The developer of this course had a very small wager placed on the University of Kansas to win the NCAA Division 1 Basketball National Championship. The ticket (contract) had been purchased in July 2021 for an outcome that would not be known until April 2022. In prediction markets, these types of wagers are called futures. The position received 18:1 odds which is quoted in the market as +1800. For each $100 position, the contract would pay off $1800 plus the original amount wagered of $100 for a total payout of $1900. The profit from the payout would be $1800.

To make the example more interesting, let's assume the initial investment was $1000, so the potential payoff for a Kansas win would be a total of $19000, and the profit would be $18000. This is not a certainty; Kansas still needed to win the national championship game. On the day of the game, KenPom.comLinks to an external site. had Kansas with a 69 percent probability of winning. Based on that probability, the expected payout would be:

0.69 x 19000 = $13,110 (Note: that probability seemed high the day of the game.)

The holder of the contract was long Kansas. To hedge the position, a short position in Kansas (long North Carolina, UNC) was needed. You may ask, why would someone want to do this? The answer is to reduce risk and lock in gains. The futures position was for Kansas to win the national championship, and they were in the championship game, which still carried some risk.

On the day of the game, UNC was the underdog and was +170 on the money line. This meant that for every $100 wagered as a money line bet for UNC, the payoff would be $170 if UNC was victorious. The market implied North Carolina has a 37 percent chance to win (KU would be 63 percent). (implied probability for positive odds = 100/(odds + 100, in this case = 100/(170+100)

Using the market-implied probability, the expected payout was:

0.63 x 19000 + 0.37 x 0 = $11,970

(the first part of the equation is the payoff if Kansas won, and the second part is if Kansas lost and position is unhedged)

To fully hedge the position, a money line position on UNC was needed. That way, no matter who won, there would be a payoff, and if fully hedged, the payoff would be $19000 no matter who won the game. The outstanding question is how large of a position in UNC was needed to generate a $19,000 payoff and guarantee a profit regardless of the outcome of the championship game. In this case, the position would be calculated by dividing the necessary payoff by the dollar amount paid for each $100 position times $100.

19,000/170 x 100 = the dollar amount to wager

= $11176.47

To completely hedge the position, we would round up to the nearest dollar, so $11,177 would be the size of the wager.

$11,177 on UNC to win on the money line, and the payout would be 19,000.90. And to check:

11,177/100 x 170 = $19,000.90)

The first part of the equation generates the number of 100-dollar bets times the $170 received per $100 position to generate the payoff of $19000 and change.

The unhedged position consisted of an initial futures contract on Kansas winning the national championship that would pay off a total of 19000 if Kansas won. To hedge that position, a position was taken on North Carolina to win at +170. So 111.77, 100-dollar bets would need to be placed.

111.77 x 170 = $19,900.90

Questions

What would be the total invested? $initial KU position + $ UNC hedge = 1000 + 11,177 So total invested would be $12,177.

With the two positions, regardless of the outcome, the payout would be about $19000 or a profit of $6,823 (19000-12,177).

Would will be hedge your position?

Assume investor is willing to take more risk than provided in the example. He wants to do no worse than doubling your $1000 to $2000. What position should he take?