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The dominance of price over value

Market prices reveal information about fundamental value indirectly. Private research produces information about fundamental value directly. Neither is a perfect indicator of fundamental value: the former due to non-fundamental market factors, and the latter due to limitations of private research. However, plausible theoretical research shows that overtime the information content of prices in respect to (known) fundamentals improves faster due to aggregation and averaging. When this happens investors rationally neglect their own fundamental research. This can erode information efficiency of the market and lead to sustained misalignments if the market as a whole misses key risks and value factors.

Michele Berardi (2016), “Herding through learning in an asset pricing model”, University of Manchester, Centre for Growth and Business Cycle Research, No. 223

The post ties in with the subject of information efficiency, particularly the section “Why markets are not (macro) information efficient“.

The below are excerpts from the quite theoretical paper. Headings and some other cursive text has been added for context and convenience of reading.

The gist

“The fundamental value of an asset summarizes the future stream of cash flows that the asset entitles to. By definition, such value is never observable, as it is always determined by events in the future. The price of an asset represents what market participants are willing to pay for it. Such value is readily observable.”

“Agents use prices, besides an idiosyncratic exogenous signal [which could be fundamental information and private research], to infer fundamental values… agents use prices as a signal because prices summarize the view of other agents about the fundamental value.”

Uncertainty about fundamentals can lead agents to over-rely on public endogenous [i.e. price] information and discount their private signals in a dynamic setting where information can be accumulated. This effect follows from the fact that the precision of the public signal is endogenous [i.e. increases rapidly due to the aggregation of research and information and the averaging out of errors], and it improves over time faster than that of the private one.”

“As agents end up relying only on prices, a form of rational herding with an informational cascade emerges: private information is disregarded and only the public signal is used…In the limit, as the relative precision of the two signals changes, they disregard their own private information and all act only on the basis of the aggregate signal represented by prices…The problem with cascades is that they prevent the aggregation of information of numerous individuals…In our framework, as the weight of private information converges to zero, private information of each individual about the fundamental value of the asset is neglected and does not contribute to the determination of prices: aggregation fails.”

“Uncertainty and learning can lead to a disconnect between fundamental values and prices.”

Key details of the theoretical analysis

“We assume agents are only concerned about the fundamental value of their portfolio, relative to its price…The fundamental value of an asset is not known and it can only be inferred using observables such as dividends and prices as indirect information.”

“We assume there is an asset available for trade on the market, whose fundamental value is represented by [a single parameter]. We can think of such value as representing a measure of the present discounted value of future dividends… [Investors] are mean variance maximizers, i.e. they try to maximize the mean with a penalty for the variance of their portfolio.…Agents need to form an expectation about the unobservable fundamental value and its conditional variance in order to implement this strategy.”

“Agents do not observe directly [the fundamental value of the asset] but observe two signals on it: one, endogenous and public, from prices and one, exogenous and private, from news [and private research]. We can think of this last component as agents receiving different news because accessing different sources of information, or as a subjective interpretation of the same news [due to different methods of private research].”

“We assume an exogenous and stochastic supply of [the asset], which [is uncertain and] follows a normal distribution… this noise term will prevent prices from being fully revealing [of fundamental value].”

“It is…optimal for agents to put some weight on prices, together with the exogenous signal, when forming beliefs about fundamental values…Bayesian theory provides the optimal weight on the two signals:…We then extend the model to a dynamic framework where agents repeatedly observe signals and can accumulate information…Agents rely on a mix of theory and evidence: we assume they know that the optimal weight depends on the relative variance of the two signals, and learn about such empirical moments [which is Bayesian learning]”

“The aggregation process that generates prices averages out some noise [in respect to the fundamental value of the asset].”

“Both private and public information [on a constant fundamental value factor] become infinitely precise in the limit, but the precision of the public signal improves faster…Because agents try to minimize the variance of their portfolio by relying more on the less volatile signal, and because the variance of prices decreases to zero faster than that of private information, agents end up disregarding their private signals. This result suggests that, if fundamental values change, they might not get factored properly into prices, thus leading to a divergence between the two…We show that in this case it is optimal for agents to put increasing weight on prices as time goes on, and in the limit the private exogenous signal is completely ignored. This can open up the door for deviations of prices from fundamental values.”

“In order to understand the robustness of this result, we extended the framework in two directions. First, in the Bayesian rational learning setting, we introduced an explicit subjective probability of change in the fundamental value: in this way agents explicitly allow for movements in the variable they are trying to infer through their signal extraction problem. Second, in the adaptive learning setting, we allowed agents to discount past information through a constant gain algorithm. In both cases our original result is shown to persist, though somewhat mitigated.”


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