Bayesian Resolution of an Information Paradox in the Theory of Investment

Proof in financial economics reveals how investors (incoming buyers) in a rationally priced market perceive a higher expected utility investment when the payoff from the risky asset has higher variance. The asset’s lower market price more than compensates for its higher risk. Because better information tends to reduce payoff variance, investors can prefer that markets be less informed—that is the paradox. The obvious retort is that less information can mean ill-informed prices and investments, and consequent losses. To grow wealth, investors prefer that the market is sufficiently well informed to allow accurate parameter estimation but not so well informed that there is little remaining payoff variance and hence no attractive investment opportunity. The “ideal investment” is a bet on a fair coin, because the probability of winning is not only “known,” it is known to be 0.5, leaving the payoff from the bet with maximum possible variance.