it is necessary to take a close look at daily price changes in a share such as Guinness. In Figure 2.2 are plotted the daily changes in closing price, over a 1000-day period up to September 1996.
Figure 2.2 The daily price changes in Guinness over a 1000-day period are plotted as relative frequency of occurrence of a change versus that change
The plot shows the relative frequency of occurrence of various price changes, with the most frequent change being zero, i.e. the price on one day is the same as that on the previous day. For comparison with Figure 2.3, the most frequent occurrence is given a frequency of 1. The largest changes shown in the figure are a rise of 21p and a fall of 21p.
The important feature of Figure 2.2 is its shape, rather than specific values.
If daily price changes in Guinness over the period of time in question were totally random, then the shape of the curve in Figure 2.2 would be identical with that shown in Figure 2.3, the classical probability shape. It can be seen that the general shape of Figure 2.2 approximates to the probability shape, with the main distortion being that the central value, corresponding to zero daily change, is too large. If this value is reduced, then the shape gets closer to the ideal, with most frequencies not too far away from the value predicted for total randomness. Thus a simple deduction from the shape of the curve in Figure 2.2 is that there is a great deal of random behaviour in the daily change in the Guinness share price, and that the major departure from total random behaviour lies in the greater than expected incidence of no-change days. Thus we can say that random and non-random daily behaviour are co-existing.
Figure 2.3 A totally random distribution of daily price changes would have the shape of this curve
A moment’s thought would lead us to the proper conclusion that since there is an indeterminate amount of random behaviour in daily price movements, and that the majority of daily movements lie within the range of plus or minus 10p (Figure 2.2), there is no profit to be made in an investment made solely on the basis of a prediction of the price movement on a particular day. We need to move from daily movements to longer-term trends where the price movement is much larger.
The first, inescapable conclusion is that since daily movements exhibit a high degree of randomness, then price trends over a succession of days built up from these individual movements must also show a high degree of randomness. This can be addressed in an unusual way.
In Figure 2.4 we show the chart of the Guinness share price covering the period since 1983. The data are weekly in this case in order to present a long price history. It can be seen that a long-term uptrend was sustained from September 1988 to mid-1992, before the price retreated somewhat and then stayed within a trading range.
Figure 2.4 The price movement in Guinness shares since 1983. The data are plotted weekly
Except for the fact that the timescale is very much longer, the chart resembles Figure 2.1, where we took the example of a random movement that then became transformed into a non-random movement by press comment. In Figure 2.4 we appear to have a random price movement occurring, which then develops quite obviously into a non-random movement for reasons which are not obvious. Unlike Figure 2.1, the price has not yet returned to its levels at the beginning of the chart period.
It is interesting to see what a randomly created share price looks like when plotted. This is done by taking a starting value, such as 200p, and then randomly setting a value for the change over the following week. The change is added or subtracted from the previous day’s calculated closing price. Such a chart is shown in Figure 2.5. The price is random in the sense that it can move upwards or downwards from the previous value, but we have put a 10% limit on the movement in either direction. This is done to come as close as possible to real life, since we know by experience that prices do not move in huge jumps from day to day. The purists might argue that in doing this we have moved away from a completely random model, but this is not a significant restriction in terms of what we are trying to achieve.
Figure 2.5 A reconstructed chart of Guinness shares made by randomly calculating the change from the previous week. The starting value is 200p
There are many similarities between the random movement in Figure 2.5 and the movement of the Guinness share price in Figure 2.4 in the sense that underlying trends can be observed with random variations superimposed upon them. It could be argued that the only thing that really distinguishes the two types of chart is the much stronger upward trend observed in the Guinness share price, but that in general the chart could be that of any share. Chartists could draw trend lines and the like on this random chart just as on any other chart of a share price. While the similarities to share charts would lead to the conclusion that share price movement is totally random, simply looking at the chart in Figure 2.5 is not a rigorous mathematical test of random behaviour.
Fortunately for us, the model of share price movement that we put forward earlier in this chapter is a better reflection of how share prices move than is a model in which we take all price movement to be totally random. Even so, our model is not perfect, being only partly true. It is true that share prices contain random day-to-day and week-to-week movement, but what is not true is the statement that the start and end of a price trend is itself a random event. Share prices are essentially driven by these trends, but the beginning and end of a trend is not a totally random event. It is this fact that makes the methods used in this book workable, since if day-to-day price movement is random and the start and end of the trends are random, then the share price is totally unpredictable.
Without getting into the realms of probability theory, it is possible to demonstrate that while individual daily or weekly price changes can be accepted as having a great deal of random content, trends are much less random. For this purpose we can define a trend as being a succession of upward movements or downward movements on a daily or weekly basis.
The procedure is to take the Guinness share weekly price movements since 1983 and note all of the weekly changes. These are put into a pool. The same starting price of 54.5p on 7th January 1983, is used. The change over the following week is determined by randomly selecting from all of the changes which have now been put into the pool. From this change the following week’s price can of course be determined. The following week another change is taken from the pool. The procedure is repeated until a reconstructed price has been obtained for Guinness over the same period as the real price change occurred. Thus we have used the actual price changes which occurred in Guinness, but randomly changed the order in which they occurred. The result of this is shown in the chart in Figure 2.6. As with the previous random chart, there is nothing unusual about it, and it could be the chart of a real share price.
Since the chart has been reconstructed by randomly selecting price changes from the pool, then by using a computer, this process can be repeated as many times as required, with the result being different in each case.
Figure 2.6 The reconstructed weekly price movement in Guinness shares since 1983. From the same starting value of 54.5p, the order of weekly price changes has been randomly changed
The usefulness of this experiment lies not in the appearance of the charts themselves, but in a calculation of the number of times the price changes direction over the timescale used. In virtually
