The number I keep returning to is not the Bitcoin price. It is a ratio.
A treasury company holding B bitcoin across S shares, trading at a market-to-NAV multiple of m, accretes bitcoin per share by the factor (1 + mx)/(1 + x) for every fractional equity issuance x. That expression has a ceiling. As x grows without bound, the factor converges to m and stops. I ran the identity across a grid of issuance sizes in Python — 5% to 200% of the existing share count, multiples from 0.8x to 3.0x — and the ceiling held for every input. One line of arithmetic does more work than every paragraph written about a company "inverting" traditional finance. Unlike the narrative, it is checkable against public filings, and I rebuilt it from the filings rather than the deck.
Perpetual preferred stock is what the name says: a preferred claim with no maturity date. It pays a fixed dividend, typically at a spread to a benchmark, and it never has to be refinanced because it never comes due. Treasury companies now fund bitcoin accumulation with a stack of these instruments alongside convertible notes and at-the-money equity programs.
The pitch is structural. A bank runs a short-liability, long-asset book, so a deposit base can walk out the door in a week, as SVB's depositors did in March 2023. A perpetual preferred holder cannot walk. There is no deposit to withdraw, no maturity to roll, no queue at the teller window. Against JPMorgan's deposit franchise, that is the comparison being drawn.
It is not a stupid comparison. Deposits are cheap and sticky until they are not, and a funding structure without a maturity wall cannot suffer a classic duration run. But the framing hides a substitution rather than a solution, and the substitution is where the engineering question lives.
I spent part of 2024 reading institutional custody documentation ahead of the spot ETH ETF approvals, comparing threshold signature schemes and multi-signature architectures against open-source equivalents like Gnosis Safe. That work taught me something that transfers directly here: risk does not disappear when you restructure a claim. It moves. It relocates into whichever dimension you did not hedge.
So the useful question is not whether perpetual preferred beats deposits in the abstract. It is which mismatch the structure actually removed, and which one it left standing.
Start with the identity, because it is the whole argument.
Take a company with 100,000 BTC and 20 million shares — 0.005 BTC per share. Suppose the market prices it at m = 1.5x the value of its holdings. It issues new shares equal to 20% of the existing count (x = 0.2) and buys bitcoin with the proceeds. The new ratio is (1 + 1.5 x 0.2)/(1 + 0.2) = 1.3/1.2 = 1.083. That is 8.3% accretion in bitcoin per share from a single issuance. At m = 0.9, the same operation yields 1.18/1.2 = 0.983 — a 1.7% loss. The threshold sits at exactly m = 1.0.
The accretion ceiling is the multiple itself. Push x toward infinity and the factor approaches m, never more. A company trading at 1.5x NAV can, through equity issuance alone, accumulate at most 50% more bitcoin per share than it started with. The machine is bounded by the premium, not powered by it. Models that draw per-share bitcoin growth as a compounding curve are drawing the wrong function.
The loop is reflexive in both directions. The multiple embeds the expectation of accretion. Issuance dilutes that expectation, the multiple softens, accretion slows, and the justification for the premium weakens further. The fixed point of the loop is m = 1.0, approached from above by the mechanism's own logic: below 1.0 no rational issuer sells equity, and the halt removes the growth catalyst that supported the premium. This is not a prediction. It is what the arithmetic does when you let it run.
Now the part that matters more than any of it. Duration was never the binding constraint.
A bank's deposit book is short-duration, but its asset side produces interest. Loans and securities generate the cash that services depositors. The liability is expensive in a run and cheap in calm, but the yield spread is what keeps the book solvent between runs.
A perpetual preferred coupon is a cash claim, senior to the common, payable on a schedule. Bitcoin generates nothing. No coupon, no rent, no dividend, no cash flow of any kind. Nothing on the asset side of the balance sheet produces the cash that services the liability on the other side of it.
Consider then what the structure actually achieved. The maturity was extended to infinity. The currency mismatch was left untouched — liabilities denominated in dollars, assets denominated in bitcoin. The cash-flow mismatch was left untouched, and in fact sharpened: the asset yields zero while the liability pays a fixed coupon forever.
A perpetual liability against a non-yielding asset is not duration-matched. It is matched in the one dimension that does not determine default, and mismatched in the two that do.
The spread between the preferred coupon and the yield on the reserve asset is negative by construction. Futures traders have a word for a position that pays to hold: contango. Holding it is rational only if expected appreciation exceeds the carry. Treasury companies are structurally long contango on a volatile, non-yielding asset, financed by instruments whose payments do not pause.
The convertible layer deserves its own line, because it is often presented as the cheap part of the stack. A note with a low coupon and a conversion strike far above spot is a sold equity call. The company sells volatility to buy a hard asset, and the buyer accepts a below-market coupon as payment for that optionality. It works — until the thing whose volatility was sold is the same thing whose premium funds the accretion. Every instrument in the stack prices off one variable, and that variable is the multiple.
There is a second-order effect that removes the last comfort. A maturity wall is a forcing function. It compels a refinancing conversation at a known date, which disciplines borrower and lender alike. Remove the maturity and the credit is not made safe; it is made continuously re-priced. Preferred stress shows up in the secondary price and in the spread demanded on the next issuance, not in a queue at a door. The risk migrated from a discrete event to a continuous variable.
Which leaves the question of what actually collateralizes the structure. Not the bitcoin. The bitcoin is the asset, but the funding engine runs on the equity premium. If m falls through 1.0, issuance stops, and the coupon must be paid from the cash reserve or from a payment-in-kind toggle that turns a liquidity problem into a dilution problem. The number to watch is the coverage ratio: cash and equivalents divided by annual coupon plus operating cost. It is disclosed. It is checkable. Zero knowledge isn't magic; it's math you can verify — and so is a capital structure.
One more variable, and it is the one I would check first. In 2024, comparing institutional custody architectures, the differences that mattered were never on the marketing tier. They were the signer set and the threshold. A corporate treasury vehicle typically signs through a corporate resolution and internal controls, not a cryptographic quorum of mutually independent parties. The trust model is a legal entity, and it is therefore only as strong as that entity's governance. The AMM model hides its truth in the invariant; so does a custody arrangement, and the invariant there is who can move the coins.
Here is the part I didn't expect when I started the model.
The intuitive read is that perpetual preferred is the conservative sleeve of the capital stack — senior to common, no maturity, fixed coupon. The intuition is fine as far as it goes. What it misses is that seniority without a maturity is not a safety feature. It is a permanent claim on cash flow with no exit for the issuer. Senior claims get their seniority tested at a maturity date or in a restructuring. Strip the maturity and you have stripped the test, not the claim.
The second thing I didn't expect is how the SVB analogy resolves when you finish it. SVB failed because of a mark-to-market hole in held-to-maturity securities plus a concentrated, uninsured depositor base. The run was the transmission mechanism, not the cause. Map that onto a treasury company and the analogy holds — but it points somewhere uncomfortable. The equivalent of the HTM hole is not a bond portfolio. It is the equity premium. A multiple is a mark. Multiples compress.
Both models can fail, then, but through different mechanisms. Deposits fail through quantity. Preferreds fail through price. An operator watching the wrong one will be surprised by the other.
Watch three numbers: the market-to-NAV multiple relative to 1.0, the cash reserve coverage of the annual coupon, and any payment-in-kind utilization in the preferred terms. If a cycle turns, expect the defense to be that perpetual means no refinancing risk. That is exactly backwards, and it will be said with confidence. The vulnerability in this structure was never the maturity wall. It is the coupon, and the coupon never expires.