OR/MS Today - June 2004

Prediction Models

Prices, Probabilities and Predictions

With prediction markets, participants put their money where their mouths are regarding worldwide events ranging from government elections to the outbreak of war. The question is, are these markets more accurate than polls and politicians?

By Sam L. Savage

The second half of the 20th century was devoted to debating the relative merits of planned economies versus free markets. In case you missed it, the winner was announced with the collapse of the former Soviet Union. The power of free markets, in which prices guide the allocation of goods and services, is now almost universally accepted as the best way to generate wealth. Prices are in effect the neurotransmitters of society, reflecting wants, needs, fears, estimates of future supply, outcomes of horse races and so on. Prices are also intertwined with the concept of probabilities, which in turn drive predictions.

My father, Leonard Jimmie Savage, was an early advocate of subjective probability. He encouraged me from a young age to think of the probability of an event as the amount I would pay for a gamble that would pay $100 if the event occurred.

In the information age the relationship between prices and probabilities has grown even more intimate. An elegant essay titled "Nuclear Financial Economics" by Nobel Laureate William Sharpe [1] shows that in some circumstances, the concepts of price and probability are interchangeable. It's on the Web; don't miss it. Two types of financial transactions are particularly tied to probabilities and predictions: futures and options.


Imagine the dismay of a farmer who has slaved away in his corn field for months only to find that when the September harvest arrives, a glut in the market has driven prices to a new low. If he could find someone willing in June to buy 100 bushels of corn for September delivery at a discounted but pre-specified price, the farmer would be protected from corn price risk. But who would buy such a contract? Due to the discount, this "September corn future" is a good deal when averaged over the long run, and if one diversified by also buying wheat, soybean and oat futures, then an unexpected glut in any one of these markets would not be enough to wipe you out. If there are a large number of buyers and sellers in such a market, then the prices of the futures carry a lot of information. For example, a classic 1984 paper by finance professor Richard Roll shows that the futures market in orange juice concentrate is a better predictor of Florida weather than the National Weather Service [2].


The simplest stock option provides you with the right but not the obligation to purchase a certain stock on a certain date at a certain price. Most readers of OR/MS Today are familiar with stock options and the famous Black/Scholes equation for their evaluation. Accordingly, I will provide a "mindle" for grasping the concept of options from a different perspective, that of a glider pilot. [The mindle does for the mind what the handle does for the hand; helps it grasp things.]

In calm air, a glider will descend at a rate of at least 100 feet per minute, regardless of the action of the pilot. In turbulent (volatile) air, the glider will also descend at 100 feet per minute on average if the pilot flies in a straight line. However, if the pilot exercises the option to fly in a circle if he is in an updraft, and exercises the option to fly somewhere else if he is in a downdraft, then the glider can climb at hundreds or even thousands of feet per minute for extended periods. Obviously these options are worthless without metrological volatility, as are stock options without price volatility. Indeed, according to the principle of "implied volatility," the price of an option in the Wall Street Journal is a surrogate for the volatility of the underlying stock of the corporation.

Prediction Markets

Corn, wheat and Colin Powell. In 1995, while idly searching the Web for stories on Colin Powell, who was considering a run for the Republican presidential nomination, I stumbled upon a link identified as the Colin Powell Nomination Market. Intrigued, I followed it to an electronic futures market run by the University of Iowa [3].

They grow a lot of corn and wheat in Iowa, so I wasn't surprised to find a futures market there. But Colin Powell? It turned out this was a market where you could trade Powell "Yes" futures, which would pay $1 if Powell accepted the Republican nomination (and zero otherwise), and "No" futures, which would pay $1 if Powell did not accept the Republican nomination (and zero otherwise). How would you start such a market, you might ask. The ingenious Iowa exchange sold these futures in bundles of one "Yes" and one "No." This was worth exactly $1 because exactly one of these two bets would pay off. But once people owned the futures, they were free to trade them at any price they pleased, and the prices were recorded daily as shown in Figure 1.

Cover of the June 2004 issue of Operations Research / Management Science Today

Figure 1: Colin Powell nomination market.

Market reaction to such events as the beginning of Powell's book tour and the O.J. Simpson verdict are clearly visible. Also, notice that the sum of the two prices remains very close to $1. If the sum was ever less than $1, then you would be guaranteed to make money by buying both. If the sum of the prices was ever greater than $1, you would be guaranteed to make money by selling both. The fact that the graph is not completely symmetric indicates that the market is not perfectly efficient, but it seems pretty close. The Iowa market, which is underwritten by the University of Iowa, is still going strong, along with a growing number of others I will describe below.

Societal instability versus corporate volatility. In 1999, I was fortunate to attend a workshop on predicting societal instability organized by U.S. Pacific Command and hosted by the Center for Army Analysis at Fort Belvoir, Va. A number of analytical techniques for predicting societal instability were presented at this fascinating conference. One statistical model, for example, indicated that when the percentage of young unmarried men in a population exceeds a critical threshold, then war is likely. Keep this in mind as you ponder the trend in a certain large country to artificially limit its number of female offspring. I also learned that there is a small country that has been known to sell its women to the large country for use as wives. This forces one to contemplate the uncomfortable trade-off between slave trafficking and war prevention.

On my way home from this eye-opening event, I realized that if you replace the words "societal" with "corporate" and "instability" with "volatility," you get "corporate volatility," which, as mentioned earlier, can in effect be read out of the Wall Street Journal as the price of an option. Why wouldn't prices be able to measure societal instability as well? For example, a sudden drop in wife prices in the importing country described above might imply that things were getting desperate in the exporting country, forcing them to flood the market.

In February 2000, a denial-of-service attack on the online trading firm e-trade caused its stock price to plummet. [A denial-of-service attack is an attack in which hackers arrange for thousands of hits to flood a Web site, rendering it unavailable to the intended visitors.] I wrote to a colleague: "Has it occurred to you that if the hackers had bought puts the day before, they are now millionaires?" [A "put" option pays off if the underlying stock drops in price, while a "call" pays off if it rises.]

I went on to conjecture that, "If you were really lucky, you might discover a twitch in the options market that would actually tip you off to an impending attack."

Put options on 9/11? Fast forward to Sept. 11, 2001. Unusually high numbers of put options were taken out on American and United Airlines just before the attack, as reported by Dave Carpenter of the Associated Press and others [4, 5 and 6]. To check this out, I created the graph shown in Figure 2 from data available at www.optionsclearing.com [7]. It displays the ratio of put and call trading volumes just before 9/11 for the following stocks: United Airlines (UAL), Southwest Airlines (LUV), Delta Airlines (DAL), American Airlines (AMR) and General Motors (GM). If there is roughly equal trading volume in puts as in calls, one would expect the ratio to be about 1. Thus the value for United Airlines on Thursday, Sept. 6 is 25 times above normal. Notice that there is no trading on weekends, so the spike in AMR puts occurs on the Monday before the Tuesday attack.

Cover of the June 2004 issue of Operations Research / Management Science Today
Figure 2: Ratio of put and call trading volumes just before 9/11 for the following stocks: United Airlines (UAL), Southwest Airlines (LUV), Delta Airlines (DAL), American Airlines (AMR) and General Motors (GM).

To add to the suspicion, the story persists that a large number of these options were never cashed in.

Could proper interpretation of this data have provided advance warning of the attack? CAUTION: Do not jump to conclusions! There are plenty of explanations that do not involve terrorism. For example, the airlines were in trouble anyway, so plenty of people were betting against them in the fall of 2001. And it is not far-fetched to think that some people would not have cashed in their options, knowing that they would be profiting from a national tragedy. The most authoritative work I am aware of on this subject is "Unusual Options Market Activity with an Application to the Terrorist Attacks of Sept. 11, 2001" by Allen M. Poteshman of the University of Illinois [8], in which the author states:

"When the option market activity in the days leading up to the terrorist attacks is compared to the benchmark distributions, the volume ratios and call volume indicators are seen to be at typical levels. The indicator of long put volume, however, appears to be unusually high, which is consistent with informed investors having traded in the option market in advance of the attacks."

To see the full range of explanations of this trading activity, ranging from lucid to lunatic, I suggest Googling "put options airlines terror."

DARPA gets into and out of the picture. Last July the Department of Defense announced its Policy Analysis Market (PAM) to harness the power of free markets to "focus on the economic, civil and military futures of Egypt, Jordan, Iran, Iraq, Israel, Saudi Arabia, Syria and Turkey, and the impact of U.S. involvement with each." PAM was just preparing to issue prediction instruments whose prices would hopefully shed light on these important foreign policy issues when the entire program was summarily scrapped due to public outrage, forcing the resignation of Defense Advanced Research Projects Agency (DARPA) head John Poindexter [9].

Cover of the June 2004 issue of Operations Research / Management Science Today

The Policy Analysis Market (PAM) had a short, controversial life before the DoD killed it.

Personally, I thought PAM was a creative idea. My main objections were, first, that such an exchange run by the U.S. Department of Defense could hardly be considered unbiased, and second, why waste taxpayer's money on something that already existed [10]? At the time there were already several "prediction markets" up and running on the Web, with people putting money where their mouths were on issues as wide-ranging as the outcome of the Kobe Bryant trial to the capture of Osama bin Laden [11, 12 and 13]. Do a Google search on "prediction markets" to learn more.

In an ironic twist, within days of the public announcement of PAM in July 2003, Tradesports.com, a Dublin-based exchange, had floated a wager that would pay $100 if Poindexter still had his job at DARPA as of Aug. 31. [Note, Tradesport contracts are actually for $10, but their graphs are all scaled for $100 or ten contracts. Therefore, to be consistent with their graphs, I have chosen to use $100 for the cost of a single contract within the text.] In the graph of the Poindexter price shown in Figure 3, 30/07 is the European convention for July 30.

June 2004 issue of Operations Research / Management Science Today

Figure 3: Shall he stay or shall he go - The Poindexter price point.

Another one of my favorites on Tradesports was a contract that paid $100 if weapons of mass destruction were found in Iraq by various dates (see Figure 4). At the time of the invasion it was selling for around $70.

June 2004 issue of Operations Research / Management Science Today

Figure 4: Contract price for finding WMD in Iraq.
Graph courtesy of Wolfers, Justin and Eric Zitzewitz (2004), "Prediction Markets," Journal of Economic Perspectives, Spring 2004.

Eventually one of the WMD futures dropped to zero well before its expiration date, and all trading was subsequently halted in this market. Listening to continued predictions on the evening news that the United States would find WMD in Iraq, while my laptop computer told me otherwise, left me feeling liberated from the traditional media.

From November 2002 to March 2003, William Saletan started a daily column in Slate Magazine called the "Saddameter," in which he subjectively estimated the odds of war [14].

June 2004 issue of Operations Research / Management Science Today

The "Saddameter" in Slate Magazine subjectively estimated
the odds of war with Iraq.

Justin Wolfers and Eric Zitzewitz of Stanford University, two experts in prediction markets, investigated the Tradesports wager on when Saddam Hussein would be captured. Before the invasion of Iraq, the higher the price, the greater the likelihood of a U.S. invasion. In "What Do Financial Markets Think of War in Iraq?"[15], the authors correlate the Tradesports Saddam prices to the S&P 500 to estimate the penalty that the market was placing on the occurrence of war.

What Works

I recommend two papers for gaining a deeper understanding of prediction markets and when they work. Wolfers and Zitzewitz in the Journal of Economic Perspectives [16] and Spann and Skiera in OR/MS Today [17] provide good introductions to this emerging field. Both papers describe criteria for successful wagers, which I will summarize very loosely here.

1) The terms of the wager must be stated with great specificity so there will be no ambiguity. The Foresight Exchange Bush04 wager [18] on the upcoming election is perhaps a bit over the top in this regard:

"This claim will be TRUE even if elections are postponed or G.W. Bush remains in power by staging a coup. If there are events which make it confusing who the U.S. president is, as of 2005-02-01, this claim is true if G.W. Bush is leading a sovereign government in at least part of the territory of the Unites States of America (as of 2001-01-01) that has recognition of at least one of the U.N. Security Council permanent members (Britain, France, China and Russia) other than the United States."

2) The participants must have some knowledge of the field. For example, Joe Grundfest of the Stanford Law School has pointed out the futility of a market to predict the veracity of "String Theory" [19]. [String Theory is a yet unproven theory that attempts to unify particle physics (the physics of the very small) with relativity (the physics of the very large.)]

3) The bet must pay off well enough to make it worth investing one's time and revealing one's true opinion. This presumes that the main players in the market are more motivated by money than by martyrdom. As a counter example, Grundfest describes how such markets might be manipulated. "Suppose you were a terrorist. If you wanted to blow up a bridge, you would try to get everybody to look every place else by buying the futures that would say, 'No, what we're going to do is blow up a power plant.' "

Not a Spectator Sport

The easiest way to participate in prediction markets is just to put your money where your mouth is, but for those with some knowledge of economics or operations research, it needn't stop there.

Iraq futures. A few months ago, I was discussing the situation in Iraq with Michael Schrage of MIT. We both agreed that there was a lot of uncertainty, and that current events were open to contradictory interpretations by politicians and the news media. I suggested that we cook up a market basket of commodities that reflected the well-being of the Iraqis and get it floated on a prediction market. Michael promptly dubbed this the "Baghdad Basket."

We took the idea to Justin Wolfers, who agreed that this was a prime candidate for a prediction market. However, it quickly became apparent that there was still too much turmoil in Iraq to accurately track commodity prices. Justin discussed the idea of an Iraq Future with Tradesports, who ultimately came up with a security that they believed would trade actively.

The IRAQ.TRANSFER.30JUN, launched on April 6, is a wager that pays $100 "if the current Coalition of Provisional Authority transfers power in Iraq by June 30 at 11:59 p.m. ET." Otherwise it expires worthless. The price history as of May 5 appears in Figure 5. As of that date, total volume was close to 12,000 trades.

June 2004 issue of Operations Research / Management Science Today

Figure 5: Price history of Iraq futures.

Business Forecasting

Spann and Skiera [17] point out that prediction markets are now being used for forecasts within business organizations where the traders are wagering on such things as "sales, market share, profit, company stock price or time-to-market of new product introductions."

NewsFutures [12] offers a software platform allowing an organization to run such markets internally. Imagine the creative opportunities within your organization to try this sort of thing. For example, MIT's Technology Review runs an "Innovation Futures" market powered by NewsFutures, which assesses the fortunes of various technologies from the relative sizes of Windows and Linux server markets to the outcome of technology-related law suits.

If my father were still living, he would be fascinated by the attempt to harness subjective probability as an economic force. But will prediction markets work? I suggest that we float a wager that will pay $100 if the consensus in five years is that they do, and pays zero otherwise.

© 2004, Sam L. Savage


This article has benefited from interactions with Breck Jeffery of U.S. Pacific Command, Meiring de Villiers of the University of New South Wales, Michael Schrage of MIT, Stefan Scholtes of Cambridge University, and Elisabeth Pate Cornell, Deborah Gordon, Ben van Roy and Justin Wolfers of Stanford University.


  1. Sharpe, William F., "Nuclear Financial Economics," http://gobi.stanford.edu/researchpapers/detail1.asp?Document_ID=734
  2. Roll, Richard, 1984, "Orange Juice and Weather," American Economic Review, Vol. 74, No. 5, pp. 861-80, American Economic Association.
  3. 3. Iowa Electronic Market, http://www.biz.uiowa.edu/iem/
  4. Carpenter, Dave, "Option Exchange Probing Reports of Unusual Trading Before Attacks," Associated Press, Sept. 18, 2001. See http://cjonline.com/stories/091901/ter_tradingacts.shtml
  5. Schoolman, Judith, "Probe of Wild Market Swings in Terror-Tied Stocks," [New York] Daily News, Sept. 20, 2001, p. 6.
  6. Toedtman, James and Charles Zehren, "Profiting from Terror?" Newsday, Sept. 19, 2001, p. W39.
  7. 7. http://www.optionsclearing.com/
  8. Poteshman, Allen M., "Unusual Options Market Activity with an Application to the Terrorist Attacks of Sept. 11, 2001," University of Illinois at Urbana-Champaign, Department of Finance, 2002, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=370741
  9. Wolfers, Justin and Zitzewitz, Eric, "The Furor Over Terrorism Futures," Washington Post, July 31, 2003, p. A19.
  10. Schrage, Michael and Savage, Sam, "If This Is Harebrained, Bet on the Hare," Washington Post, Aug. 3, 2003, Page B04, www.washingtonpost.com/wp-dyn/articles/A14094-2003Aug2.html. Sidebar: www.washingtonpost.com/wp-dyn/articles/A14095-2003Aug2.html
  11. http://www.tradesports.com/
  12. http://us.newsfutures.com
  13. http://www.ideosphere.com/fx/
  14. Saletan, William, "Saddameter," http://slate.msn.com/id/2074152
  15. Leigh, Andrew, Wolfers, Justin and Zitzewitz, Eric, "What Do Financial Markets Think of War in Iraq?" NBER Working Paper 9587, March 2003. www.nber.org/papers/w9587
  16. Wolfers, Justin and Zitzewitz, Eric, "Prediction Markets," Journal of Economic Perspectives, Vol. 18, No. 2, Spring 2004.
  17. Spann, Martin and Skiera, Bernd, "Taking Stock of Virtual Markets," OR/MS Today, October 2003, Vol. 30, No. 5, www.lionhrtpub.com/orms/orms-10-03/frfutures.html
  18. Foresight Exchange, Bush04, www.ideosphere.com/fx-bin/Claim?claim=Bush04
  19. Grundfest, Joseph, "Business Law," Stanford Magazine, November 2003, www.stanfordalumni.org/news/magazine/2003/novdec/farm/news/bizlaw.html

Sam Savage is a consulting professor of Management Science & Engineering at Stanford University.

  • Table of Contents

  • OR/MS Today Home Page

    OR/MS Today copyright 2004 by the Institute for Operations Research and the Management Sciences. All rights reserved.

    Lionheart Publishing, Inc.
    506 Roswell Rd., Suite 220, Marietta, GA 30060 USA
    Phone: 770-431-0867 | Fax: 770-432-6969
    E-mail: lpi@lionhrtpub.com
    URL: http://www.lionhrtpub.com

    Web Site Copyright 2004 by Lionheart Publishing, Inc. All rights reserved.