Endogenous Uncertainty: A Unified View of Market Volatility

Abstract

It is argued that the theory of Rational Belief Equilibria (RBE) provides a unified paradigm for explaining market volatility by the effect of "Endogenous Uncertainty" on financial markets. This uncertainty is propagated within the economy (hence "endogenous") by the beliefs of the agents who trade assets. The theory of RBE was developed in a sequence of papers assembled in a recently published book entitled Endogenous Economic Fluctuations: Studies in the Theory of Rational Beliefs, M. Kurz (Ed.), Springer Verlag, 1997. The present paper provides a non-mathematical exposition of both the main ideas of the theory of RBE as well as a summary of the main results of the book regarding market volatility. The structure of the paper is as follows. Section I starts by reviewing the standard assumptions underlying models of rational expectations equilibria (REE) and their implications to the study of market volatility. The paper then reviews four basic problems which have constituted puzzles or anomalies in relation to the assumptions of REE: (i) Why are asset prices much more volatile than their underlying fundamentals? (ii) The equity premium puzzle: why under REE the predicted riskless rate is so high and the equity risk premium so low? (iii) Why do asset prices exhibit the "GARCH" behavior without exogenous fundamental variables to explain it? (iv) the "Forward Discount Bias" in foreign exchange markets: why are interest rate differentials such poor predictors of future changes in the exchange rates? Section II outlines the basic ideas and assumptions of the theory of RBE and the main propositions which it implies in relation to the problems of market volatility. Section III first develops the simulation models of RBE which are used in the analysis of the four problems above and explains that the domestic economy is calibrated, as in Mehra and Prescott [1985], to the U.S. economy. Then for each of the four problems the relevant simulation results of the RBE are presented and compared both to the results predicted by a corresponding RBE as well as to the actual empirical observations in the U.S. The conclusion of the paper is that the main cause of market volatility is the distribution of beliefs and expectations of agents. The theory of RBE shows that if agents disagree then the state of belief of each agent, represented by his conditional probability, must fluctuate over time. Hence the nature of the distribution of the individual states of belief in the market is the root cause of all phenomena of market volatility. The paper shows that the GARCH phenomenon of time varying variance of asset prices is explained in the simulation model by the presence of both persistence in the states of beliefs of agents as well as correlation among the states of beliefs of the agents. Correlation makes beliefs either narrowly distributed (i.e. "consensus") or widely distributed (i.e. "non-consensus"). When a belief regime of consensus is established (and due to persistence it remains in place for a while) then agents seek to buy or sell the same portfolio leading to high volatility. On the other hand, the widespread disagreement in a belief regime of non-consensus entails a balance between sellers and buyers leading to low market volatility. In short, the theory proposes that the GARCH phenomenon is the result of shifts in the distribution of beliefs in the market and these shifts are caused by the dynamics of the states of beliefs of the agents. Turning to the equity risk premium, it is clear that the key question is what are the conditions on the distribution of beliefs which will ensure that the average riskless rate is low and hence the average equity risk premium is high. It turns out that the key condition requires that on average the majority of agents are relatively optimistic about the prospects of capital gains in the subsequent period. Consequently, the rationality of belief conditions require the pessimists (who are in the minority) to be on the average more intensely pessimistic. In this narrow sense of having higher intensity of beliefs, the pessimists tend to have a stronger impact on the market a significant fraction of time. When this occurs they protect their endowment by shorting the stock and increasing their purchases of the safe riskless bill. This tends to bid up the price of the bill and lowers the price of the stock resulting in a lower riskless rate and a higher equity risk premium. The "Forward Discount Bias" in foreign exchange markets is explained by the same model used to explain the other three phenomena. It is the result of the fact that in an RBE agents often make the wrong forecasts although they are right on the average. Hence, in an RBE the exchange rate fluctuates excessively due to the errors of the agents and hence at almost no date is the interest differential between two countries an unbiased estimate of the rate of depreciation of the exchange rate one period later. The bias is positive since agents who invest in foreign currency demand a risk premium on endogenous uncertainty which is above and beyond the risk which exists in an REE. Hence the size of the bias is equal to the added risk premium due to endogenous uncertainty.

JEL Classification: D81, G12