Economics, Risk and Uncertainty

Confusion about the "Law of Large Numbers"

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An important concept in the theory of risk that seems to confuse a lot of people (journalists in particular) is the law of large numbers. The law of large numbers is a statistical law which implies that the average value of a randomly selected sample is likely to be close to the average value of the population from which the sample is drawn. The law of large numbers makes important risk pooling mechanisms such as insurance economically feasible. For more information on the law of large numbers, see the Wikipedia entry on this topic, entitled “Law of large numbers”.

Lately in the media, I have heard numerous (incorrect) references to examples of the “law of large numbers” at work. For example, this morning on Bloomberg Radio, an analyst was droning on about how the “law of large numbers” works to the “disadvantage” of large companies like Walmart. This analyst correctly observed that as large firms such as Walmart grow even larger, their opportunities for further growth in the future diminishes. This is an example of the “law of diminishing returns”, not the law of large numbers.

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Economics, Risk and Uncertainty

Confusion about the "Law of Large Numbers"

Leave a comment

An important concept in the theory of risk that seems to confuse a lot of people (journalists in particular) is the law of large numbers. The law of large numbers is a statistical law which implies that the average value of a randomly selected sample is likely to be close to the average value of the population from which the sample is drawn. The law of large numbers makes important risk pooling mechanisms such as insurance economically feasible. For more information on the law of large numbers, see the Wikipedia entry on this topic, entitled “Law of large numbers”.

Lately in the media, I have heard numerous (incorrect) references to examples of the “law of large numbers” at work. For example, this morning on Bloomberg Radio, an analyst was droning on about how the “law of large numbers” works to the “disadvantage” of large companies like Walmart. This analyst correctly observed that as large firms such as Walmart grow even larger, their opportunities for further growth in the future diminishes. This is an example of the “law of diminishing returns”, not the law of large numbers.

Math and Statistics, Miscellaneous

Fooled by Randomness quote

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I really like the following quote from Fooled by Randomness (pp. 55-56): “Things are always obvious after the fact… It has to do with the way that our mind handles historical information. When you look at the past, the past will always be deterministic, since only one single observation took place.”

This describes well a common error that is made all too often, by the news media in particular. News reporting often involves studying risky phenomena after the fact; i.e., after a disaster has already occurred. Journalists are highly susceptible to this particular aspect of being fooled by randomness. Often their analysis only makes sense if one had the luxury of perfect foresight.

Economics, Risk and Uncertainty

Riskprof on adverse selection

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In my opinion, Marty Grace at Georgia State has the most useful weblog on the internet for people who are interested in risk management/insurance-related research and public policy issues, called Riskprof.  For example, check out today’s entry about empirical evidence (or the lack thereof) concerning adverse selection in insurance markets, complete with a holiday theme!

Prediction Markets

SC.CONFIRM.ALITO

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Since President Bush recently nominated Judge Samuel A. Alito to replace (retiring) Sandra Day O’Connor on the Supreme Court, this must mean that tradesports.com has a new senate confirmation contract trading, aka SC.CONFIRM.ALITO.  On its first day of trading, the price for this contract ranged from $75 to $84.90.  Lately the trading range has narrowed somewhat at a marginally higher price level (now $88.50), implying nearly a 90% likelihood of Senate confirmation.  Here’s the graph over the lifetime of the contract:

Catastrophes, Economics, Finance, Risk and Uncertainty

Finance to the Rescue

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For what it’s worth, I am one of four people (along with Jeff Holland, Liongate Capital Management founder, John W. Howton Rockbrook Capital founder, and John C. Bogle, founder and former CEO of the Vanguard) interviewed in “Finance to the Rescue”, an article that appears in the Fall 2005 issue of Baylor Business Review.  My interview is on the topic of cat bonds, which is a topic that I have previously blogged about.

Catastrophes, Public Policy

Bush’s avian flu initiative (AKA the International Partnership on Avian and Pandemic Influenza)

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The White House posted the transcript of President Bush’s speech today to the United Nations.  Of particular significance is the President’s announcement concerning the International Partnership on Avian and Pandemic Influenza (see http://www.whitehouse.gov/news/releases/2005/09/20050914.html for the complete transcript):

“As we strengthen our commitments to fighting malaria and AIDS, we must also remain on the offensive against new threats to public health such as the Avian Influenza. If left unchallenged, this virus could become the first pandemic of the 21st century. We must not allow that to happen. Today I am announcing a new International Partnership on Avian and Pandemic Influenza. The Partnership requires countries that face an outbreak to immediately share information and provide samples to the World Health Organization. By requiring transparency, we can respond more rapidly to dangerous outbreaks and stop them on time. Many nations have already joined this partnership; we invite all nations to participate. It’s essential we work together, and as we do so, we will fulfill a moral duty to protect our citizens, and heal the sick, and comfort the afflicted.”

Catastrophes, Economics, Public Policy, Risk and Uncertainty

Hurricane Katrina and the Great New Orleans Flood

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Here is a collection of readings that I have been wading through (pardon the pun) in order to try to gain some perspectives on the tragedy that we see unfolding in the Gulf Coast generally and in New Orleans in particular:

1. Katrina, Cost-Benefit Analysis, and Terrorism, by Richard Posner, Senior Lecturer in Law, University of Chicago.
2. Major Disasters and the Good Samaritan Problem, by Gary Becker, 1992 Nobel Laureate in Economics, Professor of Economics at the University of Chicago and Senior Fellow at the Hoover Institution, Stanford University.
3. Rebuilding New Orleans — and America, by Thomas Sowell, Rose and Milton Friedman Senior Fellow, The Hoover Institution, Stanford University.
4. A Fuller Picture: Beginning to understand what we are seeing in New Orleans, by Michael Novak, George Frederick Jewett Scholar in Religion, Philosophy, and Public Policy at the American Enterprise Institute.

In retrospect, it would appear that the man-made aspects of the disaster are by far and away much worse than the storm itself.  The initial damage report from risk modeling firm Risk Management Solutions (RMS) was $20–$35 billion.  Later that same day (September 2), the levees failed in New Orleans and RMS immediately revised its estimate to $100 billion.  On September 7, the Wall Street Journal published a page 1 article entitled “First Estimates on Katrina Costs For Washington Hit $200 Billion”.  The biggest long term problem (at least from a loss prevention standpoint) has been a chronic underinvestment in levee protection for most of the history of the city of New Orleans.  Interestingly (as noted in John Berlau’s piece entitled Greens vs. Levees), the Army Corps of Engineers was sued sometime back in the mid-90’s in order to prevent them from raising and fortifying Mississippi River levees.  The Corps’ rationale for this project at the time was that it was needed “…because a failure could wreak catastrophic consequences on Louisiana and Mississippi which the states would be decades in overcoming, if they overcame them at all.”

Late today (September 8), Congress approved $51.8 billion in emergency spending to pay for Hurricane Katrina recovery efforts, and thankfully this will be directed through channels other than Louisiana public officials (see Congressman Tom Tancredo (R-CO)’s letter to Speaker Dennis Hastert (R-IL) on the problem of public corruption in Louisiana).

Prediction Markets

2008 Presidential Race – current prediction markets forecast

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The idea of relying upon futures markets prices to forecast future events has an interesting history. Nearly 20 years ago, UCLA finance professor Richard Roll published a paper in the American Economic Review entitled “Orange Juice and Weather” which showed, among other things, that the futures market in orange juice concentrate is a better predictor of Florida weather than the National Weather Service. Since the only way one can earn excess profits in a speculative market is to gain an informational advantage over the competition, traders are strongly motivated to try to do just that. If markets are informationally efficient, it follows that market prices represent unbiased forecasts concerning future events. Technically, this means that on average, the market’s estimate of the average value of the event in question is likely to be quite accurate.

Consequently, I believe that political “futures” markets provide reliable indications of the odds that a political party or candidate will win an election.  Although the 2008 presidential election is still more than 3 years away, tradesports.com maintains an actively traded market for futures contracts which pay off $100 in the event that a specific political event occurs and $0 otherwise.  Essentially, prices represent “risk neutral” event probabilities. With this in mind, it is interesting to observe what the political futures markets are telling us at this time about the 2008 election.  Currently, three contracts are traded that involve bets on which party is likely to win the presidency in 2008; specifically, Democrats, Republicans, or none of the above:

Contract
PRESIDENT.DEM2008 (Democratic Party Candidate to Win 2008 Presidential Election) – 48.30% chance
PRESIDENT.REP2008 (Republican Party Candidate to Win 2008 Presidential Election) – 50.50% chance
PRESIDENT.FIELD2008 (The Field (Any Other candidate) to Win 2008 Presidential Election) – 1.20% chance

tradesports.com also makes a market in futures contracts on specific candidates winning either the Democratic or Republican nomination for president.  Currently, Senator Hillary Clinton (D., NY) leads the Democrats (43.7% chance), whereas Senator George Allen (R., Virginia) leads the Republicans (20%).  At this time, it would appear that the Republican race for the nomination is more competitive than the Democratic race; Governor Mark Warner (D., Virginia) comes in second after Hillary with a 10.9% chance, whereas Senator John McCain (R., Arizona) is close behind Senator Allen at 17.2%.  The product of the nomination probability times the party probability listed above represents the market’s best guess at who the next president will likely be.  Currently, the top 5 candidates are as follows:

Hillary Clinton – 21.11% chance
George Allen – 10.10% chance
John McCain – 8.69% chance
Rudy Giuliani – 6.57% chance
Mark Warner – 5.26% chance

Interestingly, the market believes that Governor Arnold Schwarzenegger (R., California) has a better shot of becoming president than the following set of potential candidates: Governor Brian Schweitzer (D., Montana), Retired General Colin Powell (R.), Senator Pat Leahy (D., Vermont), Senator Chris Dodd (D., Connecticut), Representative Harold Ford (D., Tennessee), Senator Joseph Lieberman (D., Connecticut), Senator Elizabeth Dole (R., North Carolina), and Retired General Tommy Franks (R.).  This would quite a feat, since in order for the Arnold to become president, it would require an amendment to the U.S. Constitution (since Arnold was born in Austria).  In other words – not going to happen – not for Arnold, and not for the rest of these “candidates”.

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