

Illinois AgriNews  May 2008
So What do Prices Tell us About, well, … other Prices?
Bruce J. Sherrick and Darrel L. Good
Department of Agricultural and Consumer Economics
University of Illinois, UrbanaChampaign
“It's tough to make predictions, especially about the future”. – Yogi Berra
Most of us are only 1 or 2 clicks away from near realtime market quotes on a dizzying array of financial securities, interest rate instruments, commodity futures, options and indexes based on other securities or baskets of positions. And, most accept the notion that these current market prices reflect the “best” possible information about the future.
It is useful to think about what other information is contained in “current” market prices. We cannot take advantage of what we learned that prices just did, but prices also contain information about the market's collective beliefs about future prices. Futures and options markets in particular are designed to elicit estimates of future price levels and the probabilities associated with different prices. Take, for example, the Dec08 corn futures contract and options traded at various strikes against that contract. The Dec contract is of particular interest as many marketing and production decisions are made with regard to a “harvest time” price estimate, and many crop insurance products have final indemnities tied to its eventual outcome. Futures markets provide a direct and easily accessible forecast of the average future price – a best guess of the price at the future expiration date. As uncertainty is resolved, the price level may change, and the resulting accuracy of the futures price as an estimate improves. Options markets provide fairly distinct information about the probabilities of future price movements of various magnitudes, and a means to recover estimates of the probabilities of other prices.
Options trade across a neatly aligned set of strikes, and in forms that value opposite directional movements differently, allowing the recovery of a complete probabilistic representation of possible prices. Consider the 5/16/08 prices on puts and calls on Dec08 corn futures. Using the component of the iFarm crop insurance evaluator that recovers futures price distributions (see payment simulator at http://www.farmdoc.uiuc.edu/cropins/index.asp ), the probabilities associated with other price levels can be found, as well as prices at predetermined probability levels (Table 1). According to the options' prices, the market collectively views there to be a 10% chance that Dec08 Futures will expire below $4.11 and a 10% chance that they will be above $8.53. Interestingly, the market views the price distribution to be fairly skewed so that although the options and futures markets both assigned a mean value to approximately $6.1675 there is also viewed to be 50% likelihood that prices will fall below $5.92 (or in the right hand panel, there is a 51.9% chance of prices falling below $6.00). Note that the RMA indemnity price of $5.40 is viewed by the market as having only a 37.4% chance of being at or above the expiration price; equivalently that there is about 63% chance of harvest price being above $5.40. The market gives about a 28% chance of price being above $7.00. Other priceprobability pairs can be read from the table.
So, prices actually can say a lot about, well, other prices and can be used to establish relevant limits of exposure to prices at levels other than the mean. And, fortunately, the options market provides that type of information fairly conveniently. Sorry Yogi.
