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The Odds of Impeachment

The Odds of Impeachment

Frank Polley, MBA Class of 2018


It’s a headline that many people want to wake up and see sprawled across the WSJ front page any day now. It’s also a headline that, based off the increasingly breathless and apocalyptic media coverage of the Trump administration, seems increasingly imminent to some. Wanting or even expecting something to happen, however, is a different enterprise than predicting exactly how likely it is to occur.

A quick Google search of “Donald Trump impeach” yields such results as “Will Donald Trump Get Impeached? Here’s How it Could Happen,” or “Professor who correctly predicted every US presidential election since 1984 is certain Donald Trump will be impeached.” These are all well and good, but being the data-driven decision-makers we here at Stern are, they are unsatisfying. We want confidence intervals. We want sigmas and alphas and betas and z-scores.

History tells us that three of the previous 44 US presidents have faced impeachment proceedings. Two of them, Andrew Johnson and Bill Clinton, were successfully impeached by the House of Representatives. However, both Johnson and Clinton were subsequently acquitted by the Senate. The third, Nixon, while never successfully impeached, did end up resigning because of impeachment proceedings. If you count Nixon, then there is a historical 1/44, or 2.27%, chance of a U.S. President being removed from office because of impeachment.

This is, obviously, unsatisfying. I think it’s safe to say there is some notable idiosyncratic risk involved in this presidency when it comes to the odds of impeachment.

How, then, can we get some data to help predict how likely it truly is that Trump will do something to get himself removed from office? First, let’s look at what it takes to get impeached. Article II, Section 4 of the Constitution states that “the President, Vice President, and all civil officers of the United States shall be removed from office on impeachment for, and conviction of, treason, bribery, or other high crimes and misdemeanors.” Furthermore, Wikipedia lists some more high crimes and misdemeanors as “perjury of oath, abuse of authority, intimidation, misuse of assets, failure to supervise, dereliction of duty, conduct unbecoming, and refusal to obey a lawful order.”

At this point, we can put our fine Stern education to use. Instead of going through and calculating the odds that our President will commit any one of the above high crimes and misdemeanors, we can outsource the work to the wisdom of the crowd. Why discount every individual cash flow of a company to get its value when you can just look at its market cap?

Popular internet betting websites serve as a fascinating proxy for using the collective wisdom of the marketplace to get a sense for how likely events are to occur. For this exercise, we can find some very interesting data around what expectations are for Trump to serve a full term as President of the United States. Of course, these odds are likely to vary between all of the different bookmakers, which can make it difficult for
everybody actually staking money to get the very best deal. However, by using a site such as BookmakerAdvisor, you can compare the odds between as many bookmakers as you want so that you get the best deal imaginable.

The website PredictIt offers some of the most easily interpreted odds. People place bets on binary events occurring by purchasing shares. If the event occurs as predicted, they receive $1 per share. If it does not go down as predicted, they get $0 per share. The market then stabilizes around what it thinks is the expected value (effectively the percentage odds of the event occurring as predicted) of a share.

Currently shares of “Yes” for “Will Trump be impeached in 2017?” are selling for $0.18, suggesting the market thinks there is an 18% chance of a Trump impeachment in his first year in office. For “Will Trump be president at year-end 2018?” the “No” shares are selling for $0.32.

Another website,, uses a more familiar form by giving 3/1 odds for “Donald Trump to be Officially Accused of Russian Collusion,” suggesting a 25% likelihood of impeachment proceedings being at least justifiable.

Other betting websites such as Bovada and Sportsbook use moneyline betting odds. For instance, Bovada gives odds that Trump will complete a full term as POTUS for “Yes” at -110 and for “No” at -120. The formula to convert moneyline odds into percent probabilities is 100 / (Moneyline + 100) for plus moneylines and Moneyline / -(100 – Moneyline) for minus moneylines. So, in this case, the market at Bovada is saying there is a 55% chance that Donald Trump will not complete a full term as President of the United States.

Sportsbook goes so far as to give different odds for whether Trump will be impeached specifically in his first term or simply not “serve full term as President of the USA,” at +160 and +125, or 38% and 44% likelihood, respectively. This is particularly interesting because it suggests the market thinks there is a 6% likelihood of Trump not finishing his term for reasons other than impeachment. These could include resignation, assassination, or even activation of the little-known Section 4 of the 25th Amendment to the Constitution, which allows the Vice President and Cabinet to remove the President from office without the input of Congress.

All this is well and good, and seems to indicate that there is an astronomically high probability, when compared to history, that Donald Trump will be removed from office before he completes his first term. But, just how wise is the crowd? How much can we really trust these betting websites to create perfectly efficient markets? Are people putting money down on these odds for empirical and quantifiable reasons, or are they putting money down for more emotional reasons? Again, it’s one thing to hope for something to happen—it’s another to know exactly how likely it is.

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