Participation in prediction markets has a social benefit: a market's prediction provides a useful baseline against which other predictions (outside the market) may be judged. A market's prediction can also be useful to individuals making decisions that depend on the outcome of the predicted event. In both cases, the social utility provided by the market remains even if the market's prediction is not perfect. The market is useful even if it only provides a general assessment of the relative probabilities of different outcomes.
Prediction markets provide baseline predictions about uncertain events. Consider the task of predicting which candidate will receive the US Democratic party's presidential nomination in 2020. In May 2019 there were 23 candidates for the nomination. The thought that each candidate is equally likely to win the nomination does not merit being described as a baseline prediction. Some candidates have a far better chance than others. Here the prediction market gives the public a general sense of which candidates are better positioned than others (Figure 1). And the public gets this for no cost.
Figure 1: The probability of one of these five candidates winning is 87%, in the judgement of PredictIt participants in late May 2019. There are many other candidates in this race. The prediction market here tells us that some candidates stand a far better chance than other candidates.
The utility of having a baseline prediction is easy to appreciate in the case of political events. With political events, we have political commentators and polling firms which deliver forecasts of what will happen. It is natural to ask whether or not these commentators or firms are skilled at forecasting. Given that polling is expensive and salaries for political commentators are non-zero, we anticipate that their predictions will approach or exceed a certain standard of utility. One standard we can use is the following: ask that their predictions tend to be more accurate than those made by prediction markets. Having prediction markets provide a standard here is particularly valuable because there are typically no other standards we can use. We cannot, for example, ask the commentator or firm to do better than the “prediction” which assumes each candidate has an equal chance of winning because virtually anyone can make better predictions than that. Prediction markets prove their worth by providing a baseline in settings where non-trivial baselines are scarce.
Consider participating in a prediction market. Even if your wagers fail to pay out, the public stands to benefit.
Are there bets with guaranteed positive return on the prediction market PredictIt?
Yes and no. “Yes” because examples of such bets do exist. “No” because these bets have negative present-value adjusted returns. (Bets with guaranteed positive returns are called “sure bets.”)
Here is one example of a bet which does indeed have a guaranteed positive return. During the spring of 2019 (e.g., April 28 to May 2) you could purchase two contracts in the 2020 U.S. presidential election market on PredictIt which, together, paid off 100¢ with certainty and cost 99¢. Specifically, you could purchase the following two contracts:
a contract which costs 0.43 paying out 1 if the Republican Party candidate does not win, and
a contract which costs 0.56 paying out 1 if the Democratic Party candidate does not win (which pays out if the Republican wins).
So for 0.99 you can receive 1 if the Republican candidate wins or does not win. As the probability of this bet paying out is 100%, this contract is guaranteed to yield a profit of 0.01. As this particular market is one of the most liquid markets on PredictIt, you could purchase 1517 of each contract for a total of \$1501.83—PredictIt imposes a limit of \$850 invested in a single contract market—and be guaranteed to receive \$1517, making a profit of \$15.17. This bet qualifies as a sure bet.
Figure 1: A sure bet on PredictIt. The sure bet shown here was available during several days in May 2019. This sure bet consists of wagering against the Republican candidate winning and also against the Democratic candidate winning. (This second wager is equivalent to betting on the Republican candidate winning.) Making these wagers costs less than 1. The bet against Republican costs 43¢ (100¢ – 58¢ + 1¢) and the bet against Democrat costs 56¢ (100¢ – 45¢ + 1¢). (The spread, in both cases, was 1¢.) Purchasing one of each contract costs 99¢.
Before you get out your wallet, recall that purchasing a contract in this market pays out in November 2020. Taking into account the present value of the future income stream makes the return on the bet negative. As the risk-free interest rate in May 2019 was 2.31%, the present value of a cash flow of \$1,517 in 18 months is \$1,465.91 ( $\frac{1517}{(1+0.0231)^{18/12}}$ ). Hence the present-value-adjusted return on the investment of \$1501.83 is an unattractive -2.4%. You would be better off investing the \$1501.83 in a high-yield savings account.
Future income flows should always be expressed in present value terms. This practice is as important in the prediction market setting as it is elsewhere. The payoffs on winning prediction market bets frequently do occur many months from the present. Indeed, it is not uncommon to see prediction market bets concerning events that might occur two or more years in the future. If the wager was made using a currency which experiences inflation, then the payoff should be discounted to reflect the change in the value of the currency. When we calculate the value of the future payoff in terms of the value of the currency today, we are calculating the present value or the present discounted value of the future income flow.
The present value of a future income flow can be illustrated with an example. Suppose the date is January 1st and it is possible to earn 2% interest on a 1-year time deposit (aka certificate of deposit) with a major bank. How much should one be willing to pay on January 1st for a future income flow of 100 in one year? Clearly it must be less than 100 because it is possible to deposit 100 with the major bank and receive 102 in one year's time. Accepting a price of 100 would “lock in” a loss of 2. The commonly accepted answer is $\frac{1}{1 + r} 100 \approx 98.04$, where $r$ is equal to the “risk-free” rate (2%). We say that the present value of 100 in a year's time is 98.04. It would be wasteful to pay more than 98.04 for a future income flow of 100 because you would be better off depositing your money in the bank and withdrawing it, with interest, in a year's time.
(Energetic students willing to engage in light algebra may derive the present value formula using principles mentioned above.)
Using a present-value adjustment in the prediction market setting is relatively straightforward. Consider a contract that costs 0.98 today and pays out with certainty in one year. (It is not difficult to find contracts fitting this description on PredictIt.) Assuming a 2% risk-free rate, what is the return on this contract, in present value terms? The present value of 1 in one year is $\frac{1}{1+r} 1 \approx 0.9804$, making the return a measly 0.04%. In fact, the return is negative if we account for PredictIt's fees. What appeared on the surface to be a sure bet is, upon reflection, a losing wager.
Figure 1: The probability of one of these five candidates winning is 87%, in the judgement of PredictIt participants in late May 2019. There are many other candidates in this race. The prediction market here tells us that some candidates stand a far better chance than other candidates.
Figure 1: A sure bet on PredictIt. The sure bet shown here was available during several days in May 2019. This sure bet consists of wagering against the Republican candidate winning and also against the Democratic candidate winning. (This second wager is equivalent to betting on the Republican candidate winning.) Making these wagers costs less than 1. The bet against Republican costs 43¢ (100¢ – 58¢ + 1¢) and the bet against Democrat costs 56¢ (100¢ – 45¢ + 1¢). (The spread, in both cases, was 1¢.) Purchasing one of each contract costs 99¢.