Asaf Manela
The value of diffusing information
Journal of Financial Economics | Volume 111, Issue 1 (Jan 2014), 181–199

How does the speed by which information diffuses affect its value to a stock market investor? Consider two drugs: Viagra treats erectile dysfunction while Allegra fights nasal allergies. Both drugs, if approved by the US Food and Drug Administration (FDA), would generate similar revenues to their publicly traded developers. When Viagra is approved, news of the approval diffuses fast because it makes for good conversation, while news of Allegra's approval travels slower. As an investor, would you pay more today to know that Viagra or Allegra will be approved tomorrow?

Faster-diffusing information can be more or less valuable

The intuitive answer to this question is that faster-diffusing information is more valuable because it translates into a quicker and less random realization of profits. But this line of reasoning ignores the fact that traders' decision to collect private information would take into account its future diffusion rate. For example, even before the two drugs are approved, one might expect news of Viagra's approval to diffuse faster than Allegra's. The model I develop accounts for this realistic feature of the world, and shows that competing informed investors trade more aggressively on faster-diffusing information. The increased private information collection impounds more information into prices, thus decreasing the returns to informational trading.

In my model, the transmission rate of information determines equilibrium asset prices and volume. The model is a four-period noisy rational expectations model, ala Grossman-Stiglitz (AER 1980), with asymmetric information about a risky asset that pays off in the post-announcement period. Information diffuses through a large population of risk-averse investors. The transmission rate controls the probability that uninformed investors in the pre-announcement period become informed for free in the announcement period. Pre-announcement, investors make their endogenous information choice, taking into account its future diffusion through both direct communication and indirect learning from prices.

The main theoretical result provides a closed-form expression for the value of information given the transmission rate that has eluded previous studies of similar settings (e.g. Hirshleifer, Subrahmanyam, and Titman, JF 1994). It is the sum of three terms. The first, and empirically dominant, term is positive and increasing in the intertemporal decline in uninformed investors' uncertainty. The transmission rate has two contrasting effects on this term. The first and more intuitive effect is that informational gains realized earlier are better than those realized only in the future that are subject to additional randomness. However, a second effect of this potential gain is that informed investors trade more aggressively, which makes pre-announcement prices more informative. The resulting reduction in pre-announcement uncertainty reduces the intertemporal decline in uncertainty and lowers the equilibrium value of information. This second effect happens holding the early informed fraction fixed. Unlike in Grossman-Stiglitz where strategic substitutability in information choice results from endogenous price informativeness, here price informativeness affects the value of information through the aggressiveness of informed investors.

The second term of the value of information is positive as well and has to do with the intertemporal decline in uncertainty of the informed relative to this decline by the uninformed. The third term is negative and represents the extent of information spillover to uninformed investors who do not pay for the signal. The relative contribution of each of these terms to the total value depends on the parameters of the model, mainly the prior variances of the noisy supply and of the terminal payoff, and remains an empirical question.

Measuring the diffusion rate of information

In order to estimate the model, we need a setting where we can measure the diffusion rate of market moving information. I estimate the parameters of the model and the magnitudes of the three terms of the value of information in a panel of FDA drug approvals, using media coverage as a proxy for the approval-specific transmission rate of information.

Specifically, I calculate media exposure for each approval as the sum of all news articles that report the approval on the official approval day and the next, weighted by the price of their adjacent advertising space. The idea is fairly intuitive. The more interesting the news, the more prominently news outlets feature its coverage, on pages where the price of advertising is high due to its high exposure to readers. One benefit of this measure over an indicator media coverage variable is that it includes moderately interesting news as well, which turns out to be most valuable to acquire.

Drug approvals provide a particularly clean laboratory for examining stock market reaction to news that varies in its prominence for several reasons, but most importantly, the unique drug names and active ingredients allow for a free-text article search that is likely to produce only articles that discuss the approval story. This is not the case for other well-studied events, such as earnings announcements, which are harder to classify and often include additional profitability-relevant soft information.

1: Stock returns around drug approvals: media exposure subsamples
The sample includes 320 Original New Drug Approvals from 1990 to 2007. Media Exposure is the sum of all articles on the approval day and the following day. The high media exposure sub-sample are the top half of drug approvals with positive media exposure (56 observations). The low exposure contains the bottom 57 observations. No media exposure are the remaining 207 observations. Variation in media exposure is related to the path of price adjustment to news.

In Figure 1, I split the sample into high, low, and zero media exposure sub-samples. All three subsamples feature a price increase in the days before the approval. The pre-approval return seems higher for drugs that would later appear in the news. This suggests insider-trading activity is increasing in future media exposure. At approval time, drugs covered by the media exhibit a higher price increase than the rest. Post-approval, the stock price of drug sponsors that received no initial media exposure continue to appreciate while low media exposure firms maintain their valuation. Interestingly, high media exposure approvals exhibit a negative drift following the approval, which continues even at a longer horizon than the one I test below. These results suggest that consistent with the model, variation in media exposure is related to the path of price adjustment to news.

The most valuable information diffuses at a moderate speed

Empirically, the value of drug approval information turns out to be hump-shaped in its diffusion speed. The most valuable information diffuses at a moderate speed. The answer to the question of how much to pay to know today that Viagra as opposed to Allegra will be approved tomorrow turns out to depend on how fast exactly news of each approval diffuses, through its effect on the intertemporal decline in uncertainty.

As mentioned above, the value of information has three terms. It turns out that the value of information stems entirely from the first term, which captures the intertemporal decline in uninformed agents' uncertainty. Moreover, the transmission rate of information has a quantitatively important effect on the value of information.

The structural estimation exercise in the paper, one of its key contributions to the literature, embarks on the ambitious goal of fitting the model to the quantitative features of the data. The results show that uninteresting news that propagates slowly is not pursued by anyone before the official announcement, because the fixed cost of information is prohibitively high. Faster-diffusing information is purchased at a higher rate, while the fastest diffusing news is somewhat less valuable.

The structural estimation approach taken here of focusing on a particular anticipated news release, namely drug approvals, using media coverage as a proxy for the transmission rate of information is novel. It can hopefully be used by future research to further improve our understanding of the diffusion of information in financial markets.