Full text: The dispersion of expectations in a speculative market

increased at the expense of cash. The case is identical with open market 
policy: The central bank as one of the participants in the market sells 
bonds and withdraws the corresponding amount of cash from the market. 
We shall now consider cases where an additional demand for bonds comes 
from outside the market, that is, where the total of disposible funds is 
not constant any more.If now a buyer from outside the market (let us say 
from abroad) enters the market with the intention of buying a certain 
amount of bonds then he will have to offer a higher price than the ruling 
price. The new price p' will be just high enough to turn a sufficient 
number of bulls into bears so as to satisfy the additional demand of the 
outside buyer. The underlying assumption is that the people who expected 
prices between p and p' are now, when the price has become p', still 
sticking to their belief that prices will not maintain themselves at the 
new level but go back to the old level again. In other words the 
underlying beliefs are conservative. They involve a conviction that there 
exists a negative feedback mechanism. This, it appears, is a condition 
for stability. If instead of the conservative expectation there is a 
belief in a positive feedback then the price movement whether up or down 
would never come to a halt. 
The above argument was based on the extremely restrictive assumption that 
every member of the population of participants has the same amount of 
financial resources. If we drop this assumption we may at the same time 
also drop the implicit assumption that every participant expects one and 
only one definite price. This is, in fact, rather artificial. In reality 
he probably considers several alternative prices and perhaps attributes 
greater or lesser probability to one or the other alternative. If this 
variety of expectations has any practical consequence it will mean that 
he divides his resources according to the prices” on which he 
speculates", acting as a bull in relation to one part and as a bear in 
relation to the other, the proportions depending on the probability he 
attributes to the various expectations. In fact the participant may be 
regarded as a divided personality consisting of various parts each of 
which holds the same amount of wealth (a standard unit which may be 
determined by the minimum amount which can be traded). Again these 
expectations of the various "subpersonalities" may be ordered 
statistically and combined with the orderings of the other participants. 
In probabilistic terms this will mean a convolution of the various 
frequency distributions of the individuals' expectations. The resulting 
total frequency distribution for all participants together will show just 
how much funds are associated with each expected price. This is a 
cumulative frequency distribution as before but without the restrictive 
assumption of equal resources for each participant. The shift from bull 
to bear or vice versa may now take place within the resources of one and 
the same person or it may take place between persons. 
The distribution function just described may now be used to define and 
measure uncertainty. A measure of uncertainty in the group of 
participants in a market may be found in the variance of the price 
expectations. This cannot be observed directly but it will show itself 
through the strength of the price response which a certain additional 
offer or demand from outside (an exogenous disturbance) will produce. If 
expectations are closely concentrated a small change in the price will 
shift a large volume of financial resources from bull to bear or the 
other way round. If they are spread out widely a large change in price 
will be necessary in order to shift a modest amount of resources. It has 
to be noted, however, that the strength of reaction will also depend on 
whether the price initially is in the middle of the distribution (near 
the mode) or nearer to one of the tails. 
The peculiarity of the above definition of uncertainty is that it does 
not apply to an individual but to a group. Instead of being psychological 
it is a social concept. This also makes it more objective than the
	        

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