THE DISPERSION OF EXPECTATIONS IN A SPECULATIVE MARKET. 
It may be assumed with some plausibility that the participants in a 
speculative market - for example a market for bonds or for foreign 
exchange - have different expectations with regard to the future price, 
or the direction in which prices are going to change. 
Contrary to some opinions this diversity of expectations is a condition 
for the attainment and maintenance of equilibrium in these markets; it 
must be fulfilled in order to assure that an additional offer coming from 
outside will find buyers or that an additional demand coming from outside 
will will find sellers. A further condition is that there must be a 
generally accepted idea of a normal price level to which prices 
ultimately tend to return. This normal price will be a range of prices 
rather than one single price. Though the estimate of this range of prices 
may not be uniform either, it is much more uniform than the earlier 
mentioned price expectations: It must have some basis in objective facts. 
Thus in the case of a manufactured good there may be some general 
information about the range of costs. In the case of an exchange rate 
there is - or at least there used to be - an idea about purchasing power 
parity or relative cost, although in our times this has obviously become 
more and more an obscure and irrelevant quantity. In the case of the long 
term rate of interest there used to be a historical experience that it 
rarely goes outside a certain range, but again this "basis in fact" has 
become more and more shaky in view of the violent fluctuations of modern 
capital markets. The undermining of concepts of normalcy in certain 
markets has been accompanied by great instability, so that it does not 
contradict but rather tends to confirm the rule that generally accepted 
ideas of a standard of normalcy are necessary in order to maintain more 
or less stable markets. 
The different expectations of participants in a market could be ordered 
in the form of a frequency distribution. It will be the distribution of 
participants in a market according to expected price. For the purpose of 
this representation we must assume that the expectations of different 
people are (approximately) independent of each other. The object of the 
expectation is the price after a certain time, or wbat is equivalent, the 
appreciation or depreciation within that time. There is thus a certain 
time horizon; we shall assume that it is given and is the same for all 
the participants. This is quite unrealistic but the purpose of the 
present note is to explain a certain approach and this would fail in its 
purpose if all the complications were taken into account. In the case of 
a market in long term bonds let us assume in the first instance that each 
of the participants has the same amount of financial resources which he 
can either invest in bonds or hold as cash ( or treasury bills ). We 
assume that the total of disposable financial funds (the "material" of 
the market, as it were) is given. We can draw a cumulative distribution 
function showing the number of people who expect a price equal to or 
lower than p, say F(p)(see figure 1). These people will hold money if the 
ruling price is p, while all the others,(1 - F(p)), will hold bonds. We 
shall first consider changes in the market which can occur while the 
total amount of funds remains unchanged. This may happen if the 
expectation of one of the bond holders changes and he shifts from the 
bulls to the bears, i.e. he wants to sell his lot of bonds. He must find 
somebody who is willing to buy them and for this purpose he must induce 
somebody to change from bear to bull. This is achieved if the market 
price declines by p so that somebody whose expectation was formerly 
below the market price finds that it is now above it. 
Another case occurs if one of the participants issues new bonds in order 
to repay some debts in cash. The market price of bonds will have to 
decline so that a number of participants will shift from bears to bulls, 
i.e. will be willing to hold bonds. The proportion of bonds will have