There was a story in the news today about someone who had collected £72,000 from the bookies after cashing in a bet on Leicester City to win the Premiership. He originally bet £50 at odds of 5,000-1 on a Leicester win, so stood to pick up a cheque for £250,050 if he was successful. Instead he chose to cash in his bet, taking home £72,000. I hope he enjoys spending his winnings, but I do wonder whether £72,000 was a fair exit price.
So I couldn’t resist doing some tinkering. First of all, it’s worth pointing out that there’s been a round of matches played since the payout, changing everybody’s odds. So rather than looking at the £72,000 payout, I’m going to be looking at the £91,000 that Ladbrookes gave quoted as an updated exit value following Leicester’s win at Watford over the weekend.
If our anonymous gambler wanted to win £250,050 in the event of Leicester not winning the league, he could do this by placing separate bets on all the other nineteen Premiership teams. So he would bet £62,513 on Spurs at 3-1, £41,675 on Arsenal at 5-1, £35,721 on City at 6-1,… all the way down to Villa. I can’t see Villa odds quoted anywhere but I can’t imagine their odds bring any shorter than the 4,500-1 I’ve seen quoted on other no hopers, so he wouldn’t need to burn more than £56 there. The total cost of these nineteen bets would be £145,434.
So is there an arbitrage opportunity here? Let’s pretend the gambler was a “wealthy investor” and that he hasn’t yet cashed in his bet. He has a choice between two low risk strategies:
(i) cashing out and collecting a guaranteed £91,000 today
(ii) spending an extra £145,434 and collecting a guaranteed £250,050 in May.
It’s equivalent to having the opportunity to pay 91,000 + 145,434 = £236,434 today in return for £250,050 in about two months’ time, earning a return of 40% pa. This suggests that the £91,000 cashout value is a bit mean.
What would a fair cashout value look like, though? It depends on what return the wealthy investor would expect, and this return would need to allow for bookmaker default risk and the risk of the gambler running off to Brazil if Leicester win the league. I’ve not put any thought into what return might be required, but 10% would suggest a cashout value of £100,676 and 20% a cashout value of £97,132.
It does make me wonder whether there’s a business opportunity for somebody out there…