I agree the company’s current price should be lower than $10 million. But if it starts at price P and I expect it to go up at the risk free rate r, then at a time T later the company’s price should be PrT in expectation. At some point, that’ll be substantially more than the $10 million I expect it to pay out.
Well there’s some probability of it paying out before then.
If the magic value is a martingale, and the payout timing is given by a poisson process then the stock price should remain a constant discount off of the magic value. You will gain on average by holding the stock until the payout, but won’t gain in expectation by buying and selling the stock.
Let’s ignore risk. Suppose the company has a market value of P right now at time T0=0, you expect the vault to open at time ΔT, and the bond rate (which equals the equities rate because this is a risk-free thought experiment) equals r. Then the value of the company at time ΔT is 10 million dollars. If the value of the company at time ΔT is 10 million dollars then the market value (price) of the company right now is 10 million dollars times r−ΔT.
Suppose vaults are a fungible liquid securitized asset and that you can buy fractions of them. Suppose you invest in these vaults. Whenever a vault opens, you immediately invest your 10 million dollars cash in more vaults. Your investment grows at a rate r, exactly equal to the bond rate.
I think what you’re missing is that whenever a vault opens you immediately reinvest the cash. The vault has different time-adjusted value depending on when it opens. On a long enough time horizon, $10 million now is worth more than $10 billion later.
I agree the company’s current price should be lower than $10 million. But if it starts at price P and I expect it to go up at the risk free rate r, then at a time T later the company’s price should be PrT in expectation. At some point, that’ll be substantially more than the $10 million I expect it to pay out.
Well there’s some probability of it paying out before then.
If the magic value is a martingale, and the payout timing is given by a poisson process then the stock price should remain a constant discount off of the magic value. You will gain on average by holding the stock until the payout, but won’t gain in expectation by buying and selling the stock.
Let’s ignore risk. Suppose the company has a market value of P right now at time T0=0, you expect the vault to open at time ΔT, and the bond rate (which equals the equities rate because this is a risk-free thought experiment) equals r. Then the value of the company at time ΔT is 10 million dollars. If the value of the company at time ΔT is 10 million dollars then the market value (price) of the company right now is 10 million dollars times r−ΔT.
Suppose vaults are a fungible liquid securitized asset and that you can buy fractions of them. Suppose you invest in these vaults. Whenever a vault opens, you immediately invest your 10 million dollars cash in more vaults. Your investment grows at a rate r, exactly equal to the bond rate.
I think what you’re missing is that whenever a vault opens you immediately reinvest the cash. The vault has different time-adjusted value depending on when it opens. On a long enough time horizon, $10 million now is worth more than $10 billion later.