| I propose a stochastic dominance method for quantifying the difference between distribution functions and develop a geometric interpretation of the method with vectors in state space. I use state space, common in academic research into investors' preferences regarding state-contingent outcomes, to obtain a geometric interpretation of the first- and second-order stochastic dominance test, which studies investors' preferences regarding probabilities. The state-space geometry allows us to develop insights into the stochastic dominance test and shows the link, as well as the differences, between two types of research into investors' preferences. I define secondary assets from given assets and convert the second-order stochastic dominance to first-order stochastic dominance.; The state-space representation of the stochastic dominance rule allows us to quantify the difference between distribution functions. I call this stochastic dominance pricing. This procedure applies stochastic dominance to pairs of assets to compare them. I extend pair-wise comparison to an “efficient market”—by definition a market showing no stochastic dominance of any one asset over any other asset within it. I claim that an asset that dominates other assets should have a higher price than the other assets by the amount necessary to eliminate the dominance of the dominant asset over each existing asset in the market. This comparison yields a price band defined as an “H-band.” The H-band is based on the weakest assumptions on fundamental risk factors, distribution functions, and preferences. I obtain the price band rather than an equilibrium price because of partial ordering due to the absence of restrictive assumptions on preferences.; I prove the existence of the H-bands in an efficient market and their properties. Then, I demonstrate use of the method by addressing several economic problems. I also identify the conditions sufficient to guarantee the existence of efficient markets and their applications. I compare implied default risk premiums for bond prices to the implied default probabilities of Broske and Levy. I also compare the H-bands with Black-Scholes prices for the call options of a stock. The new method can be applied to quantify the value of a distribution in comparison to other priced distributions under the weakest assumptions. |
