Filtering returns for unspecified biases in priors when testing asset pricing theory

Procedures are presented that allow the empiricist to estimate and test asset pricing models on limited-liability securities without the assumption that the historical payoff distribution provides a consistent estimate of the market's prior beliefs. The procedures effectively filter return data for unspecified historical biases in the market's priors. They do not involve explicit estimation of the market's priors, and hence, economize on parameters. The procedures derive from a new but simple property of Bayesian learning, namely: if the correct likelihood is used, the inverse posterior at the true parameter value forms a martingale process relative to the learner's information filtration augmented with the true parameter value. Application of this central result to tests of asset pricing models requires a deliberate selection bias. Hence, as a by-product, the article establishes that biased samples contain information with which to falsify an asset pricing model or estimate its parameters. These include samples subject to, e.g. survivorship bias or Peso problems

Neurobiological studies of risk assessment: A comparison of expected utility and mean-variance approaches

When modeling valuation under uncertainty, economists generally prefer expected utility because it has an axiomatic foundation, meaning that the resulting choices will satisfy a number of rationality requirements. In expected utility theory, values are computed by multiplying probabilities of each possible state of nature by the payoff in that state and summing the results. The drawback of this approach is that all state probabilities need to be dealt with separately, which becomes extremely cumbersome when it comes to learning. Finance academics and professionals, however, prefer to value risky prospects in terms of a trade-off between expected reward and risk, where the latter is usually measured in terms of reward variance. This mean-variance approach is fast and simple and greatly facilitates learning, but it impedes assigning values to new gambles on the basis of those of known ones. To date, it is unclear whether the human brain computes values in accordance with expected utility theory or with mean-variance analysis. In this article, we discuss the theoretical and empirical arguments that favor one or the other theory. We also propose a new experimental paradigm that could determine whether the human brain follows the expected utility or the mean-variance approach. Behavioral results of implementation of the paradigm are discussed

Risk and risk prediction error signals in anterior insula

Most accounts of the function of anterior insula in the human brain refer to concepts that are difficult to formalize, such as feelings and awareness. The discovery of signals that reflect risk assessment and risk learning, however, opens the door to formal analysis. Hitherto, activations have been correlated with objective versions of risk and risk prediction error, but subjective versions (influenced by pessimism/optimism or risk aversion/tolerance) exist. Activation in closely related cortical structures has been found to be both objective (anterior cingulate cortex) and subjective (inferior frontal gyrus). For this quantitative analysis of uncertainty-induced neuronal activation to further understanding of insula's role in feelings and awareness, however, formalization and documentation of the relation between uncertainty and feelings/awareness will be needed. One obvious starting point is the link with failure anxiety and error awarenes

Rational Price Discovery In Experimental And Field Data

The methodology of tests for martingale properties in return series is analyzed. Martingale results obtain frequently in finance. One case is focused on here, namely, rational price discovery. Price discovery is the process by which a market moves towards a new equilibrium after a major event. It is rational if price changes cannot be predicted from commonly available information. The price discovery process, however, cannot be assumed stationary. Hence, to avoid false inference in the presence of nonstationarities, event studies of field data have been advocating the use of cross-sectional information in the computation of test statistics. Under the martingale hypothesis, however, this inference strategy is shown to add little except if higher moments of the return series do not exist. On the contrary, the cross-sectional approach may even be invalid if there is cross-sectional heterogeneity in the price discovery process. The time series statistic of Patell (1976], originally suggested in the context of i.i.d. time series but cross-sectional heterosceclasticity, may be preferable. It will not provide valid inference either, if higher serial correlation coincides with higher volatility. Unfortunately, this appears to be the case in the dataset which is used in the paper to illustrate the methodological issues, namely, transaction price changes from experiments on continuous double auctions with stochastic private valuations

The Dynamics Of Equity Prices In Fallible Markets

In an efficient securities market, prices correctly reflect news about future payoffs. This paper argues that there are two aspects to correctness: (i) correct updating of beliefs from news, (ii) correct prior beliefs. Traditionally, empirical research has implicitly insisted on both. Lucas' rational expectations equilibrium theory also assumes both, explicitly. Nevertheless, rationality requires only the former, but not the latter. This paper develops restrictions on the random behavior of prices of equity-like contracts when (i) is maintained, but the market may have mistaken priors about the likelihood of the bankruptcy state, in violation of (ii). The restrictions are cast in the form of familiar martingale difference results. They do not necessarily restrict returns as traditionally computed, however. Most importantly, the restrictions appear only when the empiricist deliberately imposes a selection bias. In particular, the price histories of securities that are in the money at the terminal date are to be separated from those of securities that end out of the money (i.e., in the bankruptcy state). As a result, this paper also demonstrates that something can be learned about market efficiency from samples subject to survivorship bias or the Peso problem

Lower Bounds on Asset Return Comovement

Under standard assumptions from dynamic asset pricing theory (value additivity, complete markets, rational expectations, and strict stationarity and ergodicity) and absence of arbitrage, lower bounds on the conditional and unconditional cross-moments of the returns on two assets a.re derived. They a.re expressed in terms of the second moment of a linear combination of option premia. The restrictions a.re probed with data from the foreign exchange market covering the period 1983-1991. Assuming that the value of the economy's benchmark payoff never exceeds one, and substituting linear projection for conditional expectation, several violations of the conditional lower bounds are discovered. The violations are attributed to unit roots in the data

Asset Prices in a Speculative Market

The stochastic properties of prices in a speculative market are investigated. Agents in the market start with different priors, but update in a rational (i.e., Bayesian) way from realizations of payoffs on the risky asset. Convergence of the equilibrium price to the rational expectations price is investigated, as well as the asymptotic properties of two standard tests of rational expectations. The results are contrasted with stylized facts from forward markets

Transaction Prices When Insiders Trade Portfolios

Statistical properties of transaction prices are investigated in the context of a multi-asset extension of Kyle [1985]. Under the restriction that market makers cannot condition prices on volume in other markets, Kyle's model is shown to be consistent with well-documented lack of predictability of individual asset prices, positive autocorrelation of index returns, and low cross-sectional covariance. The covariance estimator of Cohen, e.a. [1983] provides the right estimates of the "true" covariance. However, Kyle's model cannot explain the asymmetry and rank deficiency of the matrix of first-order autocovariances. Asymmetry obtains when the insider limits his strategies to trading a set of pre-determined portfolios. If these portfolios are well-diversified, the matrix of first-order autocovariances is asymptotically rank-deficient. If the insider uses only one portfolio (as when "timing the market"), its asymptotic rank equals one, conform to the empirical results in Gibbons and Ferson [1985]