# Precise Knowledge, Risk, and Uncertainty

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certainty: Certainty, an aspect of complete information, entails precise knowledge of current and all future values of an economic variable or set of economic variables (e.g., market conditions).

uncertainty: Uncertainty exists when the current or future values of an economic variable or set of economic variables (e.g., market conditions) are not known with precision.

risk: Risk is the statistical distribution of alternative outcomes from an action, and is usually estimated by the variance, standard deviation, etc., of the possible outcomes (e.g., the probability of death plus the probability of living = 1.) If the probabilities of alternative outcomes are reasonably well known, a probability function can be constructed. In investment analysis, risk is commonly measured as the standard deviation of the expected return on total investment. Another example: An insurance actuary can estimate risks with reasonable precision if significant amounts of historical data are available, and then ascertain appropriate insurance premiums for bearing risk.

Knightian uncertainty: Knightian uncertainty (named after Frank Knight [1885-1972]) exists when the probability functions for certain broad classes of rare or exceedingly speculative events are a matter of relatively uninformed guesswork.

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In this figure, the dark blue rectangle represents certainty about events – things about which we have precise knowledge. Reasonable certainty exists, for example, about such things as: (a) the fate of the World Trade Center on 9/11/2001, or other well known historical events, (b) the results of simple math, or (c) how much we will save by using a coupon to buy a Domino’s pizza. Uncertainty is a term applied to all events about which our knowledge is imprecise. Uncertain events can be decomposed into events for which possible outcomes can be assessed with some precision (risk), and events for which outcomes are almost purely speculative.

Examples of “risky events” in the lighter blue area include gambling.

a.              Precise risk: The probabilities of alternative outcomes can be specified mathematically. Examples include the probability functions associated with cards, coin flips, or dice.

b.              Fuzzy risk: Some current information or historical data are accessible and appear useful in predicting certain outcomes. For example, the actuarial tables insurance companies use to calculate insurance premiums yield fuzzy risk in predicting morbidity, mortality, or rates of accidents. Events may occur according to an unstable or incompletely known Poisson distribution. At say, point a, the odds that a fair coin will land heads up 10 times in a row is easily calculable. At point b might be events for which odds are a bit more speculative, say a horse race. At point c, we may try to assess the likelihood of even less certain outcomes. For example, what are the odds that you will be struck by lightning next week? At point d, the probability function is becoming quite fuzzy. How likely is it that every member of your class will live to see the year 2050? (Insurance companies develop actuarial tables for these kinds of risk, but who knows? A giant meteorite astronomers haven't even spotted yet could end life on earth in the year 2037.)

c.              Knightian uncertainty: By point f in the figure, estimating the likelihood of a possible event is almost pure speculation – we can do no better than a wild guess at the probability that a terrorist will blow up the Golden Gate Bridge tomorrow, for example. We will know whether it happened after tomorrow has passed (ex post, probabilities are either 1 or zero), but from today's perspective (ex ante), is the probability 0.000000000001, or is it 0.000000000000000000000000001? We cannot know with any certitude until after the time interval elapses.

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Author: Ralph Byrns

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