Yes, the volatility argument is formal rather than empirical. Whether it actually exists in practice is dubious. Fortunately, this does not affect the core issue of the subject at hand. This discussion concerns the theoretical market. For the volatility argument to apply, all we have to assume is an efficient market, rational actors and the Law of Diminishing Returns.
By “real” do you mean physical dollars or “real value”? In this answer, I ignore inflation and treat the vault as if it contains physical dollars.
We can build a physical system that replicates the effect of your magic vault. Suppose there is a vault tied whose lock mechanism is connected to a radioactive isotope. Each second there is a small chance the isotope will decay and the vault will open and the owner will receive $10 million cash. Each second, there is a large chance the isotope will decay and the vault will remain shut. Radioactive decay is a stocastic process. Therefore if the vault remains shut then the price of the vault remains at a constant price less than $10 million.
At every instant there is a small chance Schrödinger’s vault will open and a large chance the vault will stay shut. In the quantum future where the vault stays shut you are correct and the vault’s nominal market value stays constant. The time-discounted price of a closed vault actually goes down it it stays shut.
It’s not the price of the closed vault that goes up faster than time-discounted non-risk-adjusted value. It’s the average time-discounted risk-adjusted probability-weighted price of all possible future vault states (open and closed) that goes up faster than the time-discounted non-risk-adjusted value of the initial closed vault.
Yes, the volatility argument is formal rather than empirical. Whether it actually exists in practice is dubious. Fortunately, this does not affect the core issue of the subject at hand. This discussion concerns the theoretical market. For the volatility argument to apply, all we have to assume is an efficient market, rational actors and the Law of Diminishing Returns.
By “real” do you mean physical dollars or “real value”? In this answer, I ignore inflation and treat the vault as if it contains physical dollars.
We can build a physical system that replicates the effect of your magic vault. Suppose there is a vault tied whose lock mechanism is connected to a radioactive isotope. Each second there is a small chance the isotope will decay and the vault will open and the owner will receive $10 million cash. Each second, there is a large chance the isotope will decay and the vault will remain shut. Radioactive decay is a stocastic process. Therefore if the vault remains shut then the price of the vault remains at a constant price less than $10 million.
At every instant there is a small chance Schrödinger’s vault will open and a large chance the vault will stay shut. In the quantum future where the vault stays shut you are correct and the vault’s nominal market value stays constant. The time-discounted price of a closed vault actually goes down it it stays shut.
It’s not the price of the closed vault that goes up faster than time-discounted non-risk-adjusted value. It’s the average time-discounted risk-adjusted probability-weighted price of all possible future vault states (open and closed) that goes up faster than the time-discounted non-risk-adjusted value of the initial closed vault.