Regarding the inflation/opportunity cost, I’m curious as to its effect in a more efficient market. If I believe that the probability is q but the market currently values the share of YES at a price reflecting some probability p<q, then I should believe that the market will update itself upward. That is, I expect my personal information and considerations to be eventually discovered by other people and the price to reflect that (especially if after I buy I’ll also share my information and considerations). This would mean that I don’t have to wait a long time before the price goes up, and by then I can sell.
However, I don’t think we should expect the price to go all the way up to q. In the simple case where everyone believes the probability is q, and that it would remain q until the market closes, and everyone is rational and risk-neutral, the price should reflect the expected benefit considering the opportunity cost, so that one would value buying YES and investing in other alternatives equally.
In such an efficient market, at the limit, I’d expect no difference between holding on to some stocks compared to buying and selling any time at whatever the price is. Therefore, the price pt at each time t<T (the closing time) should really be such that the following holds:
q⋅1−pt=ptrT−t, where r is the interest rate. Equivalently,
A proper prediction market (virtual one) is designed to make people reveal their expectations early. That solves the problem of “waiting for discovery”.
Regarding the inflation/opportunity cost, I’m curious as to its effect in a more efficient market. If I believe that the probability is q but the market currently values the share of YES at a price reflecting some probability p<q, then I should believe that the market will update itself upward. That is, I expect my personal information and considerations to be eventually discovered by other people and the price to reflect that (especially if after I buy I’ll also share my information and considerations). This would mean that I don’t have to wait a long time before the price goes up, and by then I can sell.
However, I don’t think we should expect the price to go all the way up to q. In the simple case where everyone believes the probability is q, and that it would remain q until the market closes, and everyone is rational and risk-neutral, the price should reflect the expected benefit considering the opportunity cost, so that one would value buying YES and investing in other alternatives equally.
In such an efficient market, at the limit, I’d expect no difference between holding on to some stocks compared to buying and selling any time at whatever the price is. Therefore, the price pt at each time t<T (the closing time) should really be such that the following holds:
q⋅1−pt=ptrT−t, where r is the interest rate. Equivalently,
pt=q1+rT−t.
A proper prediction market (virtual one) is designed to make people reveal their expectations early. That solves the problem of “waiting for discovery”.