Читать книгу Millard on Channel Analysis - Brian Millard - Страница 12

The simple response to this question would be to point out that the world’s stock exchanges depend upon prices not being random. If they were random, then one might as well pick shares for investment with a pin, or forgo the stock market altogether and leave one’s money in the money market, earning the best rate of interest available. The vast array of stock market analysts employed by various institutions would be totally superfluous and investment writers like myself would have to turn to other activities.

The existence of investment commentators, besides indicating that the movement of share prices may not be random, also raises an interesting philosophical point. Their existence may be the reason that share prices are not random, in the sense that their comments in newspapers may distort what would otherwise be a random process. Just suppose, for example, that Guinness shares were moving in a random fashion until one day the investment columns of two or three newspapers suggested that Guinness shares represented a good buy. Many of their readership will take their advice and start buying these shares. The inevitable logic of supply and demand dictates that the price of Guinness shares will then start to rise. If these same newspapers continue to push Guinness shares as a good buy, then more and more readers will begin to take notice, and the share price will continue to rise. The rise will not continue forever, but at some point will reverse itself. This is because an increasing number of these new holders of Guinness shares will decide that they have now made sufficient profit to have satisfied their objectives, or will decide that all good things must come to an end, and will now act in a contrary way to the advice being offered and will sell their shares. This selling pressure will increase, thereby causing the Guinness share price to fall. Eventually we can conclude that the Guinness share price has reverted back to its original random movement.

This example serves to show quite clearly that even if we accept the premise that some or most of the time a share price is behaving randomly, then there will be occasions when because of press comment the price will move in a non-random manner. This can be illustrated by the type of movement shown in Figure 2.1.

Figure 2.1 Random price movement becoming non-random for a period of time due to favourable press comment

Just to restate the position so far: we assumed that the Guinness share price was moving randomly until a random event (comments in newspapers) caused the price to move in a non-random fashion for a period of time. The non-random movement was caused by a bandwagon effect of investors reading and acting on comment in their newspapers.

A closer inspection of Figure 2.1 shows that the day-to-day fluctuations, when viewed in isolation, are still apparent even when the underlying long-term trend is rising.

Since we can accept that a random event such as a newspaper article was the trigger to an upward and then a downward price movement, it is but a short step to an improved model of share price movement:

1 Share prices contain random day-to-day movement.

2 Share prices contain upward and downward trends.

3 The start and end of a particular trend is a random event.

By the word “trend” we mean an underlying price movement that lasts for more than a few days, and may last as long as many years.

To determine that prices are or are not random is difficult, and would take us into a realm of mathematics that would be out of place in a book of this nature. However, we can make some progress by taking a simpler approach. To do this 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 every case, there are considerably more changes of direction in the reconstructed prices than in the real ones. Since there are fewer changes of direction in real prices, the sequences of upward or downward price movements must last longer. Thus there are more upward or downward trends in real prices, i.e. trends are more persistent in the real prices. Since the reconstructed prices have been generated by a totally random selection from the pool, this means that trends are subject to less random behaviour in share prices than would be predicted on the basis that the daily or weekly changes which go to make up the trends have a high random content. It is this increased persistence of trends that will enable us to make profits out of investment in shares.

Because of this increased persistence in the trends, and because of the fact that daily and weekly price movements, although having a high random content, do not have a 100% random content, then probably 70% of share price movement is not random, and is therefore predictable if the correct techniques are applied. The analysis of cycles in share price data, discussed in Chapter 6, also confirms this as a ball-park figure for nonrandom behaviour.

The technique of channel analysis, especially when used in conjunction with moving averages of various types, is able to extract most of this predictable movement from the share price data, thus giving the investor the most powerful prediction technique currently available.

We can predict the start and end of these price trends with a fair measure of success by adopting a realistic approach of developing “prediction boxes”. This means we do not say “the price will be 285p on 17th November 1997”. We do say “the price will enter the prediction area at the beginning of November where the downward trend will have an increasing probability of reversing direction, with the lowest price being in the range of 280p to 290p”. The difference between these two statements is the fact that in the first case we would be totally positive about a situation that it is impossible to be positive about, whereas in the second case we are taking into account the partially random nature of trends. Another important point is that the further into the future we try to predict, the greater will be the error involved in this prediction. The fact of the matter is that we do not need to know approximate price movements more than about three months ahead. This will be perfectly adequate for making substantial profits, as was discussed in the last chapter.

It is interesting to see how seriously some sections of the press take the idea of long-term prediction of share prices by some of the gurus of the industry. Just prior to the start of each new year the business sections of the quality newspapers always poll a number of analysts for their predictions of where the FTSE100 Index will be at the end of the year. Be assured this is not done as a little bit of Christmas fun, since both the columnist and the guru being polled seriously believe that this is a worthwhile exercise. They are saying between them that they know exactly what you out there will be doing on the investment scene in a year’s time! Just keep cuttings of these predictions and have your own bit of fun reading them in the future.

At some points in share price histories different trends will be featured particularly strongly, while at other times the price just seems to meander along with no apparent direction. Quite obviously, shares that move in the latter fashion will be useless to us as investors, since we will not be able to predict any future price movement. On the other hand, shares where the trends are readily observable offer the possibility of using predictive techniques in order to determine the best buying and selling times for those shares. Since there are so many shares quoted on the stock market, there will be no shortage of shares which fall into this category. We will show in this book that such is the diversity of shares that it will be possible to remain virtually fully invested, since when the time comes to sell one share, another will present itself as a good buying opportunity. It will not even be necessary to keep track of large numbers of shares. The 100 shares which comprise the FTSE100 Index, plus the shares which form the mid-250 Index, will provide plenty of opportunity. A further advantage to the investor in staying with these 350 shares is that the spread of prices, i.e. the difference between the buying and selling price of a share at a particular point in time, is much less than is the case with the shares of companies which have smaller capitalisations.