The Two Market Principles (3)

In the first two approximations, where the element of risk was considered absent, it was shown that the aggregate modification of the income streams of all individuals for every period of time was zero. What was borrowed equaled what was lent, or what was added by sale was equal to what was subtracted by purchase. The same principle still applies, for what one person pays, another person must receive. The only difference is that, in a world of chance, the actual payments may be quite different from those originally anticipated and agreed upon, that is, will often be defaulted, in whole or in part.

In the former approximations, the total present value of the prospective modifications of one's income stream was zero, that is, the present value of the loans equaled the present value of the borrowings, or the present value of the additions and subtractions caused by buying and selling balanced each other. In our present discussion, in which future income is recognized as uncertain, this principle still holds true, but only in the sense that the present market values balance at the moment when the future loans or other modifications are planned and decided upon. The fact of risk means that later there may be a wide discrepancy between the actual realization and the original expectation. In liquidation there may be default or bankruptcy. When the case is not one of a loan contract, but relates merely to the difference in income streams of two kinds of property bought and sold, the discrepancy between what was expected and what is actually realized may be still wider. Only viewed in the present is the estimated value of the future return still the equivalent of the estimated cost.

We thus see that, instead of the series of simple equalities which we found to hold true in the vacuum case, so to speak, where risk was absent, we have only a tendency toward equalities, interfered with by the limitations of the loan market, and which, therefore, result in a series of inequalities. Rates of interest, rates of preference, and rates of return over cost are only ideally, not really, equal.

We conclude by summarizing in the accompanying table the interest-determining conditions not simply for the third approximation but for all three of our three successive approximations (distinguished by the numerals 1, 2, 3).

In this summary tabulation the "Principles as to Investment Opportunity" are formally inserted, under the first approximation, in order to complete the correspondence with the other two approximations, but of course they merely re-express the hypothesis under which the first approximation was made. They are therefore bracketed, since only the remaining four conditions are of real significance for the first approximation.

The first and second approximations were, of course, merely preparatory to the third, which alone corresponds to the actual world of facts. Yet the other two approximations are of even greater importance than the third from the point of view of theoretical analysis. They tell us what would happen under their respective hypotheses. Both these hypotheses are simpler than reality; hence they lend themselves better to formal analysis and mathematical expression.

Moreover, to know what would happen under these hypothetical conditions enables us better to understand what does happen under actual conditions, just as the knowledge that a projectile would follow a parabola if it were in a vacuum enables the student of practical gunnery better to understand the actual behavior of his bullets or shells. In fact, no scientific law is a perfect statement of what does happen, but only what would happen if certain conditions existed which never do actually exist. Science consists of the formulation of conditional truths, not of historical facts, though by successive approximations, the conditions assumed may be made nearly to coincide with reality.

The second approximation gives a clear cut theory applicable to the clear cut hypotheses on which it is based. The third approximation cannot avoid some degree of vagueness.