## Explaining the Favorite-Longshot Bias in Prediction Markets

To illustrate the favorite-longshot bias, assume that, six months before an election, an investor believes the Democratic candidate has a 95% chance of winning. There are several reasons why this investor would not pay a full \$0.95 for a contract that pays off \$1 if the Democratic candidate wins. First, there is an opportunity cost of the bet being held for upwards of 6 months, because there is limited liquidity in many markets. The investor's money is tied up in this market, when it could be out doing something else: sitting in a bank, providing capital for a startup, being used to consume something, etc. The cost is literally the opportunity to be doing other things with the money while it held up in the market. Secondly, there are transaction costs of around \$0.015 per \$1 invested, thus the investor will actually bid up to whatever she determines is the optimal price minus the transaction cost that will be lost when the bet is processed. Finally, if there are two bets that are equal in expectation, the investor gains more utility from betting on a longshot. It is not clear to researchers whether investors are risk loving (i.e., they gain utility from doing risky things) or beset by misconceptions or Prospect Theory (i.e., they overvalue small probabilities and undervalue high probabilities), but it is accepted in the academic literature that they are not risk neutral.

All this brings me to the subject of Intrade's market for the Democratic Nominee for President of the United States in 2012. Currently, Mr. Obama is trading at a bid of \$0.910 per \$1 and an offer of \$0.937 per \$1 for a price of \$0.924 per \$1. If this seems too low to you, let's examine why you might be correct.

(I should note that the rules of the market specifically state that the contract is voided if any nominee in the market passes away, so that is not an issue.) Let us consider our three remaining causes of the favorite-longshot bias:

First, the market will not settle until September of 2012 (i.e.,15 to 16 months from now). This means that any money tied up in this market is lost for a consider amount of time. Thus, there is a large liquidity cost.

Second, Intrade has just switched to a flat fee model, while there are still transaction costs, they are much lower for Intrade than for any other market, so this is not a big factor in the low price.

Third, people get more utility out of holding (and dreaming about) the longshot Mrs. Clinton to be the nominee, with a bid at \$0.030 and an ask at \$0.040 per \$1, than the favorite Mr. Obama, so they are willing to bid more than is realistically likely in order to own the contract. Again, I am not sure if it is the utility of dreaming about/holding onto longshots, or is it because people are miscalculating long odds. Yet, if an investor deemed an investment in Obama and Clinton equal in their likely payout, they are going to gain more utility from the Clinton investment.

While the direct translation of these prices would say that Mr. Obama has 92.4% likelihood of the nomination and Mrs. Clinton a 3.5% likelihood of the nomination, my calculations would place it closer to 99% and 0.2%. Which one seems more realistic to you?

## Death of Osama on 2012 Election

A key question in political circles over the last few days has been the effect of the death of Osama Bin Laden by the U.S. armed forces on the outcomes of the 2012 election. Indubitably, the event is beneficial to the Democratic party and President Obama in particular. Polls conducted in the days following the event gave Mr. Obama at 9 percentage point increase in approval. There are a few points to consider on the prediction market's reaction to the event.

First, it definitely increased President Obama's probability of victory in 2012. On average his probability of victory has gone from around 60% to around 63%. Second, both Intrade and BetFair, the two leading markets, took a surprising amount of time "digesting" the information. Today, seven days after the event, they are still moving sharply. Prior to Mr. Obama's press conference announcing the death of Osama, the probability is relatively flat for weeks, but after the event there is a distinct trend in both markets that is still visible. Third, the two markets ultimately disagreed on the trajectory of the "digesting". Betfair is digesting the news by moving even further in favor of an Obama victory and Intrade, from an almost identical position, is moving back toward the pre-Osama death probability of victory. I am not going to discuss here the true underlying value of Osama's death, beyond the values provided by the markets, but I can state that in a few days arbitrage will bring these two markets together and we can have a clearer picture of what the markets feel is the underlying value of Osama's death on the 2012 Presidential election.

There appears to minimal effect on the House. The probability of the Democratic party regaining the House remained flat through the last two weeks.

## Volatility in Baseball Probabilities

Let me pose a question that address in further as this blog progresses: What is the appropriate level of volatility in an efficient forecast? Here is the forecast of the World Series winner for the three most probable teams: Phillies, Yankees, and Red Sox, based on BetFair prices. The probabilities cover the first week and a half of the season. Useful volatility represents new and meaningful information, un-useful volatility is just random movement. While the starting pitching has been a little less than amazing, the Phillies (7-2) are basically achieving at expectation and their probability remains essentially flat. Having to make the playoffs and then win three rounds, it is essentially impossible for them to move much beyond 25% this early in the season, even if they win every game. The Yankees (5-4), just dropped 2 of 3 from the Red Sox (2-7), but remain slightly up and the Red Sox slightly down from the start of the season. Does it seem reasonable that the Red Sex have a 13% of winning the World Series? Does going 0-6 in a 162 game season mean they are 25% less likely to win or does it provide minimal new information? The Yankees are clearly moving upward in because of the probability of making the playoffs the AL East winner increases their chances of doing well in the playoffs, but is that putting too much weight on the first step? These are questions I will address in later posts …

## NBA Playoffs

My local NBA team has left us, so I do not follow basketball as closely as I did in the past, but it is hard not be interested this year. The Heat are a huge news story and the playoffs will generate a buzz not felt in years. Below is the chart of how of the price of \$1 contract on the Heat winning the NBA championship and, for comparison, the Lakers are on the chart as well. The first thing to notice is how dramatically high the price was for the Heat in the early part of the season and how far it has fallen. The second thing to notice is that it has actually fallen well below the Lakers as the season nears its end.

Below is a second chart, that shows the next three most probable teams. First, look at the two West teams, notice how they mirror each other (the Mavs, not shown, have held steady at a very consistent \$0.04 to \$0.05). Second, compare the Celtics and the Heat early in the season and the Bulls and the Heat late in the season and you can see that the two teams mirrored each other for parts of the season, while the third team was relatively stable.Yet, despite the that mirroring, the sum of West teams (Lakers, Spurs, Mavs, and Thunder) has been moving slowly upward and the East teams (Heat, Bulls, Celtics, and Magic) has been moving slowly downward.

What this all means is that the market is now assuming that winning the championship, once your team gets there, is basically a toss-up, while midseason the East champion was much more likely to win the finals. Still, the main driver of the indivdual team prices are a reflection of their relative strength within the conference … right now the Lakers are looking so strong, not because they are necessarily any better than the Heat, but they have a much easier path the NBA finals.

## Mrs. Palin's Political Trouble from Saturday's Massacre

Immediately in the aftermath of Saturday's assassination attempt on Congresswoman Gifford, that resulted in the death of six people including a federal judge and a nine year old girl, the media began speculating on the political fallout to Sarah Palin's 2012 Presidential aspirations. In March she had put out an advertisement with a target on Congresswoman Gifford and then told asked that her followers "Don't Retreat, Instead – RELOAD!" Thus, after the massacre people began to discuss her contribution to both the specific target and the general heated atmosphere in politics; regardless of her complicity, and thus far there is no direct evidence the assassin followed Mrs. Palin, talk of it has political consequences. As several blogs have already noted, the market for her 2012 Republican nomination responded immediately … on Intrade. She lost over 1/3 of her probability in the immediate aftermath of the massacre. Yet, the movement a different market, Betfair, was much smaller, as it was already trading lower for Mrs. Palin; Betfair has consistently had less confidence in Mrs. Palin's viability as the Republican nominee. The chart is below:

## Obama and the 2012 Nomination &#8230;

When you think about 2012 Presidential nominations you are likely thinking about Palin, Romney, and the Republicans. But, as the year comes to close and the 111th Congress end on December 17th or so, I urge you keep an eye on the Democratic ticket. An editoral in today's Washington Post urges a Democrat to run to the left of the President to force him to hold firm on taxes, war, and social issues. First, it would be difficult for Biden to do that from within the adminstration and Clinton is not that person, thus for this to happen it would have to be an outside option. We will make sure to add that person, and you will see it coming with Obama falling. Second, notice the discrepencies between Betfair and Intrade  on Hillary and Biden.