion). By the time he gets to five transactions over which to make the 100% gain, he needs to make only just under 15% from each of the five investments.

Taking the example of the gains made, after dealing costs, from the 13 upward trends in Grand Metropolitan, the compounding effect is best illustrated by expressing gains as factors rather than percentages. The cumulative data are shown in Table 1.10. The final column shows the increasing gain, expressed as a factor as each transaction is compounded. This gain is obtained by multiplying together all of the gain factors to that date. The net result is that after 13 such transactions, the starting capital has been multiplied by a factor of over 51. In percentage terms this gives a gain of 5000%. The advantage of this compounding effect has therefore turned what would have been a gain of 757% from buying and holding into almost seven times as much.

Table 1.10 The cumulative gain obtained by reinvestment of proceeds of 13 successive transactions in Grand Metropolitan shares. Gains are adjusted for dealing costs

Table 1.11 Length of trend, percentage gain, annual rate of gain and cummulative gain for transactions in Grand Metropolitan shares

We can now begin to appreciate that although the gain per transaction starts to fall as we carry out more transactions within a time period such as 18 years, as was shown in Table 1.8, the magic of this compounding effect may well greatly outweigh this fall. To test this we can look at the situation where we carried out 41 transactions in the time period. Using the same method of multiplying together all of the gain factors, the final gain is a factor of 552, i.e. 55,100%. Similarly, for the sequence of very short-term transactions, the final gain obtained by multiplying together all of the 34 individual gain factors is 3.352, which in percentage terms is equal to 235% over the 3.1-year period.

The overall compounded gains for the various transactions we have discussed in the chapter are shown in Table 1.11. We showed earlier that the equivalent annual gain for the transactions increased dramatically as we shortened the length of time for the transaction down to 12 weeks, but that it increased only marginally as we moved to transactions which lasted only 2.6 weeks. The same effect appears to carry through when we compound the gains by reinvestment into the succeeding transaction, since the final column where these values are displayed shows a fall-off from 55,100% for the 12-week transactions to 235% for the 2.6-week transactions. However, these two figures are not directly comparable, since the last one applies to a period of only 3.1 years, and not 18 years as do all the previous figures.

To bring the 3.352 gain factor over 3.1 years to one over 18 years we first bring it to an annual gain of 1.4772 by using the method we discussed at the beginning of this chapter. By raising this value to the power 18, we get the equivalent gain over 18 years, which is 1122. In percentage terms this is 112,100%.

Note that this theoretical gain of 112,100% has been obtained with our money working for us only part of the time. Taking Grand Metropolitan shares as an example, we can work out how much of the time we were invested by multiplying the average length of the particular trend, i.e. 45 weeks, 12 weeks and 2.6 weeks respectively, by the number of such trends that occurred over the 936-week period. Taking the 12-week trends as an example, there were 41 of these in the 936-week period. This means we were invested for 41 x 12 = 492 weeks out of the possible 936. During the rest of the time we would have been earning at the rate of what now appears to be the positively miserly 6% per annum, or thereabouts, that could have been obtained in the money market over this period since 1978. Quite obviously, therefore, we have to try to reach the position where our money is invested in rising shares 100% of the time, or as close to that as possible. If we can do that then we will obviously improve the gain made over an extended series of transactions enormously.