Speculative Investor Behavior in a Stock Market with Heterogeneous Expectations

TLDR: In this paper, the authors consider a common stock that pays dividends at a discrete sequence of future times: t = 1,2, taking all other prices and the random process that determines future dividends as exogenously given, they can ask what will be the price ofthe stock?

Abstract: Consider a common stock that pays dividends at a discrete sequence of future times: t = 1,2, Taking all other prices and the random process that determines future dividends as exogenously given, we can ask what will be the price ofthe stock? In a world with a complete set of contingency claims markets, in which every investor can buy and sell without restriction, the answer is given by arbitrage. Let dtixt) denote the dividend that will be paid at time t if contingency Xj prevails, and let Ptixt) denote the current {t = 0) price ofa one dollar claim payable at time t if contingency Xt prevails. Then the current stock price must be 2(2;t,i3t(x«)dt(xf). Furthermore, in such a world it makes no difference whether markets reopen after initial trading. If markets were to reopen, investors would be content to maintain the positions they obtained initially (cf. Arrow, 1968). The situation becomes more complicated if markets are imperfect or incomplete or both. Ownership ofthe stock implies not only ownership of a dividend stream but also the right to sell that dividend stream at a future date. Investors may be unable initially to achieve positions with which they will be forever content, and thus the current stock price may be affected by whether or not markets will reopen in the future. If they do reopen, a speculative phenomenon may appear. An investor may buy the stock now so as to sell it later for more than he thinks it is actually worth, thereby reaping capital gains. This possibility of speculative profits will then be reflected in the current price. Keynes (1931, Ch. 12) attributes primary importance to this phenomenon (and goes on to suggest that it might be better if markets never reopened).