Testing Rationality of Financial Markets

Author: Bondarenko, Oleg P.

Year: 1998

Degree: Dissertation (Ph.D.)

Advisor: Bossaerts, Peter L.

Committee Members: Bossaerts, Peter L.; Strnad, Jeff; McKelvey, Richard D.; Katz, Jonathan N.

Option: Social Science

DOI: 10.7907/qjg0-vq55

Abstract

This thesis consists of three related chapters that investigate rationality of asset pricing. The point of view of this study differs from traditional analysis of rational expectations (market efficiency) in one important aspect: market participants are not required to have correct beliefs about all parameters of the economy. Instead, investors' subjective assessment of the future may be different from the objective probability distribution. Other than that, investors are assumed to be rational which means that they process new information to the market in a consistent and efficient manner.

This line of research has been inspired by Bossaerts (1996) who proposed a set of novel rationality restrictions on securities prices that are robust to investors' initial beliefs. These restrictions obtain for prices of special finite-lived securities whose payoff can be categorized into two states: "out-of-the-money" state where the payoff is zero, and "in-the-money" state where the payoff is random. The simplest example of such securities is an Arrow-Debreu (AD) type security, a binary security paying $1 in some states of the world and zero in others. More general examples include option-like contracts and, most importantly, equity.

In Chapter 1, we discuss the model of Bayesian agents with potentially biased beliefs and derive several related theoretical results. The new rationality restrictions allow one to test the central part of rational expectations, namely investors' usage of Bayes' law to update their beliefs, or rationality of learning. The strongest predictions obtain for prices of Arrow-Debreu (AD) securities and we use them in two empirical applications.

In Chapter 2, we investigate rationality and biases in expectations in the Iowa Electronic Market (IEM). The IEM, an experimental market, runs, among others, a number of winner-take-all markets with contracts based on the future prices of US stock exchange traded securities and indices. The winner-take-all contracts are classical examples of AD securities with "1-0" payoff structure and, therefore, their prices can be used in the new tests. We find that price histories of these contracts are in accordance with rational learning but not with rational expectations.

As the next application, in Chapter 3, we suggest how rationality of learning can be tested in real financial markets, where no AD securities are traded. The idea here is to estimate prices of particular AD securities, namely digital options. Each of these digitals pays $1 whenever the S&P 500 Index closing price on the expiration date is above a predetermined cutoff level, or zero otherwise. Prices of digitals can be estimated from prices of corresponding traded S&P calls and puts. The estimation procedure that we use to recover prices of digitals is in the spirit of nonparametric techniques and has several interesting features.

First, and most importantly, the estimation procedure does not require stationarity of an underlying asset's price dynamics. This means that the option formula is allowed to change over time. Second, the estimation procedure enforces rudimentary theoretical shape restrictions on options prices. Third, it proposes an alternative parametric option specification which is parsimonious, computationally very simple, and which significantly outperforms the Black-Scholes specification for the studied dataset.

The analysis of time series of the estimated digital options supports the hypothesis of rational learning. Several tests based on the martingale restriction on prices of digitals indicate that investors of the S&P 500 Index Options efficiently process new information to the market. Still, strong evidence against rational expectations surfaces, implying that investors must have started with biased priors. We characterize the investors' expectational errors and, in particular, show that, over the five-year period from 1991 to 1995, investors repeatedly underestimated the S&P 500 Index expected return and overestimated its volatility.

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