The comparative statics on asset prices based on bull and bear market measure

For single–period complete financial asset markets with representative investors, we introduce a bull market measure for uncertain state occurrence and its associated ordering between representative investors in markets based on their marginal rate of substitution between equilibrium consumption allocations among possible states. These concepts combine and generalize the likelihood–ratio–dominance relation between probability prospects of state occurrence and the Arrow–Pratt ordering of risk aversion in expected utility settings. By analyzing the comparative statics for bull market effects on equilibrium asset prices, we derive some monotone properties of the risk–free rate and discounted prices of dividend–monotone assets. Keywords– Bull and Bear Market Measure, Comparative Statics, Equilibrium Asset Price, Dividend–Monotone Asset, Total Positivity of Order 2 JEL Classification– D81, G12 ∗An earlier version of this paper was presented at the 2002 annual meetings of the Japanese Association of Mathematical Sciences and the Japanese Finance Association. The authors would like to thank Marc Bremer, Kazuhiko Ōhashi, Katsushige Sawaki and two anonymous referees for their comments and suggestions. Of course, all remaining errors are our responsibility. †Graduate School of Economics, Osaka University, 1–7 Machikaneyama–machi, Toyonaka, Osaka 560– 0043, Japan, and Daiwa Securities Chair, Graduate School of Economics, Kyoto University, Yoshida– honmachi, Sakyo–ku, Kyoto 606–8501, Japan. E–mail: [email protected] ‡Graduate School of Economics, Osaka University, 1–7 Machikaneyama–machi, Toyonaka, Osaka 560– 0043, Japan. E–mail: [email protected]