The significance of these figures for the various options for corn and oats may be found by reference to explanations in the text relating to the similar wheat table referred to above.

APPENDIX Y

DETAILS OF HIGH AND LOW GRAIN PRICES AT CHICAGO BY

YEARS

Tables 164 to 167 show the ratios of the high to the average and the average to the low prices for four grains by years. Average prices (for special groups of months) not shown in the general tables are also given. The computation of the ratio of the average to the low price instead of that of the low to the average, as would usually be done, has the effect of making the variation below the average more directly comparable with that above it.

It is unfortunate that the comparison of highs and lows for the longer period (approaching a year) can not be made on the basis of time intervals of full length and of uniform length for all the grains. The possibilities are most satisfactory for May wheat, not only because the possible length of life of the May future within the crop year is greatest, but also because actual quotations are usually available from July 1, even in the earlier years, though there are exceptions. The data under consideration are affected by this situation through the shortening of the period of trading in some of the options, but the month of beginning of May future quotations is indicated in each case, so that the comparison of cash to future is always on the same basis.

The interest of these wheat data is chiefly comparative and they are so used in section 3 of Chapter XI. It is noteworthy that the most marked relative depression of the May wheat price within the crop year below the average price was in 1914-15, the year of the opening of the war in Europe, and the greatest rise was in 1916-17, the year of the entry of the United States into the war.

TABLE 164.-High and low prices in relation to average prices for the same periods (either one year or the active life of the May option) for cash and May future wheat at Chicago, 1885-86 to 1919-20

1 No. 2 red where more than one variety is shown separately in the prices published in the annual reports of the Chicago Board of Trade. See Table I.

2 Except as noted.

8 May future quotations begin in November. 4 May future quotations begin in October. May future quotations begin in September 6 May future quotations begin in August.

1 This is one phase of the advantage of logarithms for numerical analysis where thorough-going regard for relative values is necessary. The point may be illustrated by reference to the fact that, for example, a 50 per cent decrease is not the quantitative equivalent of a 50 per cent increase. If the terms for the first ratio be reversed the effect sought in the text is obtained. Similarly a 50 per cent increase and a 33% per cent decrease are equivalent quantitatively.

TABLE 164.-High and low prices in relation to average prices, etc.-Continued

Cash, full year

Cash, July-April

May future, July-
April

The similar table for corn shows ranges on the May future that appear to be not so great as for wheat. A sufficient explanation of this result is that the period covered is shorter, or from November to April instead of from July to April. The reference is to relative or per cent ranges, hence the difference in absolute prices between wheat and corn should not affect the comparison. TABLE 165.-High and low prices in relation to average prices for the same periods (either one year or the active life of the May option) for cash and May future corn at Chicago, 1885-86 to 1919-20

In the similar table for oats futures the fluctuations are also for a shorter period than for wheat. The difference of one month, however, is hardly sufficient to affect the range or the oats fluctuations which in fact is not less than that of wheat.

TABLE 166.-High and low prices in relation to average prices for the same periods (either one year or the active life of the May option) for cash and May future oats at Chicago, 1885-86 to 1919-20

Although rye futures are little used in this report, they are included in this tabulation, though not available for the period of which the most intensive study has been made. It is presumable that the market for rye futures always was rather narrow. This makes the comparison with wheat and corn of all the more interest. This narrowness does not appear to have caused unsteadiness. The futures show a small range, according to the ratios computed, slightly smaller in fact than for any other of the four grains.

This is

not entirely due to a short period of trading, since the crop year, as with wheat, begins in July, though there are a number of years when quotations are not workable for the first months of the crop years.

TABLE 167.-High and low prices in relation to average prices for the same periods (either one year or the active life of the May option) for cash and May future rye at Chicago, 1885-86 to 1919-20

COMPARATIVE DAILY RANGES FOR GRAIN AND PROVISION FUTURES AT CHICAGO

Table 168 shows daily ranges in terms of cents for mess pork, lard, and shortrib futures at Chicago for a three-year period. The 21⁄2-cent intervals in prices are evidently customary and are appropriate to the unit of trading or of price making in provisions, which is much larger (in terms of value especially) than the bushel used for grain futures.

The higher value of the unit of trading is doubtless the reason why the distribution runs to a greater range for mess pork than for the other provision futures. Average cash prices of the three units (computed roughly on the basis of monthly highs and lows) were $20.42 for pork, $10.90 for lard, and $11.16 for ribs.

TABLE 168.—Frequency distribution of daily ranges for provision futures at Chicago, 1914 to 1916

Obviously the only significant comparison of ranges on these futures with those for the grains is by way of relatives. In order to avoid the time-consuming computation of a relative number for each individual daily range, comparative data for the frequency distribution for each future can be turned into relative numbers in the various cases by dividing through by average prices. This is done in the following table, which utilizes methods of measuring range and dispersion employed in Chapter X:

TABLE 169.-Comparative dispersion of daily ranges (cents) for Chicago grain and provision futures, 1914 to 1916

The maximum frequency (the mode) for the provision futures occurs quite uniformly at about 0.70 per cent of the price. For grain futures the similar value varies greatly but is always much larger. The same sort of comparison holds for the arithmetic average and the median value for the ranges, but in this case the grain futures are on more nearly the same level with one another and are from 11⁄2 to over 2 times as great as these values for provisions. The difference between relative quartile values is also in general greater for grain than for provision futures. This sort of figure measures the character of the dispersion, however, more directly than it does the degree of fluctuation,