The short-gamma position embedded in every BTC-treasury convertible note

A BTC-treasury company that issues a convertible note is selling a package: a fixed-income obligation plus an embedded call option on BTC (or on the company's equity, which is effectively the same thing when BTC constitutes most of the balance sheet). The fixed-income leg is marked and reported. The embedded call is sold to the noteholder for a price reflected in the coupon, and is not separately marked by the issuer. The result is an implicit short-gamma position that most overlay programmes do not account for.

The mechanics of the embedded short

A convertible note gives the holder the right to convert into equity (or, in some structures, into BTC) at a strike price established at issuance. From the issuer's perspective, this is a short call: the issuer has sold the upside above the conversion price. When BTC appreciates past the conversion threshold, the option becomes valuable to the holder and costly to the issuer, who delivers cheap equity into an expensive market. When BTC falls, the note stays as debt and the issuer carries the full liability.

This is a short-gamma structure: the issuer is worst off in the extreme outcomes on both sides. The premium for accepting this exposure is the below-market coupon. Most BTC-treasury teams model the coupon saving but not the gamma they have sold.

The overlay interaction

An overlay programme designed to hedge the BTC reserve asset but not the convert book is partially hedged. Long puts on the reserve asset reduce the downside exposure from the reserve, but the liability on the convert does not shrink with the hedge. A complete programme accounts for the short call embedded in the convert and sizes the overlay accordingly. In practice this means the optimal overlay includes some long-call exposure to offset the short embedded in the convert, or the convert is priced to reflect the cost of the hedge.

When convert issuance is still the right trade

A convert issued at a high conversion premium in a high-implied-vol environment can be a competitively priced structure. The noteholder is paying for vol that is expensive relative to where the issuer expects it to settle. If the treasury's view is that implied vol will compress and the fixed-income terms are acceptable, the convert is a reasonably-priced sale of volatility, provided the short-gamma is acknowledged and the overlay is adjusted to account for it.

The error is issuing converts for the wrong reason: because the coupon is lower than a straight note, without accounting for the short-gamma embedded in the structure and its interaction with the rest of the balance sheet. A treasury that does not recognise the embedded short is not running a derivatives programme; it is running a one-sided one.