Two-Person Dynamic Equilibrium: Trading in the Capital Market

When several investors with different risk aversions trade competitively in a capital market, the allocation of wealth fluctuates randomly between them and acts as a state variable against which each market participant will want to hedge. This hedging motive complicates the investors’ portfolio choice and the equilibrium in the capital market. Although every financial economist is aware of this difficulty, to our knowledge, this issue has never been analyzed in detail. The current paper features two investors, with the same degree of impatience, one of them being logarithmic and the other having an isoelastic utility function. They face one risky constant-return-to-scale stationary production opportunity and they can borrow and lend to and from each other. The behaviors of the allocation of wealth and of the aggregate capital stock are characterized, along with the behavior of the rate of interest and that of the security market line. The two main results are: (1) given the particular menu of assets under consideration, investors in equilibrium do revise their portfolios over time so that some trading takes place, (2) when the two investors ‘disagree’ about whether the economy should be expanding or contracting, it is possible for the allocation of wealth and the capital stock to admit steady-state distributions. It is also possible for these to randomly oscillate between two extreme attracting points. This is in contrast to the certainty case, where aggregate wealth becomes either very large or very small and one investor in the long run holds all the wealth. The existence of trading opens the way to a theory of capital flows and market trading volume.