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Group-stage contracts summing to less than two

Question

Four teams play in a group from which exactly two qualify. A contract on each team pays 11 if it qualifies and 00 otherwise. Prices: team 1 at 0.840.84, team 2 at 0.730.73, team 3 at 0.250.25, team 4 at 0.150.15. You can buy or sell any contract and buy or sell bonds paying 11, with zero interest. What up-front credit can you lock in with an arbitrage?

Short answer

0.030.03. Holding one of every contract always pays exactly 22, so the four prices should total 22; they total 1.971.97. Buy all four and short two bonds: you receive 2−1.97=0.032-1.97=0.03 now, and the payoffs cancel at the end.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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