More fundamentals of prediction markets
By Rob Knight on February 7th, 2009Before going into any more depth about prediction markets, this post should serve as an additional basic primer in the concepts of how these markets function (newcomers may also wish to read our first post). The aim of this post is to set out the basic assumptions that will be incorporated into future posts.
Firstly, a market is a vehicle for the trading of specific contracts (also known as assets or shares) which are traded (bought or sold at a price). Within a given market, only certain contracts can be traded. For example, the “Will the Conservative Party gain the most seats at the next British General Election?” market can contain only contracts for plausible answers to that question - in this case, “Yes” or “No” are the only possible answers; “yellow”, “fishcakes” or “42″ are not valid answers and so there is no way these contracts can be traded on the market. What’s important to note here is that the various contracts on the market are related - as the price for one contract goes up, the price for others on the same market falls.
The sum of the value of all contracts on the market always adds up to a certain number which depends on how the market is structured - for simplicity, many prediction markets use the number 100 as this constant. So, following the above example, if the price of “Yes” is 66, the price of “No” must be 34. If people start buying “No” contracts, pushing the price up to 37, the price of “Yes” contracts falls to 63. The same holds true for markets in which a far larger number of contracts are traded; the sum of their prices will always add up to 100.
The reason for this automatic price adjustment is the presence of a market maker, a trader that will always buy and sell at a certain price, determined by a scoring rule. For each contract bought from (or sold to) the market maker, the price shifts slightly and the prices for the other contracts on the market are adjusted accordingly. A future post is in the works to explain exactly how these calculations work.
What determines the price of a given contract is the balance between the number of outstanding contracts compared to the outstanding number of competing contracts within a market. So, if traders have bought 150 of the “Yes” contracts and only 50 of the “No” contracts, we know that the price of further “Yes” contracts will be higher (the price reflects demand, which in turn reflects the probability that the traders have assigned to the likelihood of that contract coming true and paying out). What’s important in determining the price is not the relative number of outstanding shares on either side, but the difference between the two, at least when using the logarithmic scoring rule (which will be the subject of a future post). This implies the following important facts:
When there are 100 outstanding contracts for “Yes” and for “No”, the difference is 0 and the price for both will be equal
When there are 1,000 outstanding contracts for “Yes” and for “No”, the difference is 0 and the price for both will be equal
When there are 100 outstanding contracts for “Yes”, and 150 for “No”, the difference is 50 and this will cause certain prices to be calculated (approximately Yes=37, No=63 using the logarithmic scoring rule)
When there are 1,000 outstanding contracts for “Yes”, and 1,050 for “No”, the difference is 50 and this will cause certain prices to be calculated (approximately Yes=37, No=63 using the logarithmic scoring rule)
The key point, as pointed out above, is that price calculations are made based on the difference between the number of outstanding contracts, not the relative totals. This was one of the hardest points for me to grasp when first investigating the logarithmic scoring rule, but it makes some sense once you get used to it.
Basically, this means that a fairly small shift in trading can begin to shift the price significantly. At first this may seem troubling, but it is in fact essential to how a market maker works. Once the market maker detects a shift towards a particular contract, it begins to raise its price. This is to prevent a situation where traders can buy cheap ‘dead cert’ contracts from the market maker in a situation where the market maker - as a dumb, automated process - is not aware that the outcome is a foregone conclusion. The relatively rapid escalation in price once a gap opens up is there to protect the market maker from exploitation. Of course, as prices in the more popular contract increase, prices in the less popular contracts decline. In a market where the participants disagree about outcomes, this creates an attractive buying opportunity for those who favour those other contracts. And so, although the price may be moved quite substantially by a certain trader, this can only be done by creating profitable opportunities for others - and when those opportunities are exploited, the price returns to something reflecting the consensus amongst the traders. In practice, the price tends to fluctuate around this consensus point until external events prompt a change of consensus.
Hopefully this provides some additional insight into the concepts behind prediction markets. In future posts we will be addressing not just what prediction markets are, but how they can be implemented.
Tags: market makers, scoring rules