Kelly on a mispriced prediction-market contract

Question

A binary contract pays \1 if an event happens and \0 if not. It currently trades at c = \0.40. You believe the true probability is p = 0.50, so you think it is cheap. What fraction of bankroll does Kelly say to buy, treating this as a repeatable edge?

Accepted Answer

Buying one contract at c stakes c to win 1 - c on success and lose the whole c on failure. The net odds are b = \frac{1 - c}{c} = \frac{0.60}{0.40} = 1.5, and a loss forfeits the full stake, so ordinary Kelly applies: f^ = p - \frac{q}{b} = p - \frac{(1 - p)\,c}{1 - c}. Plug in p = 0.50,\ c = 0.40: f^ = 0.50 - \frac{0.50 \cdot 0.40}{0.60} = 0.50 - \frac{0.20}{0.60} = 0.50 - 0.3333 = 0.1667. Buy about 16.7\% of bankroll. Intuition check: the contract's expected value is p - c = 0.50 - 0.40 = \0.10 of edge per \1 of payoff, and dividing that edge by the odds structure lands you near a sixth of …

Kelly on a mispriced prediction-market contract

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