As of 2:15 p.m. central standard time today, the PredictIt.org prediction market put the odds of President Trump being removed from office at 8%. Specifically, Predictit.org currently offers for sale a “share” which pays $1 if the answer to the question, “Will the Senate convict Donald Trump in his first term?, turns out to be “yes”.
Allow me to provide further context for this “prediction”. PredictIt.org is a New Zealand-based prediction market that offers “shares” on political and financial events. The idea behind PredictIt.org shares (technically, these are binary options, but I digress) is quite simple – you can buy and sell “yes” and “no” shares which pay off $1 if the answer to the contract question ends up being “yes” or “no”. If you buy yes (no) but no (yes) is the answer, then your share expires worthless and you have lost the full value of your original “investment”. However, if you sell yes (no) and no (yes) is the answer, then you don’t owe your counterparty any money and you get to pocket the price received (net of transactions costs) as profit.
Since the payoffs on PredictIt.org shares feature binary payoffs (i.e., $1 if yes and $0 if no), these shares are canonical examples of Arrow-Debreu, or “pure” securities. Arrow-Debreu securities pay $1 if a particular state (in this case, either “yes” or “no”) occurs at a particular time in the future. Thus, the current price for a given PredictIt.org share is the “state price”, which corresponds to the value today of $1 received when a particular future state of the world is realized. Breaking the state price down further, its components include 1) the probability of a particular future state of the world, 2) the rate of interest (to compensate for the time value of money), and 3) a further discount (to compensate for risk averse behavior by the bettor) or premium (to compensate for risk loving behavior by the bettor).
Prediction market prices are frequently referred to in the news media as probabilities for future state-contingent events; if prediction market participants are risk neutral and interest rates are negligible, then this is technically appropriate and roughly correct. What’s fascinating about prediction markets is that they showcase, in very pure form, how market prices reflect the statistical odds of some future event happening. Similarly, prices of speculative assets generally (e.g., corporate securities such as stocks and bonds and derivative securities such as options and futures) also reflect probabilistic beliefs about future states of the world, albeit in more of an opaque fashion.