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 behavior of the allocation of wealth is characterized, along with the behavior of the rate of interest and that of the security market line. The two main results are: (1) investors in equilibrium do revise their portfolios over time so that some trading takes place, (2) provided some conditions are satisfied, the allocation of wealth admits a steady-state distribution at an interior point; this is in contrast to the certainty case, where 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.

Target Zones Big and Small

Under different assumptions about the underlying monetary shocks, we study target zones of various widths and the effect they have on variables like the interest differential. The stochastic disturbances assumed are successively a non-zero mean random walk and a mean reverting process. The latter is used to incorporate the "leaning against the wind" policy (intrainarginal intervention) which is prevalent in the EMS.

Equilibrium Portfolio Strategies in the Presence of Sentiment Risk and Excess Volatility

Our objective is to identify the trading strategy that would allow an investor to take advantage of "excessive" stock price volatility and "sentiment" fluctuations. We construct a general-equilibrium model of sentiment. In it, there are two classes of agents and stock prices are excessively volatile because one class is overconfident about a public signal. As a result, this class of overconfident agents changes its expectations too often, sometimes being excessively optimistic, sometimes being excessively pessimistic. We determine and analyze the trading strategy of the rational investors who are not overconfident about the signal. We find that, because overconfident traders introduce an additional source of risk, rational investors are deterred by their presence and reduce the proportion of wealth invested into equity except when they are extremely optimistic about future growth. Moreover, their optimal portfolio strategy is based not just on a current price divergence but also on their expectation of future sentiment behavior and a prediction concerning the speed of convergence of prices. Thus, the portfolio strategy includes a protection in case there is a deviation from that prediction. We find that long maturity bonds are an essential accompaniment of equity investment, as they serve to hedge this "sentiment risk."

What Can Rational Investors Do About Excessive Volatility and Sentiment Fluctuations?

Our objective is to understand the trading strategy that would allow an investor to take advantage of "excessive" stock price volatility and "sentiment" fluctuations. We construct a general equilibrium model of sentiment. In it, there are two classes of agents and stock prices are excessively volatile because one class is overconfident about a public signal. This class of irrational agents changes its expectations too often, sometimes being excessively optimistic, sometimes being excessively pessimistic. We find that because irrational traders introduce an additional source of risk, rational investors reduce the proportion of wealth invested into equity except when they are extremely optimistic about future growth. Moreover, their optimal portfolio strategy is based not just on a current price divergence but also on a prediction concerning the speed of convergence. Thus, the portfolio strategy includes a protection in case there is a deviation from that prediction. We find that long maturity bonds are an essential accompaniment of equity investment, as they serve to hedge this "sentiment risk." The answer to the question posed in the title is: "There is little that rational investors can do optimally to exploit, and hence, eliminate excessive volatility, except in the very long run."

Efficient Intertemporal Allocations with Recursive Utility

In this article, our objective is to determine efficient allocations in economies with multiple agents having recursive utility functions. Our main result is to show that in a multiagent economy, the problem of determining efficient allocations can be characterized in terms of a single value function (that of a social planner), rather than multiple functions (one for each investor), as has been proposed thus far (Duffie, Geoffard and Skiadas (1994)). We then show how the single value function can be identified using the familiar technique of stochastic dynamic programming. We achieve these goals by first extending to a stochastic environment Geoffard's (1996) concept of variational utility and his result that variational utility is equivalent to recursive utility, and then using these results to characterize allocations in a multiagent setting.

Super Contact and Related Optimality Conditions: A Supplement to AvinashDixits:"A Simplified Exposition of Some Results Concerning Regulated Brownian.

Dixit (1988) observed that the mathematical construct of "regulated Brownian motion" developed by Harrison (1985) had proved useful in economic models of decision-making under uncertainty. In a recent note he provided a number of methods for calculating expected discounted payoff functions based on such processes. The purpose of this supplement is twofold: -determine to what extent the first-degree conditions reached by Dixit (his equations (12) and (13) or (12') and (13')) are simply a consequence of the definition of the expected discounted payoff, or to what extent they can be interpreted as first order conditions of some optimization problem, as has been suggested in Dumas(1988); -extend Dixit's treatment to the case where there are fixed costs of regulation as 1n Grossman-Laroque (1987).

A Test of the International CAPM Using Business Cycles Indicators as Instrumental Variables

Previous work by Dumas and Solnik (1993) has shown that a CAPM which incorporates foreign-exchange risk premia (a so-called 'international CAPM') is better capable empirically of explaining the structure of worldwide rates of return than does the classic CAPM. In the specification of that test, moments of rates of return were allowed to vary over time in relation to a number of lagged 'instrumental variables'. Dumas and Solnik used instrumental variables which were endogenous or 'internal' to the financial market (lagged world market portfolio rate of return, dividend yield, bond yield, short-term rate of interest). In the present paper, I use as instruments economic variables which are 'external' to the financial market, such as leading indicators of the business cycles. This is an attempt to explain the behavior of the international stock market on the basis of economically meaningful variables which capture 'the state of the economy'. I find that the leading indicators put together by Stock and Watson (NBER working paper no. 4014, 1992) as predictors of the U.S. business cycle also predict stock returns in the U.S., Germany, Japan and the United Kingdom. These instruments lead again to a rejection of the classic CAPM and no rejection of the international CAPM.

Currency Option Pricing in Credible Target Zones

This paper develops a model for valuing options on a currency which is maintained within a band. The starting point of our model is the well known Krugman model for exchange-rate behavior within a target zone. Results from model runs provide insight into evidence reported by other authors of mispricing of currency options by extensions of the Black-Scholes model.