Endogenous uncertainty: A unified view of market volatility

The purpose of this paper is to provide a non-technical exposition of the main conclusions of the theory of Rational Belief Equilibrium (RBE) for market volatility. 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 (See Kurz [1997]) and 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 outlines the basic assumptions underlying models of rational expectations equilibria (REE) and their implications to the study of market volatility. The paper reviews four basic problems which have constituted puzzles or anomalies in 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" behaviour 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 proposition 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 are presented and compared both to the results predicted by a corresponding REE as well as to the actual empirical observations in the U.S. An Appendix reviews the results of additional econometric studies which bear on the results presented in the main text. 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 beliefs of the different 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 leads to 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 and correlation among beliefs of the agents. Analysis of the equity risk premium shows that the key question is what are the conditions on 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 the impact of the pessimists dominate 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 simulation results also show that correlation among the beliefs of the agents can change the frequency at which prices are realised over time and this implies that the correlation can increase the equity premium by increasing the frequency of realisation of those prices in which the pessimists have the greater impact on equilibrium prices.