To hedgers: Adding insult to injury

[jrz1972]

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Suppose you believe the game is really 50:50. Imagine you start from the position of hedging 100%, with a sure win of about $475. Reducing your hedge bet by $110 is the equivalent of betting $100 to win $110. That's a good deal for you if your bankroll is at least $4500, assuming a conservative level of risk tolerance (Kelly fraction greater than 1/4), though it might not be optimal for you. With a bankroll over $450, you can at least afford to reduce the hedge by $11, risking $10 to win $11.

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For the record, this is where you're going wrong. You don't need to make up VNM utilty functions or anything to analyze this. You can get a good handle on the situation just by looking at that last, marginal hedge decision.

Like you said, if I decided to forgo that last $10 of hedge, I would be risking $10 to win $11. Is it rational for me to take that wager? The answer (and there's no way for you to get around this point), is that it depends on my level of risk aversion.

I can tell you with 100% certainty that if somebody walked into my office right now and asked me if I would like to flip a coin and get paid $11 if I win while losing $10 if I lose, I would decline the offer. I would also not take this gamble for 1/10th the stakes.

There's nothing irrational about that. I'm just risk averse. When hedging my Mansion bet, I preferred to go ahead and eliminate the risk on that last $10, even though I gave up some EV (but not EU) to do so.