Combinatorial markets for independent events: Flawed use of approach hampers price discovery

“Which teams will play in the 2007 World Series?“ An experienced market manager has created a market asking this question at the Inkling public markets, setting it up at the end of the regular season and listing contracts in each of the then possible 20 different combinations (four teams from the American League and five from the National League). With two teams left in each league championship series, just four possibilities remain.

A complete listing of the possibilities feels like a natural approach to answering the question of “which two teams will play,” but it is awkward to use in practice. For example, if at the market open a trader had a strong favorite among the American League teams but no opinion about the National League teams, it would have required trading in five contracts to obtain the desired holding. With many contracts offered, trading in some contracts will be thin – some of the unlikely pairings showed only one or two trades – and with thin trading the prices may not be reliable.

But beyond being awkward in practice, it seems flawed in principle. The two league championship series are conducted separately and the outcomes are independent of each other. Whether Colorado or Arizona wins the National League championship will have no influence on the likelihood that Boston beats Cleveland to win the AL. When the two events are independent, it would be more straightforward to use two separate markets. In this case one market would have started with four contracts and the other with five contracts, for nine total rather than 20.

The “which two teams” market isn’t the only example of the use of combinatorial contracts for independent events. Earlier this year a baseball market asked whether any pitchers would achieve 20-win seasons. The four contracts offered were: “Yes, in the American League,” “Yes, in the National League,” “Yes, in both leagues,” and “No 20-game winner.” (The contracts are exclusive such that “Yes, in the American League” means also “and not in the National League.”) This design again requires trade in two contracts to implement a single change in belief. If you decide the likelihood of a 20-game winner in the National League is 50 percent rather than the market’s 20 percent, you would need to buy both “Yes, in the National League” and “Yes, in both leagues.”

In both of these cases, independent markets for each league would allow traders to more directly express views about the outcomes of the two league championship series. Trade in American League prospects would not influence National League contract prices, which on the assumption that these are independent outcomes is just the way it should be.

A third baseball market example shows what may be a proper use of the structure. In mid-season a market was implemented asking “Will (general manager) Tim Purpura or (manager) Phil Garner be with the Houston Astros on opening day, 2008?” In this case there may be complicated dynamics at play that such a market could reveal. Perhaps it is likely that the owner would either dump both or dump neither, but not keep just one of the two. Or, perhaps firing one would make it more likely that the other remained. The combinatorial design makes it possible for the market to address these interrelationships. (As it happened, the market was only a few days old when both managers were sent packing.)

It is possible to make a case in favor of this inherently more difficult to use design. In the first two examples it appears fairly clear that the events are independent, but when it is unclear then the structure may help reveal the underlying dependence among outcomes. In addition, because of the way the multi-outcome automated market maker works at Inkling, trade in one contract can leave slight mispricings in the other contracts. Though the profit opportunities tend to be small, they may encourage the trader to keep trading until just the right relative prices emerge. In effect, the market tests just how strongly the trader feels about the precise set of prices resulting from his trades.

But from my experience tracking prices and trading in both of these markets, my sense is that the market is not tempting additional attention to small profit opportunities. Instead, these markets seem to generate prices suggesting constantly varying degrees of interdependence between apparently independent outcomes. For example, before the first game in the National League championship series the prices in the “which two teams” market implied that Boston had an 81 percent chance of beating Cleveland if Arizona beat Colorado, but only about a 70 percent chance of beating Cleveland if Colorado beat Arizona. After two games played in each series, the prices suggested a 65 percent chance for Boston to prevail if Arizona wins its series, and a 74 percent chance for Boston to prevail if Colorado wins the National League.

These relative price changes do not reflect rapidly changing views about the interdependence between events, instead they are artifacts of the mismatch between the combinatorial design and the independent events that have been joined together. In theory, combinatorial markets can be powerful tools to expose market beliefs about the underlying relationship between events. But when the event outcomes are themselves independent, and especially in play money markets where the incentives to work out small price differences can be weak, the combinatorial structure can be a barrier to effective price discovery.