G. L. S. Shackle, An Analysis of Speculative Choice (1945)

Shackle’s journal article develops a theory of asset choice under subjective uncertainty, using “potential surprise,” “focus gain,” and “focus loss” to explain speculative market movements. Its central problem is how an individual chooses holdings when future price changes admit several hypotheses rather than one certain forecast. The argument proceeds from a two-asset model through an indifference-curve explanation of market sensitivity, then extends to multiple assets and tests its assumptions against the “floating value” of development land. Its distinctive move is to make the attractiveness of imagined outcomes, rather than numerical probabilities alone, central to speculative choice.

Under certainty, an individual able to exchange assets at given prices would concentrate wealth in whichever asset promised the greatest proportional price increase. Uncertainty introduces a different comparison: hypotheses about price changes carry different degrees of potential surprise, while particular prospective gains and losses command the individual’s attention. The “focus” outcomes are those where the attraction or apprehension associated with an outcome balances the doubt attached to its realization. Shackle refers readers to his earlier work for the full conceptual apparatus, but supplies enough here to construct a geometry of choice.

For two assets, he links hypothetical price changes carrying equal potential surprise. If one asset offers both a higher focus gain and a smaller focus loss, it dominates the other. More commonly, greater prospective gain accompanies greater prospective loss. Different allocations then generate a “gambler opportunity curve,” with focus loss on the horizontal axis and focus gain on the vertical. If one asset is money, the curve begins at the origin: holding money entails neither gain nor loss of money value. The algebra establishes exact linearity for the boundaries of the range carrying negligible surprise; linearity of focus outcomes requires an additional simplifying assumption.

Preferences enter through “gambler indifference curves,” which rank combinations of focus gain and loss. Their shape depends on wealth and circumstances, because the significance of a possible loss depends on its proportion to total capital.

Thus a gambler indifference map describes the tastes, in regard to hopes and uncertainty, of a given individual in given circumstances.

These curves slope upward: accepting a larger focus loss requires a compensating focus gain. Shackle conjectures that near the origin an individual may regard equal small gains and losses as balancing each other, whereas a loss threatening the whole of one’s capital requires a disproportionately large prospective gain. The chosen allocation lies where the opportunity curve meets the most attractive attainable indifference curve. This is a psychological account expressed geometrically, not an independently established universal law of preferences.

The speculative-market explanation follows from the interaction of these curves. With roughly symmetrical upside and downside, the individual tends toward the more narrowly predictable asset. A slight upward revision of the uncertain asset’s prospects tilts the opportunity curve. If indifference curves bend only gently, this small change can move the preferred allocation a long distance, potentially from predominantly money into predominantly the speculative asset. Buying raises its price, apparently confirms the original optimistic interpretation, and can prompt another round of revised expectations and purchases.

Common sense approves the conclusion that, if such temperaments abound, small events will be the more readily able to generate booms of market activity.

The qualification matters: disproportionate market reactions depend on a sufficiently widespread temperament whose reluctance to gamble increases slowly as stakes rise relative to wealth. Shackle explains how small news can have large effects without claiming that every investor or market must behave this way.

The extension to several assets constructs a boundary of favourable opportunities from straight segments joining pure holdings. An asset can be excluded when a mixture of two others provides both a larger focus gain and a smaller focus loss. On the resulting boundary, an optimal point generally represents holdings of no more than two assets.

So long as the potential surprise functions for the ratios of price change remain valid in unchanging form, no matter how many goods are involved, there will always be, for any combination of more than two goods, some combination of not more than two goods which is superior (or, at least, not inferior) to it.

This conditional result exposes the model’s limits. Diversification across more assets suggests either that investors value qualities beyond focus outcomes, such as liquidity, or that outcomes for a portfolio cannot be derived directly from unchanged surprise functions for its components.

Development land supplies the decisive example. Drawing on evidence reported to the Uthwatt Committee, Shackle observes that separate valuations of land around a town can aggregate to far more than plausible total development would warrant. Each owner sees no identifiable obstacle to the selection of their own plot. Both development and non-development can therefore carry little potential surprise, although development of every plot is incompatible with aggregate demand.

In order to enjoy with a high intensity, or even to the full, the anticipation of some gratifying outcome, a man requires only that there should be no solid, identifiable reason to disbelieve in the possibility of this outcome: he does not require solid grounds for feeling sure that it will be the true outcome.

Buying one whole plot preserves a large possible gain; buying a sub-plot in every possible development site secures a smaller gain. Certainty does not necessarily compensate psychologically for the reduced magnitude of the hoped-for outcome. Conversely, a portfolio might become attractive by reducing focus loss through relationships between its components. The article’s relevance lies in this connection between imagined possibility, concentrated holdings, and self-reinforcing prices. Its closing author’s note acknowledges related positively sloped indifference curves in Domar and Musgrave’s analysis of taxation and risk-taking, while the substantive argument retains its distinctive emphasis on potential surprise.