David Rothschild and Glen Weyl on Posted on

There is an old saying, about something that is solid and reliable: it is “Sound as Pound.” But, recently the British Pound has not been so sound! Over the last week, as Brexit, or British Exit from the European Union, has become increasingly likely, the British Pound has moved from about 1.45 US Dollars per UK Pound to about 1.40 US Dollars per UK Pound. This falling Pound may, slightly, affect the validity of the prediction market prices for Brexit.

I am not going to go into a detailed examination of the expectation of the market over the exact exchange rate we should expect should the UK leave or stay in the EU; but, I will acknowledge that if it leaves the exchange rate with the Dollar should decrease (the Dollar will be relatively stronger) and if it stays the exchange rate should increase (the Dollar will be relatively weaker). I do not anticipate a catastrophe for the British economy as the interest rate for UK is extremely steady.

Right now it costs about 35 cents to purchase, in UK Pounds on Betfair, the UK to leave the EU, and 65 cents on the UK to stay in the EU. At the same time, the largest US-based market is charging 40 cents to purchase, in US Dollars on PredictIt, the UK to leave the EU, and 62 cents on the UK to stay in the EU. (Note: both markets moved over 5 cents towards staying in last 24 hours, so please check here for latest prices.)

If a trader was investing in the British market (ignoring for now the US market and currency exchange market) she should trade until: Prob(Stay)*(1-X(PriceStay))*S(ExchangeStay) = (1-P)*X*L(ExchangeLeave). Where S is the exchange between Pound and Dollar if the UK stays in the EU and L is the exchange rate between the Pound and Dollar if the UK leaves the EU. After a little algebra: P = X*L / ((1-X)*S + X*L). Or, at our current price, we would expect the true probability of exit to be about 62% with a price of 65% and post-Exit exchange rates of 1.3 (if UK leaves) and 1.5 (if UK stays) with the Dollar. Even if the Brexit impact was double that, moving the exchange rates to 1.2 and 1.6, the true probability would only fall to 58%.

But, the futures exchange markets are steady at the current exchange rate; anyone can lock in the current exchange rate today for a trade a week from now (i.e., the day after Brexit). If Betfair was trading at 3 pp too high for “staying” on Betfair, a trader could buy “leaving”, and sell Pounds on the currency futures to offset any currency losses in expectation. The problem, in reality is that that would (1) cost money to do (2) in most ways it is separate wager, since it is not contingent on winning (3) is not full implementable or valid if you consume in Pounds. The USA-based exchange is trading in US Dollars, the cost of currency exchange (and the fixed costs of being in both markets) makes it too expensive to arbitrage these two markets for this small of differential.

In short, I believe that the price on Betfair could be a few percentage points too high for staying, but is constrained by possible arbitrage or hedging opportunities that would be implementable if the probability was much further from the price. But, barring expectations of a true catastrophe, it is not going to stray more than a few percentage points.

I thank Nikete for pushing me on the question (sorry, I do not know your last name), and Rajiv Sethi for talking through the topic. I include my colleague Glen Weyl (welcome to New York!) as a co-author here for spending so much time with me talking through this yesterday! While they all provided insight, I take full responsibility for the ultimate conclusions and errors.