We study the debt-stabilizing properties of indexing debt to GDP using a consumption based macro-finance model. To this end, we derive quasi-analytical pricing formulas for any type of bond/equity by exploiting the discretization of the state-space, making large-scale simulations tractable. We find that GDP-linked security prices would embed time-varying risk premiums of about 40 basis points. For a fixed budget surplus, issuing GDP-linked securities does not imply more beneficial debt-to-GDP ratios in the long-run, while the debt-stabilizing budget surplus is more predictable at the expense of being higher. Our findings call into question the view that such securities tame debt.