On animal spirits and economic decisions: Value-at-Risk and Value-within-Reach as measures of risk and return

Let us suppose that presently unimagined is possible, that “the unexpected may happen” (Marshall (1920). Principles of economics, McMillan, London, p. 347). Then “human decisions affecting the future, whether personal, political or economic, cannot depend on strict mathematical expectation since the basis for making such calculations does not exist” (Keynes (1936). The general theory of employment, interest and money, Harcourt Brace, New York, NY, pp. 162–163) and “individual initiative will only be adequate when reasonable calculation is supplemented and supported by animal spirits” (Keynes (1936). The general theory of employment, interest and money, Harcourt Brace, New York, NY, p. 162)—by “a spontaneous urge to action rather than inaction” (Keynes (1936). The general theory of employment, interest and money, Harcourt Brace, New York, NY, p. 161). It is intended here to examine an investment's Value-at-Risk as a reasonable calculation of the worst threat an action appears to make possible, and its return counterpart, referred to as the investment's Value-within-Reach, as a reasonable calculation of the best hope an action appears to offer. In exploring the extension of the Value-at-Risk approach from applications to investments in financial assets to applications to investments in real assets, the properties of Value-at-Risk as a risk measure are reviewed. Recognizing that Value-at-Risk focuses exclusively on downside risk, a complementary set of properties is specified which is shown to be necessary and sufficient for the acceptance of Value-within-Reach as a measure of return. This note concludes with remarks on a distribution's focus-values, consisting of the distribution's Value-at-Risk and Value-within-Reach, as reasonable calculation of a course of action's risk and return.