Risk Free Return Fallacy

The hypothetical concept of risk free rate of return is the economic interest rate obtainable with a guaranteed return of loan principle. There is a theory that Bitcoin allows this to exist in actual practice by enforcing principle return. A corollary to the theory is that this capability can limit credit expansion generally.

The theory requires a provable fixed time covenant on the lent units of coin by the lender. The covenant ensures that the lender cannot spend the units until maturity of the loan and that ownership of the units returns to the lender at that time. The lender trades with a borrower these encumbered units in exchange for interest. The lender's opportunity cost imposed by the covenant is offset by this interest.

However, the units provide no monetary value to the borrower. Full control over the units provably returns to the lender, leaving any person who has accepted them with nothing at that time. This zero value is necessarily imputed to each exchange prior to maturity and therefore to the loan itself, invalidating the theory.

There is a related theory that the opportunity cost of the lender can be used to represent a provable expense, just as with proof-of-work. This may be used similarly to hashcash as a way to mitigate denial of service. This is true, however this is an expense and can be achieved by spending (including destroying) units. Just as with proof-of-work, this is a trade of provable capital cost for units. As such it does not constitute a loan (i.e. earns no interest), invalidating the theory.

There is a related theory that the units can be used by the borrower to instead track an asset of perpetual value. Given that the tracking expires at maturity, this theory is invalid for the same reason. There is a related theory that the loaned units can be used for tracking a fixed-term asset that expires at loan maturity (e.g. a theater ticket). This is true, however the cost of tracking, for any duration, is limited in BTC by the dust consensus rule to 1 unit. As such the opportunity cost is limited to 1 unit plus at least one transaction fee for establishing the loan.

The utility to the borrower is the reduction of the tracking cost over the loan term. At an interest rate of 10% and expiration beyond approximately 7.2 years it becomes cheaper to spend 1 unit than to borrow it. By instead spending just 1 unit outright the asset may be tracked perpetually.

While the final scenario is economically rational, it cannot be accurately described as a loan, since the unit can neither be traded nor destroyed by the so-called borrower. It would be more appropriate to refer to this as “rental” of the unit, if only to distinguish it from true lending.

Nevertheless, a return can theoretically be earned on the rental of 1 unit, up to the economic limit imposed by the interest rate (e.g. ~7.2 years at 10%). Yet the fee required for this to be economically rational must be 0 units, as the rental-establishing transaction is required, where it is not when using one’s own unit for tracking. So in the case where demand to transact exceeds the fixed confirmation supply, this scenario is not economically rational. This relation holds at any enforced coin dust level above zero to the extent that dust is an insufficient fee to finance confirmation.