Inter-market Arbitrage in Sports Betting - National Centre for ...

ways to hedge a bet in the inter-market arbitrage case. The arbitrageur can
take the long position on a given outcome at the exchange market or bookmaker
market and can bet on all contrary outcomes, effectively reselling his
contract. We will refer to this method as the long position inter-market arbitrage
strategy. An alternative is to go short at the exchange market in order
to “sell” the contract bought at the bookmaker market. We define this method
as the short position inter-market arbitrage strategy.
The first strategy is very similar to the intra-market arbitrage case. The arbitrageur
bets on all possible outcomes at the most advantageous odds. The
only exception is that he seeks favourable odds not only from the bookmaker
market but also from the exchange market. Hence, he places his bets on
max , , 1 . The stakes have to be balanced according to
, 1
8
1
∑ 1
, (8)
and the return on the long position inter-market hedged bet is
1
Π
∑ 1
1. (9)
Thus, a long position inter-market arbitrage opportunity arises if
1
1
(10)
holds.
A more elegant way to realise potential inter-market arbitrage returns is to
directly sell a bet at the exchange market. Exchange markets offer the possibility
to place a bet not only on a certain outcome (a long position bet) but
also against the outcome (a short position bet). Thus, the short position intermarket
arbitrage strategy buys a contract at the bookmaker and sells the
same contract at a more favourable price at the bet exchange. The expected
return of this arbitrage strategy is