Scattered Information’s Value to Investors

The more an investor can learn about a financial security’s value, the better his trades and the higher his profits can be.  But research is costly, and trading on one’s own information inevitably affects prices, which then reveal some of the results of that costly research to others for free.  This “information leakage” or “information free-riding” problem raises an important question: When is it worth the effort to learn about an asset’s value?  That question has taken on a new dimension as firms globalize and diversify.

The value of a financial security may comprise several distinct elements that depend on outcomes in different locations (e.g., for a multinational company), or different industries (e.g., for a conglomerate), or the supply and demand for different products and technologies, and so on. Accordingly, as various investors learn about these different pieces, information becomes scattered. Some investors may acquire information about a given location where a multinational firm does business because they are near that location. Or they may learn about an industry in which a conglomerate operates because they specialize in that industry. Or they may discover something about  a certain product a company makes because they use that product. This scattering of information is natural and pervasive in modern financial markets, but our understanding of its effects on asset prices and information acquisition has been very limited.  Is it still worth the effort to learn about only a small piece of an asset’s value?  How does the answer change as information is more widely scattered into even smaller pieces?

We answer these questions in our recent paper, available here, by generalizing the seminal financial market and information model of Grossman and Stiglitz (1980), in a novel way. Instead of looking at one element of uncertainty in the value of an asset, we consider an arbitrary number of n distinct elements. Our main – and surprising – finding is that, as information is scattered into smaller pieces, even if the cost of acquiring each piece does not decrease, the acquisition of information in the overall economy can actually increase—alleviating the information free-riding problem. This relationship holds despite the fact that the amount of information in each piece decreases. Moreover, this phenomenon is even more pronounced if information costs decrease in n, a natural scenario. Furthermore, since a higher degree of information scattering is expected for more diversified firms, our findings offer an information-driven answer to why diversified firms have higher returns than specialized firms – a major component of the long-standing “diversification discount” puzzle in corporate finance.

To better understand the surprising nature of our results, consider the following simplified example.  An asset’s value is composed of several units about which little is known. Trading in the asset will occur tomorrow, but today there is an opportunity for investors to learn more about it. Think of the asset as the total production of a farm, which consists of different types of crops in distinct growing locations. First, suppose that strategic investors for effort cost c can learn privately about the value of one-half of the farm’s units. For example, if the farm has four distinct growing locations (say A, B, C, and D), investors could fully inspect either the first two (A and B) or the second two (C and D) of those locations, selected at random, for cost c. About half of the investors who choose to become privately informed will learn fully about the first two locations while the other half will learn fully about the other two locations. Hence, information about the total asset value will be scattered into n=2 distinctly informative pieces ({A, B} or {C, D}) among those investors who choose to become informed. Naturally, these privately informed investors will have a trading advantage tomorrow relative to investors who did not make the effort to acquire private information.

Now, assume the same facts but suppose the information is scattered into, say, n=4 pieces. That is, investors can only fully inspect one of the four growing locations (only one of A, B, C, or D), selected at random, but for the same cost c as before. In this case, an investor can only learn privately about the value of a randomly selected one-fourth of the units. Would an investor who would have marginally chosen to become informed about one-half of the units in the previous case still choose to become informed about only one-fourth of the units in the present case, all else being equal? Surprisingly, the answer can be yes. In fact, such investors can even be willing to pay more to observe a smaller piece when information is more finely scattered. The essence of this example carries over to the more general framework in which we model information about an asset value as being scattered among investors.

What explains this result? One would expect that a single piece of information in an economy in which information is more scattered but still costs the same would be less useful, because it contains less information. However, traders’ decisions about becoming informed are not solely based on the information content of their piece, but depend more on how much of their information leaks to uninformed investors through market prices and how much additional profit traders can generate by acquiring information than by remaining uninformed. In the baseline case of Grossman and Stiglitz (1980) (i.e., n=1 in our model), the trade-off in becoming informed is between (1) costly reduction of uncertainty about this one piece and (2) costless partial inference from a noisy price, made possible by information leakage.

However, if information is scattered into several pieces—holding the acquisition cost per piece fixed—this baseline trade-off takes on a competing dynamic as n increases: both the informativeness of each piece and the information leakage to uninformed investors declines in n, at varying rates. Leakage of information declines more rapidly for low n than for high n. For example, going from one to two pieces doubles the inference problem for the uninformed while going from 100 to 101 pieces only worsens the inference problem by 1 percent. The benefit of less information leakage outweighs the reduction in the value of the information, resulting in a larger number of informed traders. Eventually, for large enough n, the trade-off reverses until the value of the information is so low it is no longer attractive and nobody becomes informed.

The insights arising from our analysis can also shed new light on the asset pricing consequences of corporate diversification.  Portfolio theory has long advocated the benefit to investors of diversification in the assets they hold for improving their return-to-risk trade-off. However, the net effect of diversification within firms themselves is evidently negative. Empirical studies have demonstrated a “diversification discount” puzzle in that diversified firms tend to trade at a discount (up to 15 percent) relative to the price of a portfolio of comparable single-segment firms [Lang and Stulz (1994), Berger and Ofek (1995)].  Most studies focus on how cash flow patterns might contribute to the discount, but in a contrasting branch of this literature, Lamont and Polk (2001) show that differences in expected returns between diversified and focused firms is a separate and important component of the discount.  Yet the mechanism underlying these differences in returns is not fully understood and, in particular, the role of asymmetric information has not been considered.

We provide an alternative mechanism underlying this return differential in terms of the type of information asymmetry that accompanies diversification—scattered information. The more diverse a corporation, the more varied the sources of uncertainty in its value and, hence, the more scattered the information among investors. Thus diversification tends to result in less-informed market participants, because scattered information reduces the information content of each piece of information as well as the market price. Lower information content means more conditional uncertainty, which induces a lower price in order to compensate risk-averse investors for bearing that uncertainty. Accordingly, diversified firms will tend to have higher expected returns, because scattered information reduces the price, all else being equal.

REFERENCES

Berger, Philip G., and Eli Ofek, “Diversification’s effect on firm value,” Journal of Financial Economics, 37 (1995), 39–65.

Grossman, S., and J. Stiglitz, “On the Impossibility of Informationally Efficient Markets,” American Economic Review, 70 (1980), 393–408.

Lamont, Owen A., and Christopher Polk, “The diversification discount:  cash flows versus returns,” Journal of Finance, 56 (2001), 1693–1722.

Lang, Larry H. P., and René M. Stulz, “Tobin’s q, corporate diversification, and firm performance,” Journal of Political Economy, 102 (1994), 1248–1280.

This post comes to us from Professor Christian Goulding of Michigan State University and Xingtan Zhang, a Ph.D, candidate at the University of Pennsylvania’s Wharton School. It is based on their recent paper, “The Value of Scattered Information,” available here.