I’d like to take Kevin’s $0.02 in the coin-flipping word search.
First, I’ll buy a prediction contract that I will flip Heads. This will cost $0.50 for a $1 payout.
Second, I’ll buy the right to a futures contract: After the word is revealed and his search is complete, I will be given a prediction contract which pays $1 if Tails is revealed. If his expected posterior for Heads is 0.52 then the futures contract would have a value of $0.48.
In aggregate, I’ve paid $0.98 for a guaranteed $1.00 return.
He may claim he is not willing to sell you this futures contract for $0.48 now. He expects to be willing to sell for that price in the future on average, but might refuse to do so now.
But then, why? Why would you not sell something for $0.49 now if you think, on average, it’ll be worth less than that (to you) right after?
I’d like to take Kevin’s $0.02 in the coin-flipping word search.
First, I’ll buy a prediction contract that I will flip Heads. This will cost $0.50 for a $1 payout.
Second, I’ll buy the right to a futures contract: After the word is revealed and his search is complete, I will be given a prediction contract which pays $1 if Tails is revealed. If his expected posterior for Heads is 0.52 then the futures contract would have a value of $0.48.
In aggregate, I’ve paid $0.98 for a guaranteed $1.00 return.
I think your argument is quite effective.
He may claim he is not willing to sell you this futures contract for $0.48 now. He expects to be willing to sell for that price in the future on average, but might refuse to do so now.
But then, why? Why would you not sell something for $0.49 now if you think, on average, it’ll be worth less than that (to you) right after?