### Understanding of Information Uncertainty and the Cost of Capital

Uncertainty and the Oil Fields

The reason for the review is that an Australian scholar has recently published a paper offering "A Bayesian Understanding of Information Uncertainty and the Cost of Capital." The gist of it is that traders face information uncertainty, that is, the risk of a misleading signal about the value of an asset.

"The Bayesian position," says D.J. Johnstone of the University of Sydney Business School, "is that even a highly informative signal ... can bring an increase in uncertainty, and hence an increase in the cost of capital." This is at least somewhat counter-intuitive. Surely the highly informative signals (also known as "greater transparency") will lessen uncertainty and risk, thus reducing the cost of capital.

Ah, Johnstone says, perhaps not. Consider a world in which there are two possible geological formations involved in the search for oil: A and B. There may be oil under either plot. Geologists tell us that plot A belongs to a type of geological formation with a 0.5 frequency of oil. B-type plots, on the other hand, have a 0.95 frequency of oil. It isn't always obvious which is which, and oil companies like to figure out which is which before making the final decisive test to determine whether there is oil there.

Suppose also that the prior probability of oil under a random site, before we even know if the site is A or B, is 0.635.

Now, on Day 1, an oil company owns a piece of land that has not yet been tested for oil, or even tested to determine whether it is A or B. The market will presumably assess the value of this land accordingly. Prospective buyers will consider it as having a 0.635 likelihood of bearing oil.

On Day 2, the land is tested and found to be of Type A.

Thereafter, the market will lower the value of that land, because its likelihood of bearing oil has fallen to 0.5. There is greater uncertainty post-test than there was pre-test.

A Bayesian Understanding of Information Uncertainty and the Cost of Capital

David James Johnstone

University of Sydney - Discipline of Finance

January 1, 2013

Abstract:

The term "information risk" or "information uncertainty" is defined as the risk of a misleading signal. This risk is understood Bayesianly in terms of the likelihood function f(S|φ). In Bayesian method, f(S|φ) captures the quality of signal S with respect to parameter φ. The Bayesian position is that even a highly informative signal (one with a very peaked likelihood function) can bring an increase in uncertainty, and hence an increase in the cost of capital. It can also occur that the cost of capital implied by a capital asset pricing model (CAPM) increases even when better information brings greater certainty. The role of financial reporting should be understood not in terms of its effect on the cost of capital per se, but as aiding investors to assess the probability distributions of future cash flows more accurately, thereby leading on average to higher expected utility portfolios. This is a technical version of the traditional view in accounting theory that financial disclosure should provide generally relevant information for asset valuation and other investment decisions.