During 2004/05/06, new ideas about wikinomics, web 2.0, and user generated content were being tested online. Websites like Wikipedia and prediction markets like InTrade were emerging. When I was working the night shift at Scotia, I’d spend time each night on InTrade. InTrade was an online prediction market where participants could trade the binary odds of various events. There were a wide variety of events available to trade including weather, politics, entertainment, and financial events.
What made InTrade innovative was it allowed users to trade the binary option of an event occurring with other participants instead of placing their bets with the house. InTrade made money by charging transaction fees. There was no counterparty credit risk as the trades were fully collateralized as long as InTrade itself remained solvent. The underlying odds were completely market based. The probably of the event was implied in the price of the binary option, easily expressed from 0 to 100. At the time, these markets intrigued me as I was studying the economics of option markets.
I started to focus on the financial binaries on InTrade, and specifically on the contracts based on the economic reports that are released each day such as “what will be the GDP growth for the last quarter?” and “what will the reported unemployment rate be for last month?”. These economic indicators are released by various agencies to help economists and investors to make financial decisions. Bloomberg and Reuters publish surveys of economist’s estimates of what the indicators may be prior to the numbers being released. I used the economist surveys to handicap the odds implied on the InTrade marketplace to determine whether there was a trading opportunity. I discovered the odds for the least likely probabilities on InTrade were often overestimated. This meant that the price for the least likely probabilities on InTrade were higher than their theoretical price based on economist estimates published by Reuters and Bloomberg.
Over the course of two years, I placed 362 wagers by selling the least likely probabilities. Since these were binary options, my risk was finite. It turned out that I won every wager over 362 wagers. Unfortunately for me, liquidity eventually dried up as market makers stopped posting odds and governments started to crack down on prediction markets. InTrade was eventually shut out of the US by securities regulations. Even though I made many profitable wagers, the size of these wagers was very small. I’d usually only make 25 cents to $1.50 each day. This was partly because the liquidity of InTrade was pretty shallow, but also because I was selling low probability events.
Through this process, I developed a number of theories about probability pricing. These theories are related to Option Pricing, Long Bias, Non-intuitive Probabilities, Dependant Events, and Liquidity.
Option pricing models are valuable tools. The Black-Scholes option model calculates a theoretical price for an option using a few key pieces of data such as a discount rate, volatility, and time. A future event needs to account for the time value of money. So if an event occurs in 1 week or 1 year, the value of the option needs to reflect the fact that purchasers can put their capital to work in other ways between now and the expiration of the option. An option’s time value also decays at a rate that grows faster as time progresses. So events occurring on a daily basis (such as binary options on economic events) will have very large thetas (the rate of time value decay). If an event is very volatile, one day it’s up 100%, and then down 100% the next day, this potential should be reflected in an option’s price. I found that none of these factors were implied in the price of the binary options traded on InTrade.
In trying to understand why InTrade options were not priced like I expected, I came to discover that the odds on InTrade carried a long bias. I believe the long bias is caused by the fact that many participants on InTrade were gamblers, just people having a good time, trying to hit a “big one”. After further research, I discovered that a long bias exists in all sorts of other situations. When presented with an event that will occur one every hundred times, most people would rather risk $1 to win $100 than to risk $100 to win $1, even though both of these prices are equal in the long run. A long bias is a common psychological trait. This bias accounts for the higher value of the tail risks.
Consider the price for various casino games. Different casino games have different profit margins. Gamblers placing a bet on red or black in roulette will get paid even money if their colour comes up. This is an intuitive result since there are only 2 colours. The house edge is hidden by the zeros and the house edge implied on a double zero roulette wheel with 38 spots is 5.26% (2/38). Compare this to keno, which is a type of lottery game popularized in Nevada (which does not have a state lottery) which pays out infrequently but at a higher price since the odds of hitting a 10 spot keno on 80 balls is less than 0.50%, the casino hides a larger house edge in a keno game (20% or more) compared to roulette (5.26%) since keno is a game of betting on long shots. Players accept these odds because they have a long bias towards larger less frequent payouts, and players are willing to pay a higher price for this experience.
Just as casinos have learned that they can charge a higher price for longer odds (even the house edge in craps place bets is 6.67% for 4 vs. 1.52% for 8), the free market price for longshots is higher than its theoretical price. To make a market in these long odds (which is like selling lottery tickets) a trader must have sufficient capital to bank the risk. If an event has a 1 in 10,000 chance, the risk seller must be able to sustain a $10,000 loss in order to collect $1. There is a premium to being well capitalized, and traders may find they are able to charge $2 for a risk which has a $1 chance of occurring.
So if there is a premium to making a market for longshot risks, what about events that are dependant? Either the GDP released is above or below the estimate, it can’t be both. The chance of a stock price going above $10 and the stock price going below $5 are related dependant events, since both events cannot occur simultaneously. Only one team can win the Stanley Cup, and traders can hedge their risk by selling multiple long-shots on the same risk. Selling risk on multiple dependant events will not create more profits, but it will reduce risk since only one dependant event can occur. If 5 NHL teams each have a 200 to 1 chance of winning the Stanley Cup, selling each team for $1 will create $5 in premiums but the risk will be $200 rather than $1,000.
There are also market-making opportunities associated with these longshot tail risks. Most people can intuitively guess the correct odds of throwing heads or tails (50%), but they cannot intuitively guess the correct odds of the New York Islanders winning the 2014 Stanley Cup or Nick Watney winning the 2014 Masters (both have a 0.4% chance). We cannot intuitively estimate the chances of less frequent events. I could offer 200 to 1 for the Islanders, and make a good return without understanding the correct price might be 250 for 1. There has been a lot written about the low price for tail risks, as these theories play into our long bias to sell books (i.e. The Black Swan).
