# Prediction Markets And The Risk-Free Rate

Prediction markets have caught my attention in recent months. It all started with the 2020 US Presidential Elections, where a lot of people were willing to support their favorite candidate so much, that the betting odds managed to decouple a lot from the polling results.

The US is not the only country where this has happened. An unknown candidate for the London mayoral elections had enough money to astroturf themselves into second place with the odds implying a 10%+ probability of him winning the election at one point. Nonetheless, I decided to put my money where my mouth is and take the other side of the bet. I think Vitalik Buterin explains pretty well in the Intelectual Underconfidence part of his blog post why these opportunities exist and aren’t arbitraged:

And now we have the final possibility: that many people (and smart people in particular) have a pathology that they suffer from excessive humility, and too easily conclude that if no one else has taken some action, then there must therefore be a good reason why that action is not worth taking.

If you don’t like to play with money and you like to play with internet points, Scott Alexander has written two articles about Metaculus. There’s Phil Tetlock’s book about superforecasters and the GJOpen community that goes in the same direction.

So all in the all, prediction markets have started to become more and more popular. I could be sarcastic and say that this represents an appropriation of *gambling* by the Gray Tribe. Or I could be indifferent and say that this is just a side effect of The Boredom Market Hypothesis coined by Matt Levine. But let’s explore the tail end of prediction markets and how they relate to the current low interest rate environment.

### The risk free-rate affects prediction markets

The risk free-rate of return differs by currency and by who is doing the transaction. If you are an institution and based on your definition of risk, you might consider US Treasury Bills, UK Gilts with the longest duration, LIBOR, SONIA and other suche metrics. However, I don’t think the regulators will allow my bank to use customer’s deposits to enter the prediction market.

So let’s simplify and take the “personal” risk-free rate. Currently in Britain, the top paying easy access bank account gives you an AER of 0.50% for sterling. Across the pond in the US, the interest rate is the same.

Let’s take an A or B bet where event A has a probability of 0.50% and event B has 99.50%. If we were to calculate the odds for an event with the implied probability of 0.50%, that would be 1 / (0.50 / 100) = 200. Thus, it doesn’t make sense to bet **against** an event with odds greater than 200 that takes a year to resolve, even if you know that event won’t happen. Conversely, it doesn’t make sense to bet on an event with odds lower than 1.005, since you would be better off putting the money in a savings account.

These numbers look pretty small because we are in a low interest rate environment. Let’s do a table with what would happen in more normalized environments:

Interest rate | Lower bound | Upper Bound |

0.50% | 1.005 | 200 |

1% | 1.01 | 100 |

5% | 1.05 | 20 |

10% | 1.11 | 10 |

If we were in a 10% interest rate environment, then it would not make sense for anybody to go against the bet I described related to the Mayor of London. The possibility of astroturfing would be higher, as low probability events will go higher since nobody would want to take the other side of the bet and push the odds lower.

Hence:

**The risk-free rate affects the quality of prediction markets. The lower the risk-free rate, the higher the number of people trying to go against low-probability events and take the other side of the bet.**